Jeong-Hoi Koo

Document Type

Thesis - University Access Only

Award Date


Degree Name

Master of Science (MS)

Department / School

Mechanical Engineering


This research work has studies parametric excitation and dynamic stability of a flexible cam-follower system. An automotive valve train is modeled as a single-degree-of-freedom, spring-mass-damper-system. In the analysis, transverse and rotational flexibility of the camshaft with flexibility and damping of the follower are taken into consideration. The governing equation of motion of the given cam-follower system is given by a linear, second-order, ordinary differential equation with time-dependent coefficients, Generally, this class of equations is known as second order Hill’s equation. The time response of the cam-follower system is estimated by the classical 4th order Runge-Kutta method. In addition, the stability analysis based on Hill’s infinite determinant is performed. Phase trajectory plots of the forced response of the system for different angular speed and damping are obtained. In order to evaluate the accuracy of solutions of Hill’s infinite determinant technique, different total numbers if terms in Fourier series are considered in computing a time-dependent variable. Stability charts are presented for a better understanding of the results. For the special case of the cam-follower system, it has been found that the system is stable for low value of the angular speed of the cam. As the speed is increased gradually, a few unstable regions occur. For lower numbers of terms in Fourier expansions, the solutions of Hill’s infinite determinant method are not reliable. In general, damping shows a significant effect on stabilizing the cam-follower system and periodic variables are extremely influential to the stability pf time-varying systems.

Library of Congress Subject Headings

Cams -- Vibration Cams -- Stability



Number of Pages



South Dakota State University