Compare Hertz contact-radius scaling while retaining the assumed curvature and reduced elastic modulus.
Define the circular contact model
For an elastic nonadhesive sphere/flat Hertz model, contact radius satisfies a³ = 3RF/(4E*). The reduced modulus includes the elastic response of both bodies. Primary reference: Hertz radius, equations 1–3.
Use the applicable small-contact and material assumptions before applying the relation. Radius a describes the modeled contact patch; it is not the sphere radius R. A surface coating, adhesion, plastic deformation or a noncircular geometry can require a different model.
A hypothetical scaling comparison
Assume a fictional F = 100 N, R = 0.01 m and E* = 100 GPa. The cube-root calculation gives a approximately 0.1957 mm. With the same curvature and modulus but F = 800 N, a becomes approximately 0.3915 mm. Eight times the force doubles the radius, rather than multiplying it by eight.
Under another explicit one-input comparison, eight times the reduced modulus halves a. Four times R increases a by 4^(1/3), approximately 1.587. These invented cases illustrate dependencies; they do not establish an actual contact patch, permitted pressure or component life.
Preserve the model inputs
Prepare separate fields for contact geometry, applied normal load, reduced-modulus definition and the inferred radius. Retain the constituent elastic inputs and how they were combined. A reported radius derived from a model should remain distinguishable from directly observed geometry.
Ask the responsible analyst whether the relevant contact falls within the stated assumptions and what additional pressure, stress or durability assessment is needed. No material pair, load allowance or installed HM contact result is supplied. The useful comparison checks which changed input explains the modeled patch size.
Customer Questions
Does eight times load give eight times radius?
The stated model gives a factor of two with other inputs fixed.
Is E* simply one body’s Young modulus?
Retain the reduced-modulus definition for the contact pair.
Does this radius establish a permitted load?
The actual component assessment remains necessary.
Primary References
These references support the technical principles discussed in this guide. The worked examples and review questions are educational.
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