Contact Parameters
Contact Geometry
Load P [N]1000 N
Radius R1 [mm]10.0 mm
Radius R2 [mm]∞ (flat)
Max value = flat (∞)
Elastic Modulus E1 [GPa]210 GPa
Elastic Modulus E2 [GPa]210 GPa
Poisson's Ratio ν10.30
Friction Coefficient μ0.05
Yield Stress σy [MPa]600 MPa
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Contact radius a [μm]
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Contact radius b [μm]
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Peak pressure p₀ [MPa]
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Max τ [MPa]
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τmax depth z [μm]
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Dang Van Result
Contact Ellipse Pressure Distribution (Ellipsoidal Model)
Subsurface Stress Distribution vs Depth z
Hertz Contact Theory
Equivalent modulus and equivalent radius:
$$\frac{1}{E^*} = \frac{1-\nu_1^2}{E_1} + \frac{1-\nu_2^2}{E_2}, \quad \frac{1}{R^*} = \frac{1}{R_1} + \frac{1}{R_2}$$Ball-ball contact (circular contact ellipse: a=b):
$$a = \left(\frac{3PR^*}{4E^*}\right)^{1/3}, \quad p_0 = \frac{3P}{2\pi a^2}$$Maximum subsurface shear stress: $\tau_{max} \approx 0.31\,p_0$ at depth $z \approx 0.48a$
Contact pressure distribution: $p(r) = p_0\sqrt{1 - (r/a)^2}$
CAE Integration: Ball bearing dynamic load capacity C is back-calculated from RCF life L₁₀ based on Hertz pressure p₀. In FEM, contact elements (CONTA/TARGET) reproduce Hertz analysis and assess nonlinear material and plasticity effects.