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Mathematical modeling and simulation of high-speed cam mechanisms to minimize residual vibrations

Mathematical modeling, simulation, and optimum design of equivalent one degree-of-freedom high-speed cam mechanisms used for internal combustion engines are investigated in this study. The dynamic equation governing the dynamic behavior of a typical high-speed cam–follower system of an internal combustion engine has been simplified using dimensionless analysis method. The resulting model is then used to find the optimum cam shape to reduce the residual vibrations in the follower part of the system. The Lagrange multipliers method is utilized to minimize the sum of squared error (deviation from the cam profile) over one period under continuity and smoothness constraints.