臺灣博碩士論文加值系統

滾珠螺桿為工具機中將轉動運動轉換為線性運動的關鍵零組件。為得到精確的傳動，必須消除螺桿、螺帽間的背隙，而使用施加預壓的方法可以達到此目的，並且可提高滾珠螺桿的剛性以及各方面的性能，但因而也造成過大的接觸摩擦力。
本文利用有限元素軟體ANSYS/LS-DYNA®對滾珠螺桿進行動態模擬分析，使用設定接觸來模擬滾珠螺桿中各元件的接觸關係。首先建立單顆滾珠模型進行暫態分析，由電腦模擬的結果可得知滾珠直徑改變量與預壓力之關係，並將模擬分析所得預壓力代入預壓扭矩計算公式，進而求得預壓扭矩。而後建立滾珠螺桿全模模型，並施加角位移和角速度兩種驅動方式，以有限元素法探討滾珠干涉尺寸與預壓力的關係，及預壓力對於滾珠螺桿運動特性的影響。分析結果顯示滾珠螺桿在預壓狀況時，有較好的運轉傳動效率，且對滾珠螺桿在其徑向位移的來回振動有所改善，並對其徑向加速度有減小趨勢。而對螺桿軸向方面其速度與加速度都有明顯的改善，可使得螺桿運動更趨於線性而減少振動。

Ball screw which converts rotational motion to linear motion is one of the important components for precision machine center. A ball screw is composed of screw, nut, and balls circulating system. In order to have accurate transmission, the backlash between the nut and screw must be removed. Using large size balls to create preload for the ball screw not only can achieve this goal, but also increase the stiffness and transmission performance of ball screw. However preloading would cause excessive contact friction. Therefore getting of properly preload is a critical problem in ball screw design.
In this paper, finite element analysis software ANSYS/LS-DYNA® is employed to model the ball screw dynamically and analyze the preload. In LS-DYNA model all components have been assigned identified contact entities to simulate the contact relationship of ball screw. A single ball model is established first for transient analysis. The computer simulation results from single ball model will give the relationship between ball diameter and contact force, and by using of the contact force may calculate the basic torque. Then, a whole model of ball screw is built, and the screw angular displacement and angular velocity are adopted as input of analysis. The effects of preloading have been analyzed by LS-DYNA. The results of computer simulation show that preloading for ball screw can reduce the vibration in radial direction, and can improve the efficient of transmission since the axial velocity is more linearized.

摘要.............................................................................................................i
Abstract......................................................................................................ii
目錄...........................................................................................................iii
圖目錄.........................................................................................................v
表目錄.....................................................................................................viii
第一章 緒論...............................................................................................1
1.1前言................................................................................................1
1.2文獻回顧........................................................................................2
1.3研究動機及方法............................................................................5
1.4本文大綱........................................................................................7
第二章 相關基礎理論..............................................................................9
2.1滾珠螺桿........................................................................................9
2.1.1滾珠螺桿之分類..................................................................9
2.1.2滾珠螺桿預壓方式............................................................12
2.2 赫茲接觸理論.............................................................................15
2.3 接觸碰撞分析.............................................................................17
2.3.1接觸碰撞類型....................................................................17
2.3.2接觸碰撞算法概述............................................................18
第三章 滾珠螺桿有限元模擬................................................................20
3.1 單顆滾珠預壓力分析.................................................................20
3.1.1單顆滾珠模型建立............................................................20
3.1.2 單顆滾珠有限元模擬.......................................................21
3.2滾珠螺桿全模分析......................................................................25
3.2.1滾珠螺桿全模建立............................................................25
3.2.2滾珠螺桿全模有限元模擬................................................28
第四章 分析結果與討論........................................................................35
4.1單顆滾珠預壓力分析結果.........................................................35
4.1.1鋼珠應力結果探討............................................................35
4.1.2鋼珠壓合前後直徑改變量................................................37
4.1.3鋼珠壓合後接觸力............................................................39
4.2全模滾珠螺桿分析結果.............................................................42
4.2.1定角位移............................................................................42
4.2.2定角速度............................................................................44
第五章 結論與未來展望........................................................................60
5.1結論..............................................................................................60
5.2未來展望......................................................................................62
參考文獻...................................................................................................63

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