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Simulation Study on Vehicle Ride Comfort Based on Finite Element Model and Pseudo-Excitation Method

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Abstract

This research aims to develop a new vehicle ride comfort simulation technology. The basic principle of pseudo-excitation method (PEM) is summarized, and the specific method of PEM is proposed to solve the finite element model (FEM) of vehicle. Taking a simple 7-degree-of-freedom (DOF) car spatial model as an example, the traditional and new methods are compared. Simulation results show that they are completely consistent, thereby verifying the effectiveness of the new method. At the same time, through the simulation process, the new method is simpler and more efficient without deducing complex mathematical formulas and software programming. Finally, the ride comfort simulation of a car’s complex FEM is performed. FEM can consider the parts of the vehicle as elastic bodies and closer to the real vehicle. The PEM transforms random vibration analysis into simple harmonic vibration analysis, which improves the efficiency of the solution greatly. Therefore, the combination of the FEM and the PEM cannot only solve the problem of model accuracy but also the problem of solving efficiency, which has strong practical engineering application value.

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Abbreviations

\({\tilde x}\) :

pseudo excitation

\({\tilde y}\) :

pseudo response

S x(f):

PSD of the excitation x

S y(f):

PSD of the response y

H(f):

system frequency response function

Λ :

eigenvalue

φ i :

eigenvector

\({{\tilde y}^ * }\) :

conjugate of \({\tilde y}\)

B i(f):

frequency amplitude function

T :

system kinetic energy

V :

system potential energy

D :

system dissipated energy

M:

mass matrix

C:

damping matrix

K:

stiffness matrix

Kt :

tire stiffness matrix

G i :

static load of the ith wheel

H(f)y−q :

frequency response function of y

Gq(f):

PSD of road excitation

Gq(n 0):

road roughness coefficient

n 0 :

reference spatial frequency

u :

vehicle speed

t 1 :

time delay between the rear and front axes

coh(f):

correlation function

\({{\bar a}_v}\) :

comprehensive total weighted acceleration RMS value

\({{\bar a}_{vi}}\) :

total weighted acceleration RMS value at one of the three positions of the seat pad, seat back, and foot rest

\({{\bar a}_{wx}},\,{{\bar a}_{wy}},\,{\rm{and}}\,{{\bar a}_{wz}}\) :

axial weighted acceleration RMS value in the x, y, and z axes directions, respectively

k x, k y and k z :

axis weighted coefficients in the x, y, and z axes directions, respectively

\({{\bar a}_{kj}}\) :

1/3 octave band acceleration RMS value with the central frequency, fj in k axis

f uj and f lj :

1/3 octave band upper and lower limits with the central frequency fj, respectively

\({{\bar a}_{wk}}\) :

axial weighted RMS value of acceleration

w j :

frequency weighted coefficient of the j-th 1/3 octave band

References

  • Abdelhady, M. B. A. (2002). Aerodynamic effects on ride comfort and road holding of actively suspended vehicles. SAE Paper No. 2002-01-2205.

  • Ambrósio, J. A. C. and Pereira, M. F. O. S. (1998). Flexible Multibody Dynamics with Nonlinear Deformations: Vehicle Dynamics and Crashworthiness Applications. Computational Methods in Mechanical Systems (pp. 382–419). Springer. Berlin, Germany.

    Chapter  Google Scholar 

  • Batou, A., Soize, C., Choi, C. K. and Yoo, H. H. (2015). Robust design in multibody dynamics–application to vehicle ride-comfort optimization. Procedia Iutam, 13, 90–97.

    Article  Google Scholar 

  • Baumal, A. E., McPhee, J. J. and Calamai, P. H. (1998). Application of genetic algorithms to the design optimization of an active vehicle suspension system. Computer Methods in Applied Mechanics and Engineering 163, 1–4 87–94.

    Article  MATH  Google Scholar 

  • Cole, D. J. (2001). Fundamental issues in suspension design for heavy road vehicles. Vehicle System Dynamics 35, 4–5 319–360.

    Article  Google Scholar 

  • De Rosa, S., Franco, F. and Ciappi, E. (2015). A simplified method for the analysis of the stochastic response in discrete coordinates. J. Sound and Vibration, 339, 359–375.

    Article  Google Scholar 

  • Eriksson, P. and Friberg, O. (2000). Ride comfort optimization of a city bus. Structural and Multidisciplinary Optimization 20, 1 67–75.

    Article  Google Scholar 

  • Gadala, M. E., Elmadany, M. M. and Gadala, M. S. (1986). Finite element and analytical modelling of a tractor-semitrailer vehicle. Computers & Structures 23, 6 831–836.

    Article  Google Scholar 

  • Géradin, M. and Rixen, D. J. (1997). Mechanical Vibration: Theory and Application to Structural Dynamics (2nd edn). John Wiley & Sons. Hoboken, New Jersey, USA.

    Google Scholar 

  • Guo, W., Yu, Z. W. and Guo, Z. (2011). Fast stochastic analysis for non-proportionally damped system. Mechanics Research Communications 38, 6 468–470.

    Article  MATH  Google Scholar 

  • Hu, L., Xu, Y. L. and Huang, W. F. (2013). Typhoon-induced non-stationary buffeting response of long-span bridges in complex terrain. Engineering Structures, 57, 406–415.

    Article  Google Scholar 

  • Jia, H. Y., Zhang, D. Y., Zheng, S. X., Xie, W. C. and Pandey, M. D. (2013). Local site effects on a high-pier railway bridge under tridirectional spatial excitations: Nonstationary stochastic analysis. Soil Dynamics and Earthquake Engineering, 52, 55–69.

    Article  Google Scholar 

  • Jiang, X., Yan, F. and Chen, W. (2018). Improving ride comfort of a heavy truck. SAE Paper No. 2018-01-0135.

  • Lenka, V. R., Anthonysamy, B., Londhe, A. and Hatekar, H. (2018). Multi-objective optimization to improve SUV ride performances using MSC. ADAMS and Mode Frontier. SAE Paper No. 2018-01-0575.

  • Li, G., Liu, X., Liu, Y. and Yue, Q. (2008). Optimum design of ice-resistant offshore jacket platforms in the Bohai Gulf in consideration of fatigue life of tubular joints. Ocean Engineering 35, 5–6 484–493.

    Article  Google Scholar 

  • Li, J., Qin, Y. Y. and Zhao, Q. (2010). The application of multi-point pseudo excitation method to vehicle random vibration analysis. Automotive Engineering 32, 3 254–257.

    Google Scholar 

  • Li, J., Wang, W. Z. and Zhao, Q. (2016). Random vibration analysis of military vehicle based on pseudo-excitation method. Automotive Engineeering 38, 3 368–372.

    Google Scholar 

  • Lin, J. H. and Zhang, Y. H. (2004). Pseudo Excitation Method of Random Vibration. Science Press. Beijing, China.

    Google Scholar 

  • Lin, J., Zhang, W. and Li, J. (1994). Structural responses to arbitrarily coherent stationary random excitations. Computers & Structures 50, 5 629–633.

    Article  MATH  Google Scholar 

  • Liu, X., Li, G., Oberlies, R. and Yue, Q. (2009). Research on short-term dynamic ice cases for dynamic analysis of ice-resistant jacket platform in the Bohai Gulf. Marine Structures 22, 3 457–479.

    Article  Google Scholar 

  • Mohajer, N., Abdi, H. and Nahavandi, S. (2017). Dynamic response multiobjective optimization of road vehicle ride quality–A computational multibody system approach. Proc. Institution of Mechanical Engineers, Part K: J. Multi-body Dynamics 231, 2 316–332.

    Google Scholar 

  • Parekh, D., Whittle, B., Stalnaker, D. and Uhlir, E. (1996). Laboratory tire wear simulation process using ADAMS vehicle model. SAE Paper No. 961001.

  • Qin, Y. Y., Tu, J. B., Zhao, Q. Y. and Chen, S. L. (2016). Modeling and simulation analysis of ride comfort for heavy-duty truck. Machinery Design & Manufacture, 10, 12–14.

    Google Scholar 

  • Ryu, G. and Jeon, J. (2013). Improvement of virtual vehicle analysis efficiency with optimal modes selection in flexible multi-body dynamics. SAE Int. J. Passenger Cars-Mechanical Systems 6, 2013-01-1193 382–388.

    Article  Google Scholar 

  • Sakuma, N., Kadono, I., Dohi, M. and Nakai, H. (1986). Heavy duty truck ride–comfort analysis by computer simulation. Int. J. Vehicle Design 7, 5–6 279–290.

    Google Scholar 

  • Shabana, A. (1986). Dynamics of inertia-variant flexible systems using experimentally identified parameters. J. Mechanical Design 108, 3 358–366.

    Google Scholar 

  • Standardization Administration of China (SAC) (2009). Method of Running Test-automotive Ride Comfort. Standard No. GB/T 4970-2009.

  • Thomas, D. W. (1987). Vehicle modeling and service loads analysis. SAE Paper No. 871940.

  • Thompson, A. G. and Pearce, C. E. M. (2001). Performance index for a preview active suspension applied to a quarter-car model. Vehicle System Dynamics 35, 1 55–66.

    Article  Google Scholar 

  • Thompson, A. G. and Pearce, C. E. M. (2003). RMS values for force, stroke and deflection in a quarter-car model active suspension with preview. Vehicle System Dynamics 39, 1 57–75.

    Article  Google Scholar 

  • Tian, G. N., Yang, J., Xu, Y. Z. and Li, M. J. (2012). Finite element analysis on vehicle NVH under random road excitation. Computer Aided Engineering (Jisuanji Fuzhu Gongcheng) 21, 5 53–56.

    Google Scholar 

  • Tong, Y. Y. (2000). Vehicle dynamic simulations based on flexible and rigid multibody models. SAE Paper No. 2000-01-0114.

  • Wang, J. and Lin, J. H. (2000). Seismic random vibration analysis of hysteretic systems with pseudo excitation method. Acta Mechanica Solida Sinica 13, 246–253.

    Google Scholar 

  • Wang, W., Li, J., Liu, G. and Zhang, Z. (2020). Simulation study on ride comfort of three-axle heavy vehicle spatial model based on rigid-elastic model and pseudo-excitation method. J. Advanced Mechanical Design, Systems, and Manufacturing 14, 1 1–16.

    Article  Google Scholar 

  • Williams, D. E. and Haddad, W. M. (1997). Active suspension control to improve vehicle ride and handing. Vehicle System Dynamics 28, 1 1–24.

    Article  Google Scholar 

  • Wong, J. Y. (2001). Theory of Ground Vehicle (3rd edn). John Wiley & Sons Inc. Hoboken, New Jersey, USA.

    Google Scholar 

  • Wu, G., Fan, G. and Guo, J. (2013). Ride comfort evaluation for road vehicle based on rigid-flexible coupling multibody dynamics. Theoretical and Applied Mechanics Letters 3, 1 013004.

    Article  Google Scholar 

  • Yang, S., Lu, Y. and Li, S. (2013). An overview on vehicle dynamics. Int. J. Dynamics and Control 1, 4 385–395.

    Article  Google Scholar 

  • Youn, I. and Hać, A. (1995). Semi-active suspensions with adaptive capability. J. Sound and Vibration 180, 3 475–492.

    Article  Google Scholar 

  • Zhang, D. Y., Li, X., Yan, W. M., Xie, W. C. and Pandey, M. D. (2013). Stochastic seismic analysis of a concrete-filled steel tubular (CFST) arch bridge under tridirectional multiple excitations. Engineering Structures, 52, 355–371.

    Article  Google Scholar 

  • Zhao, Z., Chen, Z., Wang, X., Xu, H. and Liu, H. (2016). Wind-induced response of large-span structures based on pod-pseudo-excitation method. Advanced Steel Construction 12, 1 1–16.

    Google Scholar 

  • Zhou, B., Han, X. and Tan, S. K. (2014). A simplified computational method for random seismic responses of a jacket platform. Ocean Engineering, 82, 85–90.

    Article  Google Scholar 

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Acknowledgement

This work is supported by the general project of Liaoning Provincial Department of Education (LJKZ0199) and the Development Fund of State Key Laboratory for Automobile Simulation of Control (20181107).

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Authors and Affiliations

  1. School of Mechatronics Engineering, Shenyang Aerospace University, Shenyang, 110136, China

    Wenzhu Wang & Gang Liu

  2. State Key Laboratory of Automotive Simulation and Control, Jilin University, Changchun, 130025, China

    Jie Li

  3. Project Management Department, Geely Automotive R&D Technology Center, No. 918, Binhai Fourth Road, Cixi, Ningbo, 315336, China

    Jun Wei

  4. Chongqing Changan Automobile Co., Ltd., No. 260, Jianxin East Road, Jiangbei District, Chongqing, 400023, China

    Zhenwei Zhang

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  1. Wenzhu Wang
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  2. Jie Li
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Correspondence to Jie Li.

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Wang, W., Li, J., Liu, G. et al. Simulation Study on Vehicle Ride Comfort Based on Finite Element Model and Pseudo-Excitation Method. Int.J Automot. Technol. 24, 1163–1174 (2023). https://doi.org/10.1007/s12239-023-0095-5

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