Determine Belt Friction Using Belt Friction Apparatus

Theory

Flat belts have been used for power delivering for many centuries. They are simple and reliable with the ability to operate for longperiods without maintenance. Consider a piece of a belt wrapped around a pulley as shown in the figure below. Suppose the tensions in either side of the belt be T1 and T2. The maximum power which driver pulley could deliver can be transmitted when the belt is on the point of slipping. So at the point of slippage belt is at highest point of friction.

At momentary analysis velocity is constant for that instant. Thus we require understanding the relationship between the tensions T1 and T2 with respect to the pulley. The difference in these tensions is the force applied to the pulley at its circumference hence the torque and power transmitted.

∑Fy = 0

T + dF – ( T + dT ) = 0

dF = dT (1)

That is the increment of friction developed over the length r dß and is equal to the change of tension in the belt over the same length.

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Resolving horizontally we obtain

dN – T

– ( T+ dT )

= 0 (2)

Remembering that as dß is small sin dß = dß.

Neglecting tiny quantities of second order yields:

dN = T dß (3)

The above equation gives us the element of normal pressure at any point on the belt in terms of the tension T in the belt at that point.

At the point of slipping:

dF = μ dN (4)

Substituting for these quantities from the expressions above, we find:

dT = μ Td

dT / T = μ d (5)

If we now integrate the above expression over the entire belt contact area we can find the ratio of the belt tensions.

= μ

ln T1/T2 = μθ (6)

T1/T2 = eμθ

This gives the ratio between the tensions on both side of the pulley. It shows that it increases very fastly with the angle of lap, θ

Procedure

• Slowly add weights to the cord hanger until the pulley is on the point of slipping. Note the two hanger loads i.e. hanger attached with belt (T1) and Load Hanger (Tcord) and the spring balance reading (T2).
• To check the spring balance reading remove the load applied via the cord and try to rotate the pulley by hand until the point of slip is reached.
• This may not be possible at higher loads so knowing the load required for slip gradually re- Set up the flat belt on the apparatus and place a load on the hanger
• Place the cord on the pulley peg in a clockwise direction and add load on hanger.
• Apply it to the cord but carefully notice the spring balance
• Repeat the experiment for every angle of lap from 30 to 90 degree

Observations and Calculations

Result

The average coefficient of static friction (μs) was calculated to be 0.2415, indicating the frictional efficiency of the belt-pulley system across the examined angles.

Conclusion

The experiment demonstrates that the angle of wrap and the pulley's dimensions significantly influence power transmission capabilities. Notably, an increase in wrap angle enhances the power that can be transmitted before slip occurs, affirming the theoretical predictions. Additionally, belt systems serve as a safeguard against overloading, protecting motors and connected machinery.

Safety Precautions

• No eating or drinking in the lab always.
• Be conscious while handling heavy equipment.
• Do not do unauthorized experiment by yourself.
• Never leave experiment that is in progress free.
• No Laboratory Work should be carried out in the absence of instructor.
• Shoes should not be slippery in order to avoid any slippage of student on lab floor. In case of serious injury, requiring professional medical attention the student should contact the Medical Center.