Comparison of the PoF Pf for different methods.

The harmonic drive is a new type of high-efficiency gear transmission system, widely used in precision machinery, robotics, and aerospace due to its compact structure and high transmission accuracy, and the multiple uncertain parameters in it will seriously affect its transmission performance. In this paper, the limit state functions for multiple failure modes of harmonic drive are established based on the stress-strength interference theory. Considering the hybrid uncertainties in the harmonic drive, the modified chaos control method and multiplicative dimension reduction method are coupled to solve the probabilistic and interval reliabilities continuously. The proposed model is simple and easy to implement, and the failure probabilities of different failure modes of harmonic reducers can be accurately and quickly evaluated. Furthermore, the differences in the influence of strength on different failure modes are demonstrated by the results of hybrid uncertainty analysis.