考虑公差原则的三维公差分析方法研究
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摘要
针对目前公差分析中普遍存在未考虑公差原则影响的现象,提出了一种考虑公差原则的三维公差建模与分析方法.基于SDT理论和模态区间方法分别建立了要素采用独立原则、包容要求、最大实体要求、最小实体要求或可逆要求时的公差模型;利用空间矢量表示三维尺寸链,基于空间矢量环叠加原理推导出了三维公差分析时的封闭环尺寸及其变动计算模型;以采用不同公差原则的工程实例进行了三维公差建模和公差分析,给出了公差分析的步骤,验证了本文所研究方法的有效性.
A method of considering tolerance principle for three dimensional tolerance analysis was put forward. Based on small displacement torsor(SDT) theory and modal interval arithmetic,the tolerance models of size tolerance and geometrical tolerance of the feature of size apply independent principle,envelope requirement,maximum material requirement,least material requirement or reciprocity requirement,were established respectively. By using the space vector to represent 3 D dimension chain,a mathematical model was built to calculate the closed loop tolerance based on space vector loop stack principle. The application of the proposed method was illustrated through presenting an example,the tolerance analysis steps were given,and the availability of the proposed method was proved successfully.
A method of considering tolerance principle for three dimensional tolerance analysis was put forward. Based on small displacement torsor(SDT) theory and modal interval arithmetic,the tolerance models of size tolerance and geometrical tolerance of the feature of size apply independent principle,envelope requirement,maximum material requirement,least material requirement or reciprocity requirement,were established respectively. By using the space vector to represent 3 D dimension chain,a mathematical model was built to calculate the closed loop tolerance based on space vector loop stack principle. The application of the proposed method was illustrated through presenting an example,the tolerance analysis steps were given,and the availability of the proposed method was proved successfully.
引文
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[2]GAO J,CHASE K W,MAGLEBY S P.Generalized3D tolerance analysis of mechanical assemblies with small kinematic adjustments[J].IIE transactions,1998,30(4):367-377.
[3]DAVIDSON J K,MUJEZINOVIC A,SHAH J J.A new mathematical model for geometric tolerances as applied to round faces[J].J Mech Des,2002,124:609-621.
[4]DESROCHERS A,GHIE W,LAPERRIERE L.Application of a unified Jacobian-torsor model for tolerance analysis[J].J Comput Inf Sci Eng,2003,3(1):2-14.
[5]LI H,ZHU H P,LI P G,et al.Tolerance analysis of mechanical assemblies based on small displacement torsor and deviation propagation theories[J].Int J Adv Manuf Technol,2014,72:89-99.
[6]彭和平,刘晓军.考虑形位公差的二维装配公差分析[J].机械传动,2008,32(3):75-82.
[7]吴常林,黄美发,程彬彬,等.基于雅可比旋量模型的装配体公差统计分析[J].机械设计与研究,2015,31(6):97-100.
[8]程彬彬,王志越,黄美发,等.装配体三维公差建模及分析研究[J].机械设计与制造,2016(4):76-79.
[9]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.
[10]吴兆强.基于小位移旋量的公差建模及公差分析[J].机械设计与制造,2010(1):205-207.
[11]方东阳,李秀明,张琳娜,等.基于GPS的形位公差项目分析和设计[J].郑州大学学报(工学版),2005,26(3):73-75.
[12]Geometrical product specifications(GPS)-geometrical tolerancing-datums and datum systems:ISO 5459:2011(E)[S].
[13]SAINZ M A,ARMENGO J,CALM R,et al.Modal interval analysis:new tools for numerical information[M].Berlin:Springer,2014.
[2]GAO J,CHASE K W,MAGLEBY S P.Generalized3D tolerance analysis of mechanical assemblies with small kinematic adjustments[J].IIE transactions,1998,30(4):367-377.
[3]DAVIDSON J K,MUJEZINOVIC A,SHAH J J.A new mathematical model for geometric tolerances as applied to round faces[J].J Mech Des,2002,124:609-621.
[4]DESROCHERS A,GHIE W,LAPERRIERE L.Application of a unified Jacobian-torsor model for tolerance analysis[J].J Comput Inf Sci Eng,2003,3(1):2-14.
[5]LI H,ZHU H P,LI P G,et al.Tolerance analysis of mechanical assemblies based on small displacement torsor and deviation propagation theories[J].Int J Adv Manuf Technol,2014,72:89-99.
[6]彭和平,刘晓军.考虑形位公差的二维装配公差分析[J].机械传动,2008,32(3):75-82.
[7]吴常林,黄美发,程彬彬,等.基于雅可比旋量模型的装配体公差统计分析[J].机械设计与研究,2015,31(6):97-100.
[8]程彬彬,王志越,黄美发,等.装配体三维公差建模及分析研究[J].机械设计与制造,2016(4):76-79.
[9]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.
[10]吴兆强.基于小位移旋量的公差建模及公差分析[J].机械设计与制造,2010(1):205-207.
[11]方东阳,李秀明,张琳娜,等.基于GPS的形位公差项目分析和设计[J].郑州大学学报(工学版),2005,26(3):73-75.
[12]Geometrical product specifications(GPS)-geometrical tolerancing-datums and datum systems:ISO 5459:2011(E)[S].
[13]SAINZ M A,ARMENGO J,CALM R,et al.Modal interval analysis:new tools for numerical information[M].Berlin:Springer,2014.