Roof Design

Objective:

To design a roof for an automobile with given master sections and satisfy the roof curvature analysis for Heat distortion and Snow Load criteria.

Design Considerations:

• Headroom clearance
• Bow roof position
• Heat distortion and Snow load criteria
• Draft analysis
  
  

Input:

Styling:

Final Design:

Roof Outer Panel with Ditch:

Front Roof Rail: Added Embosses for improved material properties.

Rear Roof Rail: Added Embossing and Darts (Stiffener) fro improved material properties.

Bow Roofs on either side of the Center roof rail:

The bow roofs and the center roof rail will be spot-welded onto the side flanges and/or the pillars from the BiW, while they will be attached to the roof outer using mastics. The front and rear roof rails will also be attached to the outer roof with mastics (sealant).

Curvature Analysis:

Heat Distortion:

This analysis aims to study the deflection of roofs in high-temperature conditions. This is predicted by calculating:

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

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];

The acceptable maximum value for W is 2.7.

Results:

HEAT DISTORTION
Roof Section	Rx	Ry	Rx*Ry	Rx+Ry	R	L	t	I	W	Status
Front - Bow 1	5726	2738	15677788	8464	3704.581	2029	0.75	462	1.676893	OK
Bow 1 - Center	4837	6742	32611054	11579	5632.793	2029	0.75	390	2.041803	OK
Center - Bow 2	3960	10672	42261120	14632	5776.534	2029	0.75	370	2.060256	OK
Bow 2 - Rear	3260	14719	47983940	17979	5337.776	2029	0.75	391	1.963069	OK

Snow Load:

This analysis aims to understand the deflection of the roof when a load is applied on top of it. This is predicted by calculating:

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)

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 front and rear reference point.

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

The width of the roof panel is 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 panel X curvature radius of length s in Side view;

The minimum acceptable Qr value is 3.1 when the value of 's' ranges between 20 and 380.

Results:

SNOW LOAD
Roof Section	Iy	Lx	Ly	L1	L2	Rx	Ry	t	Y	S	My	α	Qr	Status
Front - Bow 1	2215.9	1134	2029	462	390	4415	2776	0.75	545	426	808780	1.040055	19.92599	OK
Bow 1 - Center	2243.6	1082	2029	390	370	3780	6677	0.75	470	380	732730	0.857825	12.80761	OK
Center - Bow 2	2228.7	1058	2029	370	390.5	4284	11193	0.75	450	380.25	710550	0.795364	6.301672	OK

Draft Analysis:

The minimum draft angle for sheet metal manufacturing is 7 degrees.

Roof :

Front roof rail:

Rear roof rail:

Bow Roof 1:

Bow Roof 2:

Center roof rail: