The automobile’s knuckle is connected to the parts of the steering system and the suspension system and it is used for adjusting the direction of a rotation through its attachment to the wheel. This study changes the existing material made of GCD45 to Al6082M and recommends the lightweight design of the knuckle as the optimal design technique to be installed in small cars. Six shape design variables were selected for the optimization of the knuckle and the criteria relevant to stiffness and durability were considered as the design requirements during the optimization process. The metamodel-based optimization method that uses the kriging interpolation method as the optimization technique was applied. The result shows that all constraints for stiffness and durability are satisfied using A16082M, while reducing the weight of the knuckle by 60% compared to that of the existing GCD450.
The linking parts of the steering system and the suspension system of automobiles have a direct impact on the performance of the vehicle’s ride, durability, and steerability. Therefore, the performance of these parts is directly related to the quality of the vehicle. This paper examines the structural design of the knuckle, which can adjust the directional rotation due to its connection to the parts of the suspension system and steering system, as well as the wheel. When designing the structure of the knuckle, it is common to consider durability and stiffness [
For this purpose, the strength of the knuckle under the vehicle’s service loads is calculated and the durability is examined. Under the same load condition, the strain or deformation is also calculated and it is verified that this value is within the allowable value. If the design requirement for stiffness is not satisfied, it can be considered that the quality targets such as ride and steerability are not satisfied. In this study, the finite element analysis was used to examine the vehicle’s performance of stiffness and durability.
Because the knuckle arm has a greater weight compared to the outer tie rod, inner tie rod, control arm, and ball joint, it can have a greater impact in reducing the overall weight of the steering parts compared to the other parts. To lessen the weight of the knuckle, a material less dense than steel is used and the design methodology is applied. In this study, aluminum was used as an alternate material to steel and the structural optimization was applied as a design technique.
The shape of the knuckle arm is complex compared to the other parts. Additionally, casting and forging are mainly used in the production process of the knuckle arm. Thus, the knuckle is modeled as a solid element in the finite element analysis, corresponding to the shape optimization in the structural optimization category. The iteration can be stopped due to the mesh distortion during the optimization process in the structural optimization with complex shape. In this study, the metamodel-based optimization technique was applied to solve this problem. The optimization technique using the metamodel is suitable for the following design problems:
The following is a recent research trend related to the knuckle: Triantafyllidis et al. revealed that the fracture mechanism of the knuckle is mainly due to bending fatigue through scanning electron microscopy (SEM) images [
In this study, the lightweight design method that can be applied was suggested at the early stage in the development of the knuckle. First, the base design was completed and six shape design variables were defined. During this process, the shapes of the parts such as the strut, OTR, and spring were fixed. Al6082M, which was developed in the existing Reference [
The knuckle’s shape, designed at the early stage of development, is shown in Figure
Material properties of GCD450.
Property | Value |
---|---|
Elasticity (MPa) | 170,000 |
Density (g/cm3) | 7.9 |
Poisson’s ratio | 0.29 |
Tensile strength (MPa) | 450 |
Yield strength (MPa) | 370 |
Structure of steering parts.
FE model of knuckle.
Plastic strain and true stress curve.
The load that is delivered from the road surface to a car during the operation is transferred to the parts of the suspension and steering systems through the tire and wheel and this load affects the stiffness and strength of the vehicle. If the stiffness of each part is reduced then it induces the excessive deformation that has negative effect on the ride, handling and NVH performance. Thus, each automobile maker sets its own allowable value for the amount of deformation on each car model. In this study, the loading condition and the design criterion that Company A uses were applied. The number of entire loading cases is 12 and the equivalent plastic strain for each number is calculated and checked that it is within the allowable value.
The equivalent plastic strain,
As the boundary condition for the stiffness analysis all degrees of freedom of the wheel center, which is the center part of the knuckle hole, were constrained. Twelve load cases for the stiffness analysis can be determined by considering the ultimate load that can be received when the car operates. These load cases are shown in Table
Loading condition and case for stiffness.
Number | Loading condition | Number of load case |
---|---|---|
1 | Braking | 2 |
2 | Pothole | 6 |
3 | Wheel bump | 2 |
4 | Cornering | 2 |
Total |
|
FE model for stiffness analysis of forward-braking case.
The severe result of the stiffness analysis of the knuckle arm came from within the Pothole loading case. The maximum
Stiffness analysis result at pothole loading condition.
Automobile pats can fail by fatigue if repeated loading is applied. Therefore, it is essential to review the durability of an entire car unit or parts unit when a new car is developed. In this study, the fatigue life caused by the repeated loads acting on the knuckle parts was calculated and it is concluded that this value was less than the allowable value.
Stress-life method and strain-life method are the methods that calculate the fatigue life. The stress-life method is suitable only when stress and strain exist in the elastic area. On the other hand, the strain-life method is suitable for the problems that occur due to stress concentration causing plastic strain. In this study, the strain-life method was used to predict the fatigue life of the knuckle [
The loading case for determining the fatigue life of the knuckle arm is 23 loading cases as suggested by the Company A. These loading cases are divided into the nonbraking loading condition and the braking loading condition. The boundary condition of the nonbraking loading condition is the same as the case of the stiffness analysis. On the other hand, in the case of the braking loading condition, all degrees of freedom except for the rotational degree of freedom of
FE analysis for durability analysis of nonbraking condition.
FE model
Fatigue life
The results of the stiffness and durability analyses of the knuckle made of material GCD450 show that both results satisfy the criteria and have the marginal safety of about 10 times. In this study, the material of the knuckle was replaced with GCD450 from A16082M and the lightweight design was implemented by applying the metamodel-based optimization using the kriging model. The initial design of the optimization is the shape of a knuckle made of GCD450 material. Also, during the optimization process, the most vulnerable loading case for the stiffness analysis and the durability analysis was included on each one. The material property of A16082M is the same as shown in Table
Material properties of Al6082M.
Property | Value |
---|---|
Elasticity (MPa) | 72,000 |
Density (g/cm3) | 2.71 |
Poisson’s ratio | 0.29 |
Tensile strength (MPa) | 380 |
Yield strength (MPa) | 340 |
The areas that are the most vulnerable in the stiffness and durability analyses are the joint of the outer tie rod and knuckle and the joint of the strut and knuckle. Design variables
Definition of shape design variables.
The formulation for the structural optimization of a knuckle is expressed as follows:
The lower and upper bounds of each design variable are established by considering the quality of the geometrical shape and the mesh for the finite element analysis of a knuckle. The first inequality equation in (
For global optimization, the kriging interpolation method is introduced. Kriging is an interpolation method named after a South African mining engineer named D. G. Krige, who developed the method while trying to increase the accuracy in predicting the ore reserves. Kriging interpolation for approximation model is well explained in [
If
In this research,
To assess the kriging model, a few metrics can be utilized. In this study, the
The optimization process applied in this study is shown in Figure
Flowchart of the suggested design process.
Table
Design of experiments using LHD.
Number | Design variable (mm) | Response | |||||||
---|---|---|---|---|---|---|---|---|---|
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|
|
|
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|
|
PEEQ | SF | |
1 | 21.5 | 22.53 | 26.24 | 27.65 | 27.33 | 26.24 | 1.189 | 0.0097 | 2.67 |
2 | 23.17 | 21.73 | 28.7 | 29.69 | 27.06 | 25.96 | 1.197 | 0.0122 | 3.38 |
3 | 21.17 | 22 | 25.96 | 26.63 | 25.69 | 24.05 | 1.176 | 0.0100 | 1.94 |
4 | 27.83 | 23.87 | 28.97 | 25.27 | 25.42 | 24.87 | 1.196 | 0.0095 | 2.94 |
5 | 22.5 | 16.13 | 24.87 | 25.95 | 22.14 | 23.5 | 1.147 | 0.0215 | 3.09 |
6 | 20.17 | 17.73 | 28.15 | 23.23 | 29.24 | 22.68 | 1.167 | 0.0184 | 2.82 |
7 | 24.17 | 19.33 | 30.06 | 24.59 | 24.32 | 28.7 | 1.175 | 0.0100 | 3.18 |
8 | 22.83 | 18.27 | 25.69 | 26.97 | 26.78 | 24.32 | 1.173 | 0.0357 | 2.67 |
9 | 25.17 | 20.93 | 24.32 | 29.01 | 28.7 | 25.69 | 1.197 | 0.0089 | 2.82 |
10 | 20.5 | 17.47 | 29.24 | 23.57 | 30.06 | 26.51 | 1.175 | 0.0335 | 3.16 |
11 | 26.17 | 23.33 | 27.6 | 29.35 | 28.15 | 27.88 | 1.211 | 0.0149 | 3.09 |
12 | 24.5 | 19.87 | 24.05 | 21.53 | 24.87 | 28.42 | 1.165 | 0.0141 | 2.99 |
13 | 23.83 | 16.67 | 29.79 | 23.91 | 28.42 | 30.06 | 1.18 | 0.0272 | 3.23 |
14 | 20.83 | 23.6 | 26.78 | 25.61 | 22.41 | 26.78 | 1.17 | 0.0250 | 3.18 |
15 | 18.5 | 18.53 | 22.41 | 30.03 | 23.78 | 27.06 | 1.161 | 0.0120 | 2.5 |
16 | 19.83 | 16.4 | 29.52 | 28.33 | 27.6 | 22.96 | 1.171 | 0.0187 | 2.91 |
17 | 27.17 | 16.93 | 22.96 | 22.55 | 26.24 | 29.24 | 1.169 | 0.0242 | 3.04 |
18 | 19.17 | 20.13 | 24.6 | 27.99 | 28.97 | 24.6 | 1.179 | 0.0198 | 2.82 |
19 | 18.17 | 21.47 | 23.78 | 28.67 | 25.14 | 29.79 | 1.174 | 0.0351 | 3.04 |
20 | 26.83 | 17.2 | 25.14 | 20.51 | 29.79 | 25.42 | 1.174 | 0.0242 | 3.13 |
21 | 18.83 | 20.67 | 22.14 | 21.19 | 22.96 | 22.41 | 1.139 | 0.0228 | 2.89 |
22 | 25.5 | 21.2 | 22.68 | 24.93 | 23.5 | 28.97 | 1.173 | 0.0155 | 3.18 |
23 | 24.83 | 22.8 | 27.88 | 26.29 | 29.52 | 27.33 | 1.203 | 0.0103 | 2.74 |
24 | 22.17 | 18 | 25.42 | 20.85 | 24.6 | 27.6 | 1.153 | 0.0367 | 2.94 |
25 | 21.83 | 19.6 | 27.33 | 27.31 | 23.23 | 23.23 | 1.165 | 0.0091 | 2.75 |
26 | 19.5 | 20.4 | 27.06 | 22.89 | 24.05 | 22.14 | 1.153 | 0.0206 | 2.99 |
27 | 26.5 | 23.07 | 28.42 | 20.17 | 25.96 | 28.15 | 1.183 | 0.0357 | 3.09 |
28 | 23.5 | 18.8 | 23.5 | 24.25 | 22.68 | 29.52 | 1.159 | 0.0257 | 3.33 |
29 | 27.5 | 19.07 | 23.23 | 21.87 | 27.88 | 23.78 | 1.174 | 0.0136 | 2.89 |
30 | 25.83 | 22.27 | 26.51 | 22.21 | 26.51 | 25.14 | 1.181 | 0.0249 | 2.99 |
Optimum parameter and validation of kriging model.
Responses | Optimum parameter* | Validation | ||||||
---|---|---|---|---|---|---|---|---|
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|
CV | |
|
1.1749 | 4.4769 | 7.9588 | 0.0341 | 0.2377 | 2.2620 | 51.316 | 0.014 |
PEEQ | 0.0170 | 2.0487 | 1.9495 | 0.3696 | 0.0483 | 0.2500 | 0.2140 | 0.084 |
SF | 2.8378 | 20.705 | 28.048 | 0.0006 | 5.7071 | 0.0021 | 0.0003 | 3.129 |
Responses at initial and optimum designs.
Design | Deign variable (mm) | Response | |||||||
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|
SF | |
Initial (steel) | 18.0 | 22.0 | 23.0 | 24.0 | 21.5 | 27.5 | 3.4 | 0.0034 | 12.7 |
|
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Initial (Al) | 18.0 | 22.0 | 23.0 | 24.0 | 21.5 | 27.5 | 1.160 | 0.025 | 3.1 |
Optimum | 19.3 | 20.6 | 20.0 | 21.8 | 20.6 | 26.2 | 1.142 | 0.0199 | 2.8 |
As shown in Table
Suggested optimum design of a knuckle.
In this study of a lightweight design of the knuckle mounted to a small car, the material was changed from steel to aluminum and the metamodel-based optimization was applied. The results are as follows.
The authors declare that there is no conflict of interests regarding the publication of this paper.
This research was financially supported by the Ministry of Education Science and Technology (MEST) and the National Research Foundation of Korea (NRF) through the Human Resource Training Project for Regional Innovation (2012H1B8A2026078).