1

DESIGN OF FLAT BELTS

Condition For Maximum Power: m3P

v i= , Where Pi = (P1+P2)/2

SELECTION OF FLAT BELT FROM THE MANUFACTURES CATALOGUE: (1) (KW)max=Fa (KW)

Where (KW)max = power transmitted by the belt for design purpose

(KW) = actual power transmitted by belt in a given application

Table 13.1 Load correction factor (Fa)

Type of load Fa Normal load 1.0Steady load e.g. centrifugal pumps -fans-light machine tools-conveyors 1.2Intermittent load e.g. heavy duty fans-Blowers compressors-reciprocating pumps-line shafts-heavy duty machines 1.3

Shock load e.g. vacuum pumps-rolling mills-hammers-grinders 1.5

(2) (KW)corrected =(KW)max X Fd

Table 13.2 Arc of contact factor (Fd) αd (degrees) 120 130 140 150 160 170 180 190 200

Fd 1.33 1.26 1.19 1.13 1.08 1.04 1.00 0.97 0.94 (3) Corrected KW/belt rating:

HI SPEED belt: = 0.0118 v/5.08

FORT belt =0.0147v /5.08

HI-SPEED 0.0118 kW per mm width per ply FORT 0.0147 kW per mm width per ply

Where v= velocity of belt (m/s)

(4) Width X No. of piles = corrected power/corrected belt rating

Table: Recommended Width and Plies 3-ply 25 40 50 63 76 4-ply 40 44 50 63 76 90 100 112 125 152 5-ply 76 100 112 125 152 6-ply 112 125 152 180 200

SELECTION OF V BELT FROM THE MANUFACTURER’S CATALOGUE

ld

a

FxFxbeltratingofKWdTransmittePowerxF

beltsof.No =

Where

Fa=correction factor for industrial services (Table 13.6)

Fd= correction factor for arc of contact (Table 13.13)

Fl= correction factor for belt length (Table 13.7)

KW rating of belt (Table 13.5)

2

Table: Preferred pitch diameter of pulley (mm) 125 132 140 150 160 170 180 190 200 212 224 236 250 265 280 300 315 355 375 400 425 450 475 500 530 560 600 630 670 710 750 800 900 1000

Table 13.3 Dimensions of standard cross sections

Belt section

Width W(mm)

Thickness T(mm)

Minimum pitch

diameter of pulley

(mm) A 13 8 125 B 17 11 200 C 22 14 300 D 32 19 500 E 38 23 630

Table 13.4 Conversion of inside length to pitch length

of the belt Belt section A B C D E

Difference between pitch length and inside length (mm) 36 43 56 79 92

Table 13.5: Power rating of V-belts

(αs =1800; speed of the faster pulley=1440 rpm) (D=pulley diameter (mm); PR=power rating in kw)

Section A D PR

75 0.73

80 0.86

85 0.99

90 1.12

100 1.38

106 1.50

112 1.63

118 1.81

125 2.00

Section B D PR

125 2.24

132 2.46

140 2.77

150 3.30

160 3.60

170 4.00

180 4.39

190 4.77

200 5.23

Section C D PR

200 6.14

212 6.81

224 7.68

236 8.28

250 9.40

265 10.10

280 11.10

300 12.10

315 12.50

Section D D PR

350 15.7

375 17.5

400 19.3

425 20.60

Table 13.6 Correction factor (Fa) for industrial service

Operational hours per day Type of service 0-10 10-16 16-24

Light duty: agitators-blowers-centrifugal pumps-fans (up to 7.5 kw) and compressors

1.1 1.2 1.3

Medium duty: conveyors-fans (above 7.5 kw)-line shafts-machine tools-presses and positive displacement pumps

1.2 1.3 1.4

Heavy duty: conveyors-bucket elevators and hammers 1.3 1.4 1.5

Table 13.7 Correction factor FL for belt length (Li=nominal inside length of belt in mm)

Belt section Li A B C D E

1905 1.02 0.97 0.87 - - 1981 1.03 0.98 - - - 2032 1.04 - - - - 2057 1.04 0.98 0.89 - - 2159 1.05 0.99 0.90 - - 2286 1.06 1.00 0.91 - - 2438 1.08 - 0.92 - - 2464 - 1.02 - - - 2540 - 1.03 - - - 2667 1.10 1.04 0.94 - - 2845 1.11 1.05 0.95 - - 3048 1.13 1.07 0.97 0.86 - 3150 - - 0.97 - - 3251 1.14 1.08 0.98 0.87 - 3404 - - 0.99 - - 3658 - 1.11 1.00 0.90 - 4013 - 1.13 1.02 0.92 - 4115 - 1.14 1.03 0.92 - 4394 - 1.15 1.04 0.93 - 4572 - 1.16 1.05 0.94 - 4953 - 1.18 1.07 0.96 - 5334 - 1.19 1.08 0.96 0.94 6045 - - 1.11 1.00 0.96 6807 - - 1.14 1.03 0.99

Fig.: Selection of cross section of V-belt

3

Extension Spring

3i

i dCDF8π

=τ , 3

iimax d

CDF8π

+τ=τ Where Fi = initial tension

4it

Gd)FF(n8 −

=δ , 23

bA d

F4d

FD16Kπ

+π

=σ , )1C(C41CC4K

11

12

1b −

−−= , C1= 2R1/d

3T

B dFD8K

π=τ ,

4C41C4

K2

2T −

−= , C2=2R2/d, Where R2= side bend radius

Table1: Values of allowable shear stress, modulus of elasticity and of

rigidity for various spring materials

Table 2: Standard wire gauge (SWG) number and corresponding diameter of spring wire SWG Diameter (mm) SWG Diameter (mm) SWG Diameter (mm) SWG Diameter (mm)

7/0 12.70 7 4.470 20 0.914 33 0.2540 6/0 11.785 8 4.064 21 0.813 34 0.2337

5/0 10.973 9 3.658 22 0.711 35 0.2134 4/0 10.160 10 3.251 23 0.610 36 0.1930 3/0 9.49 11 2.946 24 0.559 37 0.1727 2/0 8.839 12 2.642 25 0.508 38 0.1524 0 8.229 13 2.337 26 0.457 39 0.1321 1 7.620 14 2.032 27 0.4166 40 0.1219 2 7.010 15 1.829 28 0.3759 41 0.1118

3 6.401 16 1.626 29 0.3454 42 0.1016

4 5.893 17 1.422 30 0.3150 43 0.0914 5 5.385 18 1.219 31 0.2946 44 0.0813 6 4.877 19 1.016 32 0.2743 45 0.711

4

Table 3: Dimensions for centre bolts

Table 4: Values of buckling factor Kb

Lf/D Hinged end spring

Built in end spring

1 0.72 0.72 2 0.63 0.71 3 0.38 0.68 4 0.20 0.63 5 0.11 0.53 6 0.07 0.38 7 0.05 0.26 8 0.04 0.19

Table 5: Dimensions of clip, rivet and bolts

Spring width (B)

in mm Clip section

(b x t) in mm2 Dia. of rivet (d1) in mm

Dia. of bolt (d2) in mm

Under 50 20X4 6 6 50,55 and 60 25X5 8 8

65,70,75 and 80 25X6 1 8 90,100 and 125 32X6 10 10

Table 6: Physical properties of materials commonly used for leaf springs

Material Condition Ultimate tensile strength (MPa)

Tensile yield strength(MPa)

Brinell hardness number

50 Cr 1 1680-2200 1540-1750 461-601

50 Cr 1 V23 1900-2200 1680-1890 534-601

55 Si 2 Mn 90

Hardened

and Tempered

1820-2060 1680-1920 534-601

WIRE ROPE

Stresses in wire ropes

1) Direct stress, A

wWd

+=σ

W=load lifted, w=weight of rope A=cross sectional area of rope

2) Bending stress, D

dxE wrb =σ

Equivalent bending load: Wb= Abσ ,

Er = Effective modulus of elasticity dw =diameter of wire, A=cross sectional area, D= sheave dia. 3) Stresses due to starting and stopping

Aax

gwW

a+

=σ , axg

wWWa+

= ,

Wa= additional load, g= acceleration due to gravity, a=acceleration of rope and load = V/t or (V2 – V1)/t (V2 – V1) = change in speed, t = time

4) Impact load on starting No Slack: ( )rsst WW2W +=

Ws = load lifted, Wr = Wt. of wire rope

If Slack is ‘h’ : ( )

σ+++=

lgahE211WWW

d

rrsst

a = acceleration of rope, h = slackness in the rope l = length of rope

AWW rs

d+

=σ is static stress in the rope neglecting

the effect of core, A = Area of metallic portion of rope 5) Effective stress in rope during:

(i) During Normal working = bd σ+σ

(ii) During starting = bst σ+σ

(iii) During acceleration = abd σ+σ+σ

Table: Wire Rope data

Type of construction

Modulus of elasticity of rope, Er (N/mm2)

Diameter of wire , dw (mm)

Metallic area of rope , A (mm2)

Sheave diameter , D (mm)

Recommended

6x7 97000 0.106dr 0.38 dr2 42 dr 72 dr

6x19 83000 0.045 dr 0.40 dr2 18 dr 27 dr

6x37 76000 0.045 dr 0.40 dr2 18 dr 27 dr

Width of leaves in mm Dia. of centre bolt in mm Dia. of head in mm Length of bolt head in mmUpto and including 65 8 or 10 12 or 15 10 or 11

Above 65 12 or 16 17 or 20 11

5

Table: Factors of safety for wire ropes

Application Class 1 Class 2 and 3 Class 4

Hoisting where jibs are supported by roes and where shock absorbing devices are provided in jib support

4.0 4.5 5.5

Cranes and hoists in general hoist blocks

4.5 5.0 6.0

Table: Breaking load and mass for 6x19 (12/6/1) construction wire ropes with fibre core

Minimum breaking load to tensile designation of wires (kN)

Nominal diameter

(mm)

Approx. mass

kg/100m) 1230 1420 1570

6 12.5 13.6 15.7 17.4

7 17.0 18.5 21 24

8 22.1 24 28 31

9 28.0 31 35 39

10 34.6 38 44 48

11 41.9 46 53 58

12 49.8 54 63 69

Table: Breaking load and mass for 6x7 (6/1) construction wire ropes

Minimum breaking load to tensile designation of wires (kN)

Nominal diameter

(mm)

Approximate mass (kg/100m) 1570 1770 1960

Fibre core

Steel core

Fibre core

Steel core

Fibre core

Steel core

Fibre core

Steel core

8 22.9 25.2 33 36 38 41 42 45 9 28.9 31.8 42 46 48 51 53 57 10 35.7 39.1 52 56 59 64 65 70 11 43.2 47.6 63 68 71 77 79 85 12 51.5 56.6 75 81 85 91 94 101

Bearings

1. Clearance C=R-r R=radius of bearing r= radius of journal 2. arc length= (π d x B)/360

3. FLAT PIVOT BEARING

Total axial force: p)dd(4

F 2i

2o −

π=

meanFrT µ= µ = coefficient of friction, p=bearing pressure, V=rubbing velocity

Thick Cylinders – Principal Stresses

CYLINDERS WITH INTERNAL PRESSURE:

( )

−

−−=σ 1

r4D

DDDp

2

2o

i2

o2

2ii

r ; ( )

+

−+=σ 1

r4D

DDDp

2

2o

i2

o2

2ii

t

At inner surface: r=Di/2: ( )( )i

2o

2i

2o

2i

rir DDDDp

;p−+

+=σ−=σ

At outer surface: r=Do/2: ( )i2

o2

i2

irr DD

Dp2;0−

+=σ=σ

Fig. : Variation of principal stresses

(cylinders with internal pressure)

6

CYLINDERS WITH EXTERNAL PRESSURE :

( )

−

−−=σ 2

2i

i2

o2

2oo

r r4D

1DD

Dp; ( )

+

−−=σ 2

2i

i2

o2

2oo

t r4D1

DDDp

At inner surface: r=Di/2: 0r =σ ( )i2

o2

2oo

t DDDp2−

−=σ

At outer surface: r=Do/2: )DD(

DD(p;pi

2o

2i

2o

20

tor −+

−=σ−=σ

Fig. : Variation of principal stresses (cylinders with external pressure)

COMPOUND CYLINDER:

,

CJ δ+δ=δ

Chain Drives Notations: P: Pitch of chain (m) D: Pitch circle diameter (m) D1: Pitch circle of smallest sprocket D2: Pitch circle of larger sprocket D0: Sprocket outside diameter Di: Diameter of chain roller K: Number of chain links Ks: Service factor Ft: Tangential driving force Fc: Centrifugal tension in the chain Fs: Tension in the chain due to sagging L: Length of chain m: Mass of chain in kg per metre N1: Speed of rotation of smaller sprocket (rpm ) N2: Speed of rotation of larger sprocket P: Power transmitted by chain T: Number of teeth on the sprocket T1:Number of teeth on smaller sprocket T2:Number of teeth on larger sprocket

n: Factor of safety W: Total load on the driving side of chain Wb : Breaking strength of chain θ: angle subtended by one pitch length at the centre of sprocket v : Average velocity of chain (m/s) x : Centre distance between sprockets(m) σb: Allowable bearing stress in MPa of N/mm² A : Projected bearing area (mm²) re : Tooth flank radius ri : Roller seating radius α : Roller seating angle ha: Tooth height above the pitch polygon Da: Top diameter Df: Root Diameter bf1: tooth width rx: Tooth side radius ba: Tooth side relief bf1 and bf2: width over teeth

Formulae for chain drives

1. T

360o

=θ

2.

=

θ=

T180sinD

2sinDp

3. Do=D+0.8d1 4. Angle of articulation= 2/θ 5. Velocity ratio, V.R.= N2/N1=T2/T1

6. 60

TpN60DNv =π

=

7

7. xp

2TT

px2

2TTKwhere,KpL

21221

π−

+++

==

8.

π−

−

+

−++

−=

2

212

2121

2)TT(8

2)TT(K

2TTK

4px

For velocity transmission ratio of 3, mm50to302

DDx 21min +

+= (For best results, min. distance centre

distance should be 30 to 50 times the pitch. Factor of safety

9. n = Wb/W 10. Wb =106 p2(Newtions) for roller chains; p – pitch in mm = 106 p (Newton) per mm width of chain for silent chains 11. FT = Power transmitted / Speed of chain = P/ v (Newtons) 12. Fc = m v2 (Newtons) 13. Fs = k m g x (Newtons) K – constant which takes into account the arrangement of chain

drive. K = 2 to 6, when center line of chain is inclined to the horizontal at

an angle less than 400. K = 1 to 1.5, when center line of chain is inclined to the horizontal at an angle greater than 400.

Power transmitted by chains

14. s

b

nKvW

P =

15. s

b

KAv

Pσ

= , Where Ks = Service factor = K1.K2.K3

Fig. : Tooth profile of sprocket

K1 = Load factor =1, for constant load = 1.25, for variable load with mild shock = 1.5, for heavy shock loads

K2 = Lubrication factor = 0.8, for continuous lubrication = 1, for drop lubrication = 1.5, for periodic lubrication

K3 = rating factor = 1, for 8 hrs/day = 1.25, for 16 hrs/day = 1.5, for continuous service

Number of teeth on smaller or driving sprocket

16. Vmax = )s/m(60

ND1π ,

D1: pitch circle diameter of smaller sprocket

17. Vmin = )s/m(60

)2/cos(ND1 θπ

Principle Dimensions of tooth profile 18. re = 0.008d1(T2+180) [max] = 0.12 d1(T+2) [min] 19. ri = 0.505 d1+0.069(d1)1/3 [max] = 0.505 d1 [min]

20. T

90140o

o −=α [max]

T

90120o

o −= [min]

21. ha = 0.625p – 0.5 d1 + 0.8p/T [max] = 0.5 (p-d1) [min]

22. ( ) ( )T/180eccospT/180sin

pD ==

23. Da = D+1.25p-d1 [max] = D+p(1-1.6/T)-d1 [min] 24. Df = D-2ri 25. bf1 = 0.93 b1 when p<= 12.7 mm = 0.95 b1 when p> 12.7 mm

26. rx = p 27. ba= 0.1p to 0.15p 28. bf2 and bf3 = (Number of strands – 1)pt + bf1 29. Design Power = Rated Power X Service factor 30. Load (W) = Rated power / Pitch line velocity

8

Table: Number of teeth on the smaller sprocket

Number of teeth at velocity ratio Type of chain 1 2 3 4 5 6

Roller 31 27 25 23 21 17 Silent 40 35 31 27 23 19

Table: Power Rating (in kW) of simple roller chain

Power ( kW) Speed of smaller sprocket or pinion (rpm)

06B 08B 10 B 12B 16B

100 0.25 0.64 1.18 2.01 4.83 200 0.47 1.18 2.19 3.75 8.94 300 0.61 1.70 3.15 5.43 13.06 500 1.09 2.72 5.01 8.53 20.57 700 1.48 3.66 6.71 11.63 27.73 1000 2.03 5.09 8.97 15.65 34.89 1400 2.73 6.81 11.67 18.15 38.47 1800 3.44 8.10 13.03 19.85 -- 2000 3.80 8.67 13.49 20.57 --

• Factor of safety (n) for bush roller and silent

chain: Table 14.38 P. 287. • Characteristics of roller chains according IS

:2403 – 1991 : P. 287 B , Table:14.40a.

Table: Maximum allowable speed for chains in r.p.m.

Chain pitch (p) in mm

Type of

chain

Number of teeth on the smaller sprocket

(T1)

12 15 20 25 30

15 2300 1900 1350 1150 1100 19 2300 2000 1450 1200 1050 23 2400 2100 1500 1250 1100 27 2550 2150 1550 1300 1100

Roller Chain

30 2600 2200 1550 1300 1100 Silent Chain 17-35 3300 2650 2200 1650 1300

Table: Permissible speed (rpm) of smaller sprocket or pinion

Pitch of chain (p) in mm Type

of chain

Number of teeth

on sprocket

pinion

12 15 20 25 30

15 2300 1900 1350 1150 1000 19 2400 2000 1450 1200 1050 23 2500 2100 1500 1250 1100 27 2550 2150 1550 1300 1100

Bush Roller chain

30 2600 2200 1550 1300 1100 Silent Chain 17-35 3300 2650 2200 1650 1300

Spur Gear P = Ft x v; P: Power ( kW), v: pitch line velocity (m/s), Ft: tangential force (kN) Ft = Fn cosα ; α: pressure angle, Fn: normal force. Static Load: Beam Strength: YbmF dbeam σ= ; where 9.5 ≤ b ≤ 12.5m

v

tsmaxt C

FCF = ; Check: Fbeam ≥ Ft max

Cs: Service factor Table: 12.20, p. 187; Cv: Velocity factor, p. 164. Form factor:

−π=

z912.0154.0Y for 20o involute full-depth tooth;

−π=

z95.0175.0Y for 20o stub tooth;

−π=

z684.0124.0Y for 14.5o tooth

Dynamic Load: refer data book p. 166 and 167 YbmFOSxFF endynen σ== ; enσ : endurance limit (=1.75BHN)

Gear Construction: 1. For pitch diameter d ≤ 14.8m+60 (mm): pinion/gear is solid disc type 2. For pitch diameter d ≥23.5m+85 (mm): gear is arm type 3. In other cases gear is web type with web thickness=(1.6-2)m (m: module) 4. Rim thickness, h= (2-4) m, Rim to be tapered 1 : 5 towards the centre. 5. Hub diameter , dh= (1.6-2)ds; ds is shaft dia. 6. Thickness of the stiffening rib, q =(1-1.25) h 7. Hub length, lh = 2ds or at least equal to face width b.

Static stress concentration factor45.015.0

t ht

rt18.0K

= for 200 pressure angle

f

dbeam K

YbmF

σ= ; Kf = fatigue stress concentration factor

Number of arms (j): j=4 (If d≤500mm); j=6 If 500 mm ≤ d ≤1500 mm j=8 If d ≥ 1500mm Section modulus of the arm

section: d

ho

j2l)dd(F

Zσ−

=