Roof challenge

AIM: According to the given Roof styling, create an assembly by developing an essential flanges on the outer roof and create the reinforcements.
Do the curvature study on the roof and perform the calculation for Heat Distortion and Snow Load Criterion to determine and justify the position of the Bow roofs.

INTRODUCTION: An automobile roof is the portion of an automobile that sits above the compartment, protecting the vehicle occupants from Sun Heat, rain wind, and other external factors.

DESIGN PROCESS:

1. Creating an assembly file and creating the seperate components for the assembly as shown in below figure.
   
   
   
2. Double clicking on the Roof1 and save the imported file in the same component.
3. Creating the reinforcement in the seperate components after activating them.
   
4. Creating the Outer Roof according to the Master sections for the Front Roof and Rear Roof.
   
   
   
5. Creating the Front Roof Rails according to the Master Section for Front Roof Rail.
   
   Master Section of Front Roof Rail
   
   
   
6. Creating the Rear Roof Rail using the Master Secion provided for Rear Roof Rail.
   
   Master Section of Rear Roof Rail
   
   
   
7. Creating the Bow Roof1 and Bow Roof2 according to the Master Section for Bow Roofs Rails.
   
   Master Section For Bow Roof
   
   
   
8. Creating the Centre Roof Rail using the Master Section for the Centre Roof Rail when Sunroof is present.
   
   Master Section of Centre Roof Rail when Sunroof is Present
   
9. Performing the calculations determine the position for the Bow Roofs Rail and Centre Roof Rail.
   

   Bow–Roof Prediction Formula

   `W = [1.73 * 10^(-3) * L] + [1.85 * 10^(-8) * (R^2)/t] + [ 1.10*10^(-3) * 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

   1. Case 1: Calculations to determine the position for the Bow Roof 1.
      Given,
      L= 2172.71 mm
      t= 0.75 mm
      l= 803.05 mm
      Rx= 3507.75 mm
      Ry= 4060.12 mm
      R= 3763.78 mm
      
      W= [1.73 x 10^(-3) x 2172.71] + [1.85 x 10^(-8) x (3763.78^2)/0.75] + [ 1.10x10^(-3) x 803.05] - 2.68 =2.412<2.7
      The position of Center Roof Rail is correct as per W=2.412<2.7.
      
      Since, there is the Sunroof pressent in the roof. We can give sufficient space for the Bow Roof 1, so the calculation for the position for the Bow roof 1 can be neglected.
      
      
   2. Case 2: Between Bow Roof1 and Center Roof Rail
      Calculations to determine the position for the Centre Bow Roof Rail, to check whether it is correct or not.
      Given,
      L= 2172.71 mm
      t= 0.75 mm
      l= 421.67 mm
      Rx= 4020.7327 mm
      Ry= 8656.0653 mm
      R= 5490.9331 mm
      
      W= [1.73 x 10^(-3) x 2172.71] + [1.85 x 10^(-8) x (5490.93^2)/0.75] + [ 1.10x10^(-3) x 421.67] - 2.68 =2.593<2.7
      The position of Center Roof Rail is correct as per W=2.593<2.7.
      
   3. Case 3: Between Centre Roof Rail and Bow Roof 2
      Calculations to determine the position of Bow Roof 2, to check whether it is correct or not.
      Given,
      L= 2172.71 mm
      t= 0.75 mm
      l= 429 mm
      Rx= 4339.7978 mm
      Ry= 13155.9581 mm
      R= 6529.6340 mm
      
      W= [1.73 x 10^(-3) x 2172.71] + [1.85 x 10^(-8) x (6529.63^2)/0.75] + [ 1.10x10^(-3) x 429.00] - 2.68 =2.601<2.7
      The position of Bow Roof 2 is correct as per W=2.601<2.7.
      
   4. Case 4: Between Bow Roof 2 and Rear Roof Rail
      Calculation to determine the position of Rear Roof Rail, to check whether it is correct or not.
      Given,
      L= 2172.71 mm
      t= 0.75 mm
      l= 368.13 mm
      Rx= 3699.08 mm
      Ry= 17993.65 mm
      R= 6136.61 mm
      
      W= [1.73 x 10^(-3) x 2172.71] + [1.85 x 10^(-8) x (6136.61^2)/0.75] + [ 1.10x10^(-3) x 368.13] - 2.68 =2.412<2.7
      The position of Rear Roof Rail is correct as per W=2.412<2.7.
      
      

      Sr. No.	BOW	Rx(mm)	Ry(mm)	R(mm)	l(mm)	L(mm)	t(mm)	R²/t(mm)	W	Remark
      1	FR & BR1	3507.75	4060.12	3763.78	803.05	2172.71	0.75	18888053.18	2.311	OK
      2	BR1 & CRR	4020.73	8656.06	5490.93	421.66	2172.71	0.75	40200416.35	2.593	OK
      3	CRR & BR2	4339.79	13155.95	6529.63	429.00	2172.71	0.75	56848090.58	2.601	OK
      4	BR2 & RR	3699.08	17993.65	6136.61	368.13	2172.71	0.75	50210643.05	2.412	OK

      
      
      
10. Calculation for the Heat Distortion using Snow Load Prediction Formula,
    

    `Qr = [Iy * t^2] / [α * s * [(Rx + Ry)/2]^2 * 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

    Judgment condition

    Qr ≥ 3.1

    250 ≤ s ≤ 380
    
    

    1. Case 1: Between Front Roof and Bow Roof 1
       In this case there is Sunroof between front roof and bow roof 1, so we can neglect this calculation because of the Sunroof.
       
       

    2. Case 2: Between Bow roof 1 and Center Roof Reinforcement
       In this case,
       Lx= 1085.45mm Ly= 2011.65mm
       Iy= 879.32mm^4 t = 0.75mm
       L1= 421.67mm L2= 429mm
       Rx= 4020.73mm Ry= 8656.07 mm
       Y = 1222.30mm
       
       S= (L1+L2)/2 =425.33 mm
       My= Y(Ly-Y) = 964822.50 mm^2
       α = My*Lx^2*10^-8 =1.1367 mm^4
       Qr =[Iy*t^2]/[α*S*{(Rx+Ry)/2}^2*10^-8]= 2.546
       
       
    3. Case 3: Between Center Roof Reinforcement and Bow Roof 2
       In this case,
       Lx= 1067.97mm Ly= 2011.65mm
       Iy= 3.250*10^3mm^4 t = 0.75mm
       L1= 429mm L2= 363.13mm
       Rx= 3699.08mm Ry= 17993.66 mm
       Y = 1649.61mm
       
       S= (L1+L2)/2 =396.07 mm
       My= Y(Ly-Y) = 597224.80 mm^2
       α = My*Lx^2*10^-8 =0.6811 mm^4
       Qr =[Iy*t^2]/[α*S*{(Rx+Ry)/2}^2*10^-8]= 5.745

Sr. No.	Iy(mm^4)	t(mm)	Lx(mm)	Ly(mm)	L1(mm)	L2(mm)	Y(mm)	Rx(mm)	Ry(mm)	Qr	Remark
1	879.32	0.75	1085.45	2011.65	421.67	429.00	1222.30	4020.73	8656.07	2.546	Not OK
2	3250	0.75	1067.97	2011.65	429.00	363.13	1649.61	3699.08	17993.66	5.745	OK

Draft Analysis of Front Roof Rail, Bow Roof 1, Bow Roof 2, Center Roof Reinforcement and Rear Roof Rail.