The lightweight design of the outer tie rod installed on an electrical vehicle was achieved through material selection and optimization technique. The aluminum alloy Al6082M was selected as a steelsubstitute, and its structural shape was optimized by applying metamodelbased optimization. In this process, finite element analysis was performed to predict the structural responses, such as buckling resistance and fatigue life. First, for an arbitrary base design made of steel, the structural responses were calculated. Then, the design variables were defined to find a lightweight design made of Al6082M. Secondly, metamodelbased optimization based on the kriging interpolation method was applied, leading to determination of an optimum design. The suggested optimum design has the minimum weight satisfying the critical design requirement. Finally, the numerical results of the buckling resistance and fatigue life were validated, through bucking and fatigue tests.
The current trend of the structural design of automobile parts is towards lightweight design. Lightweight automobile parts can be developed by selecting steel substitutes, such as aluminum, magnesium, plastic, or composite material, applying manufacturing technology and/or adopting optimization techniques [
There have been many cases of lightweight structural design in body and chassis parts during the past 20~30 years. Among the parts of suspension and steering systems, there have been many cases of lightweight design application for the control arm or knuckle, but there are very few cases for the outer tie rod [
In this study, a lightweight design of the OTR for an electrical vehicle is suggested, by substituting SM45C with Al6082M and applying optimization techniques, considering the buckling and durability performance. The structural responses of buckling and durability are considered in the structural design process of the outer tie rod. Usually, since the buckling is the critical performance, only the buckling is included in the optimization process. Then, after an optimum design is determined, the durability analysis is performed, to investigate whether the suggested design satisfies its criterion.
The most exact method to determine the optimum design is to utilize the sensitivity information of responses and a gradientbased algorithm, since it can provide one design satisfying the KT necessary condition. In contrast, a metamodelbased optimization method is suitable for problems of structural design requiring much computation time, difficult computational sensitivity problems, or problems having a wavy response function, even though it cannot give the KT point [
For the validation of the suggested optimum design, buckling and fatigue tests were performed. The design of the OTR was done using CATIA [
The OTR is a part that belongs to the steering system changing directions, according to the motion of the steering wheel. Going from steering wheel to steering gear, pitman arm, relay rod, and ITR (inner tie rod), steering power is finally delivered to the wheel through the knuckle after passing through the OTR [
The CAD model and FE model of the initial design are shown in Figure
The base model of steel OTR.
CAD model
FE model
The loading condition for buckling analysis is shown as Figure
Loading condition for buckling analysis.
Buckling analysis result of steel OTR.
In general, aluminum has been selected as a steelsubstitute material to reduce the weight, since aluminum has almost onethird of the density of steel. In this research, aluminum called Al6082M [
Material properties of SM45C and Al6082M.
Property  SM45C  Al6082M 

Yield strength (MPa)  343  340 
Tensile strength (MPa)  569  380 
Young’s modulus (GPa)  210  72 
Density (×10^{−6} kg/mm^{3})  7.85  2.71 
Based on the modified design of the steel OTR, the design variables defining its shape are represented in Figure
Shape design variables.
The optimization problem determining its optimum shape can be formulated as
Shape optimization based on the sensitivity information makes the setting of a shape variable difficult and distorts the finite elements in the optimization process [
The buckling load should be larger than the limit, 25.0 kN. However, the allowable value of
The flow chart for the structural design of the aluminum OTR is shown as in Figure
Design of experiments using LHD.
Exp. number 







1  0.2  1.8  11.1  1.5  26,083  135.1 
2  5.4  2.0  1.9  0.1  26,821  143.5 
3  7.1  1.0  5.8  0.2  28,825  143.1 
4  0.8  26,380  139.0  







49  3.5  2.3  14.0  0.2  26,429  136.2 
50  1.4  1.8  5.3  0.9  26,961  140.0 
Flow chart for the structural design of Al6082M OTR.
In the kriging model, the global approximation model
The unknown parameters
This research utilized an inhouse program [
For the kriging models of weight and buckling load, their optimum parameters are summarized in Table
Optimal parameters of kriging models.
Response 







138.6 kg_{f}  0.004  20.54  4.74  10.33 

27,690 N  0.001  5.07  18.90  50.00 
Buckling and durability analysis result of optimum Al6082M OTR.
Buckling analysis result
Durability analysis result
For the suggested optimum design, durability analysis for the unit of OTR was performed, to investigate the design requirement imposed on the OTR. The loading condition applying an equivalent load is represented as a sine curve. The loading condition and design criterion were supplied by car maker A. The fatigue life calculated from MSC Fatigue is shown in Figure
Based on the suggested optimum design, twelve specimens were made to validate the bucking and durability performance. For the buckling test, six specimens of the OTR connected with the ITR are shown in Figure
Buckling test result.
Six specimens before test
Test equipment
One specimen after test
For the durability test, six other specimens were prepared, as shown in Figure
Fatigue test result.
Six specimens before test
Test equipment
Six specimens after test
The present research suggested an optimum design of Al6082M OTR, which is one of the parts of the steering system of an electrical vehicle. The following conclusions can be made from this study.
The present research has succeeded in the development of a lightweight OTR, by replacing the current OTR, whose initial model was made of steel, with an Al6082M OTR, and applying the optimization technique. The metamodelbased optimization technique provides a realistic optimum, even though it cannot be considered as an exact solution. The weight of the suggested optimum design is 131.0 g, which is 65.3% lighter weight than the initial steel model.
It is proven that the design requirements related to the bucking and durability performance were satisfied through the tests. For the buckling test, six specimens were used, and their buckling loads were between 25,900~27,550 N. In the case of the durability test, all the fatigue lives of the six specimens exceeded the allowable cycle.
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).