基于多尺度理论的栓接结合部动力学建模
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摘要
建立准确的栓接结合部接触刚度模型对预测数控机床的动态特性至关重要。本文提出了一种基于多尺度理论的栓接结合部刚度模型,首先使用一系列叠加的三维正弦波来描述粗糙接触表面多尺度特性,每个正弦波被认为是一层频率级,推导出接触面积比与频率级的函数关系,则整体刚度可以看作不同频率级串联的弹簧模型。然后,通过数值仿真分析了结合面法向接触载荷、材料特性参数以及多尺度参数对接触刚度模型的影响。最后,设计分段梁结构进行试验验证本文模型的准确性,通过力锤敲击试验获得栓接结合部在等同预紧力下的固有频率和振型,并与仿真结果对比,结果表明本文多尺度模型固有频率与试验频率之间的相对误差小于9.94%,表明多尺度模型可以有效地预测数控机床的动态特性。
Accurate modeling of the contact stiffness of bolted joints is therefore crucial to predict the dynamic performance of CNC machine tools. This paper presents a contact stiffness model of a bolted joint based on multi-scale theory. The model uses a series of stacked three-dimensional sine waves to describe the multiple scales of roughness of the contact surface,and each frequency level is considered a layer of asperities,stacked iteratively on top of each other. The relationship between the contact area ratio and frequency level can be deduced. Moreover,the contact stiffness at each frequency level can be regarded as a spring in series in the model,therefore,the total stiffness can be obtained by summing the contact stiffness at each frequency level. The influences of contact load,material characteristic parameters and multi-scale parameters on the contact stiffness model are analyzed by mathematical simulation. An experimental setup consisting of the section beam specimen was used to validate the numerical model of the bolted joint for the case of equal pre-tightening forces. The relative error between the multi-scale natural frequencies and experimental frequencies was less than 9.94%,suggesting the multi-scale model can be effectively used in predicting the dynamic characteristics of CNC machine tools.
Accurate modeling of the contact stiffness of bolted joints is therefore crucial to predict the dynamic performance of CNC machine tools. This paper presents a contact stiffness model of a bolted joint based on multi-scale theory. The model uses a series of stacked three-dimensional sine waves to describe the multiple scales of roughness of the contact surface,and each frequency level is considered a layer of asperities,stacked iteratively on top of each other. The relationship between the contact area ratio and frequency level can be deduced. Moreover,the contact stiffness at each frequency level can be regarded as a spring in series in the model,therefore,the total stiffness can be obtained by summing the contact stiffness at each frequency level. The influences of contact load,material characteristic parameters and multi-scale parameters on the contact stiffness model are analyzed by mathematical simulation. An experimental setup consisting of the section beam specimen was used to validate the numerical model of the bolted joint for the case of equal pre-tightening forces. The relative error between the multi-scale natural frequencies and experimental frequencies was less than 9.94%,suggesting the multi-scale model can be effectively used in predicting the dynamic characteristics of CNC machine tools.
引文
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[2]Levina Z M.Research on the static stiffness of joints in machine tools[J].Advances in Machine Tool Design and Research,1968:737758.
[3]Majumdar A,Bhushan B.Fractal model of elasticplastic contact between rough surfaces[J].Journal of Tribology,1991,113(1):111.
[4]Greenwood J A,Williamson J B P.Contact of nominally flat surfaces[J].Proceedings of the Royal Society of London,1966,295(1442):300319.
[5]Kashani H,Nobari A S.Identification of dynamic characteristics of nonlinear joint based on the optimum equivalent linear frequency response function[J].Journal of Sound and Vibration,2010,329(9):14601479.
[6]Wang L Y,Yin G G,Zhang J F.Joint identification of plant rational models and noise distribution function using binaryvalued observation[J].Automatica,2006,42(4):535547.
[7]Majumdar A.Role of fractal geometry in roughness characterization and contact mechanics of surfaces[J].Trans Asme J Tribology,1990,112(2):205216.
[8]Majumdar A,Tien C L.Fractal characterization and simulation of rough surfaces[J].Wear,1990,136(2):313327.
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[10]温淑花,张学良,文晓光,等.结合部切向接触刚度分形模型建立与仿真[J].农业机械学报,2009,40(12):223227.Wen Shuhua,Zhang Xueliang,Wen Xiaoguang,et al.Fractal model of tangential contact stiffness of joint interfaces and its simulation[J].Transactions of the Chinese Society for Agricultural Machinery,2009,40(12):223227.
[11]Archard J F.Elastic deformation and the laws of friction[J].Proceedings of the Royal Society of London.Series A,Mathematical and Physical Sciences,1957,243(1233):190205.
[12]Ciavarella M.Linear elastic contact of the Weierstrass profile[J].Proceedings Mathematical Physical and Engineering Sciences,2000,456(1994):387405.
[13]Wilson W E,Angadi S V,Jackson R L.Surface separation and contact resistance considering sinusoidal elasticplastic multiscale rough surface contact[J].Wear,2010,268(1/2):190201.
[14]Jackson R L,Streator J L.A multiscale model for contact between rough surfaces[J].Wear,2006,261(11):13371347.
[15]Jackson R L.An analytical solution to an Archardtype fractal rough surface contact model[J].Tribology Transactions,2010,53(4):543553.
[16]Jackson R L,Ashurst W R,Flowers G T,et al.The effect of initial connector insertions on electrical contact resistance[C]∥Electrical Contacts2007 Proceedings of the 53rd IEEE Holm Conference on Electrical Contacts,Pittsburgh,PA,USA,2007:1724.
[17]Persson B.N.J.Theory of rubber friction and contact mechanics[J].The Journal of Chemical Physics,2001,115(8):38403861.
[18]Johnson K L,Greenwood J A,Higginson J G.The contact of elastic regular wavy surfaces[J].International Journal of Mechanical Sciences,1985,27(6):383396.
[19]Jackson R L,Green I.A finite element study of elastopastic hemispherical contact against a rigid flat[J].Journal of Tribology,2005,127(2):343354.
[20]Zhang X L,Huang Y M,Han Y.Fractal model of the normal contact stiffness of machine joint surfaces based on the fractal contact theory[J].China Mechanical Engineering,2000,11(7):727729.
[21]Kogut L,Etsion I.Elasticplastic contact analysis of a sphere and a rigid flat[J].Journal of Applied Mechanics,2002,69(5):657662.
[2]Levina Z M.Research on the static stiffness of joints in machine tools[J].Advances in Machine Tool Design and Research,1968:737758.
[3]Majumdar A,Bhushan B.Fractal model of elasticplastic contact between rough surfaces[J].Journal of Tribology,1991,113(1):111.
[4]Greenwood J A,Williamson J B P.Contact of nominally flat surfaces[J].Proceedings of the Royal Society of London,1966,295(1442):300319.
[5]Kashani H,Nobari A S.Identification of dynamic characteristics of nonlinear joint based on the optimum equivalent linear frequency response function[J].Journal of Sound and Vibration,2010,329(9):14601479.
[6]Wang L Y,Yin G G,Zhang J F.Joint identification of plant rational models and noise distribution function using binaryvalued observation[J].Automatica,2006,42(4):535547.
[7]Majumdar A.Role of fractal geometry in roughness characterization and contact mechanics of surfaces[J].Trans Asme J Tribology,1990,112(2):205216.
[8]Majumdar A,Tien C L.Fractal characterization and simulation of rough surfaces[J].Wear,1990,136(2):313327.
[9]温淑花,张学良,武美先,等.结合部法向接触刚度分形模型建立与仿真[J].农业机械学报,2009,40(11):197202.Wen Shuhua,Zhang Xueliang,Wu Meixian,et al.Fractal model and simulation of normal contact stiffness of joint interfaces and its simulation[J].Transactions of the Chinese Society for Agricultural Machinery,2009,40(11):197202.
[10]温淑花,张学良,文晓光,等.结合部切向接触刚度分形模型建立与仿真[J].农业机械学报,2009,40(12):223227.Wen Shuhua,Zhang Xueliang,Wen Xiaoguang,et al.Fractal model of tangential contact stiffness of joint interfaces and its simulation[J].Transactions of the Chinese Society for Agricultural Machinery,2009,40(12):223227.
[11]Archard J F.Elastic deformation and the laws of friction[J].Proceedings of the Royal Society of London.Series A,Mathematical and Physical Sciences,1957,243(1233):190205.
[12]Ciavarella M.Linear elastic contact of the Weierstrass profile[J].Proceedings Mathematical Physical and Engineering Sciences,2000,456(1994):387405.
[13]Wilson W E,Angadi S V,Jackson R L.Surface separation and contact resistance considering sinusoidal elasticplastic multiscale rough surface contact[J].Wear,2010,268(1/2):190201.
[14]Jackson R L,Streator J L.A multiscale model for contact between rough surfaces[J].Wear,2006,261(11):13371347.
[15]Jackson R L.An analytical solution to an Archardtype fractal rough surface contact model[J].Tribology Transactions,2010,53(4):543553.
[16]Jackson R L,Ashurst W R,Flowers G T,et al.The effect of initial connector insertions on electrical contact resistance[C]∥Electrical Contacts2007 Proceedings of the 53rd IEEE Holm Conference on Electrical Contacts,Pittsburgh,PA,USA,2007:1724.
[17]Persson B.N.J.Theory of rubber friction and contact mechanics[J].The Journal of Chemical Physics,2001,115(8):38403861.
[18]Johnson K L,Greenwood J A,Higginson J G.The contact of elastic regular wavy surfaces[J].International Journal of Mechanical Sciences,1985,27(6):383396.
[19]Jackson R L,Green I.A finite element study of elastopastic hemispherical contact against a rigid flat[J].Journal of Tribology,2005,127(2):343354.
[20]Zhang X L,Huang Y M,Han Y.Fractal model of the normal contact stiffness of machine joint surfaces based on the fractal contact theory[J].China Mechanical Engineering,2000,11(7):727729.
[21]Kogut L,Etsion I.Elasticplastic contact analysis of a sphere and a rigid flat[J].Journal of Applied Mechanics,2002,69(5):657662.