Automotive Cam Profile Synthesis and Valve Gear Dynamics from Dimensionless Analysis

The Fourier Series is used in the development of a continuous function to express cam lifts and accelerations. The mathematics is extended to generate an acceleration response curve which includes the effect of valve linkage flexibility. When a standardized acceleration diagram is established, the variables can be summarized in dimensionless design parameters. Design charts for a parabolic-shaped acceleration curve, suitable for automotive applications, are included. The variables listed as dimensionless parameters include lift, half angle of event, ramp velocity, flow factor, maximum positive acceleration, maximum negative acceleration, acceleration positive pulse width, minimum tappet diameter, base circle diameter, and minimum radius of curvature. Methods of profile synthesis for unsymmetrical half angles of event and matching of profiles to flexible linkages are explained. A dimensionless design chart for valve springs is also included.