螺旋式壓縮機轉子之設計與製造的分析

Abstract

本論文是針對螺旋式壓縮機之轉子進行設計與製造的分析，以期能自行開發、設計、並製造高效能之轉子。研究內容首先提出一種新的方法「分段創成法」，分別利用線性函式及Cubic Spline函式來擬合刀具上之資料點並創成共軛齒形。其中刀具上之資料點可由刀具之參數式計算或由三次元量測儀測量而得。在利用線性函式的分段創成法中，各小線性刀具運動參數 的工作區間之決定可解釋「二次切削」現象及說明並補償創成過程中之不連續性的現象。至於利用Cubic Spline函式的分段創成法，則可更精確而有效的求出創成的共軛運動對。所以「分段創成法」提供在設計共軛運動對與逆向工程的領域一種實際而有效的工具。接下來則是完成雙螺旋轉子輪廓線之設計分析。一螺旋轉子對是一組相對運轉之共軛運動對，由於為形成封閉之氣室，其中公、母轉子輪廓線必須同時具有「原始創成曲線」與「被創成曲線」的分佈。本研究將利用微分幾何與齒輪原理之方法，系統化完成齒形輪廓線之合成。即經由僅給定數個特定參數值，就可讓所有曲線之幾何參數完全被決定，並滿足切線連續之條件。轉子曲面之接觸線及回吹孔面積之計算也將被完成。最後將經由介面連結程式，在個人電腦上整合自動執行商用套裝分析軟體Mathematica與多功能最佳化分析軟體MOST，針對轉子輪廓曲線進行最佳化設計。接下來建立能同時切削雙邊螺旋轉子曲面之盤形刀具數學模型。本模型將有助於設計及製造高精度磨輪，來進行螺旋曲面之創成。本文將會討論具有三個幾何參數之螺旋曲面，並推導完整之盤形刀具外型分析。其中螺旋轉子之螺旋曲面、刀具外型、及轉子曲面接觸線也將以電腦圖形顯示。此外，刀具外型對製造精確度與成本之影響也將被討論。本研究將完成螺旋轉子輪廓線之設計分析及盤形刀具的設計軟體，而有助於提升泵浦及壓縮機製造廠商之設計及製造的分析能力。

This study focuses on the design and manufacture of rotors in screw compressors. A method called the "piecewise generation method" is proposed for generating the conjugate shapes from sets of data points using linear functions or cubic spline functions to fit the points. The points for a cutter can be either evaluated from the analytical from or measured from coordinate measuring machine. When using linear functions for piecewise generation, "secondary generations" can be found, but determining the working range of the kinematic parameter, , for per linear small cutter can explain the phenomenon and compensate for discontinuities in generation procedure. When using cubic spline functions for piecewise generation, the more accurate and effective results of conjugate profiles can be obtained. This method provides a practical and useful tool for conjugate-pair design and reverse engineering. And then a systematic analysis for the design method for rotor profiles of twin-rotor screw compressors is presented. A screw compressor is composed of a pair of rotors with kinematic-conjugate-pair property. Because compressors must form sealed cavities, multiple contact points usually exist along the cross section during the period of meshing. That is, the "original generating curves" and the "generated curves" always are distributed at cross-sectional profiles for both male and female rotors to keep them well-meshed with each other. This study will utilize the differential geometry and the gearing theory to synthesize rotor profiles systematically. Then, all the geometric parameters of these curves can be determined with satisfying the conditions of continuity in tangency by given only several specific parameter values. The contact lines on rotor surfaces and the blow-hole area calculation are also presented. The optimization procedure for rotor-profile design uses an interface coupler to integrate a commercial software (Mathematica) and a multi-functional optimization system tool (MOST) on the personal computers. Finally, a mathematical model of the disk-type grinding wheel used to cut both side of screw rotor surfaces will be presented in this study. This model is useful in the design and manufacture of high-precision grinding wheels for the screw surface generation. This study will discuss screw surfaces with three parameters and derives a complete analysis of the disk-type cutter profiles. Computer graphs of rotor surfaces for twin-rotor screw compressors, grinding wheels, and contact (generation) lines for meshing between rotor surfaces and cutters are presented. The influences of cutter profiles on manufacturing precision and costs are also discussed. This study completes the analysis and designing software for rotors and disk-type cutters of twin-rotor screw compressors. It will promote the abilities of analysis for designing and manufacturing of screw compressor industries.