FORMULAS FOR CONTACT STRESS CALCULATIONS


The formulas and parameters used in Hertzian Contact Stress Calculator are given below. According to the input parameters and selection of contact type from the spherical and cylindrical contacts, suitable formulas are selected from the list of equations given below for the calculation of Hertzian contact stresses.

Calculation Steps and list of equations for Hertzian Contact:

Step Parameter/Condition Symbol Equation
1 Calculation for spherical contact
1.1 Contact radius a Contact radius equation for spherical contact
1.2 Maximum pressure pmax Maximum contact pressure equation for spherical contact
1.3 Principal stress σx Principal stress (Sigma-x) for spherical contact
1.4 Principal stress σy Principal stress (Sigma-y) for spherical contact
1.5 Principal stress σz Principal stress (Sigma-z) for spherical contact
1.6 Maximum shear stress τmax Maximum shear stress (tau-max) for spherical contact
2 Calculation for cylindrical contact
2.1 Contact half-width b Contact half-width equation for cylindrical contact
2.2 Maximum pressure pmax Maximum contact pressure equation for cylindrical contact
2.3 Principal stress σx Principal stress (Sigma-x) for cylindrical contact
2.4 Principal stress σy Principal stress (Sigma-y) for cylindrical contact
2.5 Principal stress σz Principal stress (Sigma-z) for cylindrical contact
2.6 Shear stress τxz Shear stress (tau-xz) for cylindrical contact
2.7 Shear stress τyz Shear stress (tau-yz) for cylindrical contact

Note: For a plane surface, use d = ∞. For an internal surface, the diameter is expressed as a negative quantity.



List of Parameters :

Symbol Parameter
F Applied force
ν1 Object-1 Poisson’s ratio
E1 Object-1 elastic modulus
v2 Object-2 Poisson’s ratio
E2 Object-2 elastic modulus
d1 Object-1 diameter
d2 Object-2 diameter
z Depth below the surface
l Contact length of cylinders

Supplements:

Link Usage
Hertzian contact calculator Calculates contact parameters such as contact pressure, shear and Von Misses stresses for spherical and cylindrical contact cases.

Reference: