HERTZ CONTACT THEORY AND ITS APPLICATIONS

1. APPLICATION OF
HERTZ CONTACT STRESS THEORY
Presented by:
Ruchika Zalpouri
&
Kulwinder Kaur

2. CONTACT MECHANICS
• Study of the deformation of solids that touch each other at one or
more points.
• Contact mechanics provides necessary information:
 For the safe and energy efficient design of technical
systems
 For the study of tribology, contact stiffness, electrical
contact resistance and indentation hardness

3.  Earlier the solutions for calculating high stress values at point or line
of contact were either approximations or contained some unknown
empirical constant.
INTRODUCTION
 To solve this problem
 In 1882, Heinrich Hertz developed an analytical method for
solving these issues.

4. • Hertz contact theory is a classical contact theory which can
calculate the contact stress and deformation.
• The original theory was derived for two non-conforming surfaces
that in a no load situation would result in a point or line contact.
• Compressive stress that is generated when two non-conforming
surfaces are under a forced contact.
HERTZ CONTACT THEORY

5. • Contact is a point or line when there are no applied forces or moments.
• Area of contact is dependent on the force applied and shape of the
body.
• Non-adhesive, meaning the two surfaces require no force to separate.
• Hertz Contact theory maintains both surfaces are frictionless. This
means only the normal stresses will be translated between the two
surfaces.
HERTZ CONTACT THEORY

6. ASSUMPTIONS
Both are elastic bodies
No rigid body motion
Small deformation in contact area
The significant dimensions of the contact area should be much
smaller than the dimensions and the radii of curvature of the bodies
in contact

7. Further will be explained by
Kulwinder Kaur

8. Deformation of the two convex (elastic) bodies

10. Angle of contact, T:

11. Applications on
agricultural
products

12. Crop Method Result Reference
Pumpkin
seed
Hertz (1,2, 3 ) contact
theory,
Boussinesq's theory
and Hooke’s Law for
calculating
young’s modulus
Hertz contact theory
had better results but
among hertz parallel
plate showed good
results.
Emadi et al.
2011
Orange Hertz and finite
contact theory to
calculate poison ratio,
elasticity modulus and
bioyeild point
Best fit was obtained
between FEM and
Hertz theory.
Christopher
and Chika,
2017

13. 1. Parallel plates
(whole specimen)
2. Spherical
Indenter Contact
(whole specimen)
3. Spherical
Indenter Contact
(Flat Specimen)
Elastic modulus

14. Hooke’s Law
Boussinesq's theory
Elastic modulus
Where,

16. Errors might occur in products of irregular geometry and shapes.
Grinding of products while applying the force gives irregularity in result.
Dependent on size of indenter.
The sensitivity of contact point needs to be known every time.
Cannot be applied to rigid dies
Limitations Of Hertz Contact
Stress Theory

17. Thank you