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ROOF DESIGN
AIM:
To create an ASSEMBLY for the given styling surface of the roof by developing the essential flanges for the outer roof and creating the reinforcements.
OBJECTIVE:-
To design roof and roof reinforcements from the styling surface received
To calculate heat distortion and snow load calculation on the OY section of the roof.
ROOF DESIGN:
Front Roof Rail:-
This is the reinforcement provided at the front. This part is joined to the BIW body and windshield. Visibility criteria are taken into account for joining it with the windshield. It is fixed to BIW with spot welds and the roof surface is attached with the help of mastic sealants. A draft angle is provided for deep-drawing operation. Draft analysis is also done on the section to check its manufacturing ability.
Bow Roof_1:-
It is an additional reimforecmentprovided to increase the strength of the roof. It is fixed with a roof body with mastic sealants.
Centre Roof Rail:-
Centre rail roof can be considered as reinforcement joining exact center to the outer roof. It is fixed to the roof by mastic sealants and BIW by spot welds.
Bow Roof_2:-
It is similar to the bow roof_1 provided for better strength.
Rear Roof Rail:-
It is the reinforcement provided at the rear side of the roof. Backdoor and body side panels are attached to this part. It is also attached with mastic sealant and spot welds.
HEAT DISTORTION CALCULATION:
The heat distortion study plays an important role in sheet metal usage. Heat distortion temperature is a temperature limit above which the material cannot be used for structure application. This study is used to predict the heat distortion temperature at where the material is starting to soften when exposed to a fixed load at elevated temperature. To avoid bending or damages on the roof, based on heat distortion temperature, this study will predict the bow roof position on the roof to strengthen the roof.
Heat Distortion Criteria: -
W = [1.73 x 10^(-3) x L] + [1.85 x 10^(-8) x (R^2)/t] + [ 1.10x10^(-3) x l] - 2.68
Condition: OK< 2.7> 3.1
Here,
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 thickness of the roof
Roof Outer Panel,t = 0.75 mm
Front Roof Rail, t = 0.75 mm
Rear Roof Rail, t = 0.75 mm
Bow Roof Rail_1, t = 0.75 mm
Centre Roof Rail, t = 0.75 mm
Bow Roof Rail_2, t = 0.75 mm
Roof Length for styling surface(L)
For the L we want to take the total length of the styling surface don't include the ditch area
Bow Roof Span(l):-
Here we want to find the distance from the front roof rail to bow roof_1 to find the bow roof span as shown in fig, Similarly, we can measure the remaining span distance also want to measure.
Finding Rx & Ry (X & Y Curvature):-
Projects the points and make the arc
Apply the values in the formula:-
To find the Heat distortion apply all the necessary values from the roof of the given formula.
HEAT DISTORTIONS CRITIRIA CALCULATIONS:
W = [1.73 x 10^(-3) x L] + [1.85 x 10^(-8) x (R^2)/t] + [ 1.10x10^(-3) x l] - 2.68
R = 2(Rx*Ry)/(Rx+Ry)
ROOF RAILS |
Rx(mm) |
Ry(mm) |
R(mm) |
L(mm) |
t(mm) |
l(mm) |
W |
Result |
FR-BOW1 |
5708.15 |
2915.78 |
3859.89 |
2102.8 |
0.75 |
615.48 |
2.0 |
OK |
BOW1- CR |
4788.77 |
14461.6 |
3624.6 |
2102.8 |
0.75 |
1217.96 |
2.62 |
OK |
CR- BOW2 |
4061.6 |
4021.4 |
4041.4 |
2102.8 |
0.75 |
360.4 |
1.75 |
OK |
BOW2-RR |
2667.25 |
14250.2 |
4493.4 |
2102.8 |
0.75 |
1295.9 |
2.68 |
OK |
HEAT DISTORTION CALCULATIONS
From the above table, it can be concluded that all values of W<2.7 and also not W > 3.1 so thus infer that the current positioning of bow roofs are good in the state as per the design and found OK.
SNOW LOAD PREDICTION:
Snow load prediction study is done to check the durability of the roof to withstand snowfall and reflex 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]
here
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 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
To measure the Rx & Ry (X & Y curvature)
Previously we calculate the Rx & Ry in heat distortion criteria at this time we calculate the values at the center of the roof
Find the Rx Curvature and Ry Curvature
RY CURVATURE:
LX VALUES:
LY VALUE:
Moment of Inertia for the roof rails:
BOW ROOF 1:
CENTRE ROOF :
BOW ROOF 2:
Apply the values in the formula: To find the snow load applies all the necessary values from the roof to the given formula.
Qr = [Iy x t2] / [α x s x [(Rx + Ry)/2]2 x 10-8]
Where
α = My x Lx2 x 10-12 , My = Y(Ly-Y)
s = L1/2+L2/2
SNOW LOAD CRITERIA CALCULATION
Roof Rails |
Iy(mm) |
Lx(mm) |
Ly(mm) |
L1(mm) |
L2(mm) |
Rx(mm) |
Ry(mm) |
t(mm) |
Y(mm) |
S |
My |
α |
Qr |
Result |
FR-BOW_1 |
163.5 |
1158 |
2060.4 |
529 |
314.7 |
4289.3 |
2974 |
0.75 |
529 |
421.8 |
810134.77 |
1.086 |
6.67130 |
OK |
BOW_1-CR |
167.2 |
1110.7 |
2060.4 |
314.7 |
284.9 |
3816.5 |
4538 |
0.75 |
314.7 |
299.8 |
1023099.5 |
0.677 |
4.97254 |
OK |
CR-BOW_2 |
164.6 |
1089.9 |
2060.4 |
284.9 |
466.8 |
6191.7 |
5881.4 |
0.75 |
284.9 |
375.8 |
505839.9 |
0.688 |
3.56 |
OK |
It is observed from the values that obtained values of Qr > 3.1
THUS, ALL THREE ROOFS SATISFY THE SNOW LOAD CONDITION
Section Modulus:
Section modulus is a geometrical property for a given cross-section used on the design of beams or flexural members. Other geometrical properties used in the design include an area for tension and shear, the radius of gyration for compression, the moment of inertia, and the polar moment of inertia for stiffness. Any relationship between these properties is highly dependent on the shape. There are two types of section modules.
the elastic section modulus is defined as,
S=I/Y
S= section modulus
I= moment of inertia
Y is the distance between the neutral axis to the most extreme fiber.
FRONT ROOF RAIL:
Moment Of Inertia (Max), Imax= 1.1838*10^4(mm^4)
Moment Of Inertia (Min), I min= 908.9(mm^4)
Section modulus, S = I/Y,
Y= 62.5mm
by using these values, we can find the section modulus (S)
For maximum, S = 1.1838*10^4/ 62.5
= 189.4mm^3
For minimum, S = 908.9(mm^4)/ 62.5
= 14.54mm^3
REAR ROOF RAIL:
Moment of inertia (max) Imax= 6.2223*10^4[mm^4]
Moment of inertia (min) I min = 4715.486mm^4]
Section modulus (S)= I/Y
Smax = 999.5 mm^3
S min= 75.44mm^3
similarly, we can calculate the section modulus, bow roof_1, centre roof rail, bow roof_2
ROOF MODEL VIEWS
DRAFT ANALYSIS:
FRONT ROOF:
BOW ROOF 1:
CENTRE ROOF:
BOW ROOF 2:
REAR ROOF:
ROOF:
CONCLUSION:
The design of the roof, front roof rail, rear roof rail, bow roof1, bow roof2, centre roof rails by following the master section with the design parameters for the given class A surface is done.
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