Review Sheet for OPTI 521 at UA
Review Sheet for OPTI 521 at UA
Popular in Course
Popular in Department
This 3 page Class Notes was uploaded by an elite notetaker on Friday February 6, 2015. The Class Notes belongs to a course at University of Arizona taught by a professor in Fall. Since its upload, it has received 14 views.
Reviews for Review Sheet for OPTI 521 at UA
Report this Material
What is Karma?
Karma is the currency of StudySoup.
You can buy or earn more Karma at anytime and redeem it for class notes, study guides, flashcards, and more!
Date Created: 02/06/15
Review of Spherical HertZian Contact Stress James Johnson November 12 2008 OPTl 521 1 Introduction This report discusses the basics of Hertzian contact stress This is the stress created by two curved parts in contact under load If the part was both per fectly spherical without deformation with a plane they would be in contact in an in nitely small area This would lead to in nitely large pressure as 13 lt1 where F is the force applied and A is the contact area This would lead to a physical impossibility Instead the two objects slightly deform increasing the overall contact surface area The more load is applied the greater the deformation to balance it The analysis is also the basis for the contact of gears and stresses they face These stresses are what lead to failure in bearings sockets and gears Similar analysis can be done for cylindrical parts but will not be discussed here 2 Hertzian Equations Assume the two objects in contact a plane and a sphere Each has its own radius of curvature R Poisson s Ration v and Young s Modulus E Assuming a circular contact point with a given load F The two have an effective curvature of R 1 1 1 7 2 R 21le The same can be said for an effective modulus at the contact surface E 7171 17113 3 E 7 E1 E2 The two deform such that there is a nite area of contact of radiusa 3FR 13 a 4 4E This deformation results in an area over which the force is applied cre ating Hertz stress The maximum pressure appears at the center is 73PE 2 PFW lt5 The stresses along each axis can be shown as 7 SaE A R 6 Then A1 5 t 1571gti 7 UT 7 U a CO L 2a2 22 and 2 a 02 T a2 22 8 3 Example A simple example of this would be a ball bearing in contact with a surface of similar material Stainless steel has a modulus of 200GPa and a Poisson ratio of 030 If the ball has a diameter of 20mm and the two are being held together by 10N force This gives a effective radius of R 110mm 1oo1 10mm 9 and a effective modulus of E1 E 7 1 109MP 10 7 a The ball will deform by an amount 310N001mgt13 14 11 lt 4109MPa mm l The maximum Pressure that can be applied is then 800014m 109MPa A 7r 001m 388 x 106 12 Stress in 2 at the center of the sphere is 0001427717712 7 7 6 7 38398 X 10 000142mm2 0012mm2 747KPa 13 4 Conclusion This report shows a simple example of Hertzian analysis It is useful to nd the internal forces of parts in contact to see if it will exceed yield strengths References Shigley7 J Mechanical Engineering Design New York McGraW Hill 1983
Are you sure you want to buy this material for
You're already Subscribed!
Looks like you've already subscribed to StudySoup, you won't need to purchase another subscription to get this material. To access this material simply click 'View Full Document'