Designing lightweight and comfortable automotive vehicles is a primary aim of the industry. Lightweight wheel designs can have a negative effect on the dynamic impact performance of the wheel; therefore, striking a balance between these two factors is a key objective in the design of automotive vehicles. Magnesium alloy wheels were investigated as magnesium alloy has damping performance advantages over some metal materials. Damping test methods were designed to establish the damping performance parameters of the magnesium alloy material. A finite element analysis model of magnesium alloy wheels was established with certain boundary conditions and constraints. The applicability of the model was verified by free modal evaluation of the wheel. Dynamic impact simulation analysis of the designed wheels was carried out, and the dynamic speed responses of magnesium alloy wheels under the impact of a dynamic load on the road surface were obtained. Comparison of the dynamic impact performance of magnesium and aluminum alloy wheels with the same structure showed that the magnesium alloy wheel achieved the target weight reduction of 32.3%; however, the dynamic impact performance was reduced. In order to realize the lightweight design, the dynamic impact performance of the magnesium alloy wheel should not be inferior to that of the aluminum alloy wheel; therefore, the design of the magnesium alloy wheel structure was optimized. The structural design optimization of the magnesium alloy wheel was carried out by defining the structural parameters of the wheel and using the acceleration and shock response of the wheel as the outputs. The optimization of weight reduction and dynamic impact performance of magnesium alloy wheels was achieved. Consequently, the designed magnesium alloy wheel was shown to have improved ride comfort while satisfying wheel structural performance standards and providing lightweight design.
Recently, with the increasingly stringent regulatory requirements for energy conservation and emission reduction, there has been a significant increase in the use of magnesium as a structural material because of the lightness of magnesium alloys. Magnesium alloys are structural materials with favorable properties such as low density, high specific strength, high specific stiffness, good vibration dampening characteristics, and excellent castability and have been extensively studied. The use of magnesium material in cars will increase by 15% (∼227 kg) by 2020 based on future projections for magnesium [
The finite element method is currently one of the fastest developing and most popular numerical methods used in the aviation, automotive, shipbuilding, manufacturing, and electrotechnics industries [
In this work, good damping capacity was demonstrated for AZ91 magnesium alloy. Theoretical models were applied, and experimental results showed damping with nonlinearity characteristics. The rational testing and characterization of the damping capacity of AZ91 magnesium alloy carried out in this research demonstrates the damping advantages of magnesium alloys. The favorable damping characteristics of AZ91 magnesium alloy were demonstrated through the comparison of AZ91 magnesium alloy, 6061T6 aluminum alloy, and SPFH540 steel. The wheel responses for different materials and damping ratios were evaluated. Design optimization is a powerful tool for machinery design and can produce the best blueprint for structural design. In this work, the wheel structure topology optimization method is used to optimize the wheel design to satisfy the lightweight and dynamic impact performance requirements. The structure of the wheel spokes was altered in combination with the characteristics of structural damping to design different wheel structures, and the vibration damping performance was analyzed. Consequently, the designed magnesium alloy wheel was shown to have improved ride comfort while satisfying the requirements of wheel structural performance standards and lightweight design.
In this study, AZ91 magnesium alloy, 6061T6 aluminum alloy, and SPFH540 steel were used for material vibration analysis. Analysis and experiments were also carried out to analyze the damping ratio and the material damping mechanism. Three materials were used for the analysis and calculations as listed in Table
Properties of aluminum, steel, and magnesium.
Material properties  Aluminum (6061T6)  Magnesium (AZ91)  Steel (SPFH540)  

( 

Density (kg/m³)  2700  1830  7850  
Modulus of elasticity (GPa)  69  45  210  
Poisson ratio  0.33  0.35  0.3  
Yield strength (GPa)  0.276  0.16  0.355  


Material  Magnesium (%)  Aluminum (%)  Zinc (%)  Manganese (%)  Silicon (%)  Iron (%)  Other elements (%) 
( 

Magnesium (AZ91)  Remainder  8.3–9.7  0.35–1.0  0.15–0.5  0.1 max  0.004 max  0.3 max 


Material  Aluminum (%)  Silicon (%)  Iron (%)  Copper (%)  Magnesium (%)  Zinc (%)  Other elements (%) 
( 

Aluminum (6061T6)  Remainder  0.4–0.81  0.7 max  0.15–0.4  0.8–1.2  0.25 max  0.15 max 
The composition of the AZ91 magnesium alloy and 6061 aluminum alloy and their thermomechanical treatment were considered. The thermal properties of AZ91 magnesium alloy were melting temperature, ∼533°C; specific heat capacity, 1020 J/(kg·K); and thermal conductivity, 51 W/(m·K). The thermal properties of 6061 aluminum alloy were melting temperature, ∼585°C; thermal conductivity, 151–202 W/(m·K); and specific heat capacity, 897 J/(kg·K). Combined with these material properties we conduct related research [
Magnesium alloys are light metal materials. The damping of magnesium and AZ91 magnesium alloy at room temperature is primarily dislocation damping. Currently, a classic theory to illustrate the dislocation damping mechanism is the Granato and Lücke dislocation damping theory [
The vibration system can vibrate according to its natural frequency when the object leaves the equilibrium position under the action of external force and no longer requires the role of an external force. This vibration that is not under the action of an external force is known as free vibration. The period of free vibration is called the natural period. The frequency at which vibration is free is called the natural frequency and is determined by the conditions of the vibration system, independent of amplitude. When the frequency of the driving force is equal to the natural frequency of the object, the amplitude reaches the maximum, which is the resonance.
In a damped free vibration system, the vibration equation of the system can be calculated. The forced vibration equation under the simple harmonic excitation of the single degree of freedom system is as follows:
It has a stiffness property known as the system dynamic stiffness. The reciprocal is known as the transfer function. Combined with the above equation,
For the actual vibration system, the transfer function is the ratio of the vibration system measuring point
The velocity transfer function and acceleration transfer function of the system are available:
The material properties were studied based on the theory related. Combination with the attenuation waveform to obtain vibration characteristics allowed the ratio of the absolute values of two adjacent amplitudes in a half cycle to be calculated. The ratio of the absolute values of two adjacent amplitudes was the waveform attenuation coefficient. Curves of free decay vibration are shown in Figure
Curves of free decay vibration.
The frequencysweeping method is also used for testing the damping of material, as shown in Figure
Diagram of resonant peak.
The wheel spokes, disc, and rim are the main parts of a wheel. When designing wheels, safety and engineering standards must be considered. Design optimization is a powerful tool for machinery design and can establish the best method for structural design. In wheel design and optimization, the lightest weight is the optimal design goal [
Magnesium alloy wheel. (a) 3D model. (b) FE model.
In order to estimate the damping performance of the wheel, a vibration test was carried out. The use of experimental modal analysis methods to identify modal parameters of mechanical components with complex structures is also important for understanding their dynamic characteristics. It is possible to obtain modal parameters such as the natural frequency of the complex structure in the free state and the constrained state, as well as the corresponding mode shapes, and the results of the experimental analysis are extremely accurate. Analysis of the performance of the designed wheel was carried out in addition to the analysis of the materials and the vibration characteristics of the wheel.
In the damping test, the impact load is imposed on the test specimen and the waveform of the free decay vibration is obtained. The damping test of the different materials is outlined in Figure
Damping verification plate.
Based on the vibration results data for the damping ratio in Figure
Vibration amplitudes of magnesium alloy, aluminum alloy, and steel.
Model verification is necessary for finite element analysis. A vibration test was carried out in order to estimate the damping performance of the wheel. Free suspension is more repeatable than using a flexible support as it does not introduce the vibration of the supporting gantry or the surrounding experimental environment. The wheel structure as a whole is a symmetrical structure, and when determining the stimulus and response points, it can be selected in a symmetrical manner. An impact hammer and accelerator were used, by hanging the wheel in the air to set the boundary condition free, using LMS for signal acquisition. In order to ensure the accuracy of the test results, the vibration data were collected multiple times for each test and the frequency response function of each test point was obtained using computer software calculations. The vibration test was carried out as shown in Figure
Wheel modal test.
The comparison of the computational results and the experimental results is shown in Table
Comparison of computational and experimental data.
Mode 1  Mode 2  Mode 3  Mode 4  Mode 5 


Computational  







Experimental  







Mode 1  Experimental (Hz)  Computational (Hz)  Error (%)  


1  474.5  466.1  1.8  
2  480.4  494.3  2.7  
3  948.1  954.8  0.6  
4  948.5  959.1  1.1  
5  1582.8  1489.2  5.9 
It can be seen from the mode shape diagram that the mode shape of the wheel is primarily on the wheel rim, the loworder mode shapes were distributed on both sides of the rim, and the highorder mode shapes were distributed in the middle of the rim. As the natural frequency increases, the mode shape of the wheel structure becomes increasingly complex. The error between the computational and experimental results was within 10%, demonstrating the agreement between the model and test. The modal analysis evaluates the natural frequency, mode shape, and other related parameters of the object, which are the essential properties of any object with invariance and stability. Therefore, the finite element model was verified by modal experimental analysis, and the dynamic impact performance comparison of different damping material wheels such as AZ91 magnesium alloy, 6061T6 aluminum alloy, and SPFH540 steel could be carried out.
The vibration response of the AZ91 magnesium alloy and 6061T6 aluminum alloy was calculated by the frequency response analysis method. Vibration response results of the two materials under the same excitation load can be obtained. This research is primarily focused on the vertical road direction excitation and response. When applying vibration excitation to the center of the wheel with a vertical road surface, the response position is the other side of the vertical road surface where the wheel excitation point is symmetrical. An input load of 1 N with varying frequency was applied at the wheel application point. Constraints were established on the wheel rotary table. A magnesium alloy wheel and excitation load application in the finite element model of the wheel are shown in Figures
Magnesium alloy wheel.
Wheel response model.
Through the comparative analysis of the vibration acceleration and the velocity of the identical position vibration response points at the center of the wheels made of the two materials, it was determined that the AZ91 magnesium alloy wheel damping and vibration damping performance was good. The wheel response characteristics are shown in Figures
The results of simulations. (a) Magnesium alloy
Comparison of wheel response results.
The spectrograms of the corresponding velocity and acceleration are shown in Figure
While ensuring lightweight conditions, magnesium alloy wheels give acceleration and velocity changes similar to those for aluminum alloy wheels. The magnesium alloy wheel acceleration peak was 4.6 m/s^{2} as shown in Figure
Using the AZ91 magnesium alloy material with high damping ratio is effective for vibration reduction. The 6061T6 aluminum alloy acceleration peak was 4.3 m/s^{2}, and the velocity peak was 1.1 × 10^{−3} m/s. Aluminum alloy wheels showed better vibration performance than magnesium alloy wheels with the same structure. Therefore, the optimization of magnesium alloy wheel dynamic impact performance is important.
The effect of altering the wheel structures was evaluated in combination with the different damping properties of the structures. Based on the relevant theoretical knowledge, the modal and frequency response performance of the bending structure model will change. The offset positions are indicated in Figure
Structural optimization.
Combined structural design and topology optimization theory suggests that the bending structure tends to perform better in terms of the vibration performance. The simulation analysis of the pedestal support structure shows that the vibration performance improves when the structure changes from Figure
Wheel optimization.
Name  Wheel a  Wheel b  Wheel c  Wheel d  Wheel e  Wheel f 

Size, 
0  5  7.5  10  12.5  15 
The models of the optimized wheel designs combined with structural design criteria and stressstrain related parameters are shown in Figure
Different wheel structures. (a) Wheel a. (b) Wheel b. (c) Wheel c. (d) Wheel d. (e) Wheel e. (f) Wheel f.
Combining the wheel structure damping characteristics and material damping characteristics, the frequency response and vibrationrelated performance of wheels with different structures are shown in Figures
The results of the optimized wheel simulation.
Different wheel analysis results.
From the overall analysis results in Figures
On the basis of damping characteristics and the wheel structure, vibration performance analyses of different wheel structures were obtained. Acceleration and velocity data of magnesium alloy wheel b are included in Figures
The response characteristics of the wheel were obtained by changing the wheel structure. When the wheel structure was a, b, c, d, e, and f in Figure
Using a magnesium alloy structure with bent wheel spokes can effectively reduce vibration. Figure
Comparison of wheel performance.
Wheel performance  Improvement (%)  

Weight/kg  Magnesium alloy  4.0  —  
Aluminum alloy  5.9  32.3  
Steel  17.2  76.7  


Vibration  Acceleration (m/s^{2})  Aluminum alloy  4.3  13.9 
Magnesium alloy  4.6  19.5  
Magnesium alloy (optimized wheel b)  3.7  —  
Velocity (m/s)  Aluminum alloy  1.1 
11.8  
Magnesium alloy  1.2 
19.1  
Magnesium alloy (optimized wheel b)  9.7 
— 
Based on material damping and structural damping, combined with stress and total deformation analysis, the most significant structure was found to be the structure of wheel b (Figure
In order to improve the ride comfort and reduce the weight of automotive vehicles, we designed a magnesium alloy wheel based on structural optimization and dynamic impact performance. In summary of the detailed research, the results of the simulations and experiments led to the following conclusions:
Study of the damping properties of the materials showed favorable damping properties for the magnesium alloy material. Based on the findings of structural optimization and dynamic impact theory, magnesium alloy wheels were designed and manufactured. Compared with the aluminum alloy wheel, the magnesium alloy wheel design can reduce the weight by 32.3%. The designed wheels meet the lightweight requirements in comparison with aluminum wheels, which is expected to increase ride comfort by reducing vibrations.
Damping test methods for the magnesium alloy sample were designed to obtain the damping performance parameters of the magnesium alloy material. Finite element analysis models of the magnesium alloy wheels were established with certain boundary conditions and constraints. The applicability of the model was verified by the free modal experiments on the wheel. Dynamic impact simulation analysis of the designed wheels was carried out, and the dynamic speed response of magnesium alloy wheels under the impact of a dynamic load on the road surface was obtained.
By defining the structural parameters of the magnesium alloy wheel and taking the acceleration and shock response of the wheel as the output, structural design optimization of the wheel was carried out to obtain the optimal magnesium alloy wheel structural parameters. The target of lightweight and high dynamic impact performance magnesium alloy wheels was achieved through optimization. Compared with the aluminum alloy wheel, the optimized magnesium alloy wheel b reduced the acceleration by 13.9% and the velocity by 11.8%, which is expected to increase ride comfort while satisfying the requirements for a lightweight wheel.
Our study opens avenues for the next generation of wheel design. This technique can be applied to a multitude of machine components to enhance various structure vibration performance values. We believe that our analysis can also be used to enhance the response of vibration reduction and lightweight wheel design. We hope that our results will instigate a resurgence of interest in the application of damping material for wheels and motivate future exploration of the effect of other types of structures on wheel vibration behavior.
The data used to support the findings of this study are included within the article.
The authors declare that there are no conflicts of interest regarding the publication of this paper.
This research is based on work supported by the Light Weighting Electric Vehicle Project of Saitama Institute of Technology.