直升机旋翼黏弹阻尼器时域动力学建模与分析
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摘要
建立一种适用于旋翼气动弹性分析的黏弹阻尼器模型,该模型考虑了黏弹材料本身的刚度非线性及激振力频率和幅值对黏弹阻尼器应力-应变关系的影响。通过引入新型几何非线性弹簧模块,根据需要调整模型的刚度变化规律,避免了现有黏弹阻尼器模型模拟不同类型材料时因刚度变化规律差异而需重新建模的缺陷,模型适应性强。模型采用多个内变量场,既能体现阻尼器幅变特性,也能准确反映多频激励下的黏弹性特性。以两种不同类型黏弹材料制造的黏弹阻尼器为研究对象,在旋翼黏弹阻尼器的典型工作幅值和频率范围内,进行了简谐实验。利用建立的旋翼黏弹阻尼器非线性时域动力学模型,计算不同类型黏弹材料制造的阻尼器在多种应变幅值、频率下的动态特性并与实验相比较,分析了黏弹阻尼器损耗模量、储能模量频变特性和双频激励对阻尼器的影响。结果表明,建立的非线性黏弹阻尼器动力学模型能够更好地反映不同类型黏弹材料构成的黏弹阻尼器的动刚度和阻尼,适合于直升机旋翼载荷计算和气动弹性分析。
A new constitutive model of elastomer damper is presented;the model is able to capture the strain-stress relationship of the helicopter rotor elastomeric damper,which is highly influenced by the excitation frequency,amplitude and the nonlinear stiffness of the elastomeric material.This model has combined with the nonlinear spring model and the variation law of stiffness can be modified,therefore,this model can reflect various variation law of stiffness of different materials by one model and the generality is improved.Multi internal variables field is used to have better frequency and amplitude dependence.Two elastomeric dampers made of two different types of elastomers are investigated through extensive tests of amplitudes and frequencies within typical working condition of rotor elastomeric damper.Based on this model,an elastomeric damper model is developed,different kinds of elastomeric damper's dynamic properties at different frequencies,strain amplitudes and dual-frequency have been calculated and compared with the experimental data.It is shown that the presented model can predict the dynamic stiffness and damping of the elastomeric damper made from different types of elastomers with few relative errors.Therefore,the presented method can be used for helicopter rotor load calculation and aeroelastic analysis.
A new constitutive model of elastomer damper is presented;the model is able to capture the strain-stress relationship of the helicopter rotor elastomeric damper,which is highly influenced by the excitation frequency,amplitude and the nonlinear stiffness of the elastomeric material.This model has combined with the nonlinear spring model and the variation law of stiffness can be modified,therefore,this model can reflect various variation law of stiffness of different materials by one model and the generality is improved.Multi internal variables field is used to have better frequency and amplitude dependence.Two elastomeric dampers made of two different types of elastomers are investigated through extensive tests of amplitudes and frequencies within typical working condition of rotor elastomeric damper.Based on this model,an elastomeric damper model is developed,different kinds of elastomeric damper's dynamic properties at different frequencies,strain amplitudes and dual-frequency have been calculated and compared with the experimental data.It is shown that the presented model can predict the dynamic stiffness and damping of the elastomeric damper made from different types of elastomers with few relative errors.Therefore,the presented method can be used for helicopter rotor load calculation and aeroelastic analysis.
引文
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[2]Yu Z H,Yang W D,Zhang C L.Aeroelasticity analysis of rotor multibody system based on Broyden method[J].Acta Aeronautica et Astronautica Sinica,2012,33(12):2171-2182(in Chinese).虞志浩,杨卫东,张呈林.基于Broyden法的旋翼多体系统气弹动力学分析[J].航空学报,2012,33(12):2171-2182.
[3]Yeo H,Johnson W.Prediction of rotor structural loads with comprehensive analysis[J].Journal of the American Helicopter Society,2008,53(2):193-209.
[4]Jimmy C,Yeo H.Investigation of rotor blade structural dynamics and modeling based on measured airloads[J].Journal of Aircraft,2008,45(5):1631-1642.
[5]Abhishek A,Datta A,Chopra I.Prediction of UH-60A structural loads using multibody analysis and swashplate dynamics[J].Journal of Aircraft,2009,46(2):474-490.
[6]Gandhi F,Chopra I.A time-domain non-linear viscoelastic damper model[J].Smart Materials and Structures,1996,5(5):517-528.
[7]Hu G C,Liu Q,Liu X Y.Influence of nonlinear hydraulic lag damper on scaled rotor ground resonance[J].Acta Aeronautica et Astronautica Sinica,2010,31(11):2182-2188(in Chinese).胡国才,柳泉,刘湘一.液压阻尼器对模型旋翼地面共振的影响[J].航空学报,2010,31(11):2182-2188.
[8]Felker F,Lau B.Nonlinear behavior of an elastomeric lag damper undergoing dual frequency motion and its effect on rotor dynamic[J].Journal of the American Helicopter Society,1987,32(4):45-53.
[9]Muhr A H.Modeling the stress-strain behavior of rubber[J].Rubber Chemistry and Technology,2005,78(3):391-425.
[10]Wei H,Norman M W.Rate-dependent elastoslide model for single and dual frequency MR lag damper behavior[J].International Journal of Modern Physics,2005,19(7):1527-1533.
[11]Grilli R,Krishnan R.Mechanisms-based analysis of filled elastomeric dampers under single and dual frequency excitations[J].Journal of the American Helicopter Society,2008,53(3):252-266.
[12]Changkuan J.Modeling friction phenomena and elastomeric dampers in multibody dynamics analysis[D].Georgia:Georgia Institute of Technology,2009.
[13]Chazeau L,Brown J D,Yanyo L C.Modulus recovery kinetics and other insights into the payne effect for filled elastomers[J].Polymer Composites,2000,21(2):202-222.
[14]Wu Q Y,Wu J A.Polymer rheology[M].Beijing:Higher Education Press,2010:73-97(in Chinese).吴其晔,巫静安.高分子材料流变学[M].北京:高等教育出版社,2010:73-97.
[15]Yuan L W.Rheology[M].Beijing:Science Press,1986:49-92(in Chinese).袁龙蔚.流变力学[M].北京:科学出版社,1986:49-92.
[16]Miehe C,Keck J.Superimposed finite elastic viscoelastic plastoelastic stress response with damage in filled rubbery polymers,experiments,modeling and algorithmic implementation[J].Journal of the Mechanics and Physics of Solids,2000,48(2):323-365.
[17]Chagnon G,Marckmann G.A comparison of the hartsmith model with arruda-boyce and gent formulations for rubber elasticity[J].Rubber Chemistry and Technology,2004,77(4):724-735.
[18]Drozdov A D,Dorfmann A.A micro-mechanical model for the response of filled elastomers at finite strains[J].International Journal of Plasticity,2003,19(7):1037-1067.
[19]Wei H,Norman M W.Distributed rate-dependent elastoslide model for elastomeric lag dampers[J].Journal of Aircraft,2007,44(6):1972-1984.
[20]Wu J,Shangguan W B.Computational method for dynamic properties of rubber isolators using hyperelastic viscoelastic plastoelastic constitutive model[J].Journal of Mechanical Engineering,2010,46(14):109-114(in Chinese).吴杰,上官文斌.采用超弹性-黏弹性-弹塑性本构模型的橡胶隔振器动态特性计算方法[J].机械工程学报,2010,46(14):109-114.
[21]Ferry J D.Viscoelastic properties of polymers[M].New York:John Wiley&Sons,1961:116-129.
[22]Brackbill C R.Helicopter rotor aeroelastic analysis using a refine elastomeric damper model[D].State College:Pennsylvania State University,2000.
[23]Li R R,Yang W D,Yu Z H.Multiple parameters dynamic modeling and analysis of helicopter rotor multi-layer elastomeric damper[J].Journal of Aerospace Power,2014,29(4):844-851(in Chinese).李锐锐,杨卫东,虞志浩.直升机旋翼多层层压黏弹阻尼器多参数动力学建模与分析方法[J].航空动力学报,2014,29(4):844-851.
[24]Chan C,Liu G.Hysteresis identification and compen-sation using agenetic algorithm with adaptive search space[J].Mechatronics,2007,17(7):391-402.
[25]Trabia M B,Yim W,Saadeh M.Modeling of hysteresis and backlash for a smart fin with a piezoelectric[J].Journal of Intelligent Material Systems and Structures,2011,22(11):1161-1176.
[26]Lesieutre G,Bianchini E.Time domain modeling of linear viscoelasticity using anelastic displacement fields[J].Journal of Vibration and Acoustics,1995,117(4):424-430.
[2]Yu Z H,Yang W D,Zhang C L.Aeroelasticity analysis of rotor multibody system based on Broyden method[J].Acta Aeronautica et Astronautica Sinica,2012,33(12):2171-2182(in Chinese).虞志浩,杨卫东,张呈林.基于Broyden法的旋翼多体系统气弹动力学分析[J].航空学报,2012,33(12):2171-2182.
[3]Yeo H,Johnson W.Prediction of rotor structural loads with comprehensive analysis[J].Journal of the American Helicopter Society,2008,53(2):193-209.
[4]Jimmy C,Yeo H.Investigation of rotor blade structural dynamics and modeling based on measured airloads[J].Journal of Aircraft,2008,45(5):1631-1642.
[5]Abhishek A,Datta A,Chopra I.Prediction of UH-60A structural loads using multibody analysis and swashplate dynamics[J].Journal of Aircraft,2009,46(2):474-490.
[6]Gandhi F,Chopra I.A time-domain non-linear viscoelastic damper model[J].Smart Materials and Structures,1996,5(5):517-528.
[7]Hu G C,Liu Q,Liu X Y.Influence of nonlinear hydraulic lag damper on scaled rotor ground resonance[J].Acta Aeronautica et Astronautica Sinica,2010,31(11):2182-2188(in Chinese).胡国才,柳泉,刘湘一.液压阻尼器对模型旋翼地面共振的影响[J].航空学报,2010,31(11):2182-2188.
[8]Felker F,Lau B.Nonlinear behavior of an elastomeric lag damper undergoing dual frequency motion and its effect on rotor dynamic[J].Journal of the American Helicopter Society,1987,32(4):45-53.
[9]Muhr A H.Modeling the stress-strain behavior of rubber[J].Rubber Chemistry and Technology,2005,78(3):391-425.
[10]Wei H,Norman M W.Rate-dependent elastoslide model for single and dual frequency MR lag damper behavior[J].International Journal of Modern Physics,2005,19(7):1527-1533.
[11]Grilli R,Krishnan R.Mechanisms-based analysis of filled elastomeric dampers under single and dual frequency excitations[J].Journal of the American Helicopter Society,2008,53(3):252-266.
[12]Changkuan J.Modeling friction phenomena and elastomeric dampers in multibody dynamics analysis[D].Georgia:Georgia Institute of Technology,2009.
[13]Chazeau L,Brown J D,Yanyo L C.Modulus recovery kinetics and other insights into the payne effect for filled elastomers[J].Polymer Composites,2000,21(2):202-222.
[14]Wu Q Y,Wu J A.Polymer rheology[M].Beijing:Higher Education Press,2010:73-97(in Chinese).吴其晔,巫静安.高分子材料流变学[M].北京:高等教育出版社,2010:73-97.
[15]Yuan L W.Rheology[M].Beijing:Science Press,1986:49-92(in Chinese).袁龙蔚.流变力学[M].北京:科学出版社,1986:49-92.
[16]Miehe C,Keck J.Superimposed finite elastic viscoelastic plastoelastic stress response with damage in filled rubbery polymers,experiments,modeling and algorithmic implementation[J].Journal of the Mechanics and Physics of Solids,2000,48(2):323-365.
[17]Chagnon G,Marckmann G.A comparison of the hartsmith model with arruda-boyce and gent formulations for rubber elasticity[J].Rubber Chemistry and Technology,2004,77(4):724-735.
[18]Drozdov A D,Dorfmann A.A micro-mechanical model for the response of filled elastomers at finite strains[J].International Journal of Plasticity,2003,19(7):1037-1067.
[19]Wei H,Norman M W.Distributed rate-dependent elastoslide model for elastomeric lag dampers[J].Journal of Aircraft,2007,44(6):1972-1984.
[20]Wu J,Shangguan W B.Computational method for dynamic properties of rubber isolators using hyperelastic viscoelastic plastoelastic constitutive model[J].Journal of Mechanical Engineering,2010,46(14):109-114(in Chinese).吴杰,上官文斌.采用超弹性-黏弹性-弹塑性本构模型的橡胶隔振器动态特性计算方法[J].机械工程学报,2010,46(14):109-114.
[21]Ferry J D.Viscoelastic properties of polymers[M].New York:John Wiley&Sons,1961:116-129.
[22]Brackbill C R.Helicopter rotor aeroelastic analysis using a refine elastomeric damper model[D].State College:Pennsylvania State University,2000.
[23]Li R R,Yang W D,Yu Z H.Multiple parameters dynamic modeling and analysis of helicopter rotor multi-layer elastomeric damper[J].Journal of Aerospace Power,2014,29(4):844-851(in Chinese).李锐锐,杨卫东,虞志浩.直升机旋翼多层层压黏弹阻尼器多参数动力学建模与分析方法[J].航空动力学报,2014,29(4):844-851.
[24]Chan C,Liu G.Hysteresis identification and compen-sation using agenetic algorithm with adaptive search space[J].Mechatronics,2007,17(7):391-402.
[25]Trabia M B,Yim W,Saadeh M.Modeling of hysteresis and backlash for a smart fin with a piezoelectric[J].Journal of Intelligent Material Systems and Structures,2011,22(11):1161-1176.
[26]Lesieutre G,Bianchini E.Time domain modeling of linear viscoelasticity using anelastic displacement fields[J].Journal of Vibration and Acoustics,1995,117(4):424-430.
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