Clutches & Brakes

MAE 4353 – Mechanical Design II Dr Jame Jamess A. A. Kid Kidd d Module 10 Part 1: 10/31/14

Clutches, Brakes, Couplings & Flywheels •

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Static Analysis of Clutches & Brakes Internal Expanding Rim Clutches & Brakes External Contracting Rim Clutches & Brakes Frictional Contact Axial Clutches Disc Brakes Energy Considerations Temperature Rise Friction Materials Miscellaneous Clutches & Couplings Flywheels MAE 4353 F ll 2014

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Introduction •

Elements for managing rotation (transfer & storage)

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Model of Clutch • • •

Friction clutch (or brake) model Slippage between plates causes temperature rise Behaviors include: • • • •

Actuating forces Transmitted torque Energy loss Temperature rise

Fig. 16 – 1

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Static Analysis of Clutch/Brake •

General process:  –

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Estimate, model or measure pressure distribution on friction surfaces Identify relationship between largest pressure and distribution at any point Use static equilibrium to find braking force or torque and support reactions

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Brake/Clutch (“Doorstop”)

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Fig. 16 2

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“Doorstop” cont. Fig. 16 – 2

Leftward movement of floor

Rightward movement of floor

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Internal Expanding Centrifugal-acting Rim Clutches & Brakes Examples: Expanding Ring •

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Centrifugal •

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Typically for automatic operations such as electric motor drives

Magnetic •

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Textile machinery, excavators, machine tools, Clutch may be inside driving pulley

Remote or automatic systems and for complex load cycles

Hydraulic & Pneumatic •

For complex load cycles and remote operations

Fig. 16 – 3

Internal shoe rim clutch Similar approach in “drum” brakes

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Internal Friction Shoe Geometry Can’t assume uniform normal force distribution due to long shoe length

Mechanical arrangement will not allow pressure at “heel” Typically omit friction material near heel (no pressure during engagement and reduces interference when disengaged)

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Fig. 16 – 4 9

Internal Friction Shoe Geometry Evaluate pressure on friction material element at angle θ from hinge pin Designate max pressure as pa at angle θ a Determine pressure distribution via infinitesimal rotation  Δφ about pivot A on point B Deformation & pressure proportional to sinθ In terms of pressure at B and at maximum point:

MAE 4353 Fall 2014

Fig. 16 – 5 10

Pressure Distribution Characteristics •

Characteristics:  –

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Sinusoidal For short shoe (a), largest pressure on shoe is pa at shoe end For long shoe (b), largest pressure is pa at θ a = 90°

Note: Material selection is based on maximum allowable friction and maximum imposed pressure  pa, so “off -shoe” pressures are irrelevant

Fig. 16 – 6 MAE 4353 Fall 2014

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Force Analysis Efficient design concentrates frictional material near maximum pressure point (as shown): At any angle from pin there is a differential normal force:

b is frictional material face width (into the plane)

Substituting maximum pressure and associated angle gives:

Fig. 16 – 7 MAE 4353 Fall 2014

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Force Analysis, cont. Use normal force with force components to write moment of frictional forces about hinge pin:

Moment of normal forces about hinge pin:

Actuating force must balance moments: If M  N  = M  f  system is “self -locked” (no actuating force required) Can determine dimensions for self-energizing action Self-locking condition: Is this correct? MAE 4353 Fall 2014

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Force Analysis, cont. Torque applied to drum by shoe:

Hinge-pin reactions (sum of horizontal and vertical forces):

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Force Analysis, cont. If rotation is reversed for given geometry (Fig 16-7), self-energizing effect is lost and required actuating force is:

Pin reactions become:

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Force Analysis, cont. “simplifying” terms:

Clockwise rotation (Fig 16-7 geometry):

Counter-clockwise rotation:

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Assumptions •

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Pressure at any point on shoe proportional to distance from pin (zero at heel) Centrifugal force effects neglected  –

Good assumption for brakes

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Clutch analysis needs to account for centrifugal forces

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Shoes are rigid

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No variation of friction coefficient with pressure

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Discussion Problem Which shoe limits the maximum actuation force F? (F same for both shoes) F

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What if the direction of rotation is reversed?

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F

B

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Assignments •

Mid-term survey – Open till 1:00 PM Wednesday  –

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By class time Friday (10/31)  –

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Read Shigley Chapter 16 (Clutches & Brakes)

By class time Monday (11/3)  –

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Quiz for bonus points open till Friday 10:00PM

Upload Flexible Elements Problem Set (#8) (note revised date) Complete quiz and download problem set Test Review, Clutches & Brakes cont.

Tuesday (11/4) TA Study Session – 3:30 to 4:40 in EN 208 Wednesday (11/5) Test #2  –

Springs, Bearings, Flexible Elements

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