belt drive _chapter 2

CHAPTER 2

BELT DRIVES SYSTEMBELT DRIVES SYSTEM

APPLICATIONS OF BELT DRIVES

VEHICLES

INDUSTRIAL

AUTOMATION

Another method widely used in engineering practice in transmitting power between shafts is belt drive system.

Basic arrangement of a belt drive system consists of driver sheave, driven sheave and belting material such as ropes, rubber bands or chain.

The operation of belt drives depends fully on the friction generated from contact surface between the belt and sheaves. Thus, any slip occurrence on the contact surface will reduce the efficiency of the power transmitted.

The choice of type of belt to be used is important so that the required power can be delivered efficiently. Some of the factor to be considered in selecting a suitable belt type to be used for a particular application is;

- Speed of driver and driven sheaves. - Required velocity ratio - Distance between the driver sheave and driven sheave. - Workspace constraint - Total power to be transmitted

INTRODUCTION TO BELT DRIVE

BELT DRIVE ARRANGEMENTS

OPEN BELT DRIVEOPEN BELT DRIVE WITH IDLER PULLEY

CROSS BELT DRIVETIMING BELT


Compound Belt Drives


Stepped / Cone Pulley

Step or cone pulley is used for changing speed of driven shaft while the driver shaft runs at constant speed.

This is achieved by shifting the belt from one part of the step to the other.

TYPES OF BELT AND MATERIAL

Flat belt – Most commonly used in factories, workshops. Used when moderate power is to be transmitted. Limitation for centre distance is not more than 8 meter.

V-Belts – Commonly used in factories, workshops, and is used when great amount of power is to be transmitted when the centre distance is near to each other.

Circular belt / Rope – Used when great amount of power is to be transmitted when centre distance for both pulleys are more than 8 meter apart.

Material used for belts must be strong, durable and flexible. It must have high coefficient of friction, µ. The material used are;

1. Leather belt

2. Rubber belt

3. Cotton / fabric belts

The coefficient of friction of belts depends upon factors such as belt material, pulley material, slip of belt and speed of belt. Table shows some of µ value for belt and pulley material;

VELOCITY RATIO FOR BELT DRIVE SYSTEM

SLIP IN BELT DRIVE SYSTEM

ANGLE OF LAPANGLE OF LAP

It is the enclosed angle in which the belt and surface of pulley are in contact.

It is important for determining the right setting of driver and driven pulley to guarantee an effective power transmission.

For Open belt arrangement

For Cross belt arrangement

OVERALL LENGTH OF BELT DRIVE SYSTEMOVERALL LENGTH OF BELT DRIVE SYSTEM

For Open Belt arrangement

OVERALL LENGTH OF BELT DRIVE SYSTEMOVERALL LENGTH OF BELT DRIVE SYSTEM

For Cross Belt arrangement

Belt tension in a belt drive system can be expressed in terms of ratio between tension on the tight side and the slack side of the same belt when it was operating.

In order for the belt to produce torque on the wheel (whether or not it is rotating), there must be tension in both ends.

The tension in one end must be greater than the tension in the other hand. Let the tension, T+dT is larger than T, where dT is the small increment in tension. Consider an elementary length of the belt on the pulley;

BELT RATIOBELT RATIO

BELT RATIOBELT RATIO

BELT RATIO FOR VEE BELT SYSTEMBELT RATIO FOR VEE BELT SYSTEM

For Vee Belt system, the same derivation technique can be applied to get the Belt Ratio for Vee Belt system.

The wedging effect of the belt increases the reaction force between the pulley and the belt

Total reaction force R is R=2R’ sin β

Previously, dT =µR’ ,but for Vee Belt, dT = 2 µR’

Thus,

sinsin2

22 ' RRRdT

For complete derivation, integrating between the limits as previous approach,

sin

2

1 eT

T

Case Study : CVT vs Gears TechnologyCase Study : CVT vs Gears Technology

Traditional car manufacturer uses gears as the primary drive train. These gears will have interlocking, toothed wheels that help transmit and modify rotary motion and torque. A combination of planetary gears creates all of the different gear ratios that the transmission can produce. When this type of transmission cycles through its gears, the driver can feel jolts as each gear is engaged

Continuously Variable Transmissions (CVT) don't have a gearbox with set of gears.

The most common type of CVT operates on an ingenious pulley system that allows an infinite variability between highest and lowest gears with no discrete steps or shifts.

Case Study : CVT vs Gears TechnologyCase Study : CVT vs Gears Technology

The simplicity and steeples nature of CVT make them an ideal transmission for a variety of machines and devices, not just cars. CVT have been used for years in power tools and drill presses. They've also been used in a variety of vehicles, including tractors and motor scooters.

So what's different about these CVT-based cars -- cars like the Saturn Vue, the Audi A4 and A6, the Nissan Murano and the Honda Insight?

The animation below, which compares the acceleration of a car with a CVT to one without, can give a good feel for the experience;

PLAY THE ANIMATION

Example 1

Two pulleys, one 450mm dia. and the other 200 mm dia., on parallel shaft 1.95m apart are connected by a crossed belt. Find the length of the belt required and the angle of contact/lap, between the belt and each pulley.

Solution:

Example 2

A compound belt drive will have these properties.

a) Find the speed of follower pulley D in terms of above properties.

b) Find the speed of follower pulley D in terms of above properties if the thickness of belt and slip is taken into consideration. Assume S is the total slip for all pulley.

Solution :

POWER TRANSMISSION OF BELT DRIVESPOWER TRANSMISSION OF BELT DRIVES

The tension in a belt pulley increases with torque and power. The maximum power that a pulley system can transmit is limited by the strength of the belt material.

If this is a problem then more than one belt should be used to share the load.

For power to be delivered to the driven pulley, thus the driver pulley will pull the belt (tight side) and delivers it to the other side (slack side). Thus the tight side will have tension greater than the slack side.

Thus the effective driving force is the difference between tight and slack side tension (T1-T2).

MAXIMUM POWER WITH NO BELT SLIP

v

e

TP

sin

1

11

For Vee Belt, power is;

Watt

EFFECT OF CENTRIFUGAL FORCEEFFECT OF CENTRIFUGAL FORCE

MAXIMUM POWER WITH CENTRIFUGAL EFFECT INCLUDEDMAXIMUM POWER WITH CENTRIFUGAL EFFECT INCLUDED

Earlier we have shown that how to achieve maximum power at no slip condition (ideal condition). However, in practice, centrifugal force effect exist for high speed application system of belt drive. This will cause slippage likely to occur since centrifugal force tends to lift the belt off the pulley.

So, how do we maximize the full power of the belt drive system by taking consideration on the centrifugal effect ?


Example 3

A leather belt with cross sectional area of 2250mm2 is used to drive a cast iron pulley 900 mm in diameter at 336 rpm. If the angle of lap is 120° and the stress in the tight side is 2 MPa, find;

a) Effective tension on the tight side of belt

b) Centrifugal force acting on the belt

c) Effective tension on the slack side of the belt

d) Power capacity of the belt

The density of the leather is 980 kg/m3, and the coefficient of friction is 0.35


Solution :

INITIAL TENSION OF BELT DRIVESINITIAL TENSION OF BELT DRIVES

CREEP OF BELT DRIVESCREEP OF BELT DRIVES

When power is transmitted by a belt or rope, there is always a difference between the peripheral speed of the driving pulley and that of driven pulley. Because of different tensions on the two sides of the pulley, the stretch in the belt will be different.

Consider one metre length of belt when unstressed. Because of tension T1 on the tight side, the length of the belt is (1 + x1) metre, where x1 is the stretch. Similarly, due to tension T2 on the slack side, the length of the belt is (1 + x2) metre, where x2 is the stretch. Obviously x1 is greater than x2.

A length (1 + x1) metre has approached the driver, but only (1 + x2) metre has moved off the driver. Thus, the length of belt that leaves the driver pulley is less than that which has approached it.

Thus, there is some relative motion of the belt on the pulley, and the belt is said to creep. The effect of creep in belt is to reduce the speed of the follower and reduce the power output.

CREEP OF BELT DRIVESCREEP OF BELT DRIVES

Example 4:

Example 5

Design a rubber belt to drive a dynamo generating 20 kW of power at 2250 rpm, and fitted with a pulley 200 mm diameter. Assume dynamo efficiency to be 85%. The data given are;

Allowable stress for belt = 2.1 MPa

Density of rubber belt = 1000 kg/m3

Angle of lap for dynamo pulley = 165°

Coefficient of friction between belt and pulley = 0.3

Solution

GROUP PROJECT 1

DESIGN PROJECT 1

Design a belt drive that can transmit 110 kW power for a system consisting of two pulleys of diameter 0.9 m and 1.2 m, center distance of 3.6 m, belt speed of 20 m/s, coefficient of friction 0.3, a slip of 1.2% at each pulley and the belt drive is capable to carry an overload torque of 866 Nm. You can assume the safe stress of the belt is around 1.5 to 2.5 MPa. You must design the belt system by finding ;

- Type of belt drive to be use

-Speed for driver and driven pulley

-Required design torque to compensate the extra loading of 866 Nm

-Angle of lap

-Length of belt required

-The sizing of belt (cross sectional area)

-Centrifugal force effect (if exist)

belt drive _chapter 2

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