Torsional Response of a Gear Train System

A gear train system can be represented by a spring-mass system having many degrees of freedom. The transfer matrix technique [1, 2] has been applied to give the static and dynamic torsional response of a general gear train system. The method develops, directly from drawings, all equations necessary for the solution of the problem. Effects that can be included in the formulation are the gear tooth stiffnesses, gear web stiffness, nonuniform cross section of shafts, external torques, special types of joints, general boundary conditions, and multi-geared branched systems. A general computer program has been written to obtain numerical solutions. The experimental evaluation of a gear train system has been conducted using an electrohydraulic exciter and an Automatic Mechanical Impedance Transfer Function Analyzer System (TFA). The spindle shaft of a non-rotating, preloaded gear train system is excited by applied forces in the bending and torsional directions. The computed torsional natural frequencies and mode shapes correlate at low frequencies. At higher frequencies, there is a coupling effect between the motion in torsion and transverse motions. The presented analytical and experimental technique may be a practical method to evaluate the torsional response of a gear train system.