On Analytical Evaluation of Gear Dynamic Factors Based on Rigid Body Dynamics

Abstract

This paper proposes an initial step to rationalize the dynamic factor calculation and bring it under the control of the laws of mechanics. The theory is straight forward. The concept of mathematical scaling is utilized to simplify the system dynamics’ formulation. The rigid body dynamics accounts for the gear dynamic tooth loads resulting from the prescribed transmission error of each gear step—including the artificial ones. The latter converts a lumped-mass-elastic system into a rigid-bodies-transmission-error system subjected to the solution of the rigid body system dynamics according to Newton’s law. The entire concept of the solution has been implemented into a FORTRAN program approximately 600 statements in length. The results obtained through computer simulation of various test cases demonstrate the potential and effectiveness of the proposed concept. Contrary to the current practice of grossly ignoring the inertial and system effects, this paper has taken all these important factors into account. The transmission-error-induced acceleration is approximated by the second-order time derivative of one of the cubic spline curve-fitting methods. The approach is cost effective and numerically satisfactory. The model can be further improved to reduce the extent of basic assumptions, or to increase the number of conditional constraints without losing economical attractiveness.