51 American Scientific Research Journal for Engineering, Technology, and Sciences (ASRJETS) ISSN (Print) 2313-4410, ISSN (Online) 2313-4402 © Global Society of Scientific Research and Researchers http://asrjetsjournal.org/ Towards Automotive NVH Enhancement: Structural Dynamics Analysis of a Vehicle Wheel Akbar M. Farahania*, Hosein Heshmatnejadb aNoise, Vibration and Acoustics (NVA) Research center, School of Mechanical Engineering, University of Tehran, Tehran 1417614418, Iran bDepafrtment of Mechanical Engineering, Iran University of Science and Technology, Tehran 16846-13114, Iran aEmail: akbar.mazrae@gmail.com bEmail: h.heshmatnejad1986@gmail.com Abstract The pneumatic tire is a key component of a vehicle since it transmits vibrations and disturbance from a typical road to the vehicle body structure. It is important to analyze dynamics of a tire to control the NVH (Noise, Vibration and harshness) level of a whole vehicle body structure. In this paper, a finite element of a whole wheel (including a rim and a tire) has been developed and a through dynamic analysis is done to find the resonance frequencies and corresponding mode shapes. These resonance frequencies and mode shapes can be used as the input parameters for BIW (Body-In-White) design in early design phases. It can significantly enhance dynamical performance of a vehicle body structure and at the same time reduce the manufacturing cost and time. Because a reliable and precise dynamic model of the tire gives the opportunity to have an optimized design in geometries and materials, here, we have developed a finite element (FE) model for the wheel and a comprehensive dynamic analysis is conducted. Keywords: NVH optimization; Automotive Wheel FE Analysis; Resonance Frequencies; Mode Shapes. 1. Introduction There are a lot of complaints from passengers about discomfort due to vehicle body vibrations and the generated noise inside the cabin [1]. The noise and vibration of a vehicle body can be controlled and tuned in early phases thanks to the advancement in CAE (Computer Aided Engineering) technology [2,3]. ------------------------------------------------------------------------ * Corresponding author. http://asrjetsjournal.org/ American Scientific Research Journal for Engineering, Technology, and Sciences (ASRJETS) (2017) Volume 38, No 2, pp 51-58 52 The CAE methodology provides a facile, low cost and unique tool to have a better understanding of the dynamic behavior (Resonance Frequencies, mode shapes, Frequency Response Functions, Mode shape interaction) of the automotive body structure.[4-6] Noise and vibrations from the road or automotive engine directly transfer to the passenger through the seat structure. Seat structural dynamics has been analyzed [2] as it is considered as an important source of BSR noise which can be annoying for a typical passenger for a regular ride [7,8]. Tires as the primary contact of an automotive to the road plays an important role to transfer the road disturbances to the BIW [9-11]. Automotive tires have a complicated structure consisting of so many materials which can make it difficult for stress and strain analysis. The reason is that all the connections and spot welds have to be modeled correctly to have reliable results. But, from structural dynamics point of view, simpler models can be employed to investigate dynamics of the whole wheel. Concept modeling method for the whole automotive body structure has been previously discussed [12]. Previous studies show that, in general, tires have two modes of vibrations: (1) in low frequencies (10 Hz to 20 Hz) it vibrates like a uniform object (mass-spring system and [13] (2) in high frequencies (250 Hz to 500 Hz), dynamical behavior is nonlinear and it would be complicated since it is considered as a distributed system [14]. It has been shown that for frequencies less than 500 Hz, the whole wheel structure (not all the parts separately) has a modal and linear dynamical behavior [14]. Therefore, it is possible to develop a simple finite element model which is useful for vibration analysis and also does not include the detailed parts like connections [12]. In this paper, a FE model of the tire and rim has been developed using Hyperworks software. A through dynamic analysis also has been conducted to extract resonance frequencies and also mode shapes of the system. 2. Finite Element (FE) Model of the Rim Dynamical reaction between rim and the tire is important in an automotive NVH performance analysis. Tires damping also need to be modeled and considered since it is a hyperelastic material [15]. It has been shown that in the frequency range between 200 and 350 Hz, there is 5 dB difference in interior noise level for aluminum and steel rims [16]. In general, the first resonance frequency of the steel rims is 100 Hz smaller than that of aluminum ones [17]. Figure 1 shows finite element model of the ring made of steel material with diameter of 30 mm. The weight of the ring structure is 6.159 kg, and also structural damping is 0.01. This model is made with shell elements and has 3 main parts with characteristics listed in Table 1. Figure 1: FE model of the whole rim. American Scientific Research Journal for Engineering, Technology, and Sciences (ASRJETS) (2017) Volume 38, No 2, pp 51-58 53 Table 1: Properties of different components in FE modeling of the rim. Model Properties Rim Center of the wheel Elements of spot weld Material Steel Steel Steel Young’s modulus (GPa) 210 210 210 Poison’s ratio 0.3 0.3 0.3 Density (kg/m3) 7900 7900 7900 Wight (kg) 3.27 2.81 0.08 Damping 0.01 0.01 0.01 Element name PShell PShell PShell Element type 2D 2D 2D Thickness of the element (mm) 2.5 3.5 5 Another important part in FE modeling of the rim is the connection between center of the rim and the rim. These two parts are attached through welding from four areas with a length of 8 cm. Here RBE2 elements have been used to attach these parts (Figure 2) Figure 2: Welded connections to bond the rim and the center of the rim 3. Finite Element (FE) Model of the Tire 3.1. Theory of the tire models Tires as incompressible materials can be molded with hyperelastic properties [18]. Hyperelastic materials can have 500% to 1000% strain without failure. Neo Hookean model can be used when the strain of the material is small (less than 30 %), and the strain energy density function for an incompressible neo-Hookean material is: 𝑊𝑊 = 𝐶𝐶1(𝐼𝐼1 − 3) (1) Where C1 is a material constant, and I1 is the first invariant of the right Cauchy-Green deformation tensor. 3.2. Finite element model of the tire https://en.wikipedia.org/wiki/Strain_energy_density_function https://en.wikipedia.org/wiki/Incompressible https://en.wikipedia.org/wiki/Invariants_of_tensors https://en.wikipedia.org/wiki/Finite_strain_theory American Scientific Research Journal for Engineering, Technology, and Sciences (ASRJETS) (2017) Volume 38, No 2, pp 51-58 54 Figure 3 shows finite element of the tire and its cross section in Hyperworks software. 3D solid elements are used to create the model. Table 2 shows the material properties and element types of the tire. Figure 3: FE model of the tire and its cross section. Table 2: Material Properties and element types used to model the tire. Young’s modulus (MPa) 320 Damping coefficient 0.15 Poison’s ratio 0.45 Density (kg/m3) 650 Wight (kg) 6.14 Element name PSolid Element type 3D 4. Finite Element (FE) Model of the Entire Wheel Figure 4 shows FE model of the entire wheel including the rim and the tire. In order to bond the rim and the tire, RBE elements is employed. The weight of the whole structure is 12.34 kg. Figure 4: FE model of the wheel structure. American Scientific Research Journal for Engineering, Technology, and Sciences (ASRJETS) (2017) Volume 38, No 2, pp 51-58 55 5. Results In order to dynamically analyze the behavior of the wheel structure, its mode shapes and resonance frequencies have been computed and derived respectively. Resonance frequencies of the rim is listed in Table 3 starting from 250 Hz to 1370 Hz. Table 3: Mode shape and resonance frequencies of the rim. Mode Number Mode Type Frequency (Hz) 7th mode Bending mode 245 8th mode Torsion mode 257 9th mode First triangle mode 685 10th mode Second triangle mode 693 11th mode First rectangular mode 1152 12th mode Second rectangular mode 1178 13th mode Axial mode 1370 Figure 5 demonstrates the mode shapes of the rim corresponding to the resonance frequencies. Mode shapes include different modes of movement such as bending, torsional and their combinations along with higher order modes. As we expected, for higher frequencies, corresponding mode shapes are getting complicated shapes. But, our focus in NVH optimization is on the frequencies less than 500 Hz. Figure 5: Mode shapes of the rim: a) bending mode b) twisting mode c) 3rd and 4th modes d) 5th and 6th modes e) appearing of local modes American Scientific Research Journal for Engineering, Technology, and Sciences (ASRJETS) (2017) Volume 38, No 2, pp 51-58 56 Table 4: Mode shapes and resonance frequencies for the hyperelastic tire. Mode Number Shape of the mode Resonance frequency (Hz) 7th mode Elliptic 35 8th mode Triangle 70 9th mode Rectangluar 88 Table 4 shows the resonance frequency values of the tire from 35 to 88 Hz and corresponding mode shapes is also illustrated in Figure 6. Figure 6: 7th to 9th mode shapes of the tire (Higher frequencies have complicated mode shapes) Finally, the whole wheel composed of tire and the rim is analyzed to derive the resonance frequencies and mode shapes. Resonance frequencies of the wheel are tabled in Table 5. You can see that all resonance frequencies are below 200 Hz. These resonance frequencies when combined with low frequency disturbance of noise sources (road and engine) have to be studied in early design phases of the automotive body. Figure 7 demonstrates mode shapes of the wheel corresponding to resonance frequencies. Table 5: Mode shapes and resonance frequencies of the modeled wheel. Mode number Shape of the mode Resonance Frequency (Hz) 7th mode Axial mode 68 8th mode Twisting mode 93 9th mode Elliptical mode 124 10th mode Triangular mode 152 11th mode Rectangular mode 190 Figure 7: Mode shapes of the wheel: a) axial mode, b) twisting mode, c) bending mode d) elliptical mode, e&f) higher order modes American Scientific Research Journal for Engineering, Technology, and Sciences (ASRJETS) (2017) Volume 38, No 2, pp 51-58 57 6. Conclusion In conclusion, the pneumatic tire forms a vital component of a road vehicle as it interacts with the road to produce the forces necessary for support and movement of the vehicle. Tire as one of the most important components of vehicles requires fulfilling a fundamental set of functions such as: provide load-carrying capacity, cushioning and dampening, stability, reducing noise and vibration, transmit driving and braking torque, resist abrasion, generate steering response, have low rolling resistance, durability throughout the expected life span. Therefore NVH performance of the wheel (including tire and rim) is important to be analyzed. Here, as the first step, a finite element model of the wheel has been derived using Hyperworks software. Then, dynamic analysis of the structure is conducted to derive mode shapes and resonance frequencies. These resonance frequencies and mode shapes can be used in early design phase of the automotive body, since when they are coupled with resonance frequencies of the automotive body structure, interior noise level can be magnified. References [1] G. Kouroussis, D. P. Connolly, O. Verlinden, “Railway-induced ground vibrations–a review of vehicle effects,” International Journal of Rail Transportation, vol. 2, pp. 69-110, 2014. [2] M. Tatari, M. Fard, N. Nasrolahzadeh, M. Mahjoob, “Characterization of the automotive seat structural dynamics,” Proceedings of the FISITA 2012 World Automotive Congress, pp. 541-552, 2013. [3] M. Fard, N. Nasrollahzadeh, M. Tatari, and M. Mahjoob, “Automotive body-in-white concept modeling method for the NVH performance optimization,” In Proceedings of the International Conference on Noise and Vibration Engineering ISMA, Leuven, Belgium, pp. 3753–3763, September 17–19, 2012. [4] S. Donders, Y. Takahashi, R. Hadjit, T. Van Langenhove, M. Brughmans,B. Van Genechten, and W. Desmet, “A reduced beam and joint concept modeling approach to optimize global vehicle body dynamics,” Finite Elements in Analysis and Design, vol. 45, pp. 439-455, 2009. [5] C. Reed, "Applications of OptiStruct Optimization to Body in White Design," Proceedings of Altair Engineering Event, Coventry, UK, 2002. [6] L. Wang, P. K. Basu, and J. P. Leiva, “Automobile body reinforcement by finite element optimization,” Finite Elements in Analysis and Design, vol. 40, pp. 879-893, 2004. [7] M. Tatari, M. Fard, N. Nasrollahzadeh, M. Mahjoob, “CAE Characterization and Optimization of Automotive Seat Rattle Noise” World Journal of Engineering and Technology, vol. 2, pp. 201-210, 2014. [8] M. Tatari, M. Fard, N. Nasrollahzadeh, M. Mahjoob. “Nonlinear Vehicle Seat BSR Characterization Using CAE Methodology” in Nonlinear Approaches in Engineering Applications 2, R. Jazar, L. Dai, Ed. javascript:void(0) javascript:void(0) American Scientific Research Journal for Engineering, Technology, and Sciences (ASRJETS) (2017) Volume 38, No 2, pp 51-58 58 New York: Springer, 2014, pp. 231-256. [9] A. Chiesa. "Vibrational performance differences between tires with cross-biased plies and radial plies," SAE Paper No.990B, 1965. [10] C. W. Barson, V.E. Gough, J. C. Hutchinson and D. H. James. "Tyre and vehicle vibration." Proceeding of Institution of Mechanical Enginners: Automobile Devision, vol. 179, pp. 213-237, 1964. [11] C. W. Barson, D. H. James and A. W. Morcombe. “Some aspects of tyre and vehicle vibration testing,” Proceeding of Institution of Mechanical Engineers: Conference Proceedings, Vol. 182, pp. 32-42, 1967. [12] N. Nasrolazadeh, M. Fard, M. Tatari, M. Mahjoob, “Automotive Concept Modelling: Optimization of the Vehicle NVH Performance,” Proceedings of the FISITA 2012 World Automotive Congress, pp. 365- 376, 2013. [13] A. Chiesa, L. Oberto and L. Tamburini. "Transmission of tire vibrations." Automobile Engineer, vol. 54, pp. 520-530, 1964. [14] P. Kindt, D. Berckmans, F. De. Coninck, P. Sas and W. Desmet, “Experimental analysis of the structure-borne tyre/road noise due to road discontinuities,” Mechanical Systems and Signal Processing, vol. 23, pp. 2557–2574, 2009. [15] Z. Geng, A.A. Popov, D.J. Cole, “Measurement, identification and modelling of damping in pneumatic tyres,” International Journal of Mechanical Sciences, vol. 49, pp. 1077-1094, 2007. [16] E. J. Ni, D. S. Snyder, G. F. Walton, N. E. Mallard, G. E. Barron, J. T. Browell, B. N. Aljundi, “Radiated noise from tire/wheel vibration,” Tire Science and Technology, vol. 25, pp. 29-42, 1997. [17] R. L. Wheeler, H. R. Dorfi, B. B Keum. “Vibration modes of radial tires: measurement, prediction, and categorization under different boundary and operating conditions,” SAE Technical Paper, No. 2005-01- 2523, 2005. [18] G. Anghelache, R. Moisescu, "Analysis of rubber elastic behavior and its influence on modal properties." Materiale Plastice, vol. 45, pp. 143-148, 2008.