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Simulation of the perceptible feed-forward and feed-back


Vehicle System Dynamics Vol. 44, Supplement, 2006, 158–170

Simulation of the perceptible feed-forward and feed-back properties of hydraulic power-steering systems on the vehicle’s

handling behavior using simple physical models
D. AMMON, M. B?RNER, and J. RAUH*
DaimlerChrysler AG, Research and Technology, B?blingen, Germany
Today, often complex component-oriented simulation models are used to study the in?uences of hydraulic power-steering systems on the vehicle’s handling properties. In these simulation models, we have a detailed description of the vehicle suspension components (links, joints, springs, etc.) extended by complex component simulation models of tires, bushings, and of course also by powersteering models. These power-steering models contain a detailed physical description of the complex mechanical and hydraulics properties of the system, like friction in seals, aspects of hydraulic power supply, etc. On the other hand, there is a need for simple model approaches used for basic assessments and system development. These simple models should represent all the essential properties of the vehicle’s handling behavior, without the need for the large-scale parameter setup and compute-time requirements of the more complex models. For many applications in handling, we use the class of single-track two-wheel bicycle-type vehicle models. With some nonlinear extensions, these models can represent the complete operating conditions of the vehicle. The parameterization of these models can be achieved online while driving or of?ine by analysis and identi?cation, on the basis of some standard test maneuvers. In these models, all properties of steering, suspension and tire are condensed to the cornering stiffness or side-force map, a separation e.g. of the steering system in?uence does not take place. This article shows how modeling of a hydraulic power-steering system can be done to represent the essential feed-forward and feed-back properties, and how this model can be integrated to the complete vehicle’s description. This new model approach gives a better insight into the four-pole properties of steering systems and introduces a separation between the steering system and the suspension even in simple model classes. Keywords: Hydraulic power steering system; Four-pole properties; Functional simulation model; Steering torque feedback

1.

Introduction

Today, complex component-oriented simulation models are often used to study the in?uences of hydraulic power-steering systems on the vehicle’s handling properties. In these simulation models, a detailed description of the vehicle suspension components (links, joints, springs, etc.) extended by complex component simulation models of tires, bushings, and of course by powersteering models also are integrated [1, 2]. These power-steering models contain a detailed physical description of the complex mechanical and hydraulics properties of the system,
*Corresponding author. Email: jochen.rauh@daimlerchrysler.com

Vehicle System Dynamics ISSN 0042-3114 print/ISSN 1744-5159 online ? 2006 Taylor & Francis http://www.tandf.co.uk/journals DOI: 10.1080/00423110600869883

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like friction in seals, aspects of hydraulic power supply, etc. On the other hand, there is a need for simple model approaches used for basic assessments and system development [3–5]. These simple models should represent all essential properties of the vehicle’s handling behavior, without the need for the large-scale parameter setup and compute-time requirements of the more complex models [6]. These models give a deeper understanding of the underlying physical effects. Depending on the main focus of the work, functional modeling can go into more or less detail in suspension and tire modeling aspects [1, 7].

1.1

Two-wheel vehicle models

For many applications in handling analysis, the class of single-track two-wheel bicycle-type vehicle models is used, ?gure 1. With some nonlinear extensions, these models can represent the complete operating conditions of the vehicle [8]. The parameterization of these models can be achieved online while driving or of?ine by analysis and identi?cation based on standard test maneuvers [9]. In these models, all properties of steering, suspension and tire are condensed to the cornering stiffness or to the side-force – tire-side-slip angle characteristics, a separation e.g. of the steering system in?uence does not take place.

1.2

Four-pole properties of a steering system

In the following chapters, we will show how modeling of a hydraulic power-steering system can be done to represent the essential feed-forward and feed-back properties, and how this model can be integrated to the complete vehicle’s description. A ?rst point to discuss is the four-pole-property of a steering system, ?gure 2.

Figure 1. Two-wheel model: the four wheels (narrow-dotted lines) are subsumed to two-joint-wheel elements (wide-dotted lines).

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Figure 2.

Four-pole view of steering system.

Here we have four signals to discuss. They are as follows: ? ? ? ? MSW , steering-wheel torque; δSW , steering-wheel angle; Frack , rack force; yrack , rack displacement.

Any of the signals can be input or output; arrows are often used to de?ne sign convention. To derive a set of ordinary differential equations representing this system, a de?nition of system inputs has to be set. This de?nition depends on the operating mode of the steering system as follows: ? Steering-wheel angle is often used to de?ne open-loop maneuver inputs. In this case, steering wheel torque is output. ? To simulate free control (e.g. steering wheel return motion), the steering wheel torque can be considered as input and set to zero, while the steering-wheel angle is the output. In signal ?ow oriented simulators, the derived models depend on the input de?nitions, which have to be set in advance. Simulating a maneuver with a change of input de?nitions in one simulation run can be dif?cult or even impossible to implement.

2.

Steering-system model

The complete steering system of a vehicle consists of many parts. The steering gear mostly includes the power-steering functions in a very compact way, ?gure 3. Other important parts of the steering system are as follows: ? steering wheel; ? cardan(s) or similar joints, sometimes combined with steering wheel position adjustment capabilities; ? bellow sealing between passenger and engine compartment; ? ?exible hardy disk between steering column and steering gear. 2.1 Physical models To model important properties of a hydraulic power-steering system, we have to consider the mechanical and the hydraulics parts, ?gures 4 and 5. Both these ?gures show that the physical

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Figure 3.

Steering gear and valve block.

modeling of the very integrated power-steering system leads to quite complex models with the need for many parameters, which cannot be derived by simple measurements. Some of them are even, only roughly – known by the steering system supplier, which makes it sometimes very dif?cult to complete the modeling and parameterization task for the complete system.

2.2

Minimal models

To overcome the modeling and parameterization problems, we will derive some minimal models that can be seen as a kind of steering-system modeling toolbox. In ?gure 6, we start

Figure 4.

Mechanical parts of a steering gear.

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Figure 5.

Hydraulic parts of the steering gear.

Figure 6.

Functional mechanical-steering model.

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Figure 7.

Functional power-steering model.

with a pure mechanical steering system, consisting of steering wheel with its inertia, some nonlinearity due to cardan or similar joints, some elasticity and friction and the rack/pinion gear itself. In ?gure 7, we add the basic parts for a power-steering system as follows: ? the valve block with the torsion bar as torque sensor, which actuates the bridge valve, which supplies hydraulic pressure to the servo cylinder; ? the servo cylinder, which may also be equipped with damping valves making it also work as a steering damper.

Figure 8.

Functional power-steering model with parametric control.

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Figure 9.

Functional power-steering model to extend two-wheel vehicle models. Table 1. Steering-system model parameters and variables. Symbol Jst MF,P cTB Mhyd is MF,S d cG τTB Description Inertia of the steering wheel Primary friction Stiffness of torsion bar Hydraulic torque Steering ratio Secondary friction Steering damping Self-alignment Torsion of torsion bar

In ?gure 8, we add the ‘Parametric Control’ actuator to the valve block, which allows for speed dependant assist forces. This can be realized by balls pressed by speed-modulated oil pressure and thus virtually stiffening the torsion bar. In all diagrams, the condensed relevant friction contributions are graphically symbolized wherever necessary and important. 2.3 Functional model to extend two-wheel vehicle models After the principle-model overview in the last section, we now concentrate on one-model version. The model interface between steering system and suspension is de?ned by the steeringrack motion and forces or equivalent interface variables. Figure 9 shows the resulting model of the steering system. The parameters and variables used in the model are shown in table 1.

3.

Parameter identi?cation approach

The traditional parameterization approach uses directly available design parameters, known from more complex models or from the original design information. In a new approach, we succeeded in using simple driving procedures (like steady-state cornering and yaw response tests)

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Figure 10.

Steering test rig.

and test rig measurements (like parking on high and low friction) with the complete vehicle to derive all the necessary steering system parameters. These parameters are obtained by analytic and least-squares-identi?cation algorithms [10, 11]. No extra component measurements are needed to complete the parameterization process. 3.1 Test rig procedure description

To give some insight, a part of the whole process is documented here. A simple steering system test rig allows steering tests on low-friction ground simulated by almost friction-free wheel angle sensor plates below the front wheel, ?gure 10.

Figure 11.

Parking on low μ with servo hydraulics.

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Figure 12.

Parking on low μ with servo hydraulics (zoomed).

On this test rig, we run some simple tests, e.g. ? Parking on low μ with servo hydraulics, which allows ? identi?cation of primary stiffness; ? identi?cation of primary friction; ? identi?cation of the hydraulic characteristic. ? Parking on low μ without servo hydraulics, which allows ? Identi?cation of self alignment; ? Identi?cation of secondary friction; ? Identi?cation of steering damping. 3.2 Parameter identi?cation procedure Starting with the ?rst test from above, the following ?gure can be obtained, ?gure 11. To identify the primary friction and stiffness, the shaded area at the limit of the steering system has to be zoomed as in ?gure 12. From these simple measurements at the limit, the slope of both the lines can be used to derive the torsion bar stiffness and their distance to derive the primary friction. Other steering system parameters are similarly obtained from these tests in a step-by-step procedure.

4. Application examples In this section, we can show only some of the improved potentials of the complete vehicle simulation model including its power-steering model extension. We concentrate on sine-steer input as a simple open-loop maneuver and show the in?uences of three parameter variations as follows:

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? modi?cation of primary friction; ? modi?cation of secondary friction; ? modi?cation of primary stiffness. For these three variations, the following plots are shown: ? ? ? ? steering angle vs. steering-wheel angle; steering torque vs. lateral acceleration; steering torque vs. yaw rate; steering torque vs. steering-wheel angle.

Figure 13 demonstrates that a modi?cation of the primary friction does not in?uence the steer angle transfer function, and that an increase in primary friction directly makes the hysteresis in the other three plots bigger. Figure 14 shows that a modi?cation of the secondary friction in?uences the steer angle transfer function. This can be easily explained: there is a small torsion of the torsion bar, necessary to overcome the secondary friction, which has a similar effect as gear clearance would have. The increase in secondary friction also directly makes the hysteresis in the other three plots bigger, but a slightly different form of the hysteresis cycle can be observed. The in?uence of the variation of the primary stiffness (the torsion bar stiffness) is pointed out in ?gure 15. It also slightly in?uences the steer angle transfer functions, but its main effect is a variation of the power steer support: a stiffer torsion bar will less actuate the bridge valve, and thus leaves more torque feedback to the driver.

Figure 13.

Modi?cation of primary friction.

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Figure 14.

Modi?cation of Secondary Friction.

Figure 15.

Modi?cation of primary stiffness.

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Figure 16.

Model-based steering-system analysis.

5.

Summary

In this article, an implementation of a simple power-steering simulation model has been shown, which can be added to simple two-wheel vehicle dynamics models. The identi?cation of all unknown parameters and characteristics of this simulation model was based on simple test rig measurements of the complete vehicle – no disassembled component measurements were needed. The most important improvements of the complete vehicle simulation model, including its new power-steering model extension are e.g. ? ? ? ? ? steering torque feedback at the steering wheel; maneuvers with released steering wheel (free control) like higher speed stability tests; vehicle’s response to small-steering inputs; in?uences of velocity dependant steering assist functions; enhanced description of steering angle transfer function.

This new model approach gives a better insight into the four-pole properties of steering systems and introduces a separation between the steering system and the suspension even in simple model classes. Its model parameters can be interpreted as a ‘?ngerprint’of the steering system, representing all important properties of a hydraulic steering system to vehicle dynamics investigations. It also opens potentials for simulations at operating conditions where no original measurements are available – we call this last step ‘model-based testing’, ?gure 16. References
[1] Rauh, J., 2003, Virtual development of ride and handling characteristics for advanced passenger cars. Paper presented at the 18th IAVSD Symposium, Kanagawa, Japan, 25–29 August, Vehicle System Dynamics, 40(1–3), 135–155. [2] Ammon, D., 2001, Meljnikov, D., Rauh, J., Schirle, T. and Schittenhelm, H., 2001,Auf dem Weg zur verl?sslichen Ride-Simulation. Proceedings of the MKS-Simulation in der Automobilindustrie, SFT Graz. [3] Ammon, D., 1997, Modellbildung und Systementwicklung in der Fahrzeugdynamik (Stuttgart, Germany: Teubner Verlag). [4] Meljnikov, D., 2003, Entwicklung von Modellen zur Bewertung des Fahrverhaltens von Kraftfahrzeugen. Report no. 2003/4, Berichte aus dem Institut A für Mechanik. [5] Zomotor, A., 1991, Fahrwerktechnik: Fahrverhalten. 2. Au?age (Würzburg, Germany: Vogel Buchverlag).

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[6] B?rner, M., 2004, Adaptive Querdynamikmodelle für Personenkraftfahrzeuge – Fahrzustandserkennung und Sensorfehlertoleranz–, Report no. 563, VDI-Fortschrittberichte, Reihe 12, VDI-Verlag, Düsseldorf, Germany. [7] Jarlmark, J., 2004, Modelling and validation of steering system re-sponse to road and driver induced forces. Vehicle System Dynamics (supplement) 41, 371–380. [8] Kobetz, C., 2004, Modellbasierte Fahrdy-namikanalyse durch ein an Fahrman?vern parameteridenti?ziertes querdynamisches Simulationsmodell (Shaker Verlag). [9] Zomotor, Z., 2002, Online-Identi?kation der Fahrdynamik zur Bewertung des Fahrverhaltens von Pkw. Report: Berichte aus dem Institut A für Mechanik, Universit?t Stuttgart, Institut A für Mechanik. [10] Isermann, R., 1992, Identi?kation dynamischer Systeme. Band 1 und 2, 2. Au?age (Berlin: Springer Verlag). [11] Wimmer, J., 1997, Methoden zur ganzheitlichen Optimierung des Fahrwerks von Personenkraftwagen, (Methods for the Multicriteria Vehicle Chassis Optimization). Report: Vol. 12, No. 332, Fortschritt-Berichte VDI Reihe.


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