Designing a Roof of a car using CATIA V5

Aim:

The main aim is to determine the Heat Distortion criteria, Snow Load Criteria, and Section Modulus of the roof and the reinforcements and to check if they are qualifying the given criteria.

Theory:

Roof:

The roof is an upper part of the car that sits above the passenger compartment, protects the vehicle occupants from the sun, wind, rain, and other external elements.

Heat Distortion Criteria:

During summers in the Middle East, 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= [1.73xx10^-3xxL]+[1.85xx10^-8(R^2/t)]+[1.10xx10^-3xxl]-2.68`

Where,

L = Roof Length in X- Direction (mm) [Roof Dimension with OY]

R = Roof Curvature = `[2(R_x xx R_y)]/(R_x+R_y)`

Where, `R_x`= X Curvature and `R_y`= Y Curvature

t = Roof Plate Thickness (mm)

l = Bow roof Thickness (mm)

Snow Load Criteria:

During Winter Season the snow gets clogged over the Top areas of the car and the snow has some mass on it. The roof can fail if the snow load exceeds the Capacity of the Roof was designed to sustain.

`Qr=(I_yxxt^2)/( alpha xxS xx [(R_x+R_y)/2]^2 xx10^-8)`

Where,

`alpha= M_yxx(L_x)^2 xx 10^-12`

Where `M_y= Y(L_y-Y)`

t = Roof Plate thickness (mm)

`L_x`= Distance Between the left and right end of the roof on the roof bow (mm). (Width of the roof panel exposed on the surface)

`L_y` = Distance between the front and rear roof rails on the vehicle along with OY(mm) (Length of roof panel with the center point between roof rail front/ Rear as the reference point of the front and the rear.)

Y = Distance from front roof rails to Roof Bow (mm)

S = Distance for which Roof bow bears divided load (mm) = `L_1/2+L_2/2`

`I_y`= Geometric Moment of Inertia of Roof Bow (mm4) (Y cross-section)

`R_x`= Lateral Direction curvature radius of roof panel Y cross-section on roof Bow (mm) (Roof Panel curvature radius of the length Lx in the Front View)

`R_y`= Longitudinal Direction curvature radius of the roof panel X cross-section on roof bow (mm) (Roof Panel X curvature radius of the length ‘S’ in Side View)

Section Modulus:

Section modulus is a geometric property for a given cross-section used in the design of beams. Other geometric properties used in design include 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:

1. Checking the Class –A surface:

• After the file is opened, the roof part is not joined together but as the individual surfaces.
• It is also seen as the surface is perfectly symmetrical in shape which helps us to work on the half of the portion and reflect it which creates the whole roof.

2. Creating the Flanges for the Roof:

• Extract the upper roof part by selecting it.

• Now, since it is a sharp corner at the end to make it smooth, use the corner option to create a cut on the edges and split it to create the smooth corner.

• Now select an edge and sweep it with the 3-degree draft with a length of 15mm.

• From the edge of the sweep take another sweep with the 25 degree draft of length 21.5 mm (as shown in the reference dimensions).

• Follow the same procedure with the other edges.
• Now, create the curved edges by using curves as the guide curves and the multi-section surface option.

• Join the Surfaces together and give the 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, the projected element is split and the sweep is done on the free edges.

• After creating the sunroof, Embosses are given on the roof to provide better strength.
• A sketch is drawn and projected on the surface.
• The Roof is then split with the projected area.

• Now, the sweep option is used to create embossments.

3. Creating the Front roof Rail:

• Offset the roof to 2.7mm and split it with a distance of 5mm.
• Similarly, create an offset of 4.7mm and cut it.
• Now create a base offset of 32mm from the roof.
• Create the respective sweeps for these offsets and trim them together.
• Give the Edge fillets to it.

4. Creating the Rear roof Rail:

• For the rear roof, rail follows a similar procedure as the front roof and the values for it are given in the diagram.
• Make sure that the Rear roof has a positive draft angle.

5. Creating the Center Reinforcement:

• The Center Reinforcement is attached at the center yet below the roof.
• To create the center reinforcement as per the diagram, we use the offset and select the parallel curve option and give an offset value of 50mm on both sides and create a cut on the offset.
• Now create the part as per the design standards and make sure that the offset is given considering the thickness of the component.

• A dip area needs to be created so that the reinforcement is attached to the roof flange.
• To create that area, select the flange and create an offset to the length including the thickness of the roof and the connecting parts.
• Cut the Offset to the length which is less than the width of the center reinforcement.
• Create lines on the cut surface.
• Use connect option to join the lines to form curves.

• Use the Multi-section surface option to select the edges and the curves created as the guide curves to create a body.
• Join the surfaces together.

6. Creating the Bow roofs:

• 3 bow roofs are created to give strength to the roof.
• Follow the same method as with the center reinforcement to create the bow roof.
• Now, after the bow roof is created. The mastic points need to be created.
• Use the parallel curve and connect the outer edge and parallel curve to cut the elements.

• Once created use the split option to create the mastic points.

7. Creating a Solid:

• After Creating the surfaces, use the thicken option to create the solids with the proper thickness.
• The thickness for the Roof and front roof rail is 0.75mm, for the rear roof rail is 1.25mm, for the center reinforcement thickness is 1.5mm, and for the bow roof, it is 1.3mm.

8. Checking the Heat Distortion criteria:

• To calculate the Heat distortion criteria, we have to take note of few values and note it down.
• To note down, 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.
• Now create the line with a distance of 100 on both sides at the line which is at 300mm.
• Now create the line between the rails in the X direction and create 2 lines with a distance of 100mm on both sides.
• Now create a point coinciding with both the lines.

• Extract the points to the roof and create the arc using 3 points by creating two lines intersecting with each other.

• Measure the radius of the arc in the Y direction as `R_y` and X direction as `R_x`.

`R_y` Value:

`R_x` Value:

9. Checking the Snow Load Criteria:

• To calculate the Snow Load criteria, we have to take note of few values and note it down.
• To note down, first, we need to create a sketch.
• Create a line at the center of the roof part in the 0-Y axis.
• Now create the line with a distance of 100 on both sides.
• Now create the line between the rails in the X direction and create 2 lines with a distance of 100mm on both sides.
• Now create a point coinciding with both the lines.

• Extract the points to the roof and create the arc using 3 points by creating two lines intersecting with each other.

• Measure the radius of the arc in the Y direction as `R_y` and X direction as `R_x`.

`R_x` Value:

`R_y`Value:

10. Checking the Section Modulus:

• To check the section modulus, we need to create the intersection in the Y-axis.
• After the intersection is done, fill the surface with the intersection created.
• Select Measure Inertia option to measure the 2D inertia of the surface created.
• Note down the values.

Calculation:

Heat Distortion Criteria:

We need to find the heat distortion criteria for the following.

L value:

'l' value:

Center Reinforcement and second Bow roof rail:

`W= [1.73xx10^-3xxL]+[1.85xx10^-8xx(R^2/t)]+[1.10xx10^-3xxl]-2.68`

Known values

L= 2033.705 mm

t = 0.75mm

`R_x`= 4134.558mm (By measuring the arc created)

`R_y`= 9799.199mm (By measuring the arc created)

l = 239.409mm (by measuring the distance between the bow roofs)

R =`[2(R_x xxR_y)]/(R_x+R_y)= [2(4134.558xx9799.199)]/(4134.558+9799.199)=2(2907.712)`= 5815.4246 mm

`R^2/t= (5815.4246)^2/0.75=33819163.278285516/0.75`= 45092217.70438 mm

`W=[1.73xx10^-3xx2033.705]+[1.85xx10^-8xx(45092217.70438)]+[1.10xx10^-3xx239.409]-2.68`

W = 1.9358

For Second Bow roof to Third Bow Roof:

`W= [1.73xx10^-3xxL]+[1.85xx10^-8xx(R^2/t)]+[1.10xx10^-3xxl]-2.68`

Known values

L= 2033.705 mm

t = 0.75mm

R_x= 3637.271mm (By measuring the arc created)

R_y= 12391.81mm (By measuring the arc created)

l = 146.325mm (by measuring the distance between the bow roofs)

R = `[2(R_x xxR_y)]/(R_x+R_y)= [2(3637.271xx12391.81)]/(3637.271+12391.81)=2(2811.912)`= 5623.8247 mm

`R^2/t= (5623.8247)^2/0.75=31627404.256/0.75`= 42169872.3417 mm

`W = [1.73xx10^-3xx2033.705]+[1.85xx10^-8xx(42169872.3417)]+[1.10xx10^-3xx146.325]-2.68`

W = 1.7794

For the third Bow Roof and Rear Rail:

`W= [1.73xx10^-3xxL]+[1.85xx10^-8xx(R^2/t)]+[1.10xx10^-3xxl]-2.68`

Known values

L= 2033.705 mm

t = 0.75mm

`R_x`= 3229.674mm (By measuring the arc created)

`R_y`= 14924.424mm (By measuring the arc created)

l = 218.768mm (by measuring the distance between the bow roofs)

R =`[2(R_x xxR_y)]/(R_x+R_y)= [2(3229.674xx14924.424)]/(3229.674+14924.424)=2xx(2655.104)`= 5310.2086 mm

`R^2/t= (5310.2086)^2/0.75=28198315.37551396/0.75`= 37597753.8340 mm

W = `[1.73xx10^-3xx2033.705]+[1.85xx10^-8xx(37597753.8340)]+[1.10xx10^-3xx218.768]-2.68`

W = 1.7745

Snow Load Criteria:

y- Value:

For First Bow Roof to Second Bow Roof:

`Q_r=(I_yxxt^2)/(alphaxxS[(R_x+R_y)/2]^2xx10^-8`

Known Values:

`L_x`= 1073.733mm

`L_y`= 2033.705mm

`I_y`= 4352 mm4

y = 339.292 mm

`R_x`= 4195.902mm

`R_y`= 10174.952mm

`alpha= M_yxx(L_x)^2xx10^-12`

Where `M_y= Y(L_y-Y)`

`alpha= Y(L_y-Y)xx(L_x)^2xx10^-12= 339.292(2033.705-339.292)xx(1073.733)^2xx10^-12`= 0.6628

`S=L_1/2+L_2/2`

Where `L_1`= 339.292 mm and `L_2`= 253.75 mm

S=`L_1/2+L_2/2= (339.292+253.75)/2`= 296.521

`Q_r=(I_yxxt^2)/(alphaxxS[(R_x+R_y)/2]^2xx10^-8`

`Q_r=[4352xx(0.75)^2]/(0.6628xx296.521xx[(4195.902+10174.952)/2]^2xx10^-8`= 24.1250

`Q_r`= 24.1250

For Second Bow Roof to Third Bow Roof:

`Q_r=(I_yxxt^2)/(alphaxxS[(R_x+R_y)/2]^2xx10^-8`

Known Values:

`L_x`= 1058.452mm

`L_y`= 2033.705mm

`I_y`= 6176 mm4

y = 253.75 mm

`R_x`= 4329.6mm

`R_y`= 13410.404mm

`alpha= M_yxx(L_x)^2xx10^-12`

Where `M_y= Y(L_y-Y)`

`alpha= Y(L_y-Y)xx(L_x)^2xx10^-12= 253.75(2033.705-253.75)(1058.452)^2xx10^-12`= 0.506

`S=L_1/2+L_2/2`

Where `L_1`= 253.75 mm and `L_2`= 357.53mm

S=`L_1/2+L_2/2= (253.75+357.53)/2`= 305.64

`Q_r=(I_yxxt^2)/(alphaxxS[(R_x+R_y)/2]^2xx10^-8`

`Q_r=[4352(0.75)^2]/(0.506xx305.64[(4329.6+13410.404)/2]^2xx10^-8`= 28.5510

`Q_r`= 28.5510

For Second Bow Roof to Third Bow Roof:

`Q_r=(I_yxxt^2)/(alphaxxS[(R_x+R_y)/2]^2xx10^-8`

Known Values:

`L_x`= 1058.437mm

`L_y`= 2033.705mm

`I_y`= 6152 mm4

y = 357.53 mm

`R_x`= 3882.797mm

`R_y`= 17069.542mm

`alpha= M_yxx(L_x)^2xx10^-12`

Where `M_y= Y(L_y-Y)`

`alpha= Y(L_y-Y)xx(L_x)^2xx10^-12= 357.53(2033.705-357.53)xx(1058.437)^2xx10^-12`= 0.671

Here, S value can’t be calculated as the `L_2`value is not available since the Rear Roof Rail is the Final element in the roof part. Therefore the Snow load criteria for this section can’t be done.

Section Modulus:

For Roof:

`S = I/y`

Where

I = 1.238e-006 `m^4`= 1238000 `mm^4`

y =`"Total Length"/ 2= 2113.653/2`= 1056.8265 mm

Where Total Length = 2113.653mm (For Front Roof Rail)

S =`Iy= 1238000/1056.8265= 1171.4316 mm^3`

S = 114.37566 `mm^3`

For Front Roof Rail:

`S = I/y`

Where

I = 9.364e-009 `m^4`= 9364 `mm^4`

y = `"Total Length"/ 2= 126.179/2`= 63.0845 mm

Where Total Length = 126.179mm (For Front Roof Rail)

S = `I/y= 9364/63.0845= 148.44 mm^3`

S = 148.44 `mm^3`

For Rear Roof Rail:

`S = I/y`

Where

I = 5.807e-008 `m^4`= 58070 `mm^4`

y = `"Total Length"/ 2= 173.734/2`= 86.867 mm

Where Total Length = 173.734mm (For Front Roof Rail)

S =`I/y= 9364/86.867= 668.493 mm^3`

S = 668.493 `mm^3`

For Bow Roof Rail 1:

`S = I/y`

Where

I = 4.352e-009 `m^4`= 4352 `mm^4`

y = `"Total Length"/ 2= 92.025/2`= 46.0125 mm

Where Total Length = 92.025mm (For Front Roof Rail)

S =`I/y= 4352/46.0125= 94.573744 mm^3`

S = 94.573744 `mm^3`

For Bow Roof Rail 2:

`S = I/y`

Where

I = 6.176-009 `m^4`= 6176 `mm^4`

y = `"Total Length"/ 2= 107.995/2`= 53.9975 mm

Where Total Length = 107.995mm (For Front Roof Rail)

S =`I/y= 6176/53.9975= 114.37566 mm^3`

S = 114.37566 `mm^3`

For Bow Roof Rail 3:

`S = I/y`

Where

I = 6.152-009 `m^4`= 6152 `mm^4`

y = `"Total Length"/ 2= 107.588/2`= 53.794 mm

Where Total Length = 107.588mm (For Front Roof Rail)

S =`I/y= 6152/53.794= 114.36219 mm^3`

S = 114.36219 `mm^3`

For Center Reinforcement:

`S = I/y`

Where

I = 1.047-008 `m^4`= 10470 `mm^4`

y = `"Total Length"/ 2= 92.008/2`= 46.004 mm

Where Total Length = 92.008mm (For Front Roof Rail)

S =`I/y= 10470/92.008= 227.5889 mm^3`

S = 227.5889 `mm^3`

For Center Reinforcement and bow roof 1 :

`S = I/y`

Where

I = 2.469e-008 `m^4`= 24690 `mm^4`

y =`"Total Length"/ 2= 92.016/2`= 46.008 mm

Where Total Length = 92.016mm (For Front Roof Rail)

S =`I/y= 24690/46.008= 536.6458 mm^3`

S = 536.6458 `mm^3`

Result:

The roof is created with the reinforcements and the heat distortion, Snow load Criteria, and Section Modulus are calculated.

Heat Distortion Criteria:

S.No	BOW	`R_x`	`R_y`	R	l	L	t	`R^2/t`	W	OK/NG
1	Cen & I Bow	4134.558	9799.199	5815.4246	239.409	2033.705	0.75	45092217.704	1.9358	OK
2	II & III Bow	3637.271	12391.81	5623.8247	146.325	2033.705	0.75	42169872.3417	1.7794	OK
3	III & Rear	3229.674	14924.424	5310.2086	218.768	2033.705	0.75	37897753.8340	1.7745	OK

Judging Criteria: OK <2.7mm

Snow Load Criteria:

S.No	BOW	`I_y`	`alpha`	`L_x`	`L_y`	y	S	`R_x`	`R_y`	t	`Q_r`	Determination
1	Bow 1 and 2	4352	0.66	1073.733	2033.705	339.292	296.521	4195.902	10174.952	0.75	24.125	OK
2	Bow 2 & 3	6176	0.506	1058.452	2033.705	253.75	305.64	4329.6	13410.404	0.75	28.551	OK
3	Bow 3 & rear	6152	0.67	1058.452	2033.705	357.53	-	3882.797	17069.542	0.75	-	-

Judging Criteria: `Q_r >=3.1`

Section Modulus:

S.No	Component	I (`mm^4`)	y (mm)	Section Modulus(S) (`mm^3`)
1	Roof	1238000	1056.8265	1171.4316
2	Front Rail	9364	63.0845	148.44
3	Rear Rail	5807	86.867	668.493
4	Bow Roof 1	4352	46.0125	94.573
5	Bow Roof 2	6176	53.9975	114.37566
6	Bow Roof 3	6152	53.794	114.36219
7	Center Reinforcement	10470	46.004	227.5889
8	Center Reinforcement & Bow Roof 1	2469	46.008	536.6458

The above table shows that the model passes all the criteria. Some modifications can be done by changing the position of the bow roofs to increase the strength of the roof even further.

Draft Analysis:

The Draft analysis is done on the individual Parts to check if is passing the criteria.

Roof:

Front Roof Rail:

Rear Roof Rail:

Center reinforcement:

Bow Roof 1:

Bow Roof 2:

Bow Roof 3:

Final Model:

Section Views:

Front Roof Rail:

Center Reinforcement and Bow Roof 1:

Bow Roof 2 and 3:

Rear Roof Rail:

Learning Outcome:

1. Learned how to create rails as per the design.

2. Learned how to calculate and what are the criteria for the Heat Distortion, Snow Load conditions.