Validation of the mathematical model of the front drive axle suspension according to frequency response

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Abstract

Background: Power units and drivetrain units including front axle drive are highly vibration active having a sufficient influence on passengers’ comfort during the vehicle motion. Necessary noise and vibration isolation are ensured with proper dynamic behavior of bushings and local dynamic stiffness of a supporting structure where the unit is mounted. Development of target stiffness properties of bushings and supporting structures as well as analysis of the NVH issues are conducted using multibody simulation. Ensuring the adequacy of the mathematical models for solving the given tasks is necessary.

Objective: Development and validation of the multibody mathematical models of the front axle drive (FAD) suspension with different content according to criteria of correlation of frequency response at the front axle drive bushings. Formulation of requirements to the multibody mathematical model for solving the NVH tasks for units with a single stage suspension as part of a vehicle.

Methods: Mathematical modeling of the front axle drive suspension is made in the MSC Adams multibody simulation software. Different approaches of modeling of dynamic properties of rubber-metal bushings and the local dynamic stiffness of a supporting structure are considered. In simulation, frequency response is determined as a result of a swept sine unit force. Measurements of frequency response at the mounts after the hammer impact at the axle drive body in chosen directions are used as a validation basis.

Results: The best correlation of the simulation results and the validation basis was achieved using description of rubber-metal bushings based on the Pfeffer model with scaling of properties as well as considering the front subframe flexibility using the reduced finite element model. Using of more sophisticated models of rubber-metal bushings does not contribute to better model adequacy. Considering the supporting structure flexibility as values of local dynamic stiffness has both positive and negative effects.

Conclusions: In order to solve the NVH tasks of units with a single stage suspension as part of a vehicle, like a front axle drive, it is necessary to use proper inertia data, description of dynamic behavior of bushing based in the Pfeffer model and considering supporting structure flexibility in the unit mount points.

About the authors

Viktor A. Kulagin

Central Research Automobile and Automotive Engines Institute “NAMI”; Moscow Polytechnic University

Author for correspondence.
Email: viktor.kulagin@nami.ru
ORCID iD: 0000-0003-0158-1727
SPIN-code: 2488-6808

Cand. Sci. (Eng.), Leading Design Engineer of the Multibody Simulation Department of the Numerical Analysis and Virtual Validation Center, Engineer of the Virtual Testing Center of the Advanced Engineering School of Electric Transport

Russian Federation, 2 Avtomotornaya st, Moscow, 125438; 38 Bolshaya Semenovskaya st, Moscow, 107023

Rakhmatdzhon I. Rakhmatov

Central Research Automobile and Automotive Engines Institute “NAMI”; Moscow Polytechnic University

Email: rakhmatjon.rakhmatov@nami.ru
ORCID iD: 0000-0001-5987-3170
SPIN-code: 4523-0863

Cand. Sci. (Eng.), Leading Chief Specialist of the Numerical Analysis of Vibroacoustics Department of the Numerical Analysis and Virtual Validation Center, Associate Professor of the Technical Mechanics and Computer Simulation Department

Russian Federation, 2 Avtomotornaya st, Moscow, 125438; 38 Bolshaya Semenovskaya st, Moscow, 107023

Anton P. Likeev

Central Research Automobile and Automotive Engines Institute “NAMI”

Email: anton.likeev@nami.ru
ORCID iD: 0009-0002-6076-5999
SPIN-code: 5023-9134

Leading Design Engineer of the Consumer Attributes Department of the Transport Means and Systems Center

Russian Federation, 2 Avtomotornaya st, Moscow, 125438

References

  1. Kulagin V. Development of fundamentals of the method of defining the life of supporting elements of vehicle suspension on the basis of technologies of virtual and laboratory experiments [dissertation] Moscow; 2022. (In Russ.)
  2. Scheiblegger Ch, Lin J, Karrer H. New Nonlinear Bushing Model for Ride Comfort and Handling Simulation: Focusing on Linearization and the Implementation into MBS Environment. In: Proc. FISITA 2012 Wor. Auto. Con. Vol. 10. Berlin: Springer; 2013:461–473. doi: 10.1007/978-3-642-33795-6_38
  3. Koppenaal J, Van Oosten J, Porsche I, et al. General Modeling of Nonlinear Isolators for Vehicle Ride Studies. SAE International Journal of Materials and Manufacturing. 2010;3(1):585–591.
  4. Rakhmatov RI, Krutolapov VE. Vehicle structural analysis calculation method development in order to improve noise-vibration-harshness characteristics. IOP Conf. Series: Earth Envir. Sci. 2021;867. doi: 10.1088/1755-1315/867/1/012105
  5. Yudakov AA. Principles of flexible body general dynamic equations derivation based on the Craig–Bampton model and of their practically significant approximations. Vestnik Udmurtskogo Universiteta. Matematika. Mekhanika. Komp’yuternye Nauki. 2012;3:126–140. (In Russ.)
  6. Rakhmatov RI, Tremyasov VV, Likeev AP, et al. Studies of modal characteristics aimed at comprehensive validation of a calculation model by the example of a modern vehicle body. Trudy NAMI. 2023;(3):6–32. (In Russ.) doi: 10.51187/0135-3152-2023-3-6-32
  7. The Fundamentals of Modal Testing. Application Note 243-3. Agilent Technologies [internet] Accessed: 27.05.2024. Available from: https://rotorlab.tamu.edu/me459/APP%20Note%20243-3%20The%20Fundamentals%20of%20Modal%20Testing.pdf
  8. Lammens S. Frequency response based validation of dynamic structural finite element models [dissertation] Leuven; 1995.

Supplementary files

Supplementary Files
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1. JATS XML
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2. Fig. 1. Image of the multibody mathematical model of the vehicle: а — the general view; b — the scaled image of the front axle drive (FAD).

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3. Fig. 2. Comparison of dynamic curves of bushings with linear damping (red line) and frequency dependent damping (blue line): a —dynamic factor depending on excitation frequency; b — loss angle depending on excitation frequency [1].

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4. Fig. 3. Measured (points, meas_amp) and calculated (solid lines, calc_amp) data of dynamic stiffness and loss angle of the FAD bushing for the amplitudes of 0.05, 0.1 and 1 mm: а — dynamic factor depending on excitation frequency; b — loss angle depending on excitation frequency.

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5. Fig. 4. Study of accelerance of the rear left mount of the front subframe to the vehicle body a — along the longitudinal axis of a vehicle; b — along the lateral axis of a vehicle; c — along the vertical axis of a vehicle; the Целевое lines — curves of target values of accelerance versus frequency; the Test lines — curves of the results of the experimental studies; the Simulation_B lines — curves of the simulation results of the initial simulation finite-element model; the Simulation_V lines — curves of the simulation results for the model validated according to the results of the experimental studies; the lines with the ISO suffix — isolines of the corresponding experimental and simulation results.

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6. Fig. 5. Impact with the modal hammer on the body of the front axle drive.

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7. Fig. 6. Acceleration sensors installed at the mounts of the front axle drive.

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8. Fig. 7. Frequency response of the FAD at the front left mount in longitudinal direction after longitudinal impact: the Замер line — the curve of the results of the experimental studies; the I line — the curve of simulation results for the multibody model with the initial Pfeffer model-based description of the mounts and with the rigid body; the II line — the curve of simulation results for the multibody model with the corrected Pfeffer model-based description of the mounts and with the rigid body; the III line — the curve of simulation results for the multibody model with the corrected Pfeffer model-based description of the mounts and considering of local dynamic stiffness of the subframe via additional stiffness linkages; the IV line — the curve of simulation results for the multibody model with the corrected Pfeffer model-based description of the mounts and with the description of the subframe as the substructured FE-model; the V line — the curve of simulation results for the multibody model with the multivariable frequency-dependent model of the mounts and with the description of the subframe as the substructured FE-model.

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9. Fig. 8. Frequency response of the subframe at the front left mount in longitudinal direction after longitudinal impact: the Замер line — the curve of the results of the experimental studies; the I line — the curve of simulation results for the multibody model with the initial Pfeffer model-based description of the mounts and with the rigid body; the II line — the curve of simulation results for the multibody model with the corrected Pfeffer model-based description of the mounts and with the rigid body; the III line — the curve of simulation results for the multibody model with the corrected Pfeffer model-based description of the mounts and considering of local dynamic stiffness of the subframe via additional stiffness linkages; the IV line — the curve of simulation results for the multibody model with the corrected Pfeffer model-based description of the mounts and with the description of the subframe as the substructured FE-model; the V line — the curve of simulation results for the multibody model with the multivariable frequency-dependent model of the mounts and with the description of the subframe as the substructured FE-model.

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10. Fig. 9. Frequency response of the FAD at the front right mount in longitudinal direction after longitudinal impact: the Замер line — the curve of the results of the experimental studies; the I line — the curve of simulation results for the multibody model with the initial Pfeffer model-based description of the mounts and with the rigid body; the II line — the curve of simulation results for the multibody model with the corrected Pfeffer model-based description of the mounts and with the rigid body; the III line — the curve of simulation results for the multibody model with the corrected Pfeffer model-based description of the mounts and considering of local dynamic stiffness of the subframe via additional stiffness linkages; the IV line — the curve of simulation results for the multibody model with the corrected Pfeffer model-based description of the mounts and with the description of the subframe as the substructured FE-model; the V line — the curve of simulation results for the multibody model with the multivariable frequency-dependent model of the mounts and with the description of the subframe as the substructured FE-model.

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11. Fig. 10. Frequency response of the subframe at the front right mount in longitudinal direction after longitudinal impact: the Замер line — the curve of the results of the experimental studies; the I line — the curve of simulation results for the multibody model with the initial Pfeffer model-based description of the mounts and with the rigid body; the II line — the curve of simulation results for the multibody model with the corrected Pfeffer model-based description of the mounts and with the rigid body; the III line — the curve of simulation results for the multibody model with the corrected Pfeffer model-based description of the mounts and considering of local dynamic stiffness of the subframe via additional stiffness linkages; the IV line — the curve of simulation results for the multibody model with the corrected Pfeffer model-based description of the mounts and with the description of the subframe as the substructured FE-model; the V line — the curve of simulation results for the multibody model with the multivariable frequency-dependent model of the mounts and with the description of the subframe as the substructured FE-model.

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12. Fig. 11. Frequency response of the FAD at the front left mount in vertical direction after vertical impact: the Замер line — the curve of the results of the experimental studies; the I line — the curve of simulation results for the multibody model with the initial Pfeffer model-based description of the mounts and with the rigid body; the II line — the curve of simulation results for the multibody model with the corrected Pfeffer model-based description of the mounts and with the rigid body; the III line — the curve of simulation results for the multibody model with the corrected Pfeffer model-based description of the mounts and considering of local dynamic stiffness of the subframe via additional stiffness linkages; the IV line — the curve of simulation results for the multibody model with the corrected Pfeffer model-based description of the mounts and with the description of the subframe as the substructured FE-model; the V line — the curve of simulation results for the multibody model with the multivariable frequency-dependent model of the mounts and with the description of the subframe as the substructured FE-model.

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13. Fig. 12. Frequency response of the subframe at the front left mount in vertical direction after vertical impact: the Замер line — the curve of the results of the experimental studies; the I line — the curve of simulation results for the multibody model with the initial Pfeffer model-based description of the mounts and with the rigid body; the II line — the curve of simulation results for the multibody model with the corrected Pfeffer model-based description of the mounts and with the rigid body; the III line — the curve of simulation results for the multibody model with the corrected Pfeffer model-based description of the mounts and considering of local dynamic stiffness of the subframe via additional stiffness linkages; the IV line — the curve of simulation results for the multibody model with the corrected Pfeffer model-based description of the mounts and with the description of the subframe as the substructured FE-model; the V line — the curve of simulation results for the multibody model with the multivariable frequency-dependent model of the mounts and with the description of the subframe as the substructured FE-model.

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14. Fig. 13. Frequency response of the FAD at the rear mount in vertical direction after vertical impact: the Замер line — the curve of the results of the experimental studies; the I line — the curve of simulation results for the multibody model with the initial Pfeffer model-based description of the mounts and with the rigid body; the II line — the curve of simulation results for the multibody model with the corrected Pfeffer model-based description of the mounts and with the rigid body; the III line — the curve of simulation results for the multibody model with the corrected Pfeffer model-based description of the mounts and considering of local dynamic stiffness of the subframe via additional stiffness linkages; the IV line — the curve of simulation results for the multibody model with the corrected Pfeffer model-based description of the mounts and with the description of the subframe as the substructured FE-model; the V line — the curve of simulation results for the multibody model with the multivariable frequency-dependent model of the mounts and with the description of the subframe as the substructured FE-model.

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15. Fig. 14. Frequency response of the subframe at the rear mount in vertical direction after vertical impact: the Замер line — the curve of the results of the experimental studies; the I line — the curve of simulation results for the multibody model with the initial Pfeffer model-based description of the mounts and with the rigid body; the II line — the curve of simulation results for the multibody model with the corrected Pfeffer model-based description of the mounts and with the rigid body; the III line — the curve of simulation results for the multibody model with the corrected Pfeffer model-based description of the mounts and considering of local dynamic stiffness of the subframe via additional stiffness linkages; the IV line — the curve of simulation results for the multibody model with the corrected Pfeffer model-based description of the mounts and with the description of the subframe as the substructured FE-model; the V line — the curve of simulation results for the multibody model with the multivariable frequency-dependent model of the mounts and with the description of the subframe as the substructured FE-model.

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16. Cover Letter
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