Summary

Belts, ropes, brakes and clutches are examples of machine elements that employ friction to transfer energy.  The use of elastic or flexible elements such as belts in industry is undoubtly remain important in the conveying systems and in the transmission of power over comparatively long distances.  It is always happens that belts can be used as a replacement for gears, shafts, bearings and other rigid power transmission devices. The belt friction concept is very important in the application regarding power transfer and transmission especially in a long distance purposes in order to simplifies the machine design, reliability, lifetime and in the same time reduces the cost in terms of machine maintenance.

The purpose of this experiment is to determine the coefficient of friction, m between the iron-steel pulley and the belt.  There are two type of belt used that is vee and flat belt.  The apparatus used is the Belt Friction Tester.

The result of the experiment is tabulated and shown at the Data, Observation and Result section.  The graph of initial tension on the tight side, T1 against the initial tension on the slack side, T2 for both type of belt is plotted in FIGURE 1 and FIGURE 2.  Then, a fit linear line through the plotted graphs at each peg angle is plotted.  The slope of each line is obtained.  The general equation that relates the coefficient of friction (m) and the tensions is:

      T1 = e ^{(mq/ sin a)}

            T2

Where

T1 is the initial tension in the tight side

T2 is the initial tension in the slack side

m is the coefficient of friction

q is the angle being measured from the point of tangency of T1 and T2

a is the total angle of lap

(a = 90° for the flat belt)

(a = 20° for the vee belt)

**NOTE : q is in radian and a is in degree**

Below are the findings of the experiment based on the results and the plotted linear line on the graphs:

·        The T1 value will always higher than T2 value in order to gave a high horsepower transmitted. 

·        The average coefficient of friction, m for each peg angle is shown below:

·        The m value is differ from 0.32 (theoretical value) for each peg angle. It can be said that the belt behaves differently as the peg angle increased because 0.32 value is a theaoretical value that do not consider the peg angle effect. 

·        The m value varied as the peg angle change.   The m value will tend to decrease when the peg angle is increased from 30° to 150° because at higher peg angle, the friction force needed in the slack side of the belt is small in order to prevent slip from occur.  But, at a small peg angle such as at 30°, the friction effect plays an important role in order to prevent slip and creep from occur and to ensure smooth transfer of energy.  This is an important advantage as far as machine reliability and efficiency is concerned.

·        Moreover, the belt type also tend to effect the m value.  Flat belt has a higher m at each peg angle compared to the vee belt type.  A smaller lap angle of the belt will makes the m value smaller as proven in the vee belt.

·        The fit line through all the peg angle in the graph of T1 against T2 plotted in FIGURE 1 and FIGURE 2 shows a linear relationship with a slope of 1. 

In conclusion, by doing the experiment of belt friction tester, the coefficient of friction, m between iron-steel pulley and belt (vee and flat) has been determined.  The objective of the experiment is achieved and the results of the experiment has revealed the importance of friction effect in transfer of energy and the relationship between the pulley and the coefficient of friction value. The coefficient of friction, m depends on the kind of material and the type for the belt and pulley, and also on the condition of the surface such as the peg angle, moisture and lubrication effect.

Purpose / Objective

The purpose of this experiment is to determine the coefficient of friction between iron-steel pulley and the belt (Vee and Flat) at vorious peg angles.

Procedure

1.      Two 1.25 kg weights were inserted into the weight holder.  Hang the weight holder onto the cable.  Twist the cable around the flywheel for about 2 rotation.

2.      Make sure that vee belt is used.

3.      The end of the T2 spring balance was inserted onto the 30 degrees peg on the apparatus.

4.      The end of T1 spring balance was tigthten by using the nut and the bolt on the apparatus. 

5.      T1 and T2 value based on the spring balance reading was taken.

6.      The end of T1 spring balance was tigthten more by using the nut and the bolt on the apparatus. 

7.      T1 and T2 value based on the spring balance reading was taken.

8.      Repeat step 7 until 5 readings for T1 and T2 are obtained.

9.      Repeat step 3-8 with the T2 spring balance being hooked onto the 60, 90, 120 and 150 degrees peg.

10.  Step 1-9 were repeated for the flat belt.

Data, Observation and Result

The data for the T1 and T2 value for both the vee and flat belt at various peg angles were shown in the tables below.

Table 1

Table 2

From the data recorded, two graphs was plotted that is the graph of T1 against T2 for vee belt and flat belt at the various peg angles, shown in FIGURE 1 and FIGURE 2, attached next page.  A linear fit line is plotted through each graph corresponding to each of the peg angle.   

Discussion

            With reference to the experimental data tabulated and the plotted graphs in FIGURE 1 and FIGURE 2, the coefficient of friction, m between iron-steel pulley and the belt (vee and flat) is obtained.  The T1 value will always higher than T2 value in order to gave high horsepower transmitted.  The average coefficient of friction, m for each peg angle is shown in Table 3 below:

Table 3

From Table 3, the m value is compared to the value in Table 1 in the lab manual for the iron-steel pulley with rubber-covered belt.  The theoretical m value is 0.32 obtained from Table 1.  It seems that m value is absolutely differ from 0.32 for each peg angle as stated in Table 3 above.  It can be said that the belt behaves differently as the peg angle increased because 0.32 value is theaoretical value that do not consider the peg angle effect.  The m value will tend to decrease when the peg angle is increased from 30° to 150°.  This shows that at a higher peg angle, the friction between pulley surface and the belt is very small compared to the smaller peg angle.  This is because at higher peg angle, the friction force needed in the slack side of the belt is small in order to prevent slip from occur.  But, at a small peg angle such as at 30°, the friction effect plays an important role in order to prevent slip and creep from occur and to ensure smooth transfer of energy.  This also shows that friction play an important part in absorbing shock loads and in damping out and isolating the effects of vibration. This is an important advantage as far as machine reliability and efficiency is concerned.

Moreover, the belt type also tend to effect the m value.  Flat belt has a higher m at each peg angle compared to the vee belt type because flat belt has a 90° angle of lap compared to 20° angle of lap for vee belt.  This makes flat belt efficient at high speed, tougher and can transmit large amounts of power over long distances.  In contrast with flat belt, vee belt are slightly less efficient than flat belt, but a number of them can be used on a single sheave, thus making a multiple drive. 

From the graph of T1 against T2 plotted in FIGURE 1 and FIGURE 2, it is clearly that the graph is linear.  All the slope of the plotted linear graph is 1.  This shows that theoretically T1 value is equal to the T2 value but in the different direction. 

  There is an error that happened during the experiment.  It is clearly seen on the plotted graphs trend without the fit line through it.  The plotted graphs seems to be distorted and not in straight line due to the error occur.  The main source of error is the parallax and equipment error.  Parallax error happens when taking T1 and T2 value from the spring balance.  Moreover, during the experiment is performed, the spring balance is not precise in giving the results as the elasticity of the spring is very low since it is used in the experiment that is done many times before this.  All this has lead to the loss of accuracy and precision of the experiment results.

Conclusion

In conclusion, by doing the experiment of belt friction tester, the coefficient of friction, m between iron-steel pulley and belt (vee and flat) has been determined.  The m value varied as the peg angle change.  Design calculations for drives that depend on friction are subjected to these changes in the m value corresponding to different peg angle value.  The belt friction concept is very important in the application regarding power transfer and transmission especially in a long distance purposes.  Although there is an error occur during performing the experiment, it does not effect the results of the experiment.  Therefore, the objective of the experiment is achieved since the results of the experiment has revealed the imporatance of friction effect in transfer of energy and the relationship between the belt material, pulley type, peg angle conditions and the coefficient of friction value.

Appendix

General equation:

Equation that relates the coefficient of friction (m) and the tensions is:

      T1 = e ^{(mq/ sin a)}

            T2

Where        T1 is the initial tension in the tight side

T2 is the initial tension in the slack side

m is the coefficient of friction

q is the angle being measured from the point of tangency of T1 and T2

a is the total angle of lap

(a = 90° for the flat belt)

(a = 20° for the vee belt)

**NOTE : q is in radian and a is in degree**

Sample of calculation:

·        For vee belt with peg angle, q = 30° = 0.5236 radian, T1 = 50 N and T2 = 30 N

m = sin 20 °/q ln(T1/T2) = 0.33

·        For flat belt with peg angle, q = 30° = 0.5236 radian, T1 = 70 N and T2 = 40 N

m = sin 90 °/q ln(T1/T2) = 1.07

·        For vee belt with peg angle, q = 30 °

Average m        = (0.33+0.34+0.26+0.24+0.29) / 5

                        = 0.29