Car Roof Design

Aim:

To design & develop the Roof of a car with its components by following the master section and design parameters.

Objective:

• To develop the essential flanges and reinforcements using roof styling as input.
• To do a curvature study on the roof and perform calculations to determine the position of the Bow-roof.
• To determine the Heat Distortion Criteria of the car's roof.
• To find the section modulus on the O-Y section of the roof and also for all the components of it.
• To determine the Snow Load Criteria for a car's roof.
• To perform Draft Analysis on the final CAD model of the roof.

Introduction:

Car's Roof:

An automobile roof or car is the top portion of an automobile that sits above the passenger compartment, protecting the vehicle occupants from sun, wind, rain, and other external elements.

Heat Distortion Criteria:

The heat radiating from the sun causes the roof of the car to change in the metallic regions. Heat distortion criteria indicate what temperature materials start to "soften" when exposed to a fixed load at elevated temperatures.

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]

Judgement Condition: OK< 2.7mm

Snow Load Criteria:

During Winter Season the snow gets clogged over the top surface/roof of the car and the snow has some mass on it. Due to this, the roof can fail if the snow load exceeds the capacity of the roof that was designed to sustain.

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 centre point between Roof rail Front /Rear as the reference point of the front and the rear.

Lx = Distance between the Left and Right end of the roof on the Roof BOW [mm]

        Width of the roof panel 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

Judgement condition = Qr ≥ 3.1

                250 ≤ s ≤ 380

Section Modulus:

Section modulus is a geometric property for a given cross-section used in the design of beams. Other geometric properties used in the design include an area for tension, radius of gyration for compression, and moment of inertia for stiffness. The Section modulus is defined as

`S = I/y`

Where

S = Section Modulus

I = Moment of Inertia

y = Distance from the neutral axis to any given part.

Procedure:

Open the given model in CATIA V5 that is the styling surface of the car's roof.

In this challenge, we will be creating the Roof's outer panel, Front roof rail, Rear roof rail, Centre reinforcement and Bow roofs.

Roof Outer Panel:

First, we will be extracting the top half portion of the roof surface. Since the roof surface is symmetrical in shape, we can easily work only on half of the portion and reflect it at the end to create the whole roof.

Untrim this surface in order to avoid the holes. Extract the outer boundaries of the original half surface and project it on the untrim surface to get the exact outer edges of the roof.

The corners of the roof surface are sharp so using the corner option in CATIA V5 we will be giving a 5mm curve/fillet on those corners.

Now we will be creating the flanges by first sweeping the front edge to 3 deg in Y-direction and length as 16mm.

From the edge of the sweep (surface) take another sweep with 65 degrees draft in Y-direction and length as 21.5 mm.

Similarly, by following the same procedure we can create a flange on the other edges as well.

Using the Multi-Section option in CATIA create a surface on the corners by giving guide curves and support of the surfaces.

Join these Surfaces together and give the required fillets.

For the Rear end, there should be an additional area that helps to hold the back door without hitting the roof.

For creating the Sunroof, the sketch is created and then projected onto the roof.

Now, split the surface with the projected sketch and sweep the edges to create the inner portion of the sunroof.

After creating the sunroof, Embosses are given on the roof to provide better strength.

A sketch is drawn and projected on the roof surface to create the Embossments. The Roof is then split with the projected sketch. The sweep & trim option is then used to create the Embossments.

Front Roof Rail:

Following the master section which is given to us as input, we will be creating the Front Roof Rail.

First, offset the top roof surface to 32mm and using a parallel curve offset the edge to 80mm.

Split the offset surface using this edge. This surface will be now our base surface of the front roof rail.

Sweep the edges and create a surface on both sides of the roof. Make sure to sweep the edges with a draft of more than 7 degrees.

Now to create the left portion (as per the below image) extract & offset the outer roof flange to 1.7mm.

Trim this offset surface with the sweep surface of the front roof rail.

Now to create the right portion (as per the below image) offset the top roof surface to 4.2mm & 6.2mm.

Using the offset curve of 80mm (which we created for the base surface) create another 2 offset curves with a distance of 10mm & 5mm.

Split the 6.2mm offset surface with the 10mm curve and then split the 4.2mm surface with the 5mm curve respectively.

Now join the base surface, 6.2mm surface and 4.2mm surface using blend and give required fillets to all the edges.

Offset the XY plane to a certain distance and split the front roof rail with it.

Embossments are created on the front roof rail base to provide better strength.

A sketch is drawn and projected on the base surface to create the Embossments. The Roof is then split with the projected sketch. The sweep & trim option is then used to create the Embossments.

Rear Roof Rail:

Similar operations which were performed in the Front Roof Rail needs to be followed to create the Rear Roof Rail.

Center Reinforcement:

A center reinforcement is created (below the roof) to provide additional strength to the area where the roof surface is flat.

To create the center reinforcement, we first need to take an intersection with the YZ plane at a point where we want to create the reinforcement. This will give us a curve/line on the surface. Considering this curve as the center of the reinforcement, create offset lines of 42.5, 24 & 10mm on both sides.

Now offset the top roof surface to 6.5, 15 & 19.5mm respectively.

Using the 42.5 & 24mm offset lines, split the 6.5mm offset surface.

Using the 10mm offset lines, split the 15mm offset surface,

Sweep the edges of the split surface considering a draft of more than 7 degrees and trim these sweep surface with the 19.5mm offset surface.

Join all these surface and give the required fillets.

Offset the XY plane to a certain distance and split the reinforcement with it.

Bow Roofs:

Similar operations which were performed to create the center reinforcement needs to be followed to create the Bow Roofs.

In addition to the above procedure in this case a dipping area also needs to be created so that the bow roofs are attached to the roof flange.

To create that area, extract the flange of the outer roof panel and create an offset of 1.7mm.

Cut the offset surface and make sure its width is less than the bow roof's width.

Using the spline/connect option create lines connecting the bow roof edge and offset surface edge.

Now using the Multi-Section option, create a surface between the bow roof edge and offset surface edge using spline lines as guide curves.

Join all these surfaces to create the bow roof.

Solid-Body:

Once all the surfaces are created, use the symmetry option and mirror all the parts (individually) using the XY Plane and join them.

After mirroring all the surfaces successfully, use the thicken option to create the solids with the proper thickness.

The thickness for the Roof Outer Panel, front roof rail and rear roof rail is 0.75mm, for the center reinforcement thickness is 1.5mm, and for the bow roof, it is 1.25mm.

Calculating the Heat Distortion criteria:

• To calculate the Heat distortion criteria, we have to take a note of few values and note it down.
• To note down the values, first, we need to create a sketch.
• Create a line at the center of the roof part in the 0-Y axis and then draw another line with a distance of 300mm to the O-Y line.
• Now create lines at a distance of 100mm on both sides to the 300mm line.

• Create a new sketch in which we need to create lines between the bow roofs and rails coming at the center. These lines need to be created in X-direction.
• Using these center line create lines at a distance of 100mm on both sides.

• Now intersect sketch 1 (lines in Y-direction) and sketch 2(lines in X-direction). This result will give us some points where the lines (X & Y)are coinciding with each other.

• Extract the required points and project them on the roof surface. Now using these points create a 3 point arc or circle and note the radius of the arc in the X direction as `R_x` and in the Y direction as `R_y`.

Now since we got all the values for calculating the Heat Distortion, substitute these values to the below equation.

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

S.No	BOW	`R_x`	`R_y`	R	l	L	t	`R^2/t`	W	OK/NG
1	BOW 1 - CR	4695.714	7311.905	5718.80	258.2	2033.705	0.75	43606231.25	1.93	OK
2	CR - BOW 2	3945.448	10745.13	5771.63	262.6	2033.705	0.75	44415617.14	1.94	OK
3	BOW 2 - RR	3284.578	14559.33	5359.94	218.5	2033.705	0.75	38305275.73	1.78	OK

 

Note: All dimensions are in mm

Judgement Condition: OK< 2.7mm

The below image is for reference:

Note: Since there is a sunroof in between the Front Roof Rail & Bow 1, the heat distortion criteria will not be calculated for that area.

Calculating the Snow Load Criteria:

• To calculate the Snow Load Criteria, we have to take a note of few values and note it down.
• To note down the values, first, we need to create a sketch.
• Create a line at the center of the roof part in the 0-Y axis.
• Now using this O-Y line as a center create lines with a distance of 100 on both sides.

• Create a new sketch in which we need to create lines between the bow roofs and rails coming at the center. These lines need to be created in X-direction.
• Using these center line create lines at a distance of 100mm on both sides.

• Now intersect sketch 1 (lines in Y-direction) and sketch 2(lines in X-direction). This result will give us some points where the lines (X & Y)are coinciding with each other.

• Extract the required points and project them on the roof surface. Now using these points create a 3 point arc or circle and note the radius of the arc in the X direction as `R_x` and in the Y direction as `R_y`.

Now since we got all the values for calculating the Snow Load Criteria, substitute these values to the below equation.

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

S.No	BOW	`I_y`	`alpha`	`L_x`	`L_y`	y	S	`R_x`	`R_y`	t	`Q_r`	OK/NG
1	BOW 1 - CR	5700	0.72	1095.55	2033.705	358.5	360.5	3857.71	7292.006	0.75	39.80	OK
2	CR - BOW 2	11610	0.69	1069.82	2033.705	362.5	340.5	4289.69	11283.60	0.75	45.93	OK
3	BOW 2 - RR	5727	0.61	1053.87	2033.705	318.5	-	4013.35	16354.33	0.75	-	-

Note: For the Bow Roof 2 - Rear Roof Rail there will be no snow load criteria since the L2 is not available in that region.

Judgement Condition: `Q_r >=3.1`

Calculating the Section Modulus:

To calculate the section modulus, we need to take the intersection of all the components individually on the 0-Y section.

For example:

Here we have taken the intersection of Center Roof Rail (i.e Center Rail + Center Reinforcement).

Since we need to find the section modulus of Center Roof Rail, we need to remove the inner boundaries of Center Rail & Center Reinforcement.

After the intersection is done, fill the surface with the intersection created. In order to create a surface using the fill option, make sure the intersection is closed.

Select the Measure Inertia option to measure the 2D inertia of the surface created and note down the value (M1).

Once we get all the values, substitute in the below equation for every component individually.

`S = I/Y`

Section Modulus of Outer Roof Panel:

`I = 1549xx10^3 mm^4`

`Y = 1048.40 mm`

`S = 1477.48 mm^3`

Section Modulus of Front Roof Panel:

`I = 7.560xx10^3 mm^4`

`Y = 60.5 mm`

`S = 124.95 mm^3`

Section Modulus of Rear Roof Panel:

`I = 33640 mm^4`

`Y = 106.5 mm`

`S = 315.86 mm^3`

Section Modulus of Bow Roof 1:

`I = 5700 mm^4`

`Y = 40 mm`

`S = 142.5 mm^3`

Section Modulus of Bow Roof 2:

`I = 5727 mm^4`

`Y = 40 mm`

`S = 143.175 mm^3`

Section Modulus of Center Rail:

`I = 11610 mm^4`

`Y = 42.5 mm`

`S = 273.17 mm^3`

Section Modulus of Center Reinforcement:

`I = 4020 mm^4`

`Y = 42.5 mm`

`S = 94.58 mm^3`

Section Modulus of Center Rail + Center Reinforcement:

`I = 35190 mm^4`

`Y = 42.5 mm`

`S = 828 mm^3`

Draft Analysis:

Outer Roof Panel:

Front Roof Rail:

Bow Roof 1:

Bow Roof 2:

Center Rail:

Center Reinforcement:

Rear Roof Rail:

Result:

The Roof of a car has been successfully developed with all the required components and a draft analysis have also been performed for the same.

After performing the operations for determining the Heat Absorption Criteria, Snow Load Criteria and Section Modulus of all the components, the below results have been obtained.

Heat Distortion Criteria:

S.No	BOW	`R_x`	`R_y`	R	l	L	t	`R^2/t`	W	OK/NG
1	BOW 1 - CR	4695.714	7311.905	5718.80	258.2	2033.705	0.75	43606231.25	1.93	OK
2	CR - BOW 2	3945.448	10745.13	5771.63	262.6	2033.705	0.75	44415617.14	1.94	OK
3	BOW 2 - RR	3284.578	14559.33	5359.94	218.5	2033.705	0.75	38305275.73	1.78	OK

 

Snow Load Criteria:

S.No	BOW	`I_y`	`alpha`	`L_x`	`L_y`	y	S	`R_x`	`R_y`	t	`Q_r`	OK/NG
1	BOW 1 - CR	5700	0.72	1095.55	2033.705	358.5	360.5	3857.71	7292.006	0.75	39.80	OK
2	CR - BOW 2	11610	0.69	1069.82	2033.705	362.5	340.5	4289.69	11283.60	0.75	45.93	OK
3	BOW 2 - RR	5727	0.61	1053.87	2033.705	318.5	-	4013.35	16354.33	0.75	-	-

 

Section Modulus:

S.No	Component	I (`mm^4`)	y (mm)	Section Modulus(S) (`mm^3`)
1	Outer Roof Panel	1549000	1048.40	1477.48
2	Front Roof Rail	7560	60.5	124.95
3	Bow Roof 1	5700	40	142.5
4	Bow Roof 2	5727	40	143.175
5	Center Rail	11610	42.5	273.17
6	Center Reinforcement	4020	42.5	94.58
7	Center Rail + Reinforcement	35190	42.5	828
8	Rear Roof Rail	33640	106.5	315.86

Section Views:

Front Roof Rail:

Center Roof Rail (Rail + Reinforcement):

Bow Roof:

Rear Roof Rail:

Final CAD Model:

Conclusion:

• The results obtained after doing a curvature study on the roof was adequate.
• The position of the bow roofs can be arranged better (over the flat areas) which helps in increasing the strength of the roof.
• Embossments are added to improve the strength & dynamics of the roof but can be avoided if not necessary as it increases the cost of manufacturing.