摘要
近年來工具機主軸之設計,趨於高加工率,高轉速與高精密度的要求,高加工率與高轉速會造成主軸軸承剛度的改變,因而直接影響了加工的精度,因此,本文研究滾動軸承之接觸剛度。 傳統計算軸承剛度的方式是採用力平衡方法及Hertz接觸理論,由於軸承受負荷作用情況複雜,且Hertz接觸理論假設於簡單形狀的規則體與半無限空間的邊界條件,不考慮接觸區域以外之物體幾何形狀與邊界拘束影響,無法符合軸承的複雜幾何情況。 因此,本文利用有限元素方法,以懲罰函數求解接觸力與位移之關係,以有限元素分析之商用軟體ANSYS,建立軸承模型,離散元素及進行分析,探討不同的使用條件,軸承內外環之相對位移變形量與軸承剛度之變化,並與採用Hertz理論之Jones-Harris方法求得結果進行比較。 本研究在進行軸承分析之前,先根據Hertz接觸理論之解析解,驗證鋼珠與鋼板接觸模型之分析結果,並進行邊界條件,接觸參數,及元素尺寸,形狀,離散網格方式的估測,以確立適合進行接觸分析之有限元素模式。 本文針對深溝滾珠及斜角滾珠兩種滾動軸承進行接觸力學分析,忽略滑動與陀轉力矩效應,考慮轉速造成之離心力,摩擦力,大變形及非對稱接觸,分別針對軸承受徑向負荷,軸向負荷,軸向與徑向之聯合負荷,以及在有轉速及無轉速的兩種情況下,利用ANSYS的靜態求解器,以懲罰函數法求出軸承內外環之相對位移變形量與軸承剛度之改變,並將分析之結果,與傳統Jones-Harris分析方法進行比較,分析結果顯示兩者之位移變形量與剛度隨負荷之變化趨勢相同,但是傳統方法分析結果之位移較大,剛度係數較保守,其誤差之來源為Hertz之限制條件,因此,有限元素方法作為滾珠軸承之剛度計算方法,既方便又有效率,同時有較為精確的估計值。
並列摘要
Machine tools have been recently developed toward high feed rate, high spindle speed and high manufacturing precision. The high feed rate and high spindle speed change spindle bearing stiffness, and lead to the problem of the precision of the machine tools. Jones-Harris method, static force balancing and Hertz contact theory are adopted to calculate the stiffness of the bearing, however it is difficult to obtain the accurate stiffness value due to the complicated loading of the bearing. In addition Hertz contact theory is only applied to the simple shape and semi-infinite boundary condition. Therefore the penalty method has been adopted here to solve the contact problem with the consideration of large deformation and the friction. The finite element method also has been employed to establish and analyze the bearing model built with ANSYS to estimate the relative displacement of inner and outer ring and bearing stiffness under various boundary conditions. According to Hertz contact theory, its analysis result can be applied to verify the contact model of a steel ball and a plate in numerical techniques. Then the optimum contact analysis model is built for finite element in elementary mesh way to estimate the normal stiffness. The result of this investigation proofs the finite element method is more suitable than Jones-Harris method for reviewing boundary condition. To estimate the stiffness of rolling contact, two different kinds of deep-groove ball bearing and angular-contact ball bearing models are presented for finite element method. Neglecting the effects of sliding and gyroscopic, the relative displacement and stiffness of inner and outer ring of ball bearing are subjected to radial load, axial load, mixed load and centrifugal force respectively. There will be less accuracy of relative displacement and stiffness for Jones-Harris method due to the incorrect boundary condition assumption. Though both methods have the similar tendency, the errors can be modified with the method presented here. The result can be used as the reference for the design of the spindle of the machine tools.