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研究生:魏進忠
研究生(外文):Chin-Chung Wei
論文名稱:單螺帽雙圈滾珠螺桿在預負荷及潤滑作用條件下運動機制與機械性能的理論分析及實驗印證
論文名稱(外文):Analyses of Kinematics and Mechanical Performance of a Single Nut Double Cycle Ball Screw and Experimental Verification
指導教授:林仁輝
指導教授(外文):Jin-Fin Lin
學位類別:博士
校院名稱:國立成功大學
系所名稱:機械工程學系碩博士班
學門:工程學門
學類:機械工程學類
論文種類:學術論文
論文出版年:2003
畢業學年度:91
語文別:中文
論文頁數:265
中文關鍵詞:潤滑滾珠螺桿預負荷
外文關鍵詞:ball screwpreloadlubrication
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本研究的目的在於建立分析滾珠螺桿內部元件在操作時的幾何變化相互之間的運動關係,藉以了解滾珠螺桿的各項性能參數(包括滾珠、螺桿及螺帽接觸角、正向力、摩擦力、離心力…等)對於滾珠螺桿機械效率的影響。本研究較以往研究最大的不同點在於以下三點:(1) 成功建立了單圈滾珠與雙圈滾珠單螺帽滾珠螺桿複雜的幾何與運動分析模型,同時分析滾珠螺桿中滾珠、螺桿及螺帽的力與力矩平衡關係,據此求得滾珠螺桿的各項性能參數,包括接觸角、正向力、摩擦力、滾珠離心力…等,藉以分析各項性能參數間的關係及對於滾珠螺桿機械效率的影響;(2)考慮了以往研究並未考慮的重要參數,例如離心力、預負荷及潤滑作用等,建立了更完整的滾珠螺桿分析模型;(3)藉由滾珠螺桿的性能實驗驗證理論分析的正確性,同時得到影響滾珠螺桿機械效率的重要參數,包括螺桿螺旋角及預負荷。
滾珠在滾珠螺桿軌道運動時所受的的慣性力為離心力,在以往的研究中大多忽略離心力的作用而將滾珠與螺桿及滾珠與螺帽接觸面的接觸角、正向力及摩擦係數當成一樣來簡化計算。但是接觸角、正向力及摩擦係數均隨軸向負荷及螺桿轉速的變化而明顯變化,若不考慮此三個性能參數隨軸向負荷及螺桿轉速的變化關係會造成計算模型的誤差增加。因此在本文的分析中在滾珠、螺桿與螺帽的力與力矩關係式中加入離心力,反應出離心力對於各項性能參數的影響。在本文中亦分析出軸向負荷小於及大於預負荷時對於滾珠螺桿各項性能參數的影響,發現當軸向負荷的值遠離(遠大於或遠小於)預負荷時滾珠螺桿能有良好的機械性能。
本文將以單圈單螺帽滾珠螺桿模型的建立以了解滾珠、螺桿及螺帽三者的幾何關係及運動模式,可以分析滾珠螺桿在承受軸向負荷的作用後滾珠、螺桿及螺帽位置及幾何參數的變化,以及滾珠與螺桿及滾珠與螺帽之間的運動關係。同時加入高速離心力的作用以了解離心力對於各項性能參數的影響。再來建立雙圈滾珠單螺帽滾珠螺桿的理論分析模型,引用單圈滾珠螺桿的理論模型同時加入預負荷的效應。由於兩圈滾珠的受力方向及幾何關係都是不同的,在此可分析滾珠螺桿的滾珠與螺桿及滾珠與螺帽接觸面上純滾動點的位置與螺桿轉速及正向力的關係,以及軸向負荷改變時預負荷對於滾珠螺桿的各項性能參數的影響。最後在雙圈滾珠單螺帽滾珠螺桿的理論模型中加入潤滑的效應,並以實驗所得到的滾珠螺桿機械效率結果比較以驗證理論分析的正確性。同時發現軸向負荷接近預負荷時滾珠螺桿的機械效率大幅下降的現象。最後可以得到影響滾珠螺桿性能的參數為預負荷、螺桿螺旋角、軸向負荷及螺桿轉速。當軸向負荷小於並遠離預負荷時,滾珠螺桿的機械效率很高,隨著軸向負荷的增加而接近預負荷時,滾珠螺桿機械效率下降。當軸向負荷大於預負荷時,隨著軸向負荷的增加滾珠螺桿的機械效率增加,當軸向負荷為預負荷值的2.83倍以上時,滾珠螺桿有最佳的機械效率。所以預負荷的值由所使用的軸向負荷的大小決定,軸向負荷必須遠大於或遠小於預負荷方能有較佳的機械效率。螺桿螺旋角越大滾珠螺桿機械效率越差,但是較大的螺旋角可以增加滾珠螺桿的進給速率。滾珠螺桿的機械效率亦會隨著螺桿轉速的增加而減少。為使滾珠螺桿具有最佳的機械效率,必須根據使用的軸向負荷與螺桿轉速來選擇適當的預負荷及螺桿螺旋角。
The purpose of this study is to create an effective method to study kinematics and tribological behavior of a ball screw operating under different operating conditions. The analysis is able to realize how the ball screw parameters including contact angles, normal forces, friction forces and centrifugal force of ball screw affect ball screw’s mechanical efficiency. The main distinctions of the present study from the past studies are given as follows: (1) Single-cycle and double-cycle ball screw’s geometrical and kinematical analyses have been developed successfully. The force and torque balance equations of balls, screw and nut have been developed in the analyses. From the solutions of these equations we can get all mechanical performance parameters (including contact angles, normal forces, friction forces, ball’s centrifugal force… et. al.) of a ball screw. The influences of these parameters on the ball screw’s mechanical efficiency are analyzed in the present study; (2) several important factors are considered. These parameters include the centrifugal force, the ball screw’s preload and the lubrication effect. The consideration of these factors can create more perfect ball screw results; (3) the ball screw’s experimental data can verify the ball screw model developed in the present study, and can investigate several important parameters (including the helix angle and the preload, etc.) how they affect ball screw’s mechanical efficiency.
When balls moving in the raceways of a ball screw at high rotational speeds, the centrifugal force acts in the each ball. In past studies, they did not consider the effect of the centrifugal force. They all assume the contact angle, the normal force and the friction coefficient at the ball-screw and ball-nut contact areas are invariant with the each other. Actually, the contact angle, the normal force and the friction coefficient are varying significantly with the axial force and the screw’s rotational speed. The present model finds the effect of the centrifugal force on the ball screw’s performance parameters to be significant. The present model can also find the influence of the preload on the ball screw’s mechanical performance parameters. When the axial load far away (larger and smaller) from the preload is applied, the ball screw shows the better mechanical efficiency.
In this study, single ball cycle-single nut ball screw without the preload is analyzed first. From the model developed in this section one can investigate the geometrical parameters and the contact angles formed at the two contact areas varying with the operating conditions when an axial load is applied to a ball screw. This model also evaluates the influence of the centrifugal force on the mechanical performance parameters. In the second section of this study, a double cycle-single nut ball screw model is established and then analyzed. The analysis in this section has used the concept of single cycle-single nut ball screw method, and the preload applied in the system has been considered too. Because the force direction and the geometrical behavior exhibited at two cycles of balls are different, the pure-rolling points at ball-screw and ball-nut contact areas are varying with the screw’s rotational speed and the normal force. When the axial load is increased, the present model also can find the influence of the preload on the ball screw’s performance parameters. The lubrication effect is considered in double cycle-single nut ball screw model. The ball screw’s experimental results can be compared with that predicted by the theoretical model, and verify the accuracy of the present model. By the present model the ball screw’s mechanical efficiency is decreased greatly when the applied axial load is close to the preload. The preload, the helix angle, the screw rotational speed and the axial load are the four influential parameters to the ball screw mechanical efficiency. When the applied axial load is lower than the preload and is far away form the preload, the ball screw mechanical efficiency is elevated. The ball screw mechanical efficiency is increased when the applied axial load is increased greater than the preload. While the axial load is 2.83 time of the preload s, the ball screw mechanical efficiency is high. A large helix angle is advantageous to the ball screw speed, but the ball screw mechanical efficiency is decreased. The ball screw mechanical efficiency is also decreased when the screw’s rotational speed is increased. In order to get the high ball screw mechanical efficiency, one must choice the proper preload and the screw helix angle dependent upon on the axial load and the screw rotational speed.
目錄
頁數
第一章 緒 論1
1.1 文獻回顧2
1.1.1 影響滾珠螺桿效能的參數2
1.1.2 預負荷與滾珠螺桿剛性4
1.1.3 滾珠螺桿幾何分析及運動分析5
1.1.4 滾珠軸承幾何分析及運動分析6
1.2 研究動機7
1.3 論文架構8
第二章 單圈滾珠單螺帽滾珠螺桿之性能與運動行為分析14
2.1 簡介14
2.2 單圈滾珠單螺帽滾珠螺桿理論分析15
2.2.1 滾珠螺桿的結構與迴球道的種類15
2.2.2 座標系的定義與各座標系轉換關係15
2.2.3 單圈滾珠數目的計算18
2.2.4 滾珠所受慣性作用力計算20
2.2.5 滾珠運動所受慣性力矩計算25
2.2.6 滾珠公轉、自轉角速度及各接觸面間的滑動角的計算27
2.2.7 滾珠、螺桿及螺帽的接觸角的計算34
2.2.8 螺帽與滾珠的力與力矩平衡關係式37
2.2.9 滾珠螺桿的機械效率計算44
2.2.10 兩接觸面間滑動比的計算45
2.3 結果與討論50
2.3.1 程式計算流程50
2.3.2 單圈滾珠單螺帽滾珠螺桿理論分析的結果與討論54
2.3.2.1滾珠與螺桿及滾珠與螺帽接觸面接觸角的比較55
2.3.2.2 滾珠與螺桿及滾珠與螺帽接觸面的變形量比較55
2.3.2.3 滾珠公轉及自轉角速度56
2.3.2.4 滾珠所受黏滯阻力與離心力56
2.3.2.5 自旋角 及滑動比57
2.3.2.6 滾珠與螺桿及滾珠與螺帽接觸面的摩擦係數57
2.3.2.7 兩接觸面上的正向力及摩擦力58
2.3.2.8 滾珠螺桿的機械效率59
2.3.2.9 螺旋角 對於接觸角及機械效率的影響60
第三章 雙圈滾珠單螺帽滾珠螺桿在有預負荷下性能參數與運動行為分析78
3.1 簡介78
3.2 雙圈滾珠單螺帽滾珠螺桿理論分析79
3.2.1 預負荷施加方式及座標系的建立79
3.2.2 滾珠公轉及自轉角速度的計算84
3.2.2.1 軸向負荷小於預負荷時左邊滾珠公轉及自轉角速度的計算84
3.2.2.2 軸向負荷大於預負荷時左邊滾珠公轉及自轉角速度的計算96
3.2.2.3 軸向負荷小於或大於預負荷時右邊滾珠公轉及自轉角速度的計算103
3.2.3 滾珠螺桿各接觸點滑動角的計算114
3.2.3.1軸向負荷小於預負荷時左邊滾珠與螺桿接觸面間的滑動速度115
3.2.3.2軸向負荷大於預負荷時左邊滾珠與螺桿接觸面間的滑動速度
118
3.2.3.3 軸向負荷小於預負荷時左邊滾珠與螺帽接觸面間的滑動速度
119
3.2.3.4 軸向負荷大於預負荷時左邊滾珠與螺帽接觸面間的滑動速度
121
3.2.3.5 軸向負荷小於或大於預負荷時右邊滾珠、螺桿與螺帽接觸面間的滑動速度及滑動角123
3.2.4 滾珠螺桿中滾珠自轉角速度的自旋角的計算127
3.2.4.1 左邊滾珠在軸向負荷小於預負荷時滾珠與螺帽接觸面上純滾動點5在接觸面的法線方向的角速度關係式127
3.2.4.2 左邊滾珠在軸向負荷大於預負荷時滾珠與螺帽接觸面上純滾動點5在接觸面的法線方向的角速度關係式132
3.2.4.3 左邊滾珠在軸向負荷小於預負荷時滾珠與螺桿接觸面上純滾動點4在接觸面的法線方向的角速度關係式134
3.2.4.4 左邊滾珠在軸向負荷大於預負荷時滾珠與螺帽接觸面上純滾動點5在接觸面的法線方向的角速度關係式135
3.2.4.5 右邊滾珠與螺帽接觸面上純滾動點9在接觸面的法線方向的角速度關係式137
3.2.4.6 右邊滾珠與螺桿接觸面上純滾動點8在接觸面的法線方向的角速度關係式142
3.2.5 滾珠螺桿各種剛性係數的計算143
3.2.5.1 滾珠螺桿螺桿、螺帽及整體剛性係數144
3.2.5.2 滾珠螺桿中滾珠、螺桿與螺帽各接觸面剛性係數及曲率和關係式145
3.2.6 受軸向負荷時螺帽與滾珠力平衡關係式的建立148
3.2.6.1螺帽力平衡149
3.2.6.2左邊滾珠力平衡151
3.2.6.3右邊滾珠力平衡153
3.2.7 滾珠力矩平衡關係式的建立154
3.2.7.1 左邊滾珠的力矩平衡關係式154
3.2.7.2 右邊滾珠的力矩平衡關係式157
3.2.8 滾珠螺桿預負荷對幾何關係的影響159
3.2.9 滾珠螺桿機械效率的計算164
3.3 結果與討論166
3.3.1 雙圈滾珠單螺帽滾珠螺桿性能參數計算流程166
3.3.1.1滾珠螺桿整體計算流程166
3.3.1.2右邊滾珠、螺桿與螺帽性能參數計算流程167
3.3.1.3左邊滾珠、螺桿與螺帽性能參數計算流程169
3.3.2 雙圈滾珠單螺帽滾珠螺桿理論分析的結果與討論170
3.3.2.1 左邊滾珠與右邊滾珠在螺帽接觸面上的正向力變化171
3.3.2.2 左邊滾珠與右邊滾珠在螺帽接觸面上的摩擦力變化173
3.3.2.3 左邊滾珠與右邊滾珠在螺帽接觸面上的摩擦係數變化174
3.3.2.4 左邊滾珠與右邊滾珠在螺桿接觸面上的輸入力矩變化174
3.3.2.5 左邊滾珠與右邊滾珠在螺帽接觸面上的輸出軸向力175
3.3.2.6 滾珠螺桿性能參數與機械效率176
3.3.2.7 螺旋角的變化與接觸面純滾動點的分佈177
3.3.2.8 螺桿轉速的變化與接觸面純滾動點的分佈179
3.3.2.9 預負荷的變化與接觸面純滾動點的分佈180
3.3.2.10 滾珠公轉角速度181
3.3.2.11 滾珠自轉角速度182
3.3.2.12 螺帽節距變形量 182
第四章 滾珠螺桿性能理論及實驗分析218
4.1 簡介218
4.2 滾珠螺桿性能實驗218
4.2.1滾珠螺桿試驗機各元件與感測器的介紹219
4.2.2 操作條件及量測參數222
4.3理論分析222
4.3.1 沒有潤滑作用的摩擦力公式推導222
4.3.2具有潤滑作用的摩擦力公式推導223
4.4結果與討論242
4.3.1 潤滑作用的有無對於滾珠螺桿摩擦力計算的影響242
4.3.2 潤滑作用的有無對於滾珠螺桿機械效率計算的影響243
第五章 結論257
5.1 單滾珠單螺帽滾珠螺桿理論分析258
5.2 雙圈滾珠單螺帽滾珠螺桿理論分析258
5.3 滾珠螺桿性能實驗與潤滑理論分析259
滾珠螺桿未來可行之研究方向261
參考文獻262
發表之論文264
自述265
參考文獻
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9.Cuttino, J. F., Dow, T. A., and Knight, B. F., 1997, "Analytical and Experimental Identification of Non-linearities in a Single-nut, Preloaded Ball Screw," ASME Journal of Mechanical Design, Vol. 119, No. 1, pp. 15-19.
10.Lin, M. C., Ravani, B., and Velinsky, S. A., 1994, "Kinematics of the Ball Screw Mechanism," ASME Journal of Mechanical Design, Vol. 116, pp. 849-855.
11.Lin, M. C., Ravani, B., and Velinsky, S. A., 1994, "Design of the Ball Screw Mechanism for Optimal Efficiency," ASME Journal of Mechanical Design, Vol. 116, pp. 856-861.
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13.Huang, H. T., and Ravani, B., 1997, "Contact Stress Analysis in Ball Screw Mechanism Using the Tubular Medial Axis Representation of Contacting Surfaces," ASME Journal of Mechanical Design, Vol. 119, pp. 8-14.
14.Harris, T. A., 1971, "An Analytical Method to Predict Skidding in Thrust-Loaded, Angular-Contact Ball Bearings," ASME Journal of Lubrication Technology, Vol. 93, pp. 17-24.
15.Boness, R. J., 1981, "Minimum Load Requirements for the Prevention of Skidding in High Speed Thrust Loaded Ball Bearings," ASME Journal of Lubrication Technology, Vol. 103, pp. 35-39.
16.Hiwin Technology Company, Hiwin Ballscrews Technical Information, Tanchung, Taiwan.
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19.Markho, P. H., 1988, "Highly Accurate Formulas for Rapid Calculation of the Key Geometrical Parameters of Elliptic Hertzian Contacts," ASME Journal of Tribology, Vol. 109, pp. 640-647.
20.Harris, T. A., 1973, "Rolling Element Bearing Dynamics," Wear, Vol. 23, pp. 311-337.
21.Goldstein, S., 1938, Modern Developments in Fluid Dynamics, Oxford Press, London.
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