臺灣博碩士論文加值系統

滾珠螺桿為精密機械之傳動元件，由於滾珠在軌道運動時並不是純滾動，而是滾動與滑動兩種狀況並存，因此滾珠與接觸之軌道面會產生摩擦熱，尤其在高速傳動的狀態下，會使螺帽與螺桿的溫度大幅上升，此為影響熱變位之主要原因，導致其定位精度大幅下降。本文藉由有限元素分析軟體(Ansys Workbench)建立螺帽熱分析模型，其邊界條件由滾珠螺桿運動學理論，求得滾珠與螺帽、螺桿間之接觸角、正向力、摩擦係數、滑動速度等參數，並考慮滾珠螺桿在傳動時之加等減速效應，即可計算出滾珠在軌道接觸面之平均熱通量，其次則考慮螺帽在往復運動過程中受空氣強制冷卻對流之影響來設定螺帽與空氣以及與固定元件之熱傳邊界條件。該螺帽熱分析模型可預測螺帽溫升後之溫度變化，探討不同溫升情況時螺帽表面之應變量與熱效應所產生的螺帽伸長量。
在實機實驗中，本文使用垂直軸之單軸螺桿測試機對滾珠螺桿進行測試，在螺帽表面裝置熱電偶與應變規，可獲得螺帽之溫度與應變變化趨勢，並與模擬之結果互相印證，在變化趨勢以及數值上獲得良好對應。因此螺帽熱分析模型可應用於滾珠螺桿的螺帽溫度控制設計與熱變位補償機制之依據。

The ball screw is a precision mechanical transmission component, because the ball in the track motion is not only pure rolling, but also rolling and sliding at the same time. When sliding occurs, the ball contact with the track surface will generate friction heat, especially at high transmission conditions, so that the nut and the screw temperature increased significantly, the main reason for affecting on thermal deformation, led to a significant decline in positioning accuracy. Therefore, this paper used the finite element analysis software (Ansys Workbench) to establish nut thermal analysis model. At first ,the boundary condition takes kinematics theory of ball screw into consideration, and therefore we’d be able to calculate all sorts of parameter such as contact angle, normal force, friction coefficient and sliding speed between the ball and screw, and we also take considered on transmission acceleration, constant and deceleration of the ball screw into consideration, then we can calculate the average heat flux on contact surface of the ball on the track, Secondly, consider setting the nut affected by forced air cooling convection in reciprocation. The nut thermal analysis model can predict the nut''s temperature variation after temperature raised, and explore strain of the nut surface with thermal effect generated nut deformation on different temperature raised.
In the experiments, a vertical motion of the single axial screw testing machine to run tests on ball screw, and an additional thermocouple and strain gage is placed on surface of nut, which allows us to gain instant information of the temperature and strain variation of the nut. The results of our experiment are than being compared with the simulated results to increase the reliability of this paper''s construct. Heat transfer conditions at contact surfaces of nut and air, and the other fixed component are also set as boundary conditions. Thermal analysis model can be used in the basis of the ball screw''s nut temperature control design and thermal displacement compensation mechanism.

中文摘要................................................. i
英文摘要................................................. ii
誌謝.................................................... iv
表目錄................................................... vii
圖目錄................................................... viii
符號說明................................................. x
第一章 緒論.............................................. 1
1.1 前言................................................ 1
1.2 文獻回顧............................................. 2
1.2.1 預拉力與預壓力之影響................................. 2
1.2.2 摩擦力對溫升之影響................................... 2
1.2.3 滾珠螺桿運動學...................................... 2
1.2.4 滾珠螺桿熱分析...................................... 3
1.2.5 應變規之起源與應用................................... 4
1.3 研究動機..................................... ........4
1.4 研究目的..................................... ....... 4
1.5 論文架構..................................... ....... 5
第二章 理論分析........................................... 6
2.1 建立熱模型........................................... 6
2.2 滾珠螺旋接觸帶........................................ 6
2.2.1 真實接觸角......................................... 6
2.2.2 考慮轉速條件 ........................................11
2.2.3 赫茲彈性變形 ........................................11
2.2.4 上下方滾珠與軌道之接觸角範圍........................... 13
2.3 平均熱通量........................................... 14
2.3.1 單顆滾珠在軌道內的熱通量.............................. 14
2.3.2 螺帽的熱通量計算.................................... 14
2.3.3 週期內的加減等速效應................................. 16
2.3.4 面積因子........................................... 18
2.3.5 能量分率........................................... 20
2.3.6 週期內的平均熱通量................................... 22
2.4 平均熱通量之推導過程................................... 22
2.5 螺帽熱分析........................................... 24
2.5.1 邊界條件之設定...................................... 24
2.6 螺帽熱膨脹........................................... 31
2.7 螺帽熱分析模型後處理方式................................ 32
第三章 實驗方法........................................... 34
3.1 實驗目的............................................. 34
3.2 機台架設............................................. 34
3.3 感測器簡介與裝配...................................... 36
3.3.1 推拉力計簡介 ........................................36
3.3.2 預壓扭矩量測 ........................................36
3.3.3 熱電偶簡介......................................... 37
3.3.4 熱電偶裝配......................................... 37
3.3.5 應變規簡介......................................... 39
3.3.6 應變規裝配......................................... 39
3.4 實驗規劃............................................. 41
第四章 結果與討論......................................... 43
4.1 螺帽熱分析........................................... 44
4.1.1 溫度&應變&伸長量之分析............................... 44
4.1.2實驗與模擬之對照..................................... 50
4.2 螺帽伸長量計算與對照................................... 57
4.3 在不同環境溫度下之螺帽溫度.............................. 57
4.4 在不同油脂條件下之螺帽溫度.............................. 58
第五章 結論與未來展望...................................... 61
5.1 結論................................................ 61
5.2 未來展望............................................. 61
參考文獻................................................. 62
簡歷.................................................... 68

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