MMAE 545 PROJECT REPORT

PROJECT TITLE – DESIGN AND ANALYSIS OF FORMULA

SAE RACE CAR FRAME

PROJECT MEMBERS – SAURABH DHURI A20325517

Abstract

The aim of this project is to design and analyze a Formula SAE race car frame for the typical

loading tests it is subjected to. These include Torsion, Bending, Shear and Crash test. The

CAD model of the frame along with the suspension components is designed in Solidworks.

The frame is then imported to Hypermesh where the mesh model is created along with

loading and boundary conditions. Abaqus is used as a solver and Post processor. The results

obtained are analysed and checked for yielding. A convergence study is conducted by

refining the mesh density, only two iterations have been conducted since Hypermesh student

version allows for a maximum of 100000 elements. After analysing the results conclusions

are drawn and necessary modifications to the geometry or mesh are suggested.

An optimization study is also conducted on the rocker of the front push rod suspension.

Hyper works Motion view is used for the Multi Body dynamic simulation of the suspension.

The Formula SAE race car template provided by Altair University is made use of. A static

ride analysis is conducted and the loads acting on the rocker are extracted for Optimization

study using Optistruct. A min volume objective is defined for the geometry, topology

optimization study is conducted on the rocker and the regions of maximum density are

identified. The geometry is modified accordingly and a Finite element analysis is conducted

to confirm it.

Post-processing Mesh model details

Element size - 10

Element type - Shell element ( Tria3 = S3 & Quad4 = S4R )

Thickness – using the initial element size of 10 analysis was performed with

varying shell thickness values (2mm, 2.2mm, 2.5mm, 2.75mm, 3mm,3.2mm)

Thickness of 2.75 was selected from initial analysis based on the fact that

Yielding did not occur in each of the three test cases.

Element count - 35619

Node count - 35176

# of degree of freedom - 211056

Unit system - SI system (mm, N, tonne, sec, Mpa, tonne/mm3)

Material model -

*MATERIAL, NAME=AISI 4130 STEEL

*DENSITY

0.00785,

*ELASTIC

205000.0, 0.29

*PLASTIC

461.0321 , 0.0

822.7405 , 0.11421

1259.6739, 0.2177

Mesh model

Processing

The aim is to perform the standard SAE chassis tests on the designed frame as listed below

and observe the results to check if the stresses generated in each case exceed the yield stress

value. Perform a convergence study on the mesh model by refining the mesh by making it

finer. Evaluating the stress values for different mesh conditions and comparing them.

A dynamic crash test is also performed on the chassis and the deformation of the chassis is

observed. The aim is to have a self crumbling front end of the chassis so as to absorb

maximum force of impact at the same time provide a safe cockpit for the driver at the same

time have minimum displacement around the cockpit region.

Non Linear Static test

Test 1 – Torsion

Test 2 – Bending

Test 3 – Shear

Explicit Dynamic

Test 4 – Crash

Loading and Boundary condition

We have different boundary conditions for each test case. For the first three tests the

boundary conditions and loading are applied at the ends of the 1-D rigid elements which have

been created by connecting the nodes in free space which represent the suspension co-

ordinates to the set of nodes on the chassis. This can be understood better from the images

below, which show the boundary conditions and loading for the first three cases.

Torsion Boundary condition and Loading

Bending Boundary condition and Loading

Shear Boundary condition and loading

For the crash test analysis we have placed a rigid body in front of the front end of the frame

and fixed it. The test has been performed for a head on impact collision at a speed of

140kmph. The velocity has been applied to all the nodes on the chassis. The following image

shows the crash test set up.

Crash test set up

History data

*STEP, INC = 500, NLGEOM = YES

*STATIC

1.0000E-03,1.0 ,1.0000E-10,0.1

*NODE FILE

U

*EL FILE

E

*OUTPUT, FIELD

*NODE OUTPUT

U,RF

*ELEMENT OUTPUT

MISES,LE,PEEQ

For the shear and bending analysis the increments were reduced to 50 and initial increment

size was increased to 0.1 to force run the analysis since it was causing errors with the above

mentioned 500 increments and 1.000E-03 initial increment.

Post-Processing

The following is an evaluation of the results from the analysis performed.

Test 1 – Torsion

Case 1

Shell thickness 2.75mm

Element size 10

Load applied 2000 N couple

Mises stress plot

Peak stress at max deformation = 445 Mpa < Yield stress (462 Mpa)

Case 2

Shell thickness 2.75mm

Element size 8

Load applied 2000 N couple

Mises stress plot

Peak stress at max deformation = 463 Mpa > Yield stress (462 Mpa)

Test 2 – Bending

Case 1

Shell thickness 2.75 mm

Element size 10

Load applied 1000 N

Mises stress plot

Peak stress at max deformation = 168.5 Mpa < yield stress (462 Mpa)

Case 2

Shell thickness 2.75mm

Element size 8

Load applied 1000 N

Mises stress plot

Peak stress at max deformation = 200 Mpa < Yield stress (462 Mpa)

Test – 3 Shear

Case 1

Shell thickness 2.75mm

Element size 10

Load applied 500 N

Mises stress plot

Peak stress at max deformation = 143 Mpa < Yield stress (462 Mpa)

Case 2

Shell thickness 2.75mm

Element size 8

Load applied 500 N

Mises stress plot

Peak stress at max deformation = 154.9 Mpa < Yield stress (462 Mpa)

Conclusion

From all the above results it can be clearly seen that the stress values in all the cases of each

test do not exceed the yield stress value, except for in the case of torsion test it can be seen

that in the case 1 the peak stress value is 445 Mpa which is lower than the yield but upon

mesh refinement of element size to 8 the peak stress value goes up to 463 Mpa which exceeds

the yield stress value. Thus we would need to do a further convergence study by reducing the

element size and comparing the results until we get a stable stress plot. But we are unable to

do that since hyper mesh and abaqus student editions allow for only 100000 elements and

nodes limitation.

For the same reason we are unable to perform a p (element order) refinement of the mesh,

that is converting all the 1st order elements into that of 2

nd order. By doing so we again

exceed the 100000 limit.

The shear and bending tests results are safe and well below yield. The peak stress values have

increased upon mesh refinement but are still way below the yield point.

Thus from the results obtained we can conclude that the mesh model created is safe for

consideration of shear and bending point of view but needs to be analysed further for

torsional rigidity. We could either go for a higher shell thickness, but that would add more

weight which is not desirable or we could modify the geometry to make the frame more

torsionally rigid.

Test – 4 Dynamic crash test

Mises stress plot

Conclusion

It can be observed that yielding does occur as the impact velocity is very high. The peak

stress generated is 1260 Mpa.

We need to observe the displacement plot in order to check for maximum displacement areas

and to observe the deformation of the front end which should satisfy the criteria’s mentioned

earlier in the report.

Displacement plot

It can be observed that the maximum displacement of 203.2mm occurs at the central roll bar

hoop in the negative X direction. Thus further strengthening of the frame is required by

providing additional tubular support members. We cannot have a completely rigid frame

chassis as it would be inefficient in absorbing suspension, road forces. It has to be flexible

enough to absorb the various forces and at the same time be rigid enough to take the load of

the driver, engine and various other components. Thus we need to get a balance between the

two.

Further tests need to be performed after redesigning the geometry with the support members.

Energy plot for crash test

Energy plot for crash test

It can be seen in the graph above that the Artificial energy is maintained at a very low level

which is desired.

The kinetic energy drops upon impact and there is a rise in the internal energy.

The total energy remains constant.

Optimization study

A topology optimization study is conducted on the push rod suspension rocker. The

suspension co-ordinates were input into the template of the Formula SAE model provided by

Altair University. This model was run using Hyperworks Motion View. A static ride analysis

was performed on this model for a wheel travel of 45mm. The following images show the

model set up along with the actual CAD model suspension set up.

Motion view template

Actual CAD model

Model set up in Optistruct

After extracting the forces on the rocker they were transferred on to the rocker geometry in

Optistruct. The optimization model was set up with an objective for minimum volume. The

boundary conditions, loading and the design and non design properties can be seen in the

image below.

Optimization set up model

The green regions are the Design property regions on which the optimization is conducted.

The pink regions are no design property regions which are fixed points, hence they are

excluded from the optimization study.

The constraints applied are on the mounting point where the rocker is attached to the chassis

via a bolted joint which allows for rotation about the Y-axis.

The second constraint has to be applied in order to meet the constraint requirement for

Optistruct. This has been done by constraining the Dof 2,4,5&6 at the shock mount point.

The three forces acting on the rocker and the constraints are applied at the nodes generated

using kinematic couplings.

Results

The results show the element densities. Upon dragging the step bar to the optimum density

plot we get the optimized design pattern as predicted by Optistruct. The image below shows

the optimized design.

Topology optimization for Minimum volume

The generated optimized design is used to modify the CAD model accordingly. The

modifications have been made keeping in mind Manufacturability. The image below shows

the modified CAD geometry of the Rocker along with the original CAD geometry.

Conclusion

The optimization was successful in reducing the mass of the rocker down to 383.91 gms from

552.22 gms.

Optimized design

Mass – 383.91 gms

Original design

Mass – 552.22 gms

Future work

Due to shortage of time further test have not been performed. Future work includes

redesigning the geometry of the frame and performing the torsion test again as well as crash

test.

Future work also includes performing Finite element analysis on the new optimized rocker

geometry and analysing the results and checking if it yields.

Stress plot for optimized rocker design

We can see that the max stress generated is 423 Mpa which is below the yield point of 462

Mpa.