Multibody Dynamics Model of the Cycloidal Gearbox, Implemented in Fortran for Analysis of Dynamic Parameters Influenced by the Backlash as a Design Tolerance

Abstract In this study, dynamical parameters of the cycloidal gearbox working at the constant angular velocity of the input shaft were investigated in the multibody dynamics 2D model implemented in the Fortran programming language. Time courses of input and output torques and forces acting on the internal and external sleeves have been shown as a function of the contact modelling parameters and backlash. The analysis results in the model implemented in Fortran were compared with the results in the 3D model designed using MSC Adams software. The values of contact forces are similar in both models. However, in the time courses obtained in MSC Adams there are numerical singularities in the form of peaks reaching 500 N for the forces at external sleeves and 400 N for the forces acting at internal sleeves, whereas in the Fortran model, there are fewer singularities and the maximum values of contact forces at internal and external sleeves do not exceed 200 N. The contact damping and discretisation level (the number of discrete contact points on the cycloidal wheels) significantly affect the accuracy of the results. The accuracy of computations improves when contact damping and discretisation are high. The disadvantage of the high discretization is the extended analysis time. High backlash values lead to a rise in contact forces and a decrease in the force acting time. The model implemented in Fortran gives a fast solution and performs well in the gearbox optimisation process. A reduction of cycloidal wheel discretisation to 600 points, which still allows satisfactory analysis, could reduce the solution time to 4 min, corresponding to an analysis time of 0.6 s with an angular velocity of the input shaft of 52.34 rad/s (500 RPM).