1.0 Objective

To determine the coefficient of friction between belt and pulley.

To differentiate the efficiency between V-belt and flat-belt.

2.0 Introduction

Belt is flexible ban which is in power transmission. It is able to transfer the power from one

point to the other points with minimum power loss. The belt is able to work smoothly and

quietly even without the requirement of lubrication. The earliest belt used in the world was

the flat belt. In flat belt, only the bottom part of the belt is in contact with the pulley surface.

The disadvantage of flat belt is that the flat belt pulley needs to be carefully aligned to

prevent the belt from slipping. In order to solve the problem encountered by the flat belt, V-

belt is introduced. Normally, the V-belt is placed on the groove of a pulley. In V-belt, both

sides of the belt are in contact with the pulley groove. This can prevent or minimize the

chances of the belt from slipping.

Flat belts require significantly higher pre-tensioning in order to transmit a certain

torque without slippage. This especially applies to large transmission ratios and thereby low

angles of contact. Tension pulleys with defined contact pressure are recommended in cases of

this kind to reduce the transverse force. V-belts are characterized by their trapezium shaped

(v-shaped) cross-section. They consist of a tensioning section of multiple layers of endlessly

wound polyester fibre cord threads, the core which is made of a high-quality rubber mixture

and the enclosure which is made of rubberized cotton or synthetic fabric. Depending on the

intended use, different designs are used.Flat belts are not advisable for high outputs at high

speeds.

This experiment is done to determine the coefficient of friction between belt and

pulley. The factors to be discussed are the use of belt and the angle of contact between belt

and pulley. Two types of belt used in this experiment are a flat belt and V-shaped belt. This

experiment was initiated by placing a fixed weight of 1.48 kg mass at one end of a flat belt.

The value is recorded as tension, T1. The other end of spring was placed at angles of 45° to

165°. A nylon rope was attached on the rim of the pulley clockwise and end freely suspended

with a weight of value which is W. The weight of the lead pulley is taken when the pulley

starts to rotate at constant velocity. Then the tension, T2 is obtained by subtracting the total

value W from T1. The ratio of T1/T2 is taken and the value of ln (T1/T2) is calculated. A

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graph of ln (T1/T2) against contact angle was plotted to find the coefficient of sliding

friction between belt and pulley.

3.0 Equipment & Material

Spring scale, belt holder, angle display, spring scale holder, pulley with different grooves,

spring scale with screw strut, screw strut holder, wing nut and safety door

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4.0 Procedure

4.1: To determine the belt friction coefficient for Flat-belt

1. Open the safety door. (Do not open the door using the bottom right end as it may break the

acrylic cover.)

2. Insert the spring scale screw strut into the inner side hole of the screw strut holder. Tighten

it with wing nut.

3. Place the spring scale to the spring scale holder at 60°.

4. Close the safety acrylic door.

5. Apply the load to belt by turning the wing nut. (Make sure the weight is in 6kg)

6. Place the spring scale to the spring scale holder at 45°.

7. Take the reading at the other spring scale.

8. Repeat the experiment with other angle and take the reading.

4.2: To determine the belt friction coefficient for V-belt

1. Open the safety door. (Do not open the door using the bottom right end as it may break the

acrylic cover.)

2. Insert the spring scale screw strut into the inner side hole of the screw strut holder. Tighten

it with wing nut.

3. Place the spring scale to the spring scale holder at 60°.

4. Close the safety acrylic door.

5. Apply the load to belt by turning the wing nut. (Make sure the weight is in 6kg)

6. Place the spring scale to the spring scale holder at 45°.

7. Take the reading at the other spring scale.

8. Repeat the experiment with other angle and take the reading.

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5.0 RESULTS

5.1 Flat Belt

Contact angleᵦ(°)

Spring scale

T1(N)

Spring scale

T2(N)ln (T2/T1) Coefficient of

static friction, μs

45 57 60 -0.0513 1.14×10-3

75 65 60 0.0800 1.0670×10-3

105 72.5 60 0.1892 1.8020×10-3

135 75 60 0.2231 2.9747×10-3

165 70 60 0.1542 9.34551×10-3

5.2 V-belt

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Contact angleᵦ(°)

Spring scale

T1(N)

Spring scale

T2(N)ln (T2/T1) Coefficient of

static friction,μs

45 65 60 0.0800 -1.6294×10-3

75 70 60 0.1542 -1.8844×10-3

105 70 60 0.1542 -1.3440×10-3

135 80 60 0.2877 -1.9532×10-3

165 75 60 0.2231 -1.2392×10-3

6.0 DISCUSSION/EVALUATION

6.1 DISCUSSION

Belt is a loop of flexible material used to link two or more rotating shafts mechanically, most

often parallel. Belts may be used as a source of motion, to transmit power efficiently, or to

track relative movement. Belts are looped over pulleys and may have a twist between the

pulleys, and the shafts need not be parallel. In a two pulley system, the belt can either drive

the pulleys normally in one direction or the belt may be crossed, so that the direction of the

driven shaft is reversed. As a source of motion, a conveyor belt is one application where the

belt is adapted to carry a load continuously between two points.

Belt friction is a term describing the friction forces between a belt and a surface, such

as a belt wrapped around a bollard. When one end of the belt is being pulled only part of this

force is transmitted to the other end wrapped about a surface. The friction force increases

with the amount of wrap about a surface and makes it so the tension in the belt can be

different at both ends of the belt. Belt friction can be modeled by the Belt friction equation. In

practice, the theoretical tension acting on the belt or rope calculated by the belt friction

equation can be compared to the maximum tension the belt can support. This helps a designer

of such a rig to know how many times the belt or rope must be wrapped around the pulley to

prevent it from slipping. Mountain climbers and sailing crews demonstrate a standard

knowledge of belt friction when accomplishing basic tasks.

This experiment conducted to study the belt friction coefficient for V-belt and flat

belt. The experimental results obtained are plotted in two different graphs. Graph one shows

graph of coefficient of static friction versus contact angle for flat-belt, while graph two shows

graph of coefficient of static friction versus contact angle for V-belt. For both flat belt and V-

belt, their constant value of T1 and T2 are equal to 60N. As can be seen from the graph of flat

belt, there is a significant of increasing of coefficient of static friction to the contact angle.

Meanwhile, the graph of V-belt fluctuated up and down from 40º to 175º contact angle.

Comparing both graph, you can see that flat belt have higher coefficient than V-Belt. This

mean that V-belt is better than the flat belt as V-belt will lower the chances of slip occur. In

comparison to V-belts, flat belts require significantly higher pretensioning in order to

transmit a certain torque without slippage. This especially applies to large transmission ratios

and thereby low angles of contact. V-belts are characterized by their trapezium shaped (v-

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shaped) cross-section. They consist of a tensioning section of multiple layers of endlessly

wound.

The fact that high standard forces between pulleys and belts occur at low pretension

offers advantages for the V-belt. These advantages include low bearing load and reliable

operation even in the case of small angles of contact. The V-belt is less efficient in

comparison with the flat belt, as it is restricted by the high amount of flexing required.

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7.0 QUESTIONS

7.1 Plot the 2 graphs: Coefficient of static friction, μs vs Contact Angle β for flat-belt.

Enhanced coefficient of friction, μs vs Contact Angle β for V-belt

Graph attached at Appendices.

Graph 1: Flat belt

Graph 2: V-belt

7.2 When the coefficient of static friction will be equal to zero for flat belt?

Based on the graph, the coefficient of static friction will be equal to zero when the value of

contact angle decreases if the flat belt is contact to the overall surface of circumferences of

pulley. Therefore no tension on the belt and the rotation of the pulley does not occur.

7.3 Give relation between coefficient of static friction for flat belt and V belt.

a) The relation between coefficient of static friction vs contact angle for flat belt.

Based on the graph coefficient of static friction vs contact angle for flat belt, the curve show

the relation between coefficient of static friction and contact angle are inversely proportional.

As the value of contact angle increases, the value of coefficient of static friction also increase.

Therefore the enhancement of the value coefficient of static friction depends on the value of

contact angle.

b) The relation between coefficient of static friction vs contact angle for V-belt.

Based on the graph of coefficient of static friction vs contact angle for V belt, the curve show

the relation between coefficient of static friction and contact angle are fluctuate. This means

that the coefficient of static friction increase or decrease are not depends on the increase or

decrease contact angle.

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7.4 Which belt is able to transmit more power if both are operating in the same

angular speed, ω? Explain your answer.

V belt is able to transmit more power than flat belt to transmit more power if both are

operating in the same angular speed due to wedging action in the grooves, limiting ratio of

tensions is higher and thus, more power transmission can be produced. Owing to wedging

action, V-belts need little adjustments and transmit more power, without slip as compared to

flat belt.

7.5 Derive equation of coefficient of static friction, μs for V-Belt by taking normal

force ΣF x=0 andΣF y=0 .

In case of a V-belt, there are two normal reactions so that the radial reaction is equal to 2R sin

α. Thus total frictional force = 2(μR) = 2μR.

Resolving the forces tangentially,

2 μR+T cos δθ2

−(T+δT ) cos δθ2

=0

For small angle of δθ,

cos δθ2

≈ 1

δT =2 μR

Resolving the forces radially,

2 Rsinα−T sin δθ2

− (T+δT )sin δθ2

=0

As δθ is small, sin δθ2

≈ δθ2

2 Rsinα−T δθ2

−T δθ2

=0

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R= Tδθ2 sinα

Or

From (iii) and (iv),

δT¿2 μ Tδθ2 sin α

or δTT

= μδθsin α

Intergrating between proper limits,

∫T 2

T 1 dTT

=∫0

θ μdθsin α

log e

T 1

T 2= μθ

sin α

Or

T1

T2=eμθ /sin α

7.6 What are the advantages and disadvantages using flat belt?

a) Advantages using flat belt

i. Does not require grooves

ii. Minimizing the energy loss and wear from the belt wedging in

and pulling out from the grooves.

iii. Energy savings

iv. A long service life of belts and pulleys

v. Less down time and high productivity

vi. Low noise generation from a smooth belt operation

vii. Can be installed simply and securely.

b) Disadvantages using flat belt

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i. high belt tension required to transmit power often shortens

bearing life

ii. failure to track properly since they tend to climb towards the

higher side of the pulley

7.7 What are the advantages and disadvantages using v-belt?

a) Advantages using v-belti. Positive drive as slip between belt and pulley is negligible

ii. No joint troubles as V-belts are made endless

iii. Operation is smooth and quite

iv. High velocity ratio up to 10 can be obtained

v. Due to wedging action in the grooves, limiting ratio of tensions

is higher and thus, more power transmission.

vi. Multiple V-belt drive increases the power transmission

manifold.

vii. May be operated in either direction with tight sight at the top or

bottom.

viii. Can be easily installed and removed.

b) Disadvantages using v-belti. Cannot be used for large centre distances

ii. Construction of pulley is not simpleiii. Not as durable as flat beltsiv. Costlier as compared to flat belts

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8.0 CONCLUSION

As conclusion, our objective which is to determine the coefficient of friction between

belt and pulley and to differentiate the efficiency between v-belt and flat-belt was achieved.

Based on the graph of coefficient of static friction versus contact angle for v-belt and the

graph of coefficient of static friction versus contact angle for flat-belt, we can conclude that

there is a significant of increasing of coefficient of static friction to the contact angle for flat

belt and for v-belt there is fluctuated up and down contact angle. By comparing for both type

of belt, the flat-belt have higher coefficient than v-belt. We can say that V-belt is better than

the flat belt as V-belt will have lower the chances of slip occur. The high standard forces

between pulleys and belts occur at low pretension offers low bearing load and reliable

operation in the small angles of contact. Therefore, the V-belt is less efficient in comparison

with the flat belt, as it is restricted by the high amount of flexing required.

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9.0 REFERENCES

1. R.C. Hibbeler, Engineering Mechanics: Statics, 12th Edition in S.I. Unit (2010), Person

Education South Asia Pte, Ltd.

2. Ferdinand P. Beer, E. Russell Johnston, Jr., Vector Mechanics for Engineers, Static and

Dynamics, International Edition 1996, McGraw-Hill Co., New York. (436-438)

3. Wan Abu Bakr Wan Abas Ph.D. (1989). Mekanik Kejuruteraan Statik. Kuala Lumpur:

Dewan Bahasa Pustaka.

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10.0 APPENDICES

Figure 1 V-belt

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Figure 2Flat Belt

Graph 1 : Flat Belt

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Graph 2: V-Belt

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