Please use this identifier to cite or link to this item: http://hdl.handle.net/11455/1748
標題: 單螺帽歌德牙型滾珠螺桿之尺寸干涉量對預壓力影響之探討
On the Preload due to Dimensional Interference of the Gothic-Profile Ball Screw
作者: 黃惠琪
Huang, Hui-Chi
關鍵字: ball screw;滾珠螺桿;preload;interference;預壓力;干涉
出版社: 機械工程學系所
引用: [Cuttino et al., 1997] J. F. Cuttino, T. A. Dow and B. F. Knight, 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. [Chen & Dwang, 2000] J.S. Chen and I.C. Dwang, 2000, “A Ballscrew Drive Mechanism with Piezo-Electric Nut for Preload and Motion Control,” International Journal of Machine Tools and Manufacture, Vol.40, pp.513-526. [Harris, 1984] T. A. Harris, 1984, Rolling Bearing Analysis, John Wiley & Sons, New York. [Huang & Ravani, 1997] H. T. Huang and B. Ravani, 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. [Marcu, 2000] M. Marcu, 2000,“Calculating Ball Screw Life in Clamping Applications,” Machine Design, July, pp.104- 108. [Shimoda, 1999] H. Shimoda, 1999, “Stiffness Analysis of Ball Screws,” International Journal of Japan Society of Precision Machinery Engineering, Vol. 33, No. 3, pp. 168-172. [Shkapenyuk, 1990] M. B. Shkapenyuk, 1990, “Ways of Improving the Performance of Ball-screw Drives,” Stanki Instrument, Vol. 61, No. 4, pp. 9-11. [Slocum, 1992] A. H. Slocum, 1992, Precision Machine Design, Prentice-Hall. [Yang & Park, 1998] M.-Y. Yang and J.-H. Park, 1998, “Analysis of Setting Errors in Precision Ballscrew Machining and The Automatic Adjustable Center,” International Journal of Machine Tools and Manufacture. Vol. 38, pp. 965-979. [Weule & Golz, 1991] H. Weule and H.U. Golz, 1991, “Preload Control in Ball Screw - A New Approach for Machine Tool Building,” Annals of the CIRP, Vol. 40, pp. 383-386. [穆,2000] 穆立祥,2000,滾動接觸之剛度探討,國立中原大學博士論文。 [孫,2002] 孫明華,2002,預壓對滾珠螺桿磨耗之實驗探討,國立中興大學碩士論文。 [魏,2003] 魏進忠,2003,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,國立成功大學博士論文。 [曹,2005] 曹博涵,2005,滾珠螺桿預壓力、軸向剛性與尺寸及公差關係之探討,國立中興大學碩士論文。
摘要: 
滾珠螺桿為精密線性傳動與定位系統中最常用的零組件,是精密機械之重要元件,為提高其運動剛性等性能,在組裝過程需透過零組件之間的幾何干涉使其產生靜態預壓力(預壓力),因此如何透過幾何干涉量的設計以掌控滾珠螺桿的預壓力,進一步設計出其機械特性為一極重要的課題。本研究針對軸向剛性較穩定的歌德牙型滾珠螺桿,探討其滾珠、螺桿以及螺帽之間尺寸干涉量對於內部預壓力的影響。
研究首先對滾珠螺桿裝配時之干涉配合進行靜剛性與尺寸干涉量之關係推導,其中零件間之接觸以Hertz接觸理論進行探討,分析其接觸應力與變形量之關係,其分析結果顯示兩者間為非線性關係。除理論分析之外本研究並以有限元素法進行分析比較。因預壓力為滾珠螺桿內部元件干涉所產生之內力,無法直接估算,本研究以數值方法經由反覆分析各元件之接觸變形,再比較變形量與干涉量確認其ㄧ致性,據以計算因干涉量所導致的預壓力,此計算包含下列步驟:(i)假設一初始預壓力;(ii)根據此預壓力計算各元件之變形量;(iii)加成各元件之變形量,以與干涉量進行比較,若變形量等於干涉量,則該預壓力即為所求;(iv)否則以線性插值估算新的預壓力,重新進行步驟(ii)。文中以直徑9.528mm之鋼珠造成3μm之干涉量為例,經由四次反覆分析結果顯示其元件間之預壓力為44N,其解可迅速收斂。進一步探討不同干涉量對預壓力之影響,當干涉量由1μm變化至7μm時,亦即鋼珠直徑由9.526mm改變至9.532mm時,分析結果顯示每增加1μm之干涉量時,其預壓力由12N增加為25N、44N、66N、88N、119N至157N,顯示滾珠與螺桿、螺帽因干涉之故,其接觸變形為非線性關係,其靜態剛性隨干涉量增加而提升,此結果與接觸分析之理論一致。本研究之主要貢獻在於以接觸分析的方法探討滾珠螺桿之元件尺寸干涉量對其預壓力之影響,解決長久以來對於滾珠螺桿性能無法掌握之課題。

Ball screw is one of the most important components for precision machineries as it has been widely used in precision linear transmissions and positioning systems. In order to improve its performance, static preload (preload) is often introduced by geometric interferences among its components during assembly. It is therefore a critical issue to investigate how the preload of a ball screw is affected by dimensional interference. This research is aimed to investigate the relationship between preload and the interference among balls, screw and nut of the ball screw with Gothic profile.
The relationship between static deformation and dimensional interference of the ball screw is first investigated. Contact deformations among components due to preload are analyzed by Hertz contact theory. The deformation by preload is non-linear because the area of contact increases as the preload increases. In addition to theoretical analyses, deformation analyses by finite element method (FEM) are also conducted as a comparison. As the preload is an internal force that cannot be predefined nor be calculated directly in FEM, an iterative process is developed to find the preload due to dimensional interference. The process consists of the following steps. (i) An initial preload is first assumed. (ii) Compute deformations of components based on the preload. (iii) Deformations are accumulated and compared with the dimensional interference. If the accumulated deformation equals to the interference, the preload is determined. (iv) Otherwise a new preload, estimated by linear interpolation is calculated to continue the iteration to step (ii) until the accumulated deformation of components equals to the interference. With a ball screw with 3μm interference, by 9.528mm-diameter steel balls, as an example, the preload 44N is determined in four iterations by FEM. The solution is quickly converged based on the developed process. The change of preload is further investigated when the dimensional interference varies from 1μm to 7μm, equivalent to the diameter of steel ball changing from 9.526mm to 9.532mm. The result showed that the preload increases from 12N to 25N, 44N, 66N, 88N, 119N to 157N for each increment of 1μm interference. The non-linear behavior showed that the static stiffness increases when the interference increases, as predicted by the theory. The main contribution of this research is the analysis of ball screw preload due to dimensional interference among components via contact analysis. It solves the long-time issue on determining the preload by dimension design.
URI: http://hdl.handle.net/11455/1748
其他識別: U0005-2907200614065000
Appears in Collections:機械工程學系所

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