Study on the relationship between machining errors and transmission accuracy of planetary roller screw mechanism using analytical calculations and machine-learning model

Correlation between machining errors and transmission accuracy of planetary roller screw mechanism (PRSM) plays an important role in tolerance design. In this study, analytical calculations, machine learning, and experimental verification are utilized for exploring the internal correlation between the machining errors and the transmission accuracy of the PRSM. A multi-roller meshing transmission error model is established, which comprehensively considers the eccentric error, nominal diameter error, flank angle error, and cumulative pitch error of the screw, roller, and nut. The importance coefficients of various machining errors on the transmission error are determined using the random forest algorithm. A genetic algorithm-back propagation neural network algorithm-based method is utilized for training the dataset generated via analytical calculations. The results show that the proposed analytical calculation model reflects the alternate meshing characteristics of rollers during the PRSM motion, providing a more accurate prediction of the transmission error than the existing prediction methods. For an actual mean travel deviation, the most significant machining error is the cumulative pitch error of the screw, whereas for the actual bandwidth of useful travel, the most significant machining errors are the eccentric errors of the screw and nut. The proposed prediction formulae for transmission error considering the essential machining errors illustrate reasonable prediction accuracy, with an average error of 10.63% for the actual mean travel deviation and 14.27% for the actual bandwidth of useful travel compared with the experiments, which can effectively support the direct design of PRSM tolerance in engineering practice.