FOUNDATION of MECHANICS 1FOUNDATION of MECHANICS 1

Presentation06: Brakes and Clutches

OutlineOutline

• Introduction: devices exploiting the friction for their functioning.

• Reye’s hypothesis: wear; Reye’s hypothesis; Archard’s equation; application to the trust block.

• Applications: friction clutch; disc brake; conic brake; drum brake.

INTRODUCTION

Trust block Disc clutch Conic clutch

Flywheel

Driven shaft

Disc

Drivingshaft Driven

shaft

D i iDriving shaft

INTRODUCTION

Conic brake Drum brakeDisc brakeDisc

P dPads

REYE’s HYPOTHESIS

Wear

REYE’ h th i

Loss of material on the contact surfaces of two bodies in relative motion.

REYE’s hypothesis: the volume Vwear of material lost for (adhesive) wear effects is proportional to the passive work Lp done by the friction forces producing that wear.

ARCHARD’s equation

wear pV L

'N Twear c pV k A s k s k s k L

f

ARCHARD s equation

TN ;

ps s

p A f

p f p

N ;Ns Cp A f

REYE’s HYPOTHESIS

Trust block

dfp

.

0f

constM M

R2

R1 rdr0m fM M

wear pV L22

weardV r dr hdL fp r dr r

.pr const 2pdL fp r dr r

REYE’s HYPOTHESIS

Trust block

pr C2

1

2 dR

RQ p r r

2

1

22 dR

m f RM M fp r r

2 1R RM f Q f Q R2 1

2m mM f Q f Q R

APPLICATION

Disc brake

Mm

Q

JPrismatic joint

Revolute joint

( )m fM M J Jt

f t

APPLICATION

Disc brake

QQR2

2 dR

Q p r r pad

R1

α1

dR

Q p r r

QC

2

2 1

2

( )R

CR R

weardV r dr h

2

1

2 dm RM fp r r

pdL fp r dr r

pr C 2 1

2m mR RM f Q f Q R

pr C 2

APPLICATION

Disc clutch

21 Mm MfMf Mr

J1 J2

11 0fM JM

, 1, 2

11 0m fM JM 10

(t)2(t)22 0f rM JM

1 2( ) 0m rM M J J

*

1(t)1 2( )m r

t* t

APPLICATION

Disc clutch

10(t)

, 1, 2Hp.: Mm, Mf, Mr, J1, J2 are constant and known (for Mf: chosen Q, R2, and R1, the application of the

11 0m fM M J

t

*

(t)

(t)

2(t) Reye’s hypothesis makes it possible to compute Mf)

22 0

f

f r

t

M M Jt

t*

1(t)

tt

*t t*

10*

m fM MJ t

2 equations,

1 2( )m rM M J J

1

* *20

* *f r

J tM M

J t t

* *

2 unknowns

,t 2J t t

APPLICATION

Disc clutch

Single-disc brakewith 2 contact surfaceswith 2 contact surfaces

M lti l t l t hMulti-plate clutch

APPLICATION

Conic brake/clutch

2 sin( ) 2 dR

RQ p r r Rm

α

1

( )R

Q p

QC

2 12 ( ) sin( )C

R R

Q

i ( )m

ff Q RM sin( )f

APPLICATION

Shoe brake (Drum brake)fp

p

d

p

p

P

weardV R bd hP

0 cos( )pdL fp R b Rdp p

02

( sin( ))Pp

bR

4 sin( )fP RM sin( )

sin( ) 2ffM

APPLICATION

Floating shoe brake

Angle must be measured from the approaching direction