The Bajara Team simulated their off-road vehicle's roll cage structure using Ansys software prior to construction to prepare for a competition. Modal analyses found vibrational frequencies that could fatigue welding points. Collision and rollover simulations showed the roll cage would protect the pilot despite possible damage. Next steps are to modify the design to dampen vibrations and transform the vehicle into an agricultural machine suitable for small farms.

2. Introduction
The Bajara Team from the Federal University of the West of Pará,
located in Santarém - Pará - Brazil, carried out simulations of several
situations that could occur, using Ansys software, before the
construction of its off - road vehicle. The general purpose is to
participate in the 22nd SAE Brazil Baja Competition that occured in the
city of São José dos Campos - SP - Brazil. The vehicle's roll cage is the
object of study.

3. The roll cage is the sustaining structure of all vehicle subsystems. It is
also responsible for protecting the pilot's life on specific conditions of
impact. A structure for this purpose shall be deformed and ruptured
before transferring the energy of any loads suffered to the subsystems
or to the pilot.

4. Objectives
Simulate the response of vehicle's roll cage in the following situations:
free body modal analysis; rigid body modal analysis; roll cage's
behavior when it's subjected to frontal and lateral collisions; roll cage's
behavior in rollovers. All of this is necessary to the identification of
sharp or fatigue frequencies at welding points when the vehicle is
traveling on uneven ground or accidents and it is important do
determinate if pilot’s life is protected.

5. Vocabulary
The following vocabulary will be adopted :
Rear Roll Hoop (RRH) ;
Roll Hoop Overhead members (RHO);
Lower Frame Side members (LFS) ;
Front Bracing members (FBM) ;
Lateral Cross Member (LC) or (FLC);
Figure 1: Roll cage tubes.

6. Modelo de análise
Figure 2: Chassis model designed in a computer aided design program (CAD). Figure 3:Real model picture.

7. Figure 4: Details of the geometry used in ANSYS
Figure 5 : Details of the other masses (pilot, engine and steering system) that
are part of the structure.

8. Figura 6: about the mesh applied in the geometry.

9. Figure 7: units of measurement adopted..

10. O material do chassi: aço SAE 1020
Name: Steel SAE 1020
Type of model: Isotropic Linear
Flow limit :
𝟑, 𝟓𝟏𝟓𝟕𝟏 ∗ 𝟏𝟎 𝟖
𝑵
𝒎 𝟐
Strength:
𝟒, 𝟐𝟎𝟓𝟎𝟕 ∗ 𝟏𝟎 𝟖
𝑵
𝒎 𝟐
Young’s Modulus:
𝟐 ∗ 𝟏𝟎 𝟖
𝑵
𝒎 𝟐
Poisson’s ratio: 0.29
Specific mass:
𝟕𝟗𝟎𝟎
𝑲𝒈
𝒎 𝟑
Shear modulus:
𝟕, 𝟕 ∗ 𝟏𝟎 𝟏𝟎
𝑵
𝒎 𝟐
Table1:steel pipe’s material.

11. Análise moda de corpo livre
Frequency(Hz)
As the first six frequencies are zero,
Ansys had no trouble recognizing a
geometry.
Figure 8: The first six frequencies are zero in free body modal analysis.
Table 2 :the first Twelve natural frequencies of the structure.

13. Vista geral
Figure 9: six first modes of vibrating with the structure attached to the
suspension system.
Table 3: Six first frequencies of rigid body.

14. Torsional frequency capable of causing fatigue to RHO and LC joints.
Click on the image to animate

15. Torsional frequency capable of causing fatigue to LFS and USM joints.
Click on the image to animate

16. Torsional frequency capable of causing fatigue to LFS and USM joints and with greater
intensity and involving more parts of the structure.
Click on the image to animate

17. Torsional frequency capable of causing fatigue to RHO
joints causing fatigue to it's welds. Other regions of the
roll cage also dissipate energy .
Click on the image to animate

18. Torsional frequency capable of causing fatigue to the joints at the
rear of the frame where the engine and fuel tank are fixed. The
energy is also dissipated through RHO.
Click on the image to animate

19. Torsional frequency capable of causing fatigue to
RHO joints.
Click on the image to animate

20. Static structural analysis
This is true for rollover and
collision analysis.
Figure 10: details of static structural analysis.

21. Rollover
The forces applied to the roll cage were calculated with basis on
vehicle's mass and adr59 from the Australian Protocol. The forces used
are: front load; side load; vertical load. All these applied to LC upper
front. The choice of this element is due to this being the least resistant
part of the structure in a possible rollover. The hypothesis adopted for
the value of the forces is based on the speed developed by the vehicle
in the competion conditions. It is possible to deduce the height of jump
force of impact with the ground when the vehicle passes through a
ramp in its maximum speed.

22. Front load
5880N

23. Details of force
Relation time (s) Vs Force (N)

24. The previous figure and the animation above shows the deflections. It is observed in the structure that the maximum deflection
point is in the LC, exact location of application of the rollover frontal force. It is also possible to notice that the deformation is
greater in RHO tubes. The deformations presented are within the safety and comfort limits of 150 mm from SAE and 100 mm
from adr59. The largest deflections are observed in the FBM.
Click on the image to animate

25. 4440N

26. Details of force
Relation time (s) Vs Force (N)

27. The previous figure shows deflections contours. The limits of deflections are within those
recommended by the SAE (150 mm) and adr59 (100 mm). The amplitude of such displacements
begins to cause the application of undesired forces to the pilot, but is not, however, dangerous.
Click on the image to animate

28. 11760N

29. Details of force
Relation time (s) Vs Force (N)

30. The figure shows the deflections contour. The points of greatest deflection are LC and RHO. The range of displacement
shows comfort and absence of danger to the pilot.
Click on the image to animate

31. Collision Forces
The collision forces presented in the model were estimated based on
the linear momentum variation rate. The mass used was the vehicle’s
mass with all its subsystems which is approximately 250 kg. The speed
used was 60 km / h, the maximum speed in which the effects of air
resistance are negligible.

32. 249000N
249000N

33. Details of force
Relation time (s) Vs Force (N)

34. This force was estimated when the vehicle is in a straight line and with maximum speed (60 km / h). The figure shows the deflections
contour. The deflection is larger in the Front Bracing Members (FBM) and propagates to the back of the structure decreasing in
amplitude as it progresses. Its maximum value is within the limits of safety and comfort(SAE and adr59).
Click on the image to animate

35. 249000N

36. Details of force
Relation time (s) Vs Force (N)

37. The previous figure and the animation above shows the deflections contour.
Maximum deflections show that the safety limit is not exceeded, but much
of the impact energy will be transmitted to the pilot.
Click on the image to animate

38. Conclusion
The free body and rigid body modal analyzes clearly show that the built structure is subject to
vibrations that can quickly wear out your weld points when the vehicle operates under
required conditions for a long time. This problem will be solved by changing the geometry of
the cage by placing additional tubes to dampen such frequencies.
The collision and rollover assumptions adopted are the worst possible that the team was able
to identify. The simulations show that even in these situations the physical integrity of the
pilot will be protected although the chassis may suffer irreversible damage.
The next steps will gradually transform the vehicle into an agricultural equipment capable of
serving small producers who do not need very large machines, but at the same time can no
longer use hand tools. For this the design requirements will be more robust to be able to
specify a machine that, as in the initial design, is able to walk on extremely rugged terrain
and full of obstacles and can pull heavy loads.

39. Sources
• Ansys Costumer Portal(tutoriais sobre o ANSYS). Available
in<https://support.ansys.com/portal/site/AnsysCustomerPortal>
• Vehicle Standard (Australian Design Rule 59/00 – Standards For
Omnibus Rollover Strength) 2007. Available in: <
https://www.legislation.gov.au/Details/F2012C00535 >
• REGULAMENTO BAJA SAE BRASIL CAPÍTULO 7 REQUISITOS
MÍNIMOS DE SEGURANÇA. Available in: <
http://www.saebrasil.org.br/eventos/ProgramasEstudantis/site/baja2
011/Arquivos/RBSB%207%20-
%20Requisitos%20Minimos%20de%20Seguranca%20-
%20Emenda%202.pdf >