Hertz Contact Stress

the limits for hertz contact stresses are given in roark's formulas for stresses and strains. refer it.

From my memories of University:

The hertzian and bearing stresses are not directly comparable, as they are defined and evaluated in different ways. Bearing stresses are generally referred to uniaxial distribution of the stress (measuring tests aim to replicate such condition). Hertzian stresses present a spatial distribution along three coordinate directions (σx, σy, σz).

Actually, the maximum calculated hertzian stresses may result very high (even higher than limit bearing stress). But, the equivalent stresses, e.g. estimated by introducing the Mohr's circles, generally result remarkably smaller.

For example, by applying the Tresca criterion, the yield of the material will occur as the maximum shear stress reaches its allowable limit, being this condition expressed as

max[σx-σy, σy-σz σx-σz] = σ_yield

where σ_yield is the limit yield stress estimated on a tensile stress test (not a bearing stress).

Hi Cipo:

Thanks for ur reply.If hertzian and bearing stresses are not directly comparable then what is the relation between heartizan and shear stress.Because I can compare the heartiaz stress to shear stress or can I compare it to materail tensile stress.

Thanks

If you were able to calculate the three main stresses σ_x, σ_y, σ_z, the maximum equivalent shear stress would be equal to (σ_max - σ_min) / 2 (remember of Mohr's circles formulas).

But, unfortunately, the formulas from Hertz's approach provide the maximum stress on the contact surfaces, and not where the maximum shear stress actually occurs (internally to materials). Besides, the three-dimensional distribution of stresses is not known. This makes the direct application of Tresca's criterion not feasible.

Several authors have estimated the maximum equivalent stress consequent to contact pressures, for particular geometries. As a general result, this value resulted sensibly lower than the maximum stress calculated on the contact surface. This would explain why high values of Hertzian stresses, even much higher than bearing resistance of material, do not show apparent damage on the mating parts.

Roark reports some suggestion for applicable formulas and safety criteria. Otherwise, you should be able to find some suggestions on specific texts, dealing with machine design and/or formulas for stress.