Roof Design

A STUDY ON ROOF CURVATURE

The roof is one of the important part comes within a automotive body, because it directly relates the quality of the product, life and safety criteria. So for manufacturing a roof with all the above mentioned criteria has to analysed properly. Before performing the software analysis and manual testing in the designing stage itself some calculations are needed to be checked.

The calculation of is of two types:

1. Bow-Prediction or Heat disortion calculation.
2. Snow Load Prediction.

Bow–Roof Prediction:

This calculation helps to check whether the placements are bow roof rail and center roof rail are in acceptable range or any further improvements are needed. The below is the formula commonly used for bow-roof prediction. The output value should be within 2.7.

The calculation is done like for sections from front roof rail to 1st bow roof rail, 1st bow roof rail to center roof rail, center roof rail to 2nd bow roof rail and 2nd bow roof rail to back roof rail.

W = [1.7 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 obtained values from the cretaed model is used to calculate:

L=2033.70mm ; t=.75mm, where L and t remains constant for all sections.

R value for 1st section:

The value of Rx and Ry from model is 3024.76mm and 5690.20mm and the value of l is 546.7mm.

R = 2(3024.76*5690.20)/(3024.76+5690.20)

= 2(17211489.352)/(8714.96)

= 34422978.704/8714.96

R = 3949.87 mm.

W1 = [1.7 x 10^(-3) x 2033.70 ] + [1.85 x 10^(-8) x (3949.87^2)/.75] + [ 1.10x10^(-3) x 546.7] - 2.68

= 3.45729 + .3848 + .6014 - 2.68

W1 = 1.76, thus the value of W1 is within the acceptable range, so the position is Ok.

R value for 2nd section:

The value of Rx and Ry from model is 7132.37mm and 4738.84mm and the value of l is 308.8mm.

R = 2(7132.37*4738.84)/(7132.37+4738.84)

= 2(3,37,99,160.2508)/(11,871.21)

= 6,75,98,320.5016/11,871.21

R = 5,694.31 mm.

W2 = [1.7 x 10^(-3) x 2033.70 ] + [1.85 x 10^(-8) x (5,694.31^2)/.75] + [ 1.10x10^(-3) x 308.8] - 2.68

= 3.45729 + 0.7998 + 0.33968 - 2.68

W2 = 1.92, thus the value of W2 is within the acceptable range, so the position is Ok.

R value for 3rd section:

The value of Rx and Ry from model is 10321.18mm and 4027.82mm and the value of l is 277.3mm.

R = 2(10321.18*4027.82)/(10321.18+4027.82)

= 2(4,15,71,855.2276)/(14,349)

= 4,15,71,855.2276/14,349

R = 2,897.195 mm.

W3 = [1.7 x 10^(-3) x 2033.70 ] + [1.85 x 10^(-8) x (2,897.195^2)/.75] + [ 1.10x10^(-3) x 277.3] - 2.68

= 3.45729 + 0.20704 + 0.30503 - 2.68

W3 = 1.28, thus the value of W3 is within the acceptable range, so the position is Ok.

R value for 4th section:

The value of Rx and Ry from model is 14371.54mm and 3312.21mm and the value of l is 436.4mm.

R = 2(14371.54*3312.21)/(14371.54+3312.21)

= 2(4,76,01,558.5034)/(17,683.75)

= 9,52,03,117.0068/17,683.75

R = 5,383.65 mm.

W4 = [1.7 x 10^(-3) x 2033.70 ] + [1.85 x 10^(-8) x (5,383.65^2)/.75] + [ 1.10x10^(-3) x 436.4] - 2.68

= 3.45729 + 0.71493 + 0.48004 - 2.68

W4 = 1.97226, thus the value of W4 is within the acceptable range, so the position is Ok.

Snow Load Prediction:

This is mainly done to check whether the roof can withstand the load due snowfalls. Mainly the vehicles that were marketed in cold country areas need to have these calculation. Apart from this also manual load testing for the roof is also done by using dead weights.

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)

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

Judgment condition

Qr ≥ 3.1

250 ≤ s ≤ 380

For Section 1:

where t=.75 mm; Ly= 2033.70mm remains constant for all sections

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)

Y= 640.1; Lx = 1127.6mm

My= 640.1(2033.70 - 640.1)

My= 8,92,043.36 mm

α = 892043.36 x Lx² x 10^-12

=892043.36 x 1127.6^2 x 10^-12

a = 1.134

s = L1/2 + L2/2

L1 = 640mm; L2 = 387.4mm

s = 640/2 + 387.4/2

s = 513.7 mm

Iy from model is 2.1420 x 10^+3 mm^4

Rx and Ry values are 3036.26 mm and 4264.63 mm

Qr1 = [2.1420 x 10^3 x(.75)^2] / [1.134 x 513.7 x [(3036.26 + 4264.63)/2]^2 x 10^-8]

= [2.1420 x 10^3 x .5625] / [582.5358 x [0.13325748698025]

=[1,204.875] / [77.627]

= 15.52

Qr1 = 15.52 , from the value of Qr1 it shows that the minimum value is obtained and the position is ok.

For Section 2:

α = My x Lx² x 10^-12 , My = Y(Ly-Y)

Y= 1027.4; Lx = 1079.0mm

My= 1027.4(2033.70 - 1027.4)

My= 10,33,872.62 mm

α = My x Lx² x 10^-12

=10,33,872.62 x 1079.0^2 x 10^-12

a = 1.204

s = L1/2 + L2/2

L1 = 387.4mm; L2 = 357.6mm

s = 387.4/2 + 357.6/2

s = 372.5 mm

Iy from model is 2.67345811 x 10^+3 mm^4

Rx and Ry values are 7096.6 mm and 3837.1 mm

Qr2 = [2.67345811 x 10^+3 x .75^2] / [1.204 x 372.5 x [(7096.6 + 3837.1)/2]^2 x 10^-8]

= [1503.82] / [448.49 x [(5466.85)^2 x 10^-8]

=[1503.82] / [134.04]

= 11.22 from the value of Qr2 it shows that the minimum value is obtained and the position is ok.

For Section 3:

α = My x Lx² x 10^-12 , My = Y(Ly-Y)

Y= 1385; Lx = 1059.5mm

My= 1385(2033.70 - 1385)

My= 8,98,449.5 mm

α = My x Lx² x 10^-12

= 8,98,449.5 x 1059.5^2 x 10^-12

a = 1.0085

s = L1/2 + L2/2

L1 = 357.6mm; L2 = 576mm

s = 357.6/2 + 576/2

s = 466.8 mm

Iy from model is 2.71583865 x 10^+3 mm^4

Rx and Ry values are 10763.61 mm and 4249.92 mm

Qr3 = [2.71583865 x 10^+3 x .75^2] / [1.0085 x 466.8 x [(10763.61 + 4249.92)/2]^2 x 10^-8]

= [1,527.656] / [470.77 x .5635]

= 1527.656 / 265.28

Qr3 = 5.76 from the value of Qr3 it shows that the minimum value is obtained and the position is ok.

Thus, the above shows the curvature study on roof.

The below images shows the draft analysis done in each parts.

1. Front Roof Rail

2. Rear Roof Rail

3. Bow Roof 1

4. Bow Roof 2

5. Center Roof Rail

6. Outer Roof

As a reference from the images of draft analysis, in front roof rail the draft angle needed to be provided and in other roof rails the radius value need to corrected for reducing the stress concentrations.