幾何設計參數與操作條件變化對高速氣浮主軸系統之性能與穩定性影響研究

Influences of Geometric Design Parameters and Operational Conditions Variations on the Performance and Stability of a High-speed Gas Spindle System

邱昭智(Chao-Chih Chiu)

指導教授 ： 陳永樹

元智大學/工程學院/機械工程學系/博士(2009年)

摘要

氣體軸承由於具備低摩擦係數、運轉時不易產生高溫及使用壽命長等特性，已取代傳統式的滾珠軸承，並廣泛應用於精密機械與電子產業領域之加工機械中。然而，為滿足現今高精密度與高轉速的加工需求，對主軸系統的特性與穩定度的要求將更加嚴苛。在氣浮主軸系統中，軸承剛性在主軸系統運轉時的穩定度上扮演著關鍵性的角色；而主軸系統穩定性的優劣一般以量測鑽頭尖端的偏擺量來辨別；拉刀機構則用來夾持切削刀具。目前，新開發之主軸系統最高轉速不斷往上提升，因此，高轉速對於主軸系統特性所衍生之影響，將有待更深入的探究。
本研究將針對軸承設計參數與操作條件來探討對軸承剛性、主軸系統穩定性、電路板鑽孔之孔壁粗糙度的影響，並討論鑽咀與主軸界面處的接觸壓力。首先，利用實驗測試（珠擊法及力與位移關係兩種方式）來獲取軸承之剛性，相關結果亦用數值模型做驗證，此驗證後之分析模型，則用來探討不同幾何參數（徑長比、供氣壓力、供氣孔口大小、孔口節流與自成節流）對軸承剛性之影響。接著，以實驗的方法量測探討不同軸承間隙、操作條件對於主軸系統穩定性（鑽頭尖端偏擺量、噪音頻譜）與電路板之孔壁粗糙度的影響。最後，由盤型彈簧變形提供拉刀機構所需之夾持力。本研究亦由實驗與有限元素分析方式，獲取盤型彈簧之負載與變形關係，將所得之結果用以驗證模型的準確性。然後根據主軸系統中盤型彈簧的實際排列方式，分析轉速從0至30萬轉之間盤型彈簧因離心力造成之負載變化，同時也考慮盤型彈簧彼此間以及盤型彈簧與支撐界面間的摩擦係數。最後，將所得之負載代入接觸壓力之理論計算公式中，計算出鑽咀與主軸界面間之接觸壓力；並且討論不同的離心力、摩擦係數及鑽咀與主軸界面間之斜錐角度對於接觸壓力的影響。
研究結果顯示，使用較小的軸承間隙與供氣孔口直徑，或較大的供氣壓力與徑長比有助於提高軸承剛性，其中以軸承間隙對剛性的影響最大。而供氣壓力大小對於主軸系統的噪音頻譜分析與電路板的孔壁粗糙度並無明顯的影響；然而，增加軸承間隙時則會造成同步振動的不穩定現象出現；同時也造成於主軸的噪音頻譜中，在一倍頻轉速時介於4和7萬轉之間有較高的音壓值，且在低頻位置會產生噪音頻率；而低進幾率與高轉速時可獲得較佳的孔壁品質。由FEA結果也顯示，當轉速在30萬轉時離心力會造成盤型彈簧擴大導致拉刀力下降4%；亦考慮盤型彈簧彼此間摩擦係數影響，當摩擦係數從f=0.145增加至 f=0.75，兩者在盤型彈簧下壓0.8 mm時的拉刀力差額達24.5%。最後，考慮鑽咀與主軸界面斜錐角從3°增加到7°時，在0轉速與30萬轉時會造成接觸壓力降低2.5MPa到6MPa。本研究中不論軸承剛性計算之數值模型或盤型彈簧所得之有限元素分析模型，皆經過實驗結果驗證，相信研究結果對於未來高速主軸的設計，可以提供寶貴之定性與定量設計參考值。

關鍵字

高速主軸 ； 氣浮軸承 ； 軸承剛性 ； 軸承間隙 ； 供氣壓力 ； 徑長比 ； 接觸壓力 ； 拉刀機構 ； 離心力 ； 摩擦係數 ； 穩定性 ； 鑽頭偏擺 ； 噪音頻譜 ； 孔壁粗糙度

並列摘要

High-speed gas spindle systems have extensively replaced traditional ball bearing systems, due to their many advantages including low friction coefficients, low heat dissipations under high rotational speeds, and longer life spans. While these systems are currently in wide use for precision machinery and electronics manufacturing, the increasing demand for higher precision and higher rotational speeds has made it necessary to improve the stability of these spindle systems. The stability quality of a running spindle system depends largely on bearing stiffness which is measured by the run-out of the drill bit, while cutting tools are held by the drawbar mechanism. Nowadays, since manufacturers have already developed an ultra-high-speed spindle with a maximum speed of up to 250,000 rpm, it is necessary to assess in detail the effects of such high speeds on the properties of a spindle system.
Therefore, this study investigated the influences of the bearing design parameters and operational conditions on the bearing stiffness, spindle system stabilities, the roughness of hole wall quality on the printed circuit board, and the contact pressure of the collet/spindle interface in a high-speed gas spindle system. First, the ball impact test method and the relation of force and displacement were adopted to obtain bearing stiffness. Then a numerical model was developed, verified using these experimental results, and used to analyze the effects of a variety of parameters on bearing stiffness, including various length/diameter (L/D) ratios, supply pressures, orifice diameters, and two different restrictors (pocketed and inherent orifice). Next, the effects of different bearing gaps and operation conditions on the stabilities of the spindle system (run-out of the drill bit and noise spectrum) were measured with experimental methods. The relationship between the load and deflection of disc springs was obtained by conducting another experiment, and the result was used to verify the accuracy of the finite element analysis (FEA) model. Based on the arrangement of the disc springs in the spindle system, the load change was analyzed at rotation speeds ranging from 0 rpm to 300,000 rpm. Meanwhile, the friction coefficient among the disc springs and that between the disc spring stack and its support were considered. Finally, the disc spring loads were used into a formula to calculate the contact pressure of the collet/spindle interface. The influences of centrifugal force, friction coefficients, and taper angles on the contact pressure of the collet/spindle interface were discussed.
Results indicate that the bearing stiffness can be enhanced by either smaller bearing gaps and supply orifice diameter or larger supply pressure and gas bearing length/diameter ratio. Among these variables, the bearing gap has the greatest effect on the bearing stiffness. Changing the supply pressure has no obvious effect on the analysis of noise spectrum and the hole wall quality of the printed circuit board. However, increasing the bearing gap can generate synchronous vibration, cause a higher sound pressure level at rotational speeds 1X when the rotational speed falls between 40,000 rpm and 70,000 rpm, and produce new noise responses on low frequency. Hole wall roughness can be reduced by using lower feed rates and higher rotational speeds. The FEA results also show that when the rotational speed reaches 300,000 rpm, the centrifugal force will cause the disc spring to be deformed and thus result in 4% of the drawbar force. The friction coefficients among the disc springs and their support are considered to have certain effect. When the friction coefficients increases from f = 0.145 to f = 0.75, with the disc spring pressed down 0.8 mm, their difference in drawbar force is 24.5%. Additionally, while the taper angles of the collet/spindle interface increases from 3° to 7°, the contact pressure drops between 2.5 MPa and 6 MPa at 0 rpm and 300,000 rpm. Not only the numerical models calculated by bearing stiffness, but also the FEA models calculated by the contact pressure of the collet/spindle interface were all verified by the experimental results, thereby indicating that the results of this study are highly reliable. As a result, this study can be regarded as a rich resource for future designs of spindle systems.

並列關鍵字

bearing stiffness ； bearing gap ； centrifugal force ； contact pressure ； drawbar mechanism ； friction coefficient ； gas bearing ； high speed spindle ； hole wall roughness ； length/diameter (L/D) ratio ； noise spectrum ； run-out ； supply pressure ； stability

參考文獻

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