滾珠導螺桿進給驅動系統的熱變形估測

Thermal Deformation Estimation for a Ball Screw Feed Drive System

蔡勝植(Sheng-Chih Tsai)

指導教授 ： 楊安石

國立臺北科技大學/機電學院/冷凍空調工程系所/碩士(2014年)

https://doi.org/10.6841/NTUT.2014.00016

摘要

滾珠導螺桿(Ball Screws)是精密工具機驅動機構內的關鍵元件，其作用為將旋轉改變為直線之進給運動，然而高速滾珠導螺桿系統運轉一段時間後，由於摩擦作用產生大量熱，而引起螺桿溫度上升，繼而導致螺桿的熱變形，此嚴重影響滾珠導螺桿的操作定位精度。本研究考慮三維暫態熱傳導方程式模擬螺桿受熱變形行為，分析中考慮施加於螺桿軸的熱負荷主要來源為螺帽和軸承與軸間發熱源，另滾珠導螺桿和螺帽的變形是依據線彈性材料、均向性的假設為基礎建立理論模型，並利用有限元素法（Finite Element Method, FEM）計算程序探討滾珠導螺桿系統的熱變形過程。本研究中工作條件係模擬螺帽在螺桿軸上以20、 40、60 m/min不同轉速下的相對峰值速度進行往復運動，採用多區段熱源處理方法代表複雜螺帽、軸承對螺桿實際操作時摩擦之熱負荷以決定熱通量分佈。數值模擬計算穩態和暫態滾珠導螺桿詳細的溫度分佈、溫度上升和熱變形量經過實量測比較以確認數值模型正確性，預測結果亦顯示滾珠導螺桿在高速運轉條件下須採取熱補償以維持進給系統良好之定位精度。

關鍵字

熱變形 ； 滾珠導螺桿 ； 有限元素法 ； 熱傳模型 ； 定位精度 ； 工具機

並列摘要

The position error of a feed drive system was primarily caused by thermal deformation of a ball screw shaft. A high-speed ball screw system can generate massive heat after long-term operations with greater thermal expansion produced, and thereby unfavorably impact the positioning accuracy of the feed drive mechanism. In this study, we applied the computational approach using the finite element method (FEM) to simulate the thermal expansion process for estimating the deformation of the ball screw system. In the model, the deformation of the ball screw shaft was modeled by a linear elasticity manner given the assumption that the material was elastic, homogeneous, and isotropic. To emulate the reciprocating movements of the nut at the speeds of 20, 40 and 60 m/min corresponding to the screw shaft, we also utilized a three-dimensional unsteady heat conduction equation to determine the steady-state and transient temperature distributions, as well as temperature rises for calculating the thermal deformations of ball screws under operating situations. The analysis adopted the multi-zone heat loads to treat the heat generation sources from the frictions between the nut, bearings and the ball screw shaft. The predictions were compared with the experimental measurement for code validation. The simulated results showed that the countermeasures must be taken to thermally compensate great deterioration of the positioning accuracy due to vast heat production at high rotating speeds of shaft for a ball screw system.

並列關鍵字

Thermal deformation ； Ball screws ； FEM ； Heat transfer model ； Machine tool ； Positioning accuracy

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