Time-varying reliability prediction modeling of positioning accuracy influenced by frictional heat of ball-screw systems for CNC machine tools

Thermally induced elongation of a screw is the primary cause of deterioration in the positioning accuracy of half-closed-loop screw systems in machine tools. The failure mode of ball-screw feed-drive systems in relation to the positioning accuracy is defined as the response error of the carriage exceeding the axial tolerance. It is still challenging to accurately predict the thermal errors using conventional methods because the randomness of the influencing factors is not considered. This paper presents an improved random thermal network model subjected to dynamic thermal excitation for calculating real-time transient temperatures of ball-screw systems. Furthermore, a time-varying reliability model is proposed for estimating the gradual reliability of the thermally induced positioning accuracy of ball-screw systems with random thermal boundary parameters using the random thermal network. A ball-screw system of a computerized numerical controlled lathe is used as an example to show the practical application of the proposed model. Repeated experiments demonstrate the accuracy retaining ability and robustness of this method. This work provides the theoretical and practical method for real-time monitoring of the positioning accuracy reliability index for ball-screw systems and it has high accuracy considering the random parameters.