Sensitivity analysis for the tolerancing of gear profiles with stochastic errors

This paper introduces the concept of the ‘sensitivity chart’ as an applied tool to evaluate the effect of profile modifications on the load factor of gears with stochastic indexing errors and to find optimal solutions. The embedded ability to evaluate different solutions simultaneously also allows the analysis of the sensitivity of technical designs to variations in the manufacturing parameters, from which the term ‘sensitivity chart’ is derived. To build a sensitivity chart, the exact geometry of tooth meshing is incorporated into a dynamical non-linear model of the considered gear system, seamlessly embedding the effect of pitch errors, tooth separation, degree-of-freedom coupling, and profile modifications. Various possible combinations of error distributions and profile corrections are applied to the gear model, which is simulated dynamically to calculate the load factor. The sensitivity charts are compiled by post-processing and interpolation of this simulation data.