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To quickly and accurately predict the thermal error of a ball screw,this paper focuses on the modeling of temperature field of the screw.A theoretical temperature model is achieved based on the heat conduction equation of the screw and the modified boundary value conditions and a parameter α′ which is changed with the temperature are used to improve the model.Then,a model parameter identification process is proposed.The thermal error of the screw is predicted by the model and mechanical thermal deformation theory.Finally,experiments are performed to identify parameters and check up the effect of the model.Result shows that the maximum error between the predicted and the actual temperatures is 0.8℃and the maximum error between the predicted and the actual thermal errors is 3.8 μ m.It concludes that the temperature model accurately predicts the temperature distribution and the thermal error of the screw under a single heat.

The thermal characteristics of ball screws in servo systems were analyzed,then a simplified temperature filed model was established to predict the temperature distributions and variations of the ball screws quickly and accurately.The simplified model can predict the unsteady temperature rising of the ball screws,however,there are big errors when the model was used to predict the steady temperature variations of the ball screws.A new simplified model was built by introducing the factor of time modification in the simplified model.The new model has a good performance in predicting the process of steady temperature,however,there exist big errors when the new mode was used to predict the unsteady temperature rising of the ball screws.Based on the performance of the two models above,a new interval model was also built and the parameters of the new interval model were identified by the LS method.The results show that the error of temperature prediction is less than 0.5 ℃ for different single thermal sources,and less than 0.8 ℃ for the double thermal sources.It concludes that the interval model built in the paper has good performance in predicting the temperature variations of ball screws.