叶片缘板阻尼器切向接触刚度及其微滑动摩擦建模
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摘要
为有效解决叶片缘板阻尼器的微滑动摩擦建模问题,针对带圆角的平板接触模型,推导得到了阻尼器切向接触刚度的解析表达式,包括初始切向接触刚度和微滑动阶段平均切向接触刚度,并将其与平面应变有限元模型的计算结果进行对比。结果表明:初始切向接触刚度的值仅与接触体的材料属性、阻尼器轴向长度与接触区半宽度的比值有关,平均切向接触刚度还与接触面的压力分布有关;利用有限元法计算得到的切向接触刚度值与理论解之间的计算误差与文献中有限元解的误差相比减小约7.1%。基于切向接触刚度的理论分析结果,发展了一种微滑动摩擦模型,给出了模型中实验系数λ的解析表达式,对于本文研究的带圆角平板接触模型,λ的值通常在1.00~1.15。将所发展的微滑动摩擦模型用于B-G型缘板阻尼器减振特性分析中,并与宏滑动摩擦模型的计算结果进行了对比,结果表明,所发展的微滑动摩擦模型可以用来计算阻尼器接触面发生微滑动时所能提供的阻尼比。
To effectively solve the modeling problem of the microslip friction of the blade underplatform damper,analytic expressions of initial tangential contact stiffness and average tangential contact stiffness of the damper were derived based on a flat rounded contact model. The results were compared with those of the finite element models in plane strain state and show that the initial tangential contact stiffness is only related to material properties of contact bodies,ratio of axial length of the dry friction damper to half-width of the contact area. In contrast,the average tangential contact stiffness is also related to the normal pressure distribution of the contact surface. The calculation error of the tangential contact stiffness between the finite element method(FEM)and theoretical approach reduces by about 7.1% compared with that of the results calculated by FEM in the literature. A microslip friction model was built based on the results of the flat rounded contact model,and the analytic expression of experimental coefficient λ in the model was derived. As for the contact model presented in this paper,the value of λ is nearly between 1.00~1.15. The developed microslip friction model was applied to the study of the vibration characteristics of the B-G underplateform damper. The results were compared with that of the macroslip model,and show that the developed microslip friction model can be used to calculate the damping ratio of the damper when contact interfaces are both in microslip phase.
To effectively solve the modeling problem of the microslip friction of the blade underplatform damper,analytic expressions of initial tangential contact stiffness and average tangential contact stiffness of the damper were derived based on a flat rounded contact model. The results were compared with those of the finite element models in plane strain state and show that the initial tangential contact stiffness is only related to material properties of contact bodies,ratio of axial length of the dry friction damper to half-width of the contact area. In contrast,the average tangential contact stiffness is also related to the normal pressure distribution of the contact surface. The calculation error of the tangential contact stiffness between the finite element method(FEM)and theoretical approach reduces by about 7.1% compared with that of the results calculated by FEM in the literature. A microslip friction model was built based on the results of the flat rounded contact model,and the analytic expression of experimental coefficient λ in the model was derived. As for the contact model presented in this paper,the value of λ is nearly between 1.00~1.15. The developed microslip friction model was applied to the study of the vibration characteristics of the B-G underplateform damper. The results were compared with that of the macroslip model,and show that the developed microslip friction model can be used to calculate the damping ratio of the damper when contact interfaces are both in microslip phase.
引文
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[3]Wang J H,Chen W K.Investigation of the Vibration of a Blade with Friction Damper by HBM[J].Journal of Engineering for Gas Turbines&Power,1993,115(2):660-664.
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[6]Siewert C,Panning L,Schmidt-Fellner A,et al.The Estimation of the Contact Stiffness for Directly and Indirectly Coupled Turbine Blading[C].Reno:ASME Turbo Expo 2006:Power for Land,Sea,and Air,2006:841-853.
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[8]Szwedowicz J,Kissel M,Ravindra B,et al.Estimation of Contact Stiffness and Its Role in the Design of a Friction Damper[C].Reno:ASME Turbo Expo 2001:Power for Land,Sea,and Air.2001.
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[10]Schwingshackl C W,Petrov E P,Ewins D J.Measured and Estimated Friction Interface Parameters in a Nonlinear Dynamic Analysis[J].Mechanical Systems&Signal Processing,2012,28(2):574-584.
[11]李一堃,郝志明,章定国.基于六参数非均匀密度函数的伊万模型研究[J].力学学报,2015,47(3):513-520.
[12]Rajaei M,Ahmadian H.Development of Generalized Iwan Model to Simulate Frictional Contacts with Variable Normal Loads[J].Applied Mathematical Modelling,2014,38(15-16):4006-4018.
[13]Cigeroglu E,Lu W,Menq C H.One-Dimensional Dynamic Microslip Friction Model[J].Journal of Sound&Vibration,2006,292(3):881-898.
[14]Cigeroglu E,An N,Menq C H.A Microslip Friction Model with Normal Load Variation Induced by Normal Motion[J].Nonlinear Dynamics,2007,50(3):609-626.
[15]Menq C H,Bielak J,Griffin J H.The Influence of Microslip on Vibratory Response,Part I:A New Microslip Model[J].Journal of Sound&Vibration,1986,107(2):279-293.
[16]Allara M.A Model for the Characterization of Friction Contacts in Turbine Blades[J].Journal of Sound&Vibration,2009,320(3):527-544.
[17]Segalman D J,Starr M J.Inversion of Masing Models Via Continuous Iwan Systems[J].International Journal of Non-Linear Mechanics,2008,43(1):74-80.
[18]Marquina F J,Coro A,GutiéRrez A,et al.Friction Damping Modeling in High Stress Contact Areas Using Microslip Friction Model[C].Reno:ASME Turbo Expo2008:Power for Land,Sea,and Air.2008:309-318.
[19]Mcveigh P A,Harish G,Farris T N,et al.Modeling Interfacial Conditions in Nominally Flat Contacts for Application to Fretting Fatigue of Turbine Engine Components[J].International Journal of Fatigue,1999,21(99):157-165.
[20]Olofsson U,Hagman L.A Model for Micro-Slip between Flat Surfaces Based on Deformation of Ellipsoidal Elastic Bodies[J].Tribology International,1997,30(8):599-603.
[21]Wang J H,Chen W K.Investigation of the Vibration of a Blade with Friction Damper by HBM[J].Journal of Engineering for Gas Turbines&Power,1992,115(2):660-664.
[22]Chen Yu-Di,Wang Yan-Rong.A Method for the Resonant Response Evaluation of Blades System with Underplatform Dampers[C].China:International Conference Vibroengineering,2014.
[23]陈毓迪.带冠叶片阻尼模型与振动特性分析[D].北京:北京航空航天大学,2014.
[2]Griffin J.Friction Damping of Resonant Stresses in Gas Turbine Engine Airfoils[J].Journal of Engineering for Gas Turbines and Power,1980,102(2):329-330.
[3]Wang J H,Chen W K.Investigation of the Vibration of a Blade with Friction Damper by HBM[J].Journal of Engineering for Gas Turbines&Power,1993,115(2):660-664.
[4]Iwan W D.A Distributed-Element Model for Hysteresis and Its Steady-State Dynamic Response[J].Journal of Applied Mechanics,1966,33(4).
[5]陈璐璐,张大义,文敏,等.带凸肩风扇叶片振动特性及设计方法研究[J].推进技术,2015,36(9):1389-1394.(CHEN Lu-lu,ZHANG Da-yi,WEN Min,et al.Dynamical Effects of Shrouds on Fan Blade Vibration and Its Corresponding Design Method[J].Journal of Propulsion Technology,2015,36(9):1389-1394.)
[6]Siewert C,Panning L,Schmidt-Fellner A,et al.The Estimation of the Contact Stiffness for Directly and Indirectly Coupled Turbine Blading[C].Reno:ASME Turbo Expo 2006:Power for Land,Sea,and Air,2006:841-853.
[7]史亚杰,朱梓根.阻尼器切向接触刚度的有限元分析及应用[J].航空动力学报,2009,24(6):1292-1298.
[8]Szwedowicz J,Kissel M,Ravindra B,et al.Estimation of Contact Stiffness and Its Role in the Design of a Friction Damper[C].Reno:ASME Turbo Expo 2001:Power for Land,Sea,and Air.2001.
[9]郝燕平,朱梓根.叶片摩擦阻尼器切向刚度研究[J].航空动力学报,2002,17(4):426-431.
[10]Schwingshackl C W,Petrov E P,Ewins D J.Measured and Estimated Friction Interface Parameters in a Nonlinear Dynamic Analysis[J].Mechanical Systems&Signal Processing,2012,28(2):574-584.
[11]李一堃,郝志明,章定国.基于六参数非均匀密度函数的伊万模型研究[J].力学学报,2015,47(3):513-520.
[12]Rajaei M,Ahmadian H.Development of Generalized Iwan Model to Simulate Frictional Contacts with Variable Normal Loads[J].Applied Mathematical Modelling,2014,38(15-16):4006-4018.
[13]Cigeroglu E,Lu W,Menq C H.One-Dimensional Dynamic Microslip Friction Model[J].Journal of Sound&Vibration,2006,292(3):881-898.
[14]Cigeroglu E,An N,Menq C H.A Microslip Friction Model with Normal Load Variation Induced by Normal Motion[J].Nonlinear Dynamics,2007,50(3):609-626.
[15]Menq C H,Bielak J,Griffin J H.The Influence of Microslip on Vibratory Response,Part I:A New Microslip Model[J].Journal of Sound&Vibration,1986,107(2):279-293.
[16]Allara M.A Model for the Characterization of Friction Contacts in Turbine Blades[J].Journal of Sound&Vibration,2009,320(3):527-544.
[17]Segalman D J,Starr M J.Inversion of Masing Models Via Continuous Iwan Systems[J].International Journal of Non-Linear Mechanics,2008,43(1):74-80.
[18]Marquina F J,Coro A,GutiéRrez A,et al.Friction Damping Modeling in High Stress Contact Areas Using Microslip Friction Model[C].Reno:ASME Turbo Expo2008:Power for Land,Sea,and Air.2008:309-318.
[19]Mcveigh P A,Harish G,Farris T N,et al.Modeling Interfacial Conditions in Nominally Flat Contacts for Application to Fretting Fatigue of Turbine Engine Components[J].International Journal of Fatigue,1999,21(99):157-165.
[20]Olofsson U,Hagman L.A Model for Micro-Slip between Flat Surfaces Based on Deformation of Ellipsoidal Elastic Bodies[J].Tribology International,1997,30(8):599-603.
[21]Wang J H,Chen W K.Investigation of the Vibration of a Blade with Friction Damper by HBM[J].Journal of Engineering for Gas Turbines&Power,1992,115(2):660-664.
[22]Chen Yu-Di,Wang Yan-Rong.A Method for the Resonant Response Evaluation of Blades System with Underplatform Dampers[C].China:International Conference Vibroengineering,2014.
[23]陈毓迪.带冠叶片阻尼模型与振动特性分析[D].北京:北京航空航天大学,2014.