DESIGN OF FLAT BELTS Pi
Condition For Maximum Power: v =
3m
, 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 Normal load Steady load e.g. centrifugal pumps -fans-light machine tools-conveyors Intermittent load e.g. heavy duty fans-Blowers compressors-reciprocating pumps-line shafts-heavy duty machines Shock load e.g. vacuum pumps-rolling mills-hammers-grinders (2) (KW)corrected =(KW)max X Fd Table 13.2 Arc of contact factor (Fd) d (degrees)
Fd
120 1.33
130 1.26
140 1.19
150 1.13
160 1.08
170 1.04
180 1.00
190 0.97
200 0.94
(3) Corrected KW/belt rating: HI SPEED belt: belt: = 0.0118 v/5.08
HI-SPEED FORT
FORT belt =0.0147v /5.08
0.0118 kW per mm width per ply 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 belt rating Table: Recommended Width and Plies 3-ply 4-ply 5-ply 6-ply
25 40 76 112
40 44 100 125
50 50 112 152
63 63 125 180
76 76 152 200
90
100
112
125
152
SELECTION OF V BELT FROM THE MANUFACTURER’S CATALOGUE
No. of belts =
Fa x Power Transmitted KW ratingof belt x Fd x Fl
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)
1
Fa 1.0 1.2 1.3 1.5
Table 13.3 Dimensions of standard cross sections Belt Width Thickness Minimum section W(mm) T(mm) 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 0
(αs =180 ; speed of the faster D 75 Section A PR 0.73 D 125 Section B PR 2.24 D 200 Section C PR 6.14 D 350 Section D PR 15.7
Table: Preferred pitch diameter of pull ey (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 13.4 Conversion of inside length to pitch length of the belt Belt section A B C D E Difference between pitch 36 43 56 79 92 length and inside length (mm)
Table 13.5: Power rating of V-belts pulley=1440 rpm) (D=pulley diameter (mm); PR=power rating in kw) 80 85 90 100 106 112 118 125 0.86 0.99 1.12 1.38 1.50 1.63 1.81 2.00 132 140 150 160 170 180 190 200 2.46 2.77 3.30 3.60 4.00 4.39 4.77 5.23 212 224 236 250 265 280 300 315 6.81 7.68 8.28 9.40 10.10 11.10 12.10 12.50 375 400 425 17.5 19.3 20.60
Table 13.6 Correction factor (Fa) for industrial service Type of service Operational hours per day 0-10 10-16 16-24 Light duty: agitators-blowers-centrifugal pumps-fans (up to 7.5 kw) and 1.1 1.2 1.3 compressors Medium duty: conveyors-fans (above 7.5 kw)-line shafts-machine tools1.2 1.3 1.4 presses and positive displacement pumps 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
2
Extension Spring 8CDFi
τi =
δ=
πd
τ max = τi +
,
3
8n t ( F − Fi )
τB =
Gd
4
K T 8FD
πd
3
,
,
σA = K T
=
8CDFi
πd 3
K b 16FD
πd
3
+
Where Fi = initial tension
πd
− C1 − 1 , C 2R /d 1= 1 4C1 ( C1 − 1) 2
4F
, K b
2
− 1 , C =2R /d, 2 2 4C 2 − 4 4C 2
=
4 C1
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
3
Table 3: Dimensions for centre bolts Width of leaves in mm Upto and including 65
Dia. of centre bolt in mm 8 or 10
Above 65
Dia. of head in mm 12 or 15
12 or 16
Length Length of bolt head in mm 10 or 11
17 or 20
11
Table 4: Values of buckling factor Kb Table 5: Dimensions of clip, rivet and bolts Hinged end spring 0.72 0.63 0.38 0.20 0.11 0.07 0.05 0.04
Lf /D /D 1 2 3 4 5 6 7 8
Built in end spring 0.72 0.71 0.68 0.63 0.53 0.38 0.26 0.19
Spring width (B) in mm Under 50 50,55 and 60
Clip section 2 (b x t) in mm 20X4 25X5
Dia. of rivet (d1) in mm 6 8
Dia. of bolt (d2) in mm 6 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 Ultimate tensile strength Tensile yield Brinell hardness Condition (MPa) strength(MPa) number
Material 50 Cr 1 50 Cr 1 V23 55 Si 2 Mn 90
Hardened and Tempered
1680-2200
1540-1750
461-601
1900-2200
1680-1890
534-601
1820-2060
1680-1920
534-601
WIRE ROPE Stresses in wire ropes 1)
Direct stress,
σd =
W+w
4)
No Slack: Wst
A
Bending stress,
σ b =
If Slack is ‘h’ : W
E r x d w
st
D
Equivalent bending load: Wb=
W+w g
x
a
σ b A ,
A
Wa
,
=
= (Ws + Wr )1 +
1+
2ahE r
σ d lg
a = acceleration of rope, h = slackness in the rope l = length of rope
W+w g
+ Wr
Ws
σd =
Er = Effective modulus of elasticity dw =diameter of wire, A=cross sectional area, D= sheave dia. 3) Stresses due to starting and stopping
σa =
= 2(Ws + Wr )
Ws = load lifted, Wr = Wt. of wire rope
W=load lifted, w=weight of rope A=cross sectional area of rope 2)
Impact load on starting
A
is static stress in the rope neglecting
the effect of core, A = Area of metallic portion of rope 5)
xa,
Effective stress in rope during:
σ d + σ b (ii) During starting = σ st + σ b (iii) During acceleration = σ d + σ b + σ a (i) During Normal working =
Wa= additional load, g= acceleration due to gravity, a=acceleration of rope and load = V/t or (V 2 – V1)/t (V2 – V1) = change in speed, t = time
Table: Wire Rope data Type of
Modulus of elasticity 2
Diameter of
Metallic area of 2
Sheave diameter ,
of rope, Er (N/mm )
wire , dw (mm)
rope , A (mm )
6x7
97000
0.106dr
0.38 dr
2
42 dr
72 dr
0.045 dr
0.40
2 dr
18 dr
27 dr
0.40
2 dr
18 dr
27 dr
6x19 6x37
83000 76000
0.045 dr
4
D (mm)
Recommended
construction
Table: Factors of safety for wire ropes Application
Class 1
Hoisting where jibs are supported by roes and where shock absorbing devices are provided in jib support
4.0
Cranes and hoists in general hoist blocks
4.5
Table: Breaking load and mass for 6x19 (12/6/1) construction wire ropes with fibre core
Class 2 and 3
Class 4
4.5
5.5
5.0
Nominal diameter (mm)
Approx. mass kg/100m)
6
6.0
Minimum breaking load to tensile designation of wires (kN) 1230
1420
1570
12.5
13.6
15.7
17.4
7
17.0
18.5
21
24
8
22.1
24 24
28
31
9
28.0
31 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 Nominal diameter (mm)
Minimum breaking load to tensile designation of wires (kN) 1570 1770 1960 Fibre Steel Fibre Steel Fibre Steel core core core core core core 33 36 38 41 42 45 42 46 48 51 53 57 52 56 59 64 65 70 63 68 71 77 79 85 75 81 85 91 94 101
Approximate mass (kg/100m) Fibre core 22.9 28.9 35.7 43.2 51.5
8 9 10 11 12
Steel core 25.2 31.8 39.1 47.6 56.6
Bearings 1.
2.
Clearance C=R-r R=radius of bearing r= radius of journal
3.
FLAT PIVOT BEARING
Total axial force:
arc length= (π d x B)/360
T
F=
π 4
(d o
2
− d i 2 ) p
= µFr mean
µ = coefficient of friction, p=bearing pressure, V=rubbing velocity Thick Cylinders – Principal Stresses CYLINDERS WITH INTERNAL PRESSURE: PRESSURE: 2 Do2 Do 2 p i D i σ r = − 2 −1 ; σ = + +1 (D o − D 2 i ) 4r 2 t (D 2 o − D 2i ) 4r 2 p i (D 2 o + D 2 i ) At inner surface: r=Di/2: σ r = − p i ; σ r = + (D 2 o − D 2 i )
p i D i
2
At outer surface: r=Do/2:
σ r = 0; σ r = +
2 p i D 2 i
(D
2
o
− D2i ) Fig. : Variation of principal stresses (cylinders with internal pressure)
5
CYLINDERS WITH EXTERNAL PRESSURE : 2 Di2 Di 2 p o D o 1− 1+ σ r = − 2 ;σ =− (D o − D 2 i ) 4r 2 t (D 2 o − D 2 i ) 4r 2
p o D o
2
At inner surface: r=Di/2:
σ r = 0 σ t = −
2 p o D o
(D
2
− D2i ) p 0 (D 2 o + D 2 i At outer surface: r=Do/2: σ r = − p o ; σ t = − 2 2 (D o − D i ) 2
o
Fig. : Variation of principal stresses (cylinders with external pressure) COMPOUND CYLINDER:
,
δ = δJ + δC
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 s agging 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 t he 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) r e : Tooth flank radius r i : Roller seating radius α : Roller seating angle ha: Tooth height above the pitch polygon Da: Top diameter Df : Root Diameter bf1: tooth width r x: Tooth side radius ba: Tooth side relief bf1 and bf2: width over teeth
Formulae for chain drives 360
o
1.
θ=
2.
p
3. 4. 5.
Do=D+0.8d1 Angle of articulation= θ / 2 Velocity ratio, V.R.= N2/N1=T2/T1
6.
v=
T
θ 180 = D sin = D sin 2 T
πDN 60
=
TpN 60
6
L = Kp, where K =
7.
8.
x
=
p 4
K −
T1 + T2
2
T1 + T2 2
+ K −
For velocity transmission ratio of 3,
+
2x p
T −T + 2 1 2π
(T1 + T2 )
x min
D1 + D 2 2
p x
(T1 − T2 )
− 8
2
=
2
2
2π
2
+ 30 to 50 mm (For best results, min. distance centre
distance should be 30 to 50 times the pitch. Factor of safety 9. n = Wb/W 2 10. Wb =106 p (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) 2 12. Fc = m v (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 0 an angle less than 40 . K = 1 to 1.5, when center line of chain is inclined to the horizontal 0 at an angle greater than 40 . Power transmitted by chains 14.
W b v
P=
15. P
=
nK s
σ b Av ,
Fig. : Tooth profile of sprocket
Where Ks = Service factor = K1.K2.K3
K s
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 =
πD1 N
( m / s) ,
60
D1: pitch circle diameter of smaller s procket 17. Vmin =
πD1 N cos(θ / 2) 60
(m / s)
Principle Dimensions of tooth profile 2 18. r e = 0.008d1(T +180) [max] = 0.12 d1(T+2) [min] 1/3 19. r i = 0.505 d1+0.069(d1) [max] = 0.505 d1 [min] 20.
α = 140 o −
90
o
[max]
T
90 o
[min] T 21. ha = 0.625p – 0.5 d 1 + 0.8p/T [max] = 0.5 (p-d1) [min]
= 120 o −
22.
D=
p sin (180 / T )
= p cos ec (180 / T)
26. 27. 28. 29. 30.
23. Da = D+1.25p-d1 [max] = D+p(1-1.6/T)-d1 [min] 24. Df = D-2r i 25. bf1 = 0.93 b1 when p<= 12.7 mm = 0.95 b1 when p> 12.7 mm
7
r x = p ba= 0.1p to 0.15p bf2 and bf3 = (Number of strands – 1)pt + bf1 Design Power = Rated Power X Service factor Load (W) = Rated power / Pitch line velocity
Table: Number of teeth on the smaller sprocket Type of chain Roller Silent
Table: Maximum allowable speed for chains in r.p.m.
Number of teeth at velocity ratio 1 2 3 4 5 6 31 27 25 23 21 17 40 35 31 27 23 19
Chain pitch (p) in mm
Table: Power Rating (in kW) of simple roller chain Speed of Power ( kW) smaller 06B 08B sprocket or pinion (rpm) 100 0.25 0.64 200 0.47 1.18 300 0.61 1.70 500 1.09 2.72 700 1.48 3.66 1000 2.03 5.09 1400 2.73 6.81 1800 3.44 8.10 2000 3.80 8.67
•
10 B
12B
16B
1.18 2.19 3.15 5.01 6.71 8.97 11.67 13.03 13.49
2.01 3.75 5.43 8.53 11.63 15.65 18.15 19.85 20.57
4.83 8.94 13.06 20.57 27.73 34.89 38.47 ---
Factor of safety (n) for bush roller and silent chain: Table 14.38 P. 287.
•
Number of teeth on the smaller sprocket (T 1 ) 15 19 Roller 23 Chain 27 30 Silent 17-35 Chain Type of chain
Characteristics of roller chains according IS :2403 – 1991 : P. 287 B , Table:14.40a.
12
15
20
25
30
2300 2300 2400 2550 2600
1900 2000 2100 2150 2200
1350 1450 1500 1550 1550
1150 1200 1250 1300 1300
1100 1050 1100 1100 1100
3300
2650
2200
1650
1300
Table: Permissible speed (rpm) of smaller sprocket or pinion Number Pitch of chain (p) in mm Type of teeth of on 12 15 20 25 30 chain sprocket pinion 15 2300 1900 1350 1150 1000 19 2400 2000 1450 1200 1050 Bush Roller 23 2500 2100 1500 1250 1100 chain 27 2550 2150 1550 1300 1100 30 2600 2200 1550 1300 1100 Silent 17-35 3300 2650 2200 1650 1300 Chain
Spur Gear P = Ft x v; P: Power ( kW), v: pitch line line velocity (m/s), Ft: tangential force (kN) Ft = Fn cos ; α: pressure angle, Fn: normal force.
α
Static Load: Beam Strength:
Ft max
=
C s Ft Cv
F beam
= bmσ d Y ; where 9.5 ≤ b ≤ 12.5m
; Check: F beam beam ≥ F t max
Cs: Service factor Table: 12.20, p. 187; Cv: Velocity factor, p. 164. 0.912 for 20o involute full-depth tooth; Form factor: Y = π 0.154 − z
0.684 for 14.5o tooth 0.95 for 20o stub tooth; Y = π 0.124 − z z Dynamic Load: refer data book p. 166 and 167
Y = π 0.175 −
Fen
= Fdyn x FOS = bmσ en Y ; σen : endurance limit (=1.75BHN)
Gear Construction: 1. For pitch diameter d 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 Thickness of the stiffening rib, q =(1-1.25) h 7. Hub length, lh = 2ds or at least equal to face width b. 0.15
0.45
0 t t Static stress concentration factor K = 0.18 for 20 pressure angle t r h bmσ d Y ; Kf = fatigue stress concentration factor F beam =
K f
8
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: Z =
Fo (d − d h )l 2 jσ d
