Dynamic Analysis of a Radius-varying Rotating Pseudo-rigid Body
Date Issued
2006
Date
2006
Author(s)
Hsu, Shih-Ling
DOI
en-US
Abstract
In this dissertation, the problem of varying radius of a rolling wheel is
investigated. In most analysis of vehicle dynamics, the wheels are assumed to
be rigid with fixed radius of rotation; however, it has been observed that the
rolling radius of wheels is not a constant during the motion but a function of
velocity. To deal with the arising nonlinear nonholonomic constraints, the
Chetaev condition is applied to derive the equation of motion. Nevertheless,
by comparing the set of equations with that derived from Lagrange's equation,
we notice that the body may not be assumed to be rigid. A continuum model
needs to be adopted. Instead of the elastic or viscoelastic body, the
pseudo-rigid model is chosen here which allows global deformation. A
pseudo-rigid motion is simply a body with a space-wise constant deformation
during motion such that the deformation gradient tensor is only a function of
time. The resulting governing equations form a system of ordinary differential
equations, which are easier to manage.
To study the system composed of various types of bodies interacted with each
other, the Principle of Virtual Power is adopted to derive the variational
equations for both discrete and continuous systems. In addition, the
variational equation for a system consisting of rigid bodies and pseudo-rigid
bodies is deduced. The variational equation for rigid body shall be used to
study the motion of a rolling wheel subject to nonlinear kinematic
constraints, and the same problem is discussed by the method of Lagrange's
equation. We further apply the principle to establish the equations of motion
for a pseudo-rigid body with the constraint of rolling without slipping along
a line. The stability of a simplified planar motion is discussed by
linearizing the original nonlinear dynamic system. The stable solutions of
steady motion are obtained and applied to analyze the effect of a
three-connected bodies system.
Based on the previous results of a pseudo-rigid body for a wheel, we derive
the equations of motion for a vehicle consisting of one platform and two
wheels. In the system, two wheels are assumed to be either rigid or
pseudo-rigid, and the equations of motion are derived for different cases. The
torque required for a steady motion is computed for both cases numerically,
which demonstrates the effect of pseudo-rigid body. From the numerical
computation, it is seen that to maintain the same steady motion with no
dissipation, a pseudo-rigid body needs larger applied torque to rotate than
that for a rigid body. The additional consumption may be useful in the design
of the vehicle in the future.
Subjects
可變半徑
擬剛體
Radius-varying
Pseudo-rigid Body
Type
thesis
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