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**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

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**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.

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**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

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**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."

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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

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**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.

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

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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

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**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

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**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

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**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)

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**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]

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**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

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**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

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**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

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**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.

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**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.

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**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

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**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.

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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

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**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.

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**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

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**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

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**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. .

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**Construction of a silent chain**

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**Power transmission chains**

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**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

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**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.

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CHAIN DRIVE GEOMETRY

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**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.

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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

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**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.

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**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.

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**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

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**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

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**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

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**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

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**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

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**. 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,

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