On Methods for Evaluation of Parametric Stability and Response of Flexible Cam-Follower Systems


Pisano, A. and McCarthy M. and Derby, S.


A method to study parametric stability of flexible cam-follower systems is developed. This method is applied to an automotive valve train which is modeled as a single-degree-of-freedom vibration system. The inclusion of the transverse and rotational flexibilities of the camshaft results in a system governed by a second-order, linear, ordinary differential equation with time-dependent coefficients. This class of equations, known as Hill's equations, merits special notice in determination of the system response and stability. The analysis includes development of the equivalent model of the system, derivation of its equation of motion, and a method to evaluate its parametric stability based on Floquet theory. A closed-form numerical algorithm, developed to compute the periodic response of systems governed by second-order, linear, ordinary differential equations of motion with time-dependent coefficients, is utilized. The results of this study are presented in a companion paper in the forms of parametric stability charts and three-dimensional stability and response charts.

Meeting Name

21st Biennial Mechanism Conference


Mechanical and Aerospace Engineering

Keywords and Phrases

Equations of Motion; Mathematical Models; Mathematical Techniques - Differential Equations; Shafts and Shafting; Vibrations

Document Type

Article - Conference proceedings

Document Version


File Type





© 1990 American Society of Mechanical Engineers (ASME), All rights reserved.

Publication Date

01 Jan 1990

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