HERTZ CONTACT – PRACTICAL IMPLEMENTATIONS

Construction fundamentals

INTRODUCTION

Hertz contact properties like stiffness and stress can be predicted if the  contact conditions are well known. Therefore the contact should not be over constrained: only “contact points” (in fact circular or elliptical shaped areas) are considered to be useful.

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Generic – rules of thumb
• Equivalent Young’s modulus:
• Stiffness similar to:
• Trade-off between flat on flat (most stiff, high force capacity) and kinematically constrained designs (no over-constrained design, no hysteresis / micro slip).
Ball – rules of thumb
• Ball contact area: circular (radius a).
• For large stiffness use large radius, e.g. by using a segment instead of complete ball.
Convex roller – rules of thumb
• Convex roller contact area: elliptical (half axes a and b)
• Keep convex roller radius (R) max 25 times larger than roller radius (r). Larger ratios imply a line contact and thus; over-constraining the contact.
• For large stiffness use large roller radius r, e.g. by using a segment instead of complete roller.
Ball equations

Approach

Local maximum stress

Convex roller equations

Long half axis

Short half axis

Approach

Local maximum stress