Roof Design

INTRODUCTION

An automobile roof is the portion of an automobile that sits above the passenger compartment, protecting the vehicle occupants from sun, wind, rain, and other external elements. In design point of view, it is not so easy to design. Because several support rails should be designed for enough strength to withstand the load. Bow roofs are primarily fixed in flatter region to enhance strength. Front roof and Rear roof rails are fixed to the ditch area using spot weld operation. whereas front bow, rear bow and center roof rails are fixed to roof using mastic sealants.

TESTING OF ROOF:

Roof strength evaluations are conducted on a quasi-static test system. The system consists of an upright assembly and an attached loading head that can be fixed at varying heights from the ground. It also mounted at pitch angles ranging from −5 to +5 degrees to accommodate testing on the driver or passenger side. The roll angle is permanently fixed at 25 degrees. Four hydraulic actuators control the movement of the plate along two linear guides. The entire system is mounted on a T-slot bed plate anchored to the floor of the test facility.

The load is applied to 5 degrees tilted from the front end to the rear end while the load will be in 1800 mm in length and 750 mm in width . The load is applied at the position of 25 degrees from the flatness of the roof . The load is applied on the roof for almost 120 sec and the crush speed at which the load applied is 13 mm/sec.

HEAT DISTORTION STUDY:

Heat distortion temperature is a temperature limit above which the sheet material cannot be used for the structural applications . This study is used to predict the temperature at which the sheet starts to soften when it is exposed to a fixed load at an elevated temperature.

Bow–Roof Prediction Formula :

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]

Judgment Condition

OK< 2.7

Thickness for the Roof(t):

Roof Outer Panel, t= 0.75mm

Front Roof Rail, t = 0.75mm

Rear Roof Rail, t = 0.75mm

Bow Roof Rail Front, t = 0.75mm

Bow Roof Rail Rear, t = 0.75mm

Reinforcement roof rail, t = 0.75mm

ROOF LENGTH (L):

L = 2038.7298 mm

BOW ROOF SPAN (I):

Take the distance from front roof rail to bow roof front for finding the bow roof span(I), in order to measure another bow roof span.

R_X Value:

R_Y Value:

	Rx (mm)	Ry (mm)	Rx * Ry	Rx + Ry	R (mm)	L	t (mm)	I (mm)	W	Result
Front roof - Bow Front	5692.3371	2666.4154	15178135.31	8358.753	3631.675	2038.7298	0.75	457.9396	1.676066	OK
Bow Front - Centre Roof	4769.3301	6297.6021	30035343.25	11066.93	5427.944	2038.7298	0.75	431.4950	2.048391	OK
Center roof - Bow Rear	3762.2344	10475.6298	39411774.8	14237.86	5536.192	2038.7298	0.75	431.6060	2.077788	OK
Bow Rear - Rear Roof	3119.3035	13899.4713	43356669.47	17018.77	5095.158	2038.7298	0.75	328.4230	1.84863	OK

From the above table, all the values are satisfying the condition; W< 2.7 and also W> 3.1. So it is finalised that all the bow roofs areas are placed at the right place.

SNOW LOAD:

Snow load criteria study checks the durability of the roof to withstand the snow fall on it. Also the roof should reflex back to its original shape without any permanent deformation after load (snow) being removed.

SNOW LOAD CRITERIA:

Q_r = [I_Y x t²] / [α x s x [(R_X + R_Y)/2]² x 10^-8]

Where,

α = M_y x L_X² x10^-12, M_{y =} Y(L_y–Y)

Judgement condition = Q_{r ≥}3.1

250 ≤s ≤ 380

t = Roof plate thickness[mm]

L_Y = 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 rails front/ rear as the front and rear reference point.

L_X= Distance between the left and right end of the roof on the roof bow[mm],

With of the roof panel exposed on the surface.

Y = Distance between Front roof rails to roof bow [mm],

s = Distance for which roof bow bears divided load [mm],

s = L₁/2 + L₂/2

I_y = Geometrical moment of inertia of roof bow (Y cross – section) [mm4],

R_X = Lateral direction curvature radius of roof panel Y cross section on roof bow [mm4],

Roof panel curvature radius of the length L_X in front view.

R_Y = Longitudinal direction curvature radius of the roof panel X cross section on roof bow[mm4],

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

R_X Value:

Ry Value:

L_Y Value:

L_X1 Value:

L_X2 Value:

L_X3 Value:

Calculating the Moment of Inertia :

Rear Bow :

Front Bow:

Central Reinforcement Rail:

FINAL RESULTS OF SNOW LOAD CRITERIA:

With the values, the Snow load value(W)is tabulated and calculated:

	IX	LX	LY	L1	L2	Rx	RY	t	y	S	MY	((Rx+Ry)/2)^2	α	Qr	Result
Front roof - front bow	2728.2	1163.04	2038.73	422.26	506.63	2757.5839	2836.2119	0.75	422.26	464.445	682570.6	7822637.86302441	0.923287341332137	45.75	OK
Bow Front - CRR	4068.8	1122.59	2038.73	506.60	506.80	6265.4407	3122.5708	0.75	506.60	506.7	776177.1	22033689.9810331	0.978144829976964	20.96	OK
CRR- Rear Bow	2722.6	1100.44	2038.73	506.78	363.45	16194.1364	4560.4534	0.75	506.78	435.115	776361.6	107688249.441566	0.940149204332406	3.48	OK

Thus the Qr value should be greater than 3.1. And here all the three satisfies the condition.

Draft Analysis:

Front Bow:

CRR:

Rear Bow:

Rear End Rail:

Front End Rail:

Top Body Roof:

Thus the draft analysis is done which shows the components can be drafted to the minimum angle without any fatigue. Thus the parts are manufacturable.