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Modeling of the vehicle shimmy system with consideration of clearance of the steering linkage mechanism

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Abstract

The mechanism of vehicle shimmy has been paid much attention in the past decades. In which, the clearance of the steering linkage is usually neglected. Yet the prior research of the authors proved that the clearance can make great effects on the dynamic performance of the linkage. Therefore, based on nonlinear dynamics, a six-DOF dynamic model of vehicle shimmy system with consideration of the clearance was established. In which, the nonlinearity due to clearance of the movement pair in steering mechanism was taken into account. Numerical examples showed that the clearance of the movement pair could make great effects on the dynamic behavior of the vehicle shimmy system, and it is one of the key factors leading to chaos motion of the shimmy system, which provided theoretical basis for vehicle shimmy control.

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Abbreviations

I t :

Rotational inertia of the front wheel about the king pin

B :

track front

I x :

Rotational inertia of the front wheel about the radial axis through its mass center

I f :

Rotational inertia of the front axle about the tramping axis

I u :

Rotational inertia of the structures above the suspension about the rolling axis

i :

Rotational inertia of the front wheel about its rotational axis

J 1 :

Rotational inertia of the track rod about its mass center

m :

Mass of the track rod

m w :

Mass of the vehicle

m t :

Mass of the wheel

K tv :

Vertical stiffness of the tire

K s :

Lateral stiffness of the tire

K v :

Equivalent angular stiffness of the steering tie rod about the king pin

K x :

Stiffness of the suspension

C t :

Equivalent damping coefficient of the wheel rotating about the king pin

C v :

Equivalent rotational damping coefficient of the steering tie rod about the king pin

C x :

Damping coefficient of the suspension

L :

Distance between the intersection of the king pin extension and the ground with the interface of the wheel

n :

Pneumatic trail

V 1 :

Velocity of the mass center of the track rod

α :

Wheel caster

β :

Contact angle at the clearance of the movement pair

F1, F2:

Lateral force of the left front wheel and right front wheel

F x , F y :

The impact force at the clearance

e x , e y :

Eccentricity at the joint with clearance

R :

Rolling radius of the tire

R 1 :

Radius of axle pin

F Ax , F Ay :

Reactive force of left tie rod arm on steering tie rod

l :

Length of the steering tie rod

l1, l2:

Length of the left tie rod arm and the right tie rod arm

θ1, θ2:

The left and right wheel angle

r :

Radius clearance at the joint

K :

Contact stiffness at the joint

f :

Friction coefficient of the contact surface of the joint

A :

Distance between the two springs of the front suspension

γ :

Side slip angle of the front wheel

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Authors and Affiliations

  1. School of Mechanical and Automotive Engineering, Hefei University of Technology, 230009, Hefei, Anhui, China

    Jian-Wei Lu & Jue Gu

  2. School of Mechanical and Aerospace Engineering, Nanyang Technological University, 639798, Singapore, Singapore

    Meng-Jun Liu

Authors
  1. Jian-Wei Lu
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  2. Jue Gu
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  3. Meng-Jun Liu
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Correspondence to Jian-Wei Lu.

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Lu, JW., Gu, J. & Liu, MJ. Modeling of the vehicle shimmy system with consideration of clearance of the steering linkage mechanism. Meccanica 45, 53–61 (2010). https://doi.org/10.1007/s11012-009-9223-1

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  • DOI: https://doi.org/10.1007/s11012-009-9223-1

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