7 flexible mechanical elements

7/26/2019 7 Flexible Mechanical Elements

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B, , ,

.

I

,, , .


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F

C

1.B

2.F

3.F 4.

5.


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B


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B B

.

,

, . H,

.


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B B , , , ,

.

I , .

L ().

. (9098%, 95%),

,

. C .


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Cheap

Allows misalignment (parallel shafts) Protects from overload Absorbs noise and vibrations Cushion load fluctuations Needs little maintenance High efficiency (90-98%, usually 95%),

Advantages

Speed ratio is not constant (slip & stretch) Heat accumulation Speed limited 2000 m/min,

Power limited - 700 kW Endless belts needs special attention to install

sa van ages


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B


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Flat-belt geometry

Open belt

sin2

2sin2

1

1

d

D

dD

C

dD

=

+=

Crossed belt

[ ] )(2

1)(4

2/122

dD dDdDCL ++=

[ ]

)(2

1)(4

2sin2

2/1

22

1

dDdDCL

C

dD

+++=

+=


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22

22

2222

0)(

022

)(

,

)(

dF

dfmrfFd

fdSfFdfdNdF

dFFFfdNF

dSFddNdSdNd

Fd

dFFF

massbeltthemspeedbeltV

dFdmVdmrrmrddS

t

r

c

=

==

=++=

==>=+++=

==

====

d


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V

mdnVf

fFFFF

mrFfFF

FF

mrF

mrF

mrfmrFFF

mrfmrFF

sidelooseatstartstconsAmrFAmrfAF

c

c

c

c

2

121

22

2

1

22

2

22

1

222221

2222

2

22

2

22

sec/)exp(

1)exp()(

)exp(

)exp()(

)exp()(

,tan)exp(

=

==>

=

==>=

=

+==

+=

===>==>+=

= the belting equation

g

c


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Fi = initial tensionFc = hoop tension due to centrifugal forceF = tension due to the transmitted torqueTD = diameter of the ulle

VFFH )( 21 =

H = the transmitted power


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The difference between F1 and F2is related to the pulley torque.

Subtracting

adding

Dividing


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(1) provided,(2) Sustained3 in the ro er amount

For satisfactory flat-belt drive, the initial tension must be:

If Fi equals zero, then T equals zero: no initialtension, no torque transmitted.

(4) Maintained by routine inspection.

From the above equation:


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Similarly,


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Plot of initial tension Fiagainstbelt tension F1 or F2, showingthe interceptFc, the equationsof the curves, and where 2T/D is to be found.


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Manufacturers provide specifications for their belts that include allowabletension Fa(or stress all), (N/unit width) Belt life is usually several years. The severity of flexing at the pulley and

its effect on life is reflected in a pulley correction factor Cp. Speed in excess of 600 ft/min and its effect on lifeis reflected in avelocity correction factor Cv . For polyamide and urethane belts use Cv= 1. A service factor Ks is used for excursions ofload from nominal, applied to

the nominal power as Hd= HnomKsnd, where nd is thedesign factor forexigencies.

vpaa

=1

b = belt width, mmFa = manufacturers

allowed tension, N/mm

Cp = pulley correctionfactor

Cv = velocity correctionfactor

(F1)a = allowable largest

tension, N


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1. F () .

2. F F.

3. F .

4. F

5. F F2 6. F E

F.

7. C ,


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11 A A3 150

11 K= 1.25, 1.1 . . 2.4 . 150 . 450 . .

) E F .) E F1, F2, F H.

) E . I ?


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) E F .

rad

d

0165.3

)2400(2)150450(sin2 1

=

=


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b) E F1, F2, F H.

vpaa CCbFF =)( 1

N

CCbFF vpaa

1890

)0.1)(70.0)(18000)(15.0(

)( 1

=

=

=


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c) E . I ?

rad

d

0165.3

)2400(2

)150450(sin2 1

=

=


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; = ,

L = , = , N/

F = , N.


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F: , , , ,

, C D :

I

B D , , D.

B : B :


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Thin flat metal belts fabricated by laser welding and thinrolling technology made possible belts as thin as 0.002in and as narrow as 0.026 in.

High strength-to-weight ratio

Thin metal belts exhibit:

Accurate timing Usefulness to temperatures up to 700F Good electrical and thermal conduction properties


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A F1 F2. F1 F2

E


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F

()1 ()2 F1F2

=

= = P D= =


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Table: Belt Life for Stainless Steel FrictionDrives


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1. F ()

2. F ; 301,

302 .

5. F2=F1 F = F

6. F

7. =

.

.

4. F=

8. C

9. C :


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1 A

100 ( = 0.35). 0.08 . F

)

3.4 N.F 1, = =

(0.35)=1

(K = 1),

) 3.4 N.

) F F.

F 2,

F 3, 4, 5, 6


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1

)1(

681.0)4.3(22

353)10(97702)(

3)35.0exp()exp(

39

21

407.06

106

abtbDv

EtSF

NmDTF

MPaS

f

fa

f

=

=

===

==

==

213281

21368281

281)019.0(1479614796

10)(08.0()1.0)(285.01(

)10)(08.0)(10(193)10(353

21

12

1

3

2

396

1

FF

NFFF

NbF

F

a

a

a

a

++

===

===

=

[ ]

)19(

7.12

9.60069.0

13

3

14796

68

1)exp(

)exp(

14796

14796168049849)10(353

)10)(08.0(

)1.0)(285.01(

.)10(353

min

min

6

1

3

2

6

1

mmb

mmb

mmmb

f

f

a

Fb

ba

bNF

bF

a

a

=

=

==

=

=

=

==

=

)(35.00882.0'

0882.0213

281ln

1ln

1'

22

2

1

okff

F

Ff

i

109, report that NP= 10

9and t > NPLp/(720V)

The analysis of a V-belt drive can consist of the following steps:


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BEL .

1) OIL EIANBEL , . .

, BEL .

3) ANI AICBEL . .


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dD


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C

dDD

2sin2 1

+=


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. F B

I B : E . . C . NM.

#1. Design a friction metal flat-belt drive to connect a 1-hp, four-pole squirrel-cage motor turning at 1750 rev/min to a shaft 15 in away, running at half speed.


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g g y g pThe circumstances are such that a service factor of 1.2 and a design factor of

1.05 are appropriate. The life goal is 106 belt passes, f = 0.35, and theenvironmental considerations require a stainless steel belt.

Function: Hnom = 1 hp , n = 1750 rev/min , V R = 2 , C = 15 in , Ks = 1.2,Np= 10

6belt passes. Design factor: nd= 1.05

Given data

Belt material and properties: 301/302 stainless steel

Table 17-8: Sy= 175 000 psi, E = 28 Mpsi, = 0.285 Drive geometry: d = 2 in, D = 4 in Belt thickness: t = 0.003 in

Belt width b

Belt loop periphery

Designvariables:

Solutions:

The transmitting torque Tand the design power :

#1. Design a friction metal flat-belt drive to connect a 1-hp, four-pole squirrel-cage motor turning at 1750 rev/min to a shaft 15 in away, running at half speed.


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The circumstances are such that a service factor of 1.2 and a design factor of

1.05 are appropriate. The life goal is 106 belt passes, f = 0.35, and theenvironmental considerations require a stainless steel belt.

Function: Hnom

= 1 hp , n = 1750 rev/min , V R = 2 , C = 15 in , Ks = 1.2,Np= 10

6belt passes. Design factor: nd= 1.05

Given data

Belt material and properties: 301/302 stainless steel

Table 17-8: Sy= 175 000 psi, E = 28 Mpsi, = 0.285 Drive geometry: d = 2 in, D = 4 in Belt thickness: t = 0.003 in

Belt width b

Belt loop periphery

Designvariables:

Solutions:

The transmitting torque Tand the design power :


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For full friction development,

Decision #1: b = 4.5 in


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Existing friction

#3. A 60-hp four-cylinder internal combustion engine is used to drive a brick-making machine under a schedule of two shifts per day. The drive consists of

26 i h d b 12 f i h h d f 400


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two 26-in sheaves spaced about 12 ft apart, with a sheave speed of 400

rev/min. Select a V-belt arrangement. Find the factor of safety, and estimate thelife in passes and hours.

Hnom= 60 hp, n = 400 rev/min, Ks= 1.4, d = D = 26 in on 12 ftcenters.

Design task: specify V-belt and number of strands (belts).

Tentative decision: Use D360 belts.

Given data:

Lp= 360 + 3.3 = 363.3 inPitch length

Inside circumferenceQuantity to be added from table

Table 17-13: For = 180, K1 = 1


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Table 17-14: ForD360, K2 = 1.10

Table 17-12: Htab= 16.94 hp by interpolation b/n 2000 and 3000 ft/min

Number of belts, Nb


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Nb = 5

At fully developed friction


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7 flexible mechanical elements

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