Axial-Transverse Coupled Vibration Analysis of a Swinging Roller-Follower CAM Due to Flexible Follower Rod

In this paper, the equations of motion of a swinging roller-follower cam for rise-dwell-fall-dwell (RDFD) case are derived by applying Hamilton’s principle and the assumed mode method. The cycloidal displacement (sinusoidal acceleration) motion is used to describe the rise and the fall motions of the follower. The corresponding cam profile is determined using theory of envelopes. The follower rod is considered to be flexible and modeled as a Rayleigh beam including axial and transverse deflections. The roller rolls in the cam groove. The contact point between the cam and the roller is an unknown point though it is restrained in the cam groove. The contact point position depends not only on the rigid-body motions of the cam system but also the flexible vibrations of the follower rod. Two geometric constraints are formulated to restrict the roller motion and added to the Hamilton’s principle with Lagrange multipliers. The numerical integration method is applied to solve the non-linear differential-algebraic equations to obtain the vibration responses of the cam system. The numerical results for the studied cases show that the follower vibrates significantly especially for the case of high rotation speed of cam. The follower still vibrates during the dwell interval. The parameter effects including the cam rotation speed, the follower length and cross-sectional radius, and the total rise on the vibration behavior have been investigated.