Modeling and solving of temperature field of screw–nut pair based on geometric error distribution probability

Abstract

Random geometric errors are inevitable during the machining process of the screw raceway, ball and nut raceway, which makes the contact state between the ball and raceway diverse, further leading to the generation of nonequal strength heat sources inside the screw–nut pair. In the past, when studying the temperature field of the screw–nut pair, it was assumed that all the balls were evenly loaded. To achieve more accurate temperature field modeling, the modeling of temperature field of the screw–nut pair based on geometric error distribution probability was studied. First, a quantitative relationship between geometric error and contact angle are established. Second, the axial force generated by ball and raceway with different joint geometric errors is determined when subjected to axial loads. Then, on the basis of geometric error statistics, the relationship between the error probability distribution and the heat source intensity distribution is connected, and the corresponding temperature field is solved by the finite difference method. Finally, the probabilistic temperature distribution theory is verified indirectly by a multi-axis thermal deformation experiment. The probabilistic temperature distribution model shows the dynamic change process of the temperature field with the probability of geometric error distribution and has guiding significance for the temperature field modeling of the screw–nut pairs with different precision. When the joint error presents a rectangular distribution, the maximum intensity heat source will be generated, and the ultimate temperature field will be induced.