03 brakes

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CHAPTER 03

3.1. INTRODUCTION

3.2. BLOCK BRAKE OR SHOE BRAKE

3.2.1. Pivoted lever with riidl! "o#$ted %hoe

3.2.2. E&&e'tive 'oe&&i'ie$t o& &ri'tio$

3.3. SI(PLE BAND BRAKE

SAMPLE QUESTIONS

DESIGN OF BRAKES

3.1. INTRODUCTION

A )r*+e i% * "*'hi$e ele"e$t th*t i% #%ed to either %low dow$ the "otio$ o& * "ovi$ "e")er or )ri$ it to

re%t. The )r*+i$ *'tio$ relie% o$ &ri'tio$ )etwee$ * "ovi$ "e")er *$d %t*tio$*r! "e")er. D#ri$ it%

,er&or"*$'e- either +i$eti' e$er! o& the "ovi$ "e")er or ,ote$ti*l e$er! o& &*lli$ o)e't% i% *)%or)ed.

The e$er! *)%or)ed )! )r*+e% i% di%%i,*ted i$ the &or" o& he*t *$d thi% he*t %ho#ld )e di%%i,*ted to the

%#rro#$di$ *ir /or w*ter whi'h i% 'ir'#l*ted thro#h the ,*%%*e% i$ the )r*+e dr#"0 %o th*t the e'e%%ive

he*ti$ o& the )r*+i$ li$i$ doe% $ot t*+e ,l*'e.

Br*+e% *re 'o""o$l! #%ed i$ *#to"otive vehi'le- li&t%- 'r*$e% *$d "i$e hoi%t%. I$ vehi'le% the two "*i$

&#$'tio$% *re

*0 To 'o$trol or %to, the vehi'le i$ the %horte%t ,o%%i)le ti"e *t the ti"e o& $eed

)0 To 'o$trol the %,eed o& vehi'le *t t#r$% *$d *l%o *t the ti"e o& drivi$ dow$ * hill %lo,e

The! '*$ *l%o #%ed *% d!$*"o"eter &or "e*%#ri$ ,ower i$ ,ower e$er*ti$ *$d ,ower 'o$%#"i$

"*'hi$e%.

3.2. BLOCK BRAKE OR SHOE BRAKE

A )lo'+ )r*+e i% %how$ i$ i.3.1. It 'o$%i%t% o& * )lo'+ or %hoe $or"*ll! "*de o& * %o&ter "*teri*l ridi$ o$* "et*lli' )r*+e dr#" +e!ed to the %h*&t. 4he$ )r*+e %hoe% ,re%% **i$%t eter$*l %#r&*'e o& * )r*+e

dr#"- %#'h )r*+e% *re '*lled eter$*l 'lo%i$ or 'o$tr*'ti$ )r*+e%. The%e t!,e% o& )r*+e% *re $or"*ll! #%ed

o$ li&t- elev*tor- or 'r*$e.

To o)t*i$ )r*+i$ *'tio$ the )lo'+ i% ,re%%ed **i$%t the dr#" #$der * &or'e o)t*i$ed &ro" * lever. The

*'tio$ e$er*te% * re*'tio$ )etwee$ the %hoe *$d the dr#" *$d he$'e * t*$e$ti*l &ri'tio$ &or'e o$ the dr#"

to '*#%e ret*rd*tio$ o& the dr#".

3.2.1. Pivoted lever with riidl! "o#$ted %hoe

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i.3.1 %how% * riidl! "o#$ted %hoe o$ * h*$d lever whi'h i% ,ivoted *t the le&t e$d *$d *'t#*ti$ e&&ort

*'t% *t the riht e$d o& the lever. Let thi% e&&ort )e P *$d the dr#" rot*te% i$ 'lo'+wi%e dire'tio$ dr*i$ the

%hoe. The &ri'tio$ &or'e th#% *'t% to the riht o$ the %hoe *% %how$. The e5#*l *$d o,,o%ite &or'e will *'t o$

the dr#" to ret*rd it% "otio$.

Fig.3.1. Shoe brake with FBD

Co$ditio$ &'( )#l*r#" o+ lever ,elow the li$e o+ '*tio$ o+ +ri*tio$ +or*e

Co$%ider e5#ili)ri#" o& %hoe6lever *%%e")l! #$der the *'tio$ o& &ollowi$ &or'e%

*0 E&&ort P *'ti$ dow$w*rd% *t &ree e$d o& the lever )0 ri'tio$ &or'e F *t the 'e$tre o& the %hoe to the riht or i$ the dire'tio$ o& rot*tio$- *$d

'0 The $or"*l re*'tio$ N )etwee$ the %hoe *$d the dr#" *'ti$ #,w*rd *t the 'e$tre o& the %hoe

A% %how$ i$ i.3.1 the &#l'r#" i% *t * hori7o$t*l di%t*$'e a *$d verti'*l di%t*$'e c &ro" the 'e$tre o& the

)lo'+ *$d lever *r" i% l . The &#l'r#" i% )elow the 'e$tr*l ,oi$t o& the %hoe 'o$t*'t.

Now 'o$%ider the e5#ili)ri#" o& the lever #$der three &or'e% P - F - *$d N - the %#""*tio$ o& "o"e$t% *)o#t

the &#l'r#" %ho#ld *dd #, to 7ero. He$'e

Na – Fc 8 Pl or Na – μNc 8 Pl or N 8

Now 'o$%ider the e5#ili)ri#" o& the )r*+i$ dr#"

T B 8 Fr 8 μNr

or T B 8 × Pl

A% i$di'*ted )! the *)ove e5#*tio$- i& &#l'r#" i% )elow the 'e$tr*l ,oi$t o& %hoe 'o$t*'t- the &ri'tio$*l &or'e

i% hel,i$ e&&ort.

Co$ditio$ &,( )#l*r#" o+ lever o$ the li$e o+ '*tio$ o+ +ri*tio$ +or*e

I& &#l'r#" i% o$ the li$e o& *'tio$ o& &ri'tio$ &or'e- the 'o$tri)#tio$ o& &ri'tio$ &or'e will v*$i%h. I$ thi% '*%e-

c i% 7ero *$d the )r*+i$ tor5#e )e'o"e%

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T B 8 × Pl

Co$ditio$ &*( )#l*r#" o+ lever ',ove li$e o+ '*tio$ o+ +ri*tio$ +or*e

I& &#l'r#" i% *)ove the li$e o& *'tio$ o& &ri'tio$ &or'e- the &ri'tio$ &or'e o,,o%e% the e&&ort to )re*+. I$ thi%

'*%e- c i% $e*tive *$d the )r*+i$ tor5#e )e'o"e%

T B 8 × Pl

3.1.2. E++e*tive *oe++i*ie$t o+ +ri*tio$

U$i+or" -re%%#re *o$ditio$

I& the *$le o& 'o$t*'t )etwee$ %hoe *$d dr#" 2θ i% le%% th*$ or e5#*l to 9::- the 'o$ditio$ i% +$ow$ *%

#$i&or" ,re%%#re 'o$ditio$ *$d e&&e'tive 'oe&&i'ie$t o& &ri'tio$ i% e5#*l to ive$ 'oe&&i'ie$t o& &ri'tio$.

μ′ 8 μ.

U$i+or" we'r *o$ditio$

I& the *$le o& 'o$t*'t )etwee$ %hoe *$d dr#" 2θ i% re*ter th*$ 9::- the 'o$ditio$ i% +$ow$ *% #$i&or" we*r

'o$ditio$ *$d the e&&e'tive 'oe&&i'ie$t o& &ri'tio$ i% ive$ *%

μ′ 8

SAPLE PROBLES

Example 3-1 The ,lo*/0t!-e h'$d ,r'/e %how$ i$ the +i#re h'% ' +'*e width o+ 3 ""

'$d ' "e'$ *oe++i*ie$t o+ +ri*tio$ o+ .2. )or '$ e%ti"'ted '*t#'ti$ +or*e o+ N4 +i$d the

"'5i"#" -re%%#re o$ the %hoe '$d +i$d the ,r'/i$ tor6#e.

1. Dr*w the &ree )od! di*r*"

2. E&&e'tive 'oe&&i'ie$t o& &ri'tio$ i% ive$ *% μ′ 8 8 8 :.2;<

3. Nor"*l re*'tio$ N × 2:: – =:: × <:: 8 : or N 8 1::: N *$d &or'e o& &ri'tio$- F 8 :.2;< × 1::: 8 2;< N

=. ri'tio$ tor5#e- T B 8 2;< × 1<: 8 =12<: N.""

<. (*i"#" ,re%%#re o$ the %hoe- p"* 8 8 8 :.19 N>""2

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Example 3-2 The ,lo*/ t!-e h'$d ,r'/e %how$ i$ +i#re h'% ' +'*e width o+ "". The

+ri*tio$ "'teri'l -er"it% ' "'5i"#" -re%%#re o+ .7 P' '$d ' *oe++i*ie$t o+ +ri*tio$ o+.2.

Deter"i$e8 1. E++ort4 2. '5i"#" tor6#e4 '$d 3. He't e$er'ted i+ the %-eed o+ the dr#" i%

1 r-" '$d the ,r'/e i% '--lied +or %e* 't +#ll *'-'*it! to ,ri$ the %h'+t to %to-.

Given Data: μ 8 :.2=? 2θ = @::? N 8 1:: r,"? r 8 1<: ""? w 8 =< ""? p 8 :.9 N>""2? d 8 3:: ""

SOLUTION


2. E&&e'tive 'oe&&i'ie$t o& &ri'tio$ i% ive$ *% μ′ 8 8 8 :.29=

3. Allow*)le ,re%%#re o$ the %hoe- p"* 8 /or0 :.9 8

Nor"*l &or'e- N 8 <;2;.<9 N

=. T*$e$ti*l &ri'tio$ &or'e- F 8 μ′ N 8 :.29= × <;2;.<9 8 1<12.1 N

The v*rio#% &or'e% *'ti$ o$ the %hoe *re %how$ i$ &i#re. ro" the &i#re a 8 2:: ""- b 8 3:: "" *$d

c 8 :. The t*$e$ti*l &or'e ,*%%e% thro#h the &#l'r#".

E&&ort- P 8 8 8 [email protected] N

<. Tor5#e o$ the dr#"- T B 8 1<12.12 × 1<: 8 2291< N."" 8 229.1< N."

9. Power *)%or)ed- 8 8 2.3;< +>% *$d i$ < %e'o$d%- < × 2.3;< 8 11.;< +

Example 3-3 A 400 mm radius brake drum !"#a#s a si"$%e s&!e as s&!'" i" (i$ure a"d sus#ai"s

)00 N*m #!r+ue a# ,00 r-m* Take a !e((iie"# !( (ri#i!" 0*),*

a. De#ermi"e (!r %!k'ise r!#a#i!" !( drum/ i. N!rma% (!re !" #&e s&!e ii. Re+uired (!re F #!

a--%1 (!r #&e brake* iii. Hea# $e"era#ed

b. De#ermi"e (!r !u"#er %!k'ise r!#a#i!" !( drum/ i. N!rma% (!re !" #&e s&!e ii. Re+uired (!re

F #! a--%1 (!r #&e brake* iii. Hea# $e"era#ed

=

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SOLUTION

A. DRU ROTATION IS CLOCK9ISE


2. ri'tio$ tor5#e- T B8 2:: N."

3. T*$e$ti*l &ri'tio$ &or'e- F θ 8 8 2:::::>=:: 8 <:: N

=. Nor"*l &or'e- N 8 8 <::>:.2< 8 2::: N

<. A't#*ti$ &or'e – 2::: × 3<: F × 1::: <:: × =: 8 : or F 8 20 N

2* He*t e$er*ted 8 5046) k78s

B. DRU ROTATION IS COUNTER 0 CLOCK9ISE


2. ri'tio$ tor5#e- T B8 2:: N."

3. T*$e$ti*l &ri'tio$ &or'e- F θ 8 8 2:::::>=:: 8 <:: N

=. Nor"*l &or'e- N 8 8 <::>:.2< 8 2::: N

<. A't#*ti$ &or'e – 2::: × 3<: F × 1::: – <:: × =: 8 : or F 8 6)0 N

2* He*t e$er*ted 8 5046) k78s

3.3. SIPLE BAND BRAKE

A )*$d )r*+e 'o$%i%t% o& * &lei)le )*$d o& le*ther- o$e or "ore ro,e%- or %teel li$ed with &ri'tio$

"*teri*l- whi'h e")r*'e% * ,*rt o& the 'ir'#"&ere$'e o& the dr#". A )*$d )r*+e- *% %how$ i$ i.- i% '*lled *

simple band brake i$ whi'h o$e e$d o& the )*$d i% *tt*'hed to * &ied ,i$ or &#l'r#" o& the lever while the

other e$d i% *tt*'hed to the lever *t * di%t*$'e b &ro" the &#l'r#".

4he$ * &or'e P i% *,,lied to the lever *t C - the lever t#r$% *)o#t the &#l'r#" ,i$ O *$d tihte$% the )*$d o$

the dr#" *$d he$'e the )r*+e% *re *,,lied. The &ri'tio$ )etwee$ the )*$d *$d the dr#" ,rovide% the )r*+i$

&or'e. The &or'e P o$ the lever *t C "*! )e deter"i$ed *% di%'#%%ed )elow

<

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Let T 1 8 Te$%io$ i$ the tiht %ide o& the )*$d-

T 2 8 Te$%io$ i$ the %l*'+ %ide o& the )*$d-

θ 8 A$le o& l*, /or e")r*'e0 o& the )*$d o$ the dr#"-

μ 8 Coe&&i'ie$t o& &ri'tio$ )etwee$ the )*$d *$d the dr#"-

r 8 R*di#% o& the dr#"-

t 8 Thi'+$e%% o& the )*$d- *$d

r e 8 E&&e'tive r*di#% o& the dr#" 8 r t > 2.

4e +$ow th*t li"iti$ r*tio o& the te$%io$% i% ive$ )! the rel*tio$- 8 e μθ

*$d )r*+i$ &or'e o$ the dr#" 8 T 1 T 2

∴ Br*+i$ tor5#e o$ the dr#"- T B 8 /T 1 T 20 r /Nele'ti$ thi'+$e%% o& )*$d0

8 /T 1 T 20 r e /Co$%ideri$ thi'+$e%% o& )*$d0

Now 'o$%ideri$ the e+ui%ibrium !( #&e %e9er OBC . It "*! )e $oted th*t whe$ the dr#" rot*te% i$ the

clockwie directio! *% %how$ i$ i. /a0- the e$d o& the )*$d *tt*'hed to the &#l'r#" O will )e %l*'+ with

te$%io$ T 2 *$d e$d o& the )*$d *tt*'hed to " will )e tiht with te$%io$ T 1. O$ the other h*$d- whe$ the dr#"

rot*te% i$ the a!ticlockwie directio! *% %how$ i$ i. /b0- the te$%io$% i$ the )*$d will rever%e- i#e. the e$d

o& the )*$d *tt*'hed to the &#l'r#" O will )e tiht with te$%io$ T 1 *$d the e$d o& the )*$d *tt*'hed to " will

)e %l*'+ with te$%io$ T 2. Now t*+i$ "o"e$t% *)o#t the &#l'r#" O- we h*ve

P#l 8 T 1.b /&or 'lo'+wi%e rot*tio$ o& the dr#"0

*$d P#l 8 T 2.b /&or *$ti'lo'+wi%e rot*tio$ o& the dr#"0where l 8 Le$th o& the lever &ro" the &#l'r#" /OC 0- *$d b 8 Per,e$di'#l*r di%t*$'e &ro" O to the li$e o&

*'tio$ o& T 1 or T 2.

N!#es/ 5* whe$ the )r*+e )*$d i% *tt*'hed to the lever- *% %how$ *)ove i$ i. / a0 *$d /b0- the$ the &or'e / P 0

"#%t *'t i$ the #,w*rd dire'tio$ i$ order to tihte$ the )*$d o$ the dr#".

)* So"eti"e% the )r*+e )*$d i% *tt*'hed to the lever *% %how$ )elow i$ i. /a0 *$d /b0- the$ the &or'e / P 0

"#%t *'t i$ the dow$w*rd dire'tio$ i$ order to tihte$ the )*$d. I$ thi% '*%e- &or 'lo'+wi%e rot*tio$ o& the

dr#"- the e$d o& the )*$d *tt*'hed to the &#l'r#" O will )e tiht with te$%io$ T 1 *$d )*$d o& the )*$d

*tt*'hed to " will )e %l*'+ with te$%io$ T 2. The te$%io$% T 1 *$d T 2 will rever%e &or *$ti'lo'+wi%e rot*tio$ o& the dr#".

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3* I& the ,er"i%%i)le te$%ile %tre%% /$ t0 &or the "*teri*l o& the )*$d i% +$ow$- the$ "*i"#" te$%io$ i$ the

)*$d i% ive$ )! T 1 8 $ t × w × t

where w 8 4idth o& the )*$d- *$d t 8 Thi'+$e%% o& the )*$d.

4* The width o& )*$d /w0 %ho#ld $ot e'eed 1<: "" &or dr#" di*"eter /d 0 re*ter th*$ 1 "eter *$d 1::

"" &or dr#" di*"eter le%% th*$ 1 "eter. The )*$d thi'+$e%% /t 0 "*! *l%o )e o)t*i$ed )! #%i$ the e",iri'*l

rel*tio$ i#e# t 8 :.::< d &or )r*+e% o& h*$d o,er*ted wi$'he%.

SAPLE :UESTIONS

%# &e'i!e (ec)a!ical brake# *ow it di''er 'ro( a d+!a(o(eter,

-# .)at are t)e /e o' (ec)a!ical brake i! a/to(obile,

0# &raw t)e 'ree1bod+1dia2ra( o' t)e le3er a!d dr/( eparatel+#

4# .)e! t)e 'rictio!al 'orce i )elpi!2 e''ort, .)e! t)e 'rictio! 'orce oppoe t)e e''ort to break,

5# .)at are t)e /!i'or( pre/re co!ditio! a!d /!i'or( wear co!ditio! i! brake,

6# .)at do +o/ (ea! b+ e''ecti3e co1e''icie!t o' 'rictio!, .)e! it i /ed,

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03 brakes

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