Vibration of a Flexible Follower in a Cam Mechanism with Time-Dependent Boundary Effect

Abstract

A vibration analysis of a flexible follower in an oscillating follower cam system undergoing a rise-dwell-fall-dwell (RDFD) motion is performed. Owing to the time-dependent boundary effect caused by considering simultaneously the axial and the lateral displacements of the follower, two geometric constraints are formulated and added to Hamilton’s principle to establish the vibration equation of the motion of the follower. The coupled axial and lateral vibration of the flexible follower has been studied for the first time. The fast Fourier transform (FFT) spectrum generated from the time history is used for parametric studies. The numerical results of the present study show some new findings. The major spectral peaks for the lateral follower response locate at the low frequencies of 1 Ω, 3 Ω, 5 Ω, and 7 Ω and the high frequency near the fundamental natural frequency where Ω is the cam speed. The largest peak locates mostly at the frequency of 3 Ω. For the ascending and descending motions of the follower RDFD motion, three types of cam profiles are designed. Important new results are found: although the three cam profiles nearly overlap, the vibration results of the follower are quite different. By using a modified sinusoidal acceleration motion, the magnitude of the main lateral peak at low frequencies is minimized. The lateral peak amplitude near the fundamental natural frequency of the follower is the smallest when the cycloid displacement motion is adopted.