Stress Analysis of the Front Suspension of a Formula Student Racing Car Using Solidworks Simulation Tools

Abstract— the paper covers a simulation of the front suspension system which obtained a better way to analyze the problem. With the help of theoretical study, the simulation was conducted by using composite elements mesh for the system, which leads to a more accurate solution comparing to the single solid mesh model. Keywords—Suspension, Stress, Solidworks, Simulation, FEM.

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Introduction

A. Background

“The Formula SAE ® Series competitions challenge teams of university undergraduate and graduate students to conceive, design, fabricate and compete with small, formula style, autocross racing cars.

”[1] Swansea University has been involved with this competition for almost 13 years. And the main design of this year’s car is optimized by the previous car model – S12 to obtain a better performance. Therefore, the target of the simulations was based on the front suspension system of S12 model. And the analyzing process was provided with the illustration of simple components so that the advantages and optimization of the simulation approach can be presented.

B. Suspension System

The competition rules require the suspension system to ensure that the car should have good riding stability, appropriate vibration absorbing ability and competitive controlling level. Specifically, with the help of suspension system, the car should: (1) Keep stable when accelerating and braking; (2) Decrease the longitudinal incline of the main body; (3) Provide a proper camber angle when cornering; (4) Avoid movement interaction with compact connections between parts; (5) Has reliable load transfer between main body and the tires;(6) Be easy to assembly or maintain; (7) Has enough strength and working life to complete the race. The suspension system can be divided into two main types: dependent and independent.

Comparing to the dependent type, the independent suspension system has many advantages: such as less unsprung mass, less space occupied and no riding interference between right and left side tires. Due to the design flexibility of unequal double A-arms suspension system, it was chose to be the targeting structure of the independent suspension system. Furthermore, It can fulfill the different space requirements of the pull rod connections arrangement to get appropriate dynamic features of the system. The main components of the front suspension system are: (1) Wishbones; (2) Pull rod; (3) Rocker; (4) Shocks & spring; (5) Brackets and bearings; (6) Upright. In this project, the simulations will focus on the first three components to perform an analysis of the load transfer for the front suspension system. Theory

In the analyzing part, many dynamic principles were used to evaluate the movement relationship of different components and decide the basic geometries. In fact, to satisfy the strength requirements of all structures, theoretical mechanics and material dynamics study was conducted to obtain the background knowledge of the calculations. 2-bar trusses with vertical load

Figure 32-bar trusses

Forces within each bar:

F_bar=F/(2 cosα )(1)

Displacement of the top point:

δ_point= Fh/(2EA cos^3α )= FL/(2EA cos^2α )(2)

Where E is the elastic modulus of the material and A is the cross-section area of the truss Bending Stresses of simple cantilever beam wih end load

Figure 2Cantilever beam

In bending, the maximum stress and amount of deflection can be calculated from the following equations:

σ=PL/Z (3)

∆ =(PL^3)/3EI(4)

Where σ=maximum stress along the beam (N/m^2)

∆ = deflection (mm)

P=force load (N)

L=length of the beam (mm)

Z=section modulus

E=elastic modulus (N/m^2)

I=moment of inertia about bending axis

Furthermore, for the cylindrical or tube beams, Z and I can be calculated as: (1) Cylindrical

I=〖πr〗^4/4(5)

Z=(πr^3)/4(6)

Where, r is the radius of the cross-section area.

(2) Tube

I=(π(〖R_o〗^4-〖R_i〗^4))/4(7)

Z= (〖R_o〗^4-〖R_i〗^4)/R_o (8)

A comparison of FE methods for cantilever case

1. Problem definition

The simple tube was fixed at one end and applied a 100N force load to the other one. Besides, basic dimensions were set to be the same as the simulation target – pull rod. 2. FE method details

The material of the model was steel alley. And three basic element types were used to mesh it respectively: tetrahedral element, beam element and sheet element. The mesh plots are shown in Figure 3 to Figure 5:

Figure 3tetrahedral element

Figure 4beam element

Figure 5sheet element

3. Solutions

Conducting the classic Solidworks static FE simulation to the models, the average stress along the tube and the maximum displacement of the tube end can be found in Table 1 below: Table 1Simulation Results

Axial (100N)Bending (100N)

σ (MPa)∆ (μm)σ (MPa)∆ (μm)

Tetrahedral1.8853.162748.22

Beam1.8973.182658,23

Shell1.6852.801725.65

Theoretical1.8953.182678.28

4. Discussion

Considering the data above, the beam element had the closest results to the theoretical solutions while solid mesh was at the second place with the cost of very fine mesh density. However, the shell element was not appropriate for this kind of structure. After all, when choosing the type of meshing element, the original model’s structure feature will be an important parameter: (1) Solid mesh for Rocker, bearing & brackets; (2) Beam element for wishbones and pull rod.

Suspension Analysis

Design specification and material

1. Geometry and dimensions for the racing car – S12

Table 2S12 Specification

ItemsParametersValue

1Total weight280 kg

2Weight distribution (Right : Left)50 : 50

3Weight distribution (Front : Rear)45 : 55

4Cornering Max Acceleration 1.5 g

5Braking Max Acceleration2 g

6Max corning force on one side 4200N

7Max braking force on the front 5600N

2. Material Properties used in Solidworks

Table 3 Material Properties

Steel (T45)Aluminum (Normal)

Modulus of elasticity210 GPa69 GPa

Tensile strength723 MPa69 Mpa

Yield strength650 Mpa27.5 Mpa

Poisson’s ratio0.280.33

Pull rod analysis

1. Target Description

The pull rod is the contacting path of the movement from tires’ traveling to the bump or rebound of the absorber. The simple tube structure was made of steel alley and only axial load was applied along the rod body. Therefore, it was fixed at one end to perform the static analysis which can be assumed

to be a cantilever problem. 2. FE method details

Composite mesh of beam and tetrahedral elements were used to create the simulation. Material was set to be steel for all parts. 3. Solutions

The Stress plots and Displacement plot are as below.

4. Discussion

The average stress along the tube body was 1.31 MPa while the largest displacement was only 2.1μm, which means the pull rod is quite stronger than other components if under same loads.

Figure 11von Mises Stress

Figure 12Zoom plot of Figure 11

Figure 13Displacement Plot

Lower Wishbone Analysis

1. Target Description

The unequal length A-arm wishbones are the typical structures to transfer the loads from the upright to the main body frame. The system has two different levels – upper and lower in which the upper one is also linked to the pull rod. Besides, classical ball bearings are used to be as the connections to brackets or the upright. 2. General Approach

The fundamental analysis process was the same as the rocker component. A standard FEM static study was conducted to the lower wishbone: The material of the wishbone was chose to be Steel alley (detailed material properties can be found from Table 3). The two ends which connected to the brackets were set to be pivot points with only rotational movements. In the mean time, both lateral and longitudinal loads caused by corning and braking respectively were applied to the rod end left. That was the extreme situation of the driving situation. The meshing element type of the wishbone was beam element due to the constant cross – section area feature it has. 3. Solutions

The axial and bending stress distribution plot and deformed displacement plot are as below in Figure 11 and 12.

Figure 11

Figure 12

4. Discussion

From the simulation results, the maximum stress was 50.2 MPa occurring at the intersection point of the two rods which was safe from buckling. Meanwhile, nearly 0.1 mm of deformation existed in the middle of the wishbone. However, comparing to the length (352mm), it can be acceptable as well.

Above all, the beam element used for meshing saved quite a lot of the solution time and disk space. That is, it is much more efficient than the tetrahedral element for this kind of structures. Rocker Analysis

1. Target description

The rocker is a component of front suspension assembly of the racing car S12 which undertakes the movement transferring job. It consists of the main base and three bearing housings as seen in Figure below on which ball bearings are connected to pull rod and the shocks. 2. General approach

A simplified model containing only the basic structures shown in Figure below was built in Solidworks and the analysis performed on it was basic finite element static study. Above all, a stress concentration analysis was completed to prove the strength of the rocker under simple loads. The model was made up of different assembly parts with bearing and bonded connections. The material of main base was Aluminum Alley (Normal) while the bearing housings were fabricated from Steel Alley (T45). The rocker is designed to transfer the movement from pull rod to the shocks under the rule of leverage. Thus, one of the bearing housings was set as a pivot point with fixed hinge features; another one was fixed only vertically. And a pre-set load (400N) was applied to the last housing with an angle of 45 degrees to the horizontal plane. 3. Mesh and Solutions

The model was meshed using tetrahedral elements with different mesh density (From coarse mesh to fine mesh):

Figure 6 Coarse mesh

Figure 7 Medium Mesh

Figure 8 Fine Mesh

Using fine mesh model as the illustration with zoom and section clipping plot, the stresses distribution based on von Misses criterion and displacement plot with deformation are shown below in Figure 9 to 10:

Figure 9von Mises Stress

4 Figure 10Displacement Plot

4. Discussion

The maximum stress obtained for the main base is 69.6 MPa which is in general below the yield point of the material. And from the distribution situation, it can be predicted that the high stress concentration may occur at the contacting edge between the base and housing as the load increases. Moreover, the largest deformation of the whole body was around 42μm. Comparing to the basic dimensions of the base, it can be neglected in the study. By refining the mesh density, it can be found that the detected stress range was expanded and the largest displacement was also increasing. As a matter of fact, the simulation got more accurate. And the cause of the phenomena can be obtained by studying the relationship between the thickness of the base and the element size. In reality, the material added by welding or the designed fillet part will eliminate the sharp corners and straight edges which directly lead to stress concentration area. In other words, the fillets or welds will add strength to the structure. Assembly Analysis

Problem Definition

FEM Details

Solution

Discussion

More details will be provided in the final version of the paper. Summary Conclusion

The project was not finished yet. The assembly simulation with composite mesh elements will be provided in the final version. Acknowledgment

I would like to thank Dr. Ian Masters, the supervisor of the project, for all of his help and encouragement while I was writing this paper. And I also would like to thank Mr. Ed Carter and Adam Pickard, Formula student team member, for their instructions of the research work. References

SAE International community, Formula SAE Lincoln Event Guide, 2013 edtion. John C. Dixon. Suspension Geomytry and Computation. Wiley, PEP, SAE. The Open University, Great Britain..Tl.257.D59.2009 Bernd Heing and Metin Ersoy. Chasis Handbook. 3rd edtion. 978-3-8348-0994-0.2011..