工具機線性滑軌之動態特性研究

Abstract

本研究主要是提出工具機內之滾珠接觸模擬的新方法，以便對線性滑軌作更深入的探討。本研究所發展之方法乃利用Hertz接觸理論計算鋼珠與線性滑軌接觸介面的正向勁度與切線勁度，然後導入由點對點至面對面的三維有限元素模式予以分析探討。研究顯示本研究所發展之三種有限元素模式與實驗所得的結果有相當高程度的吻合度。而其中又以使用無厚度接觸元素之有限元素的方法較為理想。同時，於分析過程中可發現，模態頻率會隨著預力的增加而變高。此外，針對線性滑軌受不同力矩條件下之模態分析，此項結果顯示結構之自然振動模態頻率變化不大，但振動模態形式會隨著力矩大小而改變。此現象說明滾珠介面之剛性會因外力而做適當調整，並影響結構之動態特性。

In this project, nonlinear characteristics on the rolling interface of a linear guide in machine tools were studied by the finite element analysis and experimental verification. Contact of the ball/surface rolling interface in rolling guides was simulated as a three-dimensional contact elements without thickness. By introducing Hertzian contact theory and applying proper normal/shear stiffness to such contact elements in the overall finite element model, dynamic behaviors of linear guides affected by preload were thus investigated. In the finite element procedure, three contact models, 1-D point-to-point, 2-D point-to-point and 3-D surface-to-surface, were sequentially introduced for purpose of verification with experiments. As a validation in this project, modal tests on linear guides with different preloads were conducted and related frequency spectrums were derived. Both the finite element and the experimental results reveal that the natural frequency of a linear guide increases with the increment of the preload. In addition, the dynamic characteristics predicted by finite element analysis agree well with those measured from instrumental experiments. In the modal analysis, it was told that the natural frequencies vary a little with different loading conditions; however, the mode shapes are changed obviously with the magnitude of applied loads. Therefore, the stiffness of contact interface needs to be properly adjusted during simulation which may affect the dynamic characteristics of the machine tools.