On the dynamic response and instability in flexible cam-follower mechanisms, including the moment-stiffening phenomenom
Equivalent single- and multi-degree-of-freedom models have been developed for a flexible cam-follower mechanism. Both transverse and axial flexibility of the follower and return spring, as well as transverse and torsional flexibility of the camshaft have been included. In the multi-degree-of-freedom model, the camshaft is assigned two rotational degrees of freedom, one at the cam and the other at the flywheel. The follower mass has a degree of freedom in the axial as well as the transverse direction of the follower rod. The analytical models take into account the fluctuating camshaft angular speed as the input excitation. The governing equations of motion, with time-periodic coefficients, have been systematically developed. The return spring was believed to influence the follower response in ways previously not understood, necessitating a closer examination of its kinematics of deformation. An analytic expression for the transverse stiffness of a closed-coiled helical spring with an axial, transverse and end moment, has been derived. A closed-form expression is obtained when the ends are constrained to remain parallel. Such constraints, and the varying transverse flexibility of the return spring with axial deflection led to a newly described phenomenon of moment stiffening. A sideways tracking of the follower roller on the cam surface is observed, in an experimental cam-follower mechanism, for both the rise and return motions of the follower. It results from the camshaft deflection, causing the cam to exert a thrust load on the follower roller. The tracking gives rise to erroneous experimental cam rise and return profiles. Follower mass responses for Rise-Return-Rise and Rise-Dwell-Return-Dwell follower motion event types, and simple harmonic and polynomial cam rise and return profiles, have been investigated. The multi-degree-of-freedom model, unlike the single-degree-of-freedom model, uniformly predicts the experimental follower mass response accurately for both follower motion events. The overall frequency and amplitude contents of the analytical and experimental responses, noticeably during the top and bottom dwell periods, compare very favorably. Parametric stability charts are presented for both follower motion event types as well as the two cam rise and return profiles considered.
Midha, Purdue University.
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