双螺杆压缩机转子型线检测与表达的研究
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摘要
螺杆压缩机广泛应用于工业制冷、空气动力等行业,其主要是由一对相互啮合的螺杆转子构成,转子端截面型线的形式直接决定着螺杆压缩机的工作性能。在螺杆压缩机转子的研究方面,我国自主研究开发的转子型线与世界先进水平的转子型线还有相当大的差距,所以如何快速消化、吸收国外先进的螺杆转子型线就是本文研究的主要研究目的,而螺杆转子的逆向工程技术为此提供了新的手段。
本文主要在螺杆转子的检测技术、NURBS拟合方法、模型重构等问题上来研究和探讨了螺杆转子型线。
采用三坐标测量机(CMM)对螺杆转子进行了初步测量,在研究了转子型线CMM测量的补偿误差后,提出了基于曲面偏置测量法,以实现螺杆转子曲面的快速检测,提高检测效率。论文在理论上验证了该方法的可行性,通过在已知转子CAD原型的螺杆被测曲面及其测量所得偏距面的同一端面上分别截取一条型线进行比较输出误差。
研究了螺杆转子型线的数据预处理技术,针对螺杆转子型线测量数据的拟合,本文提出了基于移动最小二乘法的NURBS拟合螺杆型线逆向设计方法。详细介绍了移动最小二乘法(MLS)应用于NURBS曲线拟合的原理及特点,以螺杆转子端面点云数据为实例在MATLAB中实现了移动最小二乘NURBS曲线拟合,与采用传统最小二乘方法得到的拟合曲线相比,提高了精度及光滑性。
通过模型重构技术的研究,实现了螺杆转子的模型重构。
本文提出的螺杆型线逆向设计方法以及螺杆曲面模型重建的算法,已在Matlab中进实现,并通过实例验证了算法的有效性,为螺杆压缩机生产企业等提供了技术支持与参考信息。
Twin-screw compressor are widely applied in industrial refrigeration and air-conditioning. Screw rotors are the key parts of twin-screw compressor. The compressor performance is mainly determined by the screw rotor profile. This thesis concentrates on the researches of the twin-screw rotor measurement technology, fitting the measured rotor profile data and model reconstruction.
The thesis presents the mathematical model of screw rotor and proposes a measurement method for screw rotor. While measuring the rotor with Coordinate Measuring Machine (CMM), we obtain two-dimensional coordinate data of central point of the measuring ball. After fitting them to a curve, we generate a screw surface with the curve according to the screw spiral, and then offset the surface by the radius of the ball to attain another screw surface which is the measured surface after error compensation. In order to verify the feasibility of this method, the author extracts a curve in a cross-section from the compensated surface and compares it to the curve extracted from the same cross-section from the known CAD prototype of the screw rotor. In the end, theoretical error of the compensation is analyzed by Imageware which is a professional reverse engineering software.
To fit screw rotor profile measured data, the author researches fitting method based on Non-uniform Rational B-spline(NURBS). In order to solve the problem that the connections of fitting curves are not smooth enough, we further proposes a method of reverse design of screw profile based on the moving least square(MLS) of the curve fitting. This method greatly improves smoothness of the fitting curve. With the point data of the measured rotor profile as an instance, the method is realized with the MATLAB and compared with the Traditional Least- Square method.
The research achieves the measurement and expression of the advanced twin-screw compressor rotor profile, which will be useful in the rotor development, and provides effective measurement technology.
本文主要在螺杆转子的检测技术、NURBS拟合方法、模型重构等问题上来研究和探讨了螺杆转子型线。
采用三坐标测量机(CMM)对螺杆转子进行了初步测量,在研究了转子型线CMM测量的补偿误差后,提出了基于曲面偏置测量法,以实现螺杆转子曲面的快速检测,提高检测效率。论文在理论上验证了该方法的可行性,通过在已知转子CAD原型的螺杆被测曲面及其测量所得偏距面的同一端面上分别截取一条型线进行比较输出误差。
研究了螺杆转子型线的数据预处理技术,针对螺杆转子型线测量数据的拟合,本文提出了基于移动最小二乘法的NURBS拟合螺杆型线逆向设计方法。详细介绍了移动最小二乘法(MLS)应用于NURBS曲线拟合的原理及特点,以螺杆转子端面点云数据为实例在MATLAB中实现了移动最小二乘NURBS曲线拟合,与采用传统最小二乘方法得到的拟合曲线相比,提高了精度及光滑性。
通过模型重构技术的研究,实现了螺杆转子的模型重构。
本文提出的螺杆型线逆向设计方法以及螺杆曲面模型重建的算法,已在Matlab中进实现,并通过实例验证了算法的有效性,为螺杆压缩机生产企业等提供了技术支持与参考信息。
Twin-screw compressor are widely applied in industrial refrigeration and air-conditioning. Screw rotors are the key parts of twin-screw compressor. The compressor performance is mainly determined by the screw rotor profile. This thesis concentrates on the researches of the twin-screw rotor measurement technology, fitting the measured rotor profile data and model reconstruction.
The thesis presents the mathematical model of screw rotor and proposes a measurement method for screw rotor. While measuring the rotor with Coordinate Measuring Machine (CMM), we obtain two-dimensional coordinate data of central point of the measuring ball. After fitting them to a curve, we generate a screw surface with the curve according to the screw spiral, and then offset the surface by the radius of the ball to attain another screw surface which is the measured surface after error compensation. In order to verify the feasibility of this method, the author extracts a curve in a cross-section from the compensated surface and compares it to the curve extracted from the same cross-section from the known CAD prototype of the screw rotor. In the end, theoretical error of the compensation is analyzed by Imageware which is a professional reverse engineering software.
To fit screw rotor profile measured data, the author researches fitting method based on Non-uniform Rational B-spline(NURBS). In order to solve the problem that the connections of fitting curves are not smooth enough, we further proposes a method of reverse design of screw profile based on the moving least square(MLS) of the curve fitting. This method greatly improves smoothness of the fitting curve. With the point data of the measured rotor profile as an instance, the method is realized with the MATLAB and compared with the Traditional Least- Square method.
The research achieves the measurement and expression of the advanced twin-screw compressor rotor profile, which will be useful in the rotor development, and provides effective measurement technology.
引文
1.邢子文.螺杆压缩机研究进展及应用趋势[J].通用机械,2006(1):30-33
2. Stosic N. Hanjalic K. Development and optimization of screw machines with a simulation model-Part I: Profile generation[J]. ASME Transactions, Journal of Fluids Engineering 1997,119(3):659-663
3.柯映林.反求工程CAD建模理论、方法和系统[J].机械工业出版社,2005.1-78
4.罗泽刚,王弘,转子齿面的NURBS表示及啮合线的数值解法[J].华中理工大学学报,2000,28(4):93-97
5.李汗强.圆弧包络线的传动性能分析及螺杆压缩机转子型线的优化设计[J].通用机械,2006(1):82-83
6.张正华.螺杆转子型线检测技术研究[D].硕士学位论文.无锡:江南大学2008
7.隋天中,王忠本.基于半球形测头的自由曲面截形测量方法[J].计量学报,2003,24(3):174—176
8.石国荣,隋连香,查继红.螺旋曲面的数字化测量及数据处理技术[J].沈阳工业学院学报,2004,23(2):80—82
9.马仙龙.基于NURBS的双螺杆压缩机转子型线研究[D].硕士学位论文.无锡:江南大学2008
10.江洪钧,王弘,袁春.基于NURBS的双螺杆制冷压缩机转子CAD系统[J].计算机工程与科学,2002,24(3):84-88
11.罗泽刚,王弘,转子齿面的NURBS表示及啮合线的数值解法[J].华中理工大学学报,2000,28(4):93-97
12.李碧浩.金属双螺杆泵螺杆转子性能分析[D].硕士学位论文.西安:西北工业大学车辆工程系,2006
13. N. Stosic. N Profile Rotors[EB/OL]. http://www.staff.city.ac.uk/~sj376/nrot.html. 2006-04-15
14.金涛,童水光.逆向工程技术[M].北京:机械工业出版社,2003.26-127
15.陈晓荣,蔡萍,施文康.光学非接触三维形貌测量技术新进展[J].光学精密工程,2002,10(5):528—532
16.赵勇,廖延彪,赖淑蓉.复杂轮廓表面激光检测及三维重构技术的研究[J].光电技术,2002,28(2):172—173
17.王红亮,陈树越.反求工程CLI建模中复杂轮廓数据处理方法研究.华北工学院学报,2004,20(4):306—309
18.刘振凯,陈剑虹,乔志林,丁玉成,卢秉恒.层去图像法反求工程中的数据处理[J].中国机械工程,2000,11(8):929—932
19.陈文静,苏显渝,谭松新.Fourier变换轮廓术中对测量系统的基本要求[J].光电子/激光,1999,10(6):535—539
20.王红敏,石沛林.三坐标测量机测头的测球半径补偿误差的计算[J].工具技术
21.王建华.螺旋面截面测量中的测头半径补偿.西安工业学院学报,1992,12(4):18~25
22.王建华,林其骏,等.复杂型面测量中测头中心的轨迹曲面及测头半径的三维补偿.计量学报,1994,15(2):108-113
23. JRRMyaer,YAMiretal,Touch Probe radius Compensation for coordinate measurement using Krigimg interpolation. Proe.Instn.Mech.Engrs,1997,17 (211)PartB:11~18
24.侯宇,李刚.自由型曲面的测量与重建.计量学报,1999,20(4):252-255
25.范光照,蔡东宪.测量曲线和曲面的形状误差分析.机械月刊(台),1999,25(5):274~281
26.隋天中,田春芳等.精密测量螺旋面任意截形的一种方法.计量学报,1993,14(3):187-191
27. IDudas.etal,Measurement of worm gearing for 3D measuring machine. Proceeding of the Fourth International Symposium on Measurement Technology and Intelligent Instrumens.1998,9:207~211
28.林其骏,方寿平等.螺杆泵转子齿形的三坐标检测原理和应用.机床与液压.1998.(2):41-46
29.王旭蕴,张玉坤.轮廓度误差的精密测量和评定.计量学报,1995,16(1):12~17
30.黎凌霄,吕强中一种开放性结构的基于PC的可编程控制器P(MAC).机电一体化,2002,l:41-44
31.隋天中,张明川,崔虹雯.基于虚拟样机技术的VCMM构建与测量方法[J].东北大学学报(自然科学版).2006
32.李春,刘书桂.三坐标测量机的测头半径补偿与曲面匹配[J].仪器仪表学报.2003
33. K.Skalski,et a1.Identification and Geometrical Modeling of/complex Shape/surfaces using/coordinate Measuring Machine and CAD/CAM System[J].Journal of Materials Processing,1998(76):l-3.
34.唐余勇.微分几何在机械中应用[M]..北京:高等教育出版社
35.施法中.计算机辅助几何设计和非均匀有理B样条(CAGD&NURBS)[M].北京航空航天大学出版社,1994
36.陶琦.三坐标测量数据预处理系统2.0研究[D].浙江大学硕士论文,杭州,2005.3
37.吴玉梅.CAD/CAM与CMM系统集成方法的研究[D].西安理工大学硕士论文,西安,2002.3
38. Ueng W D,Lai J Y , Doong J L.Sweep-surface reconstruction from three-dimentional measrured-data[J].Computer-Aided Design,1998,30(10):791~805.
39. Narayanaswarni R,Yan J.Multiresolution modeling techniques in CAD[J].Computer-Aided Design,2003,35(3):225~240.
40. Liang S R,Lin A C.Proble-radius compensation for 3-D points in reverse engineering[J].Computers in Industry,2002,48(3):241~251.
41.汪国平,刘占平,华宣积,孙家广,陈玉健.螺旋曲面的等距曲面[J].计算机辅助设计与图形学学报,2000.
42.曾清红,卢德唐.基于移动最小二乘法的曲线曲面拟合[J].工程图学学报,2004,(1):84-89.
43.孙兴伟,王太勇,王可.基于测量的螺旋曲面实体造型方法研究[J].组合机床与自动化加工技术,2006,2:76—78
44. Lee K H, Woo H, Suk T. Data reduction methods for reverse engineering[J]. International Journal of Advanced ManufacturingTechnology,2001,17(11):735-473
45.纪小刚.增压器叶轮逆向工程中的关键技术研究[D]:[博士学位论文].南京:南京理工大学机械工程学院,2006
46.刘军强,高建民,李言,连炜.基于逆向工程的点云数据预处理技术研究[J].现代制造工程,2005,(7):73-75
47.金涛,单岩,童水光.产品反求工程中基于几何特征及约束的模型重建[J].计算机辅助设计与图形学学报.2001,13(3):202-207
48. Liu G H, Wong Y S, Zhang Y F, etal. Adaptive fairing of digitized point data with discrete curvature[J]. Computer Aided Design, 2002,34(4):309-320.
49.洪军,丁玉成,曹亮等.逆向工程中的测量数据精简技术研究[J].西安交通大学学报.2004,38(7):661-664
2. Stosic N. Hanjalic K. Development and optimization of screw machines with a simulation model-Part I: Profile generation[J]. ASME Transactions, Journal of Fluids Engineering 1997,119(3):659-663
3.柯映林.反求工程CAD建模理论、方法和系统[J].机械工业出版社,2005.1-78
4.罗泽刚,王弘,转子齿面的NURBS表示及啮合线的数值解法[J].华中理工大学学报,2000,28(4):93-97
5.李汗强.圆弧包络线的传动性能分析及螺杆压缩机转子型线的优化设计[J].通用机械,2006(1):82-83
6.张正华.螺杆转子型线检测技术研究[D].硕士学位论文.无锡:江南大学2008
7.隋天中,王忠本.基于半球形测头的自由曲面截形测量方法[J].计量学报,2003,24(3):174—176
8.石国荣,隋连香,查继红.螺旋曲面的数字化测量及数据处理技术[J].沈阳工业学院学报,2004,23(2):80—82
9.马仙龙.基于NURBS的双螺杆压缩机转子型线研究[D].硕士学位论文.无锡:江南大学2008
10.江洪钧,王弘,袁春.基于NURBS的双螺杆制冷压缩机转子CAD系统[J].计算机工程与科学,2002,24(3):84-88
11.罗泽刚,王弘,转子齿面的NURBS表示及啮合线的数值解法[J].华中理工大学学报,2000,28(4):93-97
12.李碧浩.金属双螺杆泵螺杆转子性能分析[D].硕士学位论文.西安:西北工业大学车辆工程系,2006
13. N. Stosic. N Profile Rotors[EB/OL]. http://www.staff.city.ac.uk/~sj376/nrot.html. 2006-04-15
14.金涛,童水光.逆向工程技术[M].北京:机械工业出版社,2003.26-127
15.陈晓荣,蔡萍,施文康.光学非接触三维形貌测量技术新进展[J].光学精密工程,2002,10(5):528—532
16.赵勇,廖延彪,赖淑蓉.复杂轮廓表面激光检测及三维重构技术的研究[J].光电技术,2002,28(2):172—173
17.王红亮,陈树越.反求工程CLI建模中复杂轮廓数据处理方法研究.华北工学院学报,2004,20(4):306—309
18.刘振凯,陈剑虹,乔志林,丁玉成,卢秉恒.层去图像法反求工程中的数据处理[J].中国机械工程,2000,11(8):929—932
19.陈文静,苏显渝,谭松新.Fourier变换轮廓术中对测量系统的基本要求[J].光电子/激光,1999,10(6):535—539
20.王红敏,石沛林.三坐标测量机测头的测球半径补偿误差的计算[J].工具技术
21.王建华.螺旋面截面测量中的测头半径补偿.西安工业学院学报,1992,12(4):18~25
22.王建华,林其骏,等.复杂型面测量中测头中心的轨迹曲面及测头半径的三维补偿.计量学报,1994,15(2):108-113
23. JRRMyaer,YAMiretal,Touch Probe radius Compensation for coordinate measurement using Krigimg interpolation. Proe.Instn.Mech.Engrs,1997,17 (211)PartB:11~18
24.侯宇,李刚.自由型曲面的测量与重建.计量学报,1999,20(4):252-255
25.范光照,蔡东宪.测量曲线和曲面的形状误差分析.机械月刊(台),1999,25(5):274~281
26.隋天中,田春芳等.精密测量螺旋面任意截形的一种方法.计量学报,1993,14(3):187-191
27. IDudas.etal,Measurement of worm gearing for 3D measuring machine. Proceeding of the Fourth International Symposium on Measurement Technology and Intelligent Instrumens.1998,9:207~211
28.林其骏,方寿平等.螺杆泵转子齿形的三坐标检测原理和应用.机床与液压.1998.(2):41-46
29.王旭蕴,张玉坤.轮廓度误差的精密测量和评定.计量学报,1995,16(1):12~17
30.黎凌霄,吕强中一种开放性结构的基于PC的可编程控制器P(MAC).机电一体化,2002,l:41-44
31.隋天中,张明川,崔虹雯.基于虚拟样机技术的VCMM构建与测量方法[J].东北大学学报(自然科学版).2006
32.李春,刘书桂.三坐标测量机的测头半径补偿与曲面匹配[J].仪器仪表学报.2003
33. K.Skalski,et a1.Identification and Geometrical Modeling of/complex Shape/surfaces using/coordinate Measuring Machine and CAD/CAM System[J].Journal of Materials Processing,1998(76):l-3.
34.唐余勇.微分几何在机械中应用[M]..北京:高等教育出版社
35.施法中.计算机辅助几何设计和非均匀有理B样条(CAGD&NURBS)[M].北京航空航天大学出版社,1994
36.陶琦.三坐标测量数据预处理系统2.0研究[D].浙江大学硕士论文,杭州,2005.3
37.吴玉梅.CAD/CAM与CMM系统集成方法的研究[D].西安理工大学硕士论文,西安,2002.3
38. Ueng W D,Lai J Y , Doong J L.Sweep-surface reconstruction from three-dimentional measrured-data[J].Computer-Aided Design,1998,30(10):791~805.
39. Narayanaswarni R,Yan J.Multiresolution modeling techniques in CAD[J].Computer-Aided Design,2003,35(3):225~240.
40. Liang S R,Lin A C.Proble-radius compensation for 3-D points in reverse engineering[J].Computers in Industry,2002,48(3):241~251.
41.汪国平,刘占平,华宣积,孙家广,陈玉健.螺旋曲面的等距曲面[J].计算机辅助设计与图形学学报,2000.
42.曾清红,卢德唐.基于移动最小二乘法的曲线曲面拟合[J].工程图学学报,2004,(1):84-89.
43.孙兴伟,王太勇,王可.基于测量的螺旋曲面实体造型方法研究[J].组合机床与自动化加工技术,2006,2:76—78
44. Lee K H, Woo H, Suk T. Data reduction methods for reverse engineering[J]. International Journal of Advanced ManufacturingTechnology,2001,17(11):735-473
45.纪小刚.增压器叶轮逆向工程中的关键技术研究[D]:[博士学位论文].南京:南京理工大学机械工程学院,2006
46.刘军强,高建民,李言,连炜.基于逆向工程的点云数据预处理技术研究[J].现代制造工程,2005,(7):73-75
47.金涛,单岩,童水光.产品反求工程中基于几何特征及约束的模型重建[J].计算机辅助设计与图形学学报.2001,13(3):202-207
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