Roof Design

ROOF DESIGN

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:

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.

MASTER SECTIONS

Front Roof Rail Master section

Master section of the Rear Roof Rail

Master section of Bow Roof

Master section of Center Reinforcement Rail

Heat Distortion Criteria:

During summers the Middle East, the heat radiating from the sun cause 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]

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 excedds the capacity of the roof was designed to sustain.

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 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

PROCEDURE

1. The roof part is not joined together but as the individual surfaces. The surface is perfectlu symmetrical in shape which helps us to work on the half of the portion and reflect it which crates the whole roof.

2.Creating the Flanges of 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 ut on te edges and split it to create the smooth corner.

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

From the edge of the sweep take another sweep with the 25 degree draft of lenth 21.5mm.

Follow the same procedure with the other edges.

Now, create the curved edges by using curves as 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.

3.Creating the Front roof Rail:

• Offset the roof t o2.7mm 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 procedures as 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 centre 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. Creatig Bow Roof:

• 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 Solid:

• After Creating the surfaces, use the thicken option to create the solids with the proper thickenss.
• The thickness is 0.75mm.

CALCULATION

1. HEAT DISTORTION CRITERIA:

W=[1.73×10−3×L]+[1.85×10−8×(R2t)]+[1.10×10−3×l]−2.68W=[1.73×10-3×L]+[1.85×10-8×(R2t)]+[1.10×10-3×l]-2.68

Known values

L= 2033.705 mm

t = 0.75mm

Rx= 4134.558mm (By measuring the arc created)

Ry= 9799.199mm (By measuring the arc created)

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

R=2(Rx×Ry)/Rx+Ry=2(4134.558×9799.199)/4134.558+9799.199=2(2907.712)

= 5815.4246 mm

R2/t=(5815.4246)2/0.75=33819163.278285516/0.75

= 45092217.70438 mm

W=[1.73×10-3×2033.705]+[1.85×10-8×(45092217.70438)]+[1.10×10-3×239.409]-2.68

W = 1.9358

For Second Bow roof to Third Bow Roof:

W=[1.73×10-3×L]+[1.85×10-8×(R2/t)]+[1.10×10-3×l]-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(Rx×Ry)/Rx+Ry=2(3637.271×12391.81)3637.271+12391.81=2(2811.912)= 5623.8247 mm

R2/t=(5623.8247)20.75=31627404.256/0.75

= 42169872.3417 mm

W=[1.73×10-3×2033.705]+[1.85×10-8×(42169872.3417)]+[1.10×10-3×146.325]-2.68

W = 1.7794

For the third Bow Roof and Rear Rail:

W=[1.73×10-3×L]+[1.85×10-8×(R2/t)]+[1.10×10-3×l]-2.68

Known values

L= 2033.705 mm

t = 0.75mm

Rx= 3229.674mm (By measuring the arc created)

Ry= 14924.424mm (By measuring the arc created)

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

R =2(Rx×Ry)/Rx+Ry=2(3229.674×14924.424)/3229.674+14924.424=

2×(2655.104)= 5310.2086 mm

R2/t=(5310.2086)2/0.75=28198315.37551396/0.7s=37597753.8340 mm

W = [1.73×10-3×2033.705]+[1.85×10-8×(37597753.8340)]+[1.10×10-3×218.768]-2.68

W = 1.7745

2. SNOW LOAD CRITERIA:

For First Bow Roof to Second Bow Roof:

Qr=Iy×t2α/×S[Rx+Ry2]2×10-8

Known Values:

Lx= 1073.733mm

Ly= 2033.705mm

Iy= 4352 mm4

y = 339.292 mm

Rx= 4195.902mm

Ry= 10174.952mm

α=My×(Lx)2×10-12

Where My=Y(Ly-Y)

α=Y(Ly-Y)×(Lx)2×10-12=339.292(2033.705-339.292)×(1073.733)2×10-12

= 0.6628

S=L1/2+L2/2

Where L1= 339.292 mm and L2= 253.75 mm

S=L1/2+L2/2=339.292+253.752= 296.521

Qr=Iy×t2/α×S[Rx+Ry2]2×10-8

Qr=4352×(0.75)2/0.6628×296.521×[4195.902+10174.9522]2×10-8= 24.1250

Qr= 24.1250

For Second Bow Roof to Third Bow Roof:

Qr=Iy×t2/α×S[Rx+Ry2]2×10-8

Known Values:

Lx= 1058.452mm

Ly= 2033.705mm

Iy= 6176 mm4

y = 253.75 mm

Rx= 4329.6mm

Ry= 13410.404mm

α=My×(Lx)2×10-12

Where My=Y(Ly-Y)

α=Y(Ly-Y)×(Lx)2×10-12=253.75(2033.705-253.75)(1058.452)2×10-12

= 0.506

S=L1/2+L2/2

Where L1= 253.75 mm and L2= 357.53mm

S=L1/2+L2/2=253.75+357.53/2

Qr=Iy×t2/α×S[Rx+Ry2]2×10-8

Qr=4352(0.75)2/0.506×305.64[4329.6+13410.4042]2×10-8= 28.5510

Qr= 28.5510

For Second Bow Roof to Third Bow Roof:

Qr=Iy×t2/α×S[Rx+Ry2]2×10-8

Known Values:

Lx= 1058.437mm

Ly= 2033.705mm

Iy= 6152 mm4

y = 357.53 mm

Rx= 3882.797mm

Ry= 17069.542mm

α=My×(Lx)2×10-12

Where My=Y(Ly-Y)

α=Y(Ly-Y)×(Lx)2×10-12=357.53(2033.705-357.53)×(1058.437)2×10-12= 0.671

Here, S value can’t be calculated as the L2value 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

Roof:

S=Iy

Where

I = 1.238e-006m4 = 1238000 mm4

y =Total Length/2=2113.6532= 1056.8265 mm

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

S =Iy=12380001056.8265=1171.4316mm3=1171.4316mm3

S = 114.37566 mm3

Front Roof Rail:

S=Iy

Where

I=9.346e-009m4">m4 = 9364mm4

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

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

s=I/Y= 9364/63.0845=148.44mm3

S=148.44mm3

For Rear Roof Rail:

S=I/y

Where

I = 5.807e-008 m4= 58070mm4

y = Total Length/2=173.7342/2= 86.867 mm

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

S =I/y=9364/86.867=668.493mm3

S = 668.493 mm3

Bow Roof Rail1:

S=I/Y

Where

I = 4.352e-009 m4= 4352 mm4

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=94.573744mm3

S = 94.573744 mm3

Bow Roof Rail2:

S=I/Y

Where

I = 6.176-009 = 6176 mm4

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

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

S =I/y=617653.9975=114.37566mm3

S = 114.37566 mm3

Centre Reinforcement:

S=I/y

Where

I = 1.047-008 m4= 10470 mm4

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

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

S =I/y=1047092.008=227.5889mm3

S = 227.5889 mm3

RESULT

The Roof is created with reinforcements and the heat distortion , snow load criteria and the section modulus are calculated.

FINAL MODEL

1.Rear Roof Rail:

2.Centre Reinforcement and Bow Roofs:

3.Front Roof Rail:

Multi View:

In this project , learned how to create rails as per the given mastersection and design and learned how to calculate and what are the criteria for Heat distortion and Snow load conditions.