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INPUT   DATA

♥ EXAMPLE Of Input/Output

Title

Diameter of sphere, d1		m
Modulus of elasticity of sphere, E1		109N/m2
Poisson's ratio of sphere, υ1
Modulus of elasticity of flat body, E2		109N/m2
Poisson's ratio of flat body, υ2
Force applied, F		N

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OUTPUT   VARIABLES   &   GRAPHS

VARIABLES	Values	Units
♦ Radius of area of contact, a		10-6m	Graphs:  Stresses Vs Distance in z direction in Sphere    Stresses Vs Distance in z direction in Flat body
♦ Max contact Pressure, pmax		106N/m2
♦ Relative displacement, δ		10-6m
♦ Normalized shear stress in sphere, τmax,1		pmax
♦ τ max,1 acting at normalized distance		a
♦ Normalized shear stress in flat body, τmax,2		pmax
♦ τmax,2 acting at normalized distance		a

Stresses And Strains Due to Pressure Between Elastic Bodies

Contact loading occurs between machine elements such as rolling metal wheels, meshing gear teeth and bearings. Consider a sphere on a flat body being subjected to a compressive force F. The initial point of contact develops into an area of contact over which the load is distributed. The resulting stresses and deformation are described by the following equations:

where
     F = Compressive force
     z = direction of application of the force
     a = radius of contact area
     p_max = maximum contact pressure
     δ = displacement along axis of loading
     d₁ = diameter of sphere
     E₁ = modulus of elasticity of sphere
     υ₁ = Poisson's ratio of sphere
     E₂ = modulus of elasticity of flat body
     υ₂ = Poisson's ratio of flat body
     υ = Poisson's ratio of sphere or body of interest
     σ_x = principal stress in x direction, for sphere or body
     σ_y = principal stress in y direction
     σ_z = principal stress in z direction
     τ_max = maximum shear stress

Tips

    ◊ Use link EXAMPLE Of Input/Output  to demo data entry expectations and results; you may edit & use it as starting point

BIBLIOGRAPHY

• Brown TH; Marks' Calculations for Machine Design; McGraw Hill, New York, 2005, Chapter 3.
• Young WC & Budynas RG; Roark's Formulas for Stress and Strain; 7th Edition, McGraw Hill, New York, 2002, Chapter 14.
• Moulton A, Grosjean J & Owen G; The Moulton Formulae and Methods - directly usable for calculations in mechanical engineering; Professional Engineering Publishing Ltd, London, UK, 2005.