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BMayer@ChabotCollege.edu ENGR -36_Lec-26_Belt-Friction.ppt1Bruce Mayer, PEEngineering-36: Engineering Mechanics - Statics

Bruce Mayer, PELicensed Electrical & Mechanical Engineer

BMayer@ChabotCollege.edu

Engineering 36

Appendix B:Belt Friction

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BMayer@ChabotCollege.edu ENGR -36_Lec-26_Belt-Friction.ppt2Bruce Mayer, PEEngineering-36: Engineering Mechanics - Statics

Outline - Friction

The Laws of Dry Friction Coefficient of Static Friction Coefficient of Kinetic (Dynamic) Friction

Angles of Friction Angle of static friction Angle of kinetic friction

Angle of ReposeBelt Friction Contact Angle

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BMayer@ChabotCollege.edu ENGR -36_Lec-26_Belt-Friction.ppt3Bruce Mayer, PEEngineering-36: Engineering Mechanics - Statics

Basic Friction - Review

The Static Friction Force Is The force that ResistsLateral Motion. It reaches a Maximum Value Just Prior to movement. It is Directly Proportional to Normal Force:

N F sm

After Motion Commences The Friction Force Dropsto Its Kinetic Value N F k k

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BMayer@ChabotCollege.edu ENGR -36_Lec-26_Belt-Friction.ppt5

Bruce Mayer, PEEngineering-36: Engineering Mechanics - Statics

Belt Friction cont

Write the Equilibrium Eqns for Belt Element PP if T 2>T1

2sin2sin0

2cos

2cos0

T T T N F

N T T T F

y

s x

Eliminate N from the Equations

2sin

2sin

2sin

2cos

2cos

2cos0

2sin

2sin

2cos

2cos0

2sin

2sin

T T T T T T

T T T T T T F

T T T N F

s

s x

y

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BMayer@ChabotCollege.edu ENGR -36_Lec-26_Belt-Friction.ppt6

Bruce Mayer, PEEngineering-36: Engineering Mechanics - Statics

Belt Friction cont.1

Combining Terms

2sin2

2cos0

T T T s

Divide Both Sides by

2

2sin22

cos0

T T T s

Now Recall From Trig And Calculus

d

d Lim Lim

001

sin10cos

So in the Above Eqn Let: /2 0; Which Yields

T dT T T d dT

dT T d dT

s s 2 as20

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BMayer@ChabotCollege.edu ENGR -36_Lec-26_Belt-Friction.ppt7

Bruce Mayer, PEEngineering-36: Engineering Mechanics - Statics

Belt Friction cont.2

The Belt Friction Differential Eqn

Integrate the Variables-Separated Eqn within Limits T( = 0) = T 1 T( = ) = T 2

From Calculus

Now Take EXP{of the above Eqn}

d dT T

T d dT

s s1

VarsSep

12120 lnlnln12

1 T T T T d dT T s sT

T

s s eT T ee T T 12ln 12

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BMayer@ChabotCollege.edu ENGR -36_Lec-26_Belt-Friction.ppt8

Bruce Mayer, PEEngineering-36: Engineering Mechanics - Statics

Belt Friction Illustrated

This is a VERYPOWERFULRelationship

Condsider the Case atRight. Assume A ship Pulls on the Taut

Side With A force of 4 kip

(2 TONS!) The Wrap-Angle = Three

Revolutions, or 6 s = 0.3

seT

T

1

2

The Tension, T 1, Applied bythe Worker

lbe

kipeT

T s

144

63.02

1

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BMayer@ChabotCollege.edu ENGR -36_Lec-26_Belt-Friction.ppt9

Bruce Mayer, PEEngineering-36: Engineering Mechanics - Statics

WhiteBoard Work

Lets Work Belt Friction

Problems

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BMayer@ChabotCollege.edu ENGR -36_Lec-26_Belt-Friction.ppt10

Bruce Mayer, PEEngineering-36: Engineering Mechanics - Statics

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Bruce Mayer, PEEngineering-36: Engineering Mechanics - Statics