螺栓结合部切向刚度计算模型建立及分析
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摘要
对于栓接结合部来说,当前的研究主要集中在栓接结合部整体法向刚度的研究。由于栓接结合部的切向刚度对整机静态特性也起着至关重要的作用,因此,要实现对栓接结合部静态特性的全面解析,还需提出一种计算栓接结合部切向刚度的方法。以栓接结合部法向刚度求解模型为基础,提出一种计算栓接结合部切向刚度的解析模型。最后分别通过解析计算及有限单元法对具体实例进行计算,结果表明:计算模型获得的栓接结合部的整体位移值等于8.3917e-4m,而有限元计算的结果为3.19e-4m,两者存在一定的偏差,主要原因在于有限元分析中考虑了摩擦力的影响。而在考虑摩擦力影响的情况下,数学模型计算出的总位移数值为3.104e-4m,与有限元的计算结果误差较小,故可证明所提数学模型的可行性。内容为机械系统中螺栓结合部综合刚度的求解奠定了一定的理论基础。
For the bolted joint,the current research is mainly focused on the study of the overall normal stiffness of the bolted joint.As a result of the integration of a bolted tangential stiffness of the whole machine static characteristic also plays an important role,therefore,to achieve the comprehensive analysis,the characteristics of the integration of a bolted static still need to put forward a method of the integration of a bolted tangential stiffness calculation.In this paper,an analytical model for calculating the tangential stiffness of a bolted joint is presented on the basis of the stiffness solution model of the bolted joint.Finally respectively by analytical calculation and finite element method for calculation,concrete examples results show that the calculation model for the integration of a bolted the overall displacement value is equal to 8.3917 e-4 m,and the results of finite element calculation of 3.19 e-4 m,there is a certain deviation,the main reason lies in considering the influence of friction in the finite element analysis.Considering the influence of friction,the total displacement calculated by mathematical model is3.104 e-4 m,which is less than the result of finite element analysis.Therefore,it is possible to prove the feasibility of the proposed mathematical model.The content of this paper lays a theoretical foundation for the solution of the comprehensive stiffness of the bolted joint in the mechanical system.
For the bolted joint,the current research is mainly focused on the study of the overall normal stiffness of the bolted joint.As a result of the integration of a bolted tangential stiffness of the whole machine static characteristic also plays an important role,therefore,to achieve the comprehensive analysis,the characteristics of the integration of a bolted static still need to put forward a method of the integration of a bolted tangential stiffness calculation.In this paper,an analytical model for calculating the tangential stiffness of a bolted joint is presented on the basis of the stiffness solution model of the bolted joint.Finally respectively by analytical calculation and finite element method for calculation,concrete examples results show that the calculation model for the integration of a bolted the overall displacement value is equal to 8.3917 e-4 m,and the results of finite element calculation of 3.19 e-4 m,there is a certain deviation,the main reason lies in considering the influence of friction in the finite element analysis.Considering the influence of friction,the total displacement calculated by mathematical model is3.104 e-4 m,which is less than the result of finite element analysis.Therefore,it is possible to prove the feasibility of the proposed mathematical model.The content of this paper lays a theoretical foundation for the solution of the comprehensive stiffness of the bolted joint in the mechanical system.
引文
[1]Hassan Jalali,Hamid Ahmadian,John E.Mottershead.Identification of nonlinear bolted lap-joint parameters by force-state mapping[J].International Journal of Solids and Structures,2007(44):8087-8105.
[2]杨辉,韩江,褚向前.螺栓联接结构接触应力及结合面刚度影响因素研究[J].机械强度,2015,37(1):128-132.(Yang Hui,Han Jiang,Chu Xiang-qian.Bolt coupling structure of contact stress and the influence factors of joint stiffness[J].Journal of Mechanical Strength,2015,37(1):128-132.)
[3]Levina Z M.Research on the static stiffness of joints in machine tools[C].Proc.8th International Machine Tool Design and Research Conference.1967:737-758.
[4]Thornely R H,Khoyi M R H.The significance of joints and their orientation upon the overall deformation of some machine tool structure elements[C].Machine Tool Design and Research Conference,1970.
[5]Lehnhoff T F,Ko K I,Mckay M L.Member stiffness and contact pressure distribution of bolted joints[J].Journal of Mechanical Design,1994,116(2):550-557.
[6]蔡力钢,郝宇,郭铁能.螺栓结合面法向静态刚度特性提取方法研究[J].振动与冲击,2014,33(16):18-23.(Cai Li-gang,Hao Yu,Guo Tie-neng.Method of extracting normal static stiffness of bolted joint interfaces[J].Journal of Vibration and Shock,2014,33(16):18-23.)
[7]Bickford J H.Introduction to the Design and Behavior of Bolted Joints,Fourth Edition:Non-Gasketed Joints[M].Crc Press,2007.
[8]Nassar S A,Abboud A.An improved stiffness model for bolted joints[J].Journal of Mechanical Design,2009,131(12).
[9]杨国庆,王飞,洪军.螺栓被连接件刚度理论的计算方法[J].西安交通大学学报,2012,46(7):50-56.(Yang Guo-qing,Wang Fei,Hong Jun.Theoretical analysis for bolted member stiffness[J].Journal of Xi’an Jiaotong University,2012,46(7):50-56.)
[10]杨国庆,王飞,洪军.螺栓被连接件轴向刚度高精度计算的半解析方法[J].西安交通大学学报,2012,46(9):37-42.(Yang Guo-qing,Wang Fei,Hong Jun.Semi-Analytical method for accurate evaluation of axial stiffness of bolted member[J].Journal of Xi’an Jiaotong University,2012,46(9):37-42.)
[11]Alkatan F,Stephan P,Daidie A.Equivalent axial stiffness of various components in bolted joints subjected to axial loading[J].Finite Elements in Analysis&Design,2007,43(8):589-598.
[12]Pedersen N L,Pedersen P.On prestress stiffness analysis of bolt-plate contact assemblies[J].Archive of Applied Mechanics,2008,78(2):75-88.
[13]Naruse T,Shibutani Y.Nonlinear bending stiffness of plates clamped by bolted joints under bending moment[J].Journal of Solid Mechanics&Materials Engineering,2012,6(7):832-843.
[14]Oskouei R H,Keikhosravy M,Soutis C.Estimating clamping pressure distribution and stiffness in aircraft bolted joints by finite-element analysis[J].Proceedings of the Institution of Mechanical Engineers,Part G:Journal of Aerospace Engineering.2009,223(7):863-871.
[15]Shigley J E,Mischke C R,Budynas R G.Mechanical Engineering Design[M].New York:Mc Graw-Hill,2004.
[16]Musto J C,Konkle N R.Computation of member stiffness in the design of bolted joints[J].ASME Journal of Mechanical Design,2006,128(6):1357-1360.
[2]杨辉,韩江,褚向前.螺栓联接结构接触应力及结合面刚度影响因素研究[J].机械强度,2015,37(1):128-132.(Yang Hui,Han Jiang,Chu Xiang-qian.Bolt coupling structure of contact stress and the influence factors of joint stiffness[J].Journal of Mechanical Strength,2015,37(1):128-132.)
[3]Levina Z M.Research on the static stiffness of joints in machine tools[C].Proc.8th International Machine Tool Design and Research Conference.1967:737-758.
[4]Thornely R H,Khoyi M R H.The significance of joints and their orientation upon the overall deformation of some machine tool structure elements[C].Machine Tool Design and Research Conference,1970.
[5]Lehnhoff T F,Ko K I,Mckay M L.Member stiffness and contact pressure distribution of bolted joints[J].Journal of Mechanical Design,1994,116(2):550-557.
[6]蔡力钢,郝宇,郭铁能.螺栓结合面法向静态刚度特性提取方法研究[J].振动与冲击,2014,33(16):18-23.(Cai Li-gang,Hao Yu,Guo Tie-neng.Method of extracting normal static stiffness of bolted joint interfaces[J].Journal of Vibration and Shock,2014,33(16):18-23.)
[7]Bickford J H.Introduction to the Design and Behavior of Bolted Joints,Fourth Edition:Non-Gasketed Joints[M].Crc Press,2007.
[8]Nassar S A,Abboud A.An improved stiffness model for bolted joints[J].Journal of Mechanical Design,2009,131(12).
[9]杨国庆,王飞,洪军.螺栓被连接件刚度理论的计算方法[J].西安交通大学学报,2012,46(7):50-56.(Yang Guo-qing,Wang Fei,Hong Jun.Theoretical analysis for bolted member stiffness[J].Journal of Xi’an Jiaotong University,2012,46(7):50-56.)
[10]杨国庆,王飞,洪军.螺栓被连接件轴向刚度高精度计算的半解析方法[J].西安交通大学学报,2012,46(9):37-42.(Yang Guo-qing,Wang Fei,Hong Jun.Semi-Analytical method for accurate evaluation of axial stiffness of bolted member[J].Journal of Xi’an Jiaotong University,2012,46(9):37-42.)
[11]Alkatan F,Stephan P,Daidie A.Equivalent axial stiffness of various components in bolted joints subjected to axial loading[J].Finite Elements in Analysis&Design,2007,43(8):589-598.
[12]Pedersen N L,Pedersen P.On prestress stiffness analysis of bolt-plate contact assemblies[J].Archive of Applied Mechanics,2008,78(2):75-88.
[13]Naruse T,Shibutani Y.Nonlinear bending stiffness of plates clamped by bolted joints under bending moment[J].Journal of Solid Mechanics&Materials Engineering,2012,6(7):832-843.
[14]Oskouei R H,Keikhosravy M,Soutis C.Estimating clamping pressure distribution and stiffness in aircraft bolted joints by finite-element analysis[J].Proceedings of the Institution of Mechanical Engineers,Part G:Journal of Aerospace Engineering.2009,223(7):863-871.
[15]Shigley J E,Mischke C R,Budynas R G.Mechanical Engineering Design[M].New York:Mc Graw-Hill,2004.
[16]Musto J C,Konkle N R.Computation of member stiffness in the design of bolted joints[J].ASME Journal of Mechanical Design,2006,128(6):1357-1360.