| Summary: | 碩士 === 中興大學 === 機械工程學系所 === 94 === 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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