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On the Preload due to Dimensional Interference of the Gothic-Profile Ball Screw
|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:||
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.
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