Degradation reliability modeling for two-stage degradation ball screws

The performance of ball screws degrades with two-stage features due to the deteriorating inner mechanism and environmental stress, which lowers the positioning accuracy of the ball screws. It thus affects the accuracy of computer numerical control machine tools. However, no research has been carried out on the degradation reliability for ball screws and current studies usually treat the performance degradation of ball screws as a deterministic, single-stage degradation process, ignoring the randomness and two-stage features in the degradation progress. To this end, we firstly formulated a framework of degradation reliability for ball screws, and then established a two-stage performance degradation model with eight unknown parameters. To estimate the unknown parameters, we proposed a two-phase, expectation-maximization estimation method. Finally, we established a degradation reliability model based on the degradation test data and validated the model through experimental data, which shows the model can capture the real-degradation behavior of ball screws.