Derivation of Cam Function to Suppress the Surging of Non-damped Valve Spring from the Simulation of 2DOF Bead-spring-chain System

To reduce surging of a valve spring in a reciprocal engine, we design cam functions that simultaneously damp two natural frequencies of the spring by modeling it into a series undamped 2DOF bead-spring-chain system. The cam functions are defined from a finite-time-settling function termed vibration manipulation function (VMF), which consists of half-integer trigonal functions in an arbitrary rising time. The obtained analytical conditions of the valve spring decide specific rising times of the cam. In simulations, we ascertained simultaneous suppression of the residual vibrations of two natural frequencies during translational motions of the 2DOF valve spring lifted with a designed two-dwell cam.