约束阻尼型隔振器的动力学性能分析及优化设计
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摘要
约束阻尼型隔振器的动力学性能主要包括刚度和阻尼性能,两种性能的好坏直接影响到隔振设备的抗振性与稳定性。因此,为了使设备能够在强烈振动和干扰作用下稳定的工作,需要对隔振器进行动力学性能研究分析。目前对约束阻尼型隔振器结构的动力学分析方法已经成为工程中一种非常重要的分析方法,它主要包括结构建模、分析计算以及行为预测等一整套的方案。
本文首先对隔振器的力学模型进行分析,指出隔振器设计中两个关键的动力学因素:刚度和阻尼;然后对隔振器阻尼结构形式及粘弹阻尼材料相关理论做了简单介绍,阐述了结构与材料等参数对隔振器动力学性能影响的重要性,同时也对隔振器的设计流程做了简单介绍。
本文研究了粘弹性阻尼材料的耗能机理和动态阻尼特性,采用分数导数模型,与温频等效原理相结合,得到了粘弹性阻尼材料的复模量、损耗因子与温度关系的参数化数学模型;并结合粘弹性阻尼材料的动态热机械分析实验(DMA)数据对模型参量进行了拟合,实验结果和误差分析表明拟合的数学模型能够准确反映粘弹性材料在变温条件下的动力学特性的变化情况。
其次,根据隔振器中不同类型材料的参数对结构动力学特性的影响,分别采用等效刚度法和模态应变能方法建立了结构固有频率、阻尼比与各类型材料参数之间的关系模型,然后通过隔振器力学仿真分析及隔振系统的正弦扫频实验对模型进行参量拟合、实验验证、误差分析,结果表明该预测模型能够较为准确的反映出隔振器结构动力学性能与材料参数之间的关系。
最后,本文提出了隔振器拓扑模型,分析了重要结构参数对动力学特性的影响,然后以这些参数为设计变量,在满足隔振器强度、刚度条件下,采用合适的优化算法对隔振器结构进行尺寸优化。通过优化,整体结构阻尼性能比优化前得以提高,在工作环境中具有更好的减振性能。
Constrained damping vibration isolators are widely applied in engineering. Stiffness and damping are two important dynamics performances of the vibration isolator, which would be the critical factors in vibration isolation and stability of the device. In order to ensure devices working stably in environment of intense vibration and disturbance, the research in dynamic performance of vibration isolators is required. Recently,the structure dynamics analysis about the isolator has been an important methods in engineering application, including a set of programs consisting of structural modeling, analysis and behavior prediction.
In the thesis, the mechanic model of isolator was analyzed. Through the analysis, it is recognized that stiffness and damping are two critical dynamics factors. Then theory in type of vibration structure and viscoelastic damping material were introduced, which described importance of influence in dynamic performance of vibration isolators by structure and material parameter. And then the design process of the isolator was also introduced briefly.
Energy dissipation mechanism and dynamic damping performance of viscoelastic damping material were studied in this thesis. Using fractional derivative model and temperature-frequency superposition principle, the parameterized mathematical equation were obtained, expressing the relation between complex modulus, dissipation coefficient and temperature. In the expressions, the parameters were fitted according to the experimental datum of viscoelastic damping material dynamic performance tested by Dynamic Mechanical Thermal Analyzer (DMA). Experiments results and error analysis validated the expressions.
Secondly, on the basis of effect on structure dynamics property by different material, the model was established by methods of equivalent stiffness and model strain energy. This model demonstrated the relationship between structure dynamic performance and parameters of individual material. With the work done, mechanic simulation and sinusoidal sweep frequency test could be carried out. The results of simulation and error analysis by test indicated that the model could exactly reflect the relation between structure dynamic performance of vibration isolator and its material property.
In the end, a topology model was advanced based on the damping structure, and geometrical factors influencing in dynamic performance had been analyzed. Supposing these factors as design variables, size optimization of the isolator was conducted by appropriate optimization method without destroy of strength and stiffness. After optimization, the structure damping performance was improved, and better damping performance under work condition was acquired.
本文首先对隔振器的力学模型进行分析,指出隔振器设计中两个关键的动力学因素:刚度和阻尼;然后对隔振器阻尼结构形式及粘弹阻尼材料相关理论做了简单介绍,阐述了结构与材料等参数对隔振器动力学性能影响的重要性,同时也对隔振器的设计流程做了简单介绍。
本文研究了粘弹性阻尼材料的耗能机理和动态阻尼特性,采用分数导数模型,与温频等效原理相结合,得到了粘弹性阻尼材料的复模量、损耗因子与温度关系的参数化数学模型;并结合粘弹性阻尼材料的动态热机械分析实验(DMA)数据对模型参量进行了拟合,实验结果和误差分析表明拟合的数学模型能够准确反映粘弹性材料在变温条件下的动力学特性的变化情况。
其次,根据隔振器中不同类型材料的参数对结构动力学特性的影响,分别采用等效刚度法和模态应变能方法建立了结构固有频率、阻尼比与各类型材料参数之间的关系模型,然后通过隔振器力学仿真分析及隔振系统的正弦扫频实验对模型进行参量拟合、实验验证、误差分析,结果表明该预测模型能够较为准确的反映出隔振器结构动力学性能与材料参数之间的关系。
最后,本文提出了隔振器拓扑模型,分析了重要结构参数对动力学特性的影响,然后以这些参数为设计变量,在满足隔振器强度、刚度条件下,采用合适的优化算法对隔振器结构进行尺寸优化。通过优化,整体结构阻尼性能比优化前得以提高,在工作环境中具有更好的减振性能。
Constrained damping vibration isolators are widely applied in engineering. Stiffness and damping are two important dynamics performances of the vibration isolator, which would be the critical factors in vibration isolation and stability of the device. In order to ensure devices working stably in environment of intense vibration and disturbance, the research in dynamic performance of vibration isolators is required. Recently,the structure dynamics analysis about the isolator has been an important methods in engineering application, including a set of programs consisting of structural modeling, analysis and behavior prediction.
In the thesis, the mechanic model of isolator was analyzed. Through the analysis, it is recognized that stiffness and damping are two critical dynamics factors. Then theory in type of vibration structure and viscoelastic damping material were introduced, which described importance of influence in dynamic performance of vibration isolators by structure and material parameter. And then the design process of the isolator was also introduced briefly.
Energy dissipation mechanism and dynamic damping performance of viscoelastic damping material were studied in this thesis. Using fractional derivative model and temperature-frequency superposition principle, the parameterized mathematical equation were obtained, expressing the relation between complex modulus, dissipation coefficient and temperature. In the expressions, the parameters were fitted according to the experimental datum of viscoelastic damping material dynamic performance tested by Dynamic Mechanical Thermal Analyzer (DMA). Experiments results and error analysis validated the expressions.
Secondly, on the basis of effect on structure dynamics property by different material, the model was established by methods of equivalent stiffness and model strain energy. This model demonstrated the relationship between structure dynamic performance and parameters of individual material. With the work done, mechanic simulation and sinusoidal sweep frequency test could be carried out. The results of simulation and error analysis by test indicated that the model could exactly reflect the relation between structure dynamic performance of vibration isolator and its material property.
In the end, a topology model was advanced based on the damping structure, and geometrical factors influencing in dynamic performance had been analyzed. Supposing these factors as design variables, size optimization of the isolator was conducted by appropriate optimization method without destroy of strength and stiffness. After optimization, the structure damping performance was improved, and better damping performance under work condition was acquired.
引文
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[4]戴德沛.阻尼减振降噪技术[M].西安:西安交通大学出版社,1986.
[5]何平笙.固体高聚物的力学性能(第二版)[M].中国科学技术大学出版社,2008.
[6] Y A Rossikhin, M V Shitikova. Applications of fractional calculus to dynamic problems of linear and nonlinear hereditary mechanics of solid[J]. Appl. Mech. Rev. 1997, 50(1):15-67.
[7]刘林超.分数导数型粘弹性材料的力学行为及在结构减振中的应用研究[D] .暨南大学硕士学位论文,2005.
[8] Ralf Metzler, Theo F Nonnenmacher. Fractional relaxation processes and fractional theological models for the description of a class of viscoelastic materials[J]. International Journal of Plasticity.2003,19:941-959.
[9] D Y Song, T Q Jiang. Study on the constitutive equation with fractional derivative for viscoelastie fluids-modified Jeffreys model and its application[J]. Rheol. Acta. 1998, 27:512-517.
[10]吕丽,白书欣,张虹等.粘弹性材料动态性能测试研究[J].橡胶工业,2006,53:22~624.
[11] T Vuoristo, V T Kuokkala. Creep, recovery and high strain rate response of soft roll cover materials. Mechanics of Materials. 2002, 34:493-504.
[12] Thomas W Strganac, Hunter J Golden. Predictions of Nonlinear Viscoelastic Behavior Using a Hybrid Approach[J]. Int. J. Solids. Struetures.1996, 33(30):4561-4570.
[13] A Riviere. Analysis of the low frequency damping observed at medium and high temperatures [J]. Materials Science and Engineering A. 2004, 370:204-208.
[14] C Gauthier, E Reynaud, R Vassoille. Analysis of non-linear viscoelastic behavior of silica filled styrene butadiene rubber [J]. Polymer. 2004,45:2761-2771.
[15]刘林超,张卫.服从分数导代数Maxwell本构模型的粘弹阻尼材料性能分析[J].材料科学与工程学报,2004,22(6):860-862.
[16] Ralf Metzler, Theo F Nonnenmacher. Fractional relaxation processes and fractionalrheological models for the description of a class of viscoelastic materials [J]. International Journal of Plasticity. 2003,19:941-959.
[17] Mataz Alcoutlabi, J J Martinez Vega. Modeling of the viscoelastic behavior of amorphous polymers by the differential and integration fractional method: the relaxation spectrum H (t) [J]. Polymer. 2003,44:7199-7208.
[18]刘棣华.粘弹阻尼减振降噪应用技术[M].北京:宇航出版社,1990,3-10.
[19]孙社营.船用压筋板的粘弹性阻尼处理[J].噪声与振动控制,1999,(3):25-29.
[20]杨雪,王源升,朱金华,余红伟.多层粘弹阻尼复合结构阻尼性能的研究[J],海军工程大学学报,2005,17(2):72-74,87.
[21]杨雪,王源升,朱金华,余红伟.多层粘弹阻尼复合结构阻尼性能[J],复合材料学报,2005,22(3):175-181.
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