螺旋式壓縮機具有多項優點，因此，在過去數十年間廣泛的應用於各領域中。螺旋式壓縮機的核心為一對公母轉子，藉由轉動的容積變化產生壓縮空氣。在理論設計時，公、母轉子為嚙合條件及設計參數下所創生的理論齒形，並可形成完美的接觸線密封氣體防止洩漏。但實際上，轉子因加工誤差、組裝偏擺、運轉時的熱膨脹、以及應力變形等因素，容易發生轉子干涉或咬死的情況，因此，轉子的設計流程中會將間隙加入齒形中，但間隙會造成接觸線中斷及洩漏降低效率，雖然間隙會造成諸多缺點，但間隙對於轉子是必要的。所以，適當的間隙設計是影響壓縮機效率的主要因素之一。然而，傳統間隙的量測方式耗費人力與時間，並且需仰賴特定方式或機台進行量測，同時受限於分析軟體的功能限制，無法有效的計算實際間隙，因此，本研究主要目的為發展嚙合模擬與間隙計算的方法，以預測實際組裝的情況。
本研究所發展的各項技術具體說明如下：轉子嚙合模擬技術，以轉子的幾何造型搭配角度疊代方法，主要目的為計算轉子實際嚙合的位置。接觸線間隙計算方法，藉由嚙合模擬後的轉子結合接觸線資料，以多截面疊代方法計算轉子在接觸線附近的間隙分佈。點對曲面搜尋最近點方法，建立以網格為基礎的搜尋方法，搭配計算初始值及數值疊代計算點到曲面的最近點。透過此三項技術的結合，不論齒形資料的類型或輸入的模擬條件，均可正確的計算嚙合位置及間隙分佈，與過去模擬方法最重要的不同點在於考量整根轉子而非單一截面，能夠近似實際轉子以多溝嚙合的情況。本研究除了與商用軟體計算結果以佐證本研究的正確性，同時，以實際量測間隙的結果進行比較，以驗證本方法對於間隙預測的準確性。

Twin screw compressors are for decades widely used in industry owing to advantages over other types of compressors. Due to machining imperfections, thermal expansion, pressure deformation, and assembly misalignment, these deviations from the theoretical profile often causes interference between the rotors. To compensate such deviations, it is necessary to apply clearance between the main and the gate rotors which will still provide minimum clearance to reduce the interference. However, the clearance may result in a change of the meshing conditions, such as imperfect contact, discontinuity of the sealing line, backlash and decreasing efficiency caused by the leakage of gas from a high-pressure region to a low-pressure region. Although the clearance may also lead to the above drawbacks, it is still necessary to design clearance between the rotors. Thus, the appropriate clearance between the rotors should be design carefully. Conventionally, clearance measurement must depend on the specific machines and spend lots time and effort. Also, the analysis software has limits for simulate the clearance. So, the aim of this study is to develop a new meshing simulation and clearance evaluation method to predict the real condition after assembly.
The methods developed in this study can be classified into the following three issues. The meshing simulation method is proposed to define the real meshing position for rotors by the geometry of rotor profile and angle iteration method. The clearance evaluation method is to calculate the clearance along the sealing line by the method of multiple transverses iteration. The procedure for searching the closest point between massive points and surface is based on the triangular mesh of surface and iterative method in order to comptute more rapidly. By the combination of the above methods, the meshing position and clearance can be computed correctly regardless the data type of rotor profiles or the variation simulation conditions. Specifically, the difference between this study and past researches is that the simulation method in this study considers the all lobes but not the single lobe at the same time for the purpose of approximate real meshing. Computer simulations are compared with commercial software to demonstrate the accuracy of the proposed method. Also, experimental results are presented to verify the feasibility for clearance prediction.

[1] K. B. Kumar and J. W. Bush, “Clearance distribution to reduce leakage area”, U.S. Patent No. 6167771, 2001.
[2] C. S. Holmes, “Towards a core program for the measurement of screw rotor bodies by co-ordinate measuring machine”, VDI Berichte, no. 1135, pp. 331-342, 1996.
[3] C. S. Holmes, “INSPECTION OF SCREW ROTORS FOR THE PREDICTION OF COMPRESSOR PERFORMANCE RELIABILITY, AND NOISE”, Proceedings of the 4th International Conference on Compressor and Refrigeration, Xi’an Jiaotong University, Xi’an, China, pp. 82-96, 2003.
[4] F. L. Litvin and P. H. Feng, “Computerized design, generation and simulation of meshing of rotors of screw compressor”, Mechanism and Machine Theory, Vol. 32, pp. 137-160, 1997.
[5] N. Stosic, I. K. Smith, A. Kovacevic, and C. A. Aldis, “The Design of a Twin-screw Compressor Boased on a New Rotor Profile”, Journal of Engineering Design, Vol. 8, No. 4, pp. 389-399, 1997.
[6] N. Stosic, and K. Hanjalic, “Development and optimization of screw machines with a simulation model - part I: profile generation”, ASME Transactions, Journal of Fluids Engineering, Vol. 119, pp. 659-663, 1997.
[7] K. Hanjalic, and N. Stosic, “Development and optimization of screw machines with a simulation model - part II: thermodynamic performance simulation and design optimization”, ASME Transactions, Journal of Fluids Engineering, Vol. 119, pp. 664-670, 1997.
[8] N. Stosic, “On gearing of helical screw compressor rotors”, Proc IMechE, Journal of Mechanical Engineering Science, Vol. 212, pp. 587-594, 1998
[9] N. Stosic, “Plural screw positive displacement machines”, U.S. Patent No. 6,296461 B1, 2001.
[10] N. Stosic, I. K. Smith, and A. Kovacevic, “Optimisation of screw compressors”, Applied Thermal Engineering, Vol. 23, no. 10, pp. 1177-1195, 2003.
[11] N. Stosic, I. K. Smith and A. Kovacevic, “Screw Compressors: Mathematical Modeling and Performance Calculation”, Springer - Verlag, Berlin, Heidelberg, 2005.
[12] Y. R. Wu and Z. H. Fong, “Optimization design of an explicitly defined rack for the generation of rotors for twin-screw compressors”, Mechanism and Machine Theory, Vol. 44, pp. 66-82, 2009.
[13] D. Zaytsev and C.A. Infante Ferreira, “Screw compressor rotors profile generation method based on pre-defined meshing line”, Proceedings of the 3rd international compressor technique conference, Wu’xi, China, pp. 117-127, 2001.
[14] D. Zaytsev and C. A. Infante Ferreira, “Profile generation method for twin screw compressor rotors based on the meshing line”, International Journal of Refrigeration, Vol. 28, pp. 744-755, 2005.
[15] Y. R. Wu and Z. H. Fong, “Improved rotor profiling based on the arbitrary sealing line for twin-screw compressors”, Mechanism and Machine Theory, Vol. 43, pp. 695-711, 2007.
[16] P. J. Singh and A. D. Onuschak, “A comprehensive, computerized method for twin-screw rotor profile generation and analysis”, Proceedings of the Purdue Compressor Technology Conference, Purdue, West Lafayette, pp. 519-527, 1984.
[17] P. J. Singh and P. R. Schwartz, “Exact analytical representation of screw compressor rotor geometry”, Proceedings of the International Compressor Engineering Conference, Purdue, West Lafayette, pp. 925-937, 1990.
[18] P. J. Singh and J. L. Bowman, “Calculation of blow-hole area for screw compressors”, Proceedings of the International Compressor Engineering Conference, Purdue, West Lafafette, pp. 938-948, 1990.
[19] L. Zhang and J. F. Hamilton, “Development of sealing line calculation in twin screw compressor”, Proceedings of the third international symposium on transport phenomena and dynamics of rotating machinery, Honolulu, Hawaii, pp. 623-638, 1990.
[20] L. Zhang and J. F. Hamilton, “Main geometric characteristics of the twin screw compressor”, Proceedings of the International Compressor Engineering Conference, Purdue, West Lafayette, pp. 449-456, 1992.
[21] Y. Tang and J. S. Fleming, “Obtaining the optimum geometrical parameters of a refrigeration helical screw compressor”, Proreedings of International Compressor Engineering Conference, Purdue, West Lafayette, pp. 221-227, 1992.
[22] J. S. Fleming, Y. Tang, and H. Anderson, “Optimization techniques applied to the design of a refrigeration twin screw compressor”, Proceedings of the International Compressor Engineering Conference, Purdue, West Lafayette, pp. 641-646, 1994.
[23] S. H. Su and C. H. Tseng, “Synthesis and optimization for rotor profiles in twin rotor screw compressors”, ASME Transactions, Journal of Mechanical Design, Vol. 122, pp. 543-552, 2000.
[24] H. T. Lee, “Screw-rotor machine with an ellipse as a part of its male rotor,” U.S. Patent No. 4890992, 1988.
[25] Y. Tang and J. S. Fleming, “Computer Aided Geometrical Analysis of the Geometrical Characteristics of a Helical Screw Compressor”, Proceedings of the International Compressor Technique Conference, Xi’an, China, pp. 400-408, 1993.
[26] Z. W. Xing, X. Y. Peng, and P. C. Shu, “Development and application of a software package for the design of twin screw compressors”, Proceedings of the International Compressor Engineering Conference, Purdue, West Lafayette, pp. 1011-1018, 2000.
[27] Z. W. Xing, Screw Compressor: Theory, Design and Application, China Machine Press, Beijing, 2000 (in Chinese).
[28] H. G. Wu, Z. W. Xing, and P. C. Shu, “Theoretical and experimental study on indicator diagram of twin screw refrigeration compressor”, International Journal of Refrigeration, Vol. 27, pp. 331-338, 2004.
[29] Y. Tang, and J. S. Fleming, “Clearances between the rotors of helical screw compressors: their determination, optimization and thermodynamic consequences”, Proceedings of the Institution of Mechanical Engineers, Part E: Journal of Process Mechanical Engineering, Vol. 208, No. E2, pp. 155-163, 1994.
[30] J. S. Fleming and Y. Tang, “The analysis of leakage in a twin screw compressor and its application to performance improvement”, Proceedings of the Institution of Mechanical Engineers, Part E: Journal of Process Mechanical Engineering, Vol. 209, No. E2, pp. 125-136, 1995.
[31] J. S. Fleming, Y. Tang, and G. Cook, “The twin helical screw compressor Part 1: development, applications and competitive position”, Proceedings of the Institution of Mechanical Engineers, Part C: Journal of Mechanical Engineering Science, Vol. 212, No. 5, pp. 355-367, 1998.
[32] J. S. Fleming, Y. Tang, and G. Cook, “The Twin Helical Screw Compressor Part 2: a Mathematical Model of the Working Process”, Proceedings of the Institution of Mechanical Engineers, Part C: Journal of Mechanical Engineering Science, Vol. 212, No. 5, pp. 369-380, 1998.
[33] N. Stosic, L. K. Smith, and A. Kovacevic, “Calculation of rotor interference in screw compressor”, Proceedings of the 3rd International Compressor Technique Conference, Wuxi, China, pp. 134-142, 2001.
[34] N. Stosic, L. K. Smith, and A. Kovacevic, “Rotor interference as a criterion for screw compressor design”, Journal of Engineering Design, Vol. 14, No. 2, pp. 209-220, 2003.
[35] W. Xiong and Q. Feng, “Calculation to inter-lobe clearance distribution of twin-screw compressor”, Journal of Xi’An Jiaotong University, Vol. 38, No. 7, pp. 682-685, 2004.
[36] W. Xiong and Q. Feng, “Study of rotor interference in screw compressors based on three dimensions”, Chinese Journal of Mechanical Engineering, Vol. 41, No. 6, pp. 55-59, 2004.
[37] D. Z. Sun and X. Z. Dong, “Meshing analysis of real tooth surface”, Chinese Journal of Mechanical Engineering, Vol. 36, No.8, pp. 98-101, August 2000.
[38] K. T. Gunnarson and F. B. Prinz, “CAD Model Based Localization of Parts in Manufacturing”, IEEE Computer, Vol. 20, No. 8, pp. 66-74, 1987.
[39] X. Huang, P. Gu, and R. Zernicke, “Localization and Comparison of Two Free-Form Surfaces”, Computer Aided Design, Vol. 28, pp. 1017-1022, 1996.
[40] Y. Chen and G. Medioni, “Object Modeling by Registration of Multiple Range Images”, Proceedings of IEEE Conference on Robotics and Automation, Vol. 3, pp. 2724-2729, 1991.
[41] P. J. Besl and D. McKay, “A Method for Registration of 3-D Shapes”, IEEE Transactions on Pattern Analysis and Machine Intelligence, Vol. 14, No. 2, pp. 239-256, 1992.
[42] T. M. Tucker and T. R. Kurfess, “Newton Methods for Parametric Surface Registration. Part I. Theory”, Computer Aided Design, Vol. 35, pp. 107-114, November 2003.
[43] K. S. Arun, T. S. Huang, and S. D. Blostein, “Least-Squares Fitting of Two 3-D Point Sets”, IEEE Transactions on Pattern Analysis and Machine Intelligence, Vol. 9, No. 5, pp. 698-700, 1987.
[44] T. Masuda and N. Yokoya, “A Robust Method for Registration and Segmentation of Multiple Range Images”, Computer Vision and Image Understanding, Vol. 61, No. 3, pp. 295-307, 1995.
[45] T. Masuda, “A Unified Approach to Volumetric Registration and Integration of Multiple Range Images”, Proceeding of International Conference on Pattern Recognition, Vol. 2, pp. 977-981, 1998.
[46] A. Collignon, D. Vandermeulen, P. Suetens, and G. Marchal, “Registration of 3D Multi-Modality Medical Images Using Surfaces and Point Landmarks”, Pattern Recognition Letter, Vol. 15, pp. 461-467, 1994.
[47] C. R. Maurer Jr., G. B. Aboutanos, B. M. Dawant, R. J. Maciunas, amd J. M. Fitzpatrick, “Registration of 3-D Images Using Weighted Geometrical Features”, IEEE Transactions on Medical Imaging, Vol. 15, No. 6, pp. 836-848, December 1996.
[48] W. H. Press, B. P. Flannery, S. A. Teukolsky, and W. T. Vetterling, Numerical Recipes in C: The Art of Scientific Computing, Cambridge, New York, 1992.
[49] S. J. Leon, Linear Algebra with Applications, Fourth Edition, Prentice Hall, New York, 1994.
[50] S. A. Nene and S. K. Nayar, “A Simple Algorithm for Nearest Neighbor Search in High Dimensions”, IEEE Transactions on Pattern Analysis and Machine Intelligence, Vol. 19, No. 9, pp. 989-1003, 1997.
[51] L. Piegl, and Tiller, W. The NURBS Book, Second Edition, Springer, 1995.
[52] IGES/PDES Organization, Initial Graphics Exchange Specification 5.3, 1997.
[53] B. K. Choi. Surface Modeling for CAD/CAM, Elsevier, 1991.
[54] 邱至意，「3D曲面模型網格化之研究」，國立中央大學，碩士論文，民國九十一年