Roof Design

OBJECTIVE:- To design to roof of the car by using master section of front roof rail, centre roof rail, bow roof rail and rear roof rail and skin data.

Introduction- Roof is the top most part of automobile thats sits above passanger compartments which protects the pasanger from the wheather condition like sunlight, rain, wind and other external component. Also protect the pasanger from any injury when car roll over and crash during accident.

Component of roof-

• Front roof rail
• centre roof rail
• Rear roof rail
• Bow roof rail

Designing Consideration-

1. Head roof clearance & visibility criteria- Minimum clearance between roof to head is 85mm
2. Curvature study- curv surface improve the strength of roof compare to flate surface.
3. Heat distortion and snow load criteria- Variation of temperature of atmosphere roof are expand and contract and load of snow so ability roof of car is sufficient strenght to beat this situation.
4. Draft analysis- draft should be postive minimum 7 degree becouse if draft is negative stress concentration is more and punch die life is less.

Methodology- Design of roof in NX software by using skin data given by styling team and master section

• Ditch area of outer pannel- design using master section

• Front roof rail- Front side of roof rail is join by spot welding and back side is join by mastics to improve the strenght of roof. master section & design are below

• Centre roof rail- The location of centre roof rail is to start flate suface area of outer pannel because flate region is beaker than curve region. It join by spot welding on ditch area and mastic by centre region. master section & design are below

• Rear roof rail- It is located back side of outer pannel . It is join by spot welding and hing supported by back door. master section & design are below

• bow roof rail 1 & 2- 1st bow roof location is between front roof rail and centre roof rail, 2nd Bow roof location is between centre roof rail and back roof rail. master section & design are below

• The thickness of roof is 0.75 mm
• Minimum fillet radius is 3.75 mm
• Minimum draft angle should be 7 degree

Draft analysis-

FRONT ROOF RAIL CENTRE ROOF RAIL

BACK ROOF RAIL

Bow roof 1st Bow roof 2nd

CALCULATIONS-

• HEAT DISTORTION ANALYSIS-

Bow–Roof Prediction Formula

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]

Judgment Condition

OK< 2.7

L = 2034.7498mm & t=0.75mm

• Case-l Front roof rail & bow roof 1st

Rx=5740.5656mm , Ry=2487.53039mm

R=(2x5740.5656x2487.5303)/(5740.5656+2487.5303)

R=3470.9928mm

l=376.1968mm

W = [1.73 x 10^(-3) x 2034.7498] + [1.85 x 10^(-8) x (3470.9928^2)/0.75] + [ 1.10x10^(-3) x 376.1968] - 2.68

W = 3.52+0.297+0.413-2.68

W = 1.55

• Case-ll bow roof 1st & Centre roof rail

Rx=4983.27224mm , Ry=6153.22637mm

R=(2x4983.2722x6153.2263)/(4983.2722+6153.2263)

R=5506.7940mm

l=431.3058mm

W = [1.73 x 10^(-3) x 2034.7498] + [1.85 x 10^(-8) x (5506.7940^2)/0.75] + [ 1.10x10^(-3) x 431.3058] - 2.68

W = 3.52+0.748+0.474-2.68

W = 2.06

• Case-lll Centre roof rail & Bow roof 2nd

Rx=3974.48133mm , Ry=10596.4252mm

R=(2x3974.4813x10596.4252)/(3974.48133+10596.4252)

R=5780.7376mm

l=432.1313mm

W = [1.73 x 10^(-3) x 2034.7498] + [1.85 x 10^(-8) x (5780.7376^2)/0.75] + [ 1.10x10^(-3) x 432.1313] - 2.68

W = 3.52+0.824+0.475-2.68

W = 2.14

• Case-lV Bow roof 2nd & Back roof rail

Rx=3285.72847mm , Ry=14551.7595mm

R=(2x3285.7284x14551.7595)/(3285.7284+14551.7595)

R=5360.9712mm

l=340.4779mm

W = [1.73 x 10^(-3) x 2034.7498] + [1.85 x 10^(-8) x (5360.9712^2)/0.75] + [ 1.10x10^(-3) x 340.4779] - 2.68

W = 3.52+0.709+0.374-2.68

W = 1.92

• SNOW LOAD ANALYSIS-

Snow Load Prediction Formula

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

Judgment condition

Qr ≥ 3.1

250 ≤ s ≤ 380

Ly = 1930.082 for all the cases

• CASE l Front roof rail & bow roof 1st

Y= 460.3253mm = L1 L2 = 511.82

Iy = 1897.347 mm^4 Lx = 1152.36 mm

Ry = 2517.096mm Rx = 4590.33

My = Y(Ly-Y) = 460.3253(1930.082-460.3253) = 6,76,566.19 mm^2

α = 6,76,566.19 x 1152.36² x 10^(-12) = 0.8984

^{S = 460.325/2 + 511.82/2 = 486.0725}

^{Qr = [1897.347 x 0.75^2] / [ 0.8984 x 486.0725 x [(4590.33+ 2517.09)/2]^2 x 10^-8] = 19.352}

• CASE ll bow roof 1st & Centre roof rail

Y= 968.4770mm L2 = 512.22

L1 = 511.82 mm Iy = 2367.00 mm^4

Lx = 1099.365 mm Rx = 3764.326 mm

Ry = 6101.734 mm

My = Y(Ly-Y) = 968.4770(1930.082-968.4770) = 9,31,292.32 mm^2

α = 9,31,292.32 x 1099.36² x 10^(-12) = 1.125

^{S = 511.82/2 + 512.22/2 = 512.02}

^{Qr = [2367.0028 x 0.75^2] / [ 1.125x 512.02 x [(3764.32+ 6101.73)/2]^2 x 10^-8] = 9.498}

• CASE lll Centre roof rail & bow roof 2nd

Y=1478.28mm L1 = 512.22

L2 = 465.107 mm Iy = 1866.65 mm^4

Lx = 1070.87 mm Rx = 4273.036 mm

Ry = 11046.14 mm

My = Y(Ly-Y) = 1478.28(1930.082-1478.28) = 6,67,889.86056 mm^2

α = 6,67,889.86056 x 1070.87² x 10^(-12) = 0.765

^{S = 465.107/2 + 512.22/2 = 488.66}

^{Qr = [1866.65 x 0.75^2] / [ 0.765 x 488.66 x [(4273.036 + 11046.14)/2]^2 x 10^-8] = 4.78}

RESULT & OBSERVATION:-

Heat Distorsion Table

SR. NO.	CASES	Rx	Ry	R	l	L	t	W	OK/NG
01	Front roof rail & bow roof 1st	5740.5656	2487.53039	3470.9928	376.1968	2034.7498	0.75	1.55	OK
02	Bow roof 1st & Centre roof rail	4983.2722	6153.2263	5506.7940	431.3058	2034.7498	0.75	2.06	OK
03	Centre roof rail & Bow roof 2nd	3974.4813	10596.4252	5780.7376	432.1313	2034.7498	0.75	2.14	OK
04	Bow roof 2nd & Back roof rail	3285.7284	14551.7595	5360.9712	340.4779	2034.7498	0.75	1.92	OK

Snow load Table

SR. NO.	CASES	Iy	a	Lx	Y	S	t	Rx	Ry	Qr	OK/NG
01	Front roof rail & bow roof 1st	1897.347	0.8984	1152.36	460.3253	486.072	0.75	4590.33	2517.09	19.35	OK
02	Bow roof 1st & Centre roof rail	2367.00	1.125	1099.36	968.4770	512.02	0.75	3764.32	6101.734	9.49	OK
03	Centre roof rail & Bow roof 2nd	1866.65	0.765	1070.87	1478.28	488.66	0.75	4273.036	11046.14	4.78	OK

CONCUSION:- For given master section we have design ditch area of outer roof rail, front roof rail, centre roof rail, rear roof rail and 2 bow roof rail.

• The draft angle is postive and minimum 7 degree
• Heat distribution analysis, value of w for all case-l 1.55, case-ll 2.06, case-lll 2.14 and case-lV 1.92, which is less than 2.74 and satiesfied the condistion.
• Snow load analysis, value of Qr for all case-l 19.5, case-ll 9.49 and case-lll 4.78 which is gratter than 3.1 and satiesfied the condistion.
• The roof design sufficient strength and economical for given condition.