2D thermal characteristic modeling and error prediction of a ball screw accounting for phased contact thermal resistance

Ball screws are key components of feed drive systems in CNC machine tools. Their thermal behavior directly affects machining accuracy and operational stability. Existing thermal models are mainly one-dimensional and usually treat the nut as a stationary heat source. In addition, thermal contact resistance is commonly described using fractal-based models. These simplifications limit the accuracy and applicability of such models in predicting the temperature field and thermal deformation of the screw.In this study, a two-dimensional thermal model is developed in the axial and radial directions. The moving nut is treated as a spatiotemporally varying heat source. Heat conduction within the screw and convective heat transfer at its surface are considered separately. A thermal contact resistance model is also established based on Hertzian contact theory. The contact deformation process is divided into elastic, elastoplastic, and fully plastic stages. The statistical distribution of surface asperities is described using a Gaussian function. The resulting thermal contact resistance is incorporated into the two-dimensional thermal model, which is solved using the finite difference method.Thermal experiments are conducted under different feed conditions to validate the proposed model. The prediction errors at representative temperature measurement points are below 13%. The errors in cumulative axial thermal deformation range from 11% to 14%. The predicted temperature and thermal deformation agree well with the experimental results. These results demonstrate that the proposed model can effectively characterize the transient thermal behavior of ball screws under moving operating conditions.