Hertz Contact Stresses Sullivan

Precision Machine Design ME 250

Hertz Contact Stresses

Mark Sullivan February 9, 2009

Precision Machine Design Hertz Contact Stresses

Sullivan Feb 9, 2009

Acknowledgements •  Text and figures in these lecture notes are taken from the

following sources: –  Slocum, A. H., Precision Machine Design, SME, 1992. –  Slocum, A. H., FUNdaMENTALs of Design, MIT, 2008. –  Culpepper, M., “2.75 Constraint Lecture,” MIT, 2001. –  Precision Engineering Research Group, MIT

•  http://pergatory.mit.edu/ •  http://pergatory.mit.edu/kinematiccouplings/

Hertz Contact Stresses

Chart from “FUNdaMENTALs of Design,” Slocum

Hertz Contact Stresses (2)

Equations from FUNdaMENTALs of Design, Slocum

This is the “general case.”

For solved cases, see Roark or MathCAD

Hertz Contact Stresses (3)

Radial

Compressive

Graph and equations from FUNdaMENTALs of Design, Slocum

Kinematic Coupling Analysis

Chart from FUNdaMENTALs of Design, Slocum

KC Analysis – Culpepper

KC Analysis – Culpepper (2)

KC Analysis – Culpepper (3)

Hertz Contact Stress Reduction

From FUNdaMENTALs of Design, Slocum

•  To reduce Hertz stresses: –  Decrease force (F) –  Increase “ball” radius (R) –  Decrease modulus (E)

•  To reduce deflection: –  Decrease force (F) –  Increase “ball” radius (R) –  Increase modulus (E)

•  To reduce contact area: –  Decrease force (F) –  Decrease “ball” radius (R) –  Increase modulus (E)

• Contact pressure is proportional to: –  Force to the 1/3rd power (F1/3) –  Radius to the -2/3rd power (R-2/3) –  Modulus to the 2/3rd power (E2/3)

• Deflection3 is proportional to: –  Force to the 2/3rd power (F2/3) –  Radius to the -1/3rd power (R-1/3) –  Modulus to the -2/3rd power (E-2/3)

• Contact ellipse diameter is proportional to: –  Force to the 1/3rd power (F1/3) –  Radius to the 1/3rd power (R1/3) –  Modulus to the -1/3rd power (E-1/3)

KC Analysis – Sullivan

KC Analysis – MathCAD

Pop Quiz: Contact Stress • Which 3 DOF mount has lower Hertz contact stresses? Why? • How could you make the stresses even lower?

3-Ball Nest

Tetrahedron

Hertz Contact Stresses Sullivan

Documents

80 HERTZ BROCHURE A4 WEB noBleed copy€¦ · 80 hertz studios audio post services . ao hertz ao hertz 0161 80 hertz . a c o mca s r c 0m p any history hat trick blin television a

Hertz Presentation

Adams County, Illinois...Dan Sullivan Joe Sullivan Jim Sullivan Bill Sullivan Matt Sullivan Luke Sullivan Michael Sullivan James Sullivan Jim Huff ... All tracts have impressive Crop

Contact Hertz

Hertz Case Study

Hertz Foundation

Real-World Solutions Hertz Corporation Case Study · Hertz Corporation Case Study About Hertz The Hertz Corporation is the world's largest general use car rental brand, operating

Hertz Berg Model

= 1,604,000 Hertz = 1,445,000 Hertz = 760,000 Hertz = 192,000 Hertz = 478,000 Hertz = 417,000 Hertz = 427,000 Hertz = 234,000 Hertz = 720,000 Hertz = 369,000 Hertz

Hertz Corporate Profile

Real-World Solutions Hertz Corporation Case Study Corporation Case...Hertz Corporation Case Study About Hertz The Hertz Corporation is the world's largest general use car rental brand,

Frank Hertz Experiment - University of Rochesteradvlab/reports/sliwa_richard_franck_hertz.pdf · Frank Hertz Box Control Box Multimeter Electrometer ... The Franck-Hertz Experiment

Hertz Contact Stresses

Hertz Investor Presentationfilecache.drivetheweb.com/mr5ir_hertz/349/download/BAML+Auto... · Hertz Investor Presentation ... the ultimate parent company of The Hertz ... and this

The Hertz Fellowship

Hertz HERTZ. THE AFFORDABLE WAY TO SEE EUROPE. … · hertz hertz. the affordable way to see europe. affordable europe® travel agent planning guide. highway driving between cities

Franck Hertz experiment

Hertz gives you Europe on your The Hertz Affordable Europe Explore

Hertz Recruitment

2018 Annual Report Hertz Global Holdings, Inc.filecache.investorroom.com/mr5ir_hertz/732/download/2018 Hertz A… · 2018 Annual Report Hertz Global Holdings, Inc. Title: HERTZ GLOBAL