## Lesson 26 & 27. DESIGN OF A DRIVE SYSTEM, DESIGN OF LENGTH AND THICKNESS OF BELT

Module 6. Power transmission

Lesson 26, 27
DESIGN OF A DRIVE SYSTEM, DESIGN OF LENGTH AND THICKNESS OF BELT

26.1 Introduction

Among flexible machine elements, perhaps V-belt drives have widest industrial application. These belts have trapezoidal cross section and do not have any joints. Therefore, these belts are manufactured only for certain standard lengths. To accommodate these belts the pulleys have V shaped grooves which make them relatively costlier. Multiple groove pulleys are available to accommodate number of belts, when large power transmission is required. V-belt drives are most recommended for shorter center distances. V belt can have transmission ratio up to 1:15 and belt slip is very small. As the belts are endless type, V-belt drives do not suffer from any joint failure and are quiet in operation. V-belts constitute fabric and cords of cotton, nylon etc. and impregnated with rubber.

26.2 Nomenclature of V-Belt

A typical V-belt section is shown in Fig. 26.1. The geometrical features of the belt section are indicated in the figure. The pitch line, which is also marked as N-A, is the neutral axis of the belt section. The design calculations for V-belt drives are based on the pitch line or the neutral axis. These belts are available in various sections depending upon power rating.

Fig. 26.1 Nomenclature of V-belt

26.3 Standard V-Belt Sections

The standard V-belt sections are A, B, C, D and E. The table below contains design parameters for all the sections of V-belt. The kW rating given for a particular section indicates that, belt section selection depends solely on the power transmission required, irrespective of number of belts. If the required power transmission falls in the overlapping zone, then one has to justify the selection from the economic view point also.

Table 26.1 Standard V-belt configuration

 Section kW Range Minimum pulley pitch diameter(mm) Width (mm) Thickness (mm) A 0.4-4 125 13 8 B 1.5-15 200 17 11 C 10-70 300 22 14 D 35-150 500 32 19 E 70-260 630 38 23

As for example, a single belt of B section may be sufficient to transmit the power, instead of two belts of A section. This may increase the cost as well as weight of the pulley, as two- grooved pulley is required. In general, it is better to choose that section for which the required power transmission falls in the lower side of the given range.

Another restriction of choice of belt section arises from the view point of minimum pulley diameter. If a belt of higher thickness (higher section) is used with a relatively smaller pulley, then the bending stress on the belt will increase, thereby shortening the belt life.

V- Belt Equation

V-belts have additional friction grip due to the presence of wedge. Therefore, modification is needed in the equation for belt tension. The equation is modified as,

Where,

T1= Tension in belt on tight side

T2 =Tension in belt slack side

V=Linear velocity of the belt

m= Mass of belt per unit length θ

θ is the belt wedge angle

Selection of V- belt

The transmission ratio of V belt drive is chosen within a range of 1:15.

Depending on the power to be transmitted a convenient V-belt section is selected.

The belt speed of a V-belt drive should be around 20m/s to 25 m/s, but should not exceed 30 m/s.

From the speed ratio, and chosen belt speed, pulley diameters are to be selected from the standard sizes available.

Fig. 26.2 Standard V-belt section

Depending on available space the center distance is selected, however, as a guideline,

d2 < C < 3(d2 + d1 )

Where C is the center distance between pulleys, d2 and d1 are the diameter of larger and smaller pulleys respectively.

The belt pitch length can be calculated if C, d2 and d1 are known. Corresponding inside length then can be obtained from the given belt geometry. Nearest standard length, selected from the design table, is the required belt length above, the design power and modified power rating of a belt can be obtained. Therefore,

26.4 Chain Drives

We have seen in belt and rope drives that slipping may occur. In order to avoid slipping, steel chains are used. The chains are made up of rigid links which are hinged together in order to provide the necessary flexibility for swapping around the driving and driven wheels. The wheels have projecting teeth and fit into the corresponding recesses, in the links of the chain. The wheels and the chain are thus constrained to move together without slipping and ensures perfect velocity ratio. The toothed wheels are known as sprocket wheel or simply sprockets. The sprockets and the chain are thus constrained to move together without slipping and ensure perfect velocity ratio.

Fig. 26.3 Chain Drives

The chains are mostly used to transmit motion and power from one shaft to another, when

Centre distance between their shafts is short such as in bicycles, motor cycles, agricultural machinery, conveyors, rolling mills, road rollers etc. The chains may also be used for long centre distance of up to 8metres. The chains are used for velocities up to 25 m / s and for power up to 110kW. In some cases higher power transmission is also possible.

26.4.1 Advantages and disadvantages of chain drive over belt or rope drive:

Following are the advantages and disadvantages of chain drive over belt or rope drive:

1. As no slip takes place during chain drive, hence perfect velocity ratio is obtained.
2. Since the chains are made of metal, therefore they occupy less space in width than a belt or rope drive.
3. It may be used for both long as well as short distances.
4. It gives high transmission efficiency (up to 98 percent).
5. It gives fewer loads on the shafts.
6. It has the ability to transmit motion to several shafts by one chain only.
7. It transmits more power than belts.
8. If permits high speed ratio of 8 to l0 in one step.
9. It can be operated under adverse temperature and atmospheric conditions.

1. The production cost of chains is relatively high.
2. The chain drive needs accurate mounting and careful maintenance, particularly lubrication and slack adjustment.
3. The chain drive has velocity fluctuations especially when unduly stretched.

Fig. 26.4 Rope drives

26.4.2 The following terms are frequently used in chain drive

I. Pitch of chain

It is the distance between the hinge centre of a link and the corresponding hinge center of the adjacent link; it is usually denoted by p.

Fig. 26.5 Pitch of circle

2. Pitch circle diameter of chain sprocket:

It is the diameter of the circle on which the hinge centres of the chain lie, when the chain is wrapped round a sprocket. The points A, B, C, and D are the hinge centres of the chain and the circle drawn through these centres is called pitch circle and its diameter (D) is known as pitch circle diameter.

26.4.3. Relation between pitch and pitch circle diameter

A chain wrapped round the sprocket since the links of the chain are rigid, pitch of the chain does not lie on the arc of the pitch circle. The pitch length becomes a chord. Consider one pitch length AB of the chain subtending an angle θ at the centre of sprocket

(Or pitch circle)

Or

The sprocket outside diameter (D0), for satisfactory operation is given by

D0 = D + 0.8 d1

Where d1 = Diameter of the chain roller

Relation between Chain Speed and Angular Velocity

Since the links of the chain are rigid, therefore they will have different positions on the sprocket in different instants. The relation between the chain speed (v) and angular velocity of the sprocket (ω) also varies with the angular position of the sprocket.

Theory of mechanics

For the angular position of the sprocket

v = ω x OA

and for the angular position of the sprocket

v = ω x OX = ω x OC cos (θ/2) = ω x OA cos (θ/2) (OC = OA)