A presentation that gives information about contact stress written by Eng. Mohamed Akram Hosney

1. Contact stresses
Eng.:
Mohamed Akram 1

2. Objects
1. Introduction.
2. Hertzian theory.
3. Hertzian theory assumptions.
4. Non Hertzian Contacts.
5. Common Engineering Contact Applications .
6. Real and Nominal Area of Contact Measurement.
7. Experimental Contact Stress Analysis.
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3. 1. Introduction
• contact stress is a description of the stress
within mating parts.
• It causes serious problems if not take it into
account in some cases.
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4. 1. Introduction
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5. 2. Hertzian theory
• When two curved bodies are brought into contact they
initially contact at a single point or along a line.
• With the smallest application of load elastic
deformation occurs and contact is made over a finite
area.
• A method for determining the size of this region was
first described by Heinrich Hertz in 1881.
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6. 3. Hertzian theory assumptions
• The strains are small and within the elastic limit.
• Each body can be considered as an elastic half space,
i.e., the area of contact is much smaller than the
characteristic radius of the body.
• The surfaces are continuous and non-conforming.
• The surfaces are frictionless.
• The gap (h) between the
undeformed surfaces can be
approximated by an expression of the
form
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8. • Cylinders in Contact– VerticalStressDistribution
along Centerlineof ContactArea
• The maximum shear and Von Mises stress are reached
below the contact area.
• This causes pitting where little pieces of material break out
of the surface.
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9. • Spheres in Contact– VerticalStressDistribution
at Centerof ContactArea
• The maximum shear and Von Mises stress are reached below the
contact area.
• This causes pitting where little pieces of material break out of the
surface.
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10. 4. Non-Hertzian Contacts
1. Flat Rigid Planar Punch
• A flat-ended punch, of width 2b and of infinite length in the y-
direction, pressed onto an elastic half-space with a force per
unit length P .
• The surface of the punch is assumed frictionless .
• Contact occurs across the width of the punch, 2b.
• The pressure distribution is given by:
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11. 4. Non-Hertzian Contacts
• the deflection can only be presented relative to some datum.
The normal deflection uz of the surface, outside the contact
region, is given by:
where δ is the normal deflection at an
arbitrary datum point.
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12. 4. Non-Hertzian Contacts
2. Flat Rigid Axisymmetric Punch
• In this case the punch has a circular section of radius a.
• It is pressed onto an elastic half-space with a force P.
• The surface of the punch is assumed frictionless.
• Contact occurs across a circle of radius a and the resulting pressure
distribution is (Timoshenko and Goodier, 1951)
• The penetration ∆ of the punch is given by:
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13. 4. Non-Hertzian Contacts
3. Indentation by an Angular Wedge
• If a two-dimensional wedge of semi-angle α is pressed onto a
frictionless elastic half-space with a force per unit length, P
then contact is made over a rectangular region of semi-width
b, such that
• This time the pressure distribution
has a singularity at the wedge apex
and is given by:
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14. 5. Common Engineering Contact Applications
• Gears
• Meshing gear teeth are subjected to bending stresses and contact
stresses.
• The appropriate values of R1, R2and Pare then used in the Hertz
relations to determine the geometry of the contact and associated
stresses.
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16. 5. Common Engineering Contact Applications
• Ball Bearings
• The rolling element is loaded against the conforming grooves in the
inner and outer raceways.
• For a radially loaded ball bearing the contact between the ball and
either the inner or outer raceway will be elliptical.
• The radii are readily obtained from the ball bearing geometry.
• For a bearing containing )z( balls carrying a radial load, F, the
maximum load on the ball, P(located diametrically opposite the
loading point) is approximated by :
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17. 5. Common Engineering Contact Applications
• This load and the contact radii can then be used in the
expressions for elliptical point contact to determine the
contact area and stresses.
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18. 6. Real and Nominal Area of Contact Measurement
• Electrical and Thermal Resistance
Measurement of the electrical resistance between contacting
surfaces can give information about the true area of contact
(Holm, 1967; Bowden and Tabor, 1939).
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19. 6. Real and Nominal Area of Contact Measurement
• Ultrasonic Reflection
A wave of ultrasound incident at an interface between two
materials will transmit through regions of contact and be
reflected back at air gaps.
This phenomenon can be used to investigate the true area of
contact at an interface (Kendall and Tabor, 1971)
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20. 7. Experimental Contact Stress Analysis
• Photoelasticity and Caustics
The contacting bodies are modeled in photoelastic material,
such as polycarbonate or epoxy resin. For two-dimensional
applications a planar model is fabricated and loaded in a
polariscope
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21. Thanks
M A