Research Progress of Tolerance Analysis Taking into Account the Deformation

doi:10.3901/JME.2018.07.139

Abstract

Abstract: Considering the deformation influence is one of the most important research topics of tolerance analysis. The deformation on parts will appear due to the influence of force, temperature and environment in manufacture, assembly and work. The traditional tolerance analysis model based on rigid body has been unable to consider the effect of deformation on tolerance, so it is necessary to research the methods of the tolerance analysis taking into account the deformation. Combined with the research of on tolerance analysis considered the deformation which the domestic and abroad experts are committed to in last twenty years, the methods and models are summarized. The advances of research are reviewed from the representation of tolerance and deformation, method for deformation calculation, tolerance-deformation coupled analysis, and computer-aided tolerance analysis. Some critical issues deserving further research on tolerance analysis taking into account the deformation are also summarized.

Key words: coupled, elastic deformation, representation, thermomechanics, tolerance analysis

CLC Number:

TH11

LUO Shaomin, XU Cheng. Research Progress of Tolerance Analysis Taking into Account the Deformation[J]. Journal of Mechanical Engineering, 2018, 54(7): 139-151.

References

[1] LIU S C, HU S J. An offset finite element model and its applications in predicting sheet metal assembly variation[J]. International Journal of Machine Tools and Manufacture, 1995, 35(11):1545-1557.
[2] HU S J, KOREN Y. Stream of variation theory for automotive body assembly[J]. Annals of the CIRP, 1997, 46(1):1-6.
[3] LIU S C, LEE H W, HU S J. Variation simulation for deformable sheet metal assemblies using mechanic models[J]. Transactions of NAMRI/SAE, 1995, 23(5):235-240.
[4] LIU S C, HU S J. Variation simulation for deformation sheet metal assembly using finite element methods[J]. Journal of Manufacturing Science and Engineering, 1997, 11:368-374.
[5] SAMPER S, GIORDANO M. Taking into account elastic displacements in 3D tolerancing models and application[J]. J. Mater. Process. Tech., 1998, 78:156-162.
[6] DESROCHERS A, CLÉMENT A. A dimensioning and tolerancing assistance model for CAD/CAM systems[J]. In.t J. Adv. Manuf. Technol., 1994, 9:352-361.
[7] DESROCHERS A, RIVIÈRE A. A matrix approach to the representation of tolerance zones and clearances[J]. Int. J. Adv. Manuf. Technol., 1997, 13:630-636.
[8] BOURDET P, MATHIEU L, LARTIGUE C, et al. The concept of the small displacement torsor in metrology[J]. Advanced Mathematical Tools in Metrology Ⅱ Series on Advances in Mathematics for Applied Sciences, 1996, 40:110-122.
[9] SAMPER S, GIORDANO M. Taking into account elastic displacements in 3D tolerancing models and application[J]. J. Mater. Process. Tech., 1998, 78:156-162.
[10] 张为民,陈灿,李鹏忠,等. 基于雅可比旋量法的实际工况公差建模[J]. 计算机集成制造系统, 2011, 17(1):77-83. ZHANG Weimin, CHEN Can, LI Pengzhong, et al. Tolerance modeling in actual working condition based on Jacobian-Torsor theory[J]. Computer Integrated Manufacturing Systems, 2011, 17(1):77-83.
[11] 冯(龙天),洪军,郭俊康,等. 基于新一代产品几何技术规范的工作载荷下公差建模[J]. 计算机集成制造系统, 2013, 19(7):1500-1508. FENG Yan, HONG Jun, GUO Junkang, et al. Tolerance modeling of working load based on geometrical product specifications[J]. Computer Integrated Manufacturing Systems, 2013, 19(7):1500-1508.
[12] 刘建永,乔立红. 一种考虑零件变形的装配误差计算方法[J].计算机集成制造系统, 2015, 21(1):94-100. LIU Jianyong, QIAO Lihong. Calculation method for assembly error with consideration of part deformation[J]. Computer Integrated Manufacturing Systems, 2015, 21(1):94-100.
[13] LUSTIG R, MEERKAMM H. Representation of elastic deformations as deviation zone and its connection with statistical tolerance zones[C]//Proceedings of the 9th International Design Conference, Dubrovnik, May 2006:921-928.
[14] 谢峰,方伟. 零件装配中动态尺寸链的研究[J]. 组合机床与自动化加工技术, 2006(11):69-71. XIE Feng, FANG Wei. The research of the dynamic dimensional chain in the parts assembly[J]. Modular Machine Tool & Automatic Manufacturing Technique, 2006(11):69-71.
[15] 林巨广,黄振辉,蔡高坡. 基于动态尺寸链的变速箱总成轴系装配精度的研究[J]. 机械工程师, 2009(5):40-42. LIN Juguang, HUANG Zhenhui, CAI Gaopo. Research on assembly precision of gearbox shafting assembly based on dynamic dimensional chain[J]. Mechanical Engineer, 2009(5):40-42.
[16] 武莉莉,方东阳,高琳. 受力变形对公差与配合设计的影响[J]. 河南纺织高等专科学校学报, 2005, 17(2):7-9. WU Lili, FANG Dongyang, GAO Lin. On the effects of stress deformation on tolerance and fit design[J]. Journal of Hennan Textile College, 2005, 17(2):7-9.
[17] SAMPER S, GIORDANO M. Simultaneous analysis method for tolerancing flexible mechanisms[C]//Proceedings of the 7th CIRP International Seminar on Computer Aided Tolerancing, April 24-25, 2001, Cachan, France, 2001:75-82.
[18] SAMPER S, ADRAGNA P A, FAVRELIERE H, et al. Modeling of 2D and 3D assemblies taking into account form errors of plane surfaces[J]. Journal of Computing & Information Science in Engineering, 2010, 9(4):790-792.
[19] SAMPER S, PETIT J P, GIORDANO M. Elastic clearance domain and use rate concept applications to ball bearings and gears[J]. Models for Computer Aided Tolerancing in Design and Manufacturing, 2007, 10:331-340.
[20] GRANDJEAN J, LEDOUX Y, SAMPER S. On the role of form defects in assemblies subject to local deformations and mechanical loads[J]. The International Journal of Advanced Manufacturing Technology, 2013, 65(9-12):1769-1778.
[21] CID G, THIÉBAUT F, BOURDET P. Taking the deformation into account for components' tolerancing[C/CD]//5th conference on Integrated Design on Manufacturing and Mechanical Engineering, April 5-7, Bath, UK, 2004.
[22] CID G, THIÉBAUT F, BOURDET P, et al. Geometrical study of assembly behaviour, taking into accounts rigid components' deviations, actual geometric variations and deformations[C/CD]//Proceedings of the 9th CIRP International Seminar on Computer Aided Tolerancing, Tempe, Arizona, 2005.
[23] GUO Junkang, HONG Jun, WANG Yong, et al. An ideal mating surface method used for tolerance analysis of mechanical system under loading[C]//12th CIRP Conference on Computer Aided Tolerancing, Procedia CIRP10, 2013:306-311.
[24] 胡鹏浩,费业泰,黄其圣. 考虑受热和受力变形的公差与配合设计[J]. 应用科学学报, 2000, 18(02):153-155. HU Penghao, FEI Yetai, HUANG Qisheng. Tolerance and fit design in consideration of thermal and assembling deformation[J]. Journal of Applied Sciences, 2000, 18(02):153-155.
[25] 黄其圣,张勇,胡鹏浩,等. 温度变化对机械零件配合精度的影响[J]. 机械设计, 2001, 18(3):45-47. HUANG Qisheng,ZHANG Yong,HU Penghao,et al. The influence of temperature variation on the fitting accuracy of machine elements[J]. Journal of Machine Design, 2001, 18(3):45-47.
[26] 费业泰, 罗哉. 精密技术中热变形误差影响的基本问题[J]. 纳米技术与精密工程, 2003, 1(1):79-84. FEI Yetai, LUO Zai. Basic problem about thermal deformation error in precision technology[J]. Nanotechnology and Precision Engineering, 2003, 1(1):79-84.
[27] 罗哉,费业泰,苗恩铭. 稳态温度场中孔形零件受热变形研究[J]. 材料热处理学报, 2004, 25(2):25-27. LUO Zai, FEI Yetai, MIAO Enming. Study on thermal deformation of hollow piece in steady temperature field[J]. Transactions of Materids and Heat Treatment, 2004, 25(2):25-27.
[28] 罗哉,费业泰,苗恩铭. 稳态非均匀温度场中孔型零件变形研究[J]. 应用科学学报, 2005, 23(4):424-427. LUO Zai, FEI Yetai, MIAO Enming. Thermal deformation of hollow parts in an uneven steady-state temperature field[J]. Journal of Applied Sciences, 2005, 23(4):424-427.
[29] 罗哉,费业泰,苗恩铭,等. 工作状态下孔形零件受热变形理论研究[J]. 机械设计, 2004, 21(10):24-25. LUO Zai, FEI Yetai, MIAO Enming, et al. Theoretical study on thermal deformation of hollowed parts under operating conditions[J]. Journal of Machine Design, 2004, 21(10):24-25.
[30] 罗哉. 精密机械中孔轴最佳热配合理论及应用研究[D]. 合肥:合肥工业大学, 2005. LUO Zai. Theoretical and applied research of optimal thermal fit of hollow piece and cylindrical piece[D]. Hefei:Hefei University of Technology, 2005.
[31] 芮执元,王志强,周亚敏. 热变形对电主轴电机转子与主轴过盈配合的影响[J]. 机械与电子, 2011(7):3-5. RUI Zhiyuan, WANG Zhiqiang, ZHOU Yamin. Effect of thermal deformation to the interference fit between the motor spindle's rotor and spindle[J]. Machinery & Electronics, 2011(7):3-5.
[32] JEANG A, CHEN T K, HWAN C L. A statistical dimension and tolerance design for mechanical assembly under thermal impact[J]. The International Journal of Advanced Manufacturing Technology, 2002, 20:907-915.
[33] SPRUEGEL T C, WALTER M, WARTZACK S. Robust tolerance design of systems with varying ambient temperature influence due to worldwide manufacturing and operation[C/CD]//International Design Conference, DESIG2014, 2014.
[34] BENICHOU S, ANSELMETTI B. Thermal dilatation in functional tolerancing[J]. Mechanism and Machine Theory, 2011, 46(11):1575-1587.
[35] 周启舟, 邱彪. 基于小位移旋量和热变形的平面公差建模方法研究[J]. 机械工程师, 2013(12):38-41. ZHOU Qizhou, QIU Biao. Modeling method of plane tolerance based on SDT and thermal deformation[J]. Mechanical Engineer, 2013(12):38-41.
[36] JAYAPRAKASH G, THILAK M, SIVAKUMAR K. Optimal tolerance design for mechanical assembly considering thermal impact[J]. The International Journal of Advanced Manufacturing Technology, 2014, 73:859-873.
[37] JAYAPRAKASH G, SIVAKUMAR K, THILAK M. FEA compliant parametric tolerance allocation of mechanical assembly using neural network and differential evolution algorithm[J]. International Journal of Computer Integrated Manufacturing, 2012, 25(7):636-654.
[38] JAYAPRAKASH G, THILAK M, SIVAKUMAR K. Integration of thermo mechanical strains into optimal tolerance design of mechanical assembly using NSGA Ⅱ and FE simulation[J]. Journal of Mechanical Engineering Research, 2011, 3(6):168-180.
[39] JAYAPRAKASH G, SIVAKUMAR K, THILAK M. Parametric tolerance qnalysis of mechanical assembly using FEA and cost competent tolerance synthesis using neural network[J]. Journal of Software Engineering and Applications, 2010, 3(12):1148-1154.
[40] GUO J, HONG J, YANG Z, et al. A tolerance analysis method for rotating machinery[J]. Procedia CIRP, 2013, 10:77-83.
[41] NI J, TANG W, XING Y. Three-dimensional precision analysis with rigid and compliant motions for sheet metal assembly[J]. The International Journal of Advanced Manufacturing Technology, 2014, 73(5):805-819.
[42] 倪俊,汤文成,幸研. 双弯曲反射面天线卧立转换尺寸偏差分析方法[J]. 机械工程学报, 2015, 51(17):120-127. NI Jun, TANG Wencheng, XING Yan. Dimensional variation analysis method for the assembly of double curved reflector before and after the lie-to-stand state conversion[J]. Journal of Mechanical Engineering, 2015, 51(17):120-127.
[43] PIERRE L, TEISSANDIER D, NADEAU J P. Integration of thermomechanical strains into tolerancing analysis[J]. International Journal on Interactive Design and Manufacturing (IJIDeM), 2009, 3(4):247-263.
[44] PIERRE L, TEISSANDIER D, NADEAU J P. Variational tolerancing analysis taking thermomechanical strains into account:Application to a high pressure turbine[J]. Mechanism and Machine Theory, 2014, 74:82-101.
[45] LORIN S, LINDKVIST L, SÖDERBERG R, et al. Combining variation simulation with thermal expansion simulation for geometry assurance[J]. Journal of Computing and Information Science in Engineering, 2013, 13(3):031007-031007-8.
[46] LEE D, KWON K E, LEE J. Tolerance analysis considering weld distortion by use of pregenerated database[J]. Journal of Manufacturing Science and Engineering, 2009, 131(4):583-590.
[47] PAHKAMAA A, RMEFJORD W, KARLSSON L. Combining variation simulation with welding simulation for prediction of deformation and variation of a final assembly[J]. Journal of Computing and Information Science in Engineering, 2012, 12(2):21002-21007.
[48] LORIN S, CROMVIK C, EDELVIK F, et al. Variation simulation of welded assemblies using a thermo-elastic finite element model[J]. Journal of Computing & Information Science in Engineering, 2014, 14(3):031003-031003-6.
[49] 胡敏,来新民,林忠钦,等. 车体多柔性件装配的误差分析[J]. 上海交通大学学报, 2000, 34(10):1365-1368. HU Min, LAI Xinmin, LIN Zhongqin, et al. Variation analysis for multi flexible auto-body assembly[J]. Journal of Shanghai Jiaotong University, 2000, 34(10):1365-1368.
[50] 来新民,林忠钦,陈关龙. 轿车车体装配尺寸偏差控制技术[J]. 中国机械工程, 2000, 11(11):1215-1220. LAI Xinmin, LIN Zhongqing, CHEN Guanlong. On variation control techniques for automotive body assembly[J]. China Mechanical Engineering, 2000, 11(11):1215-1220.
[51] 林忠钦,连军,倪军,等. 基于小样本的车身装配尺寸质量动态高精度评价方法[J]. 机械工程学报, 2001, 37(11):62-65. LIN Zhongqing, LIAN Jun, NI Jun, et al. High precision evaluation of the autobody assembly quality based on small sample size[J].Chinese Journal of Mechanical Engineering, 2001, 37(11):62-65.
[52] 田兆青,来新民,林忠钦. 多工位薄板装配偏差流传递的状态空间模型[J]. 机械工程学报, 2007, 43(2):202-209. TIAN Zhaoqing, LAI Xinmin, LIN Zhongqing. State space model of variations stream propagation in multistation assembly processes of sheet metal[J]. Chinese Journal of Mechanical Engineering, 2007, 43(2):202-209.
[53] 李余兵,陈关龙,来新民,等. 柔性件装配概念设计偏差分析系统架构[J]. 上海交通大学学报, 2006, 40(12):2070-2074. LI Yubing, CHEN Guanlong, LAI Xinmin, et al. An assembly variation analysis framework of flexible parts conceptual design[J]. Journal of Shanghai Jiaotong University, 2006, 40(12):2070-2074.
[54] LIAO X, WANG G G. Employing fractals and FEM for detailed variation analysis of non-rigid assemblies[J]. International Journal of Machine Tools and Manufacture, 2005, 45(4-5):445-454.
[55] LIAO X, WANG G G. Wavelets-based method for variation analysis of non-rigid assemblies[J]. International Journal of Machine Tools and Manufacture, 2005, 45(14):1551-1559.
[56] LIAO X, WANG G G. Non-linear dimensional variation analysis for sheet metal assemblies by contact modeling[J]. Finite Elem. Anal. Des., 2007, 44:34-44.
[57] XIE K, WELLS L, CAMELIO J A, et al. Variation propagation analysis on compliant assemblies considering contact interaction[J]. Journal of Manufacturing Science & Engineering, 2006, 129(5):743-752.
[58] DAHLSTRÖM S, LINDKVIST L. Variation simulation of sheet metal assemblies using the method of influence coefficients with contact modeling[J]. Journal of Manufacturing Science & Engineering, 2007, 129(3):615-622.
[59] UNGEMACH G, MANTWILL F. Efficient consideration of contact in compliant assembly variation analysis[J]. Journal of Manufacturing Science and Engineering, 2009, 131(1):123-136.
[60] LUSTIG R, MEERKAMM H. Linking elastic deformations and fabrication deviations in computer-aided-analysis[C/CD]//Proceedings of the 14th International Conference on Engineering Design, 19-21 August, Stockholm, 2003.
[61] STOCKINGER A, LUSTIG R, MEERKAMM H. Computer-based and experimental validation of an approach to combine tolerance zones with elastic deformations[C/CD]//International Conference on Engineering Design. 28-31 August, Paris, France, 2007.
[62] LUSTIG R, HOCHMUTH R, MEERKAMM H. Elastic deformations in computer aided tolerance analysis:A focus on two-dimensional contact surfaces[C]//Proceedings of the 8th International Design Conference, Dubrovnik, Croatia, 2004:1315-1320.
[63] LUSTIG R, HOCHMUTH R, MEERKAMM H. Enhancement in coupling tolerance analysis and elastic deformations on the example of a Serial linear support system[C/CD]//Proceedings of the 15th International Conference on Engineering Design, 15-18 August, Melbourne, Australia, 2005.
[64] STUPPY J, MEERKAMM H. Tolerance analysis of mechanisms taking into account joints with clearance and elastic deformations[C]//Proceedings of the 17th International Conference on Engineering Design, Stanford, August, 2009:489-500.
[65] SCHLEICH B, WARTZACK S. How to determine the influence of geometric deviations on elastic deformations and the structural performance?[C]//Proceedings of the Institution of Mechanical Engineers, Part B:Journal of Engineering Manufacture, 2013, 227(5):754-764.
[66] CAO Yanlong, MATHIEU L, JIANG J. Key research on computer aided tolerancing[J]. Journal of Zhejiang University Science A, 2015, 16(5):335-340.
[67] SHEN Z. Tolerance analysis with EDS/Vis VSA[J]. Journal of Computing & Information Science in Engineering, 2003, 3:95-99.
[68] PAWAR S Y, CHAVAN H A, CHAVAN S P. Tolerance stack up analysis and simulation using visualization VSA[J]. International Journal of Advanced Engineering Technology, 2011, 2:169-175.
[69] CHIESI F, GOVERNI L. Tolerance analysis with eM-TolMate[J]. Journal of Computing & Information Science in Engineering, 2003, 3:100-105.
[70] PRISCO U, GIORLEO G. Overview of current CAT systems[J]. Integrated Computer-Aided Engineering, 2002, 9(4):373-387.