Structural Optimization of AerMet100 Steel Torsion Spring Based on Strain Fatigue

Abstract

The torsion spring of a carrier-based aircraft landing gear is a key component, which is normally manufactured out of AerMet100 ultra-high-strength steel. The takeoff and landing performance is greatly influenced by its bearing capacity and structural durability. To carry out the structure anti-fatigue design, it is necessary to investigate the influence of the spring structure features on its fatigue life, based on which the strain fatigue analysis and parameter optimization design of the torsion spring are executed. Through the finite element analysis conducted with ABAQUS, it was determined that there exists serious stress concentration in the relief groove. Based on the theory of strain fatigue, the fatigue life of the torsion spring was obtained, and the fracture position and lifecycle were consistent with the test results. A structure optimization platform based on a parametric method was established. Samples were selected through the DOE (design of experiment), and a surrogate model was established based on RBF (radial basis functions), followed by optimization using MIGA (multi-island genetic algorithms). With the parameter optimization of the relief groove, the structure was reconstituted and reanalyzed. From the simulation results, the peak strain was reduced by 30.7%, while the fatigue life was increased by 86.2% under the same loads and constraints. Moreover, laboratory tests were performed on the torsion spring after reconstruction, which showed that the fatigue life increases by 85.6% after optimization. The method presented in this paper can provide theoretical support and technical guidance for the application and structural optimization of ultra-high-strength steel structures.

1. Introduction

Ultra-high-strength steel is widely used in aircraft landing systems, rocket engines and tail axles, together with other significant structural parts in aerospace and deep sea technology. It plays an imperative role not only in aerospace and defense equipment but also in manufacturing transformation and civil safety protection in the country. AerMet100 steel is a type of ultra-high-strength steel that contains C, Cr and Mo as reinforcements. As well as possessing excellent ductility and toughness, AerMet100 steel also exhibits superior strength, fatigue resistance and stress-corrosion cracking [1].

The spring is a part that relies on its elasticity to perform its function. When external forces are applied to it, it deforms. Once the external forces are removed, it returns to its original state. Besides serving as an energy storage component, the spring can also be used to absorb vibration and shock. In addition to transportation and aerospace, it is used in many other industries as well. The torsion spring of an aircraft landing gear is made of AerMet100 ultra-high-strength steel and plays a significant role in the landing process. It is meaningful to study its bearing capacity and structural durability.

Rivera R et al. conducted experiments and simulations on springs in elevator door control mechanisms and found that manufacturing defects can lead to spring cracking, which may be caused by inclusions and folds on the spring inner surfaces [2]. Zhang P et al. conducted tests and numerical simulations of a torsion spring made of SUS631 stainless steel and found that material defects, surface scratches and stress peaks at the stress concentration would affect the fatigue life [3]. D. Pastorcic et al. evaluated the cumulative damage of automobile springs based on the Goodman failure criterion and the Miner failure criterion. The results of the analysis allowed a prediction of the fatigue life of springs [4]. Gonzalez et al. found that the roughness and surface defects in specific zones may affect the formation of cracks [5].

The surrogate model is commonly used in solving complex and time-consuming engineering design problems. Meng, D. et al. used a surrogate model to solve a turbine blade design problem to alleviate the computational burden for uncertainties-based multidisciplinary design problems [6]. Gao, H. F. et al. proposed a probabilistic approach based on a substructure-based Kriging surrogate model and predicted the fatigue life of turbine blades [7]. Zhang, L. et al. constructed a Kriging-based multi-fidelity (MF) surrogate model to solve the time-variant fatigue reliability assessment of a T-plate welded joint [8]. Other researchers have also done a lot of work in this field [9,10,11].

It is necessary to reduce the maximum stress of the spring in order to improve its performance, as well as to optimize the structure to increase the spring fatigue life. Optimizing the structure would make it possible to design a spring with optimal characteristics. As a result of the corresponding optimization, the design variables are adjusted in such a way as to ensure the design result is always close to the optimal solution. Researchers both in China and in foreign countries have also contributed to the study in this field. Chen H et al. developed a surrogate model based on the samples obtained from the DOE and then optimized it using the multi-island genetic algorithm. It was found that under the same loads, the optimized structure had a 15.7% reduction in the stress peak and a 122% increase in fatigue life [12]. Xia T et al. optimized the bolt connection of the wing spar considering life constraints, and the weight of the optimized structure was only 85% of the original design, with the results showing that the optimized structure was the most effective [13]. Munk D J et al. applied topology optimization technology to the structural design of aircraft components and designed a light aircraft landing gear [14]. Qiu, J. et al. achieved the settlement of a T-tail structure design by combining sequential quadratic programming with a multi-island genetic algorithm [15].

Despite the fact that those researchers mentioned above have made significant progress in the fields of life prediction and structure optimization, there is a paucity of research on the fatigue life and structure optimization of ultra-high-strength steel springs. In view of the wide application of ultra-high-strength steel in aerospace, it is very necessary to conduct a study on this.

This paper proposes a complete optimization design process based on the above research status of the spring fatigue life and structure optimization, which includes tests, simulations, an optimization design and simulation validation, providing method guidance and solutions for optimizing ultra-high-strength steel structures. To begin with, the fatigue life of the torsion springs made of AerMet100 ultra-high-strength steel were obtained through tests, and the stress concentration location was determined through simulation using the commercial finite element software ABAQUS. With ANSYS nCode DesignLife software, the fatigue life was predicted based on strain fatigue methods; the predicted life was reasonable compared to the test results. The optimal Latin hypercube sampling method was applied for the DOE, and the radial basis function (RBF) surrogate model was established based on the numerical results. According to the established surrogate model, a simulation and optimization platform was built in Isight through the multi-island genetic algorithm to optimize the parameters of the characteristic parts of the torsion spring; after that, structure reconstruction and simulation was carried out and the simulation results were verified through experiments.

2. Fatigue Life Analysis

2.1. Experiment

The fatigue life of the torsion springs was obtained in the laboratory for the purpose of determining whether a certain type of torsion spring can meet the service requirements under the specified working conditions and to assess its structural durability. An angular drive was applied to one end of the torsion spring while the other was fixed. Figure 1 shows the torque curve of the torsion spring in one cycle, and Figure 2 shows the cracking locations of the torsion springs. It is estimated that the springs had an average life of 9700 cycles before they suffered fractures in the relief groove.

2.2. Numerical Analysis

The tensile properties of metal materials are generally described by the p-δ curves. The nominal stress S (or engineering stress) and nominal strain E (or engineering strain) of materials can be defined as follows.

$$\left\{\begin{array}{l}S=\frac{P}{A_0}\\ e=\frac{l-l_0}{l_0}\end{array}\right.$$

(1)

where P and A₀ are the tensile loads and the cross-sectional area before the tensile test, respectively; l₀ and l are the lengths of the specimen before and after the tensile test.

Because the length and cross-sectional area of the specimen are constantly changing during the tensile test process, nominal stress and nominal strain cannot accurately reflect the actual stress and strain in the process of material deformation. Therefore, the concepts of true stress and true strain are proposed, whose conversion formula is as follows:

$$\left\{\begin{array}{l}\epsilon =\ln (1+e)\\ \sigma =S(1+e)\end{array}\right.$$

(2)

where σ and ε are the true stress and true strain, respectively.

Figure 3 illustrates the nominal/true stress–strain curve of ultra-high-strength steel.

It was found that, when modeling the specimen, the calculation efficiency was significantly reduced due to the large number of turns of the torsion spring and the excessive number of elements in the mesh division. In order to reduce the complexity of the torsion spring structure, only one turn was kept. The simplified structure was imported into ABAQUS and meshed. The element type was C3D8I. One end face of the torsion spring is fixed to the ground through the coupling with a reference point while the other bears the load through the coupling with another reference point. The applied load is 29.178 N·m, which is measured from the test. As a result of the element sensitivity examination, the global element size and the local element size were set to 0.5 mm and 0.3 mm, respectively. The mesh independence test result under unit load (N·m) is shown in Figure 4. The true stress–strain curve and the real peak torque collected by the sensor were imported into ABAQUS for calculation. The parameters are summarized in

Table 1. Parameter settings of the finite element analysis.

Element Type	Globe Element Size (mm)	Local Element Size (mm)	Maximum Strain (με)
C3D8I	0.5	0.3	20,420

, and the simulation results are shown in Figure 5.

As can be seen from Figure 5, the peak strain of the torsion spring is 20,420 με, far beyond the yield point strain value of ultra-high-strength steel material, indicating that this region has entered the plastic region. During the test, the maximum strain position is consistent with the fracture position of the specimen.

2.3. Fatigue Life Prediction

It is common to use the strain–life curve in engineering in order to describe the relationship between material strain and life. According to the control parameters, it can be divided into the $\Delta \epsilon -N$ curve and ${\epsilon }_{eq}-N$ curve. In this paper, we rely on the former $\Delta \epsilon -N$ uses the strain amplitude at $R_{\epsilon }=1$ as a parameter to describe the lifetime characteristics of the material. When $R_{\epsilon }\ne 1$, the average stress is corrected [16]. The strain–life relation is described by the widely used Manson–Coffin formula, which is expressed as follows:

$${\epsilon }_{\mathrm{a}}={\epsilon }_{\mathrm{ea}}+{\epsilon }_{\mathrm{pa}}=\frac{{\sigma }_{\mathrm{f}}^{\prime }}{E}{(2N)}^b+{\epsilon }_{\mathrm{f}}^{\prime }{(2N)}^c$$

(3)

where ε_a, ε_ea and ε_pa are the total strain, elastic strain and plastic strain, respectively; N is the fatigue life; σ’ f is the fatigue strength coefficient; ε’ f is the fatigue ductility coefficient; b is the fatigue strength index; c is the fatigue ductility index.

The Manson–Coffin formula describes the relationship between the total strain, elastic strain, plastic strain and fatigue life. The best way to obtain the $\Delta \epsilon -N$ curve data of materials is to carry out fatigue tests in the medium life zone (10³–10⁵) under strain control. The $\Delta \epsilon -N$ curve can also be estimated using static tensile mechanical properties such as tensile strength, elastic modulus, true fracture strength and true fracture ductility.

In this section, ANSYS nCode DesignLife is used to predict the fatigue life of the torsion spring [17]. In addition to having a simple user interface, this software allows the analysis process to be constructed by simply dragging block diagrams. Figure 6 depicts the process of analyzing the fatigue life of torsion springs using ANSYS nCode DesignLife software. The fatigue parameters of ultra-high-strength steel are input into the model, as shown in

Table 2. Fatigue parameters of ultra-high-strength steel [12].

Fatigue Parameters	Value	Description
E	1.96 × 105	Elastic Modulus (MPa)
${\epsilon }_{\mathrm{f}}^{\prime }$	0.133452	Fatigue Ductility Coefficient
${\mathrm{K}}^{\prime }$	3184.5	Cyclic Strength Coefficient (MPa)
$\mathrm{Nc}$	2.00 × 108	Cut-off
${\sigma }_{\mathrm{f}}^{\prime }$	2895	Fatigue Strength Coefficient (MPa)
$\mathrm{UTS}$	1930	Ultimate Tensile Strength (MPa)
$\mathrm{YS}$	1620	Yield Strength (MPa)
$\mathrm{b}$	−0.087	Fatigue Strength Exponent
$\mathrm{c}$	−0.58	Fatigue Ductility Exponent
$\mathrm{me}$	0.3	Elastic Poisson’s Ratio
$\mathrm{mp}$	0.5	Plastic Poisson’s Ratio
${\mathrm{n}}^{\prime }$	0.15	Cyclic Strain Hardening Exponent

. The simulation results are shown in Figure 7 and

Table 3. Comparison of fatigue life between simulations and tests.

Analysis Results in nCode DesignLife	Test Results	Error (%)
10,030	9700	3.3

. The fatigue life analysis results indicate that the lowest life location of the torsion spring is the same as the fracture location of the test specimen, and that it has a fatigue life of 10,080 cycles. Based on the average life of the specimen of 9700 cycles, the error is 3.9%, demonstrating the reliability of the analysis model.

3. Surrogate Model Based on DOE

3.1. Selection of the Control Parameters

According to the finite element simulation results presented in the above section, the stress concentration at the relief groove is very severe. The maximum strain exceeds the strain value at the yield point. The U-shaped and the elliptical relief groove are designed to reduce the stress concentration in this area and increase the fatigue life of the torsion spring. Other meshing parameters remain the same. Some areas of the elliptical relief grooves cannot be divided using hexahedral elements. Because this is not the area we are concerned with, the tetrahedral elements are applied, and the element type is C3D4. The torsion springs with two types of relief grooves were imported into ABAQUS for calculation. All parameters were set in accordance with the circular relief groove torsion spring. As shown in Figure 8 and Figure 9, the results of the ABAQUS simulation analysis are presented.

It is significant to note that the axial dimensions of the three types of relief grooves remain the same, which is 2 mm. As can be seen from Figure 8 and Figure 9, the stress concentration of the U-shaped relief groove is the most serious, followed by the circular relief groove and elliptical relief groove. Due to the requirements of the installation, the existence of the flanges at both ends of the torsion spring restricts the axial dimension of the relief groove. In this case, the elliptical relief groove would perform best under the same axial size condition, so the elliptical relief groove was chosen as the optimization object. Because the spiral rising angle of the torsion spring is fixed, the major axis and minor axis of the ellipse are selected as the optimization parameters. Considering the presence of torsion spring flanges, the axial dimension of the relief groove is limited to not more than 1.5 mm.

3.2. Design of Experiments

Design of experiments (DOE), a branch of applied statistics, is a powerful tool for collecting and analyzing data suited to a variety of trials. The commonly used DOE methods include full factor design, orthogonal design, central combination design, uniform design, randomized design, Latin hypercube design, etc.

Latin hypercube sampling (LHS) is a stratified random sampling method [18]. Compared with the absolutely random Monte Carlo method, the Latin hypercube method can efficiently select samples from the distribution interval of variables. If m sample points are to be extracted from the n-dimensional vector space, the Latin hypercube sampling procedure is as follows:

(a) Divide each n-dimensional vector space into m independent regions so that the probability of each independent region is the same.

(b) Randomly select one point from each independent region of each vector space to obtain a total of $m\times n$ sample points and so we get a $m\times n$ matrix (each column represents a vector space).

(c) One sample point is randomly taken from each row to obtain a total of m sample points.

This approach ensures full coverage of each variable range by maximizing the stratification of each marginal distribution.

Based on the Latin hypercube design, the optimal Latin hypercube design improves sampling uniformity by distributing the sample points more evenly in the design space and by achieving better space-filling and uniformity.

The dimensions of the major axis and minor axis of the ellipse were selected as design variables. The optimal Latin hypercube method was applied for the DOE. A total of 100 sample points was selected, and then the parameters were used in structure refactoring. The all-built structures were imported to ABAQUS for calculation. The finite element analysis results of each sample point data and its corresponding model were obtained.

The Pareto chart illustrates how each parameter contributes to the response. Figure 10 shows the Pareto chart of the optimization process, where CZ, DZ and YJ represent the major axis, minor axis and fillet radius of the elliptical relief groove, respectively. The Pareto chart shows that the minor axis has a positive effect while the major axis has a negative effect on reducing the maximum stress. In contrast, the fillet radius has little effect on reducing the maximum stress.

3.3. Establishment of the Surrogate Model

The surrogate model is commonly used in solving engineering optimization problems, particularly when the actual problem (high-precision model) requires a great deal of computation and time. To accelerate the optimization process, the surrogate model can be used to replace the original model with a relatively simple calculation and more rapid solution. The main process for creating an agent model includes:

(a) Obtain the sample data from the DOE.

(b) Select the type of surrogate model.

(c) Initialize the surrogate model.

(d) Calculate the approximation value of the surrogate model to verify its accuracy.

If the surrogate model is not sufficiently reliable, it should be updated to improve the performance. The general approach is to obtain more sample data. When the surrogate model has enough credibility, it can be used to replace the actual, more complex model. Commonly used surrogate models include the response surface model, RBF model (radial basis function neural network model) [19], Kriging model, etc. The surrogate model chosen in this paper is the RBF model, which has the advantages of good nonlinear function approximation ability and generalization ability and has a fast convergence speed.

The classical form of the radial basis function is as follows.

$$f(x)={\displaystyle \sum _{i=1}^p{\lambda }_i{\phi }_i(||x-x_i||)}$$

(4)

where p is the number of sample points; ${\phi }_i$ is the ith basis function; ${\lambda }_i$ is the coefficient of the ith basis function; x is the vector of design variables; $x_i$ is the design variable vector at the ith sample point.

Common basis functions include:

a. The linear function

$$\phi (r)=r$$

(5)

b. The Gaussian function

$$\phi (r)=e^{-c{r}^2}, (0<c<1)$$

(6)

c. The inverse higher degree surface function

$$\phi (r)=\sqrt{r^2+c^2}, (0<c<1)$$

(7)

R², root mean square error (RMSE) and mean absolute relative error (MARE) are used to evaluate the degree of agreement between the surrogate model and the sample points.

$$R^2=1-\frac{{\displaystyle \sum _{i=1}^n{(y_i-{\tilde{y}}_i)}^2}}{{\displaystyle \sum _{i=1}^n{(y_i-\overline{y})}^2}}$$

(8)

$$\begin{array}{l}RMSE=\sqrt{\frac{1}{n}{\displaystyle \sum _{i=1}^n{(y_i-{\tilde{y}}_i)}^2}}\\ \end{array}$$

(9)

$$MARE=\frac{1}{n}{\displaystyle \sum _{i=1}^n\frac{\left|y_i-{\tilde{y}}_i\right|}{\left|y_i\right|}}$$

(10)

where $y_i$, ${\tilde{y}}_i$ and $\overline{y}$ are, respectively, the true value, approximate value and average value of the test points.

The closer the value of R² is to 1, the higher is the reliability of the model.

Table 4. Technique settings of the three surrogate models.

Surrogate Model Technique	Technique Settings	Error Analysis Method
Response surface model	Polynomial Order: Quadratic	Cross-Validation
RBF model	Smoothing Filter: None Basis Function: Radial	Cross-Validation
Kriging model	Fit Type: Anisotropic Correlation Function: Gaussian	Cross-Validation

shows the technique settings of the three surrogate models. Figure 11, Figure 12 and Figure 13 show the comparison of R², the RMSE and MARE of the three surrogate models. Clearly, for the corresponding situation in this paper, the RBF model has the greatest reliability.

4. Parameter Optimization and Structure Reconstruction

Optimization problems often occur in structural design and manufacturing engineering. Because most of the objective functions are nonlinear, discontinuous and nondifferentiable, traditional gradient optimization algorithms and direct search algorithms often fail to find the global optimal solution. In this paper, the multi-island genetic algorithm (MIGA) and the multi-objective particle swarm optimization (MOPS) are used to optimize the established surrogate model. The numerical expression of the optimization process is defined as the following:

$$\left\{\begin{array}{l}objective:minimize\hspace{1em}S(X_i)\\ s.t:X_{il} \le X_i \le X_{iu},\hspace{1em}i=1,2,3\end{array}\right.$$

(11)

where $S$ represents the maximum stress of the structure; $X_i$, $X_{il}$ and $X_{iu}$ are, respectively, the design variable, lower limit value and upper limit value of the design variable.

The genetic algorithm was first proposed by Holland in the 1960s as a stochastic adaptive global search algorithm. This method mimics the natural law of “survival of the fittest” by coding individuals in the optimal solution space and then carrying out genetic evolution operations (selection, crossover, mutation, etc.) on the entire population. This method allows the production of individuals with greater fitness than the parents from the offspring, which allows the optimization of or improvement of the solution through repeated iterations.

The multi-island genetic algorithm used in this paper is an improvement of the parallel distributed genetic algorithms (PDGAs) by M. Kaneko, M. Miki, T. Hiroyasu, et al. This algorithm offers greater computational efficiency compared to traditional genetic algorithms [20].

The multi-objective particle swarm optimization (MOPS) mimics the social behavior of animal groups such as flocks of birds or fish shoals. The process of finding an optimal design point is likened to the food-foraging activity of these organisms. MOPS uses particle swarm to search for the optimal particle in the solution space, without the crossover and mutation operation of the genetic algorithm. Therefore, compared with the genetic algorithm, MOPS has the advantage that it is simple and easy to implement, and there are not many parameters to adjust [20].

Based on the sample data obtained from the previous chapter, the three surrogate models (response surface, RBF and Kriging) were established in Isight. The two algorithms mentioned above (MIGA and MOPS) were used to carry out global optimization. The design variables and the limitations are shown in

Table 5. Constraints on different design variables.

Design Variables	Constraints	Objective
CZ	[1.0–4.0 mm]	Minimize Max-Mises
DZ	[0.5–1.5 mm]	Minimize Max-Mises
YJ	[0.5–2.0 mm]	Minimize Max-Mises

. The parameter settings of the two algorithms are shown in

Table 6. Parameter settings of MIGA [20].

Parameters	Value
Sub-population size	10
Number of islands	20
Number of generations	20
Rate of crossover	0.8
Rate of mutation	0.01
Rate of migration	0.3
Interval of migration	5
Relative tournament size	1
Elite size	0.5

and

Table 7. Parameter settings of MOPS. [20].

Parameters	Value
Maximum iterations	50
Number of particles	30
Inertia	0.9
Global increment	0.9
Particle increment	0.9
Maximum velocity	0.3

.

Considering the limitations of the manufacturing process, the optimized parameters are rounded. The rounded parameters are shown in

Table 8. Optimized parameters of the elliptical relief groove.

Parameters	CZ (mm)	DZ (mm)	YJ (mm)
MIGA—Response surface	2.6 (2.637 *)	1.5 (1.470 *)	1.1 (1.136 *)
MOPS—Response surface	2.6 (2.619 *)	1.5 (1.479 *)	1.1 (1.119 *)
MIGA—RBF	2.6 (2.573 *)	1.5 (1.486 *)	1.1 (1.129 *)
MOPS—RBF	2.6 (2.614 *)	1.5 (1.487 *)	1.2 (1.217 *)
MIGA—Kriging	2.4 (2.377 *)	1.4 (1.381 *)	1.3 (1.341 *)
MOPS—Kriging	2.3 (2.305 *)	1.4 (1.382 *)	1.3 (1.328 *)

Note: The data marked with * are initial data without rounding.

. Table 8 indicates that MIGA—RBF, MIGA—response surface and MOPS—response surface have the same rounded result.

The modified structure built in Catia was imported into ABAQUS for simulation. The ABAQUS simulation results and nCode DesignLife fatigue life analysis results are shown in Figure 14 and Figure 15, respectively. Figure 14 and Figure 15 indicate that the best optimization results come with MIGA—RBF, MIGA—response surface and MOPS—response surface. The peak strain after optimization is 14,150 με, which is 30.7% less than the 20,420 με before the optimization. In comparison with 10,080 cycles before optimization, the life of 18,770 cycles has increased by approximately 86.2%. The overall optimization effect is shown in

Table 9. Optimization results.

Parameters		Reference Scheme	Optimization Scheme	Difference (%)
Simulation results	Maximum strain (με)	20,420	14,150	−30.7
	Fatigue life (cycles)	10,080	18,770	86.2
Tests result	Fatigue life (cycles)	9700	18,000	85.6

.

According to the optimized structural parameters of the relief groove, another batch of test samples was remanufactured and the fatigue life test was carried out under the same test conditions as before. The average life of the test samples is 18,000 cycles, which is increased by about 85.6% compared with the fatigue life of the torsion spring specimen with a circular relief groove of 9700 cycles. The cracking locations of the torsion springs are shown in Figure 16. The tests results are shown in Table 9.

5. Conclusions

Based on strain fatigue, a parametric design optimization method for ultra-high-strength steel structures is proposed in this paper and verified by engineering applications. Firstly, the simulation analysis and fatigue life analysis of the torsion spring are carried out. Based on the simulation results, a parametric optimization design platform is built and the effect of the optimization is verified through simulation and experiment. The following conclusions are obtained:

(1) The finite element method was used to simulate and analyze the ultra-high-strength steel torsion spring. The stress concentration was determined in the relief groove at the end of the torsion spring. Based on the theory of strain fatigue, a prediction of the fatigue life of critical parts was made, which was in line with the test results.

(2) With regard to stress concentration, under the same axial size, the circular, the U-shaped and the elliptical relief groove torsion springs were compared. It was determined that the U-shaped relief groove had the highest stress concentration and the shortest life while the elliptical relief groove had the lowest stress concentration and the longest life.

(3) A co-simulation optimization platform was established in Isight to optimize the shape of the relief groove. The dimensions of the major axis and minor axis of the elliptical relief groove were selected as the design optimization parameters; the optimal Latin hypercube method was used for the DOE and response surface and the RBF and Kriging model were established. The MIGA and MOPS were applied to optimize the surrogate models, which resulted in a reduction of 30.7% in the maximum strain and an increase of 86.2% in the fatigue life for the optimized torsion spring according to the simulation results. The tests result shows that the fatigue life increased by about 85.6% after the optimization.