基于模态分析理论的结合部动刚度辨识
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摘要
结合部动力学特性对机械系统动力学性能具有显著影响,结合部动力学信息的准确辨识是组合结构动力学建模的重要前提。基于模态分析理论对结合部动刚度辨识方法进行了深入研究:首先,建立了包含结合部动力学信息的广义动力学模型,从模态分析理论出发,讨论了结合部动力学特性对组合结构固有频率的影响,建立了两者的映射关系;进而,采用质量单元与弹簧阻尼单元建立了理想的动力学有限元模型,通过模态分析所得的固有频率对结合部刚度进行辨识,辨识值与理论值之间最大误差为1.92%;最后,对螺栓连接组合结构进行了模态试验,以所测得的法向及切向典型振型对应固有频率为指标,通过搭建的MATLAB-ANSYS集成平台对螺栓结合部刚度进行辨识,并将所辨识的结合部刚度录入有限元模型,栓接结构固有频率的有限元预测值与实测值之间最大误差率为3.01%;数值模拟试验与现场模态试验的辨识效果均较为理想,验证了方法的可行性。同时,以栓接结构典型振型对应固有频率为指标辨识的结合部动力学刚度信息很好预测其他各阶固有频率的分布,表征和印证了栓接结构在较大预紧力作用下,螺栓结合部非线性动力学特性得到了抑制,满足线性条件假设。
Accurate identification of the dynamic information is an important prerequisite for the combination of structural dynamics modeling. In this paper,the method of the dynamic stiffness identification was studied based on the theory of modal analysis. Firstly,we constructed a generalized dynamics model containing the dynamic information,discussed the characteristics of the joint dynamics from the theory of modal analysis influencing between the natural frequency and the combination structure and established the relationship between them. Furthermore,we built an ideal finite element model by the mass and spring-damper and identified the joint stiffness by the natural frequency obtained by numerical analysis. The maximum error between the identification and the theoretical value was 1. 92%. At last,we applied modal test on bolt joints,the measured natural frequency of the typical mode of vibration in normal and tangential direction as the index,through the MATLAB-ANSYS integration platform to identify the bolt joint stiffness. Moreover,the obtained results were input to the finite element model. The maximum error between the predicted value and measured value was 3. 01%. The numerical value and the test value were all ideal,demonstrating the feasibility of the method. At the same time,the dynamic stiffness identified by the measured natural frequency of the typical mode of vibration was a very good predictor of other order natural frequency distribution of the bolt connection structure,demonstrating that the bolt in a larger pretightening force; dynamic characteristics met the linear assumption.
Accurate identification of the dynamic information is an important prerequisite for the combination of structural dynamics modeling. In this paper,the method of the dynamic stiffness identification was studied based on the theory of modal analysis. Firstly,we constructed a generalized dynamics model containing the dynamic information,discussed the characteristics of the joint dynamics from the theory of modal analysis influencing between the natural frequency and the combination structure and established the relationship between them. Furthermore,we built an ideal finite element model by the mass and spring-damper and identified the joint stiffness by the natural frequency obtained by numerical analysis. The maximum error between the identification and the theoretical value was 1. 92%. At last,we applied modal test on bolt joints,the measured natural frequency of the typical mode of vibration in normal and tangential direction as the index,through the MATLAB-ANSYS integration platform to identify the bolt joint stiffness. Moreover,the obtained results were input to the finite element model. The maximum error between the predicted value and measured value was 3. 01%. The numerical value and the test value were all ideal,demonstrating the feasibility of the method. At the same time,the dynamic stiffness identified by the measured natural frequency of the typical mode of vibration was a very good predictor of other order natural frequency distribution of the bolt connection structure,demonstrating that the bolt in a larger pretightening force; dynamic characteristics met the linear assumption.
引文
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[13]田红亮,赵春华,朱大林,等.整个螺栓结合部的法向连接动刚度及试验验证[J].西安交通大学学报,2012,46(9):31-36.TIAN Hongliang,ZHAO Chunhua,ZHU Dalin,et al.Analysis and validation on normal connection dynamic stiffness of bolted joint interface ensemble[J].Journal of Xi’an Jiaotong University,2012,46(9):31-36.
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[15]黎定仕,张以都,王鹏.基于结构阻尼的机械结合部动力学模型研究[J].振动与冲击,2010,29(8):204-208.LI Dingshi,ZHANG Yidu,WANG Peng.Dynamic model of machine joints based on structural damping[J].Journal of Vibration and Shock,2010,29(8):204-208.
[16]孙明楠,米良,干静,等.数控机床导轨结合部动态特性参数优化识别方法研究[J].四川大学学报(工程科学版),2012,44(3):217-223.SUN Mingnan,MI Liang,GAN Jing,et al.An optimum identification method of dynamic characteristic parameters of guideway joint on a NC machine tool[J].Journal of Sichuan University(Engineering Science Edition)2012,44(3):217-223.
[17]米良,殷国富,孙明楠,等.基于结合部动力学特性的立柱-主轴系统动力学模型研究[J].农业机械学报,2011,42(12):202-207.MI Liang,YIN Guofu,SUN Mingnan,et al.Column-spindle system dynamic model based on dynamic characteristics of joints[J].Transactions of the Chinese Society for Agricultural Machinery,2011,42(12):202-207.
[18]董冠华,殷勤,殷国富,等.机床结合部动力学建模与辨识方法的研究[J].机械工程学报,2016,52(5):162-168.DONG Guanhua,YIN Qin,YIN Guofu,et al.Research on dynamics modeling and identification of machine tool joints[J].Journal of Mechanical Engineering,2016,52(5):162-168.
[19]董冠华,殷勤,殷国富,等.机床结合部耦合动刚度的辨识与建模[J].上海交通大学学报,2015,49(9):1263-1268.DONG Guanhua,YIN Qin,YIN Guofu,et al.Identification and modeling of coupling dynamic stiffness in joints of machine tool[J].Journal of Shanghai Jiaotong University,2015,49(9):1263-1268.
[2]TSAI J S,CHOU Y F.The identification of dynamic characteristics of a single bolt joint[J].Journal of Sound and Vibration,1988,125(3):487-502.
[3]REN Y,BEARDS C F.Identification of joint properties of a structure using FRF data[J].Journal of Sound and Vibration,1995,186(4):567-587.
[4]CˇELICˇD,BOLTEAR M.Identification of the dynamic properties of joints using frequency-response functions[J].Journal of Sound and Vibration,2008,317:158-174.
[5]CˇELICˇD,BOLTEAR M.The influence of the coordinate reduction on the identification of the joint dynamic properties[J].Mechanical Systems and Signal Processing,2009,23:1260-1271.
[6]LIN Y,CHEN W.A method of identifying interface characteristic for machine tools design[J].Journal of Sound and Vibration,2002,255(3):481-487.
[7]GUO Q,ZHANG L.Identification of the mechanical joint parameters with model uncertainty[J].Chinese Journal of Aeronautics,2005,18(1):47-52.
[8]黄玉美,董立新,董献国,等.机械平面结合部静特性的研究及其在机床CAD中的应用[J].工程力学,1995(1):66-71.HUANG Yumei,DONG Lixin,DONG Xianguo,et al.Research on the static behavior of mechanical plane joints and its application to CAD of machine tools[J].Engineering Mechanics,1995(1):66-71.
[9]杨橚,唐恒龄,廖伯瑜.机床动力学[M].北京:机械工业出版社,1983:261-317.
[10]张学良,温淑花,徐格宁,等.结合部切向接触刚度分形模型研究[J].应用力学学报,2003,20(1):70-72.ZHANG Xueliang,WEN Shuhua,XU Gening,et al.Fractal model of the tangential contact stiffness of machined surfaces in contact[J].Chinese Journal of Applied Mechanics,2003,20(1):70-72.
[11]李玲,蔡安江,蔡力钢,等.栓接结合部动态特性参数辨识新方法[J].振动与冲击,2014,33(14):15-19.LI Ling,CAI Anjiang,CAI Ligang,et al.New method to identify dynamic characteristics of bolted joints[J].Journal of Vibration and Shock,2014,33(14):15-19.
[12]孙伟,李星占,韩清凯.螺栓联接梁结构结合部非线性特性参数辨识[J].振动工程学报,2013,26(2):185-191.SUN Wei,LI Xingzhan,HAN Qingkai.Nonlinear joint parameter identification for bolted beam structure[J].Journal of Vibration and Engineering,2013,26(2):185-191.
[13]田红亮,赵春华,朱大林,等.整个螺栓结合部的法向连接动刚度及试验验证[J].西安交通大学学报,2012,46(9):31-36.TIAN Hongliang,ZHAO Chunhua,ZHU Dalin,et al.Analysis and validation on normal connection dynamic stiffness of bolted joint interface ensemble[J].Journal of Xi’an Jiaotong University,2012,46(9):31-36.
[14]田红亮,陈从平,方子帆,等.应用改进分形几何理论的结合部切向刚度模型[J].西安交通大学学报,2014,48(7):46-52.TIAN Hongliang,CHEN Congping,FANG Zifan,et al.Tangential stiffness model for joint interface adopting the revised fractal geometric theory[J].Journal of Xi’an Jiaotong University,2014,48(7):46-52.
[15]黎定仕,张以都,王鹏.基于结构阻尼的机械结合部动力学模型研究[J].振动与冲击,2010,29(8):204-208.LI Dingshi,ZHANG Yidu,WANG Peng.Dynamic model of machine joints based on structural damping[J].Journal of Vibration and Shock,2010,29(8):204-208.
[16]孙明楠,米良,干静,等.数控机床导轨结合部动态特性参数优化识别方法研究[J].四川大学学报(工程科学版),2012,44(3):217-223.SUN Mingnan,MI Liang,GAN Jing,et al.An optimum identification method of dynamic characteristic parameters of guideway joint on a NC machine tool[J].Journal of Sichuan University(Engineering Science Edition)2012,44(3):217-223.
[17]米良,殷国富,孙明楠,等.基于结合部动力学特性的立柱-主轴系统动力学模型研究[J].农业机械学报,2011,42(12):202-207.MI Liang,YIN Guofu,SUN Mingnan,et al.Column-spindle system dynamic model based on dynamic characteristics of joints[J].Transactions of the Chinese Society for Agricultural Machinery,2011,42(12):202-207.
[18]董冠华,殷勤,殷国富,等.机床结合部动力学建模与辨识方法的研究[J].机械工程学报,2016,52(5):162-168.DONG Guanhua,YIN Qin,YIN Guofu,et al.Research on dynamics modeling and identification of machine tool joints[J].Journal of Mechanical Engineering,2016,52(5):162-168.
[19]董冠华,殷勤,殷国富,等.机床结合部耦合动刚度的辨识与建模[J].上海交通大学学报,2015,49(9):1263-1268.DONG Guanhua,YIN Qin,YIN Guofu,et al.Identification and modeling of coupling dynamic stiffness in joints of machine tool[J].Journal of Shanghai Jiaotong University,2015,49(9):1263-1268.