熱變形是影響定位精度誤差之主要來源，其中潤滑油的工作溫度也將影響油膜是否失效及後續的溫度是否會持續上升，【第一部分】針對含潤滑效應的滾珠螺桿，藉由滾珠螺桿運動學之理論分析，求解滾珠的滾動及滑動速率去建構合理的熱源模型；特別考慮潤滑劑之黏溫效應，將此加入疊代流程之中，完成螺帽整體之熱分析模型；【第二部分】藉由三個操作條件之溫度量測，將此與模擬資料庫作最小均方根誤差，找出軌道等效熱對流係數之預測曲線，並搭配第一部分之熱分析模型，進而預測不同螺桿轉速下之螺帽溫度分佈。

【第一部分】為了增加滾珠螺桿系統之定位精度與整體剛性，會以增加預負荷來達成目的；但是過大的預負荷會造成摩擦力上升，並且導致溫度之攀升，造成的熱變形反而成為精度誤差之主要來源。因此本文以有限元素法(FEM)針對填充潤滑劑之螺帽，進行探討其熱分析。有別於其它與溫度相關之研究，本文藉由滾珠螺桿運動學之理論分析，推導出平均熱通量、平均接觸帶…等模擬參數，以建構螺帽軌道內的熱源模型，並且考慮潤滑劑之黏溫效應，加入疊代流程之中，建立起螺帽的整體熱分析模型。

【第二部分】潤滑油對於工作溫度非常敏感，工作溫度也由於不同操作條件及潤滑條件而有所不同。因此本文在螺帽上鑽孔 (僅離螺帽牙溝頂端約0.56 mm)埋入熱電偶，再以銀粉填滿孔洞，以量測螺帽內部之「工作溫度」。藉由螺帽之實際量測溫度輔以第一部分熱傳導分佈之數值模擬分析模型，利用最小均方根誤差之方法，找出隨不同轉速變化下的軌道熱對流係數之預測曲線，因此藉由第一部分之熱分析模型與對流係數之預測曲線，即可預測不同轉速下之螺帽溫度分佈。

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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