hertz contact stresses sullivan
DESCRIPTION
Hertz Contact StressesTRANSCRIPT
Precision Machine Design ME 250
Hertz Contact Stresses
Mark Sullivan February 9, 2009
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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/
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Precision Machine Design Hertz Contact Stresses
Sullivan Feb 9, 2009
Hertz Contact Stresses
Chart from “FUNdaMENTALs of Design,” Slocum
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Precision Machine Design Hertz Contact Stresses
Sullivan Feb 9, 2009
Hertz Contact Stresses (2)
Equations from FUNdaMENTALs of Design, Slocum
This is the “general case.”
For solved cases, see Roark or MathCAD
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Precision Machine Design Hertz Contact Stresses
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Hertz Contact Stresses (3)
Shear
Radial
Compressive
Graph and equations from FUNdaMENTALs of Design, Slocum
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Precision Machine Design Hertz Contact Stresses
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Kinematic Coupling Analysis
Chart from FUNdaMENTALs of Design, Slocum
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Precision Machine Design Hertz Contact Stresses
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KC Analysis – Culpepper
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Precision Machine Design Hertz Contact Stresses
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KC Analysis – Culpepper (2)
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Precision Machine Design Hertz Contact Stresses
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KC Analysis – Culpepper (3)
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Precision Machine Design Hertz Contact Stresses
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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)
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Precision Machine Design Hertz Contact Stresses
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KC Analysis – Sullivan
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Precision Machine Design Hertz Contact Stresses
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KC Analysis – MathCAD
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Precision Machine Design Hertz Contact Stresses
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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