Real-time estimation of the temperature distribution and expansion of a ball screw system using an observer

Thermal deformations of ball screws directly affect the positioning errors of machine tools. In order to calibrate the thermal deformations of ball screws, an accurate estimation of the whole temperature field of the screws is required. However, it is extremely inefficient and almost impossible to acquire the whole temperature distribution by measuring the temperatures of every point. Therefore, a temperature estimator, which can estimate the whole temperature field from temperatures of just a few points, is required. In this paper, one-dimensional heat transfer problems are formulated under concepts of modal analysis and state-space design. Then an observer is designed to estimate the intensity of a heat source and the whole temperature field in real time. The reliability of the estimator is confirmed through comparisons between solutions from the proposed method and those of exact solutions. The proposed method is applied to the estimation of the intensity of the heat source and the temperature distribution of a ball screw system. It is confirmed that the proposed method estimates the whole temperature distribution of a ball screw system well without noise and time delay.