**Introduction: **

This project deals with the analysis of the roll Cage for the Formula Student Car. In a Formula Student Car, the roll cage is one of the main components. It forms the structure or the main frame of the vehicle on which other parts like engine, steering, and transmission are mounted. It must be of adequate strength to protect the driver in the event of a rollover or impact. Computer simulations are usually used to check the strength of the roll cage of a vehicle. There are many software and solvers available that are used for this purpose. We will be using Altair Hyperworks 13.0 with Radioss as the solver.

**Objective**

To simulate the impact between the roll cage and a rigid wall when the vehicle is travelling at 60 Kmph and study the:

- Stress distribution
- Deformation of the roll cage.

Then, we will calculate the Factor of Safety for the design and decide if the model is safe for commercial purposes.

**Steps to be done:**

- Perform Geometry cleanup
- Mesh the geometry
- Specify properties, material to be used and other parameters
- Design the wall
- Post-process the data
- Obtain the results

**Geometry Cleanup**

### Software used: Radioss

The mid-surface of the roll cage is extracted from the given CAD model. Since the roll cage is symmetrical in design, we can split it into two halves along the X – Direction, perform cleanup on one half of the design and then duplicate the other half. To split the existing design, we can use the **Surface trim** option. One half is moved to the new created component where the geometry is cleaned. The joints are trimmed and extended using the **Extend option**. The intersecting surface are again trimmed and deleted to ensure that the joint is a hollow joint.

In the images below, you can see the differences between an unclean geometry and a clean geometry:

Distorted Joint

Repaired hollow joint

**Meshing**

After the geometry is cleaned, we will then mesh the entire geometry by fragmenting the structure into smaller components called finite element. This is done so that the effect of the stress and deformation can be calculated across every finite element.

When a meshed geometry is impacted with a force, the force vector travels through the geometry like a wave and affects every finite element. This is called as mesh flow. It is important to ensure that this force travels without being deflected by the shape of the finite elements. In order to ensure that our model has a better mesh flow, we use the Mixed mesh type. By using a mixed mesh, we employ a mixture of tria (triangular) and quad (quadrilateral) elements throughout the whole geometry. Since tria elements are stiffer than the quad elements they are used as little as possible without compromising the mesh flow.

In this image here, you can visualize how the geometry would appear after meshing:

*One half of the geometry fully meshed.*

*Clear View of the Mesh.*

**Element Quality Parameter**

Parameter | Value |

Warpage | 15 |

Aspect | 5 |

Skew | 60 |

Chord Dev. | 0.1 |

Cell Squish | 0.5 |

Length | 6 |

Min. length | 4 |

Max. length | 8 |

Jacobian | 0.7 |

Equia. Skew | 0.6 |

Area Skew | 0.6 |

Taper | 0.5 deg |

Tria Min. angle | 20 deg |

Tria Max. angle | 120 deg |

Quad Min. angle | 45 deg |

Quad Max. angle | 135 deg |

The element quality parameter is used to specify the criteria to be fulfilled by every finite element. Only when all the elements in the meshed geometry fulfill this criteria, they are duplicated and reflected to the other half. In the table above, you can see the element quality parameters to be fulfilled by the elements in the roll cage. Once all the finite elements fall in this criteria, a full design of a clean and meshed roll cage is obtained.

*Fully meshed geometry.*

**Property Card**

Property card selected- P1 Shell

Parameter | Value |

Ishell | 24 |

Ishell | 2 |

N | 5 |

Ithick | 1 |

Iplas | 1 |

The property card is used to specify the properties of the roll cage. The thickness of the roll cage is defined in the property card as 2.5 mm.

**Material Card**

The material for the model is defined in the material card. The material parameters used in this case are:

Material defined – Steel 4013

Material Card used – M2 PLAS JOHNS ZERIL

Parameter | Value |

Density | 0.78e-6 |

Young’s Modulus | 210 |

Poisson ratio | 0.29 |

Plastic yield stress | 0.70 |

Plastic Hardening | 0.23 |

Hardening Parameter | 0.21 |

Plastic maximum stress | 0.75 |

**Contact**

Contact is defined as the point or the area where two geometries come into contact. This can happen during collision, welding etc. The model is defined with a Type – 7 contact so that it has self-contact in the event of impact. In other words, during impact, the finite elements of the geometry come into contact with each other due to the impact of the force. The contact parameters are listed below.

Parameter | Value |

Istf | 4 |

Igap | 3 |

Idel | 2 |

Gapmin | 0.5 |

Iacti | 6 |

Iform | 2 |

**Load Collector**

The load collector is used to specify the loading conditions such as initial velocity. In our case, the initial velocity is added to every node of the roll cage to replicate the forces acting on the vehicle in real life environment. The initial velocity of 16.66 mm/ms is added to the roll cage in the positive X – Direction using INVEL card in BC manager.

**Rigid Wall**

Two Rigid walls are created using the Rwall card in the side of the roll cage at the distance of 20 mm in normal to positive – X direction and at the bottom at the distance of 10 mm along the positive Z – direction. The rigid walls are created such that it acts as the master node and all the nodes in the roll cage acts the slave node. (When two nodes or surfaces interact, the master nodes indicate to the nodes that are unaffected by the forces acting on them and the slave nodes indicates the nodes which are impacted by the forces).

*The master nodes are indicated in blue and the slave nodes are indicated in red.*

**Output Block**

The Output Block is created to request results which we require. By default, the Output Block displays parameters like displacement, velocity etc. We use this to specify the data we need to extract.

**Control Card**

The control cards are defined in order to optimize the simulation. They are used to specify parameters such as the amount of time the simulation needs to run, the velocity involved etc. Basic cards that are defined are ENG_Run, ANIM_DT, ENG_Tfile and other required result cards are also requested.

Once all the above steps are completed, the simulation is made to run on the **Radioss Solver.**

**Post Processing**

### Software used: HyperView 13.0

Now the output file are examined. The animation file is loaded in the HyperView and the results like Plastic strain, Von mises stress are observed visually.

Plastic strain

Von Mises Stress

Then the graph is studied in Hypergraph by loading the T0 file. The Internal energy, Kinetic energy and the Total energy is plotted. The Total energy remains constant and the Internal energy increases while the Kinetic energy drops during the impact.

You can view the animation results here:

**Result**

The maximum Von Mises stress is 0.749 KN/mm2

Deformation = 0.478mm

Factor of safety 0.750/0.749 = 1, Which indicates the design is moderately safe (not taking human presence into account)

**Conclusion:**

Thus, we have calculated numerically, the amount of forces acting on a roll cage during impact. Since the safety factor is 1, the design is moderately safe to use. However, if we were to consider a human inside the roll cage during the impact, then this design is not safe enough to protect the person inside. By simulating the results in HyperView, we were able to visualize the areas where the force impacts the greatest. To make the design long-lasting and increase the safety factor, we can redesign the model to make the areas of higher impact more durable and then recheck the design using the steps mentioned above.

Project submitted by,

Sathesh Chandrasekar

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