# Multi-Objective Lightweight Optimization Design of the Aluminium Alloy Front Subframe of a Vehicle

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## Abstract

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## 1. Introduction

_{2}emissions will be reduced by 8 to 11 g [1]. With the rise of new energy vehicles, an increasing number of automobile enterprises have begun to use aluminium alloy subframes. Using aluminium alloy subframes not only improves vehicle handling and stability but also reduces the weight of the vehicle. The production mode of aluminium alloy subframes mainly includes the extruded profile welding type and casting type. In recent years, many scholars have performed research on the development of subframes and have obtained some research results. Li et al. [1] proposed a subframe topology optimization method from a conceptual design to a detailed design, which further reduced the overall subframe weight, met the requirements of stiffness and natural frequency, passed the durability requirements, and, finally, reduced the subframe mass from the initial structure of 82.6 kg to 21.4 kg. Kim et al. [2] proposed a subframe method based on topology optimization, which took the bar section and stiffness value as the design variables to simultaneously optimize the topology and shape of the subframe. Ali and Fraser [3] used the finite element method to analyse a certain subframe of a Chevrolet vehicle, used LS-DYNA commercial software to model the subframe, analysed the subframe under normal driving conditions and vehicle collision conditions, and established the appropriate subframe material by comparison with the performance of the original subframe of the vehicle. Nam et al. [4] proposed a fatigue life evaluation technology for the aluminium subframes of automobiles. Based on the virtual test simulation technology of the nonlinear suspension component model, this technology can effectively predict the fatigue life of the vehicle chassis structure. By testing an actual aluminium subframe, the accuracy of the model was verified. Lee et al. [5] optimized the shape and thickness of the subframe to meet the requirements of multidisciplinary design optimizations (MDOs) and meet the weight, fatigue, crash, NVH, and K & C performance requirements. The proposed method was also suitable for complex vehicle design problems. Oh et al. [6] developed a subframe using a hydraulic forming technology. To improve the stiffness of the suspension and reduce the maximum stress that affects the durability cycle life, they adopted a variety of optimization design techniques, shape, size, and topology optimization, and formed the shape of the optimized rear suspension through a hydraulic forming process. The effectiveness of this design method was proven by finite element commercial software. To improve the NVH performance of vehicles, Park et al. [7] studied the front subframe of the vehicle, optimized the dynamic stiffness of the suspension bushing of the subframe, analysed the advantages and disadvantages of the integral subframe with different total shapes, and proposed structural reinforcement and other methods to improve the overall NVH performance of the vehicle. Hur and Lee [8] designed an integrated method for pre-tests, modelled associations and updated analyses of automobile subframes, evaluated model correlations by combining modal parameters of modal tests and finite element analyses, and analysed changes in the natural frequencies and MAC values of material characteristics based on sensitivity analysis results. The iterative method was used to modify the finite element model, and good results were obtained. Belingardi et al. [9] established the goals of strength, stiffness, and natural frequency of the subframe. The subframe designed using composite materials and optimizing the placement of stiffeners was superior to the steel subframe. Chiu Huang [10] designed a hydraulic moulding mould for the subframe, which could be used to achieve a lightweight subframe design. Han et al. [11] applied composite materials to the chassis component subframe, comparing the natural frequency and damping characteristics of steel and composite test pieces, achieving a certain improvement in stiffness, strength, and NVH performance of the composite subframe compared to the steel subframe, achieving a 50% weight reduction effect. Law et al. [12] proposed a new design method for the subframe after studying the subframe structure and design methods. The subframe structure designed using this method was superior in terms of lightness of weight and durability. Jang et al. [13] conducted a lightweight optimization design for the front subframe structure of a car. After optimization, while ensuring performance indicators, the optimized front subframe mass decreased by 30%, while verifying the practicality of the optimization design method. Fichera et al. [14] conducted theoretical calculation and analysis of the performance and load of the subframe, and then conducted topology optimization on the subframe structure, which resulted in a reasonable subframe structure. Rotondella et al. [15] constructed a subframe welding model and verified the reliability of the model through comparison of experiments and simulations. This method could predict structural dynamic characteristics. Da’Quan et al. [16] used ANSYS to study the topology optimization of the subframe under complex load conditions. The study found that the structural performance of the side member of the subframe was improved, while the weight of the subframe remained unchanged. Price et al. [17] designed a cast aluminium alloy subframe that reduced the weight by 40% while maintaining the same strength as the original subframe by optimizing weight and geometry. Liao et al. [18] designed a new high-strength steel subframe structure based on the stiffness and strength analysis of the subframe under various working conditions. Through comparative analysis of various performances with the original subframe, the feasibility of the new subframe was verified. Hamdi et al. [19] optimized the design of the subframe, which resulted in a significant improvement in NVH performance and a significant reduction in quality. Through verification, this method has made a positive contribution to improving vehicle NVH performance.

## 2. Multi-Condition Topology Optimization of the Aluminium Alloy front Subframe

^{−9}t/mm

^{3}, Poisson’s ratio of 0.33, elastic modulus of 7.24 × 10

^{4}MPa, yield strength of 230 MPa, and tensile strength of 290 MPa.

## 3. Performance Analysis of the Aluminium Alloy Front Subframe

#### 3.1. Strength Performance Analysis of the Aluminium Alloy Front Subframe

#### 3.2. Static Stiffness Performance Analysis of the Aluminium Alloy Front Subframe

#### 3.3. Free Modal Analysis of the Aluminium Alloy Front Subframe

## 4. Lightweight Optimization Design Based on Multi-Objective Methods

#### 4.1. Establishment of the Parametric Model of the Aluminium Alloy Front Subframe

#### 4.2. Establishment of the Optimization Mathematical Model

#### 4.3. Experimental Design and Establishment of the Approximate Model

#### 4.4. Multi-Objective Optimization of the Aluminium Alloy Front Subframe Based on the Approximate Model

^{30}; the failed run objective value is set to 1.0 × 10

^{30}.

## 5. Performance Analysis and Verification of the Aluminium Alloy Front Subframe after Optimization

#### 5.1. Strength Performance Analysis of the Optimized Aluminium Alloy Front Subframe

#### 5.2. Static Stiffness Performance Analysis of the Optimized Aluminium Alloy Front Subframe

#### 5.3. Free Modal Performance Analysis of the Optimized Aluminium Alloy Front Subframe

#### 5.4. Fatigue Life Analysis of the Optimized Aluminium Alloy Front Subframe

^{7}, which also meets the design requirements.

^{−6}, which is far less than the target value of 0.25; thus, the design requirements are satisfied. Figure 22 shows that the minimum fatigue life of the aluminium alloy front subframe in the forward braking condition is 1.42 × 10

^{19}, which also meets the design requirements.

## 6. Test Analysis of the Aluminium Alloy Front Subframe Sample

#### 6.1. Free Modal Test Analysis of the Aluminium Alloy Front Subframe

#### 6.2. Fatigue Endurance Bench Test of the Aluminium Alloy Front Subframe

## 7. Conclusions

- The multi-operating condition topology optimization method is adopted to find the best stress path of the aluminium alloy front subframe, which prevents blindness in the design and development process of the aluminium alloy front subframe and can greatly shorten the development cycle.
- The response surface approximation model was constructed by using the optimal Latin Hypercube test method in the Isight software. Meanwhile, the multi-objective particle swarm optimization algorithm was used to carry out the multi-objective optimization design of the aluminium alloy front subframe. After 1002 iterations, the optimal structure of the aluminium alloy front subframe was obtained. After optimization, the maximum stress of the aluminium alloy front subframe corresponds to the extreme single-side pit condition, and the stress value is 179.3 MPa, which is 1.3 MPa less than that of 180.6 MPa before optimization. After optimization, the static stiffness values of each hard point of the aluminium alloy front subframe have little change, while the static stiffness values of some hard points remain unchanged. Under the premise of satisfying various performance indexes, the aluminium alloy front subframe loses 0.95 kg compared with the topology optimization, and 2.4 kg compared with the original subframe, with a lightweight rate of 12%.
- Free modal test analysis was carried out on the aluminium alloy front subframe sample after multi-objective optimizations. The error between the test results and the finite element free modal analysis results was less than 15%, which verified the accuracy of the finite element model. The fatigue endurance bench test of the aluminium alloy front subframe samples showed that the longitudinal endurance test of the aluminium alloy front subframe could reach the target value of 350,000 times, and the lateral endurance test could reach the target value of 300,000 times, satisfying the bench fatigue durability requirements.

## Author Contributions

## Funding

## Data Availability Statement

## Conflicts of Interest

## References

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**Figure 2.**Topology optimization results of aluminium alloy front subframe envelope under multiple working conditions. (

**a**) Positive results of multi-condition topology optimization. (

**b**) Rear result of multi-condition topology optimization.

**Figure 4.**Establishment of displacement and load boundary conditions for aluminium alloy front subframe.

**Figure 5.**Cloud diagram of stress results of aluminium alloy front subframe under some typical working conditions. (

**a**) Forward braking condition. (

**b**) Backward braking condition. (

**c**) Forward emergency braking condition. (

**d**) Backward emergency braking condition. (

**e**) Over one side deep pit condition. (

**f**) Ultimate steering condition.

**Figure 6.**Non-rigid body modal shapes for the front 6th order of aluminium alloy front subframe. (

**a**) First order modal shape. (

**b**) Second order modal shape. (

**c**) Third modal shape. (

**d**) Fourth modal shape. (

**e**) Fifth modal shape. (

**f**) Sixth modal shape.

**Figure 11.**The fitting results of the predicted and actual response values of the aluminium alloy front subframe. (

**a**) Results of first-order modal frequency fitting. (

**b**) Mass fitting results. (

**c**) Stress fitting results of over one side deep pit condition. (

**d**) Stress fitting results of forward braking condition. (

**e**) Stress fitting results of forward emergency braking condition. (

**f**) Fitting results of the maximum displacement of the right front point of the lower arm.

**Figure 12.**First order frequency response and variable response surface approximation model of the aluminium alloy front subframe. (

**a**) Response surface approximation model between the first order frequency of the aluminium alloy front subframe and design variables LZ_b and F_01. (

**b**) Response surface approximation model between the first order frequency of the aluminium alloy front subframe and design variables LZ_t and F_01. (

**c**) Response surface approximation model between the first-order frequency of the aluminium alloy front subframe and design variables R_01 and F_01.

**Figure 14.**Local effect diagram of each variable and response. (

**a**) Frequency local effect diagram. (

**b**) Mass Local Effect diagram. (

**c**) Local effect diagram of stress in over one side deep pit condition. (

**d**) Local effect diagram of forward braking condition.

**Figure 15.**Digital and analogue comparison before and after multi-objective optimization of aluminium alloy front subframe.

**Figure 16.**Cloud image of stress analysis results of aluminium alloy front subframe under some typical working conditions after optimization. (

**a**) Forward braking condition. (

**b**) Backward braking condition. (

**c**) Forward emergency braking condition. (

**d**) Backward emergency braking condition. (

**e**) Over one side deep pit condition. (

**f**) Ultimate steering condition.

**Figure 17.**Optimized non-rigid body modal shapes for the front 6th order of the aluminium alloy front subframe. (

**a**) First modal shape. (

**b**) Second order modal shapes. (

**c**) Third order modal shapes. (

**d**) Fourth order modal shapes. (

**e**) Fifth order modal shapes. (

**f**) Sixth order modal shapes.

**Figure 19.**Fatigue damage cloud image of aluminium alloy front subframe over one side deep pit condition.

**Figure 20.**Fatigue life cloud diagram of aluminium alloy front subframe over one side deep pit condition.

**Figure 21.**Fatigue damage cloud diagram of aluminium alloy front subframe under forward braking condition.

**Figure 22.**Fatigue life cloud diagram of aluminium alloy front subframe under forward braking condition.

Load Loading Condition | Load Extraction Position | FX/N | FY/N | FZ/N | TX/N.mm | TY/N.mm | TZ/N.mm |
---|---|---|---|---|---|---|---|

Forward braking | Left front mounting point of lower control arm | 3284.07 | −13,698.91 | 976.43 | −12,565.55 | −4972.73 | 17,758.18 |

Backward braking | −1938.66 | 5250.36 | 440.28 | 2433.93 | 7908.52 | −17,822.63 | |

Forward emergency braking | 3603.93 | −12,297.02 | 503.65 | −10,162.87 | −6142.74 | 17,802.89 | |

Backward emergency braking | −2567.50 | 5922.08 | 384.72 | 1116.05 | 10,045.76 | −19,683.54 | |

Overconvex hull | −312.96 | −2037.32 | 330.97 | −16,806.04 | 682.42 | −1978.72 | |

Over unilateral hull | −471.74 | −3045.79 | 522.29 | −17,978.29 | 624.39 | −2796.88 | |

Over one side deep pit | 2486.79 | −19,902.80 | 3368.50 | −19,125.35 | −2931.95 | 18,310.30 | |

Ultimate steering | 160.90 | 12,037.52 | −1142.56 | −14,712.09 | −395.00 | −8286.05 | |

Steering braking | 2172.52 | −4666.31 | 467.00 | −13,050.78 | −3580.23 | 14,608.78 | |

Steering drive | −1786.45 | 13,389.08 | 933.28 | 501.83 | 8327.25 | −22,282.73 | |

Maximum driving acceleration | −959.99 | 3711.35 | 661.49 | 11,256.40 | 5734.13 | −10,161.87 | |

Diagonal torsion | −330.45 | −2186.29 | 192.93 | −12,220.28 | 305.09 | −2008.30 | |

Forward braking | Left rear mounting point of lower control arm | 6415.23 | 11,730.02 | −399.92 | −17,445.81 | 4444.70 | 1461.34 |

Backward braking | −3404.68 | −6275.54 | −788.88 | 2620.12 | −84.12 | −2600.15 | |

Forward emergency braking | 7662.75 | 13,728.38 | 10.44 | −13,110.00 | 3269.03 | 2080.89 | |

Backward emergency braking | −5073.90 | −8907.96 | −945.29 | 248.28 | 838.25 | −2830.12 | |

Overconvex hull | −392.48 | −749.21 | 88.65 | −28,138.93 | 7174.87 | −3304.56 | |

Over unilateral hull | −608.28 | −1141.71 | 153.51 | −30,776.38 | 7415.47 | −3843.70 | |

Over one side deep pit | 3891.64 | 7412.00 | −1043.45 | −32,024.11 | 6871.48 | −588.33 | |

Ultimate steering | −355.88 | −657.69 | 56.79 | −23,436.62 | 6460.99 | −3803.89 | |

Steering braking | 3647.18 | 7040.50 | −319.42 | −18,503.06 | 4927.97 | 506.97 | |

Steering drive | −4046.88 | −7266.67 | −699.38 | −772.01 | 983.45 | −3228.57 | |

Maximum driving acceleration | −1541.12 | −2936.89 | −705.71 | 15,925.78 | −3253.31 | −2182.21 | |

Diagonal torsion | −439.74 | −838.45 | 42.95 | −18,237.10 | 5292.08 | −1926.40 | |

Forward braking | Steering gear left mounting point | −35.71 | 282.71 | −42.47 | −5.02 | −335.09 | −5480.94 |

Backward braking | −37.87 | −61.51 | −76.32 | 179.50 | −675.91 | 1313.98 | |

Forward emergency braking | −481.47 | 250.38 | 150.66 | 164.99 | −2733.61 | −5023.66 | |

Backward emergency braking | 352.29 | −63.17 | 64.88 | 217.27 | 1332.79 | 1586.27 | |

Overconvex hull | −89.30 | 74.38 | 9.83 | 166.08 | −829.91 | −1352.61 | |

Over unilateral hull | −150.66 | −221.96 | 79.69 | −853.46 | −1710.82 | −1956.74 | |

Over one side deep pit | 502.53 | 2156.57 | −778.59 | 1839.08 | 6405.35 | −4312.94 | |

Ultimate steering | 349.17 | 887.21 | −328.71 | −229.11 | 4762.88 | 2935.18 | |

Steering braking | 47.06 | 633.97 | −97.38 | −452.64 | 1676.53 | −2247.49 | |

Steering drive | −730.26 | −1058.18 | −224.87 | −1624.26 | −8359.98 | 2036.35 | |

Maximum driving acceleration | −290.88 | −45.50 | −356.40 | 43.70 | −1885.46 | 733.59 | |

Diagonal torsion | −98.05 | −185.83 | −19.56 | −1143.84 | −1169.12 | −1932.29 |

**Table 2.**Static stiffness analysis results of each mounting point of the aluminium alloy front subframe.

Number | Position of Mounting Point | Direction | Static Stiffness Value (N/mm) | Target Static Stiffness Value (N/mm) |
---|---|---|---|---|

1 | Lower arm left front point | X | 23,810 | 12,000 |

Y | 25,641 | 16,000 | ||

Z | 40,000 | 5000 | ||

2 | Lower swing arm left back point | X | 50,0000 | 20,000 |

Y | 90,909 | 20,000 | ||

Z | 52,631 | 5000 | ||

3 | Lower arm right front point | X | 13,889 | 12,000 |

Y | 45,455 | 16,000 | ||

Z | 45,455 | 5000 | ||

4 | Lower swing arm right back point | X | 200,000 | 20,000 |

Y | 200,000 | 20,000 | ||

Z | 62,500 | 5000 | ||

5 | Steering gear left point | X | 40,000 | 25,000 |

Y | 55,556 | 25,000 | ||

Z | 22,727 | 8000 | ||

6 | Steering gear right point | X | 71,429 | 25,000 |

Y | 90,909 | 25,000 | ||

Z | 28,571 | 8000 | ||

7 | Stabilizer bar left point | X | 58,824 | 10,000 |

Y | 76,923 | 5000 | ||

Z | 40,000 | 16,000 | ||

8 | Stabilizer bar right point | X | 100,000 | 10,000 |

Y | 111,111 | 5000 | ||

Z | 47,619 | 16,000 |

Design Variable | Initial Value (mm) | Lower Limiting Value (mm) | Upper Limit Value (mm) |
---|---|---|---|

F_01 | 0 | −20 | 10 |

R_01 | 0 | −30 | 15 |

LZ_t | 0 | −5 | 5 |

LZ_b | 0 | −8 | 0 |

Responses | Total Error |
---|---|

Freq_1 | 0.99675 |

Mass | 0.99995 |

Max_stress1 | 0.99493 |

Max_stress2 | 0.99783 |

Max_stress3 | 0.99781 |

Disp | 0.9897 |

Design Variable | Initial Value/mm | Lower Limiting Value/mm | Upper Limit Value/mm | Optimal Value/mm |
---|---|---|---|---|

F_01 | 0 | −20 | 10 | 1.5 |

R_01 | 0 | −30 | 15 | −27 |

LZ_t | 0 | −5 | 5 | −4 |

LZ_b | 0 | −8 | 0 | −4.5 |

**Table 6.**Comparative analysis results of stress before and after optimization of aluminium alloy front subframe.

Typical Working Conditions | Model Stress before Optimization/MPa | Model Stress after Optimization/MPa |
---|---|---|

Forward braking condition | 145.7 | 141.7 |

Backward braking condition | 51.9 | 50.2 |

Forward emergency braking condition | 128.4 | 124.8 |

Backward emergency braking condition | 59.7 | 57.8 |

Over one side deep pit condition | 180.6 | 179.3 |

Ultimate steering condition | 103.7 | 101.9 |

**Table 7.**Comparative analysis results of static stiffness performance of aluminium alloy front subframe before and after optimization.

Number | Position of Mounting Point | Direction | Static Stiffness Value of the Model before Optimization (N/mm) | Static Stiffness Value of Optimized Model (N/mm) |
---|---|---|---|---|

1 | Lower arm left front point | X | 23,810 | 24,390 |

Y | 25,641 | 23,809 | ||

Z | 40,000 | 37,037 | ||

2 | Lower swing arm left back point | X | 500,000 | 500,000 |

Y | 90,909 | 83,333 | ||

Z | 52,631 | 50,000 | ||

3 | Lower arm right front point | X | 13,889 | 13,888 |

Y | 45,455 | 40,000 | ||

Z | 45,455 | 40,000 | ||

4 | Lower swing arm right back point | X | 200,000 | 200,000 |

Y | 200,000 | 200,000 | ||

Z | 62,500 | 62,500 | ||

5 | Steering gear left point | X | 40,000 | 38,461 |

Y | 55,556 | 52,631 | ||

Z | 22,727 | 21,739 | ||

6 | Steering gear right point | X | 71,429 | 71,428 |

Y | 90,909 | 83,333 | ||

Z | 28,571 | 27,027 | ||

7 | Stabilizer bar left point | X | 58,824 | 58,823 |

Y | 76,923 | 83,333 | ||

Z | 40,000 | 38,461 | ||

8 | Stabilizer bar right point | X | 100,000 | 100,000 |

Y | 111,111 | 111,111 | ||

Z | 47,619 | 45,454 |

**Table 8.**Comparison of free modal analysis results before and after optimization of aluminium alloy front subframe.

Order | Model Frequency before Optimization/Hz | Optimized Model Frequency/Hz |
---|---|---|

First order modal | 97 | 96 |

Second order modal | 216 | 222 |

Third order modal | 261 | 268 |

Fourth order modal | 345 | 346 |

Fifth order modal | 376 | 373 |

Sixth order modal | 397 | 417 |

**Table 9.**The results of free modal finite element analysis of aluminium alloy front subframe are compared with the results of test analysis.

Order Number | Finite Element Analysis Frequency/Hz | Test Analysis Frequency/Hz | Error/% |
---|---|---|---|

First order modal | 96 | 84 | 14.29 |

Second order modal | 222 | 201 | 10.45 |

Third order modal | 268 | 254 | 5.93 |

Fourth order modal | 346 | 342 | 1.47 |

Fifth order modal | 373 | 389 | 1.32 |

Sixth order modal | 417 | 390 | 6.92 |

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## Share and Cite

**MDPI and ACS Style**

Meng, X.; Sun, Y.; He, J.; Li, W.; Zhou, Z.
Multi-Objective Lightweight Optimization Design of the Aluminium Alloy Front Subframe of a Vehicle. *Metals* **2023**, *13*, 705.
https://doi.org/10.3390/met13040705

**AMA Style**

Meng X, Sun Y, He J, Li W, Zhou Z.
Multi-Objective Lightweight Optimization Design of the Aluminium Alloy Front Subframe of a Vehicle. *Metals*. 2023; 13(4):705.
https://doi.org/10.3390/met13040705

**Chicago/Turabian Style**

Meng, Xiangchao, Youping Sun, Jiangmei He, Wangzhen Li, and Zhifeng Zhou.
2023. "Multi-Objective Lightweight Optimization Design of the Aluminium Alloy Front Subframe of a Vehicle" *Metals* 13, no. 4: 705.
https://doi.org/10.3390/met13040705