结合面形貌特性对模态耦合不稳定系统的影响
|
摘要
针对目前结合面微观形貌特性对由摩擦和系统结构双重引起的模态耦合系统的稳定性影响的理论研究缺少,尝试从微观角度解释结合面形貌对宏观系统的动态特性影响。基于分形理论建立结合面形貌较为准确的法向、切向接触刚度模型;以车辆制动盘为对象,将所建立的分形接触刚度模型引入其中,建立一个两自由度的典型模态耦合模型;研究了结合面切向与法向的刚度比、摩擦因数和固有频率比对系统稳定和不稳定区的影响,以及系统出现不同频率噪声的条件。研究可知,形貌参数是结合面产生振动噪声的主要影响因素;结合面形貌特性不同,系统产生振动噪声的频率和条件也不同。这些结论有助于更深入地研究结合面形貌特性对宏观系统的影响;同时可为工程设计制造合适结合面形貌提供参考,具有一定的工程意义。
Aiming at the lack of theoretical research with the surface morphology characteristics affect the stability of modal coupling system by friction and the structure of the system caused. An attempt is to explain the dynamic characteristics of the macroscopic system from the microscopic view. The more accurate model of normal and tangential contact stiffness of surface topography is established based on fractal theory. With the vehicle brake disc as the object, a typical mode coupling model with two degrees of freedom is presented and the fractal contact stiffness model is introduced. The influence of the tangential and normal stiffness ratio, friction coefficient, and the natural frequency ratio on the stability of system and the conditions of the different frequency noise arise are studied. It is concluded that these contact topography parameters are the main factors to influence the vibration noise; the vibration noise condition and the frequency of the system are different with the different characteristics of the surface topography. The conclusions obtained may help us more deeply understand the influence of the surface topography on the macroscopic system. At the same time, it can provide reference for engineering design and manufacture, and has a certain engineering significance.
Aiming at the lack of theoretical research with the surface morphology characteristics affect the stability of modal coupling system by friction and the structure of the system caused. An attempt is to explain the dynamic characteristics of the macroscopic system from the microscopic view. The more accurate model of normal and tangential contact stiffness of surface topography is established based on fractal theory. With the vehicle brake disc as the object, a typical mode coupling model with two degrees of freedom is presented and the fractal contact stiffness model is introduced. The influence of the tangential and normal stiffness ratio, friction coefficient, and the natural frequency ratio on the stability of system and the conditions of the different frequency noise arise are studied. It is concluded that these contact topography parameters are the main factors to influence the vibration noise; the vibration noise condition and the frequency of the system are different with the different characteristics of the surface topography. The conclusions obtained may help us more deeply understand the influence of the surface topography on the macroscopic system. At the same time, it can provide reference for engineering design and manufacture, and has a certain engineering significance.
引文
[1]JEARSIRIPONGKUL T,HOCHLENERT D,WAGNER U,et al.A nonlinear floating calliper disk brake model to incorporate squeal[J].SAE International,2004,2004(1):2802-2813.
[2]OUYANG O,MOTTERSHEAD J,LI W.A moving-load model for disc brake stability analysis[J].Transactions of ASME Journal of Vibration and Acoustics,2003,125(1);53-58.
[3]HECKL M,ABRAHAMS I.Curve squeal of train wheels,part I:Mathematical model for its generations[J].Journal of Sound and Vibration,2000,229(3):669-693.
[4]BEER F,JANSSENS M,KOOIJMAN P.Squeal noise of rail-bound vehicles influenced by lateral contact position[J].Journal of Sound and Vibration,2003,267(3):497-507.
[5]IBRAHIM R.Friction-induced vibration,chatter,squeal and chaos:Part I:Mechanics of contact and friction[J].ASME Appl.Mech.Rev.,1994,47(7):209-226.
[6]IBRAHIM R.Friction-induced vibration,chatter,squeal,and chaos,Part 2:Dynamicsand modeling[J].Applied Mechanics Review,1994,47(7):227-253.
[7]SPURR R.A theory of brake squeal[J].Proceedings of the Institution of Mechanical Engineers Automobile Division,1961(19):33-52.
[8]HOFFMANN N,FISCHER M,ALLGAIER R.A minimal model for studying properties of the mode-coupling type instability in friction induced oscillations[J].Mechanics Research Communications,2002,29(4):197-205.
[9]张立军,吴军,孟德建.摩擦引起的模态耦合不稳定性分析[J].机械工程学报,2015,51(21):65-72.ZHANG Lijun,WU Jun,MENG Dejian.Analysis of friction induced mode coupling instability[J].Journal of Mechanical Engineering,2015,51(21):65-72.
[10]SINOU J J,JéZéQUEL L.Mode coupling instability in friction-induced vibrations and its dependency on system parameters including damping[J].European Journal of Mechanics-A/Solids,2007,26(1):106-122.
[11]MANDELBROT B.How long is the coast of Britain?Statistical self-similarity and fractional dimension[J].Science,1967,156(3775):636-638.
[12]ERIKSSON M,BERGMAN F,JACOBSON S.Surface characterization of brake pads after running under silent and squealing condition[J].Wear,1999,232(2):163-167.
[13]EADIE D,KALOUSEK J,CHIDDICK C.The role of high positive friction(HPF)modifier in the control of short pitch corrugations and related phenomena[J].Wear,2002,253(1-2):185-192.
[14]CHEN G X,ZHOU Z R.Experimental observation of the initiation process of friction-induced vibration under reciprocating sliding condition[J].Wear,2005,259(1-6):277-281.
[15]CHEN G X,ZHOU Z R,KAPSA P,et al.Effect of surface topography on formation of squeal under reciprocating sliding[J].Wear,2002,253(3):411-423.
[16]SHERIF H.Investigation on effect of surface topography of pad/disc assembly on squeal generation[J].Wear,2004,257(7);687-695.
[17]RUSLI M,OKUMA M.Effect of surface topography on mode-coupling model of dry contact sliding systems[J].Journal of Sound and Vibration,2007,308(3):721-734.
[18]李小彭,梁亚敏,郭浩,等.结合面广义间隙的等效模型研究[J].振动工程学报,2014,27(1):25-32.LI Xiaopeng,LIANG Yamin,GUO Hao,et al.Study on the equivalent model of the generalized clearance of the joint surface[J].Journal of Vibration Engineering,2014,27(1):25-32.
[19]田红亮,钟先友,赵春华,等.计及弹塑性及硬度随表面深度变化的结合部单次加载模型[J].机械工程学报,2015,51(5):90-104.TIAN Hongliang,ZHONG Xianyou,ZHAO Chunhua,et al.One loading model of joint interface considering elastoplastic and variation of hardness with surface depth[J].Journal of Mechanical Engineering,2015,51(5):90-104.
[20]张学良,陈永会,温淑花,等.考虑弹塑性变形机制的结合面法向接触刚度建模[J].振动工程学报,2015,28(1):91-99.ZHANG Xueliang,CHEN Yonghui,WEN Shuhua,et al.The model of normal contact stiffness of joint interfaces incorporating elastoplastic deformation mechanism[J].Journal of Vibration Engineering,2015,28(1):91-99.
[21]田红亮,钟先友,秦红玲,等.依据各向异性分形几何理论的固定结合部法向接触力学模型[J].机械工程学报,2013,49(21):108-122.TIAN Hongliang,ZHONG Xianyou,QIN Hongling,et al.Normal contact mechanics model of fixed joint interface adopting anisotropic fractal geometrical theory[J].Journal of Mechanical Engineering,2013,49(21):108-122.
[22]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.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.
[23]李小彭,郭浩,刘井年,等.考虑摩擦的结合面法向刚度分形模型及仿真[J].振动、测试与诊断,2013,33(2):210-213.LI Xiaopeng,GUO Hao,LIU Jingnian,et al.Fractal model and simulation of the joint surface normal stiffness considering friction[J].Journal of Vibration,Measurement&Diagnosis,2013,33(2):210-213.
[24]李小彭,鞠行,赵光辉,等.考虑摩擦因素的结合面切向接触刚度分形预估模型及其仿真分析[J].摩擦学学报,2013,33(5):463-468.LI Xiaopeng,JU xing,ZHAO Guanghui,et al.Fractal prediction model for tangential contact stiffness of joint surface considering friction factors and its simulation analysis[J].Tribology,2013,33(5):463-468.
[25]张学良,王南山,温淑花,等.机械结合面切向接触阻尼能量耗散弹塑性分形模型[J].机械工程学报,2013,49(12):43-49.ZHANG Xueliang,WANG Nanshan,WEN Shuhua,et al.Elastoplastic fractal model for tangential contact damping energy dissipation of machines joint interfaces[J].Journal of Mechanical Engineering,2013,49(12):43-49.
[26]李小彭,王伟,赵米鹊,等.考虑摩擦因素影响的结合面切向接触阻尼分形预估模型及其仿真[J].机械工程学报,2012,48(23):46-50.LI Xiaopeng,WANG Wei,ZHAO Mique,et al.Fractal prediction model for tangential contact damping of joint surface considering friction factors and its simulation[J].Journal of Mechanical Engineering,2012,48(23):46-50.
[27]LI X P,LIANG Y M,ZHAO G H,et al.Dynamic characteristics of joint surface considering friction and vibration factors based on fractal theory[J].Journal of Vibroengineering,2013,15(2):872-883.
[28]赵光辉.固定结合面接触刚度建模与广义间隙等效方法研究[D].沈阳:东北大学,2014.ZHAO Guanghui.Study on contact stiffness modeling and equivalent method of generalized clearance of fixed joint surface[D].Shenyang:Northeastern University,2014.
[29]葛世荣,朱华.摩擦学的分形[M].北京:机械工业出版社,2005.GE Shirong,ZHU Hua.Fractal of tribology[M].Beijing:China Machine Press,2005.
[30]JOHNSON K L.Contact mechanics[M].Cambridge:Cambridge University Press,1985.
[31]KOGUT L,ETSION I.A semi-analytical solution for the sliding inception of a spherical contact[J].ASME Journal of Tribology,2003,125(3):499-506.
[32]盛选禹,雒建斌,温诗铸.基于分形接触的静摩擦系数预测[J].中国机械工程,1998,9(7):16-18.SHENG Xuanyu,LUO Jianbin,WEN Shizhu.Prediction of static friction coefficient based on fractal contact[J].China Mechanical Engineering,1998,9(7):16-18.
[2]OUYANG O,MOTTERSHEAD J,LI W.A moving-load model for disc brake stability analysis[J].Transactions of ASME Journal of Vibration and Acoustics,2003,125(1);53-58.
[3]HECKL M,ABRAHAMS I.Curve squeal of train wheels,part I:Mathematical model for its generations[J].Journal of Sound and Vibration,2000,229(3):669-693.
[4]BEER F,JANSSENS M,KOOIJMAN P.Squeal noise of rail-bound vehicles influenced by lateral contact position[J].Journal of Sound and Vibration,2003,267(3):497-507.
[5]IBRAHIM R.Friction-induced vibration,chatter,squeal and chaos:Part I:Mechanics of contact and friction[J].ASME Appl.Mech.Rev.,1994,47(7):209-226.
[6]IBRAHIM R.Friction-induced vibration,chatter,squeal,and chaos,Part 2:Dynamicsand modeling[J].Applied Mechanics Review,1994,47(7):227-253.
[7]SPURR R.A theory of brake squeal[J].Proceedings of the Institution of Mechanical Engineers Automobile Division,1961(19):33-52.
[8]HOFFMANN N,FISCHER M,ALLGAIER R.A minimal model for studying properties of the mode-coupling type instability in friction induced oscillations[J].Mechanics Research Communications,2002,29(4):197-205.
[9]张立军,吴军,孟德建.摩擦引起的模态耦合不稳定性分析[J].机械工程学报,2015,51(21):65-72.ZHANG Lijun,WU Jun,MENG Dejian.Analysis of friction induced mode coupling instability[J].Journal of Mechanical Engineering,2015,51(21):65-72.
[10]SINOU J J,JéZéQUEL L.Mode coupling instability in friction-induced vibrations and its dependency on system parameters including damping[J].European Journal of Mechanics-A/Solids,2007,26(1):106-122.
[11]MANDELBROT B.How long is the coast of Britain?Statistical self-similarity and fractional dimension[J].Science,1967,156(3775):636-638.
[12]ERIKSSON M,BERGMAN F,JACOBSON S.Surface characterization of brake pads after running under silent and squealing condition[J].Wear,1999,232(2):163-167.
[13]EADIE D,KALOUSEK J,CHIDDICK C.The role of high positive friction(HPF)modifier in the control of short pitch corrugations and related phenomena[J].Wear,2002,253(1-2):185-192.
[14]CHEN G X,ZHOU Z R.Experimental observation of the initiation process of friction-induced vibration under reciprocating sliding condition[J].Wear,2005,259(1-6):277-281.
[15]CHEN G X,ZHOU Z R,KAPSA P,et al.Effect of surface topography on formation of squeal under reciprocating sliding[J].Wear,2002,253(3):411-423.
[16]SHERIF H.Investigation on effect of surface topography of pad/disc assembly on squeal generation[J].Wear,2004,257(7);687-695.
[17]RUSLI M,OKUMA M.Effect of surface topography on mode-coupling model of dry contact sliding systems[J].Journal of Sound and Vibration,2007,308(3):721-734.
[18]李小彭,梁亚敏,郭浩,等.结合面广义间隙的等效模型研究[J].振动工程学报,2014,27(1):25-32.LI Xiaopeng,LIANG Yamin,GUO Hao,et al.Study on the equivalent model of the generalized clearance of the joint surface[J].Journal of Vibration Engineering,2014,27(1):25-32.
[19]田红亮,钟先友,赵春华,等.计及弹塑性及硬度随表面深度变化的结合部单次加载模型[J].机械工程学报,2015,51(5):90-104.TIAN Hongliang,ZHONG Xianyou,ZHAO Chunhua,et al.One loading model of joint interface considering elastoplastic and variation of hardness with surface depth[J].Journal of Mechanical Engineering,2015,51(5):90-104.
[20]张学良,陈永会,温淑花,等.考虑弹塑性变形机制的结合面法向接触刚度建模[J].振动工程学报,2015,28(1):91-99.ZHANG Xueliang,CHEN Yonghui,WEN Shuhua,et al.The model of normal contact stiffness of joint interfaces incorporating elastoplastic deformation mechanism[J].Journal of Vibration Engineering,2015,28(1):91-99.
[21]田红亮,钟先友,秦红玲,等.依据各向异性分形几何理论的固定结合部法向接触力学模型[J].机械工程学报,2013,49(21):108-122.TIAN Hongliang,ZHONG Xianyou,QIN Hongling,et al.Normal contact mechanics model of fixed joint interface adopting anisotropic fractal geometrical theory[J].Journal of Mechanical Engineering,2013,49(21):108-122.
[22]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.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.
[23]李小彭,郭浩,刘井年,等.考虑摩擦的结合面法向刚度分形模型及仿真[J].振动、测试与诊断,2013,33(2):210-213.LI Xiaopeng,GUO Hao,LIU Jingnian,et al.Fractal model and simulation of the joint surface normal stiffness considering friction[J].Journal of Vibration,Measurement&Diagnosis,2013,33(2):210-213.
[24]李小彭,鞠行,赵光辉,等.考虑摩擦因素的结合面切向接触刚度分形预估模型及其仿真分析[J].摩擦学学报,2013,33(5):463-468.LI Xiaopeng,JU xing,ZHAO Guanghui,et al.Fractal prediction model for tangential contact stiffness of joint surface considering friction factors and its simulation analysis[J].Tribology,2013,33(5):463-468.
[25]张学良,王南山,温淑花,等.机械结合面切向接触阻尼能量耗散弹塑性分形模型[J].机械工程学报,2013,49(12):43-49.ZHANG Xueliang,WANG Nanshan,WEN Shuhua,et al.Elastoplastic fractal model for tangential contact damping energy dissipation of machines joint interfaces[J].Journal of Mechanical Engineering,2013,49(12):43-49.
[26]李小彭,王伟,赵米鹊,等.考虑摩擦因素影响的结合面切向接触阻尼分形预估模型及其仿真[J].机械工程学报,2012,48(23):46-50.LI Xiaopeng,WANG Wei,ZHAO Mique,et al.Fractal prediction model for tangential contact damping of joint surface considering friction factors and its simulation[J].Journal of Mechanical Engineering,2012,48(23):46-50.
[27]LI X P,LIANG Y M,ZHAO G H,et al.Dynamic characteristics of joint surface considering friction and vibration factors based on fractal theory[J].Journal of Vibroengineering,2013,15(2):872-883.
[28]赵光辉.固定结合面接触刚度建模与广义间隙等效方法研究[D].沈阳:东北大学,2014.ZHAO Guanghui.Study on contact stiffness modeling and equivalent method of generalized clearance of fixed joint surface[D].Shenyang:Northeastern University,2014.
[29]葛世荣,朱华.摩擦学的分形[M].北京:机械工业出版社,2005.GE Shirong,ZHU Hua.Fractal of tribology[M].Beijing:China Machine Press,2005.
[30]JOHNSON K L.Contact mechanics[M].Cambridge:Cambridge University Press,1985.
[31]KOGUT L,ETSION I.A semi-analytical solution for the sliding inception of a spherical contact[J].ASME Journal of Tribology,2003,125(3):499-506.
[32]盛选禹,雒建斌,温诗铸.基于分形接触的静摩擦系数预测[J].中国机械工程,1998,9(7):16-18.SHENG Xuanyu,LUO Jianbin,WEN Shizhu.Prediction of static friction coefficient based on fractal contact[J].China Mechanical Engineering,1998,9(7):16-18.