Roof challenge

Car Roof Design and Analysis of Reinforcements

Objective:

A dumb solid body of roof CAD model is provided for which following points to be designed and analyzed are as follow,

1. Extracting the styling surface and for the given car roof styling and design the essential flanges and reinforcement, namely Ditch Area, Front Roof Rail, Rear Roof Rail, Centre Roof Rail, and Bow-Roofs.
2. Do a curvature study on the roof and perform calculations for Heat Distortion and Snow load criterion to determine and justify the position of the Bow-roofs.
3. Finding a moment of inertia and Section Modulus for Bow Roof Rails and Centre Roof Rail.
4. Perform a Draft Analysis of each reinforcement.

Software used

NX-CAD & MS Excel

Introduction

An automobile roof is the portion of an automobile that sits above the passenger compartment, protecting the vehicle occupants from sun, wind, rain, and other external elements. Under the styling surface that is seen from the outside, there are many other structures under the roof that contribute to its strength and stability. The number of such reinforcement structures/supports differ with respect to the size of the vehicle. They are primarily installed on flatter areas of the roof to enhance strength.

These are the Front Roof Rail, Rear Roof Rail, Centre Roof Rail, and Bow Roof Design which are given Mastics and spot-welded to roof flanges & ditch areas and improve NVH value by increasing the strength of the roof using mastic sealants.

Design consideration of roof:

• Visibility Criteria
• Head clearance
• Curvature study
• Heat distortion and snow load criteria
• Draft analysis.
• Safety parameters

Roof Crush Test for Passenger Car:

Safety point of view vehicle roof plays a very crucial role especially roll over kind of accidents, in which vehicle tips over onto its side of the roof. And vehicle rollover crashes are the cause of many fatalities and head, neck, and spine trauma around the world.

Therefore, passenger safety is also a very important parameter in front of OEMs. It is not only a marketing strategy but also it is an obligation stipulated by international standards that are now placed in several countries, as well as a governmental requirement. For this reason, strength is a very important criterion for designing a vehicle roof.

The strength of the roof structure to occupant protection in real-world rollover crashes, requiring the maximum moving distance of the roof structure should be less than 127 mm (5 in.) when the induced load is 1.5 times the vehicle weight.

For the test, the passenger car shall be rigidly placed or positioned on a horizontal surface with the doors locked and the window closed. Furthermore, a flat, rigid block with a lower surface a rectangle measuring 30 inches wide by 72 inches long (762mm X 1829mm) shall not move more than 5 inches(127mm), measured as the distance between the original location of the lower surface of the test device and its location as the specified force level is reached, when it is used to apply a force of 1.5 times the unloaded vehicle weight (UVW) or 5000 lbs(22224N), whichever is less, to either side or forward edge of the vehicle.

This test can be conducted on either side of the roof structure, the front left or the front right side but not on both sides in one single test and still meet the requirements of the test. The rigid plate shall not move faster than 0.5 inches/second and the force applied on the plate shall not exceed the lesser of 1.5 times the unloaded vehicle weight (UVW) expressed in kilograms multiplied by 9.8 or 5000lbs (22240N).

Also, the direction of the force shall be downward and perpendicular to the lower surface of the rigid plate and such that it moves in a straight line without rotation. The duration of the test shall not exceed 120 seconds. The longitudinal axis of the plate is pitched forward at a 5 º angle as viewed from the side of the passenger car as shown in below fig..,

The lateral axis or the roll of the plate is such that it forms a 25 º outboard angle with a horizontal surface as viewed from the front of the passenger car as shown in below fig..,

Design Methodology:

Styling Surface to Extracted Surface:

The styling team has provided the solid dump outer panel from that we are extracting the surface to model the necessary reinforcements like Ditch area, Front Roof Rail, Bow Roof Rails,Centre Roof and Rear Doof Rail.

fig; Dump part from Styling team fig; Extracted Surface from Dump body

Design a Ditch Area for Outer Roof Panel:

Styling team provided the master section for the roof ditch area, front roof rail and rear roof rail as per the parameter of visibility criteria, head room clearance and other important parameter dimension like fitment of windshield, sealant rubber etc. All these data are well calculated in the planning stage to design the peripheral component accordingly. Thus, here designing is done just to replicate those input data considering engineering parameters which should be feasible for manufacturing. Master section of front and rear section.

1. Front Ditch Area:

From dump solid part class A surface is extracted and ditch area are developed considering the parameter specified in the following master section.

Flange of around 15mm created with the law extension command, corner relief at rear flanges and positive draft more than 3 degree considering for the drawing operation process. Overall thickness of sheet metal consider 0.75mm throughout.

fig: Front Master Section fig; Front Ditch Area

2. Rear Ditch Area:

Surface is offset from the outer panel to form the ditch area and with the law extension command, corner relief at rear flanges and positive draft in required degree considering for the drawing operation process. Overall thickness of sheet metal for outer panel consider 0.75mm throughout.

fig; Rear Master Section fig; Rear Ditch Area

fig; Roof Panel with Front and Rear Ditch Area

Front Roof Rail:

The front rail underpins the rooftop external shell at the front end. It is mounted with support rooftop rail fortification on the two closures. The rails are furnished with embosses to improve the strength over length and the rail is associated with the external board utilizing mastic sealants on one side and the other joinery is spot welded.

Sheet metal thickness: T= 1 mm

Emboss height: 2 < 3T

Flange length: 13.2 > 3T+R

Radius: (R=3mm and 5mmm )> T

fig; Front Roof Rail Master Section fig; Front Roof Rail Section View

Rear Roof Rail:

It is the support which is joined to the Back Door and the Body Side Outer and the inner panels. It is also usually made from Body Side Outer scrap and therefore the thickness of the rail is 0.65 mm. Similar to the Front Roof Rail design, we have to take into consideration the rear Headroom Clearance and the rear visibility criteria while designing the Rear Roof Rail. Inputs are taken from the rear master section shown in fig.

Following points are considered

Headroom clearance: 120mm minimum

Sheet metal thickness: T= 0.75mm

Emboss height: 2 < 3T

Radius: (R=3mm and 5mmm )> T

fig; Rear Roof Rail MAster Section fig; Rear Roof Rail Section View

Bow Roof 1:

The Bow roofs are given to improve the torsional stiffness and load-bearing capacity of the roof structure. The number of bow roofs provided will depend upon the overall dimensions of the roof. Longer the roof more the bow roofs are integrated to BIW frame They are attached to the outer panel using mastic sealants. Each mastic point will have up to 80 mm circular effective area. The positioning of bow roofs is done based on curvature study. The heat distortion criteria and snow load criteria are checked to analyse the position of the bows in various conditions.

The thickness of the Bow Roof is 1 mm and also mastic area has been created.

fig; Bow Roof 1 fig; Section View

Bow Roof 2:

The Bow roofs are given to improve the torsional stiffness and load-bearing capacity of the roof structure. The number of bow roofs provided will depend upon the overall dimensions of the roof.

fig; Bow Roof 2 fig; Section View

Centre Roof Rail:

Centre roof rail is provided to effectively support the flat area of the roof as it is more susceptible to failure under the action of the load. Usually, the centre reinforcement roof rail will be placed at the centre of the roof connecting the B pillar support structure which results in added support in the roll-over test. The thickness of the centre bow roof is 1 mm thickness.

fig; Centre Roof Rail fig; Section View

Mastic Sealants:

Bow Roof Rails and Centre Roof Rail are joined with the help of Mastic Sealant. Here we cant's use the Spot welding because it damages the A class area of the Roof. So, the mastic sealant is used in this area.

Roof Top View:

Bottom View:

Roof Rails in Transparent View :

Isometric View:

Curvature Study on the Roof:

The heat distortion study plays an important role in sheet metal usage. Heat distortion temperature is a temperature limit above which the material cannot be used for structural applications. This study is used to predict the heat distortion temperature at where the material starts to soften when exposed to a fixed load at elevated temperature. In order to avoid bending or damages on roof, based on heat distortion temperature, this study will predict the bow roof position on the roof to strengthen the roof.

Bow – roof prediction Formula

Heat Distortion Criteria:

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

Judgement Condition : OK< 2.7> 3.1

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]

Thickness for the Roof:

Roof Outer Panel, t = 0.75 mm

Front Roof Rail, t = 1 mm

Bow Roof Rail, t = 1 mm

Centre Roof Rail, t = 1 mm

Bow Roof Rail 2, t = 1 mm

Rear Roof Rail, t = 1 mm

Roof Length for styling Surface (L) :

For the L we want take the total of the styling surface don't include the ditch area as shown in below fig..,

Bow Roof Span (l):

Here want to take the distance from the Front Roof Rail to Bow Roof 1 to find the Bow Roof Span as shown in fig.., remaining all the span distance also want to measure.

Rx & Ry (X & Y Curvature):

1. From 0-Y axis, at -3Y about distance 300mm is drawn parallel on the perpendicular plane as shown in fig. after that 100 mm lines are offset to either side of -3Y line. Now centre lines are drawn between each adjacent roof rail edges respectively. Intersection points are marked on the sketch and exit the sketch. Make all geometry in construction lines except the points.
2. Project the intersection points in the sketch to roof surface as shown in fig.
3. Join the projected curves using arc curve and measure the minimum radius and linear dimension as follow & put into the formula to calculate “W” .

fig; At -3Y Axis the intersection points are created

From the above fig, now project the points on the top of the Roof and draw the arc with the three points intersecting area as shown in below fig

fig; Projected Points and make arc

* Find the Rx Curvature and Ry Curvature withe the tool Simple Radius. For example shown in fig below

fig; Rx Arc Curvature

Apply the values in the formula:

To find the Heat distortion apply all the necessary values from the Roof to the given formula.

Heat Distortion Criteria Calculations:

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

R = 2(Rx*Ry)/(Rx+Ry)

Table and Calculations are Performed in MS Excel:

From the above table it can be concluded that all values of W< 2.7 and also not W>3.1 so thus infers that current positioning of Bow roof are good in state as per design and found OK.

Snow Load criteria

Snow load criteria study is done to check the durability of the roof to withstand snowfall and reflex back to its original shape without any permanent deformation once the load is removed.

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)

Judgement condition = Qr ≥ 3.1

250 ≤ s ≤ 380

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 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

Rx & Ry (X & Y Curvature):

1. At 0-Y axis on perpendicular plane to roof as shown in fig. draw 100 mm lines offset to either side of 0Y axis line. Now centre lines are drawn between each adjacent roof rail edges respectively. Intersection points are marked on the sketch and exit the sketch. Make all geometry in construction lines except the points.
2. Project the intersection points in the sketch to roof surface as shown in fig.
3. Join the projected curves using arc curve and measure the minimum radius and linear dimension.
4. Project the intersection plane bow roof and centre roof rail on the horizontal plane to find the moment of inertia of the respective section to find Iy values.
5. Put all the linear and radial dimension in following formula to calculate Qr Value.

fig; At 0Y Axis the intersection points are created

From the above fig, now project the points on the top of the Roof and draw the arc with the three points intersecting area as shown in below fig,

fig; Projected Points and make arc

* Find the Rx Curvature and Ry Curvature withe the tool Simple Radius. For example shown in fig below

fig; Rx Arc Curvature

* To find the Lx and Ly values take the styling surface of the roof

fig; Lx & Ly Values

Moment of Inertia for the Roof Rails:

fig; MOI of Bow Roof 1

fig; MOI of Centre Roof Rail

fig; MOI of Bow Roof 2

Apply the values in the formula:

To find the Snow load apply all the necessary values from the Roof to the given formula.

Snow Load Prediction Formula:

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)

s = L1/2 + L2/2

Table and Calculations are Performed in MS Excel:

It is observed from the values that obtained values of QR> 3.1

From the calculations we found Bow roof 2 has NG, So we have to ask the styling team to modify the surface with curvature in y axis (Ry) as 6356.38. If team is rejected to do modification on curvature.

* Also we can provide emboss in the roof show in the below fig. The Embosses are radically increased the strength of the roof.

Section Modulus:

Section modulus is a geometric property for a given cross-section used in the design of beams or flexural members. Other geometric properties used in the design include an area for tension and shear, the radius of gyration for compression, and the moment of inertia, and the polar moment of inertia for stiffness. Any relationship between these properties is highly dependent on the shape. There are two types of section moduli

• Elastic section modulus
• Plastic section modulus

The Elastic Section Modulus is defined as,

S = I/y

Where,

S: is the Section Modulus

I: is the second moment of area(or area moment of inertia, not to be confused with the moment of inertia)

y: is the distance from the neutral axis to any given fiber. It is often reported using y = c, where c is the distance from the neutral axis to the most extreme fiber

Bow Roof 1:

Create an intersection Curve with the help of the plane and select the Bow Roof 1.

When the intersection curve has been created and hide the model, we will get this curve shown in below fig.

Project the Curve to the XY plane to find the section analysis

Moment of Inertia (MAX), Imax = 2.009691119 x 10^4 [mm^4]

Moment of Inertia (MIN), Imin = 732.973251721 [mm^4]

Section Modulus, S = Moment of Inertia (MOI) / Distance between the neutral axis and the extreme end of the object (y)

S = I/y

y = 29.88 mm

For Maximum MOI,

S = (2.009691119 x 10^4 [mm^4]) ÷ (29.88 mm)

Section Modulus , Smax = 672.587 mm^3

For Minimum MOI,

S = (732.973251721 [mm^4]) ÷ (29.88 mm)

Section Modulus , Smin = 24.53 mm^3

Bow Roof 2:

Create an intersection Curve with the help of the plane and select the Bow Roof 1.

When the intersection curve has been created and hide the model, we will get this curve shown in below fig.

Project the Curve to the XY plane to find the section analysis.

Moment of Inertia (MAX), Imax = 2.035823252 x 10^4 [mm^4]

Moment of Inertia (MIN), Imin = 756.224610739 [mm^4]

Section Modulus, S = Moment of Inertia (MOI) / Distance between the neutral axis and the extreme end of the object (y)

S = I/y

y = 29.97 mm

For Maximum MOI,

S = (2.035823252 x 10^4 [mm^4]) ÷ (29.97 mm)

Section Modulus , Smax = 679.287 mm^3

For Minimum MOI,

S = (756.224610739 [mm^4]) ÷ (29.97 mm)

Section Modulus , Smin = 25.23 mm^3

Centre Roof Rail:

Create an intersection Curve with the help of the plane and select the Bow Roof 1.

When the intersection curve has been created and hide the model, we will get this curve shown in below fig.

Project the Curve to the XY plane to find the section analysis.

Moment of Inertia (MAX), Imax = 4.102095660 x 10^4 [mm^4]

Moment of Inertia (MIN), Imin = 1.799899449 x 10^3 [mm^4]

Section Modulus, S = Moment of Inertia (MOI) / Distance between the neutral axis and the extreme end of the object (y)

S = I/y

y = 36.45 mm

For Maximum MOI,

S = (4.102095660 x 10^4 [mm^4]) ÷ (36.45 mm)

Section Modulus , Smax = 1125.40 mm^3

For Minimum MOI,

S = (1.799899449 x 10^3 [mm^4]) ÷ (36.45 mm)

Section Modulus, Smin = 49.38 mm^3

FRONT ROOF RAIL:

Create an intersection Curve with the help of the plane and select the Bow Roof 1.

When the intersection curve has been created and hide the model, we will get this curve shown in below fig.

Project the Curve to the XY plane to find the section analysis.

Moment of Inertia (MAX), Imax = 2.014024611 x 10^5 [mm^4]

Moment of Inertia (MIN), Imin = 9.896963953 x 10^3 [mm^4]

Section Modulus, S = Moment of Inertia (MOI) / Distance between the neutral axis and the extreme end of the object (y)

S = I/y

y = 61.52 mm

For Maximum MOI,

S = (2.014024611 x 10^5 [mm^4]) ÷ (61.52 mm)

Section Modulus , Smax = 3273.77 mm^3

For Minimum MOI,

S = (9.896963953 x 10^3 [mm^4]) ÷ (61.52 mm)

Section Modulus , Smin = 160.87 mm^3

REAR ROOF RAIL:

Create an intersection Curve with the help of the plane and select the Bow Roof 1.

When the intersection curve has been created and hide the model, we will get this curve shown in below fig.

Project the Curve to the XY plane to find the section analysis.

Moment of Inertia (MAX), Imax = 6.807068056 x 10^5 [mm^4]

Moment of Inertia (MIN), Imin = 3.237667243 x 10^4 [mm^4]

Section Modulus, S = Moment of Inertia (MOI) / Distance between the neutral axis and the extreme end of the object (y)

S = I/y

y = 96.83 mm

For Maximum MOI,

S = (6.807068056 x 10^5 [mm^4]) ÷ (96.83 mm)

Section Modulus , Smax = 7029.92 mm^3

For Minimum MOI,

S = (3.237667243 x 10^4 [mm^4]) ÷ (96.83 mm)

Section Modulus , Smin = 334.37 mm^3

Draft Analysis:

The Draft Analysis command enables you to detect if the part you drafted will be easily removed. This type of analysis is performed based on colour ranges identifying zones on the analysed element where the deviation from the draft direction at any point, corresponds to specified values.

Minimum draft angle of 7° is considered for analysis . Green colour infer on the parts that that all face along the tooling direction has positive draft angle greater than 7° and passed in analysis.

Roof Outer Panel

Front Roof Rail

Bow Roof 1

Centre Roof Rail

Bow Roof 2

Rear Roof Rail

Roof Model Views:

Conclusion:

The Design of Roof, Front roof rail, Rear Roof Rail, Bow Roofs, and reinforcement roof center by following the Master section with the design parameter for the given class A surface is done.

• All reinforcement BIW parts of roof are designed according to the input data provided by the styling team. Designed parts will be submitted to CAE team to carry out further FEM analysis to obtain numerical data to improve the design.
• Made the curvature study and analysis the design for Heat distortion are found OK.
• Made the curvature study and analysis the design for Snow Load are found OK. But

  we found Bow roof 2 has NG, So we have to ask the styling team to modify the surface with curvature in y axis (Ry) as 6356.38. If team is rejected to do modification on curvature.

  * Also we can provide emboss in the roof show in the below fig. The Embosses are radically increased the strength of the roof.

• Moment of inertia, Section Modulus and Draft analysis are carried out to check the feasibility of manufacturing are found OK.