Hydropneumatic Suspension Systems [1 ed.] 3642151469, 9783642151460

Citation preview

Hydropneumatic Suspension Systems

Wolfgang Bauer

Hydropneumatic Suspension Systems

123

Dr. Wolfgang Bauer Peter-Nickel-Str. 6 69469 Weinheim Germany [email protected]

ISBN 978-3-642-15146-0 e-ISBN 978-3-642-15147-7 DOI 10.1007/978-3-642-15147-7 Springer Heidelberg Dordrecht London New York Library of Congress Control Number: 2010935667 © Springer-Verlag Berlin Heidelberg 2011 This work is subject to copyright. All rights are reserved, whether the whole or part of the material is concerned, specifically the rights of translation, reprinting, reuse of illustrations, recitation, broadcasting, reproduction on microfilm or in any other way, and storage in data banks. Duplication of this publication or parts thereof is permitted only under the provisions of the German Copyright Law of September 9, 1965, in its current version, and permission for use must always be obtained from Springer. Violations are liable to prosecution under the German Copyright Law. The use of general descriptive names, registered names, trademarks, etc. in this publication does not imply, even in the absence of a specific statement, that such names are exempt from the relevant protective laws and regulations and therefore free for general use. While the advice and information in this book are believed to be true and accurate at the date of going to press, neither the authors nor the editors nor the publisher can accept any legal responsibility for any errors or omissions that may be made. The publisher makes no warranty, express or implied, with respect to the material contained herein. Cover design: WMXDesign GmbH, Heidelberg Printed on acid-free paper Springer is part of Springer Science+Business Media (www.springer.com)

To Jingbo and Linda for their support and patience

Preface

Many people probably use daily life commodities with gas springs without even knowing or thinking about it. Like many other things in our life they’re simply there. Moreover there are quite a lot of things that are intrinsically tied to gas as an elastic medium. Maybe just in this moment you are actually sitting on a gas spring: your office chair, especially if it’s a swivel chair, is most likely equipped with such a system. In contrast to simple gas springs, like for example those used for the trunk lid of your car, the gas spring in your swivel chair is a rather sophisticated suspension system. Via a button or a lever you have the possibility to allow the transfer of gas between separate internal chambers. This feature provides the adjustment function for the seat level and you can easily adapt it to your body height – much easier than with older mechanical spindle systems like those from, for example, piano stools. If you use gas as an elastic, suspending medium, basically you always take advantage of the equation of state for the ideal gas. However, since usually the suspension motions are quick and allow little heat exchange, it is not possible to calculate with an isothermal change of state but rather with the polytropic approach. It is among others this special behavior of the gas which makes the respective spring characteristic disproportionately higher. Another advantage of gas springs is the just described possibility of easy adjustment of the suspension level. This is especially favorable in applications with different spring loads. Due to their undoubted positive characteristics, gas springs are used in many applications. However, when looking at the small hysteresis of the gas forces while cycling the spring between compression and rebound, it becomes directly obvious that a simple gas spring always needs the assistance of an additional damping element – usually a hydraulic damper. Like their mechanical counterparts (for example helical springs or torsion bars) the gas spring can dissipate only a little amount of energy during the suspension motion (except for the special so called air damping systems). The gas spring of the above mentioned swivel chair is rather special since it is only dampened by an (intentionally) high solid body friction of the setup. This is fully sufficient since this arrangement is mostly used as a shock absorber (when sitting down) and is not exposed to frequent excitation – well, except for the rather unpleasant case of an earthquake. Now is the time to take the step towards hydropneumatic suspensions. Here too, a gas volume acts as the elastic medium, so basically the same laws apply as for vii

viii

Preface

the pure gas spring. The only difference here is that the gas pressure is not directly in contact with the active surface of the spring element but is transferred by an additional component – the hydraulic fluid. It can be called a coupling medium since it acts just like a mechanical coupling rod. The fluid connection offers numerous advantages: on one hand fluids can be sealed better than gas which basically increases the possible working pressures and therefore reduces the space requirements for the suspension element. On the other hand the fluid offers the possibility to dissipate some of the motion energy into heat, just like in a regular hydraulic damper. This viscous friction inside the hydraulic fluid is more favorable for the damping of oscillations than for example the above mentioned solid body friction and it can quite easily be adapted to certain applications or even be made adjustable. So the bottom line is: a hydropneumatic suspension provides spring and damping function always in direct concurrence. Speaking for myself, I came in contact with hydropneumatic suspensions rather late, after graduation, through my employment at the John Deere Mannheim facilities (formerly Lanz tractor factory). My work on the wide field of hydraulics and, in particular, hydropneumatic suspension systems made me aware of the advantages of this technology. One important field for hydropneumatic suspensions is agricultural tractors. This is underlined by the fact that today almost every suspended tractor front axle is suspended with hydropneumatics. The reasons for this and much more is explained in the following chapters. This book is based on experience in design and testing which I gathered in the past decade. It is a translation of my initial German edition [BAU08] with some updates and additions. The intention of this book is to create a basic understanding of what is possible with a hydropneumatic suspension system and which particular advantages and peculiarities this system includes. In doing so, it is hoped that this technology will benefit many different applications in the future. I would like to express my gratitude to my parents and to all friends who encouraged me to write this book. Furthermore I am indebted to my professional colleagues, who supported me on my way from the raw version to the printable version and who created a fertile ground for new ideas in many inspiring discussions. Last but not least I thank Dr. Alastair McDonald who polished the linguistic roughness out of my English translation. Weinheim, Germany April 2010

Wolfgang Bauer

Contents

1 Suspension Systems Basics . . . . . . . . . . . . . . . . 1.1 Requirements for Suspension Systems . . . . . . . . 1.1.1 Minimize Accelerations on the Isolated Side 1.1.2 Equalize Variations of Vertical Wheel Forces 1.2 General Setup of a Suspension System . . . . . . . . 1.3 Hydropneumatic Suspensions Compared to Other Suspension Methods . . . . . . . . . . . . . . . . . 1.3.1 Comparison of Spring Characteristics . . . . 1.3.2 Comparison of Damping Characteristics . . 1.3.3 Level Control . . . . . . . . . . . . . . . . 1.3.4 Non-functional Requirements . . . . . . . . 1.4 Applications for Hydropneumatic Suspensions . . . .

. . . . .

. . . . .

. . . . .

. . . . .

. . . . .

. . . . .

. . . . .

1 1 2 4 5

. . . . . .

. . . . . .

. . . . . .

. . . . . .

. . . . . .

. . . . . .

. . . . . .

7 7 11 12 13 15

2 Spring and Damping Characteristics of Hydropneumatic Suspension Systems . . . . . . . . . . . . . . . . . . . . . 2.1 General Setup and Working Principle . . . . . . . . . . 2.2 Spring Characteristics . . . . . . . . . . . . . . . . . . 2.2.1 Thermodynamic Background . . . . . . . . . 2.2.2 Calculation Predeterminations . . . . . . . . . 2.2.3 Non-preloaded Hydropneumatic Suspensions . 2.2.4 Systems with Mechanical Preload . . . . . . . 2.2.5 Systems with Constant Hydraulic Preload . . . 2.2.6 Systems with Variable Hydraulic Preload . . . 2.3 Damping Characteristics . . . . . . . . . . . . . . . . 2.3.1 Boundary Friction Damping . . . . . . . . . . 2.3.2 Fluid Friction Damping . . . . . . . . . . . . 2.3.3 End-of-Stroke Damping . . . . . . . . . . . . 2.4 Combined Operation of Spring and Damper . . . . . .

. . . . . . . . . . . . . .

. . . . . . . . . . . . . .

. . . . . . . . . . . . . .

. . . . . . . . . . . . . .

. . . . . . . . . . . . . .

. . . . . . . . . . . . . .

19 19 21 21 25 25 35 41 48 50 51 55 62 64

3 Dimensioning of the Hydropneumatic Suspension Hardware 3.1 Dimensioning of the Hydraulic Spring Components . . . . 3.1.1 Cylinder . . . . . . . . . . . . . . . . . . . . . . 3.1.2 Accumulator Gas Precharge . . . . . . . . . . . . 3.1.3 Detailed Calculation of p0 and V0 . . . . . . . . .

. . . . .

. . . . .

. . . . .

. . . . .

67 67 69 71 73 ix

x

Contents

3.2

Dimensioning of the Hydraulic Damping Elements . . 3.2.1 Single-Acting Cylinder in a System Without Hydraulic Preload . . . . . . . . . . . . . . . 3.2.2 Double-Acting Cylinder in a System Without Hydraulic Preload . . . . . . . . . . . . . . . 3.2.3 Double-Acting Cylinder in a System with Hydraulic Preload . . . . . . . . . . . . . . . 3.2.4 End-of-Stroke Damping . . . . . . . . . . . .

4 Hydraulic Components Design . . . . . . . . . . . . . . 4.1 Cylinders . . . . . . . . . . . . . . . . . . . . . . . 4.1.1 Function and Requirements . . . . . . . . . 4.1.2 Types of Cylinders . . . . . . . . . . . . . . 4.1.3 Sealing Elements . . . . . . . . . . . . . . . 4.1.4 End-of-Stroke Damping . . . . . . . . . . . 4.1.5 Types of Support Elements . . . . . . . . . 4.2 Accumulators . . . . . . . . . . . . . . . . . . . . . 4.2.1 Function and Requirements . . . . . . . . . 4.2.2 Types of Accumulators . . . . . . . . . . . 4.2.3 Methods to Reduce Diffusion Pressure Loss 4.2.4 Integration into Available Design Space . . . 4.3 Flow Resistors . . . . . . . . . . . . . . . . . . . . . 4.3.1 Non adjustable Orifices and Throttles . . . . 4.3.2 Flow Direction Depending Resistors . . . . 4.3.3 Adjustable Flow Resistors . . . . . . . . . . 4.4 Hydraulic Lines and Fittings . . . . . . . . . . . . . 4.4.1 Function and Requirements . . . . . . . . . 4.4.2 Required Flow Cross Section . . . . . . . . 4.4.3 Tubes . . . . . . . . . . . . . . . . . . . . . 4.4.4 Hoses . . . . . . . . . . . . . . . . . . . . . 4.4.5 Fittings . . . . . . . . . . . . . . . . . . . .

. . . . . . . . . . . . . . . . . . . . . .

. . . . . .

85

. . . . . .

85

. . . . . .

88

. . . . . . . . . . . .

91 91

. . . . . . . . . . . . . . . . . . . . . .

. . . . . . . . . . . . . . . . . . . . . .

95 95 95 96 101 106 109 111 111 113 116 118 120 120 122 126 130 130 132 133 135 138

5 Level Control . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5.1 Self-Pumping Suspension Elements . . . . . . . . . . . . . . . . 5.2 Mechanical Level Control with External Hydraulic Power Supply . 5.3 Electronic Level Control with External Hydraulic Power Supply . 5.3.1 Function . . . . . . . . . . . . . . . . . . . . . . . . . . 5.3.2 Hydraulic Circuits . . . . . . . . . . . . . . . . . . . . . 5.3.3 Control Algorithms . . . . . . . . . . . . . . . . . . . .

141 141 144 147 147 148 150

6 Special Functions of Hydropneumatic Suspension Systems 6.1 Suspension Lockout . . . . . . . . . . . . . . . . . . . . 6.1.1 Lockout by Blocking the Hydraulic Circuit . . . 6.1.2 Lockout at the Compression End Stop . . . . . . 6.1.3 “Quasi-Lockout” Through High Spring Stiffness

. . . . . . . . . . . . . . . . . . . . . .

. . . . .

. . . . . . . . . . . . . . . . . . . . . .

. . . . .

. . . . . . . . . . . . . . . . . . . . . .

. . . . .

. . . . . . . . . . . . . . . . . . . . . .

. . . . .

. . . . .

157 157 158 160 161

Contents

6.2 6.3

6.4

xi

Adjustment of the Zero Position . . . . . . . . . . . . . . . . Alteration of Roll and Pitch Behavior . . . . . . . . . . . . . 6.3.1 Coupling Cylinders on Corresponding Sides . . . . . 6.3.2 Decoupling Cylinders . . . . . . . . . . . . . . . . . 6.3.3 Coupling Double-Action Cylinders on Opposite Sides Spring Rate Adjustment by Selective Connection of Accumulators . . . . . . . . . . . . . . . . . . . . . . . . .

. . . . .

. . . . .

162 163 163 164 166

. .

169

7 Design Examples . . . . . . . . . . . . . . . . . . . . . 7.1 Tractor Front Axle Suspension TLS by John Deere 7.2 Passenger Car Axle Suspension by Citroen . . . . . 7.2.1 Citroens First Hydropneumatic Suspension 7.2.2 Hydractiv Suspension . . . . . . . . . . . 7.2.3 Activa Suspension . . . . . . . . . . . . .

. . . . . .

. . . . . .

. . . . . .

. . . . . .

. . . . . .

. . . . . .

. . . . . .

. . . . . .

173 173 180 181 183 188

8 Important Patents . . . . . . . . . . . . . . . . 8.1 Improvement of Suspension Characteristics 8.1.1 DE1755095 . . . . . . . . . . . . 8.1.2 DE19719076 . . . . . . . . . . . . 8.1.3 DE10107631 . . . . . . . . . . . . 8.1.4 DE10337600 . . . . . . . . . . . . 8.1.5 DE4221126 . . . . . . . . . . . . 8.1.6 DE4234217 . . . . . . . . . . . . 8.1.7 DE4223783 . . . . . . . . . . . . 8.1.8 US6167701 . . . . . . . . . . . . 8.1.9 DE19949152 . . . . . . . . . . . . 8.1.10 US6398227 . . . . . . . . . . . . 8.1.11 DE102008012704 . . . . . . . . . 8.2 Roll Stabilization and Slope Compensation 8.2.1 GB890089 . . . . . . . . . . . . . 8.2.2 DE3427508 . . . . . . . . . . . . 8.2.3 DE10112082 . . . . . . . . . . . . 8.2.4 US4411447 . . . . . . . . . . . . 8.2.5 US6923453 . . . . . . . . . . . . 8.3 Suspension Lockout . . . . . . . . . . . . . 8.3.1 US3953040 . . . . . . . . . . . . 8.3.2 DE4308460 . . . . . . . . . . . . 8.3.3 DE4032893 . . . . . . . . . . . .

. . . . . . . . . . . . . . . . . . . . . . .

. . . . . . . . . . . . . . . . . . . . . . .

. . . . . . . . . . . . . . . . . . . . . . .

. . . . . . . . . . . . . . . . . . . . . . .

. . . . . . . . . . . . . . . . . . . . . . .

. . . . . . . . . . . . . . . . . . . . . . .

. . . . . . . . . . . . . . . . . . . . . . .

. . . . . . . . . . . . . . . . . . . . . . .

193 193 194 195 196 196 198 198 200 201 201 203 203 205 205 206 207 208 209 210 211 211 212

9 Looking into the Future . . . . . . . . . . . . . . . . . . . . . . . . .

215

Index of Symbols and Abbreviations . . . . . . . . . . . . . . . . . . . .

219

References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

223

Index . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

229

. . . . . . . . . . . . . . . . . . . . . . .

. . . . . . . . . . . . . . . . . . . . . . .

. . . . . . . . . . . . . . . . . . . . . . .

. . . . . . . . . . . . . . . . . . . . . . .

Chapter 1

Suspension Systems Basics

1.1 Requirements for Suspension Systems As already mentioned in the preface, suspension systems have a broad range of applications in our daily lives. Usually people do not even know that they exist, yet they are doing a hard job in many cases. If they malfunction it is often the first time that one starts thinking about them. For example, anybody who has ridden a bicycle with too low tire pressure will probably remember how soft and wobbly the bike felt on smooth roads and how badly he felt the bumps when there was even the slightest unevenness. A ride behavior which is unsafe and uncomfortable. In this case the spring rate of the suspension system (i.e. the tire) was too low and the available suspension travel was too small. Therefore the suspension reached the limit of its stroke and ran heavily into the end stop – rim and road surface with the rubber of the tire in between. On the other hand, a too high tire pressure and an accordingly too high spring rate can also lead to discomfort on the bike. Without sufficient tire elasticity the roughness of the road is transferred directly into the bike frame and furthermore into the rider. This again has a negative effect on the comfort of the rider. It is clear that it is necessary to find a suitable level of tire pressure and thus spring rate which fits in particular to the weight of the rider. This brings us to the first basic objective of a suspension system: it has to protect the components of its isolated side (for example, chassis and driver) from the movements and accelerations of its input side (for example, road or wheel). This isolation of the vibration ensures comfort and health for the driver and prevents components on the isolated side from damage from inertial forces. If the suspension system fulfills these requirements for vehicles, another important advantage is achieved: compared to a vehicle without a suspension system it can be driven faster at equal or even lower vibration loads on the isolated side. Particularly for wheel suspension systems there is at least one more tremendously important objective: the time history of the vertical wheel forces on the road should be as smooth as possible in order to ensure that a high level of lateral and longitudinal wheel force can be transferred to the road surface at any time. Strong peaks in the vertical wheel force vs. time curve can lead to a situation where the

W. Bauer, Hydropneumatic Suspension Systems, DOI 10.1007/978-3-642-15147-7_1,  C Springer-Verlag Berlin Heidelberg 2011

1

2

1 Safety

Suspension Systems Basics

Easier operation of operators controls Better driver’s fitness Better road holding

Minimize accelerations on the isolated side

Comfort Health

Equalize variations of vertical wheel forces

Damage prevention

Increased productivity

Higher speeds possible Increased pulling force Increased efficiency

Fig. 1.1 Tasks and functional requirements for a wheel suspension system

normal force is lower than the necessary level to create a sufficient friction force for the transfer of lateral and longitudinal forces. This then causes a transition from static to sliding friction resulting in unexpected and unsafe ride behavior. But not only is road holding better with a smooth vertical wheel force transfer; a better transfer of pulling forces with lower wheel slip results in higher efficiency and productivity especially for pulling working machines like tractors or other off-road equipment. Further objectives especially for wheel suspension systems are, for example, the prevention of road damage (by high wheel forces) and an acceptable roll and pitch behavior of the chassis. For passenger cars it is also especially important to create a subjective ride behavior that fits to the type of vehicle – from supersports car to luxury sedan. Figure 1.1 explains the relationship between several tasks and the two deduced functional requirements “minimize accelerations on isolated side” and “equalize variations of vertical wheel forces” for a wheel suspension system. These two requirements will be explained in more detail on the following pages of this section.

1.1.1 Minimize Accelerations on the Isolated Side Mechanical components on the isolated side can often be designed to withstand the prevailing vibration level. Yet in many cases it is the human as the “living component” of the isolated side who is the limiting factor: he too must not be subjected to excessive vibrations. Vibrations are perceived by humans on different parts of the body and in different frequency ranges. From 1 to 100 Hz they are sensed to be accelerations and displacements, in the frequency range of 20 Hz–10 kHz they are perceived acoustically (noise). Reimpell points out that the range from 1 to 4 Hz

1.1

Requirements for Suspension Systems

3

determines the subjective estimation of the “suspension comfort” while the range from 4 to 80 Hz influences what is called “harshness” [REI05] – low amplitude and short term accelerations resulting for example from rides over cobblestone paving. In addition ISO2631-1 indicates that excitations in the frequency range from 0.1 to 0.5 Hz are responsible for motion sickness. From a certain level of amplitude, vibrations are rated uncomfortable by humans [DUB90]. Not only is this depending on frequency but also on subjective perception. In a mild form this only causes discomfort and faster operator fatigue. In severe cases a frequent subjection to high acceleration levels can cause damage especially to the human skeleton (for example, in the disks of the lower spine) [SEI04]. At certain predominating frequencies with high amplitudes certain parts of the body will be excited with their natural frequency. This can cause motion sickness as well as gastric or cardiac troubles. So the necessity to counteract these harmful factors is obvious. The legislative body has already issued detailed directives which regulate the allowed noise exposure, for example the European Council Directive 2003/10/EC. In addition in the past years another law became res judicata which regulates the allowed exposure to hand-arm and whole body vibrations (2002/44/EC). In particular employers in Europe will have to obey these regulations which basically also refer to all employees using mobile equipment, in particular in off-road use. The level of comfort provided by a suspension system can be determined by looking at the quality of isolation of the isolated side from the input side of the system. According to ISO 2631-1 the squared average values (for a time period T) of the frequency-weighted accelerations aW (t) are calculated for the isolated side. For a driver’s workplace all rotational and translational accelerations at the seat top are used for the calculation of the whole body vibration.

aW

  τ 1  a2W (t)dt = τ

(1.1)

0

These accelerations are then combined according to the Eqs. (1.2) and (1.3) and the results are the translational vibration RMS aV,t and the rotational vibration RMS aV,r . These values take into account the effect of the direction of the respective acceleration onto the subjective assessment of level of comfort by considering weighting factors for each direction.   2  2  2 (1.2) kaW,X + kaW,Y + kaW,Z aV,t = aV,r =



 2  2  2 kX aW,RX + kY aW,RY + kZ aW,RZ

(1.3)

while k = 1, kX = 0.63, kY = 0.4 and kZ = 0.2. X is the longitudinal, Y is the lateral and Z the vertical axis for the comfort assessment of a sitting person according to

4

1

Suspension Systems Basics Extremely uncomfortable

Very uncomfortable Uncomfortable Fairly uncomfortable A little uncomfortable Not uncomfortable 0

0.5

1

1.5

2

2.5

aV [m/s2]

Fig. 1.2 Subjective assessment of comfort depending on the vibration total value

ISO2631-1. These values are then again combined and the result is the vibration total value aV which represents a measure for the comfort level. aV =

 a2V,t + a2V,r

(1.4)

The lower this value (at a given input side excitation) the better performs a suspension system in protecting the isolated side – in particular the driver – from the input side excitations and the better will be the subjective assessment of the comfort level. The relationship between the vibration total value and the subjective assessment of comfort by the driver is described in ISO2631-1 (Fig. 1.2).

1.1.2 Equalize Variations of Vertical Wheel Forces This is a very important issue for suspension systems that are used in mobile equipment for the suspension of axles and wheels. The vertical wheel force needs to be as constant as possible to provide maximum handling performance especially during longitudinal and lateral accelerations. This ensures that the vehicle is easily controllable and can be kept on the desired track. Reimpell describes a reduced but demonstrative example for a wheel going through a 60 mm deep ditch and shows impressively that a low spring rate is essential for constant vertical wheel forces [REI05]. The vertical wheel force is the normal force in the contact area of tire and road and therefore it affects directly the potential friction force and consequently also the longitudinal and lateral guiding forces. The dynamic tire load factor nR has been introduced as an assessment criterion for the steadiness of the vertical wheel forces. It is basically the standard deviation of the dynamic tire load compared to the static tire load [THO01]. The lower nR is, the smoother the time history of the vertical wheel force.

1.2

General Setup of a Suspension System

nR =



1 τ

τ

5

[F (t) − Fstat ]2 dt

0

Fstat

(1.5)

A tire load factor of up to 0.33 provides relatively good vehicle controllability, since from a statistical point of view the tire never loses contact with the road surface. The more the tire load factor exceeds this limit, the more difficult it becomes to keep control over the course of the vehicle – the vehicle’s deviations from the desired path and therefore the necessary corrective steering actions are increasing. In practical operation it was found that a tractor cannot be kept on a narrow farm track at dynamic tire load factors above 0.4 – the vehicle would leave the pavement [THO01]. In this context it needs to be mentioned that in real suspension systems only a limited displacement of the suspension elements is available. In case the entire stroke is used up, the suspension reaches the mechanical end stop of the component with the least possible stroke and therefore is blocked completely. No displacement means no equalization of vertical wheel forces and therefore the dynamic tire load factor is worsened dramatically if this happens – not to mention the unfavorable impact on comfort. Therefore it is crucial to choose the right combination of parameters for a suspension system (spring rate, damping, stroke, etc.). This will be further explained in Chap. 2. Up to this point only two essential functional requirements for a suspension system have been mentioned. Yet there are also the non-functional requirements, which basically arise from further boundary conditions. These requirements are in particular the system cost, the necessary/available design space for the components, reliability and safety, robustness and need for regular service. If the suspension system is externally visible as part of an overall system, in many cases it also needs to fit into the overall styling. Depending on the application and its boundary conditions, requirements are weighted in a different way and are considered differently when selecting the most suitable solution.

1.2 General Setup of a Suspension System A suspension system usually consists of a spring and a damper. The spring alone would already allow the decoupling of input side and isolated side just by its elastic properties and would compensate accelerations/displacements from the input side. Yet, due to the displacement, the spring would store energy and therefore the system would keep on oscillating permanently. Not only this, in case of further excitations with suitable frequency and phase, it would pick up further energy and the amplitude on the isolated side would increase even further (resonance). If this happens the

6

1

Suspension Systems Basics

result is the exact opposite of the original goal, instead of reducing the accelerations on the isolated side they are amplified above the level without a suspension system. This is why a spring is almost always used in combination with a damper. The energy that has been temporarily stored in the spring is converted into heat by the damper and the amplitude of the oscillation therefore decays. The higher the damping forces, the faster the amplitude will decay, yet the stronger is the direct (non-elastic) coupling of the input side to the isolated side and the input side excitations will be transferred with higher intensity. So to achieve the best possible result from the tuning of a suspension system, there is a lot of experience, intuition and effort (especially testing) necessary. Most commonly used dampers are hydraulic components which use the displacement of internal fluid and the respective viscosity to generate damping forces – the latter are therefore velocity dependent. Along with these viscous dampers comes usually a boundary friction which has a negative impact on the suspension behavior. In particular, the static friction is a direct link between input side and isolated side; all excitation forces that are below the static friction force level will directly be transmitted into the isolated side and cause an acceleration that reduces the comfort level. This acceleration amin also depends on the mass mF on the isolated side. amin =

Ffric,stat mF

(1.6)

However also the sliding friction has a worsening effect onto the dynamic system behavior. Both static and dynamic friction reduce the suspension quality in terms of harshness and noise transfer. That is why a lot of effort is taken to minimize the general interference factor “friction”. Figure 1.3 shows the general setup of a suspension system which isolates the excitations coming from the input side through a spring, a viscous damper and

Input side

Isolated side

Spring

m

Excitation Viscous damper

x

t

Friction

Fig. 1.3 General setup of a suspension system

Response x

t

1.3

Hydropneumatic Suspensions Compared to Other Suspension Methods

7

a friction element from being transferred into the mass on the isolated side. The amplitude of the reaction – the displacement and the acceleration of the mass – is reduced, compared to the amplitude of the excitation. An elegant and frequently used method to compensate for the amount of boundary friction is the integration of another spring-damper element in series to the hydraulic damper, for example a rubber bushing. This element has rather low damping and virtually no friction and is able to isolate the high frequency oscillations very well. A good example for this are the decoupled top mounts for shock absorbers in McPherson struts ([HAR04] and [ELL02]). In many cases suspension systems not only consist of one of the above shown oscillating systems but of multiple systems. For example, on a passenger car there are at least the tire, the wheel suspension and the seat which represent a suspension system as shown in Fig. 1.3 and all work together to isolate the driver from the excitations from the road surface.

1.3 Hydropneumatic Suspensions Compared to Other Suspension Methods Basically there are two other systems that compete with hydropneumatics in the area of suspension systems: the pneumatic and the mechanical suspension. In addition there are some exotic concepts like the suspension on an air cushion as used for a hovercraft or even the suspension on a magnetic field. Section 1.3.1 compares the (typical and most commonly used) mechanical, the pneumatic and the hydropneumatic suspension with regards to the requirements which have been explained in Sect. 1.1.

1.3.1 Comparison of Spring Characteristics For all further explanations in this section, the rule is established that all three suspension systems shall have the same spring rate at the chosen design point with its respective load so they have comparable suspension characteristics at this point. Furthermore the systems then are defined to be in the same position between both suspension end stops: the design position or normal position. The first essential difference between the systems becomes obvious when looking at the force vs. displacement curves in Fig. 1.4. While the spring rate of the mechanical spring is constant throughout the whole stroke (assuming that, for example, a linearly wound coil spring is used) both systems with gas suspension are (also depending on the layout) more or less progressive which is caused by the physical laws for a polytropic change of state of a gas. An exception is an air spring with a rolling piston with a non-cylindrical contour [MUR98]. When oscillating around the normal position with small amplitudes this has no significant impact, yet at greater amplitudes this is of importance, especially when getting close to the end stops. In particular the hydraulically preloaded hydropneumatic spring as well as the air

8

1

Suspension Systems Basics

Spring force

Design position

Displacement

Rebound (Suspension element is extended)

Compression (Suspension element is contracted)

Mechanical coil spring, linearly wound Mechanical coil spring, progressively wound, air spring with cylindrical rolling piston, non-preloaded hydropneumatic spring Hydraulically preloaded hydropneumatic spring, air spring with rolling piston with defined contour

Fig. 1.4 Force-displacement-curves for mechanical and gas-sprung systems

spring with a defined contour of the rolling piston can provide the advantage of increased spring rates near the mechanical end stops thus preventing the suspension from reaching these. An even more significant difference can be found with changing suspension load by varying the suspended mass. A suspension system without level control is compressed by increasing static load until the spring force is again equal to the static load. In Fig. 1.4 it becomes obvious that this causes an increasing spring rate for the air spring and the hydropneumatic spring (indicated by the progressively increasing inclination of these curves on the compression side of the figure), whilst the spring rate of a mechanical spring remains constant (constant inclination). This is a general problem for mechanical suspension systems with large load variations and with (as usual) no level control. The following example explains why: Assuming that a mechanically sprung passenger car is in a defined partially loaded condition (three passengers) and it therefore is in its design position (the desired position between the suspension travel limits, for example in the centre of both). If the load on the rear axle is increased by further passengers and luggage to the maximum allowed rear axle load, the suspension becomes compressed and the new neutral position is offset towards the compression end stop. Therefore the available residual suspension travel in compression direction is reduced compared to the design position. With high excitations from the input side (for example when riding over uneven ground) there is a risk that the suspension will run harshly into the end stops; even more so because the load has been increased without on the other hand increasing the spring rate and the suspension therefore becomes softer (lower natural frequency).

1.3

Hydropneumatic Suspensions Compared to Other Suspension Methods

9

So to make sure that the suspension is able to cope with these extreme conditions it must be tuned more stiffly and with higher damping overall. The problem is that this worsens the tuning for all other load cases (for example with only the driver inside). Hence it can be easily deduced that a linearly wound coil spring can only allow a compromise for most driving situations. In any case safety needs to be a major focus for the suspension tuning which means especially that the dynamic tire load factors should always be within the allowed range. It is possible to address this problem by using progressively wound coil springs but this only partially solves the root cause. Therefore in most cases a level control is the far better and the far more effective solution – after a load change it brings the suspension back to its design position and ensures constant residual suspension travel in both compression and rebound direction. On passenger cars a mechanical level control in conjunction with a coil spring can be found only rarely [ELL02]. Usually other/additional supporting elements are used for leveling: for example self pumping dampers or additional air springs are very common. Nevertheless a mechanical level adjustment – mostly manual – is for example often used on motorbikes. One reason for this is that the load ratio (maximum weight to curb weight), especially on the rear axle, is much higher than in other applications. Gas sprung suspension systems on the other hand are virtually always equipped with a level control, in most cases even automatic without need for driver input. Yet a major difference between an air spring and a hydropneumatic spring is how the desired design position is readjusted and how the spring rate is affected by this. In purely pneumatic springs the gas (usually air) is filled up or released. So the suspending gas volume of the pneumatic spring remains constant after the load change and subsequent level adjustment. The pressure of this gas volume changes linearly with the load. Therefore in purely pneumatic springs the gas mass and hence also the spring rate change in a linear correlation with the sprung mass. For a hydropneumatic suspension system it is the oil volume which is changed during the leveling process – so here it is the gas mass which remains constant at all times. Yet this gas mass changes its volume after a load change; a higher load means a smaller gas volume and therefore a higher spring rate. This is the reason why this system shows progressive behavior of the spring rate vs. the sprung mass. Figure 1.5 shows a comparison for all three systems, with the condition that they all have the same spring rate at the design load. In order to provide a constant natural frequency of the oscillating system it is basically preferable to have a spring rate increasing linearly with the spring load. Yet in some cases, depending on the reason for the load changes or the needs of the particular application, it can be favorable to change to a disproportionately higher spring rate. A spring rate that is constant at all loads, as with a linearly wound coil spring, is usually only a compromise and only recommended for suspension systems with small relative load changes. For good protection of the isolated side from the input side, the lowest possible natural frequency (obeying the motion sickness limit of 0.5 Hz) and therefore also the lowest possible spring rate needs to be aimed at, yet always considering the limited suspension stroke. A pneumatic suspension provides a constant low level of

10

1

Suspension Systems Basics

Spring rate

Spring load

Design load Mechanical coil spring, linearly wound

Mechanical coil spring, progressively wound, air spring with cylindrical rolling piston, non-preloaded hydropneumatic spring Hydraulically preloaded hydropneumatic spring, air spring with rolling piston with defined contour

Fig. 1.5 Spring rate as a function of spring load for a mechanical, a pneumatic and a hydropneumatic suspension

natural frequency for all load conditions, while the natural frequency of a hydropneumatic system will more or less increase with increasing loads, depending on the system layout. On the other hand a mechanical spring will have a high natural frequency at low loads and a low natural frequency at high loads. Figure 1.6 illustrates this for the simple example of a single-mass oscillator.

m Natural frequency

Design load

Spring load

Mechanical coil spring, linearly wound Air spring with cylindrical rolling piston, hydraulically preloaded hydropneumatic spring close to the design point, both with level control Non preloaded hydropneumatic spring with level control

Fig. 1.6 Natural frequency as a function of spring load for a mechanical, a pneumatic and a hydropneumatic suspension

1.3

Hydropneumatic Suspensions Compared to Other Suspension Methods

11

In more advanced applications it is also necessary to have the ability to change suspension properties (such as the spring rate) depending on particular operating conditions. For a mechanical spring this is quite difficult. A pneumatic spring gives some possibility by switchable additional air volumes but a hydropneumatic spring gives great possibilities by either switchable accumulators or a variable precharge pressure (more detailed information in Sect. 2.2).

1.3.2 Comparison of Damping Characteristics In Sect. 1.2 it was already explained that the necessary damping for the decay of the oscillations is in most cases provided by viscous friction of a damping fluid – usually oil. The amount of viscous damping can be defined very well for all three types of suspension systems. Therefore this is not part of the comparison. Yet a negative side effect of the components of suspension systems is the additional damping by boundary friction, in particular in bushings, dynamic sealing systems and guiding elements. Friction in bushings of mechanical links and control arms has to be minimized, yet it is similar for all kinds of suspension systems and is therefore also not part of this comparison. The friction in sealing and guiding elements needs to be avoided as far as possible. There are different causes and therefore different friction levels for different suspension systems. This sub-section explains the reasons. The mechanical coil spring with a viscous fluid damper scores best when it comes to the friction level. The spring itself has no friction; all deformation is purely reversible, i.e. elastic. Therefore in this suspension element, boundary friction originates only from the friction in the sealing and guiding elements inside the viscous fluid damper. It is a general rule that friction forces from dynamic seals increase with the differential pressures at the seal and the length of the sealing edge. This explains why a monotube damper with its internal gas pressure and the rather large rod diameter has a much higher boundary friction than a dual-tube damper (with low or even without internal gas pressure) [MUR98]. On top of that for the monotube damper there is additional friction of the seals of the floating internal piston which separates gas and oil. As far as friction in guiding elements is concerned, it is essential to avoid lateral forces and bending moments onto the sliding components – this is actually valid for all types of suspension elements. More detailed explanations are given in Sect. 2.3.1. The above mentioned standard oil damper technology is used for pneumatic suspension systems as well, so it has on the damper side similar boundary friction as to that of a coil spring suspension. Yet for a pneumatic system there is additional friction coming from the rolling bellow which originates from its necessary deformation during the suspension movement. This friction causes an additional degradation in harshness behavior and is on a level of about 20 N for the most commonly known cross ply bellow for a passenger car air suspension. The newer technology of axial ply bellows enables a reduction of bellow friction forces down below 10 N [PEL04] and finds more and more applications especially in the field

12

1

Suspension Systems Basics

of high comfort passenger car suspensions. A disadvantage of this technology is though, that the bellow needs additional guidance on the outer diameter to pick up the radial forces caused by the air pressure. The baseline is that the boundary friction in a pneumatic suspension system will always be slightly higher than in a coil spring suspension system. There is again another picture for the hydropneumatic suspension system. Although the suspension cylinder is the only component between input side and isolated side, it has to be taken into account that its seals need to cope with very high differential pressures. Therefore the level of friction would be much higher compared to the latter two suspension systems if no additional countermeasures are taken. The friction is caused on one hand by the rod seal (for single-acting cylinders) and additionally by the piston seal if a hydraulically preloaded system with a double-acting cylinder is used (see Sect. 1.3.3). The friction of the hydropneumatic suspension can be minimized by a suitable layout of the components (dimensions, pressures, see Sect. 2.3.1) as well as by the implementation of a high-grade, low friction sealing system [FIS06] (see also Sect. 4.1.3). Since spring and damper of a hydropneumatic suspension are integrated into one component it is difficult to use soft additional spring-damper-elements to decouple the direct transfer path of static damper friction as explained in Sect. 1.2. The reason behind it is that this additional element would have to carry the complete suspended mass and not only the damping forces as in the case of decoupled top mounts for passenger cars’ suspension elements. High loads and very soft rubber elements are goals that can hardly be achieved at the same time. The use of a rubber bushing is possible though and it can improve the noise transfer properties. It is obvious that boundary friction is a considerable and challenging issue when designing a hydropneumatic suspension.

1.3.3 Level Control For suspension systems with a coil spring/mechanical spring, level controls are rather seldom due to the high effort of automatic systems and their limited effect. Manual level adjustments are commonly used for example in motorbikes and for some passenger car sports suspensions. In the last years several new ideas have been developed for level control of mechanical springs. They have often been filed as patents ([US780], [JP945]) and some of them quite close to the hydropneumatic suspension technology ([US363] and with an exotic hydraulic power principle [JP103]). However, overall they currently play a minor roll in mechanical springs and therefore will not be explained any further in this book. For a hydropneumatic and a pneumatic suspension system a level adjustment is quite easily feasible by increasing/decreasing the amount of oil or gas in the system. Both systems have about the same leveling quality, maybe with slight advantages for the hydropneumatic system. Yet there is a major advantage for the hydropneumatic system in terms of leveling speed. Since it has a much higher energy density and an incompressible medium is used, the suspension can, after a load increase, be brought

1.3

Hydropneumatic Suspensions Compared to Other Suspension Methods

13

back to the normal position very quickly if the necessary power is available. If the same leveling speed had to be achieved with a pneumatic suspension system, a much higher volumetric flow rate and a higher power output would be necessary. This aspect is especially important for suspension systems that are often subjected to high load changes and if a fast readjustment of the desired normal position is necessary. In this case the hydropneumatic suspension is preferred.

1.3.4 Non-functional Requirements 1.3.4.1 Component Costs When it comes to costs the traditional mechanical spring suspension system is significantly ahead of the two gas suspended systems. One reason is that these components have been optimized over a long time of intensive development in particular concerning the costs. Another reason is that they lack the expensive cost for level control. In this context it needs to be mentioned that there are so called load sharing systems, a mechanical system in combination with a pneumatic or hydropneumatic spring. Yet they are not part of the explanations in this section; for more detailed information please refer to [EUL03]. Pneumatic and hydropneumatic suspension systems are more expensive especially due to the cost for the (mostly automatic) level control. Furthermore the pneumatic system has a slight advantage over hydropneumatics assuming that in both cases a fluid power supply needs to be provided. Yet if there already is a pneumatic or hydraulic system available in a certain application, the additional costs for both gas sprung systems will be reduced. In this case the selection between pneumatic and hydropneumatic system is often mainly based on what fluid power supply is already available. 1.3.4.2 Design Space Requirement Hydropneumatic systems have major advantages here. There are mainly two reasons for that: First is the high integration level of this suspension component, which fulfills the function of a spring and a damper at the same time. Secondly the cylinder diameters can be chosen very small due to the working principle and the high possible working pressures. Static pressures of up to 20 MPa in the design position are very common. They can be even higher if the components are selected accordingly. Therefore a suspension cylinder can be about as small as a regular oil damper. This offers advantages in particular if the available design space in the surrounding areas of the suspension system is very small. In addition to the cylinder(s), the accumulator(s) need to be accommodated. It is best to locate it close to or directly at the cylinder, yet it is not absolutely necessary. This option offers a lot of possible variations and makes the packaging of these components quite flexible. The design space for the level control system can be chosen in any position; all that has to be considered is a hydraulic line between the suspension components and the level

14

1

Suspension Systems Basics

control system. In order to keep line lengths small (due to costs, space requirements and pressure drops over this line) it is favorable to keep the all components close together. For pneumatic suspension systems there are also lines necessary for the compressed air. Yet due to the much lower working pressures (normally up to 1 MPa of static pressure in normal position), the pneumatic suspension components need much more active area and therefore also more design space compared to hydropneumatics. As a rule of thumb, it can be stated that a pneumatic spring usually can be accommodated in the design space of the respective coil spring. Yet the latter normally has no level control system and that is why the overall design space requirement for it is somewhat smaller. 1.3.4.3 Reliability, Safety, Robustness and Service Requirements In general it can be stated that reliability and safety are granted and uncritical for all mechanical, pneumatic and hydropneumatic systems if the design work has been done properly and the systems are serviced regularly. For the mechanical suspension, service requirements are quite low; basically it is only the exchange or (rarely) reconditioning of the oil dampers. The mechanical spring is virtually service free. Only for metallic springs must corrosion be kept under surveillance since the protection coating can be damaged for example by stoning. On top of that comes the exchange of (especially rubber) bushings and mounts as and when required. A pneumatic suspension system needs a slightly higher maintenance effort compared to the mechanical system, yet additional design effort is necessary to protect the rather sensitive bellows of the air cushions. Especially in off-road vehicles the bellows need to be specially protected from dirt, stoning, sharp objects, etc. The bellow material (rubber with reinforcing plies) is subjected to aging in particular due to environmental influences like UV-radiation, chemical substances, ozone etc. That is why in some cases they need to be exchanged after a certain number of operating hours (on top of the exchange of the oil dampers). The hydropneumatic system requires maintenance as well, yet depending very much on the design of the components. Usually diaphragm accumulators are used to provide the gas which suspends the system. The diaphragm is made of flexible material – rubber – and this material does not completely seal off the gas from the oil. In fact there is diffusion of gas molecules resulting in a slow decay of gas pressure. Therefore this gas pressure has to be checked regularly and eventually be brought back to its original level. There are however special diaphragm materials and designs and also special kinds of gases which strongly reduce diffusion and therefore the need for regular checks (of course at higher costs). In addition, a change of the oil can be necessary since its properties, especially viscosity, are changing over time. Similarly to regular oil dampers, the oil in hydropneumatic systems can also degrade over time for example due to the cutting of the long-chain molecules by shearing in flow restrictors and valves or due to the intrusion of water. On a vehicle, hydropneumatic suspension systems are usually connected to the vehicle’s overall hydraulic system and therefore no special oil service is necessary for

1.4

Applications for Hydropneumatic Suspensions

15

Mechanical spring and damper

Pneumatic spring and damper

Hydropneumatic system

o

++

++

++

++

+

–

+

++

++

o

–

Design space requirement

o

–

+

Reliability + robustness

+

o

+

Service requirements

+

o

o

Spring characteristics Damping and friction characteristics Level control

Cost

Fig. 1.7 Fulfillment of the requirements by the different suspension systems

the suspension hydraulics. In general hydropneumatic systems have proven their robustness especially in dirty and harsh environment and under heavy suspension loads. Special sealing systems (in particular for the rod) and the heavy duty design of cylinder tubes grant this. Sections 4.1 and 4.2 give more detailed information about this. Figure 1.7 gives an overview of the fulfillment of the various requirements by the three different suspension systems.

1.4 Applications for Hydropneumatic Suspensions From Fig. 1.7 it can be deduced that hydropneumatic suspension systems are used especially in applications where: (a) a level control is needed in particular for level readjustments after major load changes, (b) a level control needs to work frequently and needs to react quickly, (c) a manual operator control for the suspension level is desired, (d) little space is available for suspension elements,

16

1

Suspension Systems Basics

(e) possibly hydraulic cylinders are already available for control of the desired suspension degree of freedom, (f) robust components are required due to the harsh working environment, (g) a lockout of the suspension in the design position is required, (h) the spring rate needs to be adjustable, (i) a hydraulic energy supply is already available. Points a, b, f and i are the reasons why hydropneumatic suspension systems can be found in all kinds of off-road vehicles like for example construction machinery/trucks, mobile cranes, tanks, agricultural vehicles, mining and heavy load trucks as well as snow groomers. In these applications they usually provide the wheel or axle suspension and, depending on the special operation, other functions like the suspension of lift arms or implements. A further area of application is the wheel suspension in passenger cars. This has become popular since Citroen uses hydropneumatics for many of their cars’ suspension systems. In particular, the load independent constant level of the suspension (and therefore the possible low spring rate and legendary comfort) as well as the manual level adjustment (a and c) are major drivers for using hydropneumatics here. In former times the Citroens’ hydraulic power supply was not only used for the suspension but also for the brakes and the steering. Thus there was also a synergistic effect as mentioned in (i). But partly due to the high pressures that are needed for the suspension hydraulic system, Citroen introduced a separate suspension hydraulic system starting with their Hydractive III system. This way the (until then) expensive special components for steering and brakes could be replaced by much more cost effective standard components from the “regular” passenger cars (more information in Sect. 7.2). The hydropneumatic suspension is also used in rail applications. In low-platform city traffic tramcars hydropneumatics provide a major advantage in keeping the car always on the same level no matter how many people are on board (a). This way it is always perfectly aligned with the edges of the train station platforms. This allows easier entrance especially for disabled persons (wheelchairs) and families (prams). Due to the availability of hydraulic energy (i) as well as the possibility for level control (a) and therefore a soft tuning of the suspension system, John Deere – as well as many other manufacturers of agricultural equipment – has chosen a hydropneumatic system for their front axle and cabin suspensions throughout the whole range of tractors. The suspension elements are located in areas at the front and the rear axle which are exposed to heavy soiling, chemicals, high crops etc. and therefore need to fulfill highest requirements in terms of robustness (f). Furthermore there are for example boom suspensions of wheel loaders, telehandlers and front loaders on tractors as well as the suspension of the front hitches for front implement attachment on tractors. Here the cylinders that are already available for the lifting function of these devices are used as suspension cylinders by adding a hydraulic accumulator to the system (e). These heavy devices and the heavy loads that are carried by them are then suspended softly which is of great help, for example, during rides through rough terrain. For the same reason, a hydropneumatic

1.4

Applications for Hydropneumatic Suspensions

17

suspension is also available as aftermarket equipment for front ballast weights. The mass of these weights then acts as a vibration absorber mass to reduce accelerations in the tractor chassis and improve the dynamic tire load factor of the front wheels. A rather exotic area of application for hydropneumatic suspensions are the towbarless aircraft tractors. For easy ground handling on airports they lift the nose wheel of an aircraft and this way tow it to the parking or starting position. Lifted loads of up to 50 tons with curb weights of 30–40 tons make a level control inevitable. Last but not least, because of its high power density, the hydropneumatic system is perfectly suited for the axle suspension of such vehicles.

Chapter 2

Spring and Damping Characteristics of Hydropneumatic Suspension Systems

2.1 General Setup and Working Principle The simplest hydropneumatic suspension system consists of only three components: a hydraulic cylinder, a hydropneumatic accumulator, which is directly mounted on the cylinder and, of course, the hydraulic fluid. In case cylinder and accumulator need to be separated – for example due to design space reasons – additional oil lines and fittings are necessary to provide the hydraulic connection. After adjusting the hydraulic pressure to the required level (by adding or releasing hydraulic fluid) this system now already provides the suspension function. When displacing the piston rod, the fluid volume in the accumulator is changed and therewith the pressure (p1 → p2 ). This causes a change of the force at the piston rod which, in combination with the change of the position, defines the spring rate c. The external spring force FF which acts upon the piston rod is always in balance with the forces resulting from the pressures onto the piston, when neglecting inertial and friction forces (Fig. 2.1a). When the force FF is increased to FF ∗ (Fig. 2.1b) the position of the piston changes (s) and therefore some hydraulic fluid is displaced into the accumulator. This change proceeds until the pressure in the accumulator (and thus on the active surface of the piston) has reached a level which again provides a balance for the system. This balance of forces is the basis for the function and the understanding of the suspension system. It will be used in the following sections for further calculations. To allow for additional damping, a flow resistor is placed between cylinder and accumulator. It converts part of the kinetic energy of the hydraulic fluid into heat (viscous friction). This provides the desired damping in combination with the (undesirable) boundary friction caused by the cylinder sealing and guiding elements. This so called “suspension unit” consisting of cylinder, accumulator, flow resistor and hydraulic fluid already provides the suspension function and could replace the typical combination of mechanical spring and damper. Yet with this system the major advantage of hydropneumatic suspension systems is not yet used: level control. An additional level control unit provides a constant normal position of the suspension independent from the static spring load FF . The

W. Bauer, Hydropneumatic Suspension Systems, DOI 10.1007/978-3-642-15147-7_2,  C Springer-Verlag Berlin Heidelberg 2011

19

20

2

Hydropneumatic Suspension Systems p1

FF

(a)

AK p2

Δs

F F*

(b)

AK FF* = AK ⋅ p2

FF = AK ⋅ p1

c=

FF − FF* Δs

Fig. 2.1 Balance of forces at the piston of a single-acting cylinder

level control unit consists of a position sensor which, directly or via an electronic control unit, sends signals to a hydraulic control valve, which then changes the amount of hydraulic fluid in the suspension unit in order to bring the suspension back to the design position if necessary. By increasing the amount of hydraulic fluid, the level of the system is increased; reducing the amount of hydraulic fluid

1 Cylinder

2

2 Accumulator 3 Flow resistor 3

7

4 Lines and fittings

8

5 Position sensor (+ electronic controls)

6 1

4

6 Hydraulic control valve 5

7 Hydraulic pressure supply 8 Reservoir

Suspension unit

Level control unit

Fig. 2.2 General setup of a hydropneumatic suspension system

2.2

Spring Characteristics

21

decreases the level of the system. Pressurized hydraulic fluid as well as the possibility to dispose of excessive fluid (to a hydraulic reservoir) need to be provided to enable that. By combining these two parts (suspension unit and level control unit) it is possible to draw a basic schematic of a hydropneumatic suspension system (Fig. 2.2). Section 2.2 describes two main functions of a hydropneumatic system: spring characteristics and damping characteristics regarding their basic principles and theoretical background, while Chap. 3 describes how predefined characteristics can be achieved with a certain component layout. The third main function, the level control, is described in more detail in Chap. 5.

2.2 Spring Characteristics The spring rate of a hydropneumatic suspension system can be determined from the pure spring force–displacement curve measured at the suspension cylinder when the hydraulic flow resistor, as shown in Fig. 2.2, is removed. An increase of force onto the cylinder leads to an increase in hydraulic pressure and therefore to a change in position of the piston rod. This is due to the following reasons: – compression of the gas in the accumulators – widening of the (elastic) fluid lines and fittings – compression of the hydraulic fluid Each of these three effects causes an individual spring rate. So what is measured at the suspension cylinder is the spring rate of a spring which is made up by a sequential combination of these three individual springs. Using general laws of physics, the following Eq. (2.1) is obtained: cges =

cG cL cF cG cL + cG cF + cL cF

(2.1)

The stiffness of the lines and fittings as well as the compression modulus of the hydraulic fluid are usually very high, so their impact on the overall spring rate cges is low. This means that the characteristic properties of a hydropneumatic spring are mainly influenced by the properties of the gas which is enclosed in the hydraulic accumulators. So before explaining the detailed function of the various types of hydropneumatic suspensions, the properties and the thermodynamic physics of gases and their effect on the suspension function is explained.

2.2.1 Thermodynamic Background The gas in the accumulator(s) is the medium which is responsible for the elasticity of the complete setup. Because it fulfills the most important task (spring rate) its

22

2

Hydropneumatic Suspension Systems

properties are predominantly important for the behavior of the whole suspension system. In the initial state of an accumulator – with an unpressurized hydraulic system – a certain number of gas molecules and therefore a certain gas mass mG is trapped inside the accumulator. It is defined by the volume of the accumulator V0 (= gas volume if no hydraulic pressure is applied) and the accumulator precharge pressure p0 . The precharge pressure always refers to the room temperature 293.15 K (or 20◦ C) and is set during the production process of the accumulator. For this condition the equation of state for the ideal gas is: p0 V0 = mG RT

(2.2)

If the gas temperature changes during the production process (for example during paint-drying), during shipping or later during the operation of the suspension system, the gas pressure changes to a new precharge pressure according to the laws for the isochoric change of state. This temperature-dependent precharge pressure must be taken into account when laying out systems that are will be operated at various temperatures. p0,T = p0

T T0

(important: T, T0 in [K])

(2.3)

As soon as the accumulator is integrated into the hydraulic system and the system is pressurized, the gas volume in the accumulator does not change as long as the hydraulic pressure is less than or equal to the precharge pressure. As soon as the hydraulic pressure exceeds the precharge pressure, the gas volume is compressed until a balance of forces or, for equal active areas on gas and fluid side as in diaphragm accumulators, a balance of pressure is attained. The increase of hydraulic pressure can be caused for example by loading the suspension system with the suspended mass. The compression of the gas takes place rather slowly and the new pressure level is maintained over a longer period, so in this case an isothermal change of state according to Boyle-Mariotte can be assumed. The heat generated by compression dissipates into the environment and the temperature remains constant during the process. V1 = V0

p0 p1

(2.4)

This isothermal change of state can be used for the calculation of both the first time loading of the suspension system as well as all subsequent slow load changes: for example people getting on and off the suspended system, loading and unloading of payload, long term changes in external preloads and forces. The suspension movement itself, when absorbing the shocks during the regular operation of the suspension system, takes place quite rapidly. The excitation frequencies that the suspension system is able to absorb usually range from below 1 Hz to sometimes over 10 Hz. These high speed changes of state leave little time

2.2

Spring Characteristics

23

for the dissipation or adsorption of heat compared to an isothermal change of state as described above. The gas will therefore change its temperature. Assuming that no heat exchange is possible, an adiabatic change of state takes place which is described by the following equation: p1 V1κ = p2 V2κ

(2.5)

In this equation κ is the adiabatic exponent, which is the ratio of the specific heat capacity at constant pressure and the specific heat capacity at constant volume for a particular gas. In standard literature values are quoted that refer to the properties at low pressures and room temperature. These values are for example according to [DUB90]: κ ≈ 1.66 for monoatomic gases (e.g. He) κ ≈ 1.40 for biatomic gases (e.g. N2 , O2 and therefore also air) κ ≈ 1.30 for triatomic gases (e.g. CO2 ) Although it is rarely mentioned, for hydropneumatic suspension systems it is very important to consider that κ depends significantly upon temperature and gas pressure. Figure 2.3 gives an overview of the behavior for nitrogen. In real hydropneumatic suspensions there is always the possibility of a marginal heat exchange of the gas with its surrounding components and therefore there will never be the ideal adiabatic change of state. This means that hydropneumatic suspension processes are defined by a polytropic change of state characterized by 1 < n < κ. The more heat is exchanged during the change of state, the more the polytropic exponent n for this process will go from κ towards 1; the latter defines

Fig. 2.3 Adiabatic exponent κ of N2 as a function of T and p ([MUR01])

24

2

Hydropneumatic Suspension Systems

again the isothermal change of state with perfect heat exchange. The exact conditions for heat exchange are usually unknown and are very difficult to identify, which is the reason why it is extremely difficult to find out where exactly between 1 and κ the polytropic exponent needs to be chosen. Furthermore even the actual value for κ is difficult to determine due to the above mentioned effects of pressure and temperature onto κ; even more so because both parameters change constantly during the suspension processes. That is why it is only possible to estimate the polytropic exponent n for preliminary calculations. Figure 2.4 shows how much influence n has on the pressure–volume diagram. Starting from a pressure of one bar the gas is compressed. The resulting pressure can be read from the curve progression. It is clearly visible that the pressure and therefore also the force of the cylinder increases with increasing polytropic exponent. A strong impact on the spring rate can directly be deduced. Assuming a value of n = 1.3 usually works well for preliminary calculations. Only at higher pressures especially in combination with very low operating temperatures it is recommended to use n = 1.4 or higher (according to the behavior shown in Fig. 2.3). The most realistic average values for n can be deduced from measurements of force–displacement curves in experiments. Calculations need to be compared to the experiments and the polytropic exponent of the calculations needs to be readjusted to a level which provides best match of theoretical end experimental force–displacement curves. This empirically determined value for n can in the future be reused for the calculation/simulation of hydropneumatic systems with similar setups, especially concerning accumulators and their environment.

Fig. 2.4 p–V curves for different polytropic exponents

2.2

Spring Characteristics

25

2.2.2 Calculation Predeterminations All the calculations in this section are done under the following assumptions and conditions: (1) The influence of the ambient pressure is neglected. This is acceptable, since the usual working pressure levels in the cylinders as well as the precharge pressures of the accumulators (commonly specified as gauge pressure above the ambient pressure) are significantly higher than the ambient pressure – usually a factor of 50 and above for the working pressure and a factor of 25 and above for the precharge pressure. If this is not the case for special hydropneumatic suspension systems it is necessary to reconsider the question whether the influence of ambient pressure is really negligible. If not, it is necessary to multiply the ambient pressure with the externally effective active cylinder area (usually the piston rod cross-sectional area) and use this force value as a preload force without additional spring rate – please refer Sects. 2.2.3, 2.2.4, 2.2.5, and 2.2.6. Furthermore in this case the absolute accumulator precharge pressure (=specified precharge pressure + ambient pressure) needs to be used for the calculations. (2) For better comparison of the results and behaviors, all calculations are performed for a temperature of 293.15 K (or 20◦ C) – particularly important for the accumulator. Therefore the specified accumulator precharge pressure (referring to 293.15 K) can be directly used for the calculations. If the suspension behavior for other temperatures has to be calculated, it is necessary to first calculate the altered, temperature-dependent precharge pressure (see Sect. 2.2.1) and then use this value in the respective equations. (3) A polytropic exponent of 1.3 is used. (4) The suspended mass directly acts upon the suspension cylinder (i = 1). This means there is no mechanical linkage system that creates any kind of lever ratio of i = 1: cylinder force to gravitational force of the mass. This is often not the case for suspension systems but again for comparison of results this is assumed. Yet in Chap. 7 an example is given which explains the influence of a lever ratio i = 1. (5) The design position of the suspension is defined to be exactly in the center of the overall stroke between the compression and rebound end stop. (6) Damping (solid body and fluid friction) is not part of the calculations in Sect. 2.2. All hydraulic pressures do not include pressure losses (e.g. caused by flow restrictors). The focus here is purely on spring characteristics.

2.2.3 Non-preloaded Hydropneumatic Suspensions This is the simplest type of hydropneumatic suspension. This system consists of a single acting suspension cylinder and an accumulator. The suspension cylinder

26

2

Hydropneumatic Suspension Systems FF

FF

s=0

s=0 Fhydr.

(a) Plunger cylinder

s

Fhydr.

s

(b) Double-acting cylinder with interconnected cylinder sides

Fig. 2.5 Schematic illustration of non preloaded hydropneumatic suspensions

can be designed as a single-acting cylinder (for example, a plunger cylinder) or as a double-acting cylinder with interconnected pistonside and rodside of the cylinder. The latter system is able to provide higher amounts of rebound damping (more detailed information in Sect. 2.3). Both systems are depicted in Fig. 2.5. It is important to consider that the externally effective active area is only the cross-sectional area of the piston rod. It is due to the interconnection of piston chamber and rod chamber (the so-called regen(erative) system) that effectively only the fluid volume displaced by the piston rod flows into the accumulator while the other portion of the fluid displaced by the piston flows back into the rodside. The most important method to describe the behavior of a spring is the force– displacement curve for compression and rebound. It has been mentioned in Sect. 1.1 already that this curve is basically linear for a regular mechanical coil spring; other curves are possible by special winding techniques as well as parallel connection of multiple springs. The hydropneumatic spring however always has a disproportionately progressive shape of the force–displacement curve. This shape can be controlled by variation of several influencing factors. The important factors are deduced on the following pages. Before calculating the non preloaded hydropneumatic suspension it is necessary to define some of the various states that a suspension system can be in: State 0: Spring force FF0 = 0 . The pressure in the accumulator is the precharge pressure p0 , which is defined during the production process. The gas fills out the complete internal volume V0 of the accumulator. State 1: Now the static suspension force FF1 is loading the suspension system (while FF1 > FF0 ). The force is sufficient to compress the gas volume in the accumulator isothermally to the volume V1 and the pressure p1 . State 2: FF2 is the dynamic suspension force and oscillates around FF1 . Therefore the gas volume is compressed (compression) and expanded

2.2

Spring Characteristics

27

(rebound) by a polytropic change of state to the volume V2 and the pressure p2 . The starting point for the calculation is the correlation of the force acting onto the surface of the piston FK and the pressure in the piston chamber pK . FK (s) = pK (s)AK

(2.6)

Using the state equation for polytropic changes of state p1 V1n = p2 V2n

(2.7)

and the definition that an increase of the displacement s causes a compression of the gas V2 = V1 − AK s

(2.8)

p1 V1n p1 V1n = V2n (V1 − AK s)n

(2.9)

it can be deduced that: p2 =

On the basis of the isothermal change of state from 0 to 1 it is stated p1 V1 = p0 V0

(2.10)

and therefore V1 =

p0 V0 p1

(2.11)

As well as on the basis of the balance of forces at the piston FF1 = p1 AK

(2.12)

and thus p1 =

FF1 AK

(2.13)

For the following calculation it can be applied that pK (s) = p2

(2.14)

28

2

Hydropneumatic Suspension Systems

Combining all above equations brings us to FF1 AK

FK (s) = ⎛

⎛

·⎝

p0 V0

⎞n ⎠

FF1 AK

(2.15)

⎞n AK

⎝ p0 V0 − AK s⎠ F F1 AK

After canceling AK p

FK (s) = FF1  p

0 V0

FF1

0 V0

FF1

by the substitution

n

(2.16)

n −s

p0 V0 = h0F FF1

(2.17)

the following simple relationship is obtained: FK (s) = FF1 ·

hn0F (h0F − s)n

(2.18)

The dimension h0F can be interpreted easily by a virtual image. It is equivalent to the height of a column of gas with the pressure p0 (the precharge pressure) and the volume V0 which has exactly the right base area so that it supports the force FF1 . Figure 2.6 depicts this for several different static spring loads FF1 . FF1 FF1 < FF1` < F F1``

h 0F

p0

FF1``

V0 FF1` p0 V0 h0F`

p0 V0 h 0F``

Fig. 2.6 h0F for various static spring loads FF1

2.2

Spring Characteristics

29

This illustration demonstrates one of the most important features of a hydropneumatic suspension: the higher the static springload, the smaller the height of the gas column h0F and therefore the more significant the change of the gas pressure forces on the piston at a given displacement s which then means a higher spring rate. The simple background to this is the relative change of the column height (h0F − s)/h0F ; it becomes more meaningful with smaller h0F and therefore the relative volume decrease and the relative pressure increase are more significant. This is the explanation of the increasing spring rate with increasing static springload for a hydropneumatic suspension. In case a hydropneumatic suspension is subjected to a wide range of static springloads, another important characteristic curve needs to be considered: the dependency of the spring rate on this very static springload. This is deduced by the following calculation. The general mathematical expression for the spring rate is: c=

dp d(pAK ) dF = = AK ds ds ds

(2.19)

After using Eq. (2.9) and differentiation with the chain rule: dp = p1 V1n (−n)(V1 − AK s)−n−1 (−AK ) ds

(2.20)

After applying the isothermal change of state from 0 to 1 and the balance of forces at the piston according to Eq. (2.13) and furthermore Eq. (2.11): FF1 dp c = AK = AK ds AK



p0 AK V0 FF1

n



p0 AK V0 (−n) − AK s FF1

−n−1

(−AK )

(2.21)

Dissolving and again using the dimension h0F Eq. (2.17) results in: c(s) = FF1 n

hn0F (h0F − s)n+1

(2.22)

It becomes obvious that h0F is also important for the spring rate. Yet we should remember that h0F is depending upon FF1 – it is not a constant value. For s=0 and dissolving h0F we obtain the spring rate in normal (design) position: c=n

FF12 p 0 V0

(2.23)

These are now the fundamental equations on which the function of every hydropneumatic suspension system is based upon. One extremely interesting consequence is that the geometry of the suspension cylinder(s) plays no role in these equations! Solely the gas fill in the accumulator as well as the suspended load determine the contour of the force–displacement curve and therefore also the spring rate.

30

2

Hydropneumatic Suspension Systems

On one hand the gas fill in the accumulator can be described by the product of accumulator precharge pressure p0 and the accumulator volume V0 . On the other hand it can, according to the equation of state for the ideal gas, be given as mG RT. This again points out clearly that, apart from the static spring load and the mass of the gas fill mG , the spring rate is also depending upon the temperature of the gas/the accumulator. So when laying out a hydropneumatic suspension system it has to be taken into account that the precharge pressure set during the production process refers to 20◦ C temperature. The actual operating temperature can vary due to influences from the environment but can also be increased due to heat in the hydraulic fluid that arises from the viscous damping. The general rule is: higher temperatures soften the spring, lower temperatures make it stiffer. Furthermore Eq. (2.23) makes it obvious that the static spring load affects the spring rate with its second power, a characteristic property of a hydropneumatic suspension. This means that the suspension behavior of the system spring-dampermass changes with changing suspended load. This is illustrated in the following calculation using the simple example of a single-mass oscillator. Using 

c mF

(2.24)

ω = 2π f

(2.25)

FF1 = mF g

(2.26)

ω= and

and

and additionally Eq. (2.23), it is possible to calculate the natural frequency f for the non preloaded hydropneumatic suspension: 1 f = 2π



nFF1 g p 0 V0

(2.27)

It becomes obvious that the natural frequency changes proportionally with the square root of the static springload. f ∼

 FF1

(2.28)

Generally spoken and from a theoretical point of view it is a goal to keep the suspension properties of a system constant throughout all loading conditions. For

2.2

Spring Characteristics

31

vehicle suspensions this is particularly important for ride behavior, comfort and road holding. Therefore it would be ideal to have a natural frequency independent of the static springload, especially for a single-mass oscillator. Yet in many applications not only the suspended mass/static spring load but also the moment of inertia with respect to various degrees of freedom have to be taken into account. In these cases the behavior described by Eq. (2.28) is often favorable since a disproportionate change of the spring rate often results in more constant overall suspension behavior than a spring rate changing proportionally with the static spring load. An explicit example of this is the hydropneumatic suspension for the front axle of an agricultural tractor. For lifting and moving heavy masses a so called front loader is optionally available, which consist of the hydraulically liftable boom in combination with a tiltable bucket or pallet fork attached to the end of it. When lifting a heavy mass, the center of gravity (COG) of this mass is very remote to the tractor’s center of gravity which increases significantly the moment of inertia for the pitch motion of the tractor (Fig. 2.7). The natural frequency for pitch motion needs to be kept above a certain level to prevent the tractor from becoming an uncontrollable rocking chair. Therefore it is beneficial to increase the spring rate more than it would be necessary for a constant bounce frequency. Hydropneumatic suspension systems fulfill this requirement and therefore contribute a lot to comfortable, stable and controllable ride behavior during front loader work. The force–displacement curve of a hydropneumatic spring as well as the curves of spring rate and natural frequency as a function of the suspended static load provide essential information about the suspension properties of a particular suspension system. On the following pages of this section these curves are shown and explained for the various hydropneumatic suspension systems. To ensure good comparability

COG plane for the unloaded tractor COG plane for a tractor with heavy front loader

COG plane for frontloader-bucket including payload

Fig. 2.7 Relocation of the tractor’s center of gravity during front loader work

32

2

Hydropneumatic Suspension Systems

between the different systems, all characteristic curves are calculated using the following basic setup for the suspension system: Single-mass oscillator Full suspension stroke (stop-to-stop) 100 mm Design position is the center between both end stops Static load for the suspension is 10 kN System tuned to a natural frequency of 2 Hz The following Figs. 2.8, 2.9 and 2.10 show the characteristic curves for the non preloaded hydropneumatic spring. For comparison the graphs also show the respective characteristic curves for a linear mechanical spring (thin line). The curves for spring rate and natural frequency are cut off below 2500 N static spring load. This range is not applicable for non preloaded hydropneumatic suspensions due to their low allowable load ratio (with the commonly used diaphragm accumulators, refer to Sect. 3.1.3) and therefore this is not relevant for real applications. In practice numerous examples can be found for applications of non preloaded hydropneumatic suspensions. For example most boom suspensions for tractors,

Spring force [kN]

40 Hydropn. spring Mech. spring

30 20 10 0 –50

–25

0 Displacement [mm]

25

50

Fig. 2.8 Force–displacement curve for the non preloaded hydropneumatic spring

Spring rate [N/mm]

800 Hydropn. spring Mech. spring

600 400 200 0 0

5

10 15 Static spring load [kN]

Fig. 2.9 Spring rate vs. static spring load for the non preloaded hydropn. spring

20

2.2

Spring Characteristics

33

Natural frequency [1/s]

4 3 2 1

Hydropn. spring Mech. spring

0 0

5

10 15 Static spring load [kN]

20

Fig. 2.10 Natural frequency vs. static spring load for the non preloaded hydropn. spring

telehandlers or wheel loaders (Fig. 2.11) – if they are suspended – are equipped with such a simple system: a cylinder whose pistonside is connected with an accumulator. This way the boom including the bucket/pallet fork etc. and the payload is suspended softly. In particular, the pitch oscillations of the usually completely unsuspended vehicle are reduced by this means. Comfort of the driver and in most cases ride stability are increased. Furthermore the reduced vibrations and accelerations at the bucket/pallet fork ensure safe transportation of the payload. In particular, bulk goods can be carried in a bucket more safely since the suspension prevents the payload from spilling and getting lost over the bucket’s edge. More detailed information about boom suspensions can be found in [LAT03] and for example the patents [DE205] and [US491].

Boom

Payload

Bucket Suspension cylinders

Fig. 2.11 Boom suspension of a wheel loader

The already mentioned next level of sophistication of non preloaded hydropneumatic suspensions is achieved by introducing a double-acting cylinder which is run in the regenerative mode (“regen”-mode) by connecting both cylinder sides (Fig. 2.5b). This type of system allows much higher rebound damping compared to the plunger cylinder. It can be found for example in the cab suspension of 6020series tractors produced by John Deere (HCS = hydraulic cab suspension). In the course

34

2

Hydropneumatic Suspension Systems

of improvements made since the start of serial production, the external line initially used for the connection of the two cylinder chambers (as shown in Fig. 2.5b) was eliminated. It was replaced by a passage in the piston with integrated flow resistor, thus providing identical damping characteristics at better cost. In this application an increased rebound damping level is necessary due to the kinematics of the suspension linkages to prevent the cab from strong pitching due to braking or even trailing throttle in the lower gears. The example of the HCS is shown in Fig. 2.12. It shows the integrated solution with cylinder (internal oil flow via piston cross drill) and accumulator being combined to the suspension unit. The connected hose is only used to provide oil for level control.

Fig. 2.12 Cab suspension cylinders of John Deere 6020series tractors

1 Piston rod

1 2

2 Protection cover 3 Hose to leveling valve 4 Cylinder tube

3

5 Accumulator 4 5

The currently highest level of development for non preloaded hydropneumatic suspensions is represented by the so called Hydractiv chassis suspension, which is used in several of Citroen’s latest passenger cars. In Fig. 2.13 it is shown that the center valve (7) allows two different operational modes for the suspension. If it is energized (and this is shown in the illustration) both suspension units of an axle are interconnected via a control valve (6) and are furthermore able to displace hydraulic fluid into a third accumulator (3). Its additional gas mass is the reason for a relatively low spring rate in this operational mode. Due to the interconnection of the suspension units, no roll stability (torsional spring rate relative to the longitudinal axis) is provided by the hydropneumatic springs, so it is only the mechanical anti-roll bars which are operative in this mode. In case the center valve is unenergized, both suspension units are separated from each other by the control valve and therefore act as individual springs. This causes additional roll stability compared to the interconnected operation. Furthermore in

2.2

Spring Characteristics 4

1

3

35 4

2

8

5

5

3 6

6

7 5

5

1 1

2

4

1 Accumulators front 2 Accumulators rear 3 Add. accumulator

4 Damping elements 5 Additional Damping elements 6 Control valve

1 4 7 Center valve 8 Controller

Fig. 2.13 Hydraulic schematic of the Citroen Hydractiv system (mod. from [HEN90])

the closed state, the third accumulator for each axle is decoupled from the suspension units, which causes a higher spring rate for the individual springs. So by closing the control valves, higher ride stability can be achieved especially during cornering and for “sporty” driving, while for opened control valves the soft suspension setup provides a high level of comfort which is typical for Citroen and their hydropneumatic suspensions. Detailed information about this can be found in Sect. 7.2.

2.2.4 Systems with Mechanical Preload It is clearly visible in Fig. 2.9 that there is a quadratic relationship between spring rate and spring load. Although this characteristic feature can have positive effects, as mentioned earlier in this section, it is in many cases favorable to attenuate it. This can be achieved by saddling an additional internal preload onto the hydropneumatic springs which is already active even when no external load is applied. In this case the preload acts as a basic load and all other external loads are added onto it. This has the effect that, for a given change of the external static load, the relative load change for the spring of the preloaded suspension system is smaller than for the non preloaded system.

36

2

Hydropneumatic Suspension Systems

The practical application of the preload is done in two different ways: (a) For the single-acting suspension cylinder the preload is applied by a mechanical spring for example by a helical coil spring or a torsional spring (mechanical preload). (b) By using a double-acting suspension cylinder it is possible to apply a hydraulic counter-pressure on the rod side by a second hydropneumatic spring (hydraulic preload). A third theoretical possibility is to load the isolated side with an additional mass to get the desired preload. Yet this is usually not accepted in mobile hydraulics since this would add significantly to the curb weight of the vehicle. This section now explains the systems with mechanical preload, Fig. 2.14 shows its schematic. Since the mechanical spring preloads the hydropneumatic spring with a compressive force, both springs are positioned figuratively opposite to each other although from a functional point of view it is a parallel connection of these springs. This is why the force application point of the overall, externally effective spring force is in the connection point of both springs, in the center. The illustration shows clearly that the mechanical spring causes, in addition to the preload, an additional spring rate for the system. This means that the system will have an effective spring rate resulting from the parallel connection of the hydropneumatic and the mechanical spring. c = chydr + cmech

F mech.

FF s=0 s

F hydr.

(also possible with doubleacting cylinder according to Fig. 2.5)

Fig. 2.14 Schematic illustration of a hydropneumatic spring with mechanical preload

(2.29)

2.2

Spring Characteristics

37

The spring rate for the hydropneumatic spring chydr can be calculated using Eq. (2.23). It is important to keep in mind though that the sum of the static spring load FF1 and the mechanical preload FV,mech (in the normal position of the suspension) need to be considered in the equation, replacing only FF1 . The spring rate for the mechanically preloaded hydropneumatic suspension therefore can be calculated by: c(s = 0) = n

(FF1 + FV )2 + cmech p0 V0

(2.30)

and the natural frequency for a single-mass oscillator with this system is:    n(F +F )2 V F1  + c mech g p0 V0 1  f = 2π FF1

(2.31)

FF (s) = Fhydr (s) − Fmech (s)

(2.32)

The calculation for the force–displacement-curve can be deduced from Fig. 2.14:

The force of the mechanical spring is: Fmech (s) = FV − cmech s

(2.33)

In order to calculate FF (s) it is necessary to use Eq. (2.16) from Sect. 2.2.3 and then insert the sum of forces (FF1 + FV ) replacing FF1 in Eq. (2.16):

FF (s) = (FF1 + FV ) 



p0 V0 FF1 +FV

p0 V0 FF1 +FV

n

n − (FV − cmech s) −s

(2.34)

The following Figs. 2.15, 2.16 and 2.17 show the characteristic curves for the hydropneumatic suspension with mechanical preload. The preload force FV and the spring rate of the mechanical spring cmech are varied in the diagrams to show the influence of these parameters on the different curves. It is of major importance that a mechanical spring is, at a given design space, the more intricate (and therefore expensive) the higher the preload force and the higher spring rate. For this reason a preload force of 5 kN and a spring rate of 20 N/mm are chosen as a basis for the following diagrams and are varied from there. This means that for variations of the preload force, a spring rate of 20 N/mm is chosen and for the variation of spring rate in general a preload force of 5 kN is chosen. Both basis values are rather on the lower end of the optimum range, as we will see later on. Looking at the force–displacement curves one tends to assume that the properties vary only marginally in the near range around the design point at a displacement of

38

2

Hydropneumatic Suspension Systems

(a)

Spring force [kN]

40

30

FV = 0 kN FV = 5 kN FV = 10 kN FV = 15 kN

20

10

0 –50

–25

0 Displacement [mm]

25

50

25

50

(b)

Spring force [kN]

40

30

cmech = 0 N/mm cmech = 20 N/mm cmech = 40 N/mm cmech = 60 N/mm

20

10

0 –50

–25

0 Displacement [mm]

Fig. 2.15 Force–displacement curves for the hydropneumatic spring with mechanical preload. (a) Variable FV (cmech = 20 N/mm). (b) Variable cmech (FV = 5 kN)

0 mm, a static spring load of 10 kN and a natural frequency of 2 Hz. However, when looking at the areas remote from the design point and even more when looking at the curves for spring rate and natural frequency, significant differences become obvious. Increasing mechanical preload reduces the progression of the force–displacement curve as well as the progression of the spring rate over static spring load. This means a considerable reduction of some characteristic (and sometimes unfavorable) properties of a hydropneumatic suspension. The reason for this can be found in the reduced relative load change (per kN increase of static spring load) with increasing FV . The equation for the natural frequency indicates clearly, that an increased mechanical preload needs to be compensated by an increased gas mass p0 V0 if the natural frequency has to remain constant. Furthermore it can be deduced that the relative change of the characteristic curve (by changed mechanical preload) decreases, the higher FV is chosen. In Figs. 2.16a and 2.17a this can be seen from the larger distance of the curves 0–5 kN compared to the distance of the curves 10 and 15 kN.

2.2

Spring Characteristics

39

(a)

Spring rate [N/mm]

800 FV = 0 kN FV = 5 kN FV = 10 kN FV = 15 kN

600

400

200

0 0

5

10 15 Static spring load [kN]

20

(b)

Spring rate [N/mm]

800 cmech = 0 N/mm cmech = 20 N/mm

600

cmech = 40 N/mm cmech = 60 N/mm

400

200

0 0

5

10 15 Static spring load [kN]

20

Fig. 2.16 Spring rate vs. static spring load for the hydropneumatic spring with mechanical preload. (a) Variable FV (cmech = 20 N/mm). (b) Variable cmech (FV = 5 kN)

It is also clearly visible, that the trend of the curve of spring rate vs. static spring load shows a better linearity for the preloaded hydropneumatic suspension system compared to the non preloaded system. Resulting from this is a natural frequency which is very close to the design goal of 2 Hz over a broad range of static spring load. It is interesting that the minimum of the natural frequency is moved to higher static spring loads with increasing mechanical preload FV . In the example illustrated by Fig. 2.17a the natural frequency shows the best constancy in the range around the design point spring load (10 kN) when mechanical preloads between 5 and 10 kN are applied (reminder: cmech = 20 N/mm). An increase of the mechanical spring rate has a similar effect as an increase of mechanical preload. Here too, the progression of the force–displacement curve and the spring rate vs. static spring load curve decreases with increasing mechanical spring rate. This is due to the fact that more and more load is taken by the mechanical spring and off the hydropneumatic spring (same overall spring rate!) for

40

2

Hydropneumatic Suspension Systems

(a) Natural frequency [1/s]

4

3

2 FV = 0 kN FV = 5 kN FV = 10 kN FV = 15 kN

1

0 0

5

10 Static spring load [kN]

15

20

(b) Natural frequency [1/s]

4

3

2 cmech = 0 N/mm cmech = 20 N/mm cmech = 40 N/mm cmech = 60 N/mm

1

0 0

5

10 Static spring load [kN]

15

20

Fig. 2.17 Natural frequency vs. static spring load for the hydropneumatic spring with mechanical preload. (a) Variable FV (cmech = 20 N/mm). (b) Variable cmech (FV = 5 kN)

increasing mechanical spring rate. So the harder the mechanical spring the softer the hydropneumatic spring and therefore the lower its influence on the overall system behavior. However even an infinitely soft spring (cmech = 0 N/mm) cannot lower the minimum of the natural frequency as low as zero mechanical preload can. Furthermore the diagrams show that the change of the characteristic curves by increasing mechanical spring rate is independent from the original level of the mechanical spring rate. The difference between the curves for 0 and 20 N/mm is about the same as the difference between the curves for 40 and 60 N/mm. It can be easily deduced from the diagrams shown above that one drops back to the curves for a non preloaded system as of Sect. 2.2.3 if the preload FV and the mechanical spring rate cmech are both reduced to zero. A practical example for a hydropneumatic suspension system with mechanical preload is the front axle suspension system offered by the company Carraro for agricultural tractors. It is used for example in tractors built by Claas (formerly

2.2

Spring Characteristics

4

2

1 1 2 3 4 5 6

41

3

6

5

Hub Upper wishbone Lower wishbone Central axle body Inner pivot axis of lower wishbone (torsion bar invisibly behind) Suspension cylinder

Fig. 2.18 Tractor front axle suspension by Carraro

Renault), Case/Steyr, Massey Fergusson and Landini. Figure 2.18 is taken from the patent US5931486. It shows an independent wheel suspension by a double wishbone arrangement (2 and 3) which is mounted on a central axle body 4. On the inner side of each lower wishbone 3 a torsional spring is placed coaxially with the respective pivot axis 5. This torsion bar creates the mechanical preload for the hydraulic cylinders 6. An adaptation of the axle to different types of vehicles is (among other measures) enabled by changing the dimensions of the torsional spring.

2.2.5 Systems with Constant Hydraulic Preload In many cases it is difficult to integrate a mechanical preload into a hydropneumatic suspension. This is often due to the usually high demand for design space of an additional mechanical spring, which has to be able to cope with the whole stroke of the suspension. That is why it is more common to use double-acting cylinders instead and use the additional available rodside chamber to create an additional, preloading spring. This is done by pressurizing the rod chamber of the cylinder (between piston and rod end) thus applying a force which acts as the preload for the suspension. Since this active area is displaced when the piston is moved and with it the oil that is contained by the rod chamber, it too has to be connected to an accumulator, which can absorb and release the displaced hydraulic fluid of the rodside chamber. This arrangement then is basically a suspension system which consists of two individual single-acting hydropneumatic suspensions counteracting each other. The respective schematic is shown in Fig. 2.19. For a better illustration of the hydraulic

42

2

Fhydr,R

Fhydr,K

Hydropneumatic Suspension Systems

FF

FF

s=0

s=0 s

Fhydr

s

Fig. 2.19 Schematic illustration of a hydropneumatic spring with hydraulic preload

preload, pistonside and rodside are symbolically shown as separate single-acting cylinders. Again both systems are shown positioned figuratively opposite to each other although from a functional point of view it is a parallel connection of these springs. The spring rate for the overall system can be calculated as the sum of the spring rates of the pistonside spring chydr,K and the rodside spring chydr,R . (2.35)

c = chydr,K + chydr,R

The spring rates for hydropneumatic springs can simply be taken over from Sect. 2.2.3. However that preload force needs to be taken into account. It results from the preload pressure pV on the rodside and the respective hydraulically active area, the ring-shaped area of the piston. (2.36)

FV = pV AR The result for the overall spring rate is c: c=

np2V A2R n(FF1 + pV AR )2 + p0,K V0,K p0,R V0,R

(2.37)

And therefore the natural frequency can be calculated as:    n(FF1 +pV AR )2  + p0,K V0,K 1  f = 2π FF1

np2V A2R p0,R V0,R



g (2.38)

2.2

Spring Characteristics

43

Looking at Fig. 2.19 the balance of forces gives us: FF (s) = Fhydr,K (s) − Fhydr,R (s)

(2.39)

By considering the equations for the non preloaded spring, the individual forces for pistonside and rodside can be calculated:

Fhydr,K (s) = (FF1 + FV )  Fhydr,R (s) = FV 





 p0,K V0,K n FF1 +FV

p0,K V0,K FF1 +FV

 p0,R V0,R n FV

p0,R V0,R FV

+s

n −s

(2.40)

(2.41)

n

Here it is important to keep in mind that the displacement s has different preceding algebraic signs in both equations. The reason is that a positive displacement s results in a compression on the pistonside (force increases) while it leads to an expansion on the rodside (force decreases). Applying the equation for FV results in:

FF (s) = (FF1 + pV AR ) 



n p0,K V0,K FF1 +pV AR

p0,K V0,K FF1 +pV AR



 p0,R V0,R n pV AR

n − pV AR  n p0,R V0,R −s + s pV A R

(2.42)

While for the system with mechanical preload only two new parameters (FV and cmech ) were needed for the respective equation, the number of additional parameters for a system with hydraulic preload is much higher. These new parameters p0,R , V0,R , AR and pV are available to tune the suspension to the desired properties. Yet, in the equations, these parameters always show up in pairs as AR and pV , which represent (when multiplied) the hydraulic preload force, and p0,R and V0,R , which represent (when multiplied) the gas mass enclosed in the rodside accumulator. So the latter two parameters are (in combination with FV ) responsible for the spring rate of the rodside hydraulic system chydr,R . The bottom line is that here too are two additional determining factors just like for the system with mechanical preload. These two factors can be set to the desired level by changing the parameters influencing them. The following Figs. 2.20, 2.21 and 2.22 show the characteristic curves for the hydropneumatic spring with hydraulic preload. All figures are again split into two diagrams, one of them showing the influence of the preload force AR pV = FV and the other one showing the influence of the additional rodside spring rate chydr,R = (nFV2 )/(p0,R V0,R ). For a better comparison with the hydropneumatic spring with mechanical preload, a 10 kN static spring force and 2 Hz for the natural

44

2

Hydropneumatic Suspension Systems

(a)

Spring force [kN]

40

30

FV = 3 kN FV = 5 kN FV = 7 kN FV = 9 kN

20

10

0 –50

–25

0 Displacement [mm]

25

50

25

50

(b) 40

Spring force [kN]

c hydr,R = 7 N/mm c hydr,R = 14 N/mm 30

c hydr,R = 21 N/mm c hydr,R = 28 N/mm

20

10

0 –50

–25

0 Displacement [mm]

Fig. 2.20 Force–displacement curves for the hydropneumatic spring with hydraulic preload. (a) Variable FV (c = 21 N/mm). (b) Variable c (FV = 5 kN)

frequency are chosen as the basis for this design. The preload parameters have been chosen as: AR = 500 mm2 pV = 10 MPa p0,R = 5 MPa V0,R = 300, 000 mm3 This choice provides an effective preload force of 5 kN and a spring rate of the rodside hydropneumatic spring of 21 N/mm. These values are similar to those in Sect. 2.2.4, a comparison with the previous examples (Figs. 2.15, 2.16 and 2.17) is therefore easy. Please note: choosing identical values as in Sect. 2.2.4 would not show the full potential of a system with hydraulic preload, therefore this slight

2.2

Spring Characteristics

45

(a)

Spring rate [N/mm]

800 FV = 3 kN FV = 5 kN FV = 7 kN FV = 9 kN

600

400

200

0 0

5

10 15 Static spring load [kN]

20

(b)

Spring rate [N/mm]

800 c hydr,R = 7 N/mm c hydr,R = 14 N/mm c hydr,R = 21 N/mm c hydr,R = 28 N/mm

600

400

200

0 0

5

10 15 Static spring load [kN]

20

Fig. 2.21 Spring rate vs. static spring load for the hydropneumatic spring with hydraulic preload. (a) Variable FV (c = 21 N/mm). (b) Variable c (FV = 5 kN)

deviation was chosen. Furthermore this set of parameters provides an optimal ratio of pV and p0,R as will be shown in Sect. 3.1.3. For the hydropneumatic spring with hydraulic preload it can be stated that an increase of the rodside hydraulic spring rate chydr,R and an increase of the preload force FV have in general a very similar effect. This behavior can also be deduced from the Eq. (2.37) for the spring rate and Eq. (2.38) for the natural frequency. The precharge pressure and the rodside accumulator volume can be found in the denominator, while the preload force, represented by pV AR , is found in the numerator. It becomes obvious that it is basically possible to create similar curves with a hydropneumatic suspension system with hydraulic preload and with mechanical preload. One special feature is characteristic to both of them: at low static spring loads the natural frequency does not drop as drastically as for non preloaded systems. It stays on the desired level over a broad range of loads and even increases when the load gets close to zero. This can be ascribed to the preload force on one

46

2

Hydropneumatic Suspension Systems

(a) Natural frequency [1/s]

4

3

2 FV = 3 kN FV = 5 kN FV = 7 kN FV = 9 kN

1

0 0

Natural frequency [1/s]

(b)

5

10 Static spring load [N]

15

20

4

3

2 c hydr,R = 7 N/mm c hydr,R = 14 N/mm c hydr,R = 21 N/mm c hydr,R = 28 N/mm

1

0 0

5

10 15 Static spring load [kN]

20

Fig. 2.22 Natural frequency vs. static spring load for the hydropneumatic spring with hydraulic preload. (a) Variable FV (c = 21 N/mm). (b) Variable c (FV = 5 kN)

hand, which creates the effect that, even at FF1 = 0 N, there is still a significant force on the hydraulic spring and therefore spring rate available. On the other hand it is the spring rate of the mechanical spring or of the rod side system that is still effective at zero load. An increase in this preload force FV , by increasing the preload pressure, results in a weakening of the characteristic curve of the non preloaded system. The setting pV = 0 would represent the non preloaded system. Furthermore it is obvious that the spring rate depends less on the static spring load if the preload force is increased. In terms of the natural frequency an increase of FV results in a shift of the minimum of the natural frequency curve towards higher static spring loads. At high preload forces an additional characteristic effect can be seen to some extent: The progression of the force–displacement curve of the rodside hydropneumatic spring causes a strong reduction in the spring force when getting close to the rebound end stop. This effect is even more evident, if the gas mass in the rodside accumulator is changed. This is shown in the diagrams by the influence of the spring rate of the

2.2

Spring Characteristics

47

rodside chydr,R . At high chydr,R the compression of the rodside gas volume is very high at the end of the stroke close to the rebound end stop. This results in a strong force increase of the rodside hydraulic spring. One can make use of this for suspension systems. With a suitable choice of parameters, the spring rate in the range around the design position (center position) can be very low, so that the suspension is soft in its main working range. Due to the progression, the spring becomes the stiffer, the closer the piston gets to its end stops. This helps to prevent the suspension from bottoming out. The above mentioned effect can be emphasized if the preload force is reduced and a high rodside spring rate is chosen at the same time. The result is a progression of the force–displacement curve both in compression and rebound direction. The suspension can be tuned to provide this effect by the following setup of the rodside preload parameters: AR = 500 mm2 pV = 4 MPa p0,R = 1.4 MPa V0,R = 100, 000 mm3 Figure 2.23 shows the force–displacement curve for this configuration. For comparison reasons, that diagram also shows with a thin line the curve for a linear, mechanical spring. The end stop progression effect can be used without significant negative impact on the behavior of the natural frequency over static spring load. Furthermore this is also a cost effective solution since the smaller gas volume on the rodside requires only small rodside accumulators. However this can not always be used in practice since other effects and limits need to be considered – please refer to Sect. 3.1.3 for more information. Good examples of the hydropneumatic suspension with constant hydraulic preload are the front axle suspension systems on Fendt tractors as well as on John

Suspension force [kN]

40

30

Hydropn. spring Mech. spring

20

10

0 –50

–25

0 Displacement [mm]

25

50

Fig. 2.23 Force–displacement curve with distinct progression close to the end stops

48

2

Hydropneumatic Suspension Systems

Deere tractors with the so called TLS I system (Triple Link Suspension I) which can be found on their 6010 and 7010 series tractors. Yet both manufacturers go different ways when it comes to how the hydraulic preload is applied. Fendt applies the full pump pressure of about 20 MPa on a rather small rodside active area whereas John Deere applies a lower, regulated pressure as the preload pressure to a respectively larger rodside piston area. Their hydraulic control blocks contain a pressure regulating valve which enables this. The advantage of this is that the variable displacement pump used on these tractors does not have to go to full pressure during corrective action of the control system. Another advantage is cylinder friction, further explained in Sect. 2.3.1. The disadvantage is the need for a larger volume accumulator on the rodside since more oil is displaced due to the larger rodside active area. More information on the design and layout of John Deere TLS I system can be found in Sect. 7.1.

2.2.6 Systems with Variable Hydraulic Preload This is the next logical step forward from the suspension system with constant hydraulic preload. When looking at Eq. (2.37) it is easy to discover that it is possible to vary the preload and therefore the spring rate by changing a rather easily adjustable parameter: the preload pressure pV . This possibility to influence the spring characteristics allows the control of the suspension depending on other parameters such as the static spring load or other operation parameters in an open loop or even in a closed loop. A good example of the spring load dependent preload pressure control is the John Deere front axle suspension TLS II, which comprises a two-step adjustment of the spring rate level depending on the static spring load. This is enabled by using the pressure in the piston chamber as an input parameter for the control of the preload pressure in the rod chamber. Below a certain pistonside pressure limit pK,grenz , the rodside pressure is set to a high level pR,h . If the pistonside pressure is above pK,grenz , a low level of rodside pressure pR,n is set. The higher pressure level on the rodside for low pistonside pressures causes an increased spring rate at low front axle loads. The control of the rodside pressure is achieved purely by hydraulic components – one pressure switch valve and one special, switchable pressure regulating valve. Figure 2.24 illustrates schematically the relationship of spring rate and static spring load. In reality there is interaction between rodside pressure and pistonside pressure. This interaction causes a difficult to define transition area around the pressure switch point. In this area it also depends on other operational conditions whether the rodside pressure is on a high or a low level. Therefore in the schematic, the vertical part of the spring rate vs. load curve line is only idealized and does not represent the behavior in reality. There are several reasons to justify this additional effort: (1) The positive effect of the hydraulic preload on the characteristic of the curve of natural frequency vs. static spring load is further improved (constant over a wide range).

2.2

Spring Characteristics

49

Spring rate

Fig. 2.24 Spring rate vs. static spring load for the John Deere system TLS II

Rodside pressure high Rodside pressure low

Pressure switch point

Front axle load

(2) The system accounts for the fact that low front axle loads are caused by heavy implements and loads with a center of gravity far behind the tractor. These conditions increase the inertia relative to the lateral axis of the tractor which would cause a very low pitch natural frequency and therefore result in a spongy ride behavior of the tractor with frequently bottoming out suspension. The increased spring rate for these conditions compensates for this and therefore improves the suspension quality. (3) Since diaphragm accumulators are used in this suspension system, the mentioned setup helps to keep these accumulators within the allowed pressure range of operation (refer to Sect. 2.5 for more information). In a further step, a closed loop control of the rodside pressure provides the possibility to adapt the suspension to all kinds of different operating conditions. For this purpose, a parameter needs to be chosen as an input variable, which acts as a measure for the suspension quality. Therefore, if suspension quality worsens due to a change in operating conditions (for example an uneven road surface), the degradation in suspension quality can be detected and the spring stiffness can brought to a level which helps to re-improve the ride behavior and therefore the input variable. This is the step from a purely passive suspension system (yet with level control) towards an adaptive system. In this case it is usually necessary to use electronics as a support for the hydraulic system in order to set up a closed loop control for the rodside pressure. The electronic controller can monitor multiple input variables and can adjust the hydraulic system to the best possible setting by switching hydraulic valves and allowing oil to flow in and out of the hydraulic suspension units, especially their rodside portions. This system permits the use of the whole range of possible settings and spring rates allowed by the hardware components, in particular the accumulators. This means that there is no longer only the simple spring rate vs. static spring load curve of the constantly preloaded system and the more advanced curve for the two-step pressure adjusted system. For the system with fully variable rodside pressure, there is then a large area of possible operating points in the spring rate vs. spring load diagram. Figure 2.25 compares the three last-mentioned systems. A particular advantage of the continuously variable closed loop control system is the fact that it can be easily adapted to changes in vehicle dimensions/masses etc.

50

2

Hydropneumatic Suspension Systems

Spring rate

Constant rodside pressure 2-stage rodside pressure Continuously variable rodside pressure

Front axle load

Fig. 2.25 Comparison of the spring rates of the hydraulically preloaded systems with constant, 2-stage and continuously variable rodside pressure

as well as new operating conditions. It is therefore ideal for use in different vehicle platforms since it can be used universally only with specific software and without or only minor changes in hardware. The John Deere TLS Plus suspension system makes use of this advanced technology and therewith continues the consistent enhancement in hydropneumatic suspensions.

2.3 Damping Characteristics The energy that is transferred into the suspension by external excitations needs to be dissipated to achieve a decay of the resulting oscillation amplitude and to avoid increasing amplitudes due to resonance. Therefore additional elements in the suspension system are necessary to transform the kinetic and/or potential energy of the suspension. In most cases kinetic energy is transformed into heat by application of a retarding force during the motion of the suspension elements. This retarding damping force usually is based upon the principle of friction. In general two different fundamental principles create the damping in a suspension system: (1) Boundary friction, also called dry friction or solid body friction. Two solid bodies pressed onto each other with a normal force slide in their interface with a resistant force caused for example by catching of surface roughness and adhesion. The resistant force is called friction force and acts as a damping force. (2) Fluid friction, also called viscous friction or hydrodynamic friction. A flow resistor is placed in the flow path of a fluid and causes internal fluid friction which therefore causes a pressure increase upstream of the resistor. This additional pressure is acting upon the active areas of the cylinder thus creating a retarding force, a damping force.

2.3

Damping Characteristics

51

In addition to the above mentioned principles there are more rather exotic principles which are rarely used in suspension technology. For example there is the eddy-current principle, which is often used in vehicles as a wear-free retarder to reduce vehicle speed on downhill slopes. It is based upon the principle of induction of current in an electric conductor when it is moved through a magnetic field. Furthermore there are the so called gas-spring-damper-elements [GOL84], which provide the function of a spring as well as a damper only by their internal gas fill. In general one tends to keep the damping forces as low as possible to get the best possible decoupling of the suspended mass on the isolated side from the excitation on the input side. Yet if the level of damping is tuned to provide optimal results under normal operating conditions, the damping will most surely be too low under extreme operating conditions. This will result in high amplitude oscillations and, as a consequence, bottoming out of the suspension. To avoid heavy accelerations when the suspension hits the mechanical end stops, another type of damping is integrated into many suspension systems which is only active when the suspension reaches the end of its stroke: the so called end-of-stroke damping or end cushioning. Additional damping elements dissipate the excessive kinetic energy before the suspension reaches the end stop. Therefore this energy is prevented from being transferred into the isolated side by a short term but very high force peak. The following sections explain the boundary friction, the viscous friction and the special but very important area of end-of-stroke damping.

2.3.1 Boundary Friction Damping The boundary friction is a resistive force against sliding in the interface between two solid bodies which are pressed onto each other by the normal force FN . The direction of the normal force is perpendicular to the intended sliding direction, the resistive force, respectively the friction force, is acting opposed to the sliding direction (Fig. 2.26). There will be no movement in the interface as long as the tractive force FZ does not exceed a certain limit. This limit is the static friction force Fµ,H . In the case of static friction, the absolute value of the friction force Fµ is equal to the absolute

FN

v FZ

Fµ

Fig. 2.26 Forces involved in boundary friction

–FN

52

2

Hydropneumatic Suspension Systems

value of the tractive force FZ , the body is in a static balance of forces. The maximum static friction force depends upon the normal force FN and the coefficient of static friction μH . The latter depends on the properties of the two involved solid bodies, in particular the type of material and the nature of their surfaces. Fμ,H = μH · FN

(2.43)

The static friction force plays an important role in suspension systems. It is the parameter which determines the minimum level of excitation below which a suspension system cannot absorb and reduce acceleration. Up to this level of excitation, no movement between input side and isolated side is possible (hindered by the static friction, sometimes also called “stiction”). In this case the suspension components represent a fixed coupling between both sides. The level of static friction therefore very much affects what is called the response characteristic of the suspension. This describes whether it reacts sensitively on smallest excitations and irons these out or whether these excitations are passed non-elastically to the isolated side. Static friction forces are especially caused by elastomer seals in particular after long time intervals without operation and can even lead to partial damage of the seal [MUE]. It is important to notice that static friction does not contribute to the damping of the suspension system since it is only active at times without relative motion! As soon as the tractive force exceeds the static friction force, both solid bodies start to slide on each other. During sliding the so called sliding friction force Fµ,G is active, which is sometimes significantly lower than the static friction force. Just like μH , the coefficient of sliding friction μG depends mainly on the properties of the two sliding surfaces. Furthermore there can be an additional dependence for example on sliding velocity (not considered in the following equation). Fμ,G = μG FN

(2.44)

Due to the coincidence and counteraction of motion and sliding friction force, kinetic energy is transformed into heat and therefore drawn out of the suspension system. The higher the amount of energy stored in the suspension system, the larger the amplitude of the oscillation. Due to the increased displacement, the energy drawn out of the system by friction during each oscillation increases with the stored energy. This means that a damper, which works by the principle of boundary friction, is at least partially self adapting to the needs of the system. It will be shown in Sect. 2.3.2 that fluid friction is even more capable of providing this important feature. The first dampers which were used in suspension systems were based purely on the principle of boundary friction. Examples of these are the well known leaf springs, especially the laminated type, as well as the less well known torsional friction dampers which were even adjustable in friction by varying the normal force through the variation of the load of the (laminated) disk spring. Despite that, the pure friction dampers were not able to make it into modern suspension systems

2.3

Damping Characteristics

53

since they always had the negative side-effect of worsening the systems response characteristics. In all suspension systems boundary friction can be found in the kinematics’ bearings which are mandatory in providing the necessary suspension stroke. On top of that, there is the friction of suspension cylinders in hydropneumatic systems. Their friction originates from the guiding elements as well as the sealing elements of the cylinder. The friction in the guiding elements can be kept low if the lateral forces in the cylinders are kept as low as possible. Internal lateral forces arise on one hand from external lateral forces, which can originate for example from a clamped fixation of one cylinder end and on the other hand from bending moments superimposed on the cylinder. These lateral forces in the rod guiding element FSF and in the piston guiding element FKF act as normal forces which press the guiding elements onto their friction partners and therefore cause friction forces (Fig. 2.27). It becomes obvious that the supporting distance e between the rod guiding element and the piston guiding element becomes smaller, the further the rod moves in rebound direction. Apart from a potential risk of buckling or bending the piston rod, the normal forces in rod guide and piston guide increase and the respective friction forces with them – assuming constant external lateral forces and/or constant bending moment. On the other hand the friction in the elastomeric sealing elements of a suspension cylinder is inevitable, inherent to their functional principle. The sealing elements have to seal off a hydraulic pressure and therefore need a normal force which presses the sealing edge onto the respective opposite surface. An unfavorable by-product of this normal force is boundary friction. In hydropneumatic suspension systems very high pressures need to be sealed off, accordingly high friction forces can be expected. Therefore it is extremely important to put a high emphasis on the optimal design of these sealing elements ([TRA90], [GES97], [FIS06]). Among other MB

FQ

FSF

FSF FKF

e

Fig. 2.27 Lateral forces in the guiding elements of a suspension cylinder

FKF

54

2

Hydropneumatic Suspension Systems

influences it is the right choice of the seal geometry and the seal material as well as, in the very beginning of the system layout, the right choice of suspension system pressures and cylinder geometry. In particular the seal diameters have an easily illustratable influence: the larger the seal diameter, the longer the length of the sealing edge(s) and the higher the friction forces. In this context it is interesting to look at the following design task: a hydropneumatic suspension system with hydraulic preload has to be laid out. Mandatory input parameters are the piston diameter and the hydraulic preload force. For this preload force Eq. (2.36) states that FV = pV AR . This means that the same preload force can be created by a low preload pressure and a large active area on the rodside (and therefore small piston rod diameter) or with a high preload pressure and a small active area on the rodside (and therefore a large piston rod diameter). Looking at the previous explanations in this section, it becomes obvious that it makes sense to go for a small pV and a large AR for two important reasons: the sealed off pressure and the length of the sealing edge at the rod seal are lower and both effects result in lower friction forces of the rod seals. The comparison in Sect. 2.2.5 concerning the two hydropneumatic front axle suspensions with constant hydraulic preload, one with regulated low rodside pressure and one with constantly high rodside pressure (= max. vehicle system pressure) becomes even more interesting in the light of the previous explanations. A further important factor for friction is the mechanical layout of the suspension system, i.e. the kinematics. Assuming that the mechanical system is based on a simple rocker arm, there are various possibilities in terms of where to integrate the suspension cylinder. The further the cylinder is mounted away from the pivot point, the higher is the necessary stroke of the cylinder in order to provide a certain stroke of the suspension (at the wheels). Provided that the available hydraulic system pressure is obviously constant for all cylinder positions, the piston diameter of the suspension cylinder must increase, the closer the cylinder is positioned to the pivot point of the rocker arm – assuming, of course, the same suspended axle design load for all cylinder positions (Fig. 2.28). Under the assumption that a certain friction force is created per millimeter of sealing edge (type of seal and sealing pressure constant), it is possible to find a mathematical proof, that the ratio of external cylinder force to cylinder friction force improves, the closer the cylinder is positioned to the pivot point of the rocker arm. The background to this is that the hydraulically active surface increases to the power of two with the piston diameter, while the perimeter and therefore the necessary length of the seal increases only linearly. Yet in reality it has to be taken into account that the above mentioned assumption is not always true if the diameter jump is chosen to be too wide, even if the same type series of seals is used. Furthermore it is important to consider, that the forces in the cylinder bearings as well as in the rocker arm pivot bearing also increase, if the

2.3

Damping Characteristics

55

Rocker arm pivot point

Wheel-ground contact point

Fig. 2.28 Cylinder dimensions depending of its position relative to the pivot point

suspension cylinder is positioned close to the pivot axis. This also leads to an increase in friction. In the end it is the experiment which will give exact information about the quality of the layout of a suspension system, in particular concerning friction. Therefore friction test stands for hydropneumatic components as well as for complete systems are common in the industry. Interesting insight into latest investigations on friction by the technical university RWTH Aachen can be found in [VER08].

2.3.2 Fluid Friction Damping The hydraulic fluid in a hydropneumatic suspension system is used as a medium to transfer the pressure on the active areas of the piston to the accumulator(s). Due to the suspension movement and therefore the displacement of the piston, the hydraulic fluid steadily flows between cylinder and accumulator with regularly changing flow direction. If a flow resistor is placed in the fluid flow, the kinetic energy of the hydraulic fluid is transformed into heat due to shear flows inside the fluid. The flow resistor creates a pressure loss, which causes, via the active areas of the piston, a force which counteracts the motion of the piston. This force is therefore taking energy out of the oscillation and hence is a damping force (Fig. 2.29). (2.45)

FD,hyd = pAK ·

PD,hyd = FD,hyd v = p V

(2.46)

It is typical for fluid friction that the pressure loss depends very much on the amount of volume flow through the flow resistor. This is the reason, why the fluid friction damping force depends, as opposed to the boundary friction, significantly on

56

2

Hydropneumatic Suspension Systems Δp

FD,hyd

v Flow resistor AK . Volume flow V

Fig. 2.29 Active principle of fluid friction damping

the speed of the suspension motion. This means that a fluid friction damper adapts even twice to the amount of energy stored in an oscillation: firstly by the amplitude of the oscillation and therefore indirectly secondly (for the same oscillation frequency) also by the velocity of the oscillation. Simple flow resistors can be divided into two basically different types, which show a different characteristic in the dependency of pressure loss and volume flow. (a) Throttle: The flow is decelerated by a slow transition of the flow cross-section from wide to narrow and back to wide. The cross-section of a dedicated throttle for defined additional damping usually has a circular shape and is provided by an intentionally small bore in a component in the fluid path between cylinder and accumulator. The small cross-section causes high flow velocities of the hydraulic fluid. Due to the high gradient of flow velocity from the flow center to the inner wall of the bore, high shear forces and therefore high pressure losses are generated. The latter therefore is theoretically/ideally proportional to the volume flow. Another important characteristic of the throttle therefore also is the direct dependency of pressure losses on the viscosity of the hydraulic fluid. This aspect becomes especially important since most of the common hydraulic fluids have a strongly temperature dependent viscosity (Fig. 2.30) which also makes the damping effect of a throttle temperature dependent – this is most cases very unfavorable. Another remarkable fact is the change in viscosity due to the pressure level inside the fluid. The diagram in Fig. 2.30 shows that the kinematic viscosity ν at the ISO reference temperature of 40◦ C increases by about 50% when the pressure is increased from 0 to 200 bar. This means another advantageous adaptation effect of fluid friction damping in throttles depending on operating conditions: higher loads mean higher hydraulic fluid pressures and therefore a higher fluid viscosity causing higher damping. The pressure loss across a throttle bore with laminar flow can be calculated by: ·

p = V νρKD

(2.47)

2.3

Damping Characteristics

57

Fig. 2.30 Relationship of kinematic viscosity, temperature and pressure for a typical hydraulic fluid according to [FIN06]

Let KD be a constant that is related to the geometry and dimensions of the throttle bore while ρ is the density of the hydraulic fluid. KD can be calculated for the throttle geometry below:

D D D

(2.48) Typical hydraulic components with the character of a throttle are for example tubes, hoses and hose fittings without tight bends, bores with constant diameter in control blocks or also straight pipe fittings with constant inner diameter. (b) Orifice: The fluid flow is subjected to one or more sudden transitions from a wide to a narrow or a narrow to a wide flow path. This causes strong turbulence in the hydraulic fluid which is the reason for internal fluid friction and hence a transformation of fluid flow energy into heat and therefore, in the end, damping. Ideally this type of flow resistor is characterized by a quadratic dependency of the pressure loss on volume flow. Opposed to the throttle only a minor amount of additional surface is in contact with the fluid flow in regions with

58

2

Hydropneumatic Suspension Systems

high flow velocities. Therefore this type of resistor is ideally not depending on fluid viscosity and therefore temperature. ·2

(2.49)

p = V KB

Let KB be a constant that is related to the geometry and dimension of the throttle as well as the density of the hydraulic fluid. KB can be calculated for an orifice:

B D

B

(2.50) The parameter α D is called the flow coefficient and depends mainly upon the geometry of the inlet edge and the Reynolds number. Typical hydraulic components with the character of an orifice are for example components with changes in flow direction especially with a low turning radius (for example elbow fittings or crossdrills in control blocks), furthermore components with sudden changes in cross-section for example the bore in the cylinder wall for the hydraulic connection of pistonside/rodside or often also fittings with a wide jump in sizes on their connectors. Figure 2.31 compares the behavior of the (ideal) throttle and orifice and also shows the influence of fluid viscosity. More information about the throttle and orifice flow resistors can be found in the respective literature for hydraulics basics (for example [MUR01], [FIN06] and [EBE74]) and is therefore not further explained here. In these books further details can be found about flow resistance of various line routing elements. These apply to hydropneumatic suspension systems, just like they apply to all other hydraulic systems.

Pressure loss Δp

ν4

ν2

Throttle (ν1 < ν2 < ν3 < ν4)

ν1

Orifice

Fig. 2.31 Pressure loss p as a function of volume flow and viscosity

ν3

.

Volume flow V

2.3

Damping Characteristics

59

In reality you almost never have a flow resistor of purely one type but mostly a mixture of the basic throttle and orifice resistors. Therefore it is often better to assign the attribute “throttle character” or “orifice character” to a flow resistor, depending on which character prevails. In general a damping is preferred which is not depending upon fluid temperature (viscosity). Therefore, at first sight a flow resistor with a strong orifice character seems to be the best choice. But caution is necessary here. Owing to its very nature this flow resistor dampens out oscillations with low amplitudes only very weakly and therefore causes a long reverberation time. Furthermore, especially in axle wheel suspensions, this also can cause a sensation of a “loose connection” between input side and isolated side, making the driver think that he is not fully in control of the vehicle. On the other hand the orifice reacts very strongly to heavy excitations for example when driving through a pothole. Due to the quadratic relationship of pressure drop and volume flow, the p will be very high, causing a high damping force and therefore high accelerations on the isolated side. A damping system of this type therefore often is only partly satisfactory. This is the reason why special flow resistors have been contrived which often provide a rather strong basic damping already at low piston velocities by using one of the above mentioned flow resistors combined with a pressure reducing valve to avoid extreme damping forces. The high basic damping is favorable especially in axle/wheel suspensions since this provides a good feedback from the suspension system to the driver. Furthermore the higher damping forces provide better driving safety during for example evasive maneuvers, fast lane changes or “sporty” driving in general due to the reduction of the roll motion of the vehicle body. Yet to ensure that this higher basic damping does not reach extreme values for high piston velocities, the basic flow resistor is bypassed by a special kind of pressure relief valve. It opens at high differential pressures and therefore keeps the pressure loss of the overall damping valve arrangement (and with it the damping forces) on an acceptable level from a comfort perspective (Fig. 2.32, further information can be found in Sect. 4.3.2). The start of the bypassing through the pressure relief valve can be identified as the sharp bend in the damper’s characteristic curve. It is a further advantage of this valve that the opening point of the pressure relief

Damping force FD relief valve opens

Piston velocity v

Fig. 2.32 Damping force as f(v) for an automotive shock absorber

Compression

Rebound

60

2 fA=50/min

Hydropneumatic Suspension Systems F

F

s

−0.26

0.26

v [m/s]

100 mm

Fig. 2.33 Force–displacement curve and force–velocity curve derived from it

valve is mostly independent from fluid temperature, so the limiting of the damping forces always starts in about the same range which results in a fairly constant suspension behavior at different temperatures. Please consider that only in Figs. 2.32 and 2.33, opposed to the regular definition in this book, the force and the displacement during the compression stroke are negative and during the rebound stroke are positive, since this is a frequently found definition in shock absorber technology. The force-velocity curve for a damper is typically derived from force– displacements curves recorded for an amplitude of 100 mm at different excitation frequencies fA . The excitation frequency then determines the maximum piston velocity of the damper during the crossing of the center position between both ends of the stroke. Therefore experiments of this kind provide information about the damping force as a function of piston velocity. By extracting the maximum force (rebound) and minimum force (compression) at the center position for various excitation frequencies and transferring them into a diagram of force vs. piston velocity, the characteristic curve for the damper is obtained. Figure 2.33 shows the step from the force–displacement to the force-velocity curve for an excitation frequency of 50/min. The above diagrams show that the damping forces for compression are lower than for rebound. This is at first sight an unsteady distribution of damping forces. Yet it takes into account that compression motions (for example when riding over an obstacle) often cause higher piston velocities than rebound motions. Furthermore it is obvious that the increasing spring force during compression adds to the damping forces and helps to decelerate the piston velocity, while during rebound motion, the spring forces decrease and therefore damping needs to take over more of the decelerating effect. The shown ratio for rebound damping force to compression damping force of about 2:1 provides a more effective and more comfortable reduction of the accelerations on the isolated side as would be possible by equal damping forces in compression and rebound.

2.3

Damping Characteristics

61

Due to the path of the hydraulic fluid from the active area of the cylinder all the way to the accumulator diaphragm, a certain inevitable basic fluid damping of the hydropneumatic suspension system is caused by the hydraulic lines and fittings between both ends. It basically depends upon the sizing of these components. In many suspension systems on the market the fluid friction damping is purely defined by these line elements. In this case ideally they have been tested and readjusted/selected for correct layout in specific tests. However some systems show indications that this has not been or insufficiently carried out. Especially systems with long distances between suspension cylinder and accumulator show only partly the potential effect which would be achievable with shorter and/or larger diameter lines. This is why it is necessary to ensure from the very start of a design of a suspension system that suspension cylinder and accumulator are positioned close to each other. The lower the basic damping, the better the possibilities for influencing the damping characteristic of a system by targeted integration of additional damping elements. This possibility to integrate specific damping components can be used to further adapt the damping, depending on the spring rate. This is a major advantage in particular in hydropneumatic suspension systems with their wide range of spring rates depending on spring load and preload. If the operating conditions are changed, for example by a change in static spring load, it is good to adjust the spring rate in order to get (back) to the desired natural frequency, but it is better to adjust the damping characteristics on top of that, so the dissipation of oscillation energy is also adapted to the new demands. Such load adaptive damping systems are already available for example for trucks with air suspended axles. The damping elements are adjusted by the average pressure in the air bags and therefore adapted to the static spring load (ZF Sachs PDC – Pneumatic Damping Control [MUR98], [CAU01]). For a hydropneumatic suspension this could be done for example by an adjustable flow resistor which is either operated hydraulically directly by the pressure on the pistonside or operated electrically by an electronic controller which reads the pistonside pressure by a pressure sensor. The electrical adjustment offers the possibility to include further information in the algorithm for the right selection of the necessary damping forces. Significant, meaningful parameters are for example the temperature of the hydraulic fluid (and therefore viscosity), certain operating conditions or driver settings. A sufficiently fast adjustable system can even provide a semi-active damping, for example via the Skyhook-algorithm, or an end-of-stroke damping (see Sect. 2.3.3). The adjustment of the flow resistor does not necessarily have to be continuous, like for example in the ZF Sachs CDC system (Continuous Damping Control, [REI05], [EUL03], [CAU01]). An adjustable damper with a stepped characteristic might also provide good results, for example like the Bilstein ADS (Adaptive Damping System) which allows for an individual two step adjustment for both compression and rebound damping [SCM00].

62

2

Hydropneumatic Suspension Systems

2.3.3 End-of-Stroke Damping “A passive suspension system, which never gets close to its end stops during all operating conditions, is probably not tuned to be soft enough or wastes suspension travel.”

This kind of provocative sentence contains important information. Every suspension system only has a limited stroke available to isolate the excitations coming from the input side. Basically the softer a suspension system is tuned (keeping the correct relation of spring rate and damping in mind), the more it will reduce accelerations on the isolated side, yet the longer will be the displacement between input side and isolated side for certain excitations. If these excitations exceed a certain limit, the necessary displacement becomes greater than the available suspension stroke and therefore the suspension bottoms out. This causes short term high forces and accelerations which reduce subjective comfort and furthermore can overload components of the suspension system as well as components on the input side or isolated side. One way to avoid this problem would be to tune spring and damper to a harder level, so that even under the worst conditions and most extreme excitations the available suspension stroke is always sufficient. Yet, in doing so, the result is a reduced comfort level in all other operating conditions. Therefore it is important to also consider the expected frequency and amplitude distribution of the various excitations to find an optimum level for spring rate and damping. When taking this into account it becomes obvious that it can be quite acceptable to have the suspension bottoming out slightly sometimes, if in the same turn the overall comfort level in all other operating conditions is improved by a softer setting. A suspension system can be even tuned to be softer than that if an additional end-of-stroke damping is used and the (rare) cases of bottoming out are softened by an additional damper or an additional spring. All in all this results in a remarkable gain in comfort. To reduce the harshness of a bottoming out event at the end of the stroke it is necessary to reduce the velocity of the piston relative to the cylinder. So if the piston gets close to the end positions (for example the last 10% of the stroke in each direction) an additional decelerating force (damping or spring) needs to be activated. Most suitably this additional force creates a constant or slightly progressive gradient of velocity over displacement, meaning the deceleration is constant or increases slightly as the piston gets closer to the cylinder bottom. Ideally the end-of-stroke damping system recognizes the excessive kinetic energy which needs to be dissipated until the end of the stroke and then adapts its properties in a way such that a constant and lowest possible force level decelerates the piston until shortly before the end stop. Many suspension systems use elastomer elements for end-of-stroke damping. Just before hitting the end stops, the suspension motion is decelerated by an additional elastomer spring with a minor amount of damping. So strictly speaking this is more of an end-of-stroke spring than an end-of-stroke damping. The spring force and therefore also the deceleration of the piston velocity increases from the first contact to the elastomer up to the mechanical end stop. The characteristic curve of

2.3

Damping Characteristics

63

deceleration force vs. displacement is at least a linear increase but in most cases even a disproportionately higher increase, and can be shaped for example by the outer contour of the elastomer element, by internal bores or even by collars supporting the circumference of the elastomer. This layout allows soft cushioning of minor impacts with small spring forces and, on the other hand, taking even the most extreme bumps without the bottoming out of steel parts. In passenger cars this type of end-of-stroke damping is then clearly noticeable for passengers, yet it fulfills the requirement to protect the components from overload. During the rebound motion out of the end stop, the elastomer extends back to its original shape and reintroduces most of the absorbed energy back in to the suspension system. Due to a slight damping effect, a minor amount of energy remains as heat inside the elastomer, this behavior is characterized by the loss angle of the elastomeric material. A major disadvantage of the elastomer elements is the fact that the material is subjected to strong aging and settlement depending on the extent of use and the stresses induced therewith as well as the environmental conditions (UV-radiation, ozone, chemicals, etc.). This makes an exchange of the elements necessary in some applications. In order to prevent overloading of the elastomer elements, in some cases an additional mechanical end stop is designed into the system which limits the stroke and therefore reduces the maximum deformation of the elastomer to a level which is acceptable for the material in long term. In hydropneumatic suspension systems another type of end-of-stroke damping is popular since it can be designed into the suspension cylinder. Theoretically a use of elastomer elements is possible here as well, but mostly it is the hydraulic end-ofstroke damping that is used for these cylinders. Opposed to the elastomer elements, here it is not an additional spring force with minor damping but purely an additional damping force that decelerates the piston velocity. The effect of the hydraulic end-of-stroke damping is achieved by reducing the cross-section of the oil path out of the cylinder when the piston reaches a freely selectable distance to the end stop. So during a compression stroke the pistonside chamber is active while during a rebound stroke the rodside chamber is active for end-of-stroke damping. A pressure drop across the flow resistor is generated which then causes a pressure increase inside the respective cylinder chamber. The active area of the respective cylinder chamber is subjected to this additional pressure and therefore causes the damping force. If the cross-section area of the additional flow resistor is designed to be variable with cylinder stroke, a possibility is created to define the effect of the flow resistor depending on piston position. This way a more constant end-of-stroke damping force level and a lower maximum force can be achieved compared to a flow resistor with constant cross-section area. The lower force peak also reduces the maximum accelerations due to end-of-stroke damping Eq. (2.34). Please consider: It is always the same amount of energy that has to be dissipated throughout the displacement of the end-of-stroke damping. Therefore the damping force – displacement integral of both curves must be identical. More information about a suitable layout of the end-of-stroke flow resistor can be found in Sect. 3.2.4.

64

2

Hydropneumatic Suspension Systems

Force

Constant flow resistor Displacement-depending flow resistor

Start of end-ofstroke damping

Mechanical end stop

Displacement

Fig. 2.34 Damping force–displacement curve for end-of-stroke damping with a constant and a displacement-depending flow resistor

2.4 Combined Operation of Spring and Damper In Sects. 2.1, 2.2, and 2.3 the individual force components of a hydropneumatic suspension system have been described. In this section they are combined and considered as a whole system. The basis for the following explanations is a sinusoidal excitation of the input side while the isolated side is fixed. Therefore the suspension element’s displacement is a sinusoidal oscillation. These conditions are chosen similar to the method for the determination of characteristic curves for regular automotive shock absorbers, described at the end of Sect. 2.3.2 (Fig. 2.33). However the main focus will be on the force–displacement curve. The force–displacement curve can be synthesized from the individual theoretical curves for the gas spring, for boundary friction and for fluid friction – and furthermore, if applicable, the curve for end-of-stroke damping. The here mentioned example is a hydropneumatic suspension system without preload which is subjected to boundary friction and which has a simple throttle to provide fluid friction damping. The theoretical considerations of Sects. 2.1, 2.2, and 2.3 result in the individual curves shown in the Fig. 2.35. The effect of the gas spring is idealized and therefore the same for compression and rebound which make the characteristic curve only one line. In reality this is almost true; the dissipation of spring energy due to heat rejection of the accumulators is very small so virtually no hysteresis can be detected in this curve (a). On the other hand the characteristic curves (b) and (c) show a significant hysteresis. The curve for boundary friction is exaggerated for better illustration; these friction forces should be lower in practice. In the end points (left and right) at v = 0 m/s there is a transition from sliding friction to static friction to sliding friction, this explains the slight force peaks there due to the higher coefficient of sliding friction. Furthermore it is visible, that the friction forces are higher, the more the suspension is compressed. This is due to the dependency of seal friction forces on hydraulic pressure. The viscous damping forces reach their extreme values when

2.4

Combined Operation of Spring and Damper

65

FF Compression

a) Gas spring

FF1

Rebound

s

b) Boundary friction

Fµ Compression s Rebound

c) Fluid friction

FD

Compression

s Rebound

Fig. 2.35 Force–displacement curves for gas spring, boundary friction and fluid friction

the center position is crossed. Minimum and maximum have the same absolute values which indicates that the flow resistor has the same effect in both flow directions. By adding up the individual characteristic curves to one curve, the following characteristic force–displacement diagram for the hydropneumatic suspension is composed (Fig. 2.36). FF

Compression

FF1 Rebound

s

Fig. 2.36 Characteristic force–displacement diagram for hydropneumatic suspensions

66

2

Hydropneumatic Suspension Systems

This type of diagram will be found in a more or less similar shape in every experiment with a hydropneumatic suspension system when recording the force– displacement history. Such measurements provide information about the detailed character of the individual contributions spring rate, boundary friction and fluid friction. This information can be derived from the main curve by splitting it up into its individual components as shown above. Even more information can be derived when the measurements are taken at different amplitudes, static spring loads, oil viscosities (or temperatures) or with different excitation frequencies. Then conclusions can be drawn such as: (a) which adiabatic exponent has to be chosen for a calculation under the respective conditions (derived from the shape of the pure characteristic curve of the spring and matching it with the calculation); (b) whether the fluid friction damping is more like an orifice or more like a throttle (derived from relationship of damping forces to viscosity and dependency of damping forces on oscillation amplitude and frequency); (c) the magnitude of static and sliding friction and the influence of cylinder pressures on friction (derived from comparisons of measurements at different amplitudes and static spring forces). Figure 2.37 shows an actual measured force–displacement diagram of a hydropneumatic suspension. It is possible that the actual magnitude of the static friction forces has not been completely recorded due to an insufficient sample rate. However for the detailed measurement of friction forces dedicated experiments with very low frequencies (for example 0.01 Hz or 0.1 Hz) are recommended. This fully eliminates the influence of fluid friction. Simulation results like in [HYV01] show the same shape of their force–displacement curves as shown in Fig. 2.37.

Suspension force [%]

70 60

50 40 30 –30

–15

0

15

Suspension displacement [%] Fig. 2.37 Force–displacement diagram taken from actual measurements

30

Chapter 3

Dimensioning of the Hydropneumatic Suspension Hardware

At the beginning of this chapter it is important to mention that there will be no deduction of the optimum properties of the suspension system, what spring rate and which damping should be set for best performance – these topics are covered extensively in the literature for conventional suspension systems (for example [REI89], [REI05], [CAU01], [KOC]). Instead it is explained, how already known necessary system properties, such as the spring rate, can be provided by the correct layout and dimensioning of the components of a hydropneumatic suspension system.

3.1 Dimensioning of the Hydraulic Spring Components The very basis of the dimensioning process is to determine the hydraulic pressure in the suspension system. Depending on the pressure level, the elements need to have the correct dimensions to provide the right amount of active area (rodside and pistonside) and to provide enough mechanical stability to withstand inner pressure loads. A lot of factors influence this hydraulic pressure which is to some extent necessary and can to some extent be chosen appropriately. Certain factors are predefined due to external circumstances, others can be chosen freely. Figure 3.1 shows an overview of possible influencing factors which determine the static hydraulic pressure on the pistonside when the suspension is in design position. The parameters which are usually predefined by external circumstances are listed on the left side of the diagram: – Since the suspension is designed for a certain purpose/application, this automatically predetermines the necessary range for the static spring load that needs to be supported by the suspension. – The geometry of the suspension, in particular the position of the suspension cylinder as part of the suspension, is often predetermined by its packaging inside the installation space. This also predetermines the lever ratio i of the suspension kinematics.

W. Bauer, Hydropneumatic Suspension Systems, DOI 10.1007/978-3-642-15147-7_3,  C Springer-Verlag Berlin Heidelberg 2011

67

68

3 Dimensioning of the Hydropneumatic Suspension Hardware Mostly predefined:

Mostly selectable:

Load range FF1,min … FF1,max Suspension geometry/ lever ratio Max. available supply pressure

Piston diameter

Pistonside pressure

If preload: type and intensity Pressure rating of hydraulic components

Fig. 3.1 Influencing factors for the static pistonside pressure in design position

– In many cases a hydraulic supply already exists, for example in construction equipment. If it is necessary to use this supply also for the suspension hydraulics (and this is usually the case) this already defines the maximum available supply pressure. On the right hand side of the diagram, various parameters are listed which in most cases can be chosen by the system developer: – Within the given design space the piston diameter can be chosen according to the (especially load-) requirements of the system. – The type and the intensity of the preload affect especially the changes of the suspension properties when changing the static spring load. Since the preload adds to the external spring load, the piston diameter needs to be chosen to be larger, the higher the preload is – of course assuming a given, constant supply pressure. – The standard portfolio of hydraulic components is usually available in certain pressure ratings for different ranges of operating pressure. There are significant cost differences between these rating levels. If a certain pressure rating is preferred for the suspension system (for example, because this is used for all other parts of the overall system), the piston diameter can be adjusted to exploit the full pressure potential out of these components and therefore get the highest possible power density and best cost-benefit ratio. For the correct dimension of the components it is essential to consider that dynamic pressure variations (due to the suspension motion) add to the pressure in static state of the suspension (in design position). Depending on the amount of oil that is exchanged between cylinder and accumulator, and depending on the kind of operation of the accumulator (gas volume at static pressure), these additional dynamic pressure spikes are quite distinct. Therefore the suspension hydraulic system needs to be protected from them, for example by a pressure relief valve.

3.1

Dimensioning of the Hydraulic Spring Components

69

This means that the dynamic portion of the pistonside pressure mostly depends upon the suspension motion and the size and the amount of gas in the pistonside accumulator. Increasing suspension motion leads to increasing pressure variations. On the other hand, an increasing amount of gas lowers the pressure variations. The same is of course the case for the pressure in the rodside hydraulic circuit.

3.1.1 Cylinder Usually the dimensioning of the components starts with the piston diameter of the suspension cylinder, especially if a hydraulic system is already available and predetermines further development steps – and this is actually true in most cases. The piston diameter is determined by trying to make the maximum use of the available system pressure. For non preloaded systems with double-acting cylinders the rod diameter is determined instead. The following information is needed to start with the calculations: – Available maximum supply pressure psys – Maximum static spring load FF1,max , which still allows the system to readjust the level to the design position – Preload force FV which acts upon the cylinder in design position (in variable systems: maximum preload force) The basis for the calculation of the necessary piston diameter is once again the balance of forces acting upon the piston: FK = FF1,max + FV

(3.1)

Expressing FK via the active pistonside area and the system pressure acting upon it π dK2 psys = FF1,max + FV 4

(3.2)

and solving the equation for dK yields   4 FF1,max + FV dK = π psys

(3.3)

If the actually necessary preload force FV is unknown in the beginning of the dimensioning calculations, this value can be assumed to be something between one third and one quarter of the maximum static spring load. This experience-based value can be used as a basis for hydropneumatic suspension systems with diaphragm accumulators. However it can happen that in the end a significant deviation from this value is necessary to achieve the desired suspension properties.

70

3 Dimensioning of the Hydropneumatic Suspension Hardware

For FV = 0.25 · FF1,max the piston diameter can be calculated as

dK =



5FF1,max π psys

(3.4)

Please note: 1) During a leveling process the system has to get back to the design position within a limited amount of time. Therefore the parameter psys in Eq. (3.4) should not be set to the maximum system pressure, but to a pressure somewhat below this value. This is due to the fact that the pressure of the hydraulic fluid which actually reaches the cylinder is lower compared to what has been send out by the hydraulic system. The reason for this is pressure losses on the way from the pump to the cylinder. An intended and for a controlled leveling process inevitable pressure loss is created by the valve system inside the leveling control block. It is necessary to limit the volume flow to the cylinder and therefore the speed of the leveling process. The amount of additional pressure margin needs to be chosen depending on the type of the flow restriction such as throttle/orifice, flow control valve, proportional solenoid valve (please also refer to Chap. 5) and depending on drains of other volume flows (for example, for the transmission of a loadsense signal). For a system with orifices used to control the leveling flow a difference of 1 MPa has proven to be sufficient. This means that for a system with a maximum pump pressure of 20 MPa it is necessary to set psys to 19 MPa in Eq. (3.4). 2) The lever ratio i of the suspension kinematics is chosen to be 1 for the following examples to enable a clearer comparability. This means that the cylinder is in line with the sprung mass. Yet in many real applications this is often not the case and the i = 1 must be taken into account in the calculations respectively. Section 7.1 shows an example how to do that. In case a hydropneumatic suspension system with hydraulic preload is dimensioned, the next step is to choose the rod diameter. The first thing is to determine which hydraulic preload force should be created by the rodside hydraulic system. The higher the preload pressure on the rodside, the lower is the necessary active ring-shaped area on the rodside in order to generate a given preload force and therefore the larger is the rod diameter. A small active area on the rodside means on one hand that less oil is displaced during the suspension motion and therefore a smaller rodside accumulator can be chosen. On the other hand this smaller accumulator must be designed for higher operating pressures and also the friction increases according to the mechanism described in Sect. 2.3.1. In the end the decision on the right size of the rod will depend on multiple boundary conditions. The general approach is: FV = pV (dK2 − dS2 )

π 4

(3.5)

3.1

Dimensioning of the Hydraulic Spring Components

71

And therefore: dS =



dK2 −

4FV π pV

(3.6)

If the lever ratio i is different from 1, the stroke of the cylinder needs to be calculated as well from the required overall suspension stroke at the suspension reference point sB (basically the point of action of the suspended mass). The necessary stroke h of the cylinder can be calculated by (3.7)

h = sB i

Piston diameter, rod diameter and cylinder stroke are the defining parameters for a cylinder. Now it is possible to start the selection of suitable accumulators by taking into account the pressure levels on both the pistonside and the rodside. The process of dimensioning the accumulators is divided into two steps. The first step is to calculate the necessary gas fills in the accumulators by using the equations in Sect. 2.2. The second step is to find the ideal combination of p0 and V0 which works best under the given operating conditions. This will be described in the next section.

3.1.2 Accumulator Gas Precharge The equations in Chap. 2 for the calculation of the natural frequencies of the different hydropneumatic suspension systems help to calculate the necessary gas fills p0 V0 . 3.1.2.1 Non preloaded Systems and Systems with Mechanical Preload The calculation of the accumulator parameters for the non preloaded hydropneumatic suspension as well as for its alternative with mechanical preload is relatively simple since only one gas mass needs to be calculated, i.e. the gas fill of the pistonside. For the non preloaded system, Eq. (2.27) is solved for p0 V0 : p0 V0 =



1 2π f

2

nFF1 g

(3.8)

The respective result is achieved for the system with mechanical preload by solving Eq. (2.31): p0 V0 =

n(FF1 + FV )2 FF1 (2π f )2 g

(3.9)

− cmech

The respective gas fill can be obtained by inserting the desired natural frequency for a certain static spring load FF1 into the above equations. If, like in most cases,

72

3 Dimensioning of the Hydropneumatic Suspension Hardware

the spring load varies, a typical spring load (which, for example, is effective most of the time) should be used when calculating the necessary gas fill. Another method is the determination of an average spring load from a minimum and maximum spring load and then using this average to calculate the gas fill. In the case of a system with mechanical preload, the preload force and the spring rate of the mechanical spring have to be chosen in a way so the shape of the characteristic curves corresponds to the requirements of the application. Please refer to Chap. 2 for the force vs. displacement diagram, spring rate vs. spring load diagram and natural frequency vs. spring load diagram. For this purpose it is useful to create the diagrams and to watch how their shape changes as the preload force and the spring rate of the mechanical spring are changed. A kind of iterative approach towards the right setting needs to be accepted since a certain p0 V0 has to be assumed when creating the initial diagrams. 3.1.2.2 Systems with Hydraulic Preload The tricky thing about the following calculations is that two gas fills have to be determined at once, the gas mass for the piston side and the gas mass for the rodside. Yet there is only one equation available for their determination – Eq. (2.38). This means, that first one gas fill needs to be determined by another way before calculating the other one. Furthermore, like for the system with mechanical preload, a suitable setting for the rodside parameters needs to be found – rodside hydraulic spring rate and preload – which fits best to the requirements of the characteristic curves. The suspension effect is mostly dominated by the effect of the pistonside hydraulic spring; it is the latter which carries the suspended mass. Therefore the first step is to roughly determine the gas fill for the rodside, since it has less effect onto the overall spring rate. In a second step the gas fill for the pistonside is calculated. The volume of the rodside accumulator must be sufficient to accommodate all the oil which is displaced from the rodside of the suspension cylinder(s). If this was not the case, it would not be possible to reach the ends of the stroke without either destroying the accumulator (cylinder fully extended and therefore rodside completely empty) or running into cavitation (cylinder fully compressed, rodside filled with maximum amount of hydraulic fluid, accumulator empty). The volume of the accumulator therefore must at least be equal to the maximum rod chamber volume in the fully compressed cylinder, assuming of course that the accumulator is half filled when the cylinder is at the center of its stroke. Of course this is not sufficient at all; there is at least some margin necessary, especially in case diaphragm accumulators are used as shown later on. It has been proven to be a good basis for development if the volume of the rodside accumulator V0,R is predefined to be three times the rod chamber volume of the suspension cylinder(s). This has to be eventually increased for systems with variable rodside preload pressure. π  V0,R = 3h dK2 − dS2 4

(3.10)

3.1

Dimensioning of the Hydraulic Spring Components

73

The calculation of the rodside accumulator precharge pressure is based upon the assumption that the gas volume inside the accumulator is compressed to half of its original volume when the preload pressure pV is applied to the rodside system – under the assumption that the design position of the piston is exactly in the center of both end stops. This ensures that there is enough and equal margin of oil for the piston motion to both sides of the cylinder. In case the piston design position is chosen off center, the position of the rodside accumulator diaphragm when subjected to preload pressure has to be chosen accordingly. With a center design position, the accumulator precharge pressure p0,R should therefore be about half of the preload pressure pV . p0,R = 0.5pV

(3.11)

Since the parameters for the rodside accumulator are now determined, Eq. (2.38) can be solved for the pistonside gas mass p0,K V0,K =

n(FF1 + pV AR )2 FF1 2 g (2π f )

−

np2V A2R p0,R V0,R

·

(3.12)

Since p0,R and V0,R have not been chosen with regards to spring rate but for another goal, it is now necessary, just like before for the system with mechanical preload, to check with the help of the characteristic curves, whether this set of accumulator parameters provides the desired suspension properties. If this is not the case, here too an iterative approach needs to be used to determine the parameters p0,R and V0,R which provide the desired shape of the characteristic curves and therefore the desired suspension behavior. It can happen that for further optimization, also p0,K und V0,K have to be changed.

3.1.3 Detailed Calculation of p0 and V0 The accumulator gas fill is represented by the product p0 V0 which has been calculated in Sect. 3.1.2. It basically represents the mass of the gas or in other words the number of gas molecules inside the accumulator. The next step is to find suitable values for the most important accumulator parameters: p0 and V0 . For the following calculations in this section, it is predefined that the suspension level is exactly in the center between compression and rebound end stop. For hydropneumatic suspension systems usually welded diaphragm accumulators are used – you can find more information in Chap. 5. Yet it is a characteristic of this type of accumulator that it may only be operated in a certain pressure range. This pressure range is defined by two basic criteria: 1. Maximum pressure criterion: the design, in particular the material and the dimensioning of the outer shell, defines the permissible maximum pressure

74

3 Dimensioning of the Hydropneumatic Suspension Hardware

for an accumulator. It must not be exceeded in any operating condition if the accumulator has to be fatigue resistant throughout the lifetime of the suspension. 2. Diaphragm deformation criterion: the diaphragm has a permissible maximum deformation for its deflection inside the accumulator. This deformation must not be exceeded during the oscillation of the diaphragm position throughout the entire operating time of the suspension system. A simple guideline for the use of diaphragm accumulators in hydropneumatic suspensions is the 10% rule. It states that at any time during operation, the inner accumulator volume should be filled with either at least 10% hydraulic fluid or with 10% gas to ensure that the maximum deformation is not exceeded (Fig. 3.2). This rule therefore sets another upper pressure limit as well as a lower pressure limit. These limits need to be accepted to ensure fatigue resistance of the diaphragm throughout the lifetime of the suspension. The 10% rule for the application in suspension systems is actually somewhat more permissive than is usual in other applications ([MAT03], [FIN06]). This is due to the fact that the amplitude of the suspension oscillation is usually significantly lower than the full suspension stroke, which means that these extreme values are usually rarely reached. In any case it is important to discuss with the manufacturer of the accumulator whether the accumulator and in particular its diaphragm material is designed for the needs of the application. It is possible that certain materials and special suspension setups ask for other deformation limits than stated with the 10% rule. It can be deduced from the diaphragm deformation criterion that the pressure limits arising from it also depend on the precharge pressure of the accumulator. In the following, isothermal changes of state are used for the calculations since this represents the more critical condition concerning the inner volume portion of oil and gas and their minimum values. An accumulator with a precharge pressure p0 and a volume V0 must be operated (according to the diaphragm deformation criterion) between V = 0.1 · V0 and V = 0.9 · V0 . For the isothermal change of state, the minimum and maximum pressure can be calculated: pmin =

p0 V0 = 1.11p0 0.9V0

(3.13)

10% gas

90% gas 90% oil 10% oil

Fig. 3.2 Limits for diaphragm deformation for the application in a suspension system

3.1

Dimensioning of the Hydraulic Spring Components

pmax =

p0 V0 = 10p0 0.1V0

75

(3.14)

The permissible pressure ratio pmax /pmin is therefore 9. Yet this calculated ratio applies only if all changes of state take place at room temperature. If the suspension system and therefore the hydraulic fluid and the gas are (as usual) subjected to a wide range of temperatures it is essential to consider that the specified precharge pressure relates to room temperature. Yet at other temperature levels, the actual temperature-dependent precharge pressure p0,T will be different and with it changes the permissible pressure range according to the second criterion. High temperatures therefore increase the minimum pressure and low temperatures decrease the maximum pressure. For a temperature range from −20 to +60◦ C the pressure range is narrowed according to Eq. (2.3) in Sect. 3.1.2: 333.15 K = 1.26p0 293.15 K 253.15 K = 10p0 = 8.64p0 293.15 K

pmin = 1.11p0 pmax

(3.15) (3.16)

This looks like a minor change but actually the permissible pressure ratio has been reduced from 9 to the value of 6.85, which means significant functional losses for the use of the suspension system. In practice it is therefore extremely important to assess the temperature range as realistically as possible, also asking the question if in these cases of very high or low temperatures the full suspension displacement will be used up and therefore the diaphragm will be fully deflected. If the calculation is too conservative, there will be losses in performance of the system which need to be compensated by (expensive) countervailing measures – if at all possible. If the calculation is too generous, this will be penalized by a premature failure of the accumulator diaphragm, gas pressure losses and a deterioration of the suspension behavior. There is another parameter influencing the pressure ratio: the production process always contains small errors, also with regards to the gas precharge pressure. Therefore the precharge pressure will not always have the exact value but will have a slight production tolerance. For later calculations a tolerance of ±5% is assumed and the pressure limits will be even more constricted. A positive deviation of the precharge pressure will increase the minimum pressure; a negative deviation decreases the maximum pressure. pmin = 1.26 p0 × 1.05 = 1.32 p0

(3.17)

pmax = 8.64 p0 × 0.95 = 8.21 p0

(3.18)

This additionally lowers the pressure ratio to 6.2. Another peculiarity of diaphragm accumulators must be considered for the correct choice of parameters. The gas diffuses through the diaphragm into the hydraulic

76

3 Dimensioning of the Hydropneumatic Suspension Hardware

fluid and therefore is partially lost – and the suspension characteristics with it. So the accumulator is subjected to a diffusion pressure loss (Chap. 5). Although this is not a problem for the minimum pressure, it has to be considered when calculating the maximum pressure. Assuming a permissible pressure loss of 10% of the precharge pressure between service (and refill) intervals, the maximum pressure is reduced to: pmax = 8.21 p0 × 0.9 = 7.39 p0

(3.19)

The permissible pressure ratio then is 5.6. So the formerly good pressure ratio of 9 has shrunk to a value of 5.6. As a by-product the previous calculation shows why a non-preloaded hydropneumatic suspension with diaphragm accumulators is not suitable for suspension systems subjected to wide ranges of static spring loads: the accumulators would frequently be operated at or beyond their pressure limits. It is very important to mention in this context that the permissible pressure ratio of the accumulator is not the same as the permissible load ratio FF1,max to FF1,min ! The latter is even smaller since not only the variable suspended load but also the suspension movement causes pressure variations – more information can be found in Sect. 3.1.3.1. There is one further point to notice: the determination of the parameters p0 and V0 is easier to perform for a piston accumulator since the piston may be displaced throughout its complete possible stroke. There is no 10% rule like there is for the diaphragm accumulator. Therefore the minimum operating pressure of a piston accumulator would be the precharge pressure corrected by the respective temperature change and the production tolerance for the precharge. If the actual operating pressure would fall below this minimum value, cavitation in the respective part of the system would result. On the other hand, the maximum operating pressure is the maximum pressure permitted by the design of the outer shell. This pressure needs to be protected by a pressure relief valve – just like for the diaphragm accumulator. Despite these advantages, piston accumulators are rather rarely used in suspension applications due to their higher cost and their inner friction. The further explanations for a hydropneumatic suspension system with hydraulic preload therefore only deal with diaphragm accumulators as in all previous examples.

3.1.3.1 Rodside Accumulator The selection of the right parameters for the rodside accumulator is relatively simple, if it is done for a system which is always subjected to a constant rodside preload pressure. According to the diaphragm deformation criterion, the diaphragm should be in middle position if the suspension respectively the piston of the cylinder is in its center position. This ensures maximum possible margin to both sides for the deformation of the diaphragm. Middle position of the diaphragm means: V = 0.5V0

(3.20)

3.1

Dimensioning of the Hydraulic Spring Components

77

Therefore the optimum rodside accumulator precharge pressure p0 depends on the selected rodside preload pressure pV : p0 =

pV 0.5V0 = 0.5pV V0

(3.21)

If the desired gas mass for best suspension performance is already calculated (as deduced in Sect. 3.1.2), the optimal V0 for the rodside accumulator can be calculated accordingly. However in reality, accumulator manufacturers only have certain accumulator sizes in their portfolio. Although there are tricks which help to vary the V0 within the accumulator size (for example, by a partial oil fill or a solid insert on the gas side) it becomes necessary to accept a compromise for the parameters p0 and V0 . This compromise can also influence the selection of the rodside preload pressure and therefore the necessary size of the rodside active area. The next step is to check whether the filling with or the draining of hydraulic fluid during a suspension motion with full stroke leads to the deformation limits of the diaphragm being exceeded. Again the diaphragm deformation criterion is applied: 1. When the suspension cylinder is in compression stroke and the rodside system hydraulic fluid flows out of the accumulator into the cylinder’s rod chamber the volume filled by the gas inside the accumulator increases and must not exceed a portion of 90% of the total volume. The worst case for the accumulator is the maximum operating temperature, a gas fill at the upper tolerance limit during the production process and no diffusion pressure loss. All these conditions contribute to a maximum precharge pressure p0,T,korr and therefore to a diaphragm which is already bent somewhat towards the oil side of the accumulator when subjected to the regular preload pressure. Therefore the “90% gas volume” limit is reached earlier than under the normal conditions. V0 ·

h p0,T,korr + AR ≤ 0.9V0 pV 2

(3.22)

2. During the rebound motion of the cylinder and therefore when hydraulic fluid is flowing into the accumulator, the gas volume must not drop below 10% of the accumulator volume. In this case, the worst boundary conditions are the minimum operating temperature, the lower limit of the production tolerance for the precharge pressure and maximum pressure loss due to diffusion up to the limit when servicing is necessary. Again these aforementioned conditions are then accounted for in the pressure p0,T,korr , which is now down at its minimum level. V0

h p0,T,korr − AR ≥ 0.1V0 pV 2

(3.23)

At this point it is important to keep in mind that the hydraulic fluid volume AR h/2 flowing in and out of the accumulator is independent of the position of the cylinder in the kinematics of the mechanical suspension setup. Just like for the non-preloaded system, the stroke of the cylinder is changed due to the lever ratio i, but the amount

78

3 Dimensioning of the Hydropneumatic Suspension Hardware

of the displaced hydraulic fluid volume does not change since also the rodside active area changes/needs to be changed with i – assuming of course that the preload force in the suspension reference plane is the same for all configurations. Usually the above mentioned limits can be easily met for systems with constant rodside preload pressure. Yet for systems with variable rodside preload pressure another approach for the selection of p0 and V0 is necessary. Here not only does the position of the diaphragm vary with the position of the piston (and therefore the displaced hydraulic fluid) but it also varies with the selected rodside preload pressure. Like already explained for the above mentioned temperature and precharge pressure tolerance effects, this too leads to an offset of the diaphragm position towards one end of the accumulator interior (fluid side or gas side). If these offset positions are too close to the 10% limits for diaphragm deformation the suspension motion can lead to unacceptable high diaphragm deflection. In general it would be possible, according to the logic in Eq. (3.21), to assume the average of the intended minimum and maximum rodside preload pressure, to calculate a first combination of p0 and V0 . However this is quite imprecise since pressure and volume do not have a linear relationship and in the end it is the right average volume what counts for the correct layout of the system. Therefore the first step is to calculate the gas volumes at p = pV,min and p = pV,max . V(pV,min ) = V0 V(pV,max ) = V0

p0 pV,min p0 pV,max

(3.24) (3.25)

The average value of these volumes must then be equated with 0.5 · V0 , since at this point the diaphragm needs to be in its center position. p0 p0 + V0 pV,max V0 pV,min

2

=

V0 2

(3.26)

and by resolving for p0 p0 =

1 1 pV,min

+

1 pV,max

(3.27)

the optimum accumulator precharge pressure can be calculated: p0 =

pV,min pV,max pV,min + pV,max

(3.28)

The already calculated necessary gas fill allows the necessary V0 to be calculated. Again it is consequently necessary to check this set of parameters to see whether it fulfills the diaphragm deformation criterion. The Eqs. (3.22) and (3.23) need to be slightly modified by taking the lower and upper limit pV,min and pV,max of the rodside preload pressure into account.

3.1

Dimensioning of the Hydraulic Spring Components

V0 · V0

79

h p0,T,korr + AR ≤ 0.9V0 pV,min 2

(3.29)

p0,T,korr h − AR ≥ 0.1V0 pV,max 2

(3.30)

By resolving the equations above for pV,min and pV,max it is possible to calculate the actually permissible range of rodside preload pressure variation for this particular chosen combination of p0 and V0 . pV,min =

pV, max =

V0 p0,T,korr

(max. T, upper gas fill tolerance, no diffusion) (3.31)

0.9V0 − AR h2 V0 p0,T,korr 0.1V0 + AR h2

(min. T, lower gas fill tolerance, max. diffusion) (3.32)

If this calculation shows that the permissible range for the variation of pV does not extend far enough to the lower preload pressures, a slight increase of V0 (and respective decrease of p0 ) can help. If this turns out to be insufficient, an overall increase of the gas fill needs to be taken into consideration, even though the rodside hydraulic spring rate would be lowered this way. Figure 3.3 illustrates the interactions of the different parameters influencing the diaphragm position. It becomes clear that the rodside preload pressure (dark hatched area) may only vary up to the point so that at full compression and rebound of the cylinder 0% gas volume

0.1·V0 V0·(p0,t,korr/pV,max) AR·h V0·(p0,t,korr/pV,min)

0.9·V0 V0

AR·h

Diaphragm position

0.1·V0

Impermissible range for diaphragm position

Diaphragm position change due to suspension movement

100% gas volume

Diaphragm position change due to preload pressure variation

Fig. 3.3 Optimum utilization of the rodside accumulator limits according to the diaphragm deformation criterion

80

3 Dimensioning of the Hydropneumatic Suspension Hardware

(light hatched area) the diaphragm does not get deflected beyond its limits into the forbidden zone (cross hatched area). Furthermore it has to be proven, that suspension movements which compress the gas down to 10% of the accumulator volume do not cause rodside pressures which exceed the maximum operating pressure defined by the strength of the accumulator’s outer shell (maximum pressure criterion). With pV,max



V0 p0,T,korr pV,max

n

= pmax



h V0 p0,T,korr − AR pV,max 2

n

(3.33)

The maximum pressure pmax can be calculated:

pmax = pV,max 



 V0 p0,T,korr n pV,max

V0 p0,T,korr pV,max

− AR h2

n

(3.34)

In this equation, p0,T,korr is related to the state of the suspension, when the gas volume is at its minimum while the suspension cylinder is in its center position. This means it describes the state of minimum operating temperature, lowest possible precharge pressure within production tolerance and maximum diffusion pressure loss within service intervals. In case it turns out that pmax is above pzul , pV,max has to be reduced to reduce pmax and therefore ensure the fatigue endurance of the outer shells. It was already mentioned that protection of the maximum pressure by a relief valve can help, too. This is especially true if the system is layed out very aggressively and therefore with little fault-tolerance. 3.1.3.2 Pistonside Accumulator Again it is useful to recall the balance of forces at the piston as described in Sect. 2.1: or

(3.35)

p1 AK = FF1 + pV AR

(3.36)

FK = FF1 + FV

This equation helps to understand that two different cases need to be distinguished: 1) The non preloaded system and the systems with constant preload (mechanical or hydraulic). In this case there is only one variable which has an effect on p1 : the static spring load FF1 in the design position of the suspension.

3.1

Dimensioning of the Hydraulic Spring Components

81

2) The system with variable hydraulic preload. In addition to the spring load, the variable preload force FV , respectively the variable preload pressure pV also has an effect on the pistonside pressure p1 . For the first case, the calculation of the suitable parameters for the pistonside accumulator is similar to the calculation for the rodside accumulator in a system with variable rodside preload pressure. However, while the variable rodside preload pressure is actively influenced (for example, by an electronic controller), the pressure in the pistonside accumulator (with the cylinder piston in design position) is given by an external boundary condition, the static spring load. Therefore the logical steps towards the right set of pistonside accumulator parameters start with the calculation of the pressures at minimum and maximum static spring load. p1,min AK = FF1,min + FV

(3.37)

p1,max AK = FF1,max + FV

(3.38)

and therefore FF1,min + FV AK FF1,max + FV = AK

p1,min =

(3.39)

p1,max

(3.40)

According to Eq. (3.28) (for the rodside accumulator) the same kind of derivation can be performed for the optimum precharge pressure of the pistonside accumulator. The result is: FF1,min + FV FF1,max + FV AK AK p0 = FF1,max + FV FF1,min + FV + AK AK

(3.41)

and further resolved: p0 =

(FF1,min + FV ) · (FF1,max + FV ) AK (FF1,min + FF1,max + 2FV )

(3.42)

With p0 and the already calculated value for the gas fill in the accumulator, V0 can be calculated. The actually permissible minimum and maximum pistonside pressure at static spring load in suspension design position can then be calculated according to the diaphragm deformation criterion:

82

p1,min = p1,max =

3 Dimensioning of the Hydropneumatic Suspension Hardware

V0 p0,T,korr 0.9V0 − AK 2h V0 p0,T,korr 0.1V0 + AK h2

(max. T, upper gas fill tolerance, no diffusion) (3.43) (min. T, lower gas fill tolerance, max. diffusion) (3.44)

By resolving Eq. (3.35) for FF1 and applying the minimum and the maximum allowed pistonside pressure, the actually permissible range for the static spring load is obtained. FF1,min = FF1,max =

V0 p0,T,korr 0.9V0 − AK h2 V0 p0,T,korr 0.1V0 + AK 2h

AK − p V AR

(3.45)

AK − pV AR

(3.46)

If the initially required load range is not within the load range calculated above, the latter can be slightly widened at the lower end if V0 is increased – similar to the tuning possibility described for the rodside accumulator. In many cases it is the lower end of the load range which is more critical for the accumulator. An increase of the gas mass in the pistonside accumulator by increasing the volume V0 at constant precharge pressure p0 is also possible, if the decrease of the natural frequency (and therefore softening of the suspension) connected to this parameter is tolerable. Furthermore it is possible to increase the preload force pV AR . Since this internal cylinder force is acting in the same direction as the external spring load force, the latter can be further lowered without compromising the diaphragm deformation criterion. However a higher preload causes a higher spring rate. This can be compensated by increasing the gas mass in the accumulators which lowers the spring rate back to the desired level and therefore keeps the natural frequency at its design point. However it is very important to consider that, assuming a limited supply pressure, an increase of the preload force will always result in a decrease of the maximum permissible static spring load! If this load is exceeded, the system is not capable of lifting the suspension back into its design position. This leads us to the second case, the variable preload force. It is obvious that it provides the advantage that it can be changed depending, for example, on the static spring load. Therefore, if it is increased at low static spring loads, the minimum permissible static spring load FF1,min is reduced. On the other hand, the preload force can be reduced at high axle loads to allow for a FF1,max , which is as high as possible. This means that a variable preload can not only improve the ride quality by an adjustable spring rate but can also widen the permissible range for the spring load. Following the logic of Fig. 3.3 it can be shown in another diagram, how the parameters influencing the pistonside pressure (and therefore the pistonside accumulator diaphragm position) interact. These parameters are the suspension

3.1

Dimensioning of the Hydraulic Spring Components

83

Minimum preload pressure at FF1,max and maximum preload pressure at FF1,min

All preload pressures allowed at any static spring load

0% gas volume pV,max pV,min

V0

pV,min

pV,max

Diaphragm position pV,min

pV,max

AK·h

100% gas volume

Impermissible range for diaphragm position

Diaphragm position change due to suspension movement

Diaphragm position change due to preload pressure variation

Permissible range for the diaphragm position change due to the static spring load

Fig. 3.4 Optimum utilization of the pistonside accumulator limits according to the diaphragm deformation criterion

movement, the rodside preload pressure and the static spring load. It also shows how the right selection of the rodside preload pressure at the right time can lead to a wider range of permissible static spring loads (Fig. 3.4). It is clearly visible that the limits for the permissible static spring load can be extended by making ideal use of the variable rodside preload pressure. This is indicated by the length of the grey area. This allows the extension into ranges which would be impossible with constant preload force systems. The permissible load ratio can be increased significantly. As for all accumulators, here too the permissible inner pressure pzul needs to be considered to ensure a fatigue endurable outer shell. Following the logic of Eq. (3.34), the pressure on the pistonside can be calculated.

pmax = p1,max 



V 0 p0 p1,max

V0 p0 p1,max

n

− AK 2h

n

(3.47)

84

3 Dimensioning of the Hydropneumatic Suspension Hardware

After applying p1,max according to Eq. (3.40) and reducing AK , pmax is

pmax

FF1,max + FV  = AK



V0 p0 FF1,max +FV

V 0 p0 FF1,max +FV

n

−

h 2

n

If pmax exceeds pzul either the maximum static spring load FF1,max or FV need to be reduced accordingly to meet the maximum pressure criterion. A pressure relief valve in the load carrying pistonside hydraulic circuit is highly recommended. In practice there are many possible circumstances which can lead to excessive pistonside pressures: high gas precharge pressure losses, improper use in certain applications or intentional (but wrong) system changes by system users are only some examples. In the long run, the outer shell would not be able to withstand this overload. In the worst case, the result would be a burst of the accumulator. The arising damage to the suspension components and furthermore the consequential damage due to a sudden loss of the suspension function cannot be overseen and should in any case be avoided! Yet this is only the worst case; in most of these cases the accumulator failure is slow, a crack in the outer shell develops and shows the damage by increasing leakage (which is nevertheless also very problematic and needs to be avoided). With the help of the pressure in the accumulator and the gas volume, Fig. 3.5 illustrates in a p–V-diagram how the changes of state take place for a change in static spring load (isothermal) and for the suspension movement itself (polytropic). The operational limits for the gas volume and the inner pressure of the accumulator can be clearly seen.

p pmax polytropic

isothermal

A·h

polytropic

A·h

p0 0.1·V0

0.9·V0

V0

V

Fig. 3.5 Illustration of the operational limits of an accumulator in a p–V-diagram

3.2

Dimensioning of the Hydraulic Damping Elements

85

3.2 Dimensioning of the Hydraulic Damping Elements As already mentioned in Chap. 2, the hydraulic damping is generated by flow resistors which cause pressure losses. These pressure losses act upon the respective active areas inside the cylinder and ensure the necessary damping forces. The damping forces depend on the velocity of the compression and rebound motion since the pressure losses depend on the flow velocities inside the flow resistors. The damping forces are always oriented opposed to the direction of piston motion. If only a non-variable damping system is available, a compromise needs to be found for the level of damping forces. This is especially difficult for suspension systems which need to cover a wide range of static suspension loads. The damping forces must be sufficiently high to provide enough damping for the high load levels and on the other hand they must not cause a decreasing comfort at low suspension load levels due to a too stiff coupling of the suspension system’s input side to the isolated side. It is important for the determination of the necessary flow resistors that cavitation due to the pressure loss at a flow resistor must be avoided at all times. Apart from the noise and possible destruction of the internal cylinder components and the flow resistor, it is also the limitation of the damping forces due to cavitation which needs to be avoided. Depending on the type of hydropneumatic suspension the damping elements need to be dimensioned differently to ensure that no cavitation will occur.

3.2.1 Single-Acting Cylinder in a System Without Hydraulic Preload The damping force is a result of the pressure loss p at the flow resistor which acts upon the hydraulically active area, in this case the head area of the plunger AS . So the next step is to find the right size and type of the flow resistor which best fulfills the requirement for the damping forces. Please remember that, as mentioned in the introduction to this section, the determination of these requirements is not part of the explanation here. The basic equation for the calculation of the damping force is: FD,hyd = pAS

(3.48)

However, as mentioned above, there are limitations in the dimensioning which originate from the danger of excessively high pressure losses and cavitation caused thereby. The situation is illustrated in Fig. 3.6. During the compression phases, when the hydraulic fluid flows out of the cylinder, cavitation is not an issue, since the pressure, which is needed to push the fluid through the flow resistor, is directly generated by the cylinder itself. It is therefore: p = pZ − pSp pZ > pSp

(3.49)

86

3 Dimensioning of the Hydropneumatic Suspension Hardware

Rebound

Compression

pSp

p Sp AS

pz

Δp

Δp

pz

pZ > pSp

pZ < pSp

Fig. 3.6 Behavior of a single-acting cylinder during compression and rebound

and since pSp >> pKav

it is also ensured that

pZ >> pKav On the other hand during the rebound phases, when hydraulic fluid flows into the cylinder, the possible pressure loss is limited. This is due to the fact that the pressure, which forces the fluid through the flow resistor, is generated by the hydraulic accumulator. However its internal pressure pSp has a certain level (depending especially on its precharge pressure and the current fluid level inside) and therefore the possible flow rate through the flow resistor into the cylinder is limited. It is therefore obvious that the possible rebound velocity (without creating cavitation) is limited. This is shown in the following calculation. p = pSp − pZ

(3.50)

Furthermore the requirement to avoid cavitation is: pZ > pKav So it can be deduced that: p < pSp − pKav

(3.51)

According to Sect. 2.3.2 the pressure loss in a throttle is defined by: ·

p = V νρKD

(3.52)

3.2

Dimensioning of the Hydraulic Damping Elements

87

The flow rate can be replaced by the product of plunger head area AS and rebound velocity. By resolving the equation for the rebound velocity, the velocity limit vkav is obtained, which represents the point when the pressure drop p over the flow resistor gets close to the pressure in the hydraulic accumulator pSp and therefore pressure in the cylinder pZ becomes equal to the cavitation pressure limit pKav . vKav =

pSp − pKav νρKD AS

(3.53)

A correct dimensioning of the flow resistor (or rather the sum of all flow resistors in the path of the hydraulic fluid from the accumulator to the cylinder) helps to provide sufficient distance between cylinder pressure and the cavitation pressure limit. Figure 3.7 shows impressively how the cavitation affects the force–displacementdiagram in an experiment. It is clearly visible that the force-displacement curve loses its typical hydraulic-damping-specific curvature and shows a flattening around the middle of the oscillation amplitude. In this area, the damping force is at its maximum possible level of AZ (pSp − pKav ), although the rebound velocity keeps increasing up to the maximum at the center of the overall displacement (s = 0%). In the course of the further oscillation motion, the regular shape of the force–displacement curve is again adopted, when the motion velocity drops back below the critical velocity vKav . Now this limitation in the possible damping forces is, at all times, necessary for the rebound phase. This is quite unfortunate, since this phase should be dampened more strongly than the compression phase to achieve the best vibration isolation. If the maximum available damping force of a single-acting cylinder according to the above explanations is not sufficient for all operating conditions, a double-acting cylinder must be used as described in Sect. 3.2.2.

Suspension force FF [%]

140 120

compression

100 cavitation area

80

rebound

60 –30

15 0 –15 Displacement s [%]

Fig. 3.7 Shape of a force–displacement-curve with temporary cavitation

30

88

3 Dimensioning of the Hydropneumatic Suspension Hardware

3.2.2 Double-Acting Cylinder in a System Without Hydraulic Preload A double-acting cylinder is operated with two separate flow resistors, one of them being installed in the rodside hydraulic circuit, the other one in the pistonside hydraulic circuit. By correct arrangement and sizing of the flow resistors, a significantly higher rebound damping is enabled. Figure 3.8 illustrates in an exemplary manner the most obvious possibility for a hydraulic circuit of this type. Yet this system can be designed even more simply by removing the additional external fluid line, including the additional flow resistor, and instead integrating the latter into the piston, so a direct cylinder-internal connection between pistonside and rodside is created. This system too provides the advantage of high possible rebound damping, however the additional effort compared to a single-acting cylinder is relatively low (Fig. 3.9). This system is further explained in the following calculations. The calculation of the damping forces via pressure losses and the respective active areas on the piston is rather laborious and cumbersome. An easier and more elegant way is the calculation of the heat output generated inside the flow resistors from the kinetic energy of the hydraulic fluid. This heat output is equal to the damping power PD,hyd . ·

·

(3.54)

PD,hyd = pK VS +pR VR

It is important to consider that, due to the regenerative type of circuit for the suspension cylinder, in the above example the pistonside flow resistor is not subjected to the full volume flow coming from the piston chamber, but only to the volume flow ·

VS caused by the displacement of the rod with its active area AS ! By calculating: ·

VS = A S v

(3.55)

s Δ pR pR AR pSp AK

Fig. 3.8 Use of a double-acting cylinder for more rebound damping

pK

Δ pK

3.2

Dimensioning of the Hydraulic Damping Elements

89

s Alternative illustration of the hydraulic circuit:

pR AS AR

s pSp

ΔpR Δ pK AK pK

Fig. 3.9 Flow resistor in the piston provides a simplified setup

and ·

VR = A R v

(3.56)

as well as FD,hyd =

PD,hyd v

(3.57)

Resolving for FD,hyd leads us to: FD,hyd = pK AS + pR AR

(3.58)

This equation can be used for the dimensioning of the flow resistors. However it is very important to coordinate and to harmonize both flow resistors. If this is not performed, cavitation can be caused. If the rodside flow resistor is chosen to be significantly over-restrictive compared to the pistonside flow resistor, cavitation in the rod chamber of the cylinder during the compression phase will be the result. On the other hand, if the pistonside flow resistor is too restrictive, cavitation in the piston chamber of the cylinder will be caused during the rebound phase. The respective pressures and the limit for the cavitation will be further explained in the following, assuming that both pistonside and rodside flow resistor are throttles (as explained in Sect. 2.3.2). Compression: pR = pSp + pK − pR

(3.59)

pR = pSp + AS vνρKD.K − AR vνρKD,R

(3.60)

90

3 Dimensioning of the Hydropneumatic Suspension Hardware

Rebound: pK = pSp − pK

(3.61)

pK = pSp − AS vνρKD,K

(3.62)

The last equation can be used to calculate the limit for the pistonside flow resistor KD,K,grenz by setting pK = pKav and resolving for KD,K KD,K,grenz =

pSp − pKav AS vνρ

(3.63)

By setting pR = pKav in Eq. (3.60) and resolving for KD,R , the limit for the rodside flow resistor KD,R,grenz is obtained: KD,R,grenz =

pSp − pKav + AS vηKD,K AR vνρ

(3.64)

By setting KD,K,grenz for KD,K in Eq. (3.64), the result is: KD,R,grenz =

2(pSp − pKav ) AR vνρ

(3.65)

By calculating the ratio of both limit values, the ideal ratio of the maximum restricting flow resistors is obtained, therefore aiming for the maximum possible damping. If this high damping level is not required, this ratio can also be used as a basis for the selection of any other kind of throttle combination KD,R 2AS = KD,K AR

(3.66)

Both values KD,K,grenz and KD,R,grenz are of course limit values for the maximum flow restriction of the flow resistors. Please be aware that they depend in particular on the accumulator pressure, which varies throughout the suspension stroke (!), and furthermore on the piston velocity. Be also aware that the latter is moreover a variable which, at a given external excitation of the suspension, depends on the strength of the damping and therefore the size of the flow resistor. So there is mutual influence of flow resistor size/fluid damping on one hand and piston velocity on the other hand. The above is therefore only a simplified, but, as practice shows, useful calculation. Experiments are essential, especially when it comes to the fine tuning of damping of this kind. In case the restrictions due to the previously described system impede the required tuning of the damping, it is also possible to assign a check valve to each flow resistor. This needs to be done in a way so that, during the rebound phase, only the rodside flow resistor is active while the pistonside resistor is bypassed by

3.2

Dimensioning of the Hydraulic Damping Elements

91

the check valve and during the compression phase only the pistonside flow resistor is active and the rodside flow resistor is bypassed. This completely removes the problem of cavitation and allows the free choice of dedicated damping levels for compression and rebound direction. Most modern automotive suspension dampers are set up in this manner (please also refer to Sect. 4.3.2).

3.2.3 Double-Acting Cylinder in a System with Hydraulic Preload In this case the rodside and pistonside are completely separated from each other. Therefore the respective flow rates and the pressure losses resulting from them can be calculated separately which simplifies the calculation. It can therefore basically be calculated as the combination of two single-acting systems as in Sect. 3.2.1. The overall hydraulic damping force is therefore: FD,hyd = pK AK + pR AR

(3.67)

When calculating the piston velocity limits for cavitation it is important to distinguish between the pressure levels in the accumulators for the rodside and for the pistonside. vKav,Ein =

pSp,R νρKD,R AR

(3.68)

vKav,Aus =

pSp,K νρKD,K AK

(3.69)

Here too, suitable sizing of the flow restrictors, similar to the calculation in Sect. 3.2.2, helps to avoid cavitation. Again, the danger of cavitation can be eliminated completely by placing an additional check valve parallel to each flow resistor.

3.2.4 End-of-Stroke Damping It was already stated in Sect. 2.3.3 that the end-of-stroke damping should be as smooth as possible by avoiding deceleration force peaks and keeping the force level as low as possible. This can be achieved by a layout which ensures a possibly constant force level extending over the entire end-of-stroke damping range. The closer the piston gets to the end stop the lower the velocity and, for a constant force level, the more restrictive the flow resistor needs to be. This sizing of the flow resistor over the end-of-stroke damping range can be calculated as the following explanation shows. The change of the spring force throughout the end-of-stroke damping displacement as well as the general damping of the suspension system are not considered for this calculation. The influence of both is relatively small and has in

92

3 Dimensioning of the Hydropneumatic Suspension Hardware AED

v0

ΔpED

Flow resistor

m

.

xM

V

x

Fig. 3.10 Deceleration of a Mass by a Cylinder and a Flow Resistor

addition a favorable (decelerating) effect. The schematic in Fig. 3.10 shows the basic setup for the calculation. The above considerations allow the following approach: FED = ma = const.

(3.70)

FED is created from the pressure loss pED at the flow resistor multiplied with the active area during the end-of-stroke damping AED . Therefore the pressure loss is: pED =

FED ma = = const. AED AED

(3.71)

Assuming that the flow resistor has the character of an orifice, it is possible to also express the pressure loss according to Sect. 2.3.2: pED = V 2 (x)KB (x) ·

(3.72)

V (x) = v(x)AED

(3.73)

and using ·

it is possible to calculate KB (X) KB (x) =

pED v2 (x)A2ED

(3.74)

Furthermore the velocity can be calculated according to the general laws of kinematics (for example in [KUC87]): v (x) =

 v20 + 2ax

(3.75)

where v0 is the initial velocity when reaching the starting point of the end-of-stroke damping and a is the deceleration of the mass and therefore is negative. Applying Eqs. (3.71) and (3.75) to Eq. (3.74) results in the equation defining the displacement-depending orifice:

3.2

Dimensioning of the Hydraulic Damping Elements

93

v2 only defined for 0 < x < − 0 2a



ma KB (x) = 3 AED (v20 + 2ax)



(3.76)

v2 only defined for 0 < x < − 0 2a

(3.77)

And for a throttle accordingly: ma  KD (x) = A2ED νρ v20 + 2ax





For the initial velocity v0 the realistically expected maximum value v0,max must be inserted into the equations as well as the maximum decelerated mass mmax . This mass must then be decelerated by the end-of-stroke damping to v = 0 m/s within the available end-of-stroke displacement xM .

amax = −

v20,max

(3.78)

2xM

Furthermore it can be proven by calculation that in case of the application of Eq. (3.76) (orifice) no matter what the initial velocity is, the piston will always be decelerated to zero throughout the whole end-of-stroke displacement, thus granting the softest possible damping independent of the initial velocity. This way a soft impulse and a rather slow motion towards the end stop is more softly cushioned than a heavy impact. So the system dissipates energy only as much and as quickly as necessary to ensure the softest possible cushioning; it automatically adapts to the needs of the operating conditions just by its physical principle (Fig. 3.11). In practice at the beginning of the end-of-stroke damping, the flow resistance will be increased slowly to the calculated nominal value in order to ensure that there is a smooth transition into the constant deceleration process.

Force F = Fmax

F = ¼·Fmax F = 1/9 ·Fmax

v0 = v0,max

v0 = ½·v0,max v0 =1/3 ·v0,max

Start of end-ofstroke damping

Mechanical end stop

Displacement

Fig. 3.11 End-of-stroke damping force vs. displacement for an ideally designed displacementdepending orifice at different v0

94

3 Dimensioning of the Hydropneumatic Suspension Hardware

Due to this advantage and the fact that the flow resistance of an orifice is mostly independent of fluid viscosity (and therefore temperature), an orifice type flow resistor is recommended over a throttle type for the displacement-depending end-ofstroke damping. Furthermore it is important to consider for hydraulic end-of-stroke damping that it should let the piston move freely without additional damping when its direction of motion changes and it is on its way back out of the end-of-stroke damping range, away from the end stop. This ensures that the piston returns quickly to its normal operating range with normal levels of damping and comfort. The hydraulic end-of-stroke damping is virtually wear free. There is only an additional stress factor for the hydraulic fluid due to the flow conditions with higher shear stresses in additional sealing gaps or the orifice itself. Yet this can be covered by the normal oil servicing. All in all, for hydropneumatic suspension systems the hydraulic end-of-stroke damping provides functional advantages over the solution with elastomer elements.

Chapter 4

Hydraulic Components Design

The schematic setup of a simple hydropneumatic suspension system has been illustrated already in Sect. 2.1. Section 4.1 describes the design of the basic components for the suspension unit: cylinder, accumulator, flow resistors and lines/fittings.

4.1 Cylinders

4.1.1 Function and Requirements The cylinders are the load-carrying elements in the suspension system; they transfer the forces between input side and isolated side which keep the suspended mass in the intended design position. At the same time, the cylinder also provides the travel of the suspension, which enables the reduction of oscillations and respectively accelerations on the isolated side. Forces and the coincident displacements therefore lead to energy exchange between the mechanical setup (chassis, wheels, control arms etc.) and the hydraulic suspension system. Usually the geometry and the kinematics of the suspension system are designed in a way that the cylinders are subjected to a compressive force. This means that the complete surface of the piston is acting as the active area and carries the suspended mass. This way the design maximizes the use of the available cylinder diameter and therefore available space. Only very rarely has the cylinder the additional function of contributing to the kinematics in a way the regular guiding elements do (like, for example, control arms). The system is usually designed so the cylinder only transfers forces along its longitudinal axis. One reason for this is that an additional load coming from transverse forces or torsional moments can lead to an overload of the cylinder and W. Bauer, Hydropneumatic Suspension Systems, DOI 10.1007/978-3-642-15147-7_4,  C Springer-Verlag Berlin Heidelberg 2011

95

96

4

Hydraulic Components Design

therefore to its destruction. But the far more important reason is the friction caused by these types of load. This would result in a deterioration of the suspension properties especially the comfort quality as already explained in Chap. 2. If transverse forces and/or torsional moments cannot be avoided due to the chosen kinematics setup/design space limitations, they can sometimes be at least partly compensated by other design tricks. A good example of this is to have an offset angle between the line of action of the spring force and the damper longitudinal axis on McPherson struts, reducing the unfavorable loads on the damper to a minimum. In addition to the definition by a drawing or a 3-dimensional model, the following short checklist summarizes several important specification features for suspension cylinders (additional to common cylinder specifications): • Permissible operating pressures: can be above system pressure due to suspension motion! • Temperature ranges (short term, long term): can be above system and above ambient temperature due to the additional heat rejection of damping elements! • External forces or torsional moments during operation, particularly compression and rebound end stop: should the cylinder provide this function or are there external end stops? • Static and dynamic friction under different operating conditions (pressures, temperatures, piston velocities) • If applicable: hydraulic damping forces, end-of-stroke damping (at specified hydraulic fluid viscosity and piston velocity) • Maximum piston velocity • Qualification testing in particular in terms of fatigue endurance: at a certain load spectrum defined for the suspension (as far as possible, should consider short and long stroke displacements and different oscillation frequencies) • General operating and environmental conditions: especially important if the cylinder is located in a harsh environment and exposed positions such as in the wheel house or at an axle.

4.1.2 Types of Cylinders The general layout of a suspension cylinder is illustrated by a schematic partial cross section in Fig. 4.1. The key element of the cylinder is the cylinder tube. It adjoins all other elements except for the piston rod. The cylinder tube is closed at one end by the cylinder bottom, which usually also has the function of transferring the force at this end of the cylinder. The supporting element can be designed in different ways; in Fig. 4.1 for example a simple slide bearing is sketched. At the other end the cylinder tube is closed by the rod guide, which, as indicated by its name, guides the piston rod and the components attached to it along the longitudinal axis of the cylinder. At one end of the piston rod a support element is

4.1

Cylinders

97

Rodside support element Piston rod Rod guide with sealing and guiding elements Hydraulic connectors Air bleeding elements Cylinder tube Piston with sealing and guiding elements Cylinder bottom with bottomside support element

Fig. 4.1 Partial cross section of a suspension cylinder

attached, which transfers the cylinder forces at this end of the cylinder. At the other end of the rod, the piston is attached. In case of a double-acting cylinder (as shown in Fig. 4.1) the piston separates the volume inside the cylinder tube into two individual chambers: the piston chamber and the rod chamber. For a tight separation of these chambers, a seal is installed in the circumferential surface of the piston. The seal slides on the inner surface of the cylinder tube. Additionally there are guiding elements, which are supposed to transfer lateral forces between piston and inner cylinder surface with the lowest possible friction and lowest possible lateral play. The guiding elements prevent a metal-to-metal contact of piston and cylinder tube and furthermore provide a defined gap between them both to enable the best possible function of the sealing element(s). More sealing elements are located between the rod surface and the inner surface of the rod guide. Their function is to separate the rod chamber from the environment. The guiding of the piston rod is either by metallic contact of rod and rod guide surfaces or by additional guiding elements similar to the piston. In case no piston is integrated into single-acting cylinders the rod sealing elements are the only dynamic seals (example: Fig. 4.2 plunger cylinder). Furthermore hydraulic connectors are provided which enable the flow of hydraulic fluid in and out of the cylinder chambers. In the above example, the connectors are connected to the cylinder tube, yet they might as well be part of, for example, the rod guide and/or the cylinder bottom. Special air bleeding elements are provided in particular for suspension cylinders. They ensure that the suspension function, especially the damping, is not spoiled by any residual air in the hydraulic fluid. These elements are located at the very ends of the respective chambers to ensure best bleeding results. The location of the bleeding elements also needs to be selected considering the position of the installed suspension cylinder in the overall system. Not only must they be in the highest position of each cylinder chamber, but they also must be able to be reached by service personnel.

98

4 Single-acting cylinders with plunger

with piston

Hydraulic Components Design

Double-acting cylinders differential cylinder

synchronous cylinder

Fig. 4.2 Functional principle of the most common types of cylinders

Other elements (not shown in Fig. 4.1) are integrated in the cylinder depending on its function and type. Such elements include an end-of-stroke damping, sensors or special connection flanges, for example, to directly mount accumulators at the cylinder. There are basically two possibilities to categorize cylinders: their functional principle and their design principle. The functional principle can be distinguished between the single-acting cylinder designed either with a plunger or with piston and rod, and furthermore the double-acting cylinder designed as a differential cylinder or a synchronous (i.e. double-rod) cylinder. The design principle is subdivided into different basic types which differ especially with respect to the type of connection between the three main cylinder components rod guide, cylinder tube and cylinder bottom. Well known and frequently used connection types are especially welding connections for the connection cylinder bottom to cylinder tube and the screw-intype or the drop-in-type connection for the connection of cylinder tube and rod guide. Furthermore the tie rod design and the crimped design are used for the overall cylinder in special cases. These short explanations will be further explained in Sects. 4.1.2.1 and 4.1.2.2. 4.1.2.1 Functional Principle Figure 4.2 categorizes cylinders according to their different functional principles. Suspension systems with only low static spring load variations or with external mechanical preload can be run with single-acting cylinders. If the requirements in terms of rebound damping are not too high, a simple plunger cylinder can be used. Its particular advantages are low production cost, a high safety factor for buckling

4.1

Cylinders

99

and a robust connection of the rodside support element. On the other hand there is, when built from solid material, a relatively high component weight with the additional disadvantage of the increase of unsprung mass. If this is a critical design criterion, the rod of the plunger cylinder can be designed hollow. Another possibility is to use the more complex single-acting cylinder with piston and rod, while the rod chamber is ventilated or connected to the hydraulic fluid reservoir and only the piston chamber is subjected to hydraulic pressure. The double-acting cylinder with piston and rod should be used, when higher rebound damping is required. As described in Sect. 3.2.2 this cylinder is equipped with a bore in the piston which connects piston and rod chamber. The flow through this bore is limited by a flow resistor (for example, an orifice) and thus an increased rebound damping is possible. If normal flow resistors are used, providing the same restriction in both flow directions, a suitable sizing is necessary to avoid cavitation. Compared to regularly used double-acting cylinders the cylinder here can be operated without a piston seal. The gap between the circumferential surface of the piston and inner cylinder wall and the guiding element are then the only sealing design features between pistonside and rodside. In particular, if the guiding element has a special shape to provide minimum leakage, this is usually sufficient for these types of cylinders. Furthermore it has no rodside oil connectors like a regular double-acting differential cylinder. However it is still more expensive than a simple plunger type single-acting cylinder. If a suspension system is subjected to wide load variations, it is common to implement a hydropneumatic suspension system with hydraulic preload and therefore with a double-acting cylinder. The differential cylinder is the best choice in this case; the necessary preload pressure is set in its rod chamber and then the pressure in the piston chamber is brought to a level which enables it to support the static spring load and the preload forces and therefore can keep the suspension level in the desired position. This directly implies that the piston chamber and the rod chamber must be separated from each other by a sealing element at the piston. This logically means that this cylinder also needs a separate hydraulic connector for the rod chamber. This sealed separation of piston chamber and rod chamber also helps to provide an effective damping of the suspension motion by integrating flow resistors between the cylinder chambers and their respective accumulators. Just by the nature of the preload, the general level of suspension hydraulics pressures is higher than in the single-acting systems. Accordingly the risk of cavitation during fast suspension motions is smaller. The synchronous cylinder with a rod and a rod guide at each end of the cylinder tube is also very well known in standard hydraulics – for example, for steering systems. The diameter of both rods is the same, therefore the cylinder has equal active areas on both sides of the piston. For hydropneumatic suspensions this is only interesting for some exotic applications, for example, if separate roll stabilization is required (please also refer to Sects. 6.3 and 8.2). Therefore this type of cylinder is not described in detail here.

100

4

Hydraulic Components Design

There are of course other types of cylinders, usually for special applications with other functional principles, such as cylinders with three different active chambers. However they are only rarely used and are also not included here. 4.1.2.2 Design Principle Figure 4.3 shows three different design principles which can be used universally for the aforementioned types of cylinders. The welded design is a very common concept and is particularly characterized by its high degree of robustness. In this case the cylinder bottom is welded to the cylinder tube and the rod guide (if installed) is screwed into the cylinder tube; sometimes it is also only dropped in and mechanically interlocked, for example, with a steel ring. The sealing between rod guide and cylinder tube is provided by standard sealing components, usually by o-rings. Such cylinders can withstand high forces in longitudinal and also lateral direction. Due to the compact design, their space requirements are relatively low. The tie rod design abstains completely from welding by tying the components rod guide, cylinder tube and cylinder bottom together with the help of outboard located threaded rods. The sealing among the different components and towards the environment is provided by standard elastomeric sealing elements. This way all the problems arising from a weld are completely ruled out (welding distortion, changes to the material structure, residual stresses, etc.). A further advantage is that

screwed or dropped in welded

with tie rod

Fig. 4.3 Examples for design principles of suspension cylinders

crimped

4.1

Cylinders

101

the leakage test for porous welds, often performed on 100% of the welded production cylinders, can be omitted for the tie rod design. The machining of the cylinder tubes is relatively simple; in best case, it is sufficient to cut to length, deburr and chamfer (this helps the assembly of the seals). The hydraulic connectors are then usually integrated in the cylinder bottom and the rod guide (not shown in Fig. 4.3). For the tie rod design it is essential to keep a close eye on the exact positioning of the components especially with regards to the longitudinal axis of the cylinder. This means additional effort for machining of the respective mating surfaces as well as for the final assembly. Due to their very nature, tie rod cylinders may not be subjected to high lateral forces or high longitudinal overload. This means in particular that in many cases the cylinder cannot provide the end stop function and it is therefore necessary to plan on external mechanical end stops, for example, as part of the suspension kinematics. A further disadvantage is the additional space requirement for the external tie rods and the lateral tie rod supports at both the rod guide and the cylinder bottom. The crimped design is quite common for mass production shock absorbers in the automotive industry as well as for small damping elements. Here too the problems of a welded design are avoided. Serviceability of the cylinders is sacrificed for the benefit of lower production cost. The cylinder bottom and the rod guide are crimp-connected to the cylinder tube. The sealing of these connections is usually an elastomeric element like in the tie rod design, yet in some cases connections can be found where one of the two mating components is designed similarly to a cutting ring of a hydraulic connection. When crimped, this cutting ring is pressed into the surface of the mating surface and this way seals the connections. However, the manufacturing of the crimped design gets increasingly difficult with increasing cylinder tube wall thickness. That is the reason why crimping has only a limited applicability for hydraulic cylinders with their rather large wall thickness, unless a suitable manufacturing process can be developed.

4.1.3 Sealing Elements Sealing technology is of especially high importance for suspension cylinders. Seals are distinguished into the group of static seals and the group of dynamic seals, which are again distinguished into rotary and translational dynamic seals. The latter seals are responsible for the level of friction in a suspension cylinder and therefore have a major influence on the ride quality that can be provided by a suspension cylinder and therefore by the whole suspension system. In particular the sealing element between rod and rod guide as the separating element between hydraulic fluid and the environment is of major importance. On one hand it is subjected to a high pressure difference and therefore causes the major amount of the overall friction. On the other hand it has the important task of avoiding oil leaks out of the cylinder into the environment and at the same time of keeping dirt particles from the environment out of the hydraulic system.

102

4

Hydraulic Components Design

Due to its very nature, the functional principle of a dynamic seal should rather be called a controlled minimum leakage. The reason is that an extremely thin lubricating film on the sliding surface of the seal is necessary to ensure smooth sliding. This lubricating film usually is thinner than 1 µm, which is about the order of magnitude of the surface roughness of the sliding partner [MUE]. The lubricating film helps to keep the friction forces low and this also keeps the friction induced heat rejection low. The remaining heat rejection is partially absorbed by the lubricating film and therefore dissipated into the hydraulic fluid in the cylinder chambers. Low friction forces and low temperatures provide the additional benefit of low wear of the sealing edge(s). During the relative motion of both sliding partners of the sealing system, the lubricating film takes along hydraulic fluid through the sealing gap. To make sure that this does not cause leakage, this amount of hydraulic fluid has to be brought back to its original side during the motion in the opposite direction. The amount of hydraulic fluid drawn through the sealing gap is in particular depending on the gradient of the contact pressure at the sealing edge along the path from one side of the seal to the other. In particular the maximum contact pressure gradient for both motion directions individually is responsible for the transportation of the hydraulic fluid through the gap. The higher the gradient’s maximum, the lower the amount of hydraulic fluid escaping through the gap. Mueller has illustrated this relationship very colorfully by a truck that carries hydraulic fluid on its open, bowl-shaped cargo area over a hill. The hill is the shape of the pressure-position curve along the path of the oil from the high-pressure side to the low-pressure side. Now, the steeper the inclination of the hill on the high-pressure side, the more hydraulic fluid will get spilled out of the transportation bowl on the truck and therefore the less oil he will bring to the low-pressure side [MUE]. Figure 4.4 exemplifies how the contour of the sealing element (b) pressed onto the sliding surface (c) by the normal force (a) affects the formation of this pressure gradient. The lower the gradient of the contact pressure curve (d), the higher is the leakage (e) in the respective direction (indicated by the size of the arrow). It is important to realize that the pressure curve is also affected in particular by the pressure difference from oil to air side (in many cases this changes the normal force) and by the fluid forces of the hydraulic film between sealing edge and sliding surface. The radius of the sealing edge has a major influence as well: The larger the radius, the easier the hydraulic fluid can get between sealing element and sliding surface and the lower will be the friction, however the higher will be the leakage.

a b c

Fig. 4.4 Schematic relationship of seal contour, pressure gradient and leakage

d e

4.1

Cylinders

103

Since it is very important for a rod sealing element that it is virtually leakage-free, the seal contour needs to have a rather high angle on the hydraulic fluid side (low leakage during cylinder extension) and a lower angle on the air side (good transportation of hydraulic fluid back into the rod chamber during cylinder compression). This ensures that during the frequent cylinder position oscillations more hydraulic fluid can be transported back than is leaking out of the cylinder. For sealing elements between piston and inner wall of the cylinder tube it is necessary that the seal’s fluid transportation behavior is as symmetric as possible to avoid pumping hydraulic fluid from one chamber into the other during the piston movement. Therefore piston seals favorably have a similar contour on both sides of the seal, but also depending on the (average) pressure difference between both sides. It is obvious that the properties of the sliding surface play an important role as well. In case the roughness is too high, the result is a thicker lubricating film yet also stronger wear at the sealing edges due to a scratching effect of the surface roughness peaks. In case the roughness is too low, a lack of indentations which can accommodate hydraulic fluid leads to reduced lubrication and hence an increase of the friction forces. Special surface coatings can help improving the situation. For example, high quality shock absorbers and front forks for motorbikes are equipped with rods coated with the gold-colored titanium nitride, providing a substantial and durable reduction of friction. An important issue is that the dynamic seals should have a reliable sealing function also in a static state. Especially important is the transition from the static to the dynamic state. Static friction is an important factor here. Since in the static state no friction-reducing lubricating film is available, the level of static friction is usually higher than the sliding friction. Moreover for a suspension system, the static friction determines the minimum level of excitation for the proper function of the suspension. The higher the static friction, the higher are these accelerations. When selecting the sealing elements, it is also important to avoid the stick-slip effect which arises on one hand from a high difference in static and sliding friction coefficient, on the other hand from the elastic behavior of the sealing elements and other components. The following factors are of major importance for the selection of suitable dynamic sealing elements for suspension cylinders: Low friction No leakage (especially for rod seals) Maximum sliding velocity (compression and rebound) Pressure level (maximum pressure can be above hydraulic system pump pressure!) – Robustness and permissible operating temperatures (in particular for seals in exposed suspension cylinders in off-road equipment) – – – –

To achieve proper dynamic sealing, it is common to combine several sealing elements in a complete sealing system. This way the positive characteristics of each type of sealing element can be specifically used for an overall improved sealing

104

4

Hydraulic Components Design

function. The following explanations describe the sealing locations rod to rod guide and piston to cylinder tube in more detail.

4.1.3.1 Rod Seal System As mentioned above, one requirement for the rod seal system is to be leakagefree in static and dynamic sealing condition. To be able to ensure this, especially considering the low friction requirements, it is common to arrange two sealing elements in series to keep the hydraulic fluid inside the cylinder. Additionally, on the low pressure-side (air side) a wiper is installed to keep dirt particles, water etc. away from the delicate sealing edges of the fluid seals and out of the hydraulic system in general (Fig. 4.5). It is state of the art to design the first seal (primary seal, counted from the fluid side) as a very low friction seal with a therefore thicker lubricating film. This is often a PTFE sealing ring (polytetrafluorethylene, a low friction thermoplastic) with a step-shaped contour which is preloaded and therefore pressed onto the rod by an O-ring. Normally this sealing element catches most of the pressure difference between fluid side and air side. To enable this, it must be designed in a way so it has a pump effect towards the fluid chamber, this way keeping the chamber between primary and secondary seal free of excessive hydraulic fluid and therefore free of pressure. The secondary seal is then designed more conservatively to further reduce the film thickness during the extension stroke and hence to prevent leakage. It is usually a lip seal ring in particular a u-ring. Since the latter must only catch a small portion of the overall pressure difference, its friction is relatively low. The friction level of a suspension cylinder with this type of rod sealing system therefore is a good indication of the proper functioning of the primary seal. If it loses its sealing function, the pressure in the chamber between primary and secondary seal increases and the u-ring is loaded with higher pressure thus causing higher friction. If it has to catch the whole pressure difference between fluid and air side this will cause a drastic increase of friction (factor 2 and more).

primary seal rod guide

high pressure side (hydraulic fluid)

Fig. 4.5 Rod sealing system

secondary seal

wiper piston rod

low pressure side (air)

4.1

Cylinders

105

For an even lower friction it is possible to use special rod sealing systems, known from servo-hydraulic test benches, although a higher leakage comes along with it, since in many cases this is basically a very tight sealing gap. Now instead of sealing the leakage with another sealing element, which would build up a pressure difference and therefore cause friction, the leakage can also be routed back to the hydraulic reservoir via a leakage oil return line. Therefore the secondary seal can be designed with almost no friction since it is basically only an oil wiper. This element and its low additional friction can even be omitted if a gaiter is used to protect the complete piston rod from dirt and keep the hydraulic fluid away from the environment. This type of design is used in the hydropneumatic suspensions for Citroen passenger cars to reach the lowest possible level of friction. The non leakage free rod sealing system is probably one of the reasons why vehicles with these hydropneumatic suspensions very slowly drop down onto the compression end stops during longer standstill periods. 4.1.3.2 Piston Seal Since the piston seal only seals internally, it is not so important to have an absolutely leakage free seal. Indeed during standstill (no excitations on the input side) and therefore in case of static sealing, it is desired to have possibly low leakage to keep the suspension level in its design position. But when excitations arise and the suspension is in operation, it is not a problem to have a slight leakage at the piston seal due to the sliding over the inner cylinder tube wall. For the sake of lower friction and therefore better ride comfort it will be usually accepted that the leveling system needs to be activated from time to time to bring the suspension back to the design position. In a suspension cylinder the piston seal usually consists of a PTFE slide ring which is preloaded by an o-ring. This type of arrangement makes use of the positive properties of both types of material just like the primary seal mentioned for the rod seal system. At the dynamic sealing location low-friction and low-wear PTFE provides the sealing. To ensure that this function is given in long term, a preload must be applied which does not decrease throughout the life of the suspension system. This function is provided by an elastomeric O-ring. It has the additional advantage that, due to its elastic deformation under pressure, it provides the more radial preload for the slide ring, the higher the differential pressure between both cylinder chambers. On top of that, the O-ring has the function to seal the possible leakage path between slide ring and piston through the groove (Fig. 4.6). The companies Merkel Freudenberg Fluidtechnik and Weber-Hydraulik were able to further improve the sealing properties (especially the friction) by a special rounded shape of the contact surface of the slide ring. This reduces the pressure gradient and therefore the transition from mixed friction to hydrodynamic friction at the sealing element can be reached more easily. This seal reduced the friction by more than 30% compared to standard slide rings (average value for the different main operation pressure ranges of the suspension cylinder). It was further possible to prove that the leakage during the dynamic sealing function is on the same level as

106

4

Hydraulic Components Design cylinder tube guiding element PTFE slide ring O-ring for preload piston longitudinal axis of cylinder

Fig. 4.6 Slide ring and O-ring for piston seal

for standard slide rings. The seal enables the compensation of the higher fluid film thickness by providing the same thickness for both sliding directions [FIS06].

4.1.4 End-of-Stroke Damping It is the basic principle of a hydraulic end-of-stroke damping to reduce the opening for the hydraulic fluid flow out of the respective chamber from a certain point of suspension displacement/piston position. This creates a differential pressure which retroacts into the respective cylinder chamber and therefore onto its hydraulically active area. This leads to an additional decelerating force in the cylinder. A widely used design solution is to cut off the cylinder chamber from the outlet port starting from a certain piston position towards the end of the stroke. In addition to that, a predefined (sometimes also displacement-dependent) opening area is created, which then is the only path for the outflowing hydraulic fluid to the outlet port. Here the simplest solution is to create a bypass-bore which contains a (eventually externally adjustable) flow resistor. Figure 4.7 shows the example of a rodside endof-stroke damping which becomes effective during rebound phases. An additional check valve can be found in the arrangement. It is responsible for enabling an unhindered motion back towards the design position of the suspension once the rebound motion has come to an end. However a disadvantage of this whole setup is that the constant flow resistor does not allow an even and low level of deceleration. Due to the flow rate dependency of the flow resistance, it has a high deceleration peak at the beginning of the end-of-stroke damping (high piston velocity → high flow) with a subsequently decreasing damping force. Sizing the constant flow resistor therefore is always a compromise: if its opening area is chosen to be too large, the deceleration might not be sufficient and the suspension will bottom out harshly. On the other hand if it is chosen to be too small, the flow resistance and therefore the deceleration is too high. In both cases a noticeably high level of acceleration will reduce the comfort.

4.1

Cylinders

107 piston

flow resistor

rodside port

check valve

effective displacement

pistonside port

Fig. 4.7 Bypass-bore with fixed flow resistor

To avoid this disadvantage, a displacement-depending end-of-stroke damping flow resistor is necessary. This way, the high initial velocity can be evenly reduced to a very low velocity level when reaching the mechanical end stop. This requires a constant level of decelerating force and therefore a constant pressure loss at the flow resistor. At the beginning of the end-of-stroke damping the opening area therefore must be high and then gradually be reduced – please refer to Sect. 2.3.3. There are different possibilities to provide such a characteristic of the opening area vs. displacement. It is very common to machine grooves into the part of the piston which shuts off the cylinder chamber from the outlet port. These grooves flatten out until the end of the cylinder stroke and therefore fulfill the requirement of a reducing opening area. The grooves can be arranged axially as well as helically (Fig. 4.8) [KON07]. It was already mentioned above that it is important for the end-of-stroke damping to be only active during the motion towards the end stop but should let the piston move freely on the way back to the design position. The check valve function of the setup presented in Fig. 4.7 can, for example, be provided by a ball valve, which has to be sized correctly for high flow (unfavorably large ball diameter), or by a spring loaded washer. In the setup shown in Fig. 4.9 the damping element itself has been modified to provide this function. The ring contains on its outer circumference the axial grooves which define the opening area of the end-of-stroke damping and additionally is designed to be axially

Fig. 4.8 End-of-stroke damping grooves

axially

helically

108

4

a) Motion towards end of the stroke

Hydraulic Components Design

b) Motion back towards design position

Fig. 4.9 Floating ring provides check valve function

slidable on the rod. During the motion of the piston towards the end of the stroke the ring slides towards its own end stop which is located, due to the pressure difference, in the motion direction of the piston. Here the ring seals at its front surface and the hydraulic fluid can only pass the path through the axial grooves. The motion is therefore decelerated according to the depth of the grooves. During the motion back towards the design position, the ring again slides on the rod in the direction of the piston motion and now hits the end stop at the piston. Yet this side of the front surface is additionally machined with radial grooves which open up an additional path for the hydraulic fluid through the annular gap between ring and rod into the rod chamber. If the opening area of this flow path is chosen to be sufficiently large, the motion back to design position can be unrestricted, only subjected to the regular fluid damping. Another possibility to create the function of an end-of-stroke damping is given, when a rapidly adjustable damping system and a position sensor are available. If the electronic controller discovers with the help of the sensor signal, that the piston is close to one of its end stops – or will get there soon due to the energetic conditions of the suspension system – the damping element can be adjusted to prevent the system from bottoming out. Since the rapidly and electronically adjustable dampers are usually only used for semi-active suspension systems, the end-of-stroke damping algorithm can be expected to be part of the overall damping logic. Usually end-of-stroke damping has the disadvantage that it adds to the overall length of the cylinder, which is unfavorable especially in tight packaging conditions. That is why cylinder manufactures try to find solutions to avoid additional length. One possible solution is to make use of extendable elements, which, during end-ofstroke damping are reduced in length. Some examples are described in the patents [DE960] and [EP721]. One further possibility to provide an end-of-stroke damping shall be mentioned although it is not commonly used in hydropneumatic suspensions: an axial groove in the inner wall of the cylinder. Here it can only be used for regeneratively operated non hydraulically preloaded systems with a double acting cylinder (see Sect. 3.2.2). The axial groove extends over the portion of the stroke for which the regular damping is desired. Fluid can then flow through the groove from one cylinder chamber to the other. The size and therefore the flow resistance of the groove has a main

4.1

Cylinders

109

influence on the damping behavior in this range. If the piston position exceeds this range, the flow path through the grooves is closed and the fluid must take an alternative path from one cylinder chamber to the other, for example, through the piston. The flow resistance of this path determines the strength of the end-of-stroke damping. This principle is known especially from automotive shock absorbers and is used there especially to create a soft damping around the design position and an increased damping when getting outside of this range [CAU01].

4.1.5 Types of Support Elements It was already mentioned that cylinders usually are not used as guiding elements in suspension systems. Yet a suspension system usually has a 2-dimensional often also 3-dimensional suspension kinematic setup. Therefore the cylinders must be hinged at both ends to avoid unfavorable tension resulting from bending moments or lateral forces. In the simplest case, a pivot bearing is sufficient and it can be designed, for example, as a slide bearing. If a 3-dimensional movement requires a cardanic bearing, for example, a spherical slide bearing or a rubber-metal bushing can be integrated (Fig. 4.10). Independently of the selection of the support element, it is important that the bending moments transferred through the support element are as low as possible since they cause lateral forces in the cylinder’s guiding elements and therefore cause friction. This means especially that the center of the support elements needs to be on the cylinder longitudinal axis as precisely as possible since the slightest eccentricity causes bending moments in the cylinder. In particular, if a sliding bearing is used, the radius of the sliding surface (and therefore the effective radius for its sliding friction) should be chosen as small as possible. From the range of sliding bearings fulfilling the specified durability goals, the type with the smallest possible sliding interface radius should be chosen for lowest cylinder friction. Spherical slide bearing

rubber-metal bushing cylinder bottom boss outer ring rubber inner ring pin

Fig. 4.10 Spherical slide bearing and rubber-metal bushing

110

4

Hydraulic Components Design

Furthermore the selection of sliding bearings should also be focusing on a possibly low coefficient of friction inside the bearing. This means for a steel slide bearing that a regular and sufficient injection of lubricant needs to be ensured. Unfortunately in practice this is not always the case. In particular in suspension systems with many greasing locations (including the mechanical setup) the lubrication intervals are prone to be stretched due to the high effort for greasing. A possible but costly solution for this is a centralized lubrication system, possibly with automatic control. On the other hand there are maintenance free sliding bearings with sliding surfaces made from or covered with synthetic low-friction material with lifetime self-lubricating properties, for example, combinations of PTFE, bronze, graphite etc. For them the best possible protection against external contaminations like dirt, water or chemicals is very important. When the cylinders are used in dirt-exposed areas the use of maintenance-free bearings is only recommended, if a special protection comes with it. Despite this, a certain amount of wear of sliding bearings and therefore the formation of internal play during their lifetime is usually inevitable. Up to a certain amount of wear/play, this is usually not a problem especially if the bearing is permanently loaded in one direction. Since the bearing then always has the same contact surface, the play will not be noticeable. However, if the load direction changes, especially if it changes by 180◦ to the opposite direction (for example, during fast transitions between compression and rebound) the contact surface will also change to the opposite side of the bearing. In this transition of contact surfaces the play of the bearing causes a short period without force. As soon as the inner and outer ring come in contact again, a short force peak is the result. This force peak spreads out into the overall system and can cause damage and/or discomfort if the play is too large and the peak is too high. The play can be completely avoided by the use of rubber-metal bushings. However, since they provide the desired degrees of freedom by the deformation of the rubber, the disadvantage arises that the elasticity of the rubber causes a relative displacement between inner and outer ring of the bushing. This is the main load direction for the use in cylinders and therefore it has to be ensured that the rubber’s deformation limit is not exceeded even at maximum axial load of the cylinder. This can either be achieved by a sufficiently large surface and/or high stiffness of the rubber, or an internal metallic end stop can be designed in to limit the deformation. However if this end stop is active, it will cause friction in the bearing and therefore also bending moments in the cylinder. Due to the elastic properties of the rubber, it is part of the very nature of rubbermetal bushings to create a returning torque when twisted. This can have a negative impact on the cylinder friction, too. Therefore when considering the fatigue endurability and its vibration properties the softest possible bushing should be selected to ensure lowest cylinder friction. Variables are, for example, the shore hardness of the elastomer as well as the dimensions of the bushing and the internal preload of the rubber element. As mentioned in Chap. 1 already, rubber-metal bushings have the positive characteristic to isolate excitations (to a limited extent) which would be otherwise transferred directly into the isolated side. These are especially high frequency, low

4.2

Accumulators

111

amplitude excitations with low accelerations which do not create sufficient forces to overcome the friction forces inside the suspension cylinder. So the rubber-metal element can help to reduce noise transfer on the path through the suspension elements. Another positive thing about rubber-metal bushings is their freedom from maintenance. Since the rubber is only deformed elastically but no relative motion between surfaces takes place, there are no dynamic sealing locations and therefore no possibility for the intrusion of contamination. It has proven to be a major advantage to make use of these positive properties of the rubber-metal bushing in combination with the high load capacity of a maintenance-free slide bearing. This way the rubber-metal element can be laid out very softly (and adds only low bushing torques) and provides the best sealing of the arrangement while the main load is carried by the maintenance free bushing.

4.2 Accumulators

4.2.1 Function and Requirements Accumulators are the element in the hydropneumatic suspension system which provide the elastic medium for the spring function. For these systems almost exclusively gas-filled accumulators are used. Mechanically loaded accumulators (helical spring or mass loaded) are usually not used in suspension systems and are therefore not further explained. In particular, accumulators preloaded by an external mass (basically upright hydraulic cylinders with a mass pushing down the rod) don’t make any sense for a suspension system since they provide a constant pressure independent from the absorbed amount of hydraulic fluid. Therefore the force displacement curve of a cylinder connected to such an accumulator is a flat line. This means no restoring forces are available and no spring rate can be generated. The gas fulfills these requirements for restoring forces: it is compressible and provides increasing pressure with increasing compression according to the laws of gas physics. The characteristic force–displacement curve results from these laws (see Chap. 2). Usually nitrogen (N2 ) is used as the filling gas, in some cases other gases like tetrafluormethane CF4 (R14) are used. Since the enclosed pressurized gas represents a potential hazard, accumulators are subjected to certain regulations such as the German pressure vessel directive and the European pressure equipment directive 97/23/EC. These directives determine, for example, how to lay out and dimension an accumulator for the respective

112

4

Hydraulic Components Design

pressure ranges, what needs to be considered for their production, what the qualification tests should cover and which regular and recurring examinations of the accumulators have to be performed. Since in practice sometimes hair-raising examples of misuse of accumulators can be found and service intervals are sometimes completely ignored, it is very wise that accumulators need to satisfy stringent safety regulations. All maintenance and repair activities performed on a hydropneumatic suspension system require highest caution. A very important basic rule before starting any kind of work, especially when opening the suspension hydraulic circuit, is to release all pressure enclosed in these circuits. This also means that the design has to include the possibility to drain the system. If the system is not drained before opening, major damage can be caused to both people and equipment, for example, by: • • • •

High pressure fluid jet Hot hydraulic fluid Parts, especially accumulator(s), rapidly shooting around Sudden and rapid movement of the suspension and parts connected to it due to sudden pressure changes in the connected cylinder(s)

It was mentioned in Chap. 3 already that all different kinds of accumulators have certain limits with regards to the operating pressure, which depend in particular on the type of accumulator. If these limits are disrespected, in the long run a premature aging and possibly destruction of the accumulator can be the result. Furthermore most accumulators have in common the slow loss of gas precharge pressure due to diffusion of the gas into the hydraulic fluid (see Sect. 4.2.3). This pressure loss can further constrict the operating limits of the accumulator. As part of the regular maintenance this precharge pressure loss must be compensated by refilling gas to the specified pressure level in order to keep the performance of the suspension system. For the refill it is crucial to use the right kind of filling gas specified on the accumulator or in the manual. Carbon dioxide, oxygen or acetylene as commonly found in workshops must not be used! From a designer’s point of view it is a further possibility to permanently connect the accumulator’s gas side connector to an additional gas pressure vessel. This way the amount of gas suspending the system can be further increased which is another possibility and degree of freedom in finding the optimum setup of the suspension. In addition to the geometrical definition by a drawing or a 3-dimensional model, the following short checklist summarizes several important specification features for accumulators used in hydropneumatic suspensions: • Nominal precharge pressure at 20◦ C including tolerance and type of gas • Inner volume of the accumulator, possibly also the deformation limits of the diaphragm • Maximum flow rate (in and out) • Permissible operating pressures can be above system pressure due to suspension motion!

4.2

Accumulators

113

• Temperature ranges (short term, long term) can be above system and above ambient temperature due to the additional heat rejection of damping elements! • Permissible diffusion gas pressure loss at a given pressure and temperature range with a certain number of operating hours (usually the time between service intervals) • If applicable hydraulic pressure losses (for example, if a flow restrictor is integrated into the hydraulic port of the accumulator) • Qualification testing in particular in terms of fatigue endurance: at a certain load spectrum defined for the suspension (as far as possible, should consider high and low flow rate amplitudes and different oscillation frequencies) • General operating and environmental conditions and if applicable the respective protective countermeasures.

4.2.2 Types of Accumulators Basically a gas pressure accumulator is made up of the elements: fluid-side connector, outer shell, fluid/gas-separating element, gas, gas-side connector with cover. Depending on the type of the accumulator these elements are designed differently. The most common types of gas pressure accumulators are illustrated in sketches in Fig. 4.11. It is differentiated between the diaphragm accumulator (a), bladder accumulator (b), the rarely mentioned flexible sleeve accumulator (c) (for example, in [EBE74]) and the piston accumulator (d). The metallic gaiter accumulator (not shown in Fig. 4.11) works similar to the piston accumulator, however without a piston seal, only using the sealing function of the gaiter. In general, the naming of the accumulator already gives information about which element is used to separate the fluid from the gas. Figure 4.11 shows each accumulator with the fluidside connector in the lower portion and the gasside connector in the upper portion of the shell. Furthermore diaphragm accumulators are distinguished into welded and screwed versions. The latter offer more possibilities for the design of the inner contour of the

a Fig. 4.11 Types of accumulators

b

c

d

114

4

Hydraulic Components Design

shell and therefore can provide a better permissible pressure ratio. Additionally, a worn out diaphragm can be exchanged. A detailed description of these accumulators is skipped here since a lot of information can be found in the respective literature (for example, [GAU04] and [FIN06]). Flexible sleeve accumulators are used only in special cases in suspension systems such as the “Nivomat”-suspension of the ZF Sachs corporation (more explanations in Sect. 5.1). Compared to the other types of accumulators, the cylindrical shape of the sleeve fits best into the contour of the strut and therefore allows perfect use of the given design space. Due to their exceptional, rather exotic position, no further information is given for the flexible sleeve accumulators. For hydropneumatic suspension systems, the most important specification accumulator features are, apart from the basic data precharge pressure and inner volume, the permissible pressure ratio and the maximum flow rate. The latter is especially important since the motion of the suspension is often characterized by rapid, shock-type events causing high flow rates. A rough calculation will further illuminate this: A chassis suspension system is given with a suspension cylinder which displaces 0.5 l of hydraulic fluid during a full stroke (rebound end stop to compression end stop). Assuming a frequency of 2 Hz, a full stroke is performed four times per second. This therefore causes an average flow of 2 l/s or 120 l/min. However during a ride over major ground irregularities and over heavy single event excitations the flow rates can be much higher than this if the cylinder is compressed. For a short term, a factor of 2 or more is possible. The accumulators need to be designed accordingly. For diaphragm and bladder accumulators the deformation velocities and therefore strain rates for the elastic material need to be considered, especially at low temperatures where rubber shows brittle behavior. For piston accumulators on the other hand, the permissible relative velocity for the dynamic seal is an important limiting factor. Furthermore accumulators have to be designed in a way so the jets created by high flow fluid intrusion into the accumulator cannot damage any sensitive internal parts such as the rubber diaphragm. Figure 4.12 shows an overview of the characteristic features of diaphragm, bladder and piston accumulators (table created from basic data [GAU04] modified with information from [FIN06], [MAT03] and others). It can be deduced from the diagram data that the bladder accumulators are no option for wide-load-range hydropneumatic suspensions due to their low pressure ratio. Furthermore, the accumulator size required for usual suspension systems is rather at the low end of the bladder accumulator range which makes these accumulators relatively expensive. This is why bladder accumulators are only rarely used in hydropneumatic suspensions. Piston accumulators, too, are rather high in cost and have the additional disadvantage of friction in the piston sealing system. This friction results in a hysteresis of the pressure that is necessary to move the piston of the accumulator. In particular for low-leakage gas-tight sealing systems this pressure hysteresis can be up to 2 MPa [FIN06]. This friction is added onto the friction in the cylinders and worsens the response characteristic of the suspension. Therefore piston accumulators are only sometimes used in suspensions. The piston seal of the

4.2

Accumulators

115

Diaphragm accu. welded

Diaphragm accu. screwed

Bladder accumulator

Piston accumulator

Size [l]

0.2−4

0.1−10

0.2−450

0.5−2500

Max. pressure [bar]

250 (350)

750

1000

1000

Flow rate [l/s]