AUTOMOBILE STEERING SYSTEM

1.INTRODUCTION

Steering systems of heavy vehicles were originally designed for manual driving. The

inertia and the aligning torque of the steering system are large for heavy vehicles,

and the reaction forces from the road are much larger when the vehicle is parked than

driving. A power assist mechanism is added to help the driver to be able to steer

equally at ease both in ordinary driving and parking. Therefore, the assist level of the

hydraulic system is deliberately designed to be different for different driving

conditions and driving speed, and for varying drivers’ intention. The drivers’

intention is arameterized by the torsion bar torque.

Steering Subsystem

A schematic diagram of the steering system of the experi- mental vehicle,

a tractor–semitrailer, is shown in Fig. 2. The steering system consists of

handwheel, steering column, power assist unit, steering linkages and front

wheel assembly. The steering linkages connect the hydraulic power assist

unit to the front wheel assembly. Turning of the handwheel by an angle

results in turning of the front wheel by an angle . The hydraulic assist

mechanism provides a torque amplification thus making the driver’s task

of steering easier. There are mainly two types of hydraulic power assisted

steering systems: recirculating ball type and rack-and-pinion type. The

rack-and-pinion type system is more precise than the recirculating ball

type system but provides lower steering gain. Therefore, it requires more

effort from the driver. So far, it is the most widely used type on passenger

cars. On the other hand, the recirculating ball type system has an ad-

vantage of providing larger steering gain in a more compact space with

relatively low friction level. Its applications are usually lim- ited to trucks

and large cars.

Fig. 2. Schematic diagram of steering subsystem of freightliner tractor.

Steering Actuator and Sensors

The steering system of the experimental vehicle has been ret- rofitted with an

electric steering actuator custom developed by the NSK Corporation. It is mounted

on the steering column just below the handwheel in order to take ad- vantage of the

torque boost provided by the hydraulic assist mechanism, and to reduce the

compliance between the hand- wheel and the steering column. The actuator consists

of a cur- rent controlled dc motor, a clutch, and an electric control unit (ECU). The

ECU is a motor current controller which provides current proportional to the

command voltage. The clutch can be turned on and off by a command signal from

the ECU. There- fore, it forms one of the active components of the safety system.

The steering actuator has two sensors, an encoder and a po- tentiometer. The

potentiometer measures the absolute rotation angle of the steering column and the

encoder measures the rela- tive rotation angle of the steering column with higher

resolution and lower measurement noise.

A front wheel angle sensor is installed on the pitman arm, the output of the

hydraulic assist mechanism whose rotation angle is proportional to the steering

angle. The sensor consists of an off-the-shelf potentiometer and a home-made

aluminum sector with constant radius which converts angular displacements to

linear ones.

MODELING OF STEERING SYSTEM

A physical model is derived to analyze the dy- namical characteristics and

structure of the steering system.

The input to the steering system is the voltage command to the ECU.

ECU regulates the current in the dc motor to a value- proportional to the

command signal. Assuming that the motor constant is a fixed value, the

steering command is equivalent to the motor torque, tr . For this reason,

the voltage command to the ECU is referred as the torque command. Fig.

4 represents a schematic diagram of the steering system and Fig. 5

shows free-body diagrams of the upstream mass and downstream mass.

Fig. 4. Two-mass model of steering subsystem.

Fig. 5. Free-body diagrams. (a) Upstream mass. (b) Downstream mass.

θr : the rotation angle of the steering column

θh : the rotation angle of the input shaft of the hydraulic power assist unit

tr : the motor torque

tt : the torsion bar torque

Kt : the spring constant

Js: moment of inertia of the upstream mass

Ds: damping coefficient of the upstream mass

Jw the moment of inertia of the downstream mass

Dw : damping coefficient of the downstream mass

tf : the nonlinear friction existing in the downstream mass

The steering column is connected to the hydraulic assist unit by a torsion bar. It is

the only linear element of the vehicle steering subsystem.

The equation of motion for the upstream mass is given by

Let η be the ratio of the rotation angles of the input to output shafts,

Then,

tmech: the torque contributed by the direct mechanical connection

thydr : the hydraulic assist torque

ψ :static nonlinear boost curves

V: the vehicle’s traveling velocity

Therefore , tw , the input to the downstream mass.

and, the equation of motion of the downstream mass is given by

tf is position dependent and the aligning torque is modeled as linear spring,

Kw: the stiffness between the tire and the ground

Summarizing , the model of the steering subsystem is represented by the

following two differential equations:

and

Linearization of the Physical Model

First, we linearize the boost curve for each speed as

Second, we ignore the position dependent friction term, tf. With these simplifications,

the equations of motion for the steering subsystem can be reformulated as

and

Taking Laplace transformation of linear equations, we get

and

Therefore, we have

Then, eliminate Θ w(s) ,

and

By substituting θs given in equations, we obtain

The transfer function of the system is

Θ w(s)Θ s (s )

= ❑❑

Open-Loop Experiments and Nominal Linear Model

Figure, Control structure of steering subsystem.