Abstract: assembly variation analysis of parts that have flexible curved surfaces is much more difficult than that of solid bodies, because of structural deformations in the assembly process. Most of the current variation analysis methods either neglect the relationships among feature points on part surfaces or regard the distribution of all feature points as the same. In this study, the problem of flexible curved surface assembly is simplified to the matching of side lines. A methodology based on Bézier curves is proposed to represent the side lines of surfaces. It solves the variation analysis problem of flexible curved surface assembly when considering surface continuity through the relations between control points and data points. The deviations of feature points on side lines are obtained through control point distribution and are then regarded as inputs in commercial finite element analysis software to calculate the final product deformations. Finally, the proposed method is illustrated in two cases of antenna surface assembly.

基于Bézier曲线的柔性曲面装配变动分析

[1]Cai N, Qiao LH, 2011. Dimensional variation analysis of compliant sheet metal assembly. 2^nd Int Conf on Digital Manufacturing and Automation, p.429-432.

[2]Camelio JA, Hu SJ, Marin SP, 2004. Compliant assembly variation analysis using component geometric covariance. J Manuf Sci Eng, 126(2):355-360.

[3]Chaumette D, 2006. Technical evaluation report. Meeting on multifunctional structures/integration of sensors and antennas, p.T1-T10. https://doi.org/10.14339/RTO-MP-AVT-141

[4]Choi W, Chung H, 2015. Variation simulation of compliant metal plate assemblies considering welding distortion. J Manuf Sci Eng, 137(3):031008.

[5]Gerbino S, Patalano S, Franciosa P, 2008. Statistical variation analysis of multi-station compliant assemblies based on sensitivity matrix. Int J Comput Appl Technol, 33(1): 12-23.

[6]Guo JK, Li BT, Liu ZG, et al., 2016. Integration of geometric variation and part deformation into variation propagation of 3-D assemblies. Int J Prod Res, 54(19):5708-5721.

[7]Huang WZ, Liu JY, Chalivendra V, et al., 2014. Statistical modal analysis for variation characterization and application in manufacturing quality control. IIE Trans, 46(5): 497-511.

[8]Lancaster HO, Seneta E, 2005. Chi-Square Distribution. John Wiley & Sons, New York, USA.

[9]Liao XY, Wang GG, 2005a. Employing fractals and FEM for detailed variation analysis of non-rigid assemblies. Int J Mach Tools Manuf, 45(4-5):445-454.

[10]Liao XY, Wang GG, 2005b. Wavelets-based method for variation analysis of non-rigid assemblies. Int J Mach Tools Manuf, 45(14):1551-1559.

[11]Lindau B, Wärmefjord K, Lindkvist L, et al., 2014. Method for handling model growth in nonrigid variation simulation of sheet metal assemblies. J Comput Inform Sci Eng, 14(3):031004.

[12]Liu J, Jin JH, Shi JJ, 2010. State space modeling for 3-D variation propagation in rigid-body multistage assembly processes. IEEE Trans Autom Sci Eng, 7(2):274-290.

[13]Liu SC, Hu SJ, 1997. Variation simulation for deformable sheet metal assemblies using finite element methods. J Manuf Sci Eng, 119(3):368-374.

[14]Marciniak Z, Duncan JL, Hu SJ, 2002. Mechanics of Sheet Metal Forming (2^nd Ed.). Butterworth-Heinemann, Oxford, UK.

[15]Qu XT, Li XN, Ma Q, et al., 2016. Variation propagation modeling for locating datum system design in multi-station assembly processes. Int J Adv Manuf Technol, 86(5-8):1357-1366.

[16]Rocca P, Anselmi N, Massa A, 2014. Interval arithmetic for pattern tolerance analysis of parabolic reflectors. IEEE Trans Antennas Propag, 62(10):4952-4960.

[17]Tonks MR, Chase KW, 2004. Covariance modeling method for use in compliant assembly tolerance analysis. Int Design Engineering Technical Conf and Computers and Information in Engineering Conf, p.49-55.

[18]Yang Z, McWilliam S, Popov AA, et al., 2013. A probabilistic approach to variation propagation control for straight build in mechanical assembly. Int J Adv Manuf Technol, 64(5-8):1029-1047.

[19]Yu KG, Yang ZH, 2015. Assembly variation modeling method research of compliant automobile body sheet metal parts using the finite element method. Int J Automot Technol, 16(1):51-56.