# Dynamic Modeling and Analysis of a Driving Passenger Vehicle

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## Abstract

**:**

## 1. Introduction

## 2. Dynamic Vehicle Model

^{2}, and ${I}_{y}=2495$ kg·m

^{2}. The products of inertia were neglected in this study because they were relatively small.

## 3. Dynamics Model Verification

## 4. Results and Discussion

#### 4.1. Natural Frequencies and Mode Shapes

#### 4.2. Dynamic Responses

## 5. Summary and Conclusions

- The natural frequencies of the vibration modes associated with the sprung mass were much lower than those of the modes associated with the unsprung masses.
- When one of the front and rear wheel suspension stiffnesses increases, the natural frequencies for the roll mode, the associated wheel modes, and one of the bounce–pitch modes increase, whereas the frequencies of the other modes remain constant.
- When both the front- and rear-wheel suspension stiffnesses increase simultaneously, the natural frequencies of all modes for the sprung and unsprung masses increase.
- When only one of the two anti-roll bars’ torsional stiffnesses increases, the natural frequencies of the roll mode and the corresponding out-of-phase wheel mode increase, while the natural frequencies of the other modes remain unchanged.
- When the two torsional stiffnesses of the front and rear anti-roll bars increase simultaneously, the natural frequencies of the roll mode and out-of-phase wheel modes increase, while those of the bounce–pitch modes and the in-phase wheel modes remain unchanged.

- The bounce displacement and roll angle decrease with the suspension stiffness.
- When the suspension stiffness is large, the bounce displacement and roll angle have high-frequency oscillations because of the bounce–pitch mode and the roll mode, respectively.
- The oscillation amplitudes in the bounce acceleration and roll angular acceleration increase with the suspension stiffness.
- Suspension damping contributes to reducing the dynamic responses of the vehicle, including both the displacements and accelerations for bounce and roll motions.
- The torsional stiffness of the anti-roll bar reduced both the displacements and accelerations of the bounce and roll motions.

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Data Availability Statement

## Conflicts of Interest

## References

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**Figure 6.**Suspension deformations measured during the slalom test: (

**a**) at the left front wheel; (

**b**) at the right front wheel; (

**c**) at the left rear wheel; and (

**d**) at the right rear wheel.

**Figure 7.**Comparison of the vertical suspension deformations during the slalom test between the simulation and experiment: (

**a**) at the left front wheel; (

**b**) at the right front wheel; (

**c**) at the left rear wheel; and (

**d**) at the right rear wheel.

**Figure 9.**Comparison of the vertical suspension deformations during the double lane change test between the simulation and experiment: (

**a**) at the left front wheel; (

**b**) at the right front wheel; (

**c**) at the left rear wheel; and (

**d**) at the right rear wheel.

**Figure 11.**Comparison of the vertical suspension deformations during the step steer test between the simulation and experiment: (

**a**) at the left front wheel; (

**b**) at the right front wheel; (

**c**) at the left rear wheel; and (

**d**) at the right rear wheel.

**Figure 12.**Mode shapes of the sprung mass: (

**a**) the bounce–pitch mode with the natural frequency of 1.44 Hz; (

**b**) the bounce–pitch mode with the natural frequency of 1.62 Hz; and (

**c**) the roll mode with the natural frequency of 1.99 Hz.

**Figure 13.**Mode shapes of the unsprung mass: (

**a**) the in-phase front wheel mode (12.73 Hz); (

**b**) the out-of-phase front wheel mode (13.78 Hz); (

**c**) the in-phase rear wheel mode (15.45 Hz); and (

**d**) the out-of-phase rear wheel mode.

**Figure 16.**Natural frequencies when the front and rear suspension stiffnesses change simultaneously.

**Figure 17.**Natural frequencies for the variation of the torsional stiffness of the front anti-roll bar.

**Figure 18.**Natural frequencies for the variation of the torsional stiffness of the rear anti-roll bar.

**Figure 19.**Natural frequencies when the torsional stiffnesses of the front and rear anti-roll bars change simultaneously.

**Figure 20.**Dynamic responses of the displacements for three values of the suspension stiffness: (

**a**) the bounce and (

**b**) the roll.

**Figure 21.**Dynamic responses of the accelerations for three values of the suspension stiffness: (

**a**) the bounce and (

**b**) the roll.

**Figure 22.**Dynamic responses of the displacements for three values of the suspension damping: (

**a**) the bounce and (

**b**) the roll.

**Figure 23.**Dynamic responses of the accelerations for three values of the suspension damping: (

**a**) the bounce and (

**b**) the roll.

**Figure 24.**Dynamic responses of the displacements for three values of the torsional stiffness of the anti-roll bar: (

**a**) the bounce and (

**b**) the roll.

**Figure 25.**Dynamic responses of the accelerations for three values of the torsional stiffness of the anti-roll bar: (

**a**) the bounce and (

**b**) the roll.

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**MDPI and ACS Style**

Yun, S.; Lee, J.; Jang, W.; Kim, D.; Choi, M.; Chung, J.
Dynamic Modeling and Analysis of a Driving Passenger Vehicle. *Appl. Sci.* **2023**, *13*, 5903.
https://doi.org/10.3390/app13105903

**AMA Style**

Yun S, Lee J, Jang W, Kim D, Choi M, Chung J.
Dynamic Modeling and Analysis of a Driving Passenger Vehicle. *Applied Sciences*. 2023; 13(10):5903.
https://doi.org/10.3390/app13105903

**Chicago/Turabian Style**

Yun, Seen, Jeonga Lee, Woojae Jang, Daeji Kim, Minseok Choi, and Jintai Chung.
2023. "Dynamic Modeling and Analysis of a Driving Passenger Vehicle" *Applied Sciences* 13, no. 10: 5903.
https://doi.org/10.3390/app13105903