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3 years ago

12

4. Determine the size of the contact patch, relative displacement and the maximum contact pressure for a 20-mm-dia steel ball ro

lled against a flat aluminum plate with 1 kN force. Take Esteel = 200 GPa, νsteel = 0.3, EAl = 70 GPa and νAl = 1/3.

1 answer:

wel3 years ago

3 0

Answer:

0.0806 mm

735.588 MPa

Explanation:

Given data:

Esteel = 200 GPa

vsteel = 0.3,

EAI = 70 GPa, vAI = 1/3

diameter of steel ball = 20-mm

Applied force = 1 kN force

density of steel ( ρ ) = 8050 kg/m^3

weight of steel = ρvg = 0.33 N

<u>Calculate the size of </u>

<u><em>i) contact patch</em></u>

size of contact patch = $\sqrt[3]{\frac{3FR}{4E} }$ ----------- ( 1 )

where: F = 1000 + 0.33 = 1000.33 N , r = 0.01 m,

E = 57.26 * 10^9 ( calculated value )

Input values into equation 1

size of contact patch ( a ) = 0.0806 mm

<u><em>ii) maximum contact pressure </em></u>

P = 3F / 2πa^2

= ( 3 * 1000.33 ) / 2π(0.0806)^2

= 735.588 MPa

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