Section Modulus calculation and optimization

Aim - Calculate section modulus of automotive hood and optimise for higher strength.

Objectives -

• Calculate section modulus of automotive hood.
• Optimise section modulus by comparing with improved section.

Moment of Inertia - When a body is free to rotate around an axis, torque must be applied to change its angular momentum. The amount of torque needed to cause any given angular acceleration (the rate of change in angular velocity ) is proportional to the moment of inertia of the body.Moment of inertia may be expressed in units of kilogram meter squared (kg-m^2) in SI units. Mathemaically,

I = M × r²

where,
M = Mass of body
r = Distance from the axis of rotation

Section Modulus - Section modulus is a geometric property for a given cross-section used in the design of beams or flexural members. It is termed as the ratio of the second moment of area and distance from the neutral axis to the extreme fiber.

Formula for section modulus,

S = I/y

Where,

S = Section Modulus

I = Moment of Inertia

Y = Distance between the neutral axis and the extreme end of the object.

Section Modulus for Automotive Hood

We calculating the sections modulus for automotive hood using the NX CAD.

• Import the Hood desiged model to the NX CAD

• Using the intersection curve tool , we get the intersection of the hood outer and inner panel with respect to the mirror plane.

• Project the intersection curve on Plane and join the both side of the curve to form a closed curve
  

• Measure the distance from left end to the right end , because it is important to finding the section modulus.

The measured distance is equal to 486 mm.

• We get the Moment of Inertia using the Section Inertia Analysis tool. In section inertia analysis tool we select the curve and make the section type to hollow and the thickness is 0.75mm .

CALCULATION

Moment of inertia (max) = 1.55666*10^7 mm^4

Moment of inertia (min) = 1.144303*10^5 mm^4

Distance between both end = 486 mm

So Y = 486/2 = 243 mm

Section Modulus = MOI / Y

so

Maximum Section modulus,

Smax = (1.55666*10^7) / 243 = 64060.1 mm^3

Minimum section modulus,

Smin = (1.144303*10^5) / 243 = 471 mm^3

Improved Section Modulus

We improved the section modulus by offseting the inner panel to 0.5mm to opposite of the outer panel for increasing the area.

PROCEDURE :

• Offset the inner panel to the 0.5mm .

• Using the intersection curve tool , we get the intersection of the hood outer and offseted inner panel with respect to the mirror plane.

• Project the intersection curve on Plane and using the sketch , join the both side of the curve to form a closed curve.

• Measure the distance from left end to the right end , because it is important to finding the section modulus.

The measured distance is equal to 486 mm.

• We get the Moment of Inertia using the Section Inertia Analysis tool. In section inertia analysis tool we select the curve and make the section type to hollow and the thickness is 0.75mm .

• 

CALCULATION

Moment of inertia (max) = 1.55225*10^7 mm^4

Moment of inertia (min) = 1.185815*10^5 mm^4

Distance between both end = 486 mm

So Y = 486/2 = 243 mm

Section Modulus = MOI / Y

so

Maximum Section modulus,

Smax = (1.55225*10^7) / 243 = 63878.6 mm^3

Minimum section modulus,

Smin = (1.185815*10^5) / 243 = 488 mm^3

CONCLUSION

Thus sectional modulus for hood design is calculated and optimized design is also done to increase the section modulus of the hood.

From this we concluded that, as we improving the cross section the moment of inertia and section modulus increases which means the strength of component is increases. That is Moment of Inertia is directly proportional to the strength of the material.