滾珠螺桿靜態軸向剛性分析

Static Axial Rigidity Analysis of Ball Screw

羅亦廷(Yi-Ting Lo)

指導教授 ： 單秋成

國立臺灣大學/工學院/機械工程學研究所/碩士(2013年)

https://doi.org/10.6342/NTU.2013.02749

摘要

隨現代科技演進，製造生產已邁向高度自動化階段，同時對自動化設備有低耗能及高精度的要求，而傳動元件的發展即為其重要一環，滾珠螺桿出現，更提升了整體製造技術的水平。滾珠螺桿將多顆滾珠裝配於螺帽與螺桿之間，以滾珠於螺帽螺桿間的滾動接觸取代傳統螺桿的滑動接觸，大幅減低摩擦造成的能量損耗。由於精密製造對系統穩定性及精密度有高度的要求，而滾珠螺桿剛性對傳動進給系統的定位精度有著決定性的影響，因此對珠螺桿軸向剛性的研究也成為重點技術環節之一。
本研究計算部分首先找出螺桿的螺旋軌道幾何方程，求得滾珠與螺桿螺帽接觸點處主曲率值，再利用Hertz接觸理論計算滾珠受壓時的變形量，推得螺桿軸向位移，並由負載得到軸向剛性，推導出理論解。另輔以有限元素法軟體(Abaqus)建立模型進行分析，模擬其受負載時變形量及應力分布情形，求得軸向位移並觀察其趨勢。最後架設實驗，選擇三種不同型號的滾珠螺桿，將滾珠螺桿於材料試驗機上施以負載，用自行設計之位移計量測其軸向變形量，三者交互參照驗證。
觀察理論、模擬及實驗三者結果，理論及模擬差異極小，主要原因為兩者皆在理想狀態下，排除所有人為因素可能造成的影響，估計若再將有限元網格數量提高，可更逼近理論的解析解，但在現有的資源下此模擬結果已極具參考價值。而實驗結果顯示滾珠螺桿的剛性與理論值相比偏低，除加工精度與實驗人為因素導致的誤差，如治具剛性、量具架設及施力軸心若有些許偏移也可能影響實驗結果，且材料參數、物理特性及機械性質等皆會與理想情況有所差異，使實際量測到的剛性偏低，因此基本上此結果顯示剛性比理論值低是有合理的。

關鍵字

滾珠螺桿 ； 軸向剛性 ； 赫茲接觸 ； 有限元素

並列摘要

With rapid advances in modern technology, manufacturing has become highly automated. At the same time, the automation equipment has low energy consumption and high precision requirements. The invention of the transmission components was an important development in this area. The appearance of ball screws further enhanced the standard of manufacturing technology. The ball screw is assembled by multiple balls between the nut and the screw. The rolling contact between the balls and the nut and screw replaced the traditional sliding contact of the screw, dramatically reducing the energy lost from friction. Since precise manufacturing has high requirements on system stability and precision, and the rigidity of the ball screw has a decisive impact on the positioning accuracy of the system, research on the axial rigidity of the ball screw has become one of the focus of the technical aspects.
In the calculation section of this study, the geometric equations for the screw spiral track was found first to obtain the principal curvature values of the contact point between the ball and the screw nut. Then, Hertz contact theory was used to calculate the deformation of the ball under pressure, which is used to calculate the axial displacement of the screw. With the addition of a load, the analytical solution for the axial rigidity can thus be derived. By creating a model with the finite element method software (Abaqus), the deformation under load can be simulated and the stress distribution can be analyzed. The axial displacement can therefore be obtained and observed. Finally, to set up the experiment, choose 3 different types of ball screws. In the material testing system, subject the ball screws to loads and measure the axial deformation using a self-designed displacement gage. Cross-reference the data from the 3 types of screws for validation. From observing the results of the calculation, the simulation, and the experiment, there are minimal differences in the calculation and the simulation mainly due to the fact that both are under ideal conditions, excluding any factors that may have negative impacts on the results. If the finite element mesh is increased, the solution is estimated to be even close to the theoretical analytical solutions. However, with the existing resources available, this simulation results are highly significant. When compared to the theoretical values of the rigidity of the ball screw, the experimental results are lower. In addition to errors such as the experimental precision machining errors and human errors, any slight offset in the fixture rigidity, tools setup, and axial force may also affect the results. Furthermore, the material parameters, physical characteristics, and mechanical properties, etc. are all somewhat different from the ideal values. When considering the accumulation of all those errors, the experimental results of lower rigidity than the theoretical value is reasonable.

並列關鍵字

Ball screw ； Axial rigidity ； Hertz contact ； Finite element method (FEM)

參考文獻

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