Roof Design

ROOF WITH REINFORCEMENTS:

BOW ROOF 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

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]

Abbreviations:
Front roof rail - FRR; Bow roof rail - BRR; Center roof rail - CRR; Rear roof rail - RRR

Sections	Rx	Ry	R	l	W
1- FRR to BRR1	5692.9	3013.12	3940.58	532.04	1.79
2- BRR1 to CRR	4754.71	7072.35	5686.44	334.87	1.99
3- CRR to BRR2	3985.21	10551.03	5785.27	297.6	1.98
4- BRR2 to RRR	3326.37	13794.81	5360.21	434.18	2.01

L=2028mm, t=0.75mm

W<2.7 Satisfied for all sections.

NOTE:

• all dimensions are in mm if not mentioned and W is unitless
• BRR1 is in between FRR and CRR

PROCEDURE:

1. Here, Y-axis is the horizontal axis spliting the roof into two symmetrical halves & X-axis is perpendicular to that as shown in above picture.
2. Curve is taken at 300mm offset from Y-axis onto the left half of roof.
3. Along its length of Y-axis, four curves are taken which divide the roof into 5 parts w.r.t. Y-axis. Curves lies within same distance to reinforcement on either sides.
4. Then all curves are trimmed on both side at an offset of 100mm each, which results in curves as shown in above picture.
5. Now Rx and Ry are measured for each sections using curves obtained.

SNOW LOAD CALCULATIONS:

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

α = My x Lx² x 10^-12 ,

My = Y(Ly-Y)

Where,
α = My x Lx² x 10^-12 , My = Y(Ly-Y)

t = Roof plate thickness [mm] (0.75mm)

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]

SECTIONS	Lx	Ly	Y	My (in mm^2)	α (in mm^4)	Rx	Ry	s	Iy (in mm^4)	Qr
1. FRR to BRR1	1127.67	2033	623.04	878461.4	1.13	4270.89	3024.2	520.205	3521.27	25.32
2. BRR1 to CRR	1079.34	2033	417.37	674314.49	0.78	3830.65	7030.71	390.23	5658.76	34.92
3. CRR to BRR2	1058.24	2033	375.1	621878.29	0.69	4272.1	11043.14	506.115	2285.51	6.29
4. BRR2 to RRR	1044.64	2033	637.13	889350.65	0.97	4075.53	15970.79

In all cases, Qr>3.1

NOTE: all dimensions are in mm if not mentioned and Qr is unitless

PROCEDURE: In this calculation similar procedure is followed for Rx and Ry calculation as in bow roof, only difference being the mid point of intersecting curve lies on 0-Y axis rather than 300-Y in bow roof.

DRAFT ANALYSIS:

Green: Draft angle >7deg
Yellow: Positive Draft angle<7deg

1. ROOF OUTER PANEL:
   
   
   
   Negative Draft at front and rear is due to use of single tooling axis.
   Ideally, two separate methods will be performed for achieving both the geometries.
   
   
   
2. FRONT ROOF RAIL:
   
   
   
   
   
3. REAR ROOF RAIL:
   
   
   
   
   
4. CENTER ROOF RAIL:
   
   
   
   
   
5. BOW ROOF FRONT SIDE:
   
   
   
   
   
6. BOW ROOF REAR SIDE: