Implementation of the Spur Involute Gear Model on Modelica

A procedure to build up a dynamical model of the gearbox with spur involute mesh is being described. The main attention is paid to the design technology of the cylindrical bodies elastic contact models. To track geometry of contact implicit equations of algebraic/transcendental or differential-algebraic type are being used. At the same time dynamical models of the bodies involved, gearwheels and gearbox housing, continue to be three-dimensional. Analytical computational procedures to obtain gradients and Hessians are constructed for implementing the contact tracking algorithm for the involute guided cylindrical surfaces. 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. A detailed analysis of the virtual setup dynamic model is carried out.