Physically-Oriented Computer Model for the Spur Involute Gear Dynamics
A dynamical model of the gearbox with spur involute mesh is under construction.The main attention is paid to the design technology of the cylindrical bodies elastic contact models.In general, to track geometry of contact implicit equations of algebraic/ transcendental or differential-algebraic type are usually applied.In the case under consideration a contact tracking algorithm takes into account properties of an involute mesh in the most efficient way: direct computational formulae are used to construct the cylindrical surfaces contact patch.These formulae turned out to be the fastest way for tracking of contact and to compute teeth involutes mutual penetration for the normal elastic force computation algorithm.At the same time dynamical models of the bodies involved, gearwheels and gearbox housing, continue to be threedimensional.The known Johnson model is applied for computing the contact elastic normal force.This force is defined as an implicit function of the mutual penetration depth at contact.Regular algorithm to compute the normal elastic force is built up.This algorithm is proved to be convergent.Contact model provides a full possibility to take into account unilateral nature of teeth interacting while meshing.The backlash may arise dynamically for any side of teeth pairs at contact.In particular, the model simulates dynamics for arbitrary regimes of the pinion rotation acceleration/deceleration.The mesh construct is such that for any side (for both the forward and backward contacting) of teeth at contact the mesh ratio is greater than one.The mesh multiplicity for real gears prevents potential jamming for gearwheels while the teeth pairs switching process.Thus our implementation assumes mesh cycles overlapping: new contact arises beforehand the old one will vanish.A detailed analysis of the virtual setup dynamic model is carried out.In particular, the dynamic transmission error is analysed to verify the whole model under development.The experimental results produced independently were used for verifying the model under presentation.These results were obtained by finite-element numeric and physical experiments, and they turned out to be almost identical to the corresponding numeric experiments with the model being built up.In addition, the model is verified using one of an ideal geometrically rigid contact between teeth of the gearwheels.Some details of the model computer implementation using language of objectoriented modeling and simulation are also described.
Ivan Kosenko Ilya Gusev
Department of MechanicsDorodnitsyn Computing CenterRussian Academy of SciencesMoscow,119333,Russia Department of Natural and Engineering Sciences Russian State University of Tourism and Service Mosco
国际会议
上海
英文
1-8
2012-08-26（万方平台首次上网日期，不代表论文的发表时间）