1. Belt drives and chain drives are the major types of flexible power transmission elements
Objectives of the chapter:
Describe the basic features of a belt drive system
Describe of several types of belt drives
Specify suitable types and sizes of belts and sheaves
Specify the primary installation variables for belt drives
Describe the basic features of a chain drive system
Describe several types of chain drives

2. Area application of the belt drives
Belt drives are applied where the rotational
speeds are relatively high .
The linear speed of a belt is m/min, which results in relatively low tensile forces in the belt.
The high speed of the electromotor makes belt drives somewhat ideal for that first stage of reduction.
Belts operate on sheaves or pulleys, whereas chains operate on toothed wheels called sprockets.

3. Disadvantages of the belt drives
At lower speeds, the tension in the belt becomes too large
for typical belt cross sections, and slipping up tp 3%may
occur between the sides of the belt and the pulley that
carries it.
At higher speeds, dynamic effects such as centrifugal
forces, belt whip, catch of air, and vibration reduce the
effectiveness of the drive and its life.
Improvement of the belt drives
Some belt designs employ high-strength, reinforcing
strands and a cogged design that engages matching
grooves in the pulleys to enhance their ability to transmit
the high forces at low speeds.
Disadvantages of the belt drives

4. Basic belt drive geometry
The belt is placing around the two sheaves while the center
distance between them is reduced, then sheaves are moved apart
Friction causes the belt to grip the driving sheave, increasing the
tension in one side, called the "tight side," of the drive
The opposite side of the belt is still under tension (at a smaller value) that is called the "slack side."

5. TYPES OF BELT DRIVES
Types of belts: flat belts, grooved or cogged belts, standard V-belt, double-angle V-belts, and others.
Wrapped
construction
Die cut, cog type
Synchronous belt
Vee – band
Double angle V-belt
Poly-rib belt

6. The belt drives are classified on the basis of peripheral speed
1. Light drives: the transmission of small powers at belt
speeds up to 12m/s (agriculture machines, small
machine tools, etc)
2. Medium drives: for medium powers at 12 – 24 m/s
(machine tools, cars, etc).
3. Heavy drives: for large powers and speed > 24m/s
(generators, compressors, main drives) 1.

7. The flat belt is the simplest type, and made from leather, fabric or rubber-coated fabric.

8. Crossed belt or
twist belt drive
Belt drive with idle
pulley or Jockey pulley
The coefficient of friction between the belt material and
the pulley surface: μ = 0.15 – 0.5
Tension for the belt material f = 0.27 – 1.7 N/mm2

9. Stress in the belt b – width of a belt Tension ft = F/bt
1. Initial tension fi = f1 + f2
2. Stress due to bending of the belt over the pulley
fb = E(t/D)
E – module of elasticity of the belt material

10. There are standard belt width (25 – 600)mm, and thickness (5 – 12)mm
3. Stress due to the effect of centrifugal force
fc = Fc/bt = ρV2,
fc= 0, if V < 10 m/s
ρ – density of the belt material (1000 – 1400)kg/m3
V = 15-20m/s – recommended
4. The maximum stress fmax = fi + fb + fc
5. Ratio of driving and driven forces F1/F2 = eμθ
There are standard belt width (25 – 600)mm, and
thickness (5 – 12)mm

11. Design of the belt drives
The belt drive is designed for the power to be transmitted
that depends upon:
difference in belt tension,
coefficient of friction,
area of contact and
center distance
Design power P = (F1 – F2)Vs = TtV (w)
F1 – tension on the tight side (N)
F2 – tension on the slack side (N)
V – belt speed (m/s)
Ft – net belt pull (N)
s = (1.2 – 1.4) service factor (oily, jerky loads,
shock, reversed load)

12. bt =F1/(ft – ρV2)C1 for V > 10 m/s
Belt section
bt = F1/ftC1 for V < 10 m/s
bt =F1/(ft – ρV2)C1 for V > 10 m/s
ft – allowable stress in a belt (N/mm2)
C1 = 0.6 – a corrector factor depending upon
the angle of center line of drive with horizontal,
type of drives
General belt equation
F1 – F2 = bt(ft - ρV2)[(eμθ – 1)/ eμθ]

13. Pulley size D > 50t D = 1.2(P/nmax)1/3 B = 1.2b d = 0.005D + 3
Number of spokes n = 4 (D = ), n = 6 D > 450,
H = 0.8do, h = H/2

14. V-belt drive is a widely used type of belt
in industrial drives and vehicular application.
The V-shape causes the belt to wedge tightly
into the groove, increasing friction and allowing
high torques to be transmitted
The belts have high-strength cords positioned
at the pitch diameter of the belt cross section
to increase the tensile strength of the belt.
The cords, made from natural fibers, synthetic
strands, or steel. are embedded in a firm rubber
compound

15. Advantages of the V – belts drive
Higher velocity ratio up to 7 – 10
Provide long life, 3 –5 years
Possibility of using small center distance
Transmit higher torsional moment at less width and tensions
Disadvantages
Cannot be used with large center distances
Subjected to a certain amount of creep
More complex design
Belt life above 82oC and below – 15o is shortened
Centrifugal force prevents the use at speed above 50m/s and at speed below 5m/s are not economical

16. Typical V-belt section and groove geometry
The pulley has a circumferential groove 2. The size of a sheave is indicated by its pitch diameter, slightly smaller than the outside diameter of the sheave.

17. 2. The linear speed of the pitch line of both sheaves is
The speed ratio between the driving and the driven sheaves is inversely proportional to the ratio of the sheave pitch diameters (if no slipping).
V-BELT DRIVES
2. The linear speed of the pitch line of both sheaves is
the same as and equal to the belt speed, vb. Then
vb = R1w1 = R2w2 = DIw1/2 = D2w2/2
The angular velocity ratio is
3. The maximum total stress occurs where the belt enters the
smaller sheave. The design value of the ratio of the tight side tension to the slack side tension is 5.0 for V-belt drives.

18. The angles of contact of the belt on each sheaves is
The relationships between pitch length, L, center distance, C, and the sheave diameters
L = 2C (D2 + D1) + (D2 - D1)2/4C
B = 4L – 6.28(D2 + D1)
The angles of contact of the belt on each sheaves is
The length of the span between the two sheaves, over which
the belt is unsupported, is

19. Cog belts are applied to standard sheaves. The cogs give the belt
Synchronous belts
Synchronous belts, (timing belts) ride on sprockets having mating grooves into which the teeth on the belt seat.
Cog belts are applied to standard
sheaves. The cogs give the belt
greater flexibility and higher
efficiency compared with standard
belts.
Synchronous belts are constructed with ribs or teeth across the underside of the belt. The teeth providing a positive drive without slippage.

20. CHAINS
Chain drives are used to transmit rotational motion and torque from one shaft to another, smoothly, quietly, and inexpensively. Chain drives provide the flexibility of a belt drive with the positive engagement feature of a gear drive. Chain drives are suited for applications with large distances (8m) between the respective shafts, slow speed, and high torque. More complex design than a belt drive

21. Chains are made from a series of interconnected links.
Types of Chains
Chains are made from a series of interconnected links.
Roller chain
. A roller chain is the most common type of chain used for power transmission.
Large roller chains are rated to 450 kW. The roller chain design provides quiet and efficient operation but must be lubricated.

22. Multiple-strand roller chain
Multiple-strand chains used to increase the amount of
power transmitted by the chain drive.
Equation is used to calculate the power transmitted through
each chain.
A multi-strand factor has been experimentally determined.
Power per chain =
total power transmitted/multi-strand factor

23. Construction of bush-roller chain
Standard sizes: p = (6.35 – 76.0) mm,
d = (7.772 – )mm, l = (6.35 – )mm,
t = – 9.525)mm,
Tensile strength F = – kN

24. Offset sidebar roller chain
An offset sidebar roller chain is less expensive than a roller chain but has slightly less power capability.
It has an open construction that allows it to withstand dirt and contaminants, which can wear out other chains.
Silent chain
An inverted tooth, silent chain is the expensive chain to manufacture. It efficiently used in applications that require high-speed, smooth, and quiet power transmission (machine tools). Lubrication is required to keep these in reliable operation. .

25. Construction of a silent chain

26. Power transmission chains

27. Dimensions of the various parts of the chain
Roller diameter d = (5/8)*pitch
Pin diameter dp = 5/16)*pitch
Chain width bi = (5/8)*pitch
Thickness of link plates t = (1/8)*pitch
Width between outer plates b0 = bi + 2t
Maximal height of roller link h = 0.82*pitch
Length of roller l = 0.9bi – 0.15

28. Chains are classified by a pitch, p,
Chain Pitch
Chains are classified by a pitch, p,
which is the distance between the pins
that connect the adjacent links.
Roller chains have a size designation
according to the power transmission
requirements.
Sprockets
­teeth.
Sprockets are the toothed wheels that connect to the shaft and mate with the chain. The teeth on the sprocket are designed with geometry to conform to the chain pin and link.

29. CHAIN DRIVE GEOMETRY

30. The number of teeth, N, in the sprocket is a commonly referenced property.
Sprockets should have at least 17 teeth, unless they operate at very low speeds, under 100 rpm.
The larger sprocket should normally have no more than 120 teeth.
It is preferable to have an odd number of teeth on the driving sprocket (17, ) and an even number of pitches (links) in the chain to avoid a special link.

31. The pitch diameter, D, of the sprocket is measured to the point on the teeth where the center of the chain rides.
The pitch diameter of a sprocket with N teeth for a chain with a pitch of p is determined by
The chain length, L, is the total length of the chain expressed in number of links, or pitches, computed as

32. The center distance for a given chain length computed as
The angle of contact, θ, is a measure of the angular
engagement of the chain on each sprocket.
Θ ≥ 1200 – recommendation of manufacturers.
In operation, chain drives should be designed so that
the slack side is on the bottom or lower side.

33. CHAIN DRIVE KINEMATICS
The velocity ratio VR is defined as the angular speed of the driver sprocket divided by the angular speed of the driven sprocket.
VR = ωdr/ ωdn = ω1/ ω2 = D2/D1 = N2/N1.
VR > 1 is typically ratio
Chains speed computed by Vc = D1/2ω1 = D2/2ω2
Lubrication for the chain is important for the drive and there are recommendations:
1. Low speed Vc < 100 m/min – manual lubrication;
2. Moderate speed Vc < 500 m/min – bath lubrication;
3. High speed Vc > 500 m/min – oil stream lubrication.

34. Selection of a chain For a given application: life expectance, space,
speed, and cost
Choice of a drive will depend upon:pitch, number
of chains, and sprocket size
The following factors should be analyzed:
Type of chain (speed recommendations)
Number of teeth in the wheel (min. and max.)
Chordal action Vmin=2πnRcos(π/z), Vmax=2πnR
n – angular velocity,
z – number of teeth,
R – pitch radius of the
sprocket

35. 4. Chain velocity and drive ratio 6:1 and no more then <9:1 (pitch, number of teeth in pinion)
5. Wheel centers and length of chain
6. Chain pitch (6.25; 8; 9.525; 12.7; …76.2)
For bushed and roller chain, p = n(P*k/zωpbx)1/3,
coefficient n = 28, pb = 35N/mm2 at n < 50 rev/min
pb = 13.7 N/mm2 at n = 2800 rev/min
For silent chain, p = n(P*k/zωpbb)1/3, n = 60,
pb = 20 N/mm2 at n < 50 rev/min
pb = 7.8 N/mm2 at n = 2800 rev/min
P - power(kW), k = – load factor, z – number of teeth, ω – an angular velocity of the driving sprocket, x – number of chain strands, b = (1.5-8)– the width of the chain, pb – the allowable bearing pressure

36. 8. Chain designation and specification
7. Sprockets
8. Chain designation and specification
Sprocket
Dp = p/sin(π/z) – pitch diameter,
α = [1400-(900/z)] to [1200-(900/z)] – roller setting angle
Do = Dp + d – outer diameter

37. Dr = Dp – d – root diameter
R = p – tooth flank radius
t = 0.93b for p < 12.7 simple chain wheels
t = 0.91b for duplex and triplex chain wheels
t = 0.88b for quardplex chain wheels and above
t1 = (number of chain strands –1)*pt + t
pt – transverse pitch of strands (strands spacing) – standard – 5.64 – 91.27

38. Design of the chain drive
Design calculation are carried out to find the best proportions of chain and sprockets in the next steps:
Select the type of chain (given speed)
Find the number of teeth of smaller sprocket (table)
Select the chain pitch (formula or table)
Calculate the total load Fo= F + Fc + Ff,
F(N) = P(kW)/V(m/s)– driving force on tight side. (force on slack side is considered 0)
. Fc = wV2/g (w – weight) – centrifugal force of inertia
. Ff = kfwC – sagging force, coefficient of arrangement of chain kf = 1 for vertical position; kf = 2 centerline inclined at angle up to 45o; kf = 4 – horizontal drives

39. . Safety factor Fs = Fu/Fo (compare with table)
Fu = 106p2(N) breaking strength of roller chain ,
p – pitch
Fu = 106p(N) for silent chain
5. The chain is checked for wear by unit pressure in joints pb = Fk/A (N/mm2),
k – load factor,
A – projection of the joint pivot,
A = (dp +lb)*z – for roller chain, dp – diameter of joint pivot, lb =(bi+2tp) - bush length, z – number of chain strands
A = 0.76dpb for silent chain, b – chain width,