垂直傳動雙螺帽預壓滾珠螺桿之螺桿熱膨脹分析與驗證

Thermal Expansion Analysis and Verification of Screw on the Vertical Translation Preloaded Double Nut Ball Screw

王睿棋(Jui-Chi Wang)

指導教授 ： 魏進忠

國立虎尾科技大學/工程學院/動力機械工程系機械與機電工程碩士班/碩士(2016年)

摘要

滾珠螺桿為高精密線性傳動元件，但在運動過程中，會使得滾珠螺桿內部的滾珠與接觸之軌道面產生磨耗及摩擦熱，造成元件的熱膨脹，進而影響了平台的傳動精度及穩定性。本文根據滾珠螺桿運動學理論，計算滾珠、螺帽及螺桿間的正向力、摩擦係數與滑動速度等參數，考慮滾珠螺桿在傳動時的加、等、減速效應，求得滾珠在軌道接觸面之平均熱通量，再以熱阻抗的概念，計算滾珠、螺帽及螺桿三者間的熱分配率，將螺桿上所受到的總熱通量代入有限元素分析軟體進行熱分析，並將螺桿在旋轉運動過程中所受的空氣對流冷卻影響加入螺桿與空氣以及固定元件之熱傳邊界條件設定。將熱分析結果的溫度變化及螺桿伸長量與實驗數據互相驗證，並探討因運動過程造成內部預壓力變化時，螺桿溫度的變化情形，以及改變不同的設計參數，包括接觸角及曲率半徑，分析螺桿溫度與伸長量變化，提出對於滾珠螺桿幾何設計之方向。
　　研究結果顯示，螺帽內部預壓力變化會影響螺桿的整體溫度，且隨著預壓力的下降，螺桿表面所受到的熱通量也隨之下降，造成螺桿溫度及伸長量下降，影響平台的定位精度。而本文所建構之熱分析模型，在溫度方面與實驗比較誤差最高約8%左右，在變形量方面及平台定位精度的模擬誤差則是在15%上下，而透過此模型探討不同設計參數的螺桿溫度及伸長量，可發現螺桿溫度隨著軌道曲率半徑增加而下降，以及在初始接觸角45˚之後會隨著接觸角變大而下降，在50˚時螺桿整體溫度會是最低的。

關鍵字

滾珠螺桿 ； 雙螺帽 ； 熱膨脹 ； 磨擦熱 ； 有限元素分析

並列摘要

The ball screw is a transmission element of high precision; however, the transmission element is displaced within the process because it causes wear and frictional heat between the ball and the orbital plane. Still, it also influences the platform’s transmission accuracy and stability. According to the kinematics of the ball screw, this research calculates the normal force, friction coefficient, and sliding velocity of the ball, the nut, and the screw. And consider the effect when the ball screw drive in the accelerate, isokinetic, and decelerate, to calculated the average heat flux of ball with contact surfaces on the track. Then, calculated the heat distribution rate between the ball, the nut, and the screw with the concept of heat resistance. Next, analyzed with Finite element method (FEM) of the total heat flux on the screw. Finally, set up the heat transfer boundary conditions. Both the change of temperature and the displacement of the screw are supported with each other. Therefore, it explores that the change of the temperature when preload appears within the process. And change to a different design parameters, include the radius of curvature and the contact angle,to analysis of screw temperature and deformation, than were made to the direction of the ball screw geometry.

　　The results show that, the preload will affect the overall temperature of the screw, and with the decline in preload, the heat flux by the screw groove surface can be decreased, resulting in temperature and deformation decreased, and affecting the accuracy of the positioning. In terms of temperature and experimental comparison error is only less than 8%, and the deformation is less than 15% by the thermal analysis model, this range has met our expectations, and explore the screw temperature and deformation with different design parameters of this model, can be found the contact angle increases to temperature decreases after the initial contact angle of 45˚, the overall temperature of screw is the lowest when 50˚.

並列關鍵字

Ball screw ； Double nut ； Thermal expansion ； Friction heat ； Finite Element Method

參考文獻

[1] 葉育宗，2012，”滾珠螺桿之熱效應分析與實驗印證”，國立虎尾科技大學機械與機電工程研究所碩士論文。

[3] 洪邑，2015，”雙螺帽滾珠螺桿之螺帽熱分析與驗證”， 國立虎尾科技大學機械與機電工程研究所碩士論文。

[2] 林謙育，2014，”雙螺帽滾珠螺桿之螺帽熱分析與驗證”， 國立虎尾科技大學機械與機電工程研究所碩士論文。

[16] 余思緯，2009，”滾珠螺桿系統螺帽熱分析”，國立成功大學奈米科技暨微系統工程研究所碩士論文。

[5] Nakashima, K., and Takafuji, K., 1987, ”Stiffness of A Pre-loaded Ball Screw”,日本機械學會論文集,Vol. 53, No492, pp.1898-1905.