Mechanical Engineering Chapter 12 Shaft Design

For SAE 4140 OQT 1200; ݏ௬ൌͳͳͶǢݏ௨ൌͳ͵ͲǢݏ௡ൌͶ͸ሺͷെͳͳሻ

ݏ௡

ᇱൌܥ

௦ܥோݏ௡ൌሺͲǤͻሻሺͲǤͺͳሻሺͶ͸݇ݏ݅ሻൌ͵͵Ǥͷ

36. Data from Figure 10-8 to 10-12 and Example Problems 10-4 and 10-5.

Pinion:

ܶൌʹ͸͵ήǢܯாൌξʹʹͲଶ൅ͻ͸Ǥ͸ଶൌʹͶͲήǢܰൌ͵ǡܭ௧ൌʹǤͲሺሻ

SAE 1040 OQT 1200; ݏ௬ൌ͸͵Ǣݏ௨ൌͻ͵Ǣݏ௡ൌ͵͸

V

(lb)

V

(lb)

M

(lbin)

M

(lbin)

Vertical

plane Horizonta

l

plane

336

ݏ௡

ᇱൌሺͲǤͺ͸ሻሺͲǤͺͳሻሺ͵͸ሻൌʹͷǤͳ

ܦாൌቆଷଶሺଷሻ

గටቀଶǤ଴ሺଶସ଴ሻ

ଶହଵ଴଴ ቁଶ൅ଷ

ସቀଶ଺ଷ

଺ଷ଴଴଴ቁଶቇଵȀଷ ൌ૙Ǥૡ૝ܑܖ

Gear:

ܶൌ͹ͺͺήǢܯிൌͶͲͶήǢܰൌ͵Ǣܭ௧ൌʹǤͲሺሻ

ܦிൌቆଷଶሺଷሻ

గටቀଶǤ଴ሺସ଴ସሻ

ଶହଵ଴଴ ቁଶ൅ଷ

ସቀ଻଼଼

଺ଷ଴଴଴ቁଶቇଵȀଷ ൌ૚Ǥ૙૚ܑܖǢ࡯࢙ൌ૙Ǥૡૡ Ok

37. ܶீ௘௔௥ ൌ͸͵ͲͲͲሺͶǤͲሻȀ͸ͲͲൌͶʹͲήǢܶ௦௣ ൌͶʹͲȀʹൌʹͳͲή each

ܨ஼ଵ ൌܨ

஼ଶ ൌ்ೄು

ହൌଶଵ଴

ହൌͶʹ Ȟൌݐܽ݊ିଵሺͶͷȀͳͷሻൌ͹ͳǤ͸ι

ܹ௧೒ൌ்ಸ

M

(lbin) 0 0

M

(lbin)

V

(lb) V

(lb)

337

38. ܲൌͳͷǤͲǢ݊ଵൌͳ͹ʹͷǢ݊ଶൌͷ͹ͷǢ݊ଷൌʹͺ͹Ǥͷ

ͳൌܶଵൌܶ

஺ൌ͸͵ͲͲͲሺͳͷሻȀͳ͹ʹͷൌͷͶͺή

ʹൌܶଶൌܶ

஻ൌ͸͵ͲͲͲሺͳͷሻȀͷ͹ͷൌͳ͸Ͷ͵ή

Figure

P12-38

338

ܯൌξͻͳ͵ଶ൅͵͵͵ଶൌͻ͹ʹή

  ܶൌͷͶͺήǢܣ

ܦ

୫୧୬ ൌͲǤͷͺͻ





ʹǣܵܦଵǢܦଶ௠௜௡ ൌͲǤͷͺͻ





͵ǣ Depends on D4





Ͷǣܯൌͻ͹ʹή

 ǣ

339

ܦ

ଵൌͲǤ͹ͷͲ

ʹ

ܶ

ଶൌͳ͸Ͷ͵ή

ܹ

௧಴ൌ்మ



V

(lb) V

(lb)

340



ǣ

ܯൌͲǢܶൌͲ ܸ

஺ൌξ͸͸͹ଶ൅ͺͲଶൌ͸Ͷͳ



ǣ

ܯ

஻ൌξʹͲͲͳଶ൅ʹͶͲଶൌʹͲͳͷή

ݏ

௡ൌ͵ͲͲͲͲǢݏ௡

ᇱൌʹͲʹͷͲሺͳሻ

ܦ

ଶǣ

ܦସǣ

ܯ

஼ൌʹ͵͵ͻήǢܶൌͳ͸Ͷ͵ήǢሺܭ௧ൌʹǤͷሻ

ܦ

ସ௠௜௡ ൌʹǤͲ͸ͺ



Gear C drives Gear D

DC = 4.00 in

8.00 in

Shaft

2

341

ܦ

ହǣ

ܦ

ହ௠௜௡ ൌඥʹǤͻͶܭ௧ܸܰȀݏ௡

ܦ

ଵǣ ܸ஺ൌ͸͹ͳ՜ܦଵ೘೔೙ ൌͲǤͺͷͷ

ǣࡰ

૛ൌ૛Ǥ૛૞૙ܑܖǢࡰ૝ൌ૛Ǥ૝૙૙ܑܖǢࡰ૜ൌ૛Ǥ૟૙૙ܑܖ

ܦ

ଵܦହ

͵



Horizontal

342

  ͳʹǤ

ܥ

௦ൌͲǤͺͲǢݏ௬ൌ͹ͳͲͲͲǢݏ௡

ᇱൌͳͺͲͲͲ





ʹǣ

  ܯൌͳ͵ͳʹήǢܶൌ͵ʹͺ͹ήǢܭ௧ൌʹǤͷ

ǣ

ࡰ

૚ൌ૚Ǥ૜ૠૡ૙ܑܖሺ૜૞࢓࢓ሻǢ۰܍܉ܚܑܖ܏૟૛૙ૠ

  ࡰ૛ൌ૛Ǥ૙૙૙ܑܖ

 

Gear D

g

͵ͻǤ  ܲൌͳʹǤͲǢ݊௠௢௧௢௥ ൌͳͳͷͲǢͳʹെ͵ͻ

 ǣ

  ൌܨேൌ்

  Ǥ

Ǥ

  ǣ

  

  ͳʹǦ͵ͺǤ

  ͵ͺǣ

ܥǣܹ

௧಴ൌ்భ

V-belt

drive

V-belt

drive

344

  ͳ



 ǣ

 ǣ

ܴ

஻ൌξʹͶͷଶ൅ʹ͵ʹଶൌ͵ͷͺ

ܴ

஽ൌξ͸Ͷͻଶ൅͵ͶͶଶൌ͹͵ͷ

 ͳǣ͵ͺǤ

 ʹǣ͵ͺǤ

  ܤǣܹ௧ಳൌܹ

௧ಲൌͳͲͻ͸՚Ǣܹ௥ಳൌܹ

௥ಲൌ͵ͻͻ՝

Horizontal plane Vertical plane

Sheave

Bearing

D

Gear

V

(lb)

V

(lb)

345

  ʹൌ݊ଶൌ݊ଵேಲ

ேಳൌʹͷ͸ൈଶସ

ସ଼ ൌͳʹͺ

 ͵ǣ͵ͺǤ

ǣܹ

௧ವൌܹ

௧಴ൌͳͶ͹ͻ՚Ǣܹ௥ವൌܹ

௥಴ൌͷ͵ͺ՛

 ͵ǣ

ǣ݊

ଷൌ݊ଶൈே಴

ேವൌʹͷ͸ൈଶସ

ସ଼ ൌͳʹͺ



346

ܨ

஽೤ൌܨ

ேܿ݋ݏʹͲιൌሺʹͺͳ͹݈ܾሻܿ݋ݏʹͲιൌʹ͸Ͷ͹՛



ǣ

ܯ

஻ൌξ͵͸͸͸ଶ൅͵Ͳͻ͸ଶൌͶ͹ͻͺή

 ǣ

 ǣ



Sprocket

V

(lb) V

(lb)

347

ͶͲǤ  ͳʹǦͶͲǣʹǣ݊ൌͶͺͲǢܥ ൌʹʹǤͷ

 ܣൌͳͷǢܧ ൌ͹Ǥͷ

 ȂܰൌͶǤ

ସ଼଴୰ୣ୴

 ܥൌଶଶǤହൈଵ଴య୒ή୫Ȁୱ

ହ଴Ǥଶ଻୰ୟୢȀୱ ൌͶͶ͹ή

ǣ

ܣǣܹ

௧ಲൌ்ಲ

௥ಲൌଶଷ଼୒ή୫

ହ଴୫୫ ൈଵ଴య୫୫

୫ൌͷͻ͸Ͳ՚



Torque in shaft

Gear Q drives

Gear C

348



ǣ

ܯ

஻ൌξͷͻ͸ଶ൅ʹͳ͹ଶൌ͸͵Ͷή

 ǣ

ܴ

஻ൌξͺͲʹ͹ଶ൅ͳͺͶ͸ଶൌͺʹ͵͹



(N)

349



 ܭ௧ൎʹǤͷǡݎଶǡݎ଺Ǣܭ௧ൌ͵ǤͲ

 ൎͳǤͲ͸ൈǤ

 ǣ

  ͶͳͶͲͳͲͲͲǡݏ௨ൌͳͳ͸Ͳǡݏ௬ൌͳͲͷͲ

  ͳ͹ΨȂǤ



D1D2D3D4D5 D6D7 D8

D9

350



 ͳʹǦʹͶȂǣሺ



ൌͶሻ



ǣ

x ܦଶܦଷͳͶǦ͵Ǥ

x ȗܦସǤ

x ͺͲǤͲܦସǡܦହǡܦ଺Ǥ







ܯሺήሻ ܶሺήሻ ܦ௠௜௡ 



ܦଵ ʹǤͷ Ͳ ʹͻͺͲͲͲ ʹǤͳͷ͸ ͷͲǤͲ

ܦଶ ͳǤͷ ͸͵ͶͲͲͲ ʹͻͺͲͲͲ ͷ͵Ǥͳ͵ ͸ͲǤͲ

ܦଽ ʹǤͷ Ͳ ͳͶͻͲͲͲ ͳ͹Ǥͳͳ ͶͷǤͲ

351

ͶͳǤ  ͳʹǦͶͳǤܨଵൌʹͲ

ܨ

ଶൌܨ

ଵሺ͸Ͳ݉݉ሻȀሺͶͲ݉݉ሻൌʹͲǣൌܨଵൈ͸ͲൌͳʹͲͲήǤ

ܥ

௦ൌͲǤͻǡܥ

ோൌͲǤ͹ͷǢݏ௡

Ǥ

 Ǥ







Ǥ



M

0

(

Nmm

)

Lever 2

352

 ܭ௧ൌʹǤͷ



Ǥܭ௧ൌͳǤͲ



Ǥ 

 Ǥ

గටቀ௄೟ಳெ

௦೙

ସቀ௄೟೅்

௦೙





ǣ

ଷଶሺଷሻ





ǣ

ଷଶሺଷሻ

 ǣ

  ǡͶǤͲൌ





  ǣݏ௡

ᇱൌͳ͹ͷǢߪௗൌ௦೙

ᇲ

ேൌଵ଻ହ

ଷൌͷͺǤ͵

353

݄ൌ

ඥ͸ܵȀܾൌඥ͸ሺʹͲǤͷ͹݉݉ଷሻȀͶǤͲ݉݉ൌͷǤͷͷ

  ͳͲǤͲǡǤ



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