CHAPTER 22
MOTION CONTROL:
CLUTCHES AND BRAKES
ͳǤ ǤʹʹǦͳǣܶ ൌ ܥܲܭȀ݊ ൌ ሺ͸͵ͲʹͷሻሺͷǤͲሻሺʹǤ͹ͷሻȀͳ͹ͷͲ ൌ ͶͻͷήCK
ʹʹǦͶǤ
 ʹǦ͹Ǥ
     
ʹ ͷʹͷʹ ͹ͷ ͷǤͲ ʹͷͲͲ ͹ͺͺή
͵ ͸͵Ͳʹͷ ͲǤͷͲ ͳǤͷ ͳͳͷͲ Ͷͳή
Ͷ ͸͵Ͳʹͷ ͷǤͲ ʹǤ͹ͷ ͳͺͲ ͶͺͳͶή
ͷǦͳ ͸͵Ͳʹͷ ͷǤͲ ͳǤͲ ͳ͹ͷͲ ͳͺͲή
ͺǤ ǣ DαʹͶǤͲǢRαͳʹǤͲǢLαʹǤͷͲǢR2αͲǢ
ଶൌ௅൫ோభ
రିோమ
ర൯
ଷଶଷǤଽ ൌଶǤହ଴൫ଵଶǤ଴రି଴൯
ଷଶଷǤଽ ή
ଶൌ ͳ͸Ͳή
ଶ
ௐ௞మሺο௡ሻ
412
ͻǤ 

ͳ ʹ  ʹ
 ͲǤ͸ʹͷ Ͳ ͳ͸ǤͲ ͲǤͲͲ͹ͷͶ
 ͳǤͷͲ ͲǤ͸ʹͷ ʹǤʹͷ ͲǤͲ͵Ͷͳ
ͳͳǤͲͲ ͲǤ͸ʹͷ ͳǤͺͲ ͲǤͲͲͶ͹
ଷ଴଼௧ ൌሺଵଶǤଵ଴ଶሻሺ଻଻ହሻ
ଷ଴଼ሺଵǤହ଴ሻൌ ૟૙Ǥૢ
ͳͲǤ Ǥ
 ʹǣ݊ଶൌ ͳ͹ͷͲቀସǤ଴଴
ଵହǤ଴଴ቁ ൌ Ͷ͸͸Ǥ͹
 ǤʹʹǦͶሺ݊Ȁ݊௖ሻଶൌሺ݊ଶȀ݊ଵሻଶൌ ሺͶ͸͸Ǥ͹Ȁͳ͹ͷͲሻଶൌ ͲǤͲ͹ͳͳ

ͳ ʹ  ʹ ݇௘
ଶ
 ʹǤͲͲ Ͳ ͵ǤͲͲ ͲǤͳͶͺʹ ͲǤͳͶͺʹ
 ͹ǤͷͲ ͳǤʹͷ ͵ǤͲͲ ʹͻǤʹͺ͵͵ ʹǤͲͺʹͶ
ʹ ͳǤʹͷ Ͳ ͷͶǤͲ ͲǤͶͲ͹Ͳ ͲǤͲʹͺͻ
413
ͳͳǤ  ൌ ͷͲȀ
ൌ

 ൌ ௩
ோൌ
ͷͲ

ൈ ଵ
ସǤ଴଴௜௡ൈ
ͳʹ

ൌ ͳͷͲ


ൌɘ
 ൌ ݊ ൌଵହ଴

ൈ

ൌ ʹ͵Ǥͺ͹
ǣܹ݇௘
߱ቁଶൌ ͸ͲͲ൬ͷͲ
ͳͷͲ
Ȁ
൰ଶൌ ͸͸Ǥ͸͸͸͹
ή
Ǣܹ݇ଶൌ ͻǤͶͳͷͶ൅͸͸Ǥ͸͸͸͹ ൌ ͹͸ǤͲͺή

ʹ
ͳʹǤ ȋȌ ǣ
 ααͳͳͷͲαnc

414
ଷ଴଼௧ ൌሺଵǤ଼଺ଵ଻ሻሺଵଵହ଴ሻ
ଷ଴଼ሺଶǤ଴ሻൌ͵
ȋȌ Ǥ͵ͺαǤ

ܶ
௕ൌௐ௞మο௡
ଷ଴଼௧ ൌሺଵସ଺ଵǤହሻሺଷ଼ሻ
ଷ଴଼ሺଶǤ଴ሻൌ ૢ૙Ǥ૛
ή
[Note:Tb/Ta=90.2/3.48=25.9]
ͳ͵Ǥ ǤʹʹǦͺǣܶ௙ൌ݂ܴܰ
௠Ǣܴ௠ൌܶ
௙Ȁ݂ܰ ൌ ሺ͹ͷ
ή
ሻȀሾሺͲǤʹͷሻሺͳͷͲሻሿ ൌ ʹǤͲͲ
ܲ
௙ൌ்೑௡
଺ଷ଴଴଴ൌ
ሺ଻ହሻሺଵଵହ଴ሻ
଺ଷ଴଴଴ ൌ ͳǤ͵͹ȏʹʹǦͳͲȐ
ǣ ܹܴ ൌ ͲǤͳͲȀ
ʹ
ൌܲ
௙Ȁܣ ȏʹʹǦͳͳȐ
Aൌ ܲ௙Ȁܹܴ ൌ ͳǤ͵͹ȀͲǤͳͲȀ
ʹ
ൌ ͳ͵Ǥ͹
ʹ
ܣൌߨ
ሺܴ௢
ଶെܴ௜
ଶሻǢܴ௠ൌሺܴ௢൅ܴ௜ሻȀʹܱݎʹܴ௠ൌܴ
ை൅ܴ௜
ǣܴ
଴ൌͳǤͷܴ
௜ǣʹܴ௠ൌͳǤͷܴ
௜൅ܴ௜ൌʹǤͷܴ
௜Ǣ ܴ௜ൌଶோ೘
ଶǤହ ൌଶሺଶǤ଴଴௜௡ሻ
ଶǤହ ൌ ͳǤ͸Ͳ
ܴைൌͳǤͷ
ሺͳǤ͸ͲሻൌʹǤͶͲǢܣൌߨ
ሺʹǤͶͲଶെͳǤ͸Ͳଶሻൌ ͳͲǤͲͷሺሻ
 ǡܴைൌ ͳǤ͹ͷܴ௜
ܴ
௜ൌ ͳǤͶͷǢܴைൌ ʹǤͷͷǢ࡭ ൌ ૚૜Ǥૠ૞
૛ሺࡻࡷሻ

ͳ ʹ  ʹ ܹ݇௘
ଶ
 ͳǤ͹ͷ Ͳ ͺǤͲͲ ͲǤʹ͵ͳ͸ ͲǤʹ͵ͳ͸
 ͺǤͲͲ Ͳ ʹǤͷͲ ͵ͳǤ͸ͳͶ͹ ͲǤͲ͵ͶͶ
ʹ ͶǤͲͲ ʹǤͲͲ ͶǤͲͲ ʹǤͻ͸͵ͻ ͲǤͲͲ͵ʹ

ʹ
ʹ ʹǤͻ͸͵ͻ
 Ͷ͹ͶǤʹʹͲͶ
415
ͳͶǤ ͻǣܶ௙ൌ ͸ͶήǢܴ௠ൌͳǤͷͲǢ݂ൌͲǤʹͷ
ܰൌ
்೑
௙ൈோ೘ൌ଺ସǤ଴
ሺ଴ǤଶହሻሺଵǤହ଴ሻൌ ͳ͹Ͳ
ܲ
௙ൌ்೑ൈ௡
଺ଷ଴଴଴ ൌሺ଺ସሻሺ଻଻ହሻ
଺ଷ଴଴଴ ൌ ͲǤ͹ͻ
ଶ
ͳͷǤ ʹʹǦͳ͵ǣ
Ƚ
ା௙
Ƚ
ሻ
୪ୠή୤୲
ሺ

ଵଶιା଴Ǥଶହ

ଵଶιሻ

ͳ͸Ǥ ܶ௙ൌ ͸ͶήǢܮ݁ݐ݂ ൌ ͲǤʹͷǢܴ௠ൌ ʹǤͲǢߙ ൌ ͳʹι

ଵଶιା଴Ǥଶହ

ଵଶιሻ
ሺ଴ǤଶହሻሺଵǤ଴ሻ ൌ ૚૚૟
ͳ͹Ǥ ܶ௙ൌ ͳͷͲήൈͳʹȀ ൌ ͳͺͲͲή ൌ ܨ௙ܦ௢Ȁʹ
௅ൌሺଷ଴଴
ଶସǤ଴
୧୬
ͳͺǤ ǦǢWδͲǤ
௔
ͳͻǤ ܶ௙ൌ ͳͲͲήൈͳʹȀ ൌ ͳʹͲͲή
ǣܦ
௢ൌ ͳͲǤͲǢ݂ ൌ ͲǤʹͷ
௅ൌଶସ଴ቀమǤబ
ଵ଼ ൌ ૛૟Ǥૠ
ʹͲǤ ܶ௙ൌ ͳͲͲήൈͳʹȀ ൌ ͳʹͲͲή
Ǣ݂ ൌ ͲǤʹͷǢ݌ ൎ ͵Ͳ
 ȋʹʹǦʹͲȌ
ܯ
ேൌͲǤʹͷ
ሺʹͻǤͲሻሺ͵Ǥʹͷሻሺ͸ǤͲሻሺͻǤͲሻሾʹሺͳǤͷ͹ሻെʹ͹Ͳι൅ͻͲιሿ
ܯ
ேൌ ૟૞૝૙
ή
417
ܲ
௙ൌܶ
௙݊Ȁ͸͵ͲͲͲ ൌ ሺͳʹͲͲሻሺͶͺͲሻȀ͸͵ͲͲͲ ൌ ૢǤ૚૝
஺ൌଽǤଵସ
ଶ଻Ǥ଺

ʹ
ʹͳǤ ǣܶ௙ൌ ͹ͷήሺͳʹ
Ȁ
ሻൌ ͻͲͲήǢ݊ ൌ ͵ͷͲ
 ǡ݌௠௔௫ ൌ ʹͷǤͲǢ݂ ൌ ͲǤʹͷ
ǣ ݎ ൌ ͸ǤͲǢߠ ൌ ʹͳͲιሺ͵Ǥ͸͹

ሻǢݓൌʹǤͷ
ܲ
ଵൌ݌
௠௔௫ݎݓ ൌ ሺʹͷǤͲȀଶሻሺ͸ǤͲሻሺʹǤͷሻൌ ͵͹ͷ
ܲ
ଶൌ௉భ
௘೑ഇ ൌଷ଻ହ௟௕
௘ሺబǤమఱሻሺయǤలళሻ ൌ ͳͷͲ
ܶ
௙ൌሺܲଵെܲ
ଶሻݎ ൌ ሺ͵͹ͷെͳͷͲሻሺ͸ǤͲሻൌ ͳ͵ͷͲήሺሻ
ǣ ݎ ൌ ͷǤͷͲǢߠ ൌ ʹͳͲιǢݓ ൌ ʹǤͲ
418
ʹʹ ʹʹǦʹʹǣ
a.ǡܫ ൌଵ
ଶ௪
௚ܴଶ
wααߩܸǢߩ௦௧௘௘௟αͲǤʹͺ͵Ȁ͵ǢVαǢgα͵ʹǤʹȀʹ
 ǢͶǤͲͲǡͺǤͲͲǡͳ͸ǤͲͲǤ
 ǦͶǤͲͲαLIαͳʹǤͲͲ
 ǦͺǤͲͲαLIIαͳ͸ǤͲͲ
b.ǡDǡͺͲͲͷǤͲǣ
Dαοఠ
ο௧ ൌି଼଴଴୰୮୫
ହୱ αǦͳ͸ͲȀଶగ௥௔ௗ
௥௘௩ ଵ௠௜௡
଺଴௦ αǦ16.76rad/s2=
D