The differential steering-by-wire (DSBW) system eliminates the need for steering
gear, i.e., rack and pinion, while preserving a trapezoidal steering structure
with knuckles. This design offers significant advantages for vehicles equipped
with in-wheel motors, primarily due to reduced vehicle weight and the
maintenance of front wheel alignment parameters. However, the noise force acting
on one steering wheel will directly transmit to the other in this differential
steering mechanism due to a lack of mechanical connection to the vehicle body
through the steering gear, which increases the risk of steering wheel shimmy
(SWS). This article qualitatively analyzes the shimmy characteristics of the
steering wheel based on a three-degrees-of-freedom (3-DOF) DSBW shimmy model
established using Lagrange’s equation and the Hopf bifurcation theorem. The
results indicate the vehicle range that this steering system will shimmy, and
the maximum steady amplitude is [4.80 m/s, 31.57 m/s] and 0.1516 rad,
respectively, much bigger than those of the traditional steering systems
incorporating steering gear. Key parameters, such as wheel weight, half the
length of tire patch, and caster angle, are found to substantially affect the
shimmy characteristics of the steering system. Furthermore, the stiffness and
damping coefficients of the tie rod influence the phase offset of the steering
angle between the left and right wheels, whereas the effects of other
parameters, including the stiffness and damping coefficients of the suspension,
are relatively minor.