mechanical design data book.pdf

7/27/2019 Mechanical Design Data Book.pdf

1/69

Shinto Mathew

MAYOTH

Mechanical Design Data Book


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1

Design Data Hand Book

Contents:-

1 Friction Clutches

Single plate clutches05

Multi plate clutches05

Cone clutches06

Centrifugal clutches06

2 Brakes

External Contracting Brakes08

Internal Expanding Brake09

Band Brakes10

Thermal Considerations11

3 Belt Drives

Geometrical Relationships12

Analysis of Belt Tensions13 Condition for Maximum Power13

Selection of Flat Belts from the ManufacturesCatalogue13

Selection of V-Belts15

4 Chain Drives

Roller Chains20

Geometrical Relationships20

Power Rating of Roller Chains21 Sprocket Wheels24

5 Rolling Contact Bearings

Stribecks Equation25

Equivalent Bearing Load26


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Load Life Relationship26

Selection of Bearing from the ManufacturesCatalogue27

Selection of Taper Roller Bearings32

Design for Cyclic Load and Speed38

Bearing With a Probability of Survival Other Than90 Percent38

6 Sliding Contact Bearings

Effect of Temperature on Viscosity39

Hydrostatic Step Bearing40

Energy Losses in Hydrostatic Bearing40

Reynolds Equation41

Raimondi and Boyd Method41

Temperature Rise43

Bearing Design Selection of Parameters44

7 Spur Gears

Standard System of Gear Tooth45

Force Analysis50

Beam Strength of Gear Tooth47

Effective Load on Gear Tooth48

Estimation of Module Based on Beam Strength50

Wear Strength of Gear Tooth50

Estimation of Module Based on Wear Strength51

Gear Design for Maximum Power TransmittingCapacity51

8 Helical Gears

Virtual Number of Tooth52

Tooth Proportions53

Beam Strength of Helical Gears54 Effective Load on Gear Tooth54

Wear Strength of Helical Gears55

9 Bevel Gears

Force Analysis57


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Beam Strength of Bevel Gears58

Wear Strength of Bevel Gears59

Effective Load on Gear Tooth60

10Worm Gears

Proportions of Worm Gears62

Force Analysis64

Friction in Worm Gears64

Strength Rating of Worm Gears65

Wear rating of worm gears67


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4

FRICTION CLUTCHES

Notations:-

D = outer diameter of friction disk.

d = inner diameter of friction disk.

p = intensity of pressure.

P = total operating force.

( )ft

M = torque transmitted by friction.

z = number of pairs of contacting surfaces, for single plate

clutch z=one. (z = number of plates 1).

= coefficient of friction.

ap = intensity of pressure at the inner edge. = semi cone angle.

dr = radius of the drum.

gr = radius of the centre of gravity of the shoe in engagedposition.

m = mass of each shoe.

cfP = centrifugal force.

=sP Spring force

2 = running speed. (Rad/sec)

1 = speed at which engagement starts. (Rad/sec)


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Single Plate & Multi Plate Clutches

Uniform pressure theory

)(4

22dDP =

( ))(

)(

3 22

33

dD

dDPzM

ft

=

Uniform wear theory)(

2dD

dpP a =

( ) )(4

dDPz

Mft

+=


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6

Cone Clutches

Uniform pressure theory

)(4

22dDP =

( ))(

)(

sin3 22

33

dD

dDPzM

ft

=

Uniform wear theory

)(2

dDdpP a =

( ) )(sin4

dDPz

Mft

+=

Centrifugal Clutches

1000

2

1 g

s

rmP

=

( )1000

)( 212

2 =

zrmrM

dg

ft

Note: - here z = number of shoes.


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Brakes

Notations:-

E = total energy absorbed by the brake.K.E = kinetic energy absorbed by the brake.P.E = potential energy absorbed by the brake.m = mass of the system.I = mass moment of inertia of the rotating body.k = radius of gyration.

21,vv = Initial and final velocities of the system

21, = Initial and final angular velocities of the body

tM = braking torque.

= angle through which the brake drum rotates during thebraking period.

mghEP

mkEK

IEK

vvmEK

=

=

=

=

.

)(2

1.

)(2

1.

)(2

1.

2

2

2

1

2

2

2

2

1

2

2

2

1

tME=


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External Contracting Brakes

Block brake with short shoe

NRMt = Where

tM = Braking Torque

R = Radius of the Brake Drum

= Coefficient of Friction

N = Normal reaction

plwN = Where

p = Permissible pressure between the block andthe brake drum

l = length of the blockw = width of the block

)( PNRNR

Y

X

==

Nb

caP

=

)(

Pivoted block brake with long shoecosmaxPP =

2sin2

sin4

+=

Rh


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9

sin2 max2wpRMt =

)2sin2(2

1max += RwpRY

Internal expanding brake

( ) ( )[ ]

max

2121max

sin4

2cos2coscoscos4

=

hRRwpMf

( ) ( )[ ]

max

1212max

sin4

2sin2sin2

=

RwhpMn

max

21max

2

sin

)cos(cos

=

wpR

Mt

C

MMP

fn = (Clock wise rotation of the brake drum)

C

MMP

fn += (Anti clock wise rotation of the brake drum)

0

2

0

max 9090 >= when 0

22max 90


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fM = moment due to friction.

nM = moment due to normal force.

tM = elemental torque due to frictional force.

R = radius of the brake lining.w = face width of frictional lining.

Band Brakes

1

P = tension on the tight side of the band.

2P = tension on the loose side of the band.

= angle of wrap (rad).

tM = torque capacity of the brake.

R = radius of the brake drum.RPPMt )( 21 =

Rw

Pp =

Rw

Pp 1max =

p = intensity of pressure.w = width of the frictional lining.Differential band brake.

l

ebaPp

)(2

=


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11

Thermal Considerations

mc

Et =

Where t = temperature rise of the brake drum assembly( C0 )

E = total energy absorbed by the brakem = mass of the brake drum assemblyc = specific heat of the brake drum material


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12

Belt Drives

GEOMETRICAL RELATIONSHIPS

Open belt drive

)2(sin2180 1

C

dDs

=

)2(sin2180 1

CdD

b +=

C

dDdDCL

4

)(

2

)(2

2+

++=

Cross belt drive

)2(sin2180 1

C

dDbs

++==

C

dDdDCL

4

)(

2

)(2

2++

++=


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Analysis of belt tension

fe

mvP

mvP=

2

2

2

1

(For flat belts)

)2

1sin(

2

2

2

1f

emvP

mvP

=

(For V-belts)

Power transmitted= vPP )( 21

Condition for maximum power transmission

m

Pv i

3=

SELECTION OF FLAT BELT FROM THE

MANUFACTURES CATALOGUE

)()( max kWFkW a=

Where max)(kW = power transmitted by the belt for the

design purpose


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)(kW = actual power transmitted by the belt

aF = load correction factor

Type of load aF

(i) Normal load 1.0

(ii) Steady load, e.g. centrifugal pumps-fans-lightmachine tools-conveyors 1.2

(iii) Intermittent load, e.g. heavy duty fans-

blowers-compressors- reciprocating pumps-lineshafts-heavy duty machines

1.3

(iv) Shock load, e.g. vacuum pumps-rolling mills-hammers-grinders 1.5

Arc of contact factor

s (degrees)120 130 140 150 160 170 180 190 200

dF 1.33 1.26 1.19 1.13 1.08 1.04 1.00 0.97 0.94

HI-SPEED 0.0118 kW per mm width per ply

FORT 0.0147 kW per mm width per ply


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Standard widths of the belt are as

follows

3-Ply 25 40 50 63 764-Ply 40 44 50 63 76 90 100 112 125 1525-Ply 76 100 112 125 1526-Ply 112 125 152 180 200

dcorrected FkWkW = max)()( For HI-SPEED belt,

Corrected kW rating= (5.08)

0.0118v

For FORT belt,

Corrected kW rating=(5.08)

0.0147v

SELECTION OF V-BELTS

Dimensions of standard cross-sectionsBelt Section Width

W(mm)Thickness

T(mm)Minimum pitch

diameter of pulley(mm)A 13 8 125B 17 11 200C 22 14 300D 32 19 500

E 38 23 630


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Conversion of inside length to pitch length of the beltBelt section A B C D E

Difference between pitch length andinside length (mm) 36

43 56 79

92

Preferred values for pitch diameters (mm)

125 132 140 150 160 170 180 190 200 212 224236 250 265 280 300 315 355 375 400 425 450475 500 530 560 600 630 670 710 750 800 9001000


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ld

a

FFbeltofratingkWFkWinpowerdtransmittebeltsofNumber

=

___)___(__

Where aF = correction factor for industrial service

dF = correction factor for arc of contact

lF= correction factor for belt length


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22/69

21

++

+=

2

12

2

2121

28

224

zzzzL

zzL

pa nn

POWER RATING OF ROLLER CHAINS

1000

1vPkW =

Where

1P = allowable tension in the chain (N)

v = average velocity of chain


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kW rating of chain =( )

21

___

KK

KdtransmittebetokW s

Where sK = service factor

Multiple strand factors )( 1K

Number of strands 1K1 1.02 1.73 2.5

4 3.35 3.96 4.6


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Tooth correction factor )( 2K

Number of teeth on thedriving sprocket 2

K

15 0.85

16 0.9217 1.0018 1.0519 1.11

20 1.1821 1.2622 1.29

23 1.3524 1.41

25 1.4630 1.73


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Rolling Contact Bearing

Stribecks Equation

( ) ...............2cos2cos2 3210 +++= PPPC

cos

1

2 =

32

1

2

1

2

=

P

P

MPC 10 =

Where,

( ) ( ) 2525 2cos2cos21 ++=M

0C = Static load

..., 21 = radial deflections at the respective balls.

z

360=

Wherez is number of balls

M

zis practically constant and Stribeck suggested a value of

5 for

M

z

105

1zPC

=


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2

1 kdP = Where d is, the ball diameter and factor kdepends upon radii of curvature at the point of contact andon the modulii of elasticity of the materials.

Stribecks Equation

5

2

0

zkdC =

Equivalent Bearing Load

ar YFXFP += Where, P= equivalent dynamic load

rF = radial load

aF = axial or thrust load

X and Y are radial and thrust factors respectively andthere values are given in the manufactures catalogue.

Load Life Relationship

p

P

CL

=

Where L = bearing life (in million revolutions)

C = dynamic load capacity (N)p = 3 (for ball bearing)p = 10/3 (for roller bearing)


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Relationship between life in million revolutions and and life inworking hours is given by

610

60 hnL

L =

Where hL =bearing life (hours)

n = speed of rotation (rpm)

Selection of bearing from manufacturescatalogue

X and Y factors for single-row deep groove ball bearings

0C

Fa

eF

F

r

a

eF

F

r

a >

e

X Y X Y

0.0250.0400.0700.1300.250

0.500

11111

1

00000

0

0.560.560.560.560.56

0.56

2.01.81.61.41.2

1.0

0.220.240.270.310.37

0.44

ar YFXFP +=


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52 15 14000 6950 620562 17 22500 11400 630580 21 35800 19600 6405

30 42 7 3120 2080 61806

55 9 11200 5850 1600655 13 13300 6800 600662 16 19500 10000 620672 19 28100 14600 630690 23 43600 24000 6406

35 47 7 4030 3000 6180062 9 12400 6950 1600762 14 15900 8500 6007

72 17 25500 13700 620780 21 33200 18000 6307

100 25 55300 31000 6407

40 52 7 4160 3350 6180868 9 13300 7800 1600868 15 16800 9300 600880 18 30700 16600 620890 23 41000 22400 6308

110 27 63700 36500 640845 58 7 6050 3800 61809

75 10 15600 9300 1600975 16 21200 12200 600985 19 33200 18600 6209

100 25 52700 30000 6309120 29 76100 45500 6409

50 65 7 6240 4250 61810

80 10 16300 10000 1601080 16 21600 12300 601090 20 35100 19600 6210

110 27 61800 36000 6310130 31 87100 52000 6410

55 72 9 8320 5600 61811


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30

90 11 19500 12200 1601190 18 28100 17000 6011

100 21 43600 25000 6211120 29 71500 41500 6311

140 33 99500 63000 641160 78 10 8710 6100 61812

95 11 19900 13200 1601295 18 29600 18300 6012

110 22 47500 28000 6212130 31 81900 48000 6312150 35 108000 69500 6412

65 85 10 11700 8300 61813

100 11 21200 14600 16013100 18 30700 19600 6013120 23 55900 34000 6213140 33 92300 56000 6313160 37 119000 78000 6413

70 90 10 12100 9150 61814110 13 28100 19000 16014110 20 37700 24500 6014

125 24 61800 37500 6214150 35 104000 63000 6314180 42 143000 104000 6414

75 95 10 12500 9800 61815115 13 28600 20000 10615115 20 39700 26000 6015130 25 66300 40500 6215160 37 112000 72000 6315

190 45 153000 114000 6415


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Dynamic load capacityp

P

CL

=


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32

Selection of Taper Roller Bearings

YFF ra 5.0=

Where Y is the thrust factor

Equivalent dynamic load for single row taper roller bearingsis given by

( )

( ) eFFwhenYFFP

eFFwhenFP

raar

rar

>+=

=

4.0

Dimensions, Dynamic capabilities and calculation factors forsingle row taper roller bearing

d D B C Designation e Y20 42 15 22900 32004X 0.37 1.6

47 15.25 26000 30204 0.35 1.752 16.25 31900 30304 0.30 2.052 72.25 41300 32304 0.30 2.0

25 47 15 25500 32005X 0.43 1.452 16.25 29200 30205 0.37 1.652 19.25 34100 32205B 0.57 1.0552 22 44000 33205 0.35 1.7

62 18.25 41800 30305 0.30 2

62 18.25 35800 31305 0.83 0.7262 25.25 56100 32305 0.30 2

30 55 17 33600 32006X 0.43 1.462 17.25 38000 30206 0.37 1.6

62 21.25 47300 32206 0.37 1.662 21.25 45700 32206B 0.57 1.05


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50 80 24 64400 33010 0.31 1.9

85 26 80900 33110 0.40 1.590 21.75 70400 30210 0.43 1.490 24.75 76500 32210 0.43 1.4

90 32 108000 33210 0.40 1.5100 36 145000 T2ED050 0.35 1.7105 32 102000 T7FC050 0.88 0.68110 29.25 117000 30310 0.35 1.7

110 29.25 99000 31310 0.83 0.72110 42.25 161000 32310 0.35 1.7110 42.25 151000 32310B 0.54 1.1

60 95 23 76500 32012X 0.43 1.4

95 27 85800 33012 0.33 1.8100 30 110000 33112 0.40 1.5110 23.75 91300 30212 0.40 1.5110 29.75 119000 32212 0.40 1.5

110 38 157000 33212 0.40 1.5115 39 157000 T5ED060 0.54 1.1115 40 183000 T2EE060 0.33 1.8

125 37 145000 T7FC060 0.83 0.72

130 33.5 161000 30312 0.35 1.7130 33.5 134000 31312 0.83 0.72130 48.5 216000 32312 0.35 1.7

130 48.5 205000 32312B 0.54 1.170 110 25 95200 32014X 0.43 1.4

110 31 121000 33014 0.28 2.1

120 37 161000 33114 0.37 1.6125 26.25 119000 30214 0.43 1.4

125 33.25 147000 32214 0.43 1.4125 41 190000 33214 0.40 1.5

130 43 220000 T2ED070 0.33 1.8140 39 168000 T7FC070 0.88 0.68140 32 264000 T4FE070 0.44 1.35150 38 209000 3014 0.35 1.7


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35

70 150 38 176000 31314 0.83 0.72

150 54 275000 32314 0.35 1.7150 54 264000 32314B 0.54 1.1

80 125 29 128000 32016X 0.43 1.4

125 36 157000 33016 0.28 2.1130 37 168000 33116 0.43 1.4140 28.25 140000 30216 0.43 1.4140 35.25 176000 32216 0.43 1.4

140 46 233000 33216 0.43 1.4145 46 264000 T2ED080 0.31 1.9170 42.5 255000 30316 0.35 1.7170 42.5 212000 31316 0.83 0.72

170 61.5 358000 32316 0.35 1.7170 61.5 336000 32316B 0.54 1.1

90 140 32 157000 32018X 0.43 1.4140 39 205000 33018 0.27 2.2

150 45 238000 33118 0.40 1.5155 46 270000 T2ED090 0.33 1.8160 32.5 183000 30218 0.43 1.4

160 42.5 238000 32218 0.43 1.4

190 46.5 308000 30318 0.35 1.7190 46.5 251000 31318 0.83 0.72190 67.5 429000 32318 0.35 1.7

100 145 24 119000 T4CB100 0.48 1.25150 32 161000 32020X 0.46 1.3150 39 212000 33020 0.28 2.1

165 47 292000 T2EE100 0.31 1.9180 37 233000 30220 0.43 1.4

180 49 297000 32220 0.43 1.4180 63 402000 33220 0.40 1.5

215 51.5 380000 30320 0.35 1.7215 56.5 352000 31320X 0.83 0.72215 77.5 539000 32320 0.35 1.7

150 225 48 347000 32030X 0.46 1.3


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150 270 49 402000 30230 0.43 1.4

270 77 682000 32230 0.43 1.4320 72 765000 30330 0.35 1.7320 82 837000 31330X 0.83 0.72

200 280 51 446000 32940 0.40 1.5310 70 704000 32040X 0.43 1.4360 64 737000 30240 0.43 1.4360 104 1140000 32240 0.40 1.5

300 420 76 990000 32960 0.40 1.5


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Design for Cyclic Load and Speeds

3

3

=

N

BPPe

Bearing With a Probability of Survival Other

Than 90 Percent

b

e

e

R

R

L

L

1

90

90 1log

1log

=

Where b = 1.17


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Sliding Contact Bearing

Effect of Temperature on Viscosity


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Hydrostatic Step BearingThe following notations are used in the analysis,W = Trust load

0R = outer radius of the shaftiR = inner radius of the shaft

iP = supply of inlet pressure

oP = outlet or atmospheric pressure

0h = fluid film thickness

Q = flow of the lubricant

= viscosity of the lubricant

=

i

e

i

R

R

hPQ

0

3

0

log6

=

ie

ii

R

R

RRPW

0

22

0

log

2

Energy Losses in Hydrostatic Thrust

Bearing

)10)(()( 60= PPQkW ip

pkW)( = power loss in pumping

0

44

0

2

6

)(

1005.58

1)(

h

RRnkW if

=

fkW)( = power loss due to friction


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fpt kWkWkW )()()( +=

tkW)( = total power loss

Reynolds Equation

=

+

x

hU

z

ph

zx

ph

x633

Raimondi and Boyd Method

Dimensionless performance parameters for full

journal bearings with side flow

d

l

c

h0 S

fc

r

lrcn

Q

s

Q

Qs

maxp

p

0 1.0 70.92 0 _0.1 0.9 0.240 69.10 4.80 3.03 0 0.826

0.2 0.8 0.123 67.26 2.57 2.83 0 0.8140.4 0.6 0.0626 61.94 1.52 2.26 0 0.7640.6 0.4 0.0389 54.31 1.20 1.56 0 0.6670.8 0.2 0.021 42.22 0.961 0.760 0 0.4950.9 0.1 0.0115 31.62 0.756 0.411 0 0.358

0.97 0.03 _ _ _ _ 0 _1.0 0 0 0 0 0 0 0

1

0 1.0 85 0 _0.1 0.9 1.33 79.5 26.4 3.37 0.150 0.5400.2 0.8 0.631 74.02 12.8 3.59 0.280 0.5290.4 0.6 0.264 63.10 5.79 3.99 0.497 0.4840.6 0.4 0.121 50.58 3.22 4.33 0.680 0.415

0.8 0.2 0.0446 36.24 1.70 4.62 0.842 0.3130.9 0.1 0.0188 26.45 1.05 4.74 0.919 0.247


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0.97 0.03 0.00474 15.47 0.514 4.82 0.973 0.1521.0 0 0 0 0 0 1.0 _

0 1.0 88.5 0 _0.1 0.9 4.31 81.62 85.6 3.43 0.173 0.523

0.2 0.8 2.03 74.94 40.9 3.72 0.318 0.5060.4 0.6 0.779 61.45 17.0 4.29 0.552 0.4410.6 0.4 0.319 48.14 8.10 4.85 0.730 0.3650.8 0.2 0.0923 33.31 3.26 5.41 0.874 0.2670.9 0.1 0.0313 23.66 1.60 5.69 0.939 0.206

0.97 0.03 0.00609 13.75 0.610 5.88 0.980 0.1261.0 0 0 0 0 _ 1.0 0

0 1.0 89.5 0 _0.1 0.9 16.2 82.31 322.0 3.45 0.180 0.5150.2 0.8 7.57 75.18 153.0 3.76 0.330 0.4890.4 0.6 2.83 60.86 61.1 4.37 0.567 0.4150.6 0.4 1.07 46.72 26.7 4.99 0.746 0.3340.8 0.2 0.261 31.04 8.8 5.60 0.884 0.2400.9 0.1 0.0736 21.85 3.50 5.91 0.945 0.180

0.97 0.03 0.0101 12.22 0.922 6.12 0.984 0.1081.0 0 0 0 0 _ 1.0 0

c = R-rWhere c = radial clearance (mm)

R = radius of bearingr = radius of journal

c

e=

Where e =eccentricity ratio,

= eccentricity ratio

=

c

h01

Where 0h =film thickness


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43

c

h0is called the minimum film thickness variable

The Sommerfed number is given by

p

n

c

rS s2

=

Where sn =journal speed

p = unit bearing pressureThe Coefficient of Friction Variable (CFV) is given by

fc

r

CFV

=)(

Where f is the coefficient of friction

Frictional power 610

2)(

fWrnkW sf

=

The Flow Variable (FV) is given by

lrcn

QFV

s

=)(

Where l = length of the bearingQ= flow of the lubricant

Temperature Rise

)(

)(3.8

FV

CFVpt=

2tTT iav +=


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Bearing Design Selection of

Parameters


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45

Spur GearsThe pitch circle diameter is given by

mzd =1

Centre to centre distance,

2

)( gpn zzma

+=

Here transmission ratiog

p

p

g

n

n

z

zi ==

Standard System of Gear Tooth

Choice 1(preferred)

1.005.00

1.256.0

1.508.00

2.0010.00

2.512.00

3.0016.00

4.020.00

Choice2 1.12

5.5

1.375

7.00

1.75

9.00

2.25

11.00

2.75

14.0

3.50

18.00

4.5

Addendum( )ah =(m)

Dedendum ( )fh =1.25m

Clearance(c) =0.25mTooth thickness = 1.5708m

Fillet radius = 0.4m


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Force Analysis

n

kWMt

2

)(1060 6=

1

2

d

mp tt =

tantr PP =

cos

t

N

PP =

Number of Teeth

2minsin

2=z

Pressure angle ( ) 05.14 020 025

minz (Theoretical)32 17 11

minz (Practical)27 14 9

Face Width(3m)


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Beam Strength of Gear Tooth

YmbS bb =

Values of the Lewis form factor Y for 20 0 full depth involutesystem

z Y z Y z Y

15 0.289 27 0.348 55 0.415

16 0.295 28 0.352 60 0.421

17 0.302 29 0.355 65 0.425

18 0.308 30 0.358 70 0.429

19 0.314 32 0.364 75 0.43320 0.320 33 0.367 80 0.436

21 0.326 35 0.373 90 0.442

22 0.330 37 0.380 100 0.446

23 0.333 39 0.386 150 0.458

24 0.337 40 0.389 200 0.463

25 0.340 45 0.399 300 0.47126 0.344 50 0.408 Rack 0.484


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Effective Load on Gear Tooth

(1)For ordinary and commercially cut gears made with formcutters with v


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(2) C.I Pinion with C.I gear:

( )222121

3785 rr

rbrzenP

pp

d

+=

(3) Steel Pinion with C.I Gear

( )222121

92.03260 rr

rbrzenP

pp

d

+=

e = sum of errors between two meshing teeth (mm)

gp eee +=

where pe =error for pinion

ge =error for gear

Type of drivenmachines

Source of power

Electricmotor

Turbine/Multicylinder engine

Single-cylinderengine

Generators-feedingmechanisms-belt conveyors-

blowers-compressors-agitators

and mixers

1.10 1.25 1.50

Machine tools-hoist andcranes-rotary drives-pistonpumps-distribution pumps

1.25 1.50 1.75

Blanking and shearing presses-rolling mills-centrifuges-steel

work machinery

1.75 2.00 2.25


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50

Estimation of Module Based on BeamStrength

( ) ( )

31

6

3

1060

=

YS

m

bznC

fsCkWm

utv

s

Wear Strength of Gear Tooth

( )4.1

11cossin 212 EE

K c+

=


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51

KbQdS pw1=

pg

g

zz

zQ

=2

Expression for the load stress factor K can be simplifiedwhen all the gears are made of steel with a 20 0 pressureangle . in this special case,

2

21 207000 mmNEE == 020=

2))(81.9(27.0 mmNBHNc = where BHN=Brinell Hardness Number.Therefore,

2

10016.0

=

BHNK

Estimation of Module Based on

Wear Strength

( ) ( )

31

2

61060

=

QKm

bCnz

fsCkWm

vpp

s

Gear Design for Maximum Power

Transmitting Capacitydw PS 2=

2

w

dt

SPP ==


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52

Helical gears

cos

PPn =

cosmmn =

nm = normal module

m = transverse module

tan

ppa =

tan

tancos n=

cos

nzmd =

cos2

)( 21 zzma n+

=

p

g

g

p

z

zi ==

Where i=speed ratio for helical gearSuffixes p and g refer to the pinion and gear respectivelya is the centre to centre distance between two helical gearshaving 1z and 2z as the number of teeth.

The normal pressure angle is usually 020 .

Virtual number of teeth

31

cos

zz =


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53

Tooth proportionsIn helical gears, the normal module nm should be selected

from standards. The first preference values of the normal

module are nm (mm) 1, 1.25, 1.5, 2, 2.5,3,4,5,6,8 and10.The standard proportions of the addendum and dedendumare,

Addendum na mh =)(

Dedendum nf mh 25.1)( =

Clearance nmc 25.0)( =

Addendum circle diameter ad is given by

+= 2cos

zmd na

Dedendum circle diameter fd is given by

= 5.2

cos

zmd nf

sin

nmb

This is the minimum face width.Force Analysis

=tp Tangential component

=rp Radial component

=ap Axial or thrust component

coscos nt pp = tanta pp =


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54

=

cos

tan ntr pp

dmp tt 2=

Beam strength of helical gears

YmS bnb =

Effective load on gear tooth

n

kWMt

2

)(1060 6=

d

MP tt2

=

v

ts

effC

PCP =

sC = service factor (from table)

vC = velocity factor

The velocity factor ,

vCv

+=6.5

6.5

Dynamic load is given by


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55

2

2

2

1

21

2530 rr

rbrzenP

pp

d

+=

)coscos( ndtseff PPCP +=

)( fsPS effb =

Wear strength of helical gears

2cos

KbQdS

p

w =

11

12

pg

g

zz

zQ

+=

pg

g

zzzQ+

= 2

for internal helical gear

pg

g

zz

zQ

=2

4.1

11cossin

21

2

+

=EE

K

nnc


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57

Bevel Gears

cos2

Drb =

cos

1 zz =

g

p

z

z=tan

p

g

z

z=tan

2

=+

The cone distance 0A is given by22

022

+

=

gp

DDA

Force Analysis

=2

sin

2

bDr

p

m

Where mr

= radius of the pinion at the mid point along theface widthb = face width of the tooth


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58

m

tt

r

MP =

tants PP =

Where tP = tangential or useful component which isperpendicular to the plane of the paper.

sP = the separating force between the two meshingteeth

sintancostan

ta

tr

PP

PP

=

=

Beam Strength of Bevel Gears

=0

1A

bYmbS bb

Where bS beam strength of the toothm = module at the large end of the toothb = face width

b = permissible bending stress ( 3utS )Y = Lewis form factor based on formative number of

teeth

0A = cone distance

D

MP tt2

=

face width of the bevel gear is generally taken as (10 m) or( 30A ) whichever is smaller


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59

b = (10 m) or ( )30A (Whichever is smaller)

WEAR STRENGTH OF BEVEL GEARS

Buckinghams equationKbQdS pw1=

Where wS = wear strengthb = face width of gears

Q = ratio factors1

pd = pitch circle diameter of the formative pinion

K = material constant

bp rd 21=

cos

75.0 KbQDS

p

w = (Buckinghams equation)

tan

2

pg

g

zz

zQ

+=

4.1

11cossin2

+

=gp

cEE

K

When pinion as well as the gear is made of steel with 020 pressure angle, the value of K is given by

2

10016.0

=

BHN

K


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60

EFFECTIVE LOAD ON GEAR TOOTH

n

kWMt

2

)(1060 6=

D

MP tt2

=

v

ts

effC

PCP =

s

C= service factor (from table)

Type of drivenmachines

Source of power

Electricmotor

Turbine/Multicylinder engine

Single-cylinderengine

Generators-feedingmechanisms-belt conveyors-

blowers-compressors-agitatorsand mixers

1.10 1.25 1.50

Machine tools-hoist andcranes-rotary drives-pistonpumps-distribution pumps

1.25 1.50 1.75

Blanking and shearing presses-rolling mills-centrifuges-steel

work machinery

1.75 2.00 2.25

vC = velocity factor

The velocity factor for cut teeth is given by


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62

Worm Gears

Notations:-

1z = number of starts on the worm2z = number of teeth on the worm wheel

q = diametral quotientm = module

1d = pitch circle diameter of the worm

1ad = outer diameter of the worm

2ad = outer diameter of the worm wheel

2d = pitch circle diameter of the worm wheell = lead of the worm

xp = axial pitch of the worma = the centre distancei = the speed ratio.F = the effective face width

rl = the length of the root of the worm gear teeth.

Proportions of Worm Gears


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63

m

dq 1=

1zpl x=

22 mzd = mp x =

1mzl =

)(2

12zqma +=


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64

1

2

z

zi =

)1(2 += qmF

++=

cd

F

cdla

ar2sin)2( 1

1

1

Force Analysis

tP )( 1 = tangential component on the worm

aP )( 1 = axial component on the worm

rP )( 1 = radial component on the worm

1

1 2)(dMP tt =

( )( )

cossincos

sincoscos)()( 11

+

= ta PP

)cossin(cos

sin)()( 11

+= tr PP

Friction in worm gears

sv = rubbing velocity

1v = pitch line velocity of the worm

2v = pitch line velocity of the worm wheel

)1000)(60(

111

ndv

=

cos)60000(

11ndvs =

( ))cot(

tancos

+

=

cas


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65

Strength Rating Of Worm Gears

cos65.17)(

cos65.17)(

2222

2111

dmlSXM

dmlSXM

rbbt

rbbt

=

=

1)( tM , 2)( tM = permissible torque on the worm wheel

1bX , 2bX = speed factors for the strength of worm andworm wheel

1bS , 2bS = bending stress factors for worm and wormwheel


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66

m = module

rl = the length of the root of the worm gear teeth.

2d = pitch circle diameter of the worm wheel

= lead angle of the wormPower transmitting capacity of the worm gear based on thebeam strength is given by

61060

2

= t

nMkW

Where )( tM is the lower value between 1)( tM and 2)( tM .


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67

Wear Rating of Worm Gears

mdYSXM

mdYSXM

Zcct

Zcct

8.1

2224

8.1

2113

)(64.18)(

)(64.18)(

=

=

3)( tM , 4)( tM = permissible torque on the worm wheel

1cX , 2cX = speed factors for the strength of worm andworm wheel

1cS , 2cS = surface stress factors of the worm and worm

wheel

zY = zone factor

Thermal Considerations

kWHg )1(1000 =

Where gH = rate heat generation


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68

= efficiency of the of the worm gear (fraction)kW = power transmitted by the gears

AttkHd )( 0=

Where dH = rate of heat dissipationk = overall heat transfer coefficient of housing

walls ( )CmW 02 t = temperature of the lubrication oil. ( C0 )

0t = temperature of the surrounding air( C0 )A = effective surface area of housing

kA

kWtt

AttkkW

)1(1000

)1(1000

)(

0

0

+=

=

mechanical design data book.pdf

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