An Optimization of Rubber Mounting for Vehicle Interior Noise Reduction

Transcription

1 An Optimization of Rubber Mounting for Vehicle Interior Noise Reduction N. TSUJIUCHI, T. KOIZUMI, and T. TAKENAKA T. IWAGASE Department of Mechanical Engineering Doshisha University Kyotanabe, Kyoto JAPAN Tire Advanced Technology Department TOY0 TIRE & RUBBER Co.,Ltd. Itami, Hyogo JAPAN Abstract Generally, it is well known that the road noise generated by the vibration transmitted from tire and suspension can be reduced by stiffness change of rubber mounts installed in suspension system. However, those mount stiffness is barely changed to avoid the aggravations of riding comfort and so on. In this paper, a stiffness optimization of rubber mounts that reduces road noise and improves riding comfort as well is presented. In the process, the Road Noise Contribution Analysis (RNCA) is applied to the target vehicle for specifying the major factor of road noise. Furthermore, the suspension system is investigated by Sensitivity Analysis using Measured FRF data (SAMF) for identifying an optimal stiffness combination of rubber mounts. As a result, an effective stiffness combination of 2 mounts to reduce road noise and improve of riding comfort is specified. 1. Introduction It is important to reduce vehicle interior noise for progress of vehicle quality. Road noise, a factor of interior noise, is usually classified in structure-borne noise and air-borne one. The former, generated by driveline, engine and tire-to-road sources, is of significant concern, For reduction of structure-borne noise, it is effective to change stiffness of rubber mount, between suspension system and body, located in transmission path of source vibration. In practice however, it is hardly changed because of difficulty in compatibleness with riding comfort, controllability and stability. In this paper, an optimization method of rubber mount for road noise reduction compatible with improvement of riding comfort (harshness) is demonstrated. The objective rubber mounts, which are installed in front and rear side of a lower arm on front suspension system in the target vehicle, are shown in Fig.]. To change mount stiffness effectively, it is important to grasp the following items in detail. (1) Contribution relationship between suspension system s vibration and interior noise (2) Suspension resonance that exist in the problem frequency band (3) Mount location sensitive to vibration that causes road noise and riding discomfort First, to make clear the item (I), Road Noise Contribution Analysis (RNCA) is performed by the noise and vibration data measured by in-operation test at a road noise evaluation course. The theory used here is based on the multiple inputs single output (MISO) analysis technique proposed by J. S. Bendat [1][2]. Furthermore, the item (2) is clarified by the experimental modal analysis for the suspension system that is separated from the target vehicle and fixed in the rigid support (called suspension tester). For the item (3), Mount location (either one of front side or rear side of lower arm) sensitive to road noise and riding comfort is selected by Sensitivity Analysis using Measured FRF data (SAMF) based on the substructure synthesis method. The advantage of the SAMF method is that the frequency dependence of rubber mount s stiffness can be considered and dynamic characteristics after modified rubber mount s stiffness are predicted accurately. In this paper, the 275

2 validity of the SAMF is evaluated by comparing predicted FRFs with experimental ones on suspension tester, and this method is applied for rubber mounts. ShOdi aear: abrorber Rubber nlouot ;; z E H 40 e - 30!in etlr Fig. 1 Targeted front suspension system 2. Road Noise Contribution Analysis (RNCA) In this chapter, an in-operation test is performed to identify the problem frequency band of road noise, and the multiple inputs single output analysis technique is applied to the target vehicle to specify the relationship between interior noise and accelerations on the suspension system. 2.1 In-operation test An in-operation test is carried out in the road noise evaluation course with speed of 60kmih for the target vehicle. The schematic diagram of measurement points is shown in Fig.2. The accelerations are measured at total of 6 points i.e. 4points (steering knuckle, shock absorber, lower arm and cross member) on the targeted front suspension system and 2points (steering knuckle, shock absorber) on the rear suspension system in order to consider the influence. The interior noise is measured at the driver s ear position. The l/3 octave band level of the interior noise measured in this test is shown in Fig.3. The conditions of 160 and 3 I5Hz bands are much worse than the other bands. Especially, the 160Hz band is often reported as a problem frequency band of road noise in other papers. Therefore, the 160 Hz band is paid attention to and discussed in this paper. Pml Frequency [Hz] Fig octave band level of the interior noise measured at the driver s ear position 2.2 Theoretical background of RNCA For example, let us consider a three-inputs /single-output system shown in Fig.4 to illustrate the theory of RNCA. The inputs.r, are the accelerations at arbitrary points on the suspension system, and the output JJ is the sound pressure at the driver s ear position. However, if the inputs are mutually coherent among them for the real system, the frequency response functions H cannot be estimated by well-known estimation method (Hl, H2 and so on). So, the system shown in Fig.4 should be denoted to an alternative system, Fig.5, with mutually incoherent inputs having conditioned (residual) spectrums. The conditioned power and cross-spectral density functions can be calculated as follows. s I.1 =s,-4,x, i,j =2,3,y (I) Where s,,, are the conditioned power and cross-spectral density functions obtained by eliminating the linear effects of the input x, from power and cross-spectral density functionss,,, and L,, are the frequency response functions in the alternative system. The linear effect of the input x2 is eliminated from all spectrums by following equation as well. S i 12 = s,, I -L,,S,, I I,/ =3,y (2) Now, the frequency response functions L in Eqs. (I) and (2) can be obtained in the conditioning process as Interior noise 0 A Acceleration Fig.2 Measurement points in RNCA L, =s,, c,-,r ~X.,,-,,l i,/=1,2,3;,>i (3) The ordinary coherence functions are defined as follows using previously calculated quantities. 276

3 u: = Is, I2 m, s, 1 l., = 1,2,3,y (4) Moreover, the partial coherence functions are given by r:,., =I%, l~2u*2.1~~w 1) (5) r:, 12 =ISJ (~33 12.sw 12). (6) The multiple coherence function between the output and the all of inputs satisfy r: x =I-(l-Y:J-Y:,,)(1-Y:,.,,). (7) By this multiple coherence function, how much all of the selected inputs contribute into the output can be judged. In other words, the validity of the selected input locations can be verified. The coherent output power spectrum is useful to evaluate the noise source because it indicates how much of conditioned spectral density function is due to the unique effect of a particular input x,[3]. In this example, the coherent output power spectrums for each input X, are given as follows. 4, = r:, 23 S, 23 (8) 4, = r:, 13 S, I3 (9) 4, = r:, 12.s, 12 (10) Hence, the contribution ranking of each input to the output can be decided by the coherence output power spectrums. t- II, t t yjtv / Fig.4 A three input/single output system (With mutual coherent inputs) 2.3 Analytical result and discussion of RNCA For performing the RNCA effectively and adequately, it is important that the number of inputs is reduced and the measurement locations of acceleration data as the inputs are chosen so that the multiple coherence function takes the highest value. In this study, among the acceleration data measured in the 6 points on the suspension system, the data for the best 2 points should be used as the inputs for RNCA. The one should be measured on the targeted front suspension system; another on the rear suspension system in order to consider the influence. As the result of the examination, when the acceleration data measured at the center of cross member in the front and also the upper attachment location of shock absorber in the rear is used as the inputs in RNCA, the value of the multiple coherence function is the highest, and it is proven appropriate as the inputs. The multiple coherence function between the selected inputs and the interior noise is shown in Fig.6. According to the reference [I], it is desirable that multiple coherence function takes the value over 0.8, when the MIS0 system is analyzed. Fig.6 shows that multiple coherence function can be secured more than 0.8 in the problem frequency band of 160 Hz. Therefore, it can confirm the high reliability of this analysis. The coherent output power spectrums in the problem frequency band of road noise are shown in Fig.7. For the targeted front suspension, it is clear that the lateral vibration of cross member contributes to the interior noise the most because the value of its coherent output power spectrum is the largest, d Frequency lhz/ Fig.6 Multiple coherence function between the selected inputs and the interior noise Fig.5 Alternative system of Fig.4 (With mutual incoherent inputs) 277

4 $ 50 is 0 z g k I Frequency [Hz] Fig.7 Coherent output power spectrums of front suspension system 3.2 Resonant modes The resonant mode that exists in the problem frequency band of road noise is shown in Fig.9. At 165Hz, one of the two resonant frequencies, shock absorber generates bending resonance for lateral direction, tire and wheel vibrate for lateral direction in opposite phase each other, and lower arm moves laterally. Thus, it is clear that the bending mode of shock absorber is the cause of the lateral vibration of cross member described in previous chapter. Note that the mode at 148Hz is also the bending mode of shock absorber for lateral direction. From Hz, which is related to riding comfort (harshness) characteristics, the fore and aft resonance of un-sprung mass exists as shown in Fig Resonant modes of the suspension system In this chapter, the resonances of the suspension system are specified by the experimental modal analysis, and the cause of lateral vibration of the cross member is clarified. 3.1 Suspension tester The passenger car assembled by various components has many resonances. Therefore, it is most desirable that the suspension system is separated from car body and fixed in a rigid support to identify only the suspension system resonances. Then, the suspension system detached from car body is fixed in the support (called the suspension tester in this paper) as shown in Fig.8, and the excitation test is carried out in the similar condition with quiescent state of actual vehicle. The FRF data used in the curve fit process is collected by an impulse hammer to provide excitation force to wheel axle. Fig.9 Resonant mode (At 165Hz) Fig. 10 Resonant mode (At 22Hz) suspension tester 4. Sensitivity Analysis using Measured FRF data (SAMF) In this chapter, Sensitivity Analysis using Measured FRF data (SAMF) is applied to the front suspension system, and the stiffness combination of the front and rear side mounts to reduce resonant peaks of FRFs effectively is examined. 4.1 Theoretical background of SAMF As an example of structural modification, a system 278

5 shown in Fig.1 1 is considered. In this example, the point a means the FRF (Inertance) evaluation point at the center of cross member, and the point 6 is the excitation point at the wheel axle. The points c and d are the stiffness modification points in which the rubber mounts are installed. Stiffness change of a rubber mount is taken into account by considering the additional complex stiffness between c and d. The additional complex stiffness is defined as follows. KCf) = Kchanged (f) - Kmirra/ (f) = k, u-1 + ik2 (f) Where k, is difference storage stiffness, and k2 is difference loss stiffness, from initial mount. Note that the additional complex stiffness, K, is defined as the function of frequency because of the frequency dependence of rubber stiffness. Considering the force equilibrium between c and d, it is possible to obtain the FRFs after stiffness addition by the substructure synthesis method. Especially, the FRF between the excitation point b and the evaluation point a, HO,, is obtained as follows. k~=ha~+(~~~-~,)+(h,-h;,)-o,!kcf) (Hot, - Ho, k% - H, ) (11) (12) Note that Eq. (12) requires the inverse matrix operations when 3 translational degrees of freedom are considered, and the equation is expanded in 3 X 3 matrix. It is possible that the peak, not existing originally, generates if the FRF matrix would be in ill condition, and the accurate inverse matrix operations could not be done. Therefore, with the singular value decomposition (SVD) technique, the negative effect of ill condition is suppressed by making singular value under a threshold to be zero [4][5]. The stiffness sensitivity, which means the FRF change ratio per unit additional stiffness, can be obtained as follows. Where ~ i,,,,,, s, = finmtz - Hoh (13) ff <, is calculated by substituting the unit stiffness for K fl of the second term in Eq. (12). Evaluation point: P Stiffness /modification point 1: e Target system Additional stiffness KC0 Excitation point: b Fig. 11 An example system for structural modification 4.2 Analysis procedure The FRF data used in SAMF is acquired experimentally by an impulse excitation test for the suspension system fixed in the suspension tester. 3-translational degrees of freedom are considered for the input force and the responses. The excitation force is provided at specific points as shown in Fig.12, to constitute the 3 X 3 full matrix of FRFs. Each point is equipped with the rigid and small excitation adapter and is indirectly excited due to the structural restriction. The response is measured by a tri-axial accelerometer at each point. As the evaluation point and direction of the response, the lateral direction at the center of front cross member is selected for the cause vibration of road noise mentioned in Chapter 2. Moreover, the same location, the center of the cross member is selected as the evaluation point for the riding comfort characteristics, considering the evaluation of the input force to the body. The evaluation direction is the fore and aft because harshness is generally sensed as the fore and aft vibration [6]. Note that the input and response directions of the evaluation FRFs are the same. Stiffness Fro,: StifTness moddiratwn pomiq,,,rubbe~rrynt nwditic7 pant: n, ~~~~~ &hit (whet axtc, : b Stithess / Stiftness \ madifievtion point: c2 Rubber mount moditic~tion pointi d, Fig. 12 Setting of various points for the front suspension system in SAMF J 279

6 4.3 Verification The experimental and analytical results with the rubber hardness (Japanese Industrial Standard, Shore A) of the front and the rear side mount increased by IO degree are shown in Fig. I3 and Fig. 14. Near l60hz band and 22Hz, the SAMF predicts the trend of FRF change from the initial mount condition accurately. Therefore, it can be judged that this analysis method is -31 =: h 2 E s ; -40 ij r D Frequency [Hz] Fig. I3 Comparison of predicted FRF with measured FRF (Near 160Hz band) -80 I I I Frequency [Hz] Fig.14 Comparison of predicted FRF with measured FRF (Near 22Hz) 4.4 Optimal stiffness combination of rubber mount To avoid aggravations of stability and controllability and so on, it is more effective and desirable to modify either one of the two rubber mounts set on the front suspension. Then, one mount, which has the highest stiffness sensitivity for road noise and riding comfort, is chosen from two mounts in the front and rear side of lower arm, and the optimum stiffness combination is examined. The stiffness sensitivity calculated by SAMF for the front side mount and the rear side one in the case of 30% stiffness change is shown in Fig. 15. For the cause vibration of road noise, the amplitude of the FRF between wheel axle and cross member decreases by 10% in I48Hz and 18% in 165Hz when the stiffness of the front side mount is reduced by 30%, and it is proven that the sensitivity of front side mount is the highest for road noise. For 22 Hz peak relating to riding comfort, the sensitivity of the rear side mount, in which its stiffness reduced by 30%, is the highest, and the reduction effect of 23% is shown. However, the front side mount also shows the reduction effect of 14% for the resonant peak of 22Hz. Therefore, totally, it is most effective to reduce the initial stiffness of front side mount for the target vehicle k y B 0 s.z -10 e e, -20 F.s v -30 Front: Rear: Front: Rear: +30[%] +30[%] -3O[%] -30[%1 Fig. I5 Stiffness sensitivity of rubber mounts 5. Conclusion This paper describes an optimization of rubber mounts with the identification of source vibration of road noise and sensitive mount for the characteristics of road noise and riding comfort. Consequently following conclusive remarks can be obtained.. The road noise in the target vehicle is the most intimate with lateral vibration at front cross member generated by the bending resonance of the shock absorber. * As the result of examining the stiffness sensitivity for the front side mount and the rear side one by SAMF, the sensitivity of the front side rubber mount is high for the vibration that causes road noise, and it is highly sensitive for the riding comfort (harshness) characteristics as well. Therefore, it is possible that road noise and riding comfort characteristics of the target vehicle are most effectively improved by reducing the stiffness of the front side rubber mount. Acknowledgment This work is partially supported by Grant-in-Aid Scientific Research(c). for 280

7 References [I] Bendat, J. S., Solutions for the Multiple Input/Output Problem, Journal of Sound and Vibration, 44(3), pp3l l-325, (1976) [2] Bendat, J. S., Modern analysis procedures for multiple input/output problems, Journal of Acoustical Society of America, 68(2), ~~ , (1980) [3] Wang, M. E., Cracker, M. J., On the application of coherence techniques for source identification in a multiple noise source environment, Journal of Acoustical Society of America, 74(3), ~~ , (1983) [4] Lim, T. C., Steyer, G. C., Hybrid Experimental-Analytical Simulation of Structure-Borne Noise and Vibration Problems In Automotive Systems, SAE Paper No , (1992) [5] Nakamura, M., Nagamatsu, A. et al., Automotive s Vibration Analysis by Dynamic Impedance Method, Journal of Robotics and Mechatronics, 7(4), ~~ , (I 995) [6] Takata, N., Ikura, S. et al., The Analysis of Harshness and Shimmy, Mazda technical review, (2), ~~22-3 I, (I 984) 281