Characteristic Analysis of Passenger Car Door Vibration Transfer Function

2017 2 nd International Conference on Artificial Intelligence and Engineering Applications (AIEA 2017) ISBN: 978-1-60595-485-1 Characteristic Analysis of Passenger Car Door Vibration Transfer Function XIQUAN QI, YANSONG WANG, HUI GUO and LIHUI ZHAO ABSTRACT In order to study the vibration transfer characteristics of passenger car door, modal and vibration transfer function of passenger car door are simulated by using HyperMesh and Nastran synthetically. The accuracy of the finite element model is verified through modal analysis. According to the first two modes, the position of transfer function response points is confirmed. The vibration transfer functions are simulated and the accuracy of the simulation is verified by test. The research shows that the natural frequency of a passenger car door is not necessarily a pole of the passenger car door transfer function. On the contrary, a pole of transfer function is bound to be a natural frequency of the passenger car door, which is of directive significance to study the NVH characteristics of the passenger car door structure. KEYWORDS Passenger Car Door; Vibration Transfer Function; the Finite Element; Modal Analysis. INTRODUCTION As people s pursuit of car comfort become higher and higher, the research on NVH characteristics [1] becomes more and more thorough. As an important part of the car body, the door is the main channel to connect the passengers and the outside environment, so it is very important to study its NVH characteristics. Because the vibration of the door mainly comes from the engine and the road excitation, the vibration of the door provides an effective scheme and train of thought for the study of the NVH characteristics of the whole vehicle. Zhang Jinhuan et al [2] carried out an experimental study on the abnormal vibration of a medium-sized passenger car door. The experimental modal analysis method was used to analyze the mechanism of abnormal vibration of the car door. By using DASP data acquisition and analysis system, Lei Ming et al [3] calculated the transfer function [4] of each measuring point, and calculated the modal frequency of each order by the polylscf method in DASP software modal analysis module. CJ Kim et al [5] proposed a vibration testing model for SLAM testing, which presented a failure model for impact tests to assess their fatigue resistance. At present, the research on car door vibration is mainly through the experimental test or simulation software (ANSYS, HyperWorks, Xiquan Qi,939702433@qq.com, Corresponding author: Yansong Wang loveqrxql@163.com, Hui Guo, hgsues@163.com and Lihui Zhao, Pheigoe@qq.com. School of Automotive Engineering, Shanghai University of Engineering Science, Shanghai 201620, China 885

etc.) to conduct the modal analysis of the car door. There is less analysis from the perspective of the vibration transfer function. The finite element software HyperMesh and Nastran are taken to carry out the vibration transfer function simulation analysis and the accuracy of simulation is verified by test. Then the relation between the transfer function and the natural frequency of the system is analyzed, so as to provide the basis for reducing vibration and noise of the vehicle door or even the whole car. CAR DOOR MODEL AND ANALYSIS THEORY Car Door Model The car door is an important component of the car body. It consists of shell, accessory and trim board. The shell is composed of inner plate and outer plate et al which are connected by welding, bonding and other processes. The inner and outer plates are punched by steel plates, and the shape of the outer plate is coordinated with the whole vehicle. The inner plate is provided with various shapes of holes, nests and reinforcing ribs so as to increase strength and install accessories. Various reinforcing plates and brackets are welded on the inner plate to increase strength and rigidity. After the door is installed, the inner panel is covered with the trim board to harmonize with the interior decoration. A car door is taken as the research object in this paper, as shown in Fig 1. A car door is mainly consisted of the inner plate 1 and the outer plate 2, and the inner plate is welded with reinforced plate 3. 4, 5 in Figure 1 are car door hinge, and 6 is door lock. The finite element model of the car door is established in HyperMesh. The geometry such as fillet and corner of the CAD model is cleaned up before meshing. Too large mesh size will cause the inadequate calculation accuracy and too small grid size will increase the time of calculation, so the grid size is set as 8mm based on the size of small parts such as the small hole and door hinges in the door. Most of the components of the door are thin-walled stampings, so the shell element is used to discretize them. The welding spots on the door are replaced by rigid connections, and two sheets are connected by adhesive connection. Figure 1. Car Door Model. 886

TABLE 1. PERFORMANCE PARAMETER OF CAR DOOR MATERIAL. Modulus Of Elasticity Poisson Ratio Density Damping 2.1 10 5 MPa 0.3 7.9 10-9 t/mm 3 0.025 Different parts of the door are made of different grades of steel, the difference is mainly in strength, elongation and other parameters, and the basic performance parameters related are the same, as shown in Table 1. Modal Analysis Theory Modal analysis is a modern method to study the dynamic characteristics of structures. It is the application of system identification method in engineering vibration field. Mode is the natural vibration characteristic of mechanical structure, and each mode has specific natural frequency, damping ratio and mode shape. The vibration differential equations of the multiple-degree-of-freedom system after discrete treatment can be transformed into the dynamic problems in structural dynamics modal analysis. [ M ]{ xt ( )} { xt ( )} [ K]{ xt ( )} { f( t)} (1) Where [M] is the mass matrix, [C] is the damping matrix, [K] is the stiffness matrix, {f(t)} is the excitation vector, and {x(t)} is the response vector. It is assumed that the vibration system is free vibration and that damping is neglected: [ M]{()} x t [ K]{()} x t 0 (2) This is the two order constant coefficient homogeneous linear differential equations. The form of its solution is Bring (3) into (2): {()} x t {} e iwt (3) 2 ([ K] w [ M]){ } 0 (4) This is a generalized eigenvalue problem. For the n degrees of freedom system, the characteristic solution (w12, {φ1}), (w22, {φ2}),, (wn2, {φn}) can be obtained by solving the equations, where the w1, w2,, wn represent the n natural frequencies corresponding to the system (orthogonal modes). Since the structure is a linear combination of different modes of vibration in any mode of vibration, the real effect of vibration can be achieved by linear superposition of different modes when forced vibration occurs. Transfer Function Theory The transfer function is the relationship between the input and output of the object which has a linear characteristic between the output waveform and the input waveform represented by the ratio of the Laplasse transform [6]. For linear systems, there is an 887

incentive or input, it must have an input and output. However, the linear system is not only a single input - single output but also a single input- multiple output [7]. The linear system theory shows that there is a definite relationship between the excitation and the response of the single input and single output system. If the excitation is a time-domain function x(t), and the response is another time-domain function y(t), there is also a time-domain function in the linear system, called the impulse response function h(t). There is a convolution relation between these three functions: y( t) h( t)* x( t) h( ) x( t ) d t (5) 0 Does Fourier transform on both sides of equation (1), and equation (6) is obtained according to convolution theorem Yw ( ) HwXw ( ) ( ) (6) Where X(w),Y(W) and H(w) are the Fourier transform [8] of the excitation function x(t), the response function y(t) and the impulse response function h(t) respectively, and H(w) is called the transfer function or frequency response function of the linear system [9]. The vibration of a car door can be seen as the result of the actions of multiple excitations. The outer surface must be measured in different parts of the engine, so the engine should be considered as a multiple input and multiple output system. The relationship between Fourier transform of excitation and response and transfer function can be expressed as equation (7). N Y( w) H ( w) X ( w) (7) i ji r r 1 Where Hji(w) is the transfer function between the r point and the j point. The equations of motion for single degree of freedom linear systems in time domain are considered: my () t cy () t ky() t x() t (8) Where m is mass, c is damping, k is stiffness, and Fourier transform is conducted on both sides of equation (8), so there is a relationship among the Fourier transformation of velocity response, acceleration response and displacement response in equation (9) and equation (10). Yw ( ) iwyw ( ) (9) 2 Yw ( ) wyw ( ) (10) The equation (8) is converted to equation (11). 2 ( wm iwc ky ) ( w) X( w) (11) 888

Transfer function H(w) can be obtained in equation (12). Hw ( ) 1 (12) 2 wm iwc k It can be seen from the equation (12) that when the mass, stiffness and damping of the structure are certain, the transfer function H(w) is only a function of frequency, so the transfer function has nothing to do with the excitation. It only reflects the inherent characteristics of the mechanical system itself. In general, as a complex function of frequency, H(w) can be expressed by module H(w) and amplitude φ(w) and can also be expressed by the real part Re[H(w)] and the imaginary part Im[H(w)], where the H(w), φ(w), Re[H(w)] and Im[H(w)] are called the amplitude frequency characteristic and phase frequency characteristic, frequency characteristic and imaginary frequency characteristics [10-11]. Therefore, the transfer function establishes the quantitative relationship between the input and output of the system, and can estimate the structural response of each exciting force on the surface of the system to predict the vibration condition of the car door. In addition, through the identification and analysis of each transfer function, the dynamic parameters of the structure can be obtained to conduct the modal identification of the system, which provides the basis for the design improvement and the attachment layout. The structure is calculated by the finite element method, then discrete structure, divided into a plurality of units, the formation of [M], the mass matrix stiffness matrix and damping matrix of [K] [C], when the given frequency domain load x (W), displacement, velocity and acceleration can be obtained in the frequency domain response. If the {x (W)}={1} is the unit array, then there is { Yw ( )} [ Hw ( )] {1} { Hw ( )} (13) Thus, the transfer function of the system n frequencies can be obtained. MODAL ANALYSIS The modal analysis of the car door is carried out in Nastran. The mode of vibration is shown in fig. 2. (a)one (b)two (c)three (d)four (e) five (f)six Figure 2. Modal Shape Diagram. TABLE 2. MODAL FREQUENCIES OF THE FIRST SIX ORDERS. Number of Order 1 2 3 4 5 6 Simulation 45.13 50.58 56.15 57.86 61.91 75.41 Test 45.06 50.12 55.79 57.48 61.72 74.96 889

Figure 3. Distribution of Excitation Points and Response Points. It can be seen from figure 2 that the maximum vibration amplitude of the door is concentrated in the middle of the door, window frame, inner and outer plate, so the vibration characteristics of these parts should be analyzed mainly. The modal test is carried out in the semi anechoic chamber to avoid the influence of external vibration on the test. The first six order modes of the car are measured by hammering method. The contrast of first six modes of frequency simulation and test is shown in Table 2. It can be seen from table 2 that the results of corresponding simulation and experimental frequency of each order modal are relatively close, and proved the accuracy of the finite element model. SIMULATION AND VERIFICATION of TRANSFER FUNCTION Transfer Function Simulation of car door The simulation of transfer function is analyzed in Nastran, and the excitation and response points are shown in Figure 3. According to the actual door and body connection position, the incentive point is respectively 1, 2, 3, The response points A and B are set in the position of the first maximum amplitude modes and second modes. The simulation is divided into six operating conditions. Three excitation points correspond to two response points. the unit force is applied at the excitation point, and then the acceleration of the response point is obtained. Transfer Function Test of Car Door The hammer method is used in the tests of mode and transfer function, and the test system mainly uses the non-fixed excitation system. As shown in Figure 4, the system includes white door, force hammer, acceleration sensor, and LMS data acquisition system and so on. The test is carried out in a semi anechoic chamber to avoid the effect of external vibration on the test and make the result more accurate. According to the characteristics of the door structure, the outer surface of the door is regared as a test selection. The layout of the sensor is based on the exciting position of simulation. The measuring points are uniformly arranged on the outer surface of the door, so that the number of measuring points are in less than 30. The location coordinates of the measuring points should be input to the data acquisition system. The door geometric 890

model is established with the door hanging freely on the bench. The hammer is treated as input, the acceleration sensor is tested as output, and then the transfer function can be gotten through the inverse method. The simulation and verification results are shown in figure 5. Figure 4. Validation Test. (a) (b) (c) (d) (e) (f) Figure 5. Comparison Of Simulation And Test. 891

TABLE 3. THE RELATION BETWEEN THE POLES OF THE TRANSFER FUNCTION AND THE NATURAL FREQUENCY. natural frequency 45.06 50.12 55.79 57.48 61.72 74.96 Figure a Figure b Figure c Figure d Figure e Figure f As can be seen from Figure 5: 1),Among the poles in figure (a) and (b), the poles in the frequency of 50.12 Hz, 57.48 Hz and 74.96 Hz are same with the second order, fourth order and sixth order natural frequency of the door; 2), Among the poles in figure (c) and (f), the poles in the frequency of 45.06 Hz, 50.12 Hz, 57.48 Hz and 61.72 Hz are Corresponding to the first order, second order, fourth order and fifth order natural frequency of the door; 3), Among the poles in figure (d) and (e), the poles in the frequency of 45.06 Hz, 50.12 Hz, 57.48 Hz, 61.72 Hz and 74.96 Hz are similar to the first order, second order, fourth order, fifth order and sixth order natural frequency of the door. In Figure 5 the simulation results fit well with experimental results, error is less than 5%, indicating that the simulation method is effective; the corresponding relationship between the door and the pole transfer function of each natural frequency is shown in Table 3, which said transfer function pole is corresponding to the inherent frequency of the door. CONCLUSION In this paper, the finite element simulation analysis method is used to analyze the vibration transmission characteristics of car doors. The following conclusions are obtained by experimental verification. (1) The vibration transfer function of car door is analyzed by finite element analysis method based on HyperMesh and Nastran, and its feasibility and effectiveness are verified by experiments. (2) The region without in Table 3 said that there is no corresponding pole between the natural frequency and the corresponding transfer function, which Indicate that a natural frequency of the door is not a pole of the transfer function of the door; on the contrary, The area with in Table 3 said that a pole of transfer function has a corresponding natural frequency which means that a pole of the transfer function is bound to be a natural frequency of the door. Therefore, the poles of transfer function cannot be obtained by all the natural frequencies of the door. ACKNOWLEDGMENTS The authors express their sincere and heartfelt thanks to the editor and reviewers for their constructive suggestions to improve the quality of this paper. This work is 892

financially supported by the Chinese National Natural Science Fund under Grant No. 51675324 and No. 51175320 and Shanghai Natural Science Fund under Grant No. 14ZR1418600. The authors declare that we have no conflicts of interest regarding this work. Corresponding author: Yansong Wang, loveqrxql@163.com. School of Automotive Engineering, Shanghai University of Engineering Science, Shanghai 201620, China REFERENCES 1. A Corsini, F. Rispoli and L.D. Santoli et al., A Review of Experimental Techniques for NVH Analysis on a Commercial Vehicle, Energy Procedia, vol. 82, pp. 1017-1023, Dec. 2015. 2. Zhang Jinhuan, Zhu Xichan and Huang Shilin et al., Experimental research on abnormal vibration of medium bus door, Chinese Journal of Automotive Engineering, no. 2, pp. 40-44, 1995.. 3. Lei Mingzhun, Zhang Fengli and Wang Jiannan et al., Modal Analysis and Study on Optimization of Car Door Based on Finite Element Method, Automotive Technology, vol. 12, pp. 4-7, Dec. 2008. 4. N. Suzuki, Y. Kurata and T. Kato et al., Identification of transfer function by inverse analysis of self-excited chatter vibration in milling operations, Precision Engineering, vol. 36, no. 4, pp. 568-575, 2012. 5. C.J. Kim, B.H. Lee and Y.J. Kang, Accelerated Slam Testing of Vehicle Door Plate Module Using Vibration Exciter, Journal of Testing & Evaluation, vol. 41, no. 4, Feb. 2012. 6. U. Filobello-Nino, H. Vazquez-Leal and Y. Khan et al., Laplace transform-homotopy perturbation method as a powerful tool to solve nonlinear problems with boundary conditons defined on finite intervals, Computational & Applied Mathematics, vol. 34, no. 1, pp. 1-16, 2015. 7. D.J. Nefske, S.H. Sung and D.A. Feldmaier, Correlation of a beam type exhaust system finiteelement model for vibration analysis, Canadian Medical Association Journal, vol. 121, no. 5, pp. 521-521, 2003. 8. Wang Daoxian, Duan Xiaohui, Yang Guanglin, Discussion about the Existence Condition of Signal Fourier Transform, Journal of Electronics & Information Technology, vol. 35, no. 11, pp. 2790-2794, Nov. 2013. 9. T.P. Dobrowiecki, J. Schoukens, P. Guillaume, Optimized excitation signals for MIMO frequency response function measurements, IEEE Transactions on Instrumentation & Measurement, vol. 55, no. 6, pp. 2072-2079, 2006. 10. He Suxia, Le Liqin, The research and simulation of phase-frequency characteristics based on the amplitude frequency characteristics, Electronic Design Engineering, vol. 21, no. 21, pp. 123-125, 2013. 11. B. Kong, E. Wang and Z. Li et al., Acoustic emission signals frequency-amplitude characteristics of sandstone after thermal treated under uniaxial compression, Journal of Applied Geophysics, vol. 136, pp. 190-197, 2017. 893