臺灣博碩士論文加值系統

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。

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.

目錄

摘 要 i
ABSTRACT ii
誌 謝 iv
目錄 v
圖目錄 vii
表目錄 viii
第一章緒論 1
1.1研究背景及動機 1
1.2文獻回顧 2
1.2.1智能化進給系統應用於工業界之發展 2
1.2.2進給系統之發展 4
第二章 理論分析 7
2.1理論模型 7
2.1.1基本假設 9
2.1.2統御方程式 9
2.1.3數值方法 10
2.2邊界條件 11
2.2.1運轉參數 13
2.3建構模型 15
第三章實驗架構及量測 19
3.1實驗模型與量測系統 19
第四章 結果與討論 22
4.1數值分析與實驗結果驗證 22
4.1.1網格獨立性測試 22
4.1.2時間解析獨立性測試 23
4.2螺桿溫昇預測 24
4.2.1滾珠螺桿2000轉速下暫態溫度預測 24
4.2.2滾珠螺桿不同轉速之溫度分佈預測 26
4.3滾珠螺桿熱變形量預測 29
第五章 結論 32
參考文獻 33
符號彙編 35

參考文獻
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