机械结合面法向接触刚度和阻尼的理论模型
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摘要
基于统计接触理论和等效粗糙接触表面假设,考虑微凸体在加卸载及动态载荷下的变形特征,建立了结合面法向静、动态接触模型,获得了单位面积法向静、动态接触刚度与接触阻尼(基础特性参数)。基于Kadin和Etsion的粗糙表面弹塑性卸载接触模型,通过引入微凸体卸载过程中残余变形与最大变形量及最大接触载荷之间的函数关系,建立静态加卸载接触模型。针对结合面间简谐动态相对位移,利用泰勒公式对静态接触载荷和接触刚度进行展开,得出了动态接触载荷、接触刚度的增量以及动态接触载荷下的能量损耗,建立了法向动态接触刚度和接触阻尼的计算模型。分析了结合面面压、动态位移幅值及振动频率对动态接触刚度和接触阻尼的影响规律,研究表明:法向动态接触刚度相对静态接触刚度有微小偏移增量,动态接触刚度增量和接触阻尼随法向面压及动态位移幅值的增大而非线性增大,动态接触刚度增量随振动频率增加呈非线性增大,而接触阻尼则随振动频率增加呈非线性减小。通过理论计算与试验结果的对比分析,证明了本文建立的结合面法向静、动态接触刚度及接触阻尼理论模型的正确性。
Based on the statistical contact theory and the assumption of equivalent joint surface, and the asperity deformation characteristics are considered under the loading, the unloading and the dynamic loading. Then, the static and dynamic contact model can be established, and the basic characteristic parameter can be obtained, which include the static and dynamic contact stiffness and contact damping in the unit area. Firstly, based on the Kadin's and Etsion's unloading model of rough surfaces in elastic plastic stage, the relationship of residual deformation and maximum deformation and maximum contact load is introduced. Then the static loading and unloading contact model can be created. Secondly, aimed at the dynamic harmonic displacement between contact surfaces, the static contact load and contact stiffness are expanded by using Taylor's formula. The dynamic load, the contact stiffness increment and the energy dissipation in the dynamic loading can be obtained. Then the model of dynamic contact stiffness and damping is built. Thirdly, influences of the combined surface pressure, dynamic displacement amplitude and vibration frequency on the dynamic contact stiffness and contact damping are analyzed. The research shows that the normal dynamic contact stiffness is slightly offset compared with the static contact stiffness, and the dynamic contact stiffness increment and contact damping increase with the increase of normal pressure and dynamic displacement amplitude, and the dynamic contact stiffness increases linearly with the increase of the vibration frequency, and the contact damping decreases with the increase of the vibration frequency. Lastly, through the comparison of theoretical calculation and experimental results, it is proved that the theoretical model of the combined surface method of the static and dynamic contact stiffness and contact damping is correct.
Based on the statistical contact theory and the assumption of equivalent joint surface, and the asperity deformation characteristics are considered under the loading, the unloading and the dynamic loading. Then, the static and dynamic contact model can be established, and the basic characteristic parameter can be obtained, which include the static and dynamic contact stiffness and contact damping in the unit area. Firstly, based on the Kadin's and Etsion's unloading model of rough surfaces in elastic plastic stage, the relationship of residual deformation and maximum deformation and maximum contact load is introduced. Then the static loading and unloading contact model can be created. Secondly, aimed at the dynamic harmonic displacement between contact surfaces, the static contact load and contact stiffness are expanded by using Taylor's formula. The dynamic load, the contact stiffness increment and the energy dissipation in the dynamic loading can be obtained. Then the model of dynamic contact stiffness and damping is built. Thirdly, influences of the combined surface pressure, dynamic displacement amplitude and vibration frequency on the dynamic contact stiffness and contact damping are analyzed. The research shows that the normal dynamic contact stiffness is slightly offset compared with the static contact stiffness, and the dynamic contact stiffness increment and contact damping increase with the increase of normal pressure and dynamic displacement amplitude, and the dynamic contact stiffness increases linearly with the increase of the vibration frequency, and the contact damping decreases with the increase of the vibration frequency. Lastly, through the comparison of theoretical calculation and experimental results, it is proved that the theoretical model of the combined surface method of the static and dynamic contact stiffness and contact damping is correct.
引文
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[5]GAO Y F,BOWER A F,KIM K S,et al.The behavior of an elastic-perfectly plastic sinusoidal surface under contact loading[J].Wear,2006,261(2):145-154.
[6]尤晋闽,陈天宁.结合面静态接触参数的统计模型研究[J].振动与冲击,2010,29(11):47-50.YOU Jinmin,CHEN Tianning.Statistical model for static contact parameters of joint surfaces[J].Journal of Vibration and Shock,2010,29(11):47-50.
[7]尤晋闽,陈天宁.结合面法向动态参数的分形模型[J].西安交通大学学报,2009,43(9):91-94.YOU Jinmin,CHEN Tianning.Fractal model for normal dynamic parameters of joint surfaces[J].Journal of Xi'an Jiaotong University,2009,43(9):91-94.
[8]田红亮,赵美云,郑金华,等.新的柔性结合部法向接触刚度和接触阻尼方程[J].西安交通大学学报,2015,49(1):118-126.TIAN Hongliang,ZHAO Meiyun,ZHENG Jinhua,et al.New equations of normal contact stiffness and damping for flexible joint interface[J].Journal of Xi'an Jiaotong University,2015,49(1):118-126.
[9]王雯,吴洁蓓,傅卫平,等.机械结合面法向动态接触刚度理论模型与试验研究[J].机械工程学报,2016,52(13):123-130.WANG Wen,WU Jiebei,FU Weiping,et al.Theoretical and experimental research on normal dynamic contact stiffness of machined joint surfaces[J].Journal of Mechanical Engineering,2016,52(13):123-130.
[10]KADIN Y,KLIGERMAN Y,ETSION I.Unloading an elastic–plastic contact of rough surfaces[J].Journal of the Mechanics&Physics of Solids,2006,54(12):2652-2674.
[11]ETSION I,KLIGERMAN Y,KADIN Y.Unloading of an elastic–plastic loaded spherical contact[J].International Journal of Solids&Structures,2004,42(13):3716-3729.
[12]ZHAO Y,CHANG L.A model of asperity interactions in elastic-plastic contact of rough surfaces[J].Journal of Tribology,2001,123(4):857-864.
[13]倪振华.振动力学[M].西安:西安交通大学,1989.NI Zhenhua.Vibration mechanics[M].Xi'an:Xi'an Jiaotong University,1989.
[14]NANDA B K,BEHERA A K.Study on damping in layered and jointed structures with uniform pressure distribution at the interfaces[J].Journal of Sound&Vibration,1999,226(4):607-624.
[15]LIANG J W,FEENY B F.Identifying coulomb and viscous friction from free-vibration decrements[J].Nonlinear Dynamics,1998,16(16):337-347.
[2]赵利波.数控机床直线滚动导轨动力学特性研究[D].杭州:浙江工业大学,2011.ZHAO Libo.Study on the dynamic performance of linear rolling guide of CNC machine tool[D].Hangzhou:Zhejiang Wniversity of Technology,2011.
[3]GREENWOOD J A,WILLIAMSON J B P.Contact of nominally flat surfaces[J].Proceedings of the Royal Society A Mathematical Physical&Engineering Sciences,1966,295(295):300-319.
[4]CHANG W R,ETSION I,BOGY D B.An elastic-plastic model for the contact of rough surfaces[J].Journal of Tribology,1987,109(2):257-263.
[5]GAO Y F,BOWER A F,KIM K S,et al.The behavior of an elastic-perfectly plastic sinusoidal surface under contact loading[J].Wear,2006,261(2):145-154.
[6]尤晋闽,陈天宁.结合面静态接触参数的统计模型研究[J].振动与冲击,2010,29(11):47-50.YOU Jinmin,CHEN Tianning.Statistical model for static contact parameters of joint surfaces[J].Journal of Vibration and Shock,2010,29(11):47-50.
[7]尤晋闽,陈天宁.结合面法向动态参数的分形模型[J].西安交通大学学报,2009,43(9):91-94.YOU Jinmin,CHEN Tianning.Fractal model for normal dynamic parameters of joint surfaces[J].Journal of Xi'an Jiaotong University,2009,43(9):91-94.
[8]田红亮,赵美云,郑金华,等.新的柔性结合部法向接触刚度和接触阻尼方程[J].西安交通大学学报,2015,49(1):118-126.TIAN Hongliang,ZHAO Meiyun,ZHENG Jinhua,et al.New equations of normal contact stiffness and damping for flexible joint interface[J].Journal of Xi'an Jiaotong University,2015,49(1):118-126.
[9]王雯,吴洁蓓,傅卫平,等.机械结合面法向动态接触刚度理论模型与试验研究[J].机械工程学报,2016,52(13):123-130.WANG Wen,WU Jiebei,FU Weiping,et al.Theoretical and experimental research on normal dynamic contact stiffness of machined joint surfaces[J].Journal of Mechanical Engineering,2016,52(13):123-130.
[10]KADIN Y,KLIGERMAN Y,ETSION I.Unloading an elastic–plastic contact of rough surfaces[J].Journal of the Mechanics&Physics of Solids,2006,54(12):2652-2674.
[11]ETSION I,KLIGERMAN Y,KADIN Y.Unloading of an elastic–plastic loaded spherical contact[J].International Journal of Solids&Structures,2004,42(13):3716-3729.
[12]ZHAO Y,CHANG L.A model of asperity interactions in elastic-plastic contact of rough surfaces[J].Journal of Tribology,2001,123(4):857-864.
[13]倪振华.振动力学[M].西安:西安交通大学,1989.NI Zhenhua.Vibration mechanics[M].Xi'an:Xi'an Jiaotong University,1989.
[14]NANDA B K,BEHERA A K.Study on damping in layered and jointed structures with uniform pressure distribution at the interfaces[J].Journal of Sound&Vibration,1999,226(4):607-624.
[15]LIANG J W,FEENY B F.Identifying coulomb and viscous friction from free-vibration decrements[J].Nonlinear Dynamics,1998,16(16):337-347.