滾珠螺桿已廣泛地應用於高精密度機構的傳動，為精密工業重要的關鍵組件，故如何掌握其性能為一重要的課題。滾珠螺桿性能中剛性為一重要指標，但剛性取決於螺桿、螺帽及滾珠間的預壓，其性能與零組件間之公差配合有密切關係，故本研究探討滾珠螺桿預壓力受公差之影響。研究中首先對滾珠螺桿在理想裝配情形上的尺寸配合進行靜剛性與尺寸干涉的關係推導，並以有限元素法驗證干涉量增加同時影響剛性之合理性，分析結果顯示隨著預壓力的增加其變形量呈減緩的情形，說明干涉量會提升其剛性。同時透過尺寸靈敏度與公差靈敏度分析公差對滾珠螺桿預壓力的影響，結果顯示在理想裝配情形下，螺桿內徑為靈敏度最高之尺寸，其公差需特別控制。進一步透過公差靈敏度分析，顯示滾珠導螺桿剛性變化對於鋼珠直徑的公差變化最為敏感，表示若要放寬或緊縮滾珠導螺桿剛性變化，調整鋼珠直徑的公差最為有效。

Ball screw has been widely applied to the transmission of precision machinery and is a crucial component for precision industry. It is thus an important issue to understand and to control the performance of Ball screw. The rigidity, one of the important performances of a ball screw, depends on the preload among the nut, the screw and the ball. The rigidity is strongly related to the dimensional tolerancing of these components. This research is aimed to investigate the relationship among preload, axial stiffness, dimensions and tolerancing of the ball screw. We first investigate the relationship among the axial stiffness and interferences among these components and verify the model by finite element analysis (FEA). Both the model and FEA showed that the deformation of components saturated as the preload increases. In other words, the stiffness of the ball screw increases when the interferences among components increase. Furthermore, a series of sensitivity analyses are conducted to investigate the effects of dimensions and tolerances on the preload of ball screw. It revealed that the stiffness is strongly affected by the size of the internal diameter. It reflects that size tolerance of the internal diameter is crucial and must be strictly controlled. Further investigation via tolerance sensitivity analysis showed that the variation of stiffness is mostly sensitive with respect to the ball diameter. That reflects the most effective way to control the variation of stiffness is to adjust the tolerance of the ball.

摘要 I
ABSTRACT II
誌謝 III
目錄 IV
圖目錄 VI
表目錄 VII
符號表 VIII
第一章 緒論 1
1.1研究動機 1
1.2文獻回顧 2
1.3研究方法 5
1.4本文大綱 6
第二章 滾珠螺桿受力變形分析 7
2.1滾珠螺桿元件受力與變形的關係 8
2.2滾珠螺桿元件的剛性分析 11
第三章 滾珠螺桿預壓對剛性的影響探討 13
3.1滾珠螺桿預壓與幾何干涉之關係 13
3.2 干涉情形下螺桿之軸向剛性分析 19
3.3有限元素分析 22
第四章 滾珠螺桿預壓與尺寸及公差之靈敏度分析 28
4.1靈敏度分析 28
4.2尺寸靈敏度分析 29
4.3百分比尺寸公差之靈敏度 32
第五章 結論與展望 40
5.1 結論 40
5.2未來展望 41
參考文獻 42
附錄一、以MAPLE計算Qo之結果 44
附錄二、施加不同預壓力之圖3- 11 1/8圓干涉變形量與干涉應力關係 47

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