1 hertzian contact stresses december 2011 nicholas lecain opti 521 optomechanical engineering
TRANSCRIPT
1
Hertzian Contact Stresses
December 2011Nicholas LeCain
OPTI 521 Optomechanical Engineering
• Overview• Hertzian Contact Stresses• Non-Hertzian Contact Stresses• Failure modes• Implications in Opto-Mechanics• Summary
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OPTI 521 Optomechanical Engineering
• Contact stresses– Stress developed from
two radii in contact– Stress
• σ=F/A• Force is constant• Area is infinitely small• Stress approaches infinity
– Deformation occurs until area is large enough to reduce stress to below elastic limit of parts.
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Overview
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OPTI 521 Optomechanical Engineering
Ball with no contact force Deformation Caused by Hertzian
Contact Stresses
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Hertzian Contact StressesOPTI 521
Optomechanical Engineering
• Hendrick Hertz first published his work on contact stresses in 1881.
• Work was based on a few assumptions. – Frictionless – Elastic bodies– Isotropic materials– Homogeneous materials– No external shear stress
• Without these assumptions the equations get out of hand pretty quickly and an FEA approach to analysis is required.
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Hertzian Contact Stresses
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OPTI 521 Optomechanical Engineering
• Spherical Equations
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Hertzian Contact StressesSpherical Bodies
Radius of deformed contact area
Maximum pressure from force applied Note: For a flat surface R would equal
infinity and for a concave surface like a spherical hole R would be negative
OPTI 521 Optomechanical Engineering
• Principle and Shear Stresses
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Hertzian Contact Stresses Spherical Bodies cont.
OPTI 521 Optomechanical Engineering
• For Cylindrical contacts instead of a circular contact area an elliptical contact area is produced. The equations below cover this change.
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Hertzian Contact StressesCylindrical Bodies
OPTI 521 Optomechanical Engineering
• Note: In the cylindrical case the principle stresses are not constant. For more detailed information on this see Mechanical Engineering Design, Shigley 2004
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Hertzian Contact StressesCylindrical Bodies cont.
OPTI 521 Optomechanical Engineering
• Applications where the assumptions listed in the previous slide do not apply fall under Non-Hertzian contact stresses. – These applications must be handled with finite
element analysis or with the Smith-Liu equations
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Non-Hertzian Contact StressesOPTI 521 Optomechanical Engineering
• Permanent Plastic Deformation of parts• Fatigue damage
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Failure Modes
Fatigue damage on bearing.
http://www.vibanalysis.co.uk/vibcases/vibch13/vibch13p1.jpg
Plastic Deformation of Aluminum
OPTI 521 Optomechanical Engineering
• Weight limits for kinematic mounts
• Design limits of Sharp Edge lens seats
• Point Contacts for mirror supports
• Point Contacts of micrometers
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Implications in Opto-Mechanics
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http://www.optics.arizona.edu/optomech/Fall11/Notes/27%20Mounting%20of%20lenses.pdf
OPTI 521 Optomechanical Engineering
• Hertzian equations apply to contact stresses created by the contact of radii.
• Hertzian Equations work well if the stated above assumptions apply
• If there are exceptions to the assumptions FEA or more complicated equations must be used.
• In the field of opto-mechanics Hertzian equations work well for the analysis of Kinematic mounts and lens seats.
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SummaryOPTI 521 Optomechanical Engineering