DEPARTMENT OF BIOMEDICAL ENGINEERINGFACULTY OF ENGINEERING

UNIVERSITY MALAYA

Lab 3 : Belt Friction Experiment

ObjectiveTo determine the sliding coefficient of friction, μ between the belt and the pulley.

IntroductionBasically, belt friction is a term which use to describe the frictional forces between a belt

and a surface, and in this experiment, it will be the frictional force with the surface of the pulley. There are two types of belt, which are flat belt and V-belt. Based on belt friction equation or Capstan equation,

T1=T2eμθ for flat-belt

T1=T2

e

μθ

sinβ2

for V-belt

Where T1 = tension of the pulling side (weight of fixed load) T2 = tension of the resisting side μ = sliding coefficient of friction Θ = angle of contact between belt and pulley (in radian) β = angle of the V-belt

By using these two equations, we can calculate the sliding coefficient of the friction, μ. There are few assumptions had to be made before applying the equations,

1. The rope used during the experiment must be non-elastic.2. The rope is on the verge of full sliding during the experiments.3. The rope must be not rigid as to avoid losing of force during the bending of the belt.

The sliding coefficient of the flat belt will be different with the sliding coefficient of the V-belt. This is because different in surface area in contact between the belts and the pulleys and also because of V-belt having certain angle.

Diagram 1 Diagram 2By referring to the diagrams, we can say that

T1 = T2 + WT2 = T1 – W

Thus, we can obtain the values of the T2 by using this equation.

Equipments1. Pulley2. A set of loads (0.5N, 1N, 2N, 5N, 10N, 20N and 50N)3. A flat belt4. A V-belt5. A S-hook6. 2 Weight hangers7. Nylon rope

Procedure

Figure 3.11. The apparatus are setup as shown in the Figure 3.1.2. The position of the Stud S is at 30˚ position.3. A flat belt is picked and the end A of the flat belt is hooked onto S using S hook. Another end

which is end B of the flat belt is passed over the pulley in the anti-clockwise direction.4. A weight hanger is hook onto the end B of the flat belt and a known weight are put on it. The

weight is known as T1.5. The nylon rope of the pulley is wind up in the clockwise direction while another weight

hanger(P) is hooked onto the free end of the nylon rope.6. Weights are slowly added to the weight hanger (P) until the pulley rotates slowly with a

constant velocity(no acceleration). The weight added are counted and recorded as weight W.7. Steps 2-6 are repeated by changing the T1 with 100N and 150N8. Steps 2 to 6 are repeated again with angles 60˚, 90˚, 120˚ and 150˚.9. For each experiment, the readings obtained are recorded and tabulated. A graph T1 against T2

and graph of lnT 1T 2

against θ are drawn.

10. The sliding coefficient, μ are calculated.

11. The whole experiment is repeated by using V-belt.

Results(a) Flat Belt

T1(N) T2(N)/Contact Arc(θ)

150

30˚ 60˚ 90˚ 120˚ 150˚

W T2 W T2 W T2 W T2 W T2

30 100 30 120 39 111 46 104 58 92

100 20 80 30 70 30 70 44 56 40 60

50 10 40 20 30 17 33 20 30 21 29

(B) V-Belt

T1(N)

T2(N)/Contact Arc(θ)

30˚ 60˚ 90˚ 120˚

W T2 W T2 W T2 W T2

80 32 48 54 26 62 18 70 10

60 22 38 35 25 45 15 55 5

40 13 27 22 18 29 11 35 5

20 6 14 9 11 13 7 18 2

To find T2 for part (a) and (b),T1=T2+WT2=T1-W

For Flat Belt, since T1=T2eμθ, compare to y=mx,T1 =yT2=xeμθ=m1 (gradient of the graph)

Therefore, T 1T 2

=eμθ=m1

Because the graph is T2 against T1, thus the gradient of the graph will be 1m1

.

For V-Belt, since T1=T2

e

μθ

sinβ2

, compare to y=mx

T1 =yT2=x

e

μθ

sinβ2

=m2 (gradient of the graph)

Therefore, T 1T 2

=

e

μθ

sinβ2

=m2

Because the graph is T2 against T1, thus the gradient of the graph will be 1m2

.

Flat Belt V-Belt

Contact Arc(θ)Gradient(T 2

T 1)

Gradient(T 1T 2

)log e

T 1T 2

Contact Arc(θ)Gradient(T 2T 1

)Gradient(T 1

T 2)

log eT 1T 2

30 0.60 1.667 0.511 30 0.565 1.770 0.571

60 0.90 1.111 0.105 60 0.260 3.846 1.347

90 0.78 1.282 0.248 90 0.185 5.405 1.687

120 0.74 1.351 0.301 120 0.120 8.333 2.120

150 0.63 1.587 0.462

30 50 70 90 110 130 1500

20

40

60

80

100

120

140

f(x) = 0.63 x − 2.66666666666666f(x) = 0.74 x − 10.6666666666667f(x) = 0.78 x − 6.66666666666667f(x) = 0.9 x − 16.6666666666667

f(x) = 0.6 x + 13.3333333333333

T2 against T1(Flat Belt)

30˚Linear (30˚)60˚Linear (60˚)90˚Linear (90˚)120˚Linear (120˚)150˚Linear (150˚)

T1(N)

T2(N)

10 20 30 40 50 60 70 80 900

10

20

30

40

50

60

f(x) = 0.12 x − 0.5

f(x) = 0.185 x + 3.5

f(x) = 0.26 x + 7

f(x) = 0.565 x + 3.5

T2 against T1 (V-Belt)

30˚Linear (30˚)60˚Linear (60˚)90˚Linear (90˚)120˚Linear (120˚)

T1(N)

T2(N)

0 0.5 1 1.5 2 2.5 30

0.5

1

1.5

2

2.5

ln (T1/T2) against θ

Flat BeltLinear (Flat Belt)V-BeltLinear (V-Belt)

θ/rad

ln (T2/T2)

To calculate the sliding coefficient, μFor Flat Belt, since T1=T2eμθ

lnT 1T 2

=μθ

μ=Δ ln

T 1T 2Δθ

μ=0.301−0.105

(120−60)×3.142180

μ= 0.1961.0473

μ=0.187 (sliding coefficient for Flat belt)

For V-Belt, since T1=T2

e

μθ

sinβ2

lnT 1T 2

=μθ

sinβ2

μ=Δ ln

T 1T 2sinβ2

Δθ

μ=(2.120−0.571 )sin β

2

(120−30 )× 3.142180

μ=0.52981.571

μ=0.337 (sliding coefficient for V-belt)

Discussion(a) Comparisons

1. From the values obtained through the calculations, sliding coefficient for Flat belt is 0.187 which is less than the sliding coefficient of the V-belt which is 0.337.

2. By refer to the graphs, we can see that the ln(T 1T 2

) are increase linearly with θ. The

straight line graph showing that the equations are actually obeys the linear equation, Y=mX+C. From the equation, we also can determine the values of sliding coefficient directly instead of doing calculations. This is because,

i. mFlat belt=lnT 1T 2θ

ii. mV-belt=lnT 1T 2sinβ2

θ

iii.

(b) Error

1. There is some errors data in part (a) which lnT 1T 2

for 30˚ is 0.511 which is abnormally

larger than the predicted value. This may be is because of several causes as below:i. The belts used are having mass.

ii. The difficulty is to determine the pulleys are moving with constant acceleration just by observation and without having any measurement of technique to measure it.

iii. The nylon rope is not hundred percent elastic and it will also produce frictional force with the surface of the pulley and also with itself.

2. The way to overcome the errors and the precautions:i. As to obtain a more accurate value of the sliding coefficient of the Flat belt

and V-belt, the experiments should be repeated as to obtain average readings.

ii. Avoid winding the nylon rope too heavily as the nylon rope can rotate easily and avoiding too much friction forces between the nylon rope and the surface of the pulley.

(c) The advantages and disadvantages of using the Flat belt and V-belt.i. Advantages of V-belts are

a) Higher torque can be transmit by using with lesser width and tension compared to flat belt

b) V-belt can be used in areas with very less arc of contact of the belt.ii. Disadvantages of V-belts are

a) The V-belt losses its efficiency by around 3% as the wedging action will increase the winding and bending of the belt.

b) The V-belt still having probabilities of slipping and will easily damage if slipping occurred.

c) V-belt need special designed pulley as to maximize the efficiency of the application of the V-belt.

iii. Disadvantages of flat belta) The flat belt need to be aligned properly to the pulley as to prevent

slipping occurred.(d) Application

i. By using a belt with smaller sliding coefficient of friction, less friction between the pulley and the belt and thus reducing the heat produced during the operation of a machine according to the theory.

ii. V-belts and Flat belts are mainly being used in the engine.

ConclusionThe sliding coefficient of friction between belt and pulley are determined where sliding coefficient for Flat belt and pulley is 0.187 which is less than the sliding coefficient of the V-belt and pulley which is 0.337.

References1. 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 Bakar Wan Abas Ph.D. (1989). Mekanik Kejuruteraan Statik. Kuala Lumpur:

Dewan Bahasa Pustaka.