Roof Design

The Curvature Study of the Designed model is carried out and shown below.

Bow–Roof Prediction Formula (Heat Distortion Calculation)

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

Case-I

L = 2029.2422 mm

R = 2(Rx*Ry)/(Rx+Ry)

Rx = 5692.1634 mm

Ry = 2083.0927 mm

R = 2(5692.1634*2083.0927)/(5692.1634+2083.0927)

R = 3050.0098 mm

t = 0.75 mm

I = 516.5042 mm

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

W = [1.73 x 10^(-3) x 2029.2422] + [1.85 x 10^(-8) x (3050.0098^2)/0.75] + [ 1.10x10^(-3) x 516.5042] - 2.68

W = 1.6280

W(1.6280) < 2.7

Hence given criteria for bow roof heat distortion are satisfied

Case-II

L = 2029.2422 mm

R = 2(Rx*Ry)/(Rx+Ry)

Rx = 4833.5330 mm

Ry = 13699.5671 mm

R = 2(4833.5330*13699.5671)/( 4833.5330+13699.5671)

R = 7145.8427 mm

t = 0.75 mm

I = 287.5003 mm

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

W = [1.73 x 10^(-3) x 2029.2422] + [1.85 x 10^(-8) x (7145.8427^2)/0.75] + [ 1.10x10^(-3) x 287.5003] - 2.68

W = 2.4062

W(2.4062) < 2.7

Hence given criteria for bow roof heat distortion are satisfied

Case-III

L = 2029.2422 mm

R = 2(Rx*Ry)/(Rx+Ry)

Rx = 5672.5545 mm

Ry = 4081.3143 mm

R = 2(5672.5545*4081.3143)/( 5672.5545+4081.3143)

R = 4747.1374 mm

t = 0.75 mm

I = 419.1475 mm

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

W = [1.73 x 10^(-3) x 2029.2422] + [1.85 x 10^(-8) x (4747.1374^2)/0.75] + [ 1.10x10^(-3) x 419.1475] - 2.68

W = 1.8473

W(1.8473) < 2.7

Hence given criteria for bow roof heat distortion are satisfied

Case-IV

L = 2029.2422 mm

R = 2(Rx*Ry)/(Rx+Ry)

Rx = 4365.3568 mm

Ry = 4574.1332 mm

R = 2(4365.3568*4574.1332)/( 4365.3568+4574.1332)

R = 4467.3070 mm

t = 0.75 mm

I = 355.4454 mm

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

W = [1.73 x 10^(-3) x 2029.2422] + [1.85 x 10^(-8) x (4467.3070^2)/0.75] + [ 1.10x10^(-3) x 355.4454] - 2.68

W = 1.7136

W(1.7136) < 2.7

Hence given criteria for bow roof heat distortion are satisfied

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)

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 centre 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

Case-I

t = 0.75 mm

α = My x Lx² x 10^-12

Y = 613.7666 mm

Ly = 1965.6246 mm

My = 613.7666(1965.6246-613.7666)

My = 829725.2883

Lx = 1129.4773 mm

α = 829725.2883 x 1129.4773² x 10^-12

α = 1.058

s = L1/2 + L2/2

L1 = 613.7666 mm

L2 = 367.4695 mm

s = 613.7666/2 + 367.4695/2

s = 490.6180 mm

Rx = 6406.3931 mm

Ry = 2939.3733 mm

Iy = 1.7067 X 10^3

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

Qr = [1.7067 X 10^3 x 0.75²] / [1.058 x 490.6180 x [(6406.3931 + 2939.3733)/2]² x 10^-8]

Qr = 8.4681

Qr(8.4681) ≥ 3.1

Hence given criteria for snow load are satisfied

Case-II

t = 0.75 mm

α = My x Lx² x 10^-12

My = Y(Ly-Y)

Y = 979.6518 mm

Ly = 1965.6246 mm

My = 979.6518 (1965.6246-979.6518)

My = 965910.0282

Lx = 1081.5808 mm

α = 965910.0282 x 1081.5808² x 10^-12

α = 1.1299

s = L1/2 + L2/2

L1 = 367.4695 mm

L2 = 499.1276 mm

s = 367.4695/2 + 499.1276/2

s = 433.2985 mm

Rx = 2960.1084 mm

Ry = 6730.9924 mm

Iy = 2.3091 X 10^3

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

Qr = [2.3091 X 10^3 x 0.75²] / [1.1299 x 433.2985 x [(2960.1084 + 6730.9924)/2]² x 10^-8]

Qr = 11.3083

Qr(11.3083) ≥ 3.1

Hence given criteria for snow load are satisfied

Case-III

t = 0.75 mm

α = My x Lx² x 10^-12

My = Y(Ly-Y)

Y = 1476.1868 mm

Ly = 1965.6246 mm

My = 1476.1868 (1965.6246-1476.1868)

My = 722501.6197

Lx = 1058.5030 mm

α = 722501.6197 x 1058.5030² x 10^-12

α = 0.8095

s = L1/2 + L2/2

L1 = 499.1276 mm

L2 = 492.1049 mm

s = 499.1276 /2 + 492.1049/2

s = 495.6296 mm

Rx = 4267.7542 mm

Ry = 10976.0438 mm

Iy = 1.7150 X 10^3

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

Qr = [1.7150 X 10^3 x 0.75²] / [0.8095 x 495.6296 x [(4267.7542 + 10976.0438)/2]² x 10^-8]

Qr = 4.1309

Qr(4.1309) ≥ 3.1

Hence given criteria for snow load are satisfied

Heat Distortion Results
Sr. No.	Location	Rx	Ry	R	I	L	t	W	Criteria	Remark
1	Front Rail	5692.1634	2083.0927	3050.0098	516.5042	2029.2422	0.75	1.628	W < 2.7	Satisfied
2	Roof Rail 1	4833.533	13699.5671	7145.8427	287.5003	2029.2422	0.75	2.4062	W < 2.7	Satisfied
3	Centre Rail	5672.5545	4081.3143	4747.1374	419.1475	2029.2422	0.75	1.8473	W < 2.7	Satisfied
4	Roof Rail 2	4365.3568	4574.1332	4467.307	355.4454	2029.2422	0.75	1.7136	W < 2.7	Satisfied

Snow Load Results
Sr. No.	Location	Iy	α	Lx	Ly	y	s	Rx	Ry	t	Qr	Criteria	Remark
1	Front Rail	1.7067x10^3	1.05	1129.477	1965.6246	613.7666	490.618	6406.3931	2939.3733	0.75	8.4681	Qr ≥ 3.1	Satisfied
2	Roof Rail 1	2.3091x10^3	1.1299	1081.5808	1965.6246	979.6518	433.2985	2960.1084	6730.9924	0.75	11.3083	Qr ≥ 3.1	Satisfied
3	Centre Rail	1.7150x10^3	0.8095	1058.503	1965.6246	1476.1868	495.6296	4267.7542	10976.0438	0.75	4.1389	Qr ≥ 3.1	Satisfied

Manufacturing Technologies required for the production of Roofs are,

1. Bending- Bends are provided in the roofs at the location after studying visibility and headroom clearance for the passengers, they are provided to increase strength and specific angles of drafts are provided for the bends for ease of manufacturing.

2. Spot Welding- Spots are welded wherever required to keep the outer roof and roof rails in continuous contact. It is an alternative process of joining two metal parts together.

3. Mastic pads- They are provided between the outer roof and roof rails to reduce noise, vibration and harnesses of a vehicle, it also provides a type of contact between the outer roof and roof rails as sealant is applied at both ends.

Draft Analysis are performed for the roof rails and the images are seen below,

1. Draft Analysis of Front Roof Rail

2. Draft Analysis of Front Bow Roof Rail.

3. Draft Analysis of Centre Roof Rail

4. Draft Analysis of Rear Bow Roof Rail

5. Draft Analysis of Rear Roof Rail

Conclusion

From the above tables, it is validated that from the given class A surface the parts modelled are satisfying heat distortion and snow load criteria, if the criteria are not satisfied then we have to provide the necessary embossed to the class A surface to enhance the strength of the roof.

Draft analysis is performed for all the rails and all the rails satisfy the manufacturing criteria and are producible without any modification.