Question

4. Determine the size of the contact patch, relative displacement and the maximum contact pressure for a 20-mm-dia steel ball rolled against a flat aluminum plate with 1 kN force. Take Esteel = 200 GPa, νsteel = 0.3, EAl = 70 GPa and νAl = 1/3.

Answer 1

0.0806 mm

735.588 MPa

Step-by-step 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

Calculate the size of

i) contact patch

size of contact patch =
`\sqrt[3]{(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

ii) maximum contact pressure

P = 3F / 2πa^2

= ( 3 * 1000.33 ) / 2π(0.0806)^2

= 735.588 MPa