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Abstract
In this paper, a torsional dynamic model of multi-stage idler spur and helical gears is presented which combines mesh internal excitations and external forcing terms such as time-varying external torque. Each contact line in the various base planes is discretized in elemental cells which are all attributed a time-varying mesh stiffness element and initial separation to account for tooth shape deviations from ideal involute flanks. The mesh stiffness functions are estimated from the formulae of Weber & Banaschek and their relative phasing is determined based on gear geometry and relative positioning. The corresponding non-linear differential system is solved by combining a Newmark’s numerical time-step integration scheme and a normal contact algorithm. A number of simulation results are presented on the combined influence on dynamic tooth loads of errors and shape deviations along with external excitations.
Highlights
The objective of this paper is to present a simplified torsional model that can simulate dynamic tooth loads on several idler gears in the presence of time-varying mesh stiffness functions and tooth shape modifications
A simplified torsional dynamic model of multi-stage gears has been presented which can account for N stages with any relative orientation of their lines of action
The results highlight the influence of the power circulation in multi-mesh gear units along with the contributions of external excitations such as periodic torques on dynamic tooth loads and critical speeds
Summary
The objective of this paper is to present a simplified torsional model that can simulate dynamic tooth loads on several idler gears in the presence of time-varying mesh stiffness functions and tooth shape modifications. The main contribution is the analysis of the influence of power circulation when several constant or time-varying torques are applied which have been rarely tackled in the literature. Unlike the majority of the models, transmission errors are one of the results of the simulations and dynamic responses are derived by the simultaneous solution of the instant contact conditions on the teeth and the equations of motion
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