Equation 51 Where: is the radius of ball in the ball-on-flat contact, in meters (m). The ball radius is 6 mm or 6E-3 m The reduced modulus, Young’s Equation 52 Where: and are the ratios of the contacting bodies and respectively; Poisson’s ‘A’ ‘B’ and are the moduli of the contacting bodies and respectively (Pa). Young’s ‘A’ ‘B’ The ratio for steel, is 0.3 and its is 2.1 x 1011 Pa. Poisson’s Young’s modulus, The ratio [] for grey cast iron (GCI), is 0.211 and its is 92.30 Poisson’s Young’s modulus, GPa. The radius of the contact area, a, is given by: Equation 53 Where: is the radius of the contact area, m; is the normal load, N; is the reduced radius of curvature, m; is the reduced Pa. Young’s modulus, The maximum, and average, contact pressures, in MPa, are expressed as follows: Equation 54 Equation 55 The maximum is given by the expression: deflection, δ,
Equation 51 Where: is the radius of ball in the ball-on-flat contact, in meters (m). The ball radius is 6 mm or 6E-3 m The reduced Young’s modulus, Equation 52 Where: and are the Poisson’s ratios of the contacting bodies ‘A’ and ‘B’ respectively; and are the Young’s moduli of the contacting bodies ‘A’ and ‘B’ respectively (Pa). The Poisson’s ratio for steel, is 0.3 and its Young’s modulus, is 2.1 x 1011 Pa. The Poisson’s ratio [] for grey cast iron (GCI), is 0.211 and its Young’s modulus, is 92.30 GPa. The radius of the contact area, a, is given by: Equation 53 Where: is the radius of the contact area, m; is the normal load, N; is the reduced radius of curvature, m; is the reduced Young’s modulus, Pa. The maximum, and average, contact pressures, in MPa, are expressed as follows: Equation 54 Equation 55 The maximum deflection, δ, is given by the expression: