With the rapid growth of the electric car market, particularly in the context of China EV development, there is an increasing demand for improved ride comfort and vehicle durability. As a key component in electric car body structures, the rear wheel cover liner is susceptible to vibrations induced by road surface excitations, which can lead to structural fatigue, noise issues, and reduced passenger comfort. In this study, we investigate the vibration characteristics of an electric car rear wheel cover liner using finite element analysis (FEA) and propose structural optimization strategies to mitigate resonance effects. The focus is on enhancing the performance of China EV components through numerical simulations, including modal and harmonic response analyses, to identify weak stiffness areas and implement effective damping solutions.
We begin by establishing a finite element model of the rear wheel cover liner, which is simplified as a simply supported plate to represent the thin-walled sheet metal structure commonly used in electric car designs. The model employs S4R shell elements, and material properties are defined based on typical steel and aluminum alloys used in China EV manufacturing. The governing equation for free vibration analysis is derived from the general form of the dynamic equation for a continuous system:
$$ M \ddot{u} + C \dot{u} + K u = 0 $$
where \( M \) is the mass matrix, \( C \) is the damping matrix, \( K \) is the stiffness matrix, and \( u \) represents the displacement vector. For modal analysis, we solve the eigenvalue problem to determine the natural frequencies and mode shapes:
$$ (K – \omega_i^2 M) \phi_i = 0 $$
Here, \( \omega_i \) is the angular frequency for the i-th mode, and \( \phi_i \) is the corresponding mode shape. The natural frequency \( f_i \) is related by \( f_i = \frac{\omega_i}{2\pi} \). We compute the first eight modal frequencies to assess the liner’s dynamic behavior, as low-frequency modes are critical for avoiding resonance with road-induced excitations in electric cars.
The material properties used in our simulations are summarized in Table 1, which includes parameters for steel and aluminum, commonly employed in China EV components. These values are essential for accurate FEA modeling and reflect the industry standards for electric car parts.
| Material Type | Young’s Modulus (GPa) | Poisson’s Ratio | Density (kg/m³) |
|---|---|---|---|
| Steel | 206 | 0.3 | 7800 |
| Aluminum | 72 | 0.33 | 2700 |
In the modal analysis, we set boundary conditions to simulate free vibration, meaning no constraints or external loads are applied. This allows us to capture the inherent dynamic characteristics of the electric car liner. The results for the first eight modal frequencies are presented in Table 2, highlighting the low fundamental frequency that could coincide with typical road excitation frequencies in China EV applications, potentially leading to resonance.
| Mode Order | 1st | 2nd | 3rd | 4th | 5th | 6th | 7th | 8th |
|---|---|---|---|---|---|---|---|---|
| Natural Frequency (Hz) | 24.52 | 33.12 | 61.69 | 65.63 | 80.18 | 96.88 | 125.46 | 133.75 |
The harmonic response analysis is conducted to evaluate the liner’s steady-state vibration under sinusoidal loading, simulating road-induced excitations in an electric car. We apply a force of 10 N at the geometric center of the liner, with a frequency sweep from 0 to 1000 Hz. The equation for forced vibration is:
$$ M \ddot{u} + C \dot{u} + K u = F_0 \sin(\omega t) $$
where \( F_0 \) is the amplitude of the applied force and \( \omega \) is the excitation frequency. Using the modal superposition method, we compute the amplitude-frequency response, which reveals resonance peaks where the vibration amplitude is maximized. For instance, at around 33 Hz, the amplitude reaches approximately 8.23 mm, indicating a critical resonance point that could affect the performance of China EV systems. The mode shapes at these frequencies show localized vibrations, with lower-order modes having larger deformations and higher-order modes exhibiting symmetric patterns that have less impact on overall structural integrity.
To address these vibration issues in electric car components, we propose two structural optimization approaches: adding vibration-damping materials and implementing cross-stiffeners. The first method involves applying a layered composite of butyl rubber and aluminum to the liner surface. The material properties for these damping layers are provided in Table 3, which include damping coefficients to account for energy dissipation in China EV applications.
| Material Type | Young’s Modulus (MPa) | Poisson’s Ratio | Density (kg/m³) | Damping Coefficient |
|---|---|---|---|---|
| Butyl Rubber | 7.8 | 0.48 | 960 | 1.000 |
| Aluminum | 72,000 | 0.33 | 2700 | 0.002 |
We model the damping layers using bonded constraints in the FEA software, and the harmonic response analysis after optimization shows a significant reduction in resonance amplitudes. For example, the peak amplitude decreases from 8.23 mm to about 0.27 mm, and the number of resonance points is reduced. The first natural frequency increases to 64 Hz, which helps avoid excitation frequencies common in electric car operations. The mode shapes post-optimization display more symmetric distributions and lower deformation magnitudes, confirming improved stiffness for China EV liners.
The second optimization technique involves adding cross-stiffeners to the liner through a punching process, which enhances structural rigidity without adding significant mass. This is particularly relevant for electric car designs where weight savings are crucial. The modified structure is analyzed again using modal and harmonic response methods. The updated modal frequencies are listed in Table 4, demonstrating a substantial increase in natural frequencies, such as the first mode rising to 52.36 Hz, thereby reducing the risk of resonance in China EV environments.
| Mode Order | 1st | 2nd | 3rd | 4th | 5th | 6th | 7th | 8th |
|---|---|---|---|---|---|---|---|---|
| Natural Frequency (Hz) | 52.36 | 73.18 | 86.29 | 89.85 | 122.48 | 150.38 | 155.68 | 198.02 |
The harmonic response after cross-stiffener optimization shows further improvement, with resonance peaks reduced to around 0.2 mm and fewer critical frequency points. A comparison of the two methods can be quantified using the vibration reduction ratio \( R \), defined as:
$$ R = \frac{A_{\text{initial}} – A_{\text{optimized}}}{A_{\text{initial}}} \times 100\% $$
where \( A_{\text{initial}} \) and \( A_{\text{optimized}} \) are the initial and optimized vibration amplitudes, respectively. For the damping material approach, \( R \) is approximately 96.7%, while for cross-stiffeners, it reaches about 97.6%, indicating superior performance in minimizing vibrations for electric car liners. This aligns with the goals of enhancing China EV reliability and passenger comfort.
In conclusion, our study demonstrates that finite element analysis is an effective tool for evaluating and optimizing the vibration characteristics of electric car rear wheel cover liners. Through modal and harmonic response analyses, we identified critical resonance frequencies and implemented two optimization strategies—damping material addition and cross-stiffeners—both of which significantly improved structural performance. The cross-stiffener method proved more effective in increasing natural frequencies and reducing resonance amplitudes, making it a preferred choice for China EV applications. These findings contribute to the broader effort of advancing electric car technology by ensuring components meet rigorous durability and comfort standards. Future work could explore hybrid optimization techniques or real-world testing to validate these simulations further.