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Procedía Engineering 15 (2011) 474 - 478

Procedía Engineering

www.elsevier.com/Iocate/procedia

Advanced in Control Engineering and Information Science

Study on Electric Power Steering System Based on ADAMS

Hao Chena*, YaliYanga, Ruoping Zhanga

aShanghai University of Engineering Science, Shanghai 201620, China

Abstract

Electric Power Steering (EPS) is a full electric system, which reduces the amount of steering effort by directly applying the output from an electric motor to the steering system. This research aims at developing EPS boost curve embody into the assist characteristics, improving steer portability and stability. A model for the EPS system has been established, including full vehicle mechanical system, EPS mechanical system, and EPS electric control system. Based on this model, a straight line boost curve was designed and evaluated in this environment to improve the performance of EPS system. Results showed that EPS system with the designed boost curve reduced reacting time and overshoot value, thus ensure the dynamic reaction and stability.

© 2011 Published by Elsevier Ltd. Selection and/or peer-review under responsibility of [CEIS 2011]

KEYWORDS: Boosting curve, Electric power steering, simulation, ADAMS

0. Introduction

Electric power steering (EPS) system is a very important component for improving automotive handling and stability [1]. An EPS system includes mechanical subsystem and electronic and control subsystem, and it has to work in the full vehicle mechanical system. In the development process of the EPS system, different subsystems have to be developed in parallel so as to reduce time and cost of system development. Cooperation between engineers for developing different subsystems is also needed. Therefore, a model-based development is a rational way for this parallel developing and cooperation [2-4].

* Corresponding author. Tel.: +86 13585901312; fax: +86 21 67791152. E-mail address: pschenhao@163.com.

1877-7058 © 2011 Published by Elsevier Ltd. doi:10.1016/j.proeng.2011.08.090

One of the most important parts of the EPS system is the electric control system, which receives signals collected by sensors for vehicle speed, steering angle, steering torque and controls the assistant motor for giving required assistant torque. The key of this control system is to find a boosting curve to embody the assist characteristic. Most researchers of EPS emphasize on the control strategy. Few of assist characteristics is studied. In Refs. [5] and [6] , a boost curve is given but without calculation formula. Refs. [7] and [8] study the steering assist value just from road feel.

A model-based development method for EPS system has been explored. A model for the EPS system has been established in a full vehicle mechanical system environment. A straight line boost curve was designed and evaluated in this environment to improve the performance of EPS system.

1. Modeling

1.1. Full vehicle model

The system-level model includes a mechanical subsystem model for a full vehicle, and for steering system in detail. This mechanical model for the full vehicle and the steering system is established in the software MSC.ADAMS. It includes suspensions for the four corners. The steering system's mechanical model includes steering wheel, steering column, steering rack/pinion, and some connection poles. The chassis model is coupled with the road surface by tire model, which is built based on the MSC.ADAMS/TIRE module. This method is used in vehicle dynamics modeling, and the full vehicle model is shown in Fig. l.The model consisted of 15 degrees of freedom, including 6 for vehicle body, 2 for front suspension, 2 for rear suspension, 4 for wheels and 1 for steering wheel.

Fig.l Full vehicle's mechanical system model

1.0. EPS model

The EPS subsystem model is described by the angular rate and position of the steering column and motor, the linear velocity and displacement of the steering rack. Fig. 2 shows the schematic diagram of a steering mechanism equipped with EPS.

It can be formally subdivided into three subsystems: 1) mechanical steering system consisting of steering wheel, steering column, torsion bar, and steering rack; 2) brush-type direct current (DC) motor, which provides assisting torque; 3) electronic control unit (ECU) with related sensors, such as steering torque, steering angle sensor, and motor current sensor.

The principal mode of operation can be summarized as follows. If driver turns the steering wheel, the torsion bar is twisted and a steering torque is generated, which in turn moves steering rack. The change of the vehicle direction depends on the change of steering rack position, which causes the change of the rack

force. In order to assist driver and provide a good steering feeling, a certain amount of rack force is compensated by the servo force generated by assistant motor.

2. Design of boost curve

The power-assisted characteristic of EPS has curves of sorts. Among the three kinds of power-assisted characteristic curves, the straight-line boost curve is the most widely used one. The assist torque is proportional to the torque of steering wheel. Thus, road feel intensity is a constant, which is convenient to design and adjust the control system easily. The assist torque for straight line type is calculated as follow.

0 0 < Td < Td0

Kr (V) ■ (Td - Td0) Td0 < Td < Tdmax

T T > T

max d d max

Where Tm is assist torque, Td is steering wheel torque, Td0 is steering wheel torque when assist torque begin to generate, Tdmax is the steering wheel torque when maximum assist torque is applied, KV(V) is assist coefficient, Tmax is the maximum torque for steering wheel.

Td0 and Tdmax are related to the feeling of driver. Thus, their values can be obtained by experiment, on the basis of steering portability and road feel. According to Ref [9], assist torque generated for cars when Td0=1.0N.m, while the maximum assist torque Tdmax is 7.0N.m. Based on the model established, the maximum torque for steering wheel was gained through simulation.

1.1. Assist t/rque whee vel/city is 1km/h

The maximum assist torque under 0km/h velocity can be calculated by Eq.2.

^"raJS "^rtïiajiQ1 ''draajc (1)

In which, is the maximum steering resistance force when velocity is Okm/h, which can be

calculated by Eq.3.

In which, f is coefficient of sliding friction, G1 is load for the front axle, P is tire pressure, i is steering gear angle ratio,n is the efficiency of steering gear.

1.1. Assist t/rque whee vel/city is 11km/h, 41km/h, 61km/h,81km/h aed 111km/h

The torque of steering wheel was recorded by rotating uniformly to one side limit position, under the velocity of 20km/h, 40km/h, 60km/h, 80km/h and 100km/h. The maximum value for each velocity represented its Tmax, shown in Table 1.

The assist torque range is 1.0 N.m to 7.0 N.m. Therefore, the assist torque in this range can be obtained by using interpolation methods. The assist torque can be calculated by Eq. 4.

(Td Td 0)(Tmax Td max)

Td max Td 0 (4)

Taking all these values into the above equations, the assist coefficient KV(V) was calculated under different velocities, shown in Table 1.

Hao Chen et al. /Procedia Engineering 15 (2011) 474 - 4-78 Table 1 Maximum steering wheel torque and assist coefficient under different velocities

Velocity

0[km/h]

20[km/h]

40 [km/h]

60 [km/h]

80 [km/h]

100[km/h]

Tmax Kv(V)

28.1 3.52

20.3 2.23

16.7 1.62

11.4 0.73

8.9 0.32

Along with the increase in velocity, the value of assist coefficient was reduced. When velocity was 100km/h, Tmax<Tdmax, there was no need for assist torque.

0.3. Boosting curve

By using polynomial regression, the assist coefficient was obtained.

KV (V) = 3.4754 - 0.0606v + 0.0003v2 (R2=0.9928)

Therefore, the straight line boost curve can be established, shown in Fig.5.

0 < T < T

(3.4754 - 0.0606V + 0.0003V2) • (Td -1) Td0 < Td < Tdi

d d max

Fig.3 showed the assist force curve in different velocities.

3. Simulation and results

Based on the designed straight line boosting curve, simulation experiment was done to illustrate its effect on assist characteristics. Angle step function response experiment was done in ADAMS software. The initial velocity was 80 km/h. The input is 100 degree angle step, which imitated the angle input of steering wheel, shown in Fig.4. Output was the angular velocity of the whole vehicle, which can show the stability of vehicle. Simulation result with and without EPS were shown in Fig.5. As time went by, angular velocity for the curve without EPS system was obviously higher than that with EPS system using the straight line boosting curve. Both reacting time and overshoot value reduced when using straight line boost curve EPS system, which can ensure the dynamic reaction and stability

Fig.3 Straight line boost curve under different velocities

when car was moving.

Conclusion

On the basis of whole-vehicle model, the straight line type boost curve was designed and evaluated in a whole vehicle model condition. Simulation showed that the designed boost curve reduced reacting time and overshoot value, thus ensure the dynamic reaction and stability when car was moving. Further research is under way on application of electronic control with the aim of further improving functions and performance.

Acknowledgement

This research is supported by '085' Knowledge Innovation Project of Universities in Shanghai, Project for Excellent Young Teacher in Shanghai (gjd09012) and Start-up Scientific Research Fund of Shanghai University of Engineering Science(09-12) . The financial supports from above funds and organization are gratefully acknowledged.

References

[1] H. P. Schoener, P. Hille, in: Proceedings of the 31st IEEE Annual Power Electronics Specialists Conference, IEEE Press, Galway, Ireland, Vol. 1(2000), 6-11.

[2] E. J. Haug: Computer aided kinematics and dynamics of mechanical systems. In Basic methods, vol. I (1989) , (Allyn and Bacon, Boston).

[3] M. Kristine, H.Tanaka, and N. Inoue: SAE (2002) .

[4] W. Ren, H. Chen, and J. Song, in: Proceeding of IMechE 2008 Vol. 222(2008), 1265-1269.

[5] C. Chabaan Rakan, L.Y. Wang: JSAE Review Vol. 22 (2001), 435-444.

[6] Takayuki Kifuku , Shun' ichi Wada: Mitsubishi Electric Advance, March (1997) .

[7] A. Zaremba , R. Davis, in: Proceeding of ACC, Seattle , Washington (1995), 4253-4257.

[8] A.T. Zaremba, M.K. Liubakka and R.M. Stuntz: Preprint of the Int Conf on Control of Oscillations and Chaos. St Petersburg, Vol . 3(1997), 453-456.

[9] H. Chen, Y.L. Yang, L.H. Chen: Advanced Material Research Vols.(2010),97-101.

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Fig.5 Angular velocity response curve with and without EPS