A New Correlation Equation for Calculating the Frictional Torque of the Nut at Different Feed Velocities and Nut Tempera
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International Journal of Precision Engineering and Manufacturing https://doi.org/10.1007/s12541-020-00448-z
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A New Correlation Equation for Calculating the Frictional Torque of the Nut at Different Feed Velocities and Nut Temperatures Tzu‑Chien Kuo1 · Yih‑Chyun Hwang2 · Wen‑Hsin Hsieh3 Received: 3 March 2020 / Revised: 11 November 2020 / Accepted: 24 November 2020 © Korean Society for Precision Engineering 2020
Abstract Among the errors in precision machining, thermal error has been recognized as the most significant error. The heat of the nut in the feed drive system plays an important role in the thermal error generated by the feed drive system. To better estimate and further understand the increase in temperature and thermal deformation of the ball screw during operation, a new correlation equation for the frictional torque of the nut is proposed and determined in this study for the calculation of the frictional torque of the nut and the heat generated by the nut at different feed velocities and nut temperatures. In this study, a set of devices for measuring the frictional torque of the nut under different feed velocities and different nut temperatures is designed and established. Various experimental conditions are designed to measure the frictional torque of the nut at different feed velocities and different nut temperatures to establish a correlation equation for the frictional torque of the nut. In addition, for further confirmation, the method for measuring the frictional torque of the nut used in this study is compared with the method using a handheld digital force gauge. The correlation equation for the frictional torque of the nut established in this study is based on the LuGre model and the formula of the frictional torque due to the viscosity of the lubricant of the bearing at different temperatures. The results show that the root-mean-square error between the frictional torque of the nut calculated by the correlation equation and that measured experimentally is 0.0301 N-m, indicating that the correlation equation for the frictional torque of the nut proposed in this study is accurate and feasible. Keywords Correlation equation · Frictional torque of the nut · Feed velocity · Nut temperature
1 Introduction In the feed drive systems of various precision processing machines, a ball screw is widely used because of the high efficiency, good rigidity, cost-effectiveness, and long life of this system [1–3]. In the design and operation of the ball screw, different levels of preload are usually applied to the nut of the ball screw to eliminate backlash and provide the required rigidity for dynamic processes. The level of the preload will affect the life of the ball screw. In general, the expected service life of the ball screw can be estimated from * Wen‑Hsin Hsieh [email protected] 1
Department of Mechanical Engineering, National Chung Cheng University, Chiayi 621, Taiwan, ROC
2
HIWIN Technologies Corp, Taichung 408, Taiwan, ROC
3
Department of Mechanical Engineering and Advanced
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