基于传递矩阵法的碳纤维复合材料传动轴模态分析
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摘要
以某汽车传动轴为参考对象设计出碳纤维复合材料(CFRP)传动轴铺层方案,采用传递矩阵法(TMM),把CFRP传动轴离散为若干个盘轴单元,建立集中质量圆盘左右截面的点传递矩阵,建立轴段的场传递矩阵,进而构建整根轴的传递矩阵。根据传动轴两端自由的边界条件,推导出其转子频率方程,利用MATLAB编程求解出CFRP传动轴的一阶临界转速及其对应的振型,并与传统的经验公式及有限元仿真软件Abaqus计算出的结果作比较。结果表明,对于传动轴一阶弯曲固有频率,传递矩阵法相比于有限元仿真计算误差为1.6%,一阶振型的最大偏差为0.015。表明传递矩阵法能较精确的计算CFRP传动轴的固有频率以及对应的模态振型。
A paving program of carbon fiber reinforced composite drive shaft on a vehicle is designed.By applying the transfer matrix method,the CFRP drive shaft is discretized into a number of disc-shaft unites.A point transfer matrix of the left and right section of a concentrated mass disc is established,and a field transfer matrix of the shaft section is established,and then the whole transfer matrix is constructed of the whole shaft.According to the free boundary condition of both ends of the drive shaft,a rotor frequency equation is established,and by MATLAB programming the first order critical speed and corresponding vibration mode of the CFRP drive shaft can be get.The results will be compared with the traditional empirical formula and the finite element simulation software.The comparison result shows,as for the first order bending natural frequency of the shaft,the result of transfer matrix method has a calculation error of 1.6% with the result of the simulation and 0.015 calculation error of the first order vibration mode,indicating that transfer matrix method has feasibility on calculating the modal information of the CFRP drive shaft.
A paving program of carbon fiber reinforced composite drive shaft on a vehicle is designed.By applying the transfer matrix method,the CFRP drive shaft is discretized into a number of disc-shaft unites.A point transfer matrix of the left and right section of a concentrated mass disc is established,and a field transfer matrix of the shaft section is established,and then the whole transfer matrix is constructed of the whole shaft.According to the free boundary condition of both ends of the drive shaft,a rotor frequency equation is established,and by MATLAB programming the first order critical speed and corresponding vibration mode of the CFRP drive shaft can be get.The results will be compared with the traditional empirical formula and the finite element simulation software.The comparison result shows,as for the first order bending natural frequency of the shaft,the result of transfer matrix method has a calculation error of 1.6% with the result of the simulation and 0.015 calculation error of the first order vibration mode,indicating that transfer matrix method has feasibility on calculating the modal information of the CFRP drive shaft.
引文
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[7]Zhang G L,Zhou Z D,Zhang J G.Design and analysis of a CFRP drive shaft[J].Advanced Materials Research,2013(690-693):3042-3045.
[8]Dabrowski Z,Deuszkiewicz P.Dynamic model of carbon fiber drive shaft[J].Solid State Phenomena,2015(236):39-52.
[2]Rao B J P,Srikanth D V,Kumar T S.Design and analysis of automotive composite propeller shaft using fea[J].M aterials Today Proceedings,2016,3(10):3673-3679.
[3]Kim W,Argento A,Mohanty P S.Bending natural frequencies of circular CFRP shafts with a metal core or casing[J].Journal of Composite Materials,2004,38(6):475-494.
[4]M A Badie,A Mahdi,A R Abutalib.Automotive composite driveshafts:investigation of the design variables effects[J].International Journal of Engineering and Technology,2006,3(2):227-237.
[5]Ratnam C.Design of composite drive shaft for optimal first natural frequency[J].Journal of the Institution of Engineers(India):Mechanical Engineering Division,2006,87(7):7-11.
[6]李丽,顾力强.碳纤维复合材料传动轴临界转速分析[J].汽车工程,2005,27(2):239-240.(Li Li,Gu Li-qiang.Analysis of the critical speed of the carbon fiber reinforced composite drive shaft[J].Automotive Engineering,2005,27(2):239-240.)
[7]Zhang G L,Zhou Z D,Zhang J G.Design and analysis of a CFRP drive shaft[J].Advanced Materials Research,2013(690-693):3042-3045.
[8]Dabrowski Z,Deuszkiewicz P.Dynamic model of carbon fiber drive shaft[J].Solid State Phenomena,2015(236):39-52.