OPTI 521 Optomechanical Engineering Hertzian Contact Stresses December 2011 Nicholas LeCain 1 OPTI 521 Optomechanical Engineering • • • • • • Overview Hertzian Contact Stresses Non-Hertzian Contact Stresses Failure modes Implications in Opto-Mechanics Summary 2 OPTI 521 Optomechanical Engineering Overview • 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. L-3 Insight Technology http://t0.gstatic.com/images?q=tbn:ANd9GcT30f7OpEmou XxTqMSO4X0Mx0HIx3tWEQqXLnnap 3 OPTI 521 Optomechanical Engineering Hertzian Contact Stresses Ball with no contact force Deformation Caused by Hertzian Contact Stresses L-3 Insight Technology 4 OPTI 521 Optomechanical Engineering Hertzian Contact Stresses • 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. L-3 Insight Technology http://t3.gstatic.com/images?q=tbn:ANd9GcQFrTP2mp T7mzxryu0OSUB0ifFE5vh8P2ILcHtfo9dx6CjcfYB8CQ 5 OPTI 521 Optomechanical Engineering Hertzian Contact Stresses Spherical Bodies • Spherical Equations 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 L-3 Insight Technology 6 OPTI 521 Optomechanical Engineering Hertzian Contact Stresses Spherical Bodies cont. • Principle and Shear Stresses L-3 Insight Technology 7 OPTI 521 Optomechanical Engineering • Hertzian Contact Stresses Cylindrical Bodies For Cylindrical contacts instead of a circular contact area an elliptical contact area is produced. The equations below cover this change. L-3 Insight Technology 8 OPTI 521 Optomechanical Engineering • Hertzian Contact Stresses Cylindrical Bodies cont. Note: In the cylindrical case the principle stresses are not constant. For more detailed information on this see Mechanical Engineering Design, Shigley 2004 L-3 Insight Technology 9 OPTI 521 Optomechanical Engineering Non-Hertzian Contact Stresses • Applications where the assumptions listed in the previous slide do not apply fall under NonHertzian contact stresses. – These applications must be handled with finite element analysis or with the Smith-Liu equations L-3 Insight Technology 10 OPTI 521 Optomechanical Engineering Failure Modes • Permanent Plastic Deformation of parts • Fatigue damage http://www.vibanalysis.co.uk/vibcases/vibch13/vibch13p1.jpg Fatigue damage on bearing. Plastic Deformation of Aluminum L-3 Insight Technology 11 OPTI 521 Optomechanical Engineering Implications in Opto-Mechanics • Weight limits for kinematic mounts • Design limits of Sharp Edge lens seats • Point Contacts for mirror supports • Point Contacts of micrometers http://assets.newport.com/web900w-EN/images/8566.jpg http://www.optics.arizona.edu/optomech/Fall11/Notes/27%20 Mounting%20of%20lenses.pdf L-3 Insight Technology 12 OPTI 521 Optomechanical Engineering Summary • 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. L-3 Insight Technology 13