Roof challenge

DESIGN OF ROOF AND CURVATURE ANALYSIS

Roof Analysis:

The primary objective of a roof is to prevent the ejection of passengers, protection against hard local contact and various environmental conditions like heat, snow, rain etc. The roof panel serves as a connection of body sides, front, and rear roof members. Steel sheets of thickness in the range of 0.70 to 0.85 mm are used conventionally for construction of the roof.

Fig.1: Top view of the roof

Objectives:

• For the Given Roof styling, Develop the essential flanges and reinforcements.

• Provide appropriate dimension and check for Draft analysis and perform section modulus analysis on the 0-Y section.

• Do a curvature study on the roof and perform calculations to determine the position of the Bow-roof.

Roof of an automobile:

Types of roof reinforcements are as follows:-

• Front roof rail reinforcement (FR)
• Centre roof rail reinforcement (CR)
• Bow roof 1 rail reinforcement (BR1)
• Bow roof 2 rail reinforcement (BR2)
• Rear rail enforcement (RR)

Fig.2: Parts of the roof assembly

1. Ditch Area:

It is the extended portion of the main roof concealed by other BIW panels and not a styling surface. Headroom clearance, visibility criteria, clearance for windshield and backdoor are some of the factors to be considered while designing the ditch area.

Fig.3: Roof with ditch area

2. Front Roof Rail:

It is the support that is joined with the windshield glass, bodyside outer and the inner panels. It is usually made from body side outer scrap and therefore the thickness of the rail is 0.65 mm. A draft angle of 3-5 degrees is provided for deep-drawing operation. The visibility criteria and the headroom clearance of the passenger are taken into consideration for the bottommost flange. Windshield end and the roof end are spot welded and the other end of the front roof rail is joined with the roof using mastic sealants for increased strength.

Fig.4: Front Roof Rail

3. Rear Roof Rail:

It is the support that is joined to the backdoor, the bodyside outer and the inner panels. Inputs from the backdoor design is also taken to accommodate the required clearance along with headroom clearance and the rear visibility criteria while designing the rear roof rail. Spot welds are applied at the backdoor end of the rail and the other end is joined with the roof using mastic sealants.

Fig.5: Rear Roof Rail

4. Centre Roof Rail and Bow Roofs:

Similar to other rail designs, we have to take into consideration the headroom clearance and the visibility criteria while designing the centre roof rail and bow roofs. Unlike the front and rear roof rails, spot welds are not applied for joining these rails to the roof. Mastic sealants are introduced at both the ends instead of spot welds since centre roof rail and row roofs are fully positioned under the styling surface of the roof.

Fig.6: Bow roof 1

Fig.7: Center rail roof

Fig.8: Bow roof 2

Calculations to determine bow position:

1. Heat Distortion Criteria:

Heat distortion temperature is the temperature at which the metal softens and deforms under a specific load. This study is done to check the ability of the roof to withstand high temperature with respect to the positioning of the reinforcements which contribute to increased strength.

W = [1.73 x 10^(-3) x L] + [1.85 x 10^(-8) x (R^2)/t] + [ 1.10x10^(-3) x l] - 2.68

Judgement Condition : OK<2.7<NG

Where,

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]

ROOF	L	Rx	Ry	R	t	l	W	Condition
FR & B1	2028.53	6367.56	2511.72	3602.44	0.75	358.6	1.54	OK
B1 & CRR	2028.53	5336.7	6109.52	5697.02	0.75	384.4	2.05	OK
CRR & B2	2028.53	4056.7	11331.78	5974.55	0.75	367.8	2.11	OK
B2 & RR	2028.53	3361.1	16412.92	5579.59	0.75	265.6	1.89	OK

From the above table, it is concluded that the designed roof satisfies the heat distortion criteria.

2. Snow Load Criteria:

Snow load criteria study is done to check the ability of the roof to withstand snowfall and bounce back to its original shape without any permanent deformation once the load is removed.

Snow load Prediction formula

Qr = [Iy x t²] / [α x s x [(Rx + Ry)/2]² x 10^-8]

Note: The Qr value given over here is correct. There was a typo error in the formula given in the video.

Where

α = My x Lx² x 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 center 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 Front Roof Rail to Roof BOW[mm]

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

s = L1/2 + 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	AREA MOMENT OF INERTIA I(y)	t	Y	Ly	Lx	My	alpha	L1	L2	S	Rx	Ry	Qr	CONDITION
FR & B1	1589	0.75	471.6	1954.1	1109.21	699147	0.860207	471.6	581.2	494.9	4336.6	2513.6	17.89	OK
B1 & CRR	1662	0.75	518.4	1954.1	1071.47	744266	0.854468	581.4	502.7	510.55	3798.5	6121.4	8.71	OK
CRR & B2	1604	0.75	502.7	1954.1	1053.14	729618	0.809223	502.7	461.4	485.05	4517	11270	3.71	OK

From the above table, it is concluded that the designed roof satisfies the snow load criteria.

Section modulus:

1. Front roof rail:

2. Bow roof 1

3. Center rail roof

4. Bow roof 2

5. Rear rail roof