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
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
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