Roof Design

DESIGNING A ROOF OF A CAR USING CATIA

Aim:

            The main aim is to determine the Heat Distortion criteria, Snow Load Criteria, and Section Modulus of the roof and the reinforcements and to check if they are qualifying the given criteria.

Roof:

An automobile roof or car top is the portion of an automobile that sits above the passenger compartment, protecting the vehicle occupants from sun, wind, rain, and other external elements. Because the earliest automobiles were designed in an era of horse-drawn carriages, early automobile roofs used similar materials and designs.

Roof has the following functions:

• Protects from external damage
• Act as a safety gear when a roll-over accident occurs
• Luggage carrier
• Design of the roof also affects in giving aerodynamic shape to vehicle
• Sunroof
• Solar panelled roof in EV

Since the roof has numerous functions. Therefore, the roof has to be stronger enough to withstand the damage experienced by it while roll-over. For that, the roof should have good strength and stiffness. So, the roof is made with embosses and some reinforcements, such as

• Front roof rail 
• Rear roof rail
• Centre roof rail
• Bow roofs

Roof Surface:

Roof is modelled using the styling surface as reference, then the ditch area and emboss are created on it.

The thickness of Main roof is 0.75 mm.

 

Fig 1 Roof surface

They are bonded with the roof through the spot welding and mastic sealant.

While designing the roof, few criteria should be followed, they are visibility, headroom clearance, heat distortion, snow load, curvature study.

Ditch area is provided on all the four sides of the roof. Roof ditch areas are provided to mount roof to the main body of the car also to mount windshield glass for the front ditch area, and to mount tailgate to rear ditch are

Front roof rail:

Front roof rail design should consider headroom clearance and visibility criteria and has mounting area for windshield glass. For additional strength, embosses are been provided.

The thickness of front roof rail is 0.65 mm.

 

 

Fig 1.1 Front roof rail

Rear roof rail:

Rear roof rail is similar to the front roof rail. Rear headroom and rear visibility criteria are considered and also tailgate will be mounted on the rear roof rail so tailgate conditions have to be considered while designing the rear roof rail.

 

Fig 1.2 Rear roof rail

Centre roof rail:

Centre roof rail is a reinforcement support for the roof and it has the bracket for cabin light mount.

 

Fig 1.3 Centre roof rail

Bow roof:

Bow roof has been provided for additional strength especially against snow conditions and rollover situations. In this model, one bow roof has been provided between front roof rail and Centre roof rail and another bow roof has been provided between Centre roof rail and rear roof rail. But the number of bows on the roof is based on the size of the car like small cars do not require a bow because it increases the weight of the car as well as the other rails are enough to provide the support for the roof. But for large cars 3 or more bows are needed to support the roof.

The thickness of Bow roof rails is 0.65 mm each.

 

Fig 1.4 Bow roof 1

 

Fig 1.4.1 Bow roof 2

 

Fig 1.4.2

 

Fig 1.4.3

Assembly:

Front and rear rails are placed and mated in the front and rear of the main-roof respectively. The bow roofs, centre rail and the lamp bracket are placed and mated with the main-roof. The rails are mounted with the main-roof through the mastic sealants and spot welds.

 

Fig 1.4 Assembly surface

Position Analysis:

The position and moment of all the reinforcements are taken and checked, whether it satisfies the heat distortion test and snow load test. Necessary modifications should be taken if it fails to meet the requirements.

Heat distortion criteria:

The roof is directly exposed to sunlight. The temperature changes with respect to time and season, it causes deformation in the roof. In order to prevent failure, it should be designed in such a way else, it gets failure.

It is checked using the formula,

W = [1.73x10^-3xL] +[1.85x10^-8x(R²/t)] +[1.10x10^-3xL]-2.68

Were,

L = Roof Length in X-Direction [mm] (Roof dimension in 0-Y)

R = Roof curvature

R = 2(Rx*Ry) / (Rx+Ry)

Rx = X curvature

Ry = Y curvature

t = Roof plate thickness [mm]

l = Bow Roof Span [mm]

Judgement Condition: OK < 2>

 

From Front roof rail to Bow roof 1

W = [1.73 x 10^-3xL] +[1.85x10^-8x(R²/t)] +[1.10x10^-3xl] -2.68

Were,

R = 2(Rx*Ry) / (Rx+Ry)

= 2(2285.905*5738.279) / (2285.905+5738.279)

R= 3269

W= [1.73 * 10^-3*1921.146] + [1.85 * 10^-8 *(3269.406²/0.75)] + [1.10 * 10^-3*305.508] – 2.68

= 3.323 + 0.263 + 0.336 – 2.68

W=1.242

From Bow roof 1 to Centre  Reinforcement Roof

W = [1.73 x 10^-3xL] +[1.85x10^-8x(R²/t)] +[1.10x10^-3xl] -2.68

R = 2(Rx * Ry) / (Rx + Ry)

= 2(5744.469 * 5077.400) / (5077.400+5077.400)

R= 5390.375

W = [1.73 * 10^-3*1921.146] + [1.85 * 10^-8 *(5390.375²/0.75)] + [1.10 * 10^-3*346.731] – 2.68

= 3.323 + 0.716 + 0.381 – 2.68

W= 1.740

From Centre Reinforcement roof to Bow roof 2

W = [1.73 x 10^-3xL] +[1.85x10^-8x(R²/t)] +[1.10x10^-3xl] -2.68

R = 2(Rx * Ry) / (Rx + Ry)

= 2(9556.682* 4180.246) / (9556.682+4180.246)

R= 5816.343

W = [1.73 * 10^-3*1921.146] + [1.85 * 10^-8 *(5816.343²/0.75)] + [1.10 * 10^-3*361.283] – 2.68

= 3.323 + 0.834 + 0.397 – 2.68

W= 1.874

From Bow Roof 2 to Rear Roof Rail

W = [1.73 x 10^-3xL] +[1.85x10^-8x(R²/t)] +[1.10x10^-3xl] -2.68

R = 2(Rx * Ry) / (Rx + Ry)

= 2(13460.240 * 3454.447) / (13406.240 + 3454.447)

R=5497.906

W = [1.73 * 10^-3*1921.146] + [1.85 * 10^-8 *(5497.906²/0.75)] + [1.10 * 10^-3*460.791] – 2.68

= 3.323 + 0.745 + 0.506 – 2.68

W= 1.672

Table 1. Heat distortion Calculation

 

“l” value

 

“L” value

 

 

 

“R_x & R_y” Value

Snow Load Criteria:

Snow load test used to verify that roof assembly exhibited no permanent deflection due to distributed load representing snow load.

• To calculate the snow load condition, we have a snow load formula
• To measure the required values
• I created a sketch and draw a line on OY axis from the centre if the roof 
• From that line draw a parallel line distance of 100mm on both sides
• Then make intersection points of these lines and draw a three-point arc
• Measure the Radius of the arcs, the arc on the OY axis going to be our Ry and the perpendicular arcs will be Rx.

Qr=Iy×t² / α×S[(Rx+Ry)/2]²×10−8

 

Were,

α = My * L_x ²* 10^-12,

My = Y(Ly-Y)

Judgement condition = Qr ≥ 3.1

250 ≤ s ≤ 380

t = Roof plate thickness [mm]

Ly = Distance between the front and rear roof Rails on the Vehicle along with 0Y[mm]

Length of Roof panel with the centre point between Roof rail Front/Rear as the reference point of the front and the rear.

Lx = Distance between the Left and Right end of the roof on the Roof BOW [mm]

Width of the roof panel exposed on the surface.

Y = Distance front Roof Rail to Roof BOW [mm]

s = Distance for which Roof BOW bears divided load [mm]

s = L₁ / L₂ + L₂ / 2

Iy = Geometrical moment of inertia of Roof BOW (Y cross-section) [mm4]

Rx = Lateral direction curvature radius of roof panel Y cross-section on Roof BOW [mm]

Roof panel curvature Radius of the Length Lx in Front view

Ry = Longitudinal Direction curvature radius of the Roof panel X cross-section on Roof BOW [mm]

Roof panel X curvature radius of length s in Side view.

 

 

R_X Value

 

R_Y Value

Snow load criteria calculation

From front roof rail to Bow roof 1

 

Qr=Iy×t² / α×S[(Rx+Ry)/2]²×10−8

 

α = M_y * L_x² * 10^-12

were,

M_y = y * (L_y – y)

 

α = 305.508 * (1921.146 - 305.508) * (1139.540)² * 10^-12

α = 0.640

 

s = L₁ / L₂ + L₂ / 2.

s = (305.508 / 346.731) + (346.731/2)

s = 174.247

 

known values are,

L_x = 1139.540

L_y = 1921.146

I_y = 2567

y = 305.508

R_x = 4264.629

R_y = 3036.256

Qr=2567×0.75² / 0.640×174.247 [(4264.629+3036.256)/2]²×10−8

Q_r = 97.16

 

Snow Load Tabulation:

Table 2. Snow load calculation

 

In cases where the criterion is not met even after changing the positions of the Bow roofs, changes to the curvature is proposed.

Addition of local embosses on the main roof also increases its strength, apart from enhancing its physical appearance.

 

Section modulus:

 

Section modulus formula

S = I/y

S = Section Modulus

I= Moment of Inertia

y = distance between the neutral axis and the extreme end of the object 

 

Section modulus calculation:

For Roof

 

 

S = I/y

Were,

I = 2007000 mm⁴

y = Total length / 2 = 2135.546 / 2

y = 1067.773

S = 2007000 / 1067.773

Section modulus = 1879.61 mm³

 

 

For Bow roof 1

 

S = I/y

Were,

I = 2567 mm⁴

y = Total length / 2 = 74.956 / 2

y = 37.478

S = 2567 / 37.478

Section modulus = 68.493 mm³

 

For Bow Roof 2

 

S = I/y

Were,

I = 3105 mm⁴

y = Total length / 2 = 74.981/ 2

y = 37.490

S = 3105 / 37.490

Section modulus = 82.820 mm³

 

For Centre Reinforcement Roof

 

S = I/y

Were,

I = 3094 mm⁴

y = Total length / 2 = 84.093 / 2

y = 42.046

S = 3094 / 42.046

Section modulus = 73.585 mm³

 

 

 

For Front Roof Rail

 

S = I/y

Were,

I = 9404 mm⁴

y = Total length / 2 = 124.57 / 2

y = 62.285

S = 9409 / 62.285

Section modulus = 151.063 mm³

 

 

For Rear Roof Rail

 

 

S = I/y

Were,

I = 4306 mm⁴

y = Total length / 2 = 194.63 / 2

y = 97.315

S = 4306 /97.315

Section modulus = 44.248 mm³

 

Section modulus calculation:

Components	I	Y	Section modulus (s)
Roof	2007000	1067.773	1879.61
Front Roof Rail	9404	62.285	151.063
Rear Roof Rail	4306	97.315	44.248
Bow Roof 1	2567	37.478	68.493
Centre Reinforcement Roof	3094	42.046	73.585
Bow Roof 2	3105	37.490	82.820

Draft analysis:

 

Roof

 

Front roof rail

 

Rear roof rail:

 

Bow roof 1:

 

Bow roof 2:

 

Centre reinforcement roof:

I have given the condition for draft angle with a maximum deviation. Anything within that limit is shown in green, which means that the part is producible.

 

Final Assembly

 

 

Conclusion:

Thus, the required reinforcements and Ditch Area for the Roof were designed and developed from the given styling. The curvature study was done after performing calculations for the Heat Distortion and Snow load conditions with the position criterion met for all reinforcements.

Further the Section Modulus study was conducted and Draft Analysis were done for each reinforcement successfully.