Analysis and optimization for generated axial force of a drive-shaft system with interval uncertainty

In the design of a drive-shaft system, the magnitude of the generated axial force (GAF) by the tripod joint constitutes an important design goal. Owing to the uncertainties associated with the drive-shaft system operating environment, and dimensional and material parameters, the GAF exhibits considerable uncertainty. In this study, a comprehensive model of a drive-shaft system is formulated together with interval uncertainties using Chebyshev polynomials for an accurate and efficient analysis of the GAF. The input torque, the articulation angle, the angular position of the drive-shaft, the pitch circle radius (PCR) of the tripod joint, and the friction coefficient between the rollers and the tracks that affect the GAF are taken as interval variables. The upper and lower bounds (ULB) of the proposed GAF model are subsequently established considering the interval uncertainty parameters using the vertex method, so as to assess the influence of GAF on the drive-shaft system response. The results suggest that the vertex method is far more computationally efficient and accurate for establishing the ULB of the GAF compared with the Monte Carlo method. The proposed model together with the vertex method is used to identify favorable drive-shaft design parameters through minimization of the upper bound (UB) response considering the uncertainty of the design and operating parameters. The effectiveness of the proposed method for the analysis and optimization of the interval uncertainty of the GAF is demonstrated through numerical examples and experiments. It is concluded that the interval uncertainty analyses and design optimization are essential in order to ensure that the UB of the GAF remains within the specification under interval uncertainties.