螺栓连接是应用最广泛的装配形式之一，表征栓接结合部连接参数是进行装配体结构动力学分析的关键，针对各向同性虚拟材料模型不能准确表征结合面压力分布不均匀性的问题，提出并开发一种基于梯度虚拟材料的栓接结合面连接参数表征模型。首先根据结合面压力分布特征，以及结合面法向、切向刚度与压力分布间的映射关系，建立了等效虚拟材料参数随位置坐标的变化规律模型；分别采用等参梯度单元和高斯积分点料属性梯度分布单元等效表征结合部连接参数，采用结构静力学、动力学分析方法进行分析，通过对比不同类型单元静力学、动力学计算结果，验证梯度材料单元的准确性；进而研究了基于代理模型的梯度虚拟材料参数辨识方法，采用拉丁超立方采样来获取样本点，采用Kriging模型拟合连接参数，应用遗传算法优化虚拟材料参数。采用均匀虚拟材料模型、各向异性虚拟材料模型及梯度虚拟材料模型的仿真结果与试验数据对比，表明梯度虚拟材料模型是一种表征栓接结合部压力/刚度分布特性的有效方法。
Bolt connection is one of the most widely used forms of assembly, and the key of the dynamic analysis of the assembly structure is to characterize the connection parameters of the bolted joint. Because the virtual isotropic material model can't accurately characteristic the problems of asymmetrical surface pressure distribution, this paper put forward the parametric representation model of bolted joint surface, which based on Gradient virtual material. First, according to the characteristics of the pressure distribution of the joint surface and the mapping relationship between the normal and tangential stiffness with the pressure distribution, the change rule model of equivalent virtual material parameters with position coordinates is established. Using different gradient unit, including isoparametric graded finite elements and Gaussian unit which the material of integral point is gradient distribution characterize the junction parameters and the structural static and dynamic analysis method are used to analyze the accuracy of the gradient material unit by comparing the static and dynamic calculation results of different types of units. Furthermore, the parametric identification method of gradient virtual material based on agent model is studied, and the Latin hypercube sampling is used to get sample points, by using the Kriging model fitting connection parameters, using genetic algorithm to optimize the virtual material parameters. Comparing the simulation results of uniform virtual material, anisotropic virtual material, and gradient virtual material with the experimental results, shows that the gradient virtual material model is an effective method to characterize the pressure/stiffness distribution characteristics of bolted joint.
[1] YOSHIMURA M. Computer-aided design improvement of machine tool structure incorporating joint dynamics data[J]. Annals of the CIRP, 1979, 28(1):241-246.
[2] IZUMI S, YOKOYAMA T, KIMURA M, et al. Loosening-resistance evaluation of double-nut tightening method and spring washer by three-dimensional finite element analysis[J]. Engineering Failure Analysis, 2009, 16(5):1510-1519.
[3] WILLIAMS J G, ANLEY R E, NASH D H, et al. Analysis of externally loaded bolted joints:Analytical, computational and experimental study[J]. International Journal of Pressure Vessels and Piping, 2009, 86(7):420-427.
[4] YANG G, HONG J, WANG N, et al. Member stiffnesses and interface contact characteristics of bolted joints[C]//Assembly and Manufacturing (ISAM), 2011 IEEE International Symposium on. IEEE, 2011:1-6.
[5] MORTEZA I, HAMID A. Identification of nonlinear bolted lap joint models[J]. Computersand Structures, 2012, 96-97:1-8.
[6] 范世荣,张学良,温淑花,等. 基于各向同性虚拟材料的固定结合面修正模型[J]. 太原科技大学学报, 2017, 38(04):302-306. FAN Shirong, ZHANG Xueliang, WEN Shuhua, et al. Fixed binding surface modification model based on isotropic virtual materials[J]. Journal of Taiyuan University of Science and Technology, 2017, 38(04):302-306.
[7] 王世军,赵金娟,张慧军,等. 一种结合部法向刚度的预估方法[J]. 机械工程学报, 2011, 47(21):111-115, 122. WANG Shijun, ZHAO Jinjuan, ZHANG Huijun, et al. A method of estimating normal stiffness of joint[J]. Journal of Mechanical Engineering, 2011, 47(21):111-115, 122.
[8] MUÑOA G J, AGUIRRE R G, GOROSTIAGA A M. Inertia damper for suppressing vibrations in a machine tool:EP, EP2708316[P]. 2014-09-10.
[9] 谭峰,殷国富,董冠华,等. 基于子结构综合法的螺栓结合部切向动刚度优化辨识[J]. 四川大学学报, 2015(s2):171-177. TAN Feng, YING Guofu, DONG Guanhua, et al. Optimization identification of tangential dynamic stiffness of bolt joint based on substructure synthesis[J]. Journal of Sichuan University, 2015(s2):171-177.
[10] YOSHIMURA M, OKUSHIMA K. Measurement of dynamic rigidity and damping property for simplified joint models and simulation by computer[J]. Annals of the CIRP, 1977, 25(1):193-198.
[11] LIU J, OUYANG H, FENG Z, et al. Study on self-loosening of bolted joints excited by dynamic axial load[J]. Tribology International, 2017, 115:432-451.
[12] 田小龙,王雯,傅卫平,等. 考虑微凸体相互作用的机械结合面接触刚度模型[J]. 机械工程学报, 2017, 53(17):149-159. TIAN Xiaolong, WANG Wen, FU Weiping, et al. The model of asperity interactions in contact[J]. Journal of Mechanical Engineering, 2017, 53(17):149-159.
[13] 傅卫平,娄雷亭,高志强,等. 机械结合面法向接触刚度和阻尼的理论模型[J]. 机械工程学报, 2017, 53(9):73-82. FU Weiping, LOU Leiting, GAO Zhiqiang, et al. Heoretical model for the contact stiffness and damping of mechanical joint surface[J]. Journal of Mechanical Engineering, 2017, 53(9):73-82.
[14] 党会鸿. 机械结合面接触刚度研究[D]. 大连:大连理工大学, 2015. DANG Huihong. The research on contact stiffness of joint surface[D]. Dalian:Dalian University of Technology, 2015.
[15] 杨红平,傅卫平,王雯,等. 基于分形几何与接触力学理论的结合面法向接触刚度计算模型[J]. 机械工程学报, 2013, 49(1):102-107. YANG Hongping FU Weiping, WANG Wen, et al. Calculation model of the normal contact stiffness of joints based on the fractal geometry and contact theory[J]. Journal of Mechanical Engineering, 2013, 49(1):102-107.
[16] LEON R T, HU J W. Mechanical modeling of bolted t-stub connections under cyclic loads-part I:Stiffness modeling[J]. Journal of Constructional Steel Research, 2011, 67(11):1710-1718.
[17] 黄信. 考虑结合面接触的螺栓连接刚度研究[D]. 大连:大连理工大学, 2016. HUANG Xin. Research on stiffness of bolted joints considering joint surfaces contact[D]. Dalian:Dalian University of Technology, 2016.
[18] 田红亮. 机械结构固定结合部动力学建模[D]. 武汉:华中科技大学, 2011. TIAN Hongliang. Dynamic modeling on fixed joint interface virtual material in mechanical structure[D]. Wuhan:Huazhong University of Science and Technology, 2011.
[19] 黄勇. 圆截面梁的高阶理论和梯度梁的动静态与稳定性分析[D]. 长沙:中南大学, 2010. HUANG Yong. Higher-order theory of circular cylindrical beam and static/dynamic and stability analysis of graded beams[D]. Changsha:Central South University, 2010.
[20] 黄立新,姚祺,张晓磊,等. 基于分层法的功能梯度材料有限元分析[J]. 玻璃钢/复合材料, 2013(2):43-48. HUANG Lixin, YAO Qi, ZHANG Xiaolei, et al. Finite element analysis of functionally graded materials based on layering method[J]. Fiber Reinforced Plastics/Composites, 2013(2):43-48.
[21] HILBER H M, HUGHES T J R. Collocation, dissipation and[overshoot] for time integration schemes in structural dynamics[J]. Earthquake Engineering & Structural Dynamics, 1978, 6(1):99-117.
