| Summary: | 碩士 === 國立成功大學 === 奈米科技暨微系統工程研究所 === 97 === Most of the positioning errors of ball screws come from thermal deformation. The working temperature of the lubricant renders the lubricant film ineffective, and the temperature would continue to rise. This master thesis (1st part) focuses on lubricating ball screws to study the thermal distribution of nuts through an appropriate heat analyzing model. The heat source model derived from sliding and rolling velocities of a ball’s motion would be the first time such a heat source generated from friction is modeled under lubricating conditions of kinematics. Specifically, we consider the relationship between the temperature and viscosity of lubricant, and include it in our simulated flow chart so as to construct a complete thermal analytic model of nuts. In the second part, we measure the temperature from only three operating conditions and take the root mean square error method with the experimental results and the thermal analyzing model from the first part. According to procedure, we can find the predicting curve of the convection coefficient on the groove, and use it in conjunction with the thermal analyzing model to forecast the temperature distribution of nuts at other revolution speeds.
【1st Part】 A preload was added to improve the rigidity and position accuracy of the ball screws. However, more preload will induce increased friction between moving and stationary elements as well as drastic temperature rise. This results in thermal deformation, one of the major accuracy errors of ball screws. In this thesis, we used FEM to construct a thermal analyzing model of nuts under lubricating conditions. The distinguishing point of this thesis is modeling the heat source using kinematic theory, such as average heat flux, average contact band, etc. The appropriate heat source boundary conditions for constructing a heat source model were derived from sliding and rolling velocities of moving balls. The thermal distribution of the nuts would be obtained from the FEM analysis with appropriate boundary conditions. We then considered the relation between the lubricant’s temperature and viscosity, and included it in our simulated flow chart to build a complete thermal analytic model of nuts.
【2nd Part】The lubricant, especially it viscosity, is very sensitive to the ball screws’ working temperature. The operating and lubricating conditions affect the working temperature rise as well. Therefore, we measured the temperature inside the nuts by embedding six thermocouples in drilled holes filled with silver powder. Using the root mean square error method along with the heat analyzing model and experimental results, we can identify the predicting curve of the convection coefficient on the groove with varying revolution speeds. We can thus forecast the temperature of nuts under other speeds after only measuring three operating temperatures.
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