Linear dynamic analysis of multi-mesh transmissions containing external, rigid gears

Abstract

This paper extends the multi-body dynamics modeling strategy for a gear pair [6] to multi-mesh transmissions with external, fixed center, helical or spur gears. Each gear is modeled as a rigid body with six degrees of freedom. A multi-dimensional, position-dependent formulation is used to describe the gear mesh stiffness which is assumed to be distributed along the line of action. A simplified model of the shaft-bearing subsystems is included since the focus of this study is on the gear dynamics. Excitation to the system is considered in the form of either external torque pulsation or internal static transmission error. The governing equations are linearized to yield a formulation with position or time-varying coefficients (LTV). Subsequently, three examples of linearized time-invariant (LTI) transmission systems are solved, and eigensolution predictions of the multi-body dynamics model compare very well with finite element calculations. Then the periodic response of a non-unity gear pair system is studied in depth. New results including a comparison between LTI and LTV models are presented. It has been demonstrated that both time and frequency domain solutions can be efficiently and accurately constructed by using the multi-term harmonic balance method, provided that several shaft and gear mesh harmonics are included.