BELT FRICTION NAME: Niranjan S. REG. NO.: E/20/270 GROUP: M7 SEMESTER: 3 DATE: 17/11/23 INTRODUCTION In the field of engineering, the efficient transmission of power is fundamental to countless applications, ranging from industrial machinery to everyday devices. The utilization of drives, mechanisms designed to transfer rotational motion and power from one component to another, plays a pivotal role in the seamless operation of diverse systems. Drives are integral to the functioning of machinery, allowing for controlled motion and power distribution. In engineering practice, the selection of suitable drives is crucial for optimizing performance, ensuring reliability, and enhancing overall efficiency. Common types of drives include gear drives, chain drives, belt drives, and rope drives. Among the array of drive systems employed in engineering, belt and rope drives stand out as prevalent and versatile solutions. These mechanisms, based on the principles of frictional engagement, find application in various industries due to their simplicity, costeffectiveness, and adaptability. Belt and rope drives serve as fundamental components in the transmission of power across distances, accommodating a wide range of torque and speed requirements. Belt Drives: Belt drives operate on the principle of friction between a belt and pulley system, offering a reliable means of transmitting power. They are commonly employed in scenarios where smooth, continuous power transmission is essential. Industries such as manufacturing, agriculture, and automotive rely on belt drives for applications like conveyor systems, power transmission in machinery, and auxiliary components in engines. The flexibility of belt drives allows for the transmission of power around corners and over long distances with minimal energy loss. Figure 01: Belt drive Rope Drives: Similar to belt drives, rope drives rely on the principle of friction for power transmission but use ropes instead of belts. Rope drives find applications in scenarios where the need for a higher degree of flexibility and durability is paramount. They are often employed in heavyduty machinery, mining operations, and elevators, providing robust power transmission capabilities. The inherent strength and resilience of ropes make them well-suited for demanding environments where precise and reliable power transmission is critical. Figure 02: Rope drive Knowing and understanding the coefficient of friction between the belt (or rope) and the pulley is paramount for the efficient design and operation of belt and rope drive systems. This coefficient of friction directly influences power transmission efficiency, guiding engineers in optimizing the system for effective energy transfer. It plays a crucial role in tension analysis, helping to prevent issues such as slipping or excessive wear by ensuring appropriate tension levels. Additionally, the coefficient of friction informs key design considerations, guiding material selection for belts and pulleys based on desired frictional characteristics. This knowledge is instrumental in preventing slippage, which can lead to energy losses and premature wear. Moreover, it aids in predicting and analyzing heat generation and wear, allowing engineers to implement preventive measures. The coefficient of friction is central to system stability, ensuring smooth operation under varying conditions, and is essential for safety considerations, helping design systems with the necessary safety margins to prevent unexpected failures. In summary, a comprehensive understanding of the coefficient of friction is fundamental for optimizing power transmission, ensuring reliability, and enhancing the safety and efficiency of belt and rope drive systems. This purpose of this experiment was primarily intended to investigate and determine the coefficient of friction between the belt and the pulley, which is a critical parameter influencing the efficiency and performance of belt drive systems. In order to find this, a specific load was applied and the required lap angle was systematically modified and their impacts on the coefficient of friction were observed. Then the principle of the experiment involves measuring the tension in the belt under different loads and at different angles of contact with the pulley. The wrap angle is the angle between the tangent to the belt at the point of contact with the pulley and the line of action of the tension force. As the wrap angle increases, the friction force between the belt and the pulley also increases. Through systematic data collection, we can quantify the coefficient of friction and provide insights into the behaviour of the belt under different operating conditions. NOTATION Symbol Definition Unit T1 Tension in the slack side N T2 Tension in the tight side N F Frictional force N θ Lap Angle Rad µ Coefficient of Friction - APPARATUS A belt friction apparatus is a laboratory device used to measure the coefficient of friction between a belt and a pulley. It is used in a variety of engineering applications, such as power transmission, conveyor systems, and automotive belts. The apparatus consists of a pulley, a belt, and a weight hanger. The pulley is mounted on a stand and the belt is wrapped around the pulley and attached to the weight hanger. The weight hanger is then loaded with weights until the belt just begins to slip. Figure 03: Experimental setup of belt friction THEORY T + δT Figure 04: Forces acting on the belt T1 : Tension in the slack side T2 : Tension in the tight side T : Tension in the belt at point P T + δT : Tension in the belt at point Q RN : Normal Reaction F : Friction force μ : Coefficient of friction between the belt and the pulley θ : Lap angle From figure 1, Resolving all the forces horizontally, ο Since π π = π π ππ πΏπ 2 πΏπ 2 is very small, π ππ πΏπ + (π + πΏπ)π ππ 2 πΏπ πΏπ = 2π π ππ + πΏπ π ππ 2 2 πΏπ 2 ≈ πΏπ 2 and since both πΏπ and πΏπ terms are very small, πΏπ x (1) πΏπ 2 ≈ 0. From (1), πΏπ +0 2 π π = π πΏπ π π = 2π (2) Resolving all the forces vertically, πΏπ πΏπ − π πππ 2 2 πΏπ = πΏππππ 2 ↑ πΉ = (π + πΏπ)πππ Since πΏπ 2 is very small, πππ πΏπ 2 (3) ≈ 1 . From (3), πΉ = πΏπ (4) For friction, πΉ = ππ π . Substituting from (2) and (4) πΏπ = ππ πΏπ πΏπ = π πΏπ 2 π2 π ππ ∫ = π ∫ ππ π1 π 0 π2 ππ ( ) = ππ π1 (5) π2 = π ππ π1 π2 = π ππ π1 (6) PROCEDURE The experiment is to be carried out in two parts. Part 1 l. Using the locking mechanism, set the lap angle at 180Λ 2. 3. 4. 5. Place the belt (or rope) over the pulley. Place a load (w1) on the scale pan on the right and record its value. Place an equal load on the second scale pan on the left of the first. Gradually increase the load on the second scale pan until it just begins to move downwards and note the value (w2) at this stage. 6. Repeat the above procedures for several values of w1. Part 2 1. Set the lap angle (Ρ²) at 800 by rotating the frame supporting the pulleys. 2. Apply a weight (w1 = 2.5 kg) to the first scale pan. 3. Place an equal weight on the second scale pan. 4. Increase the weight (w2) in the second scale pan gradually and record the value when it begins to move downwards. 5. Repeat the above procedure for different values of Ρ² and record the corresponding values of Ρ² and w2. Note: For belt and rope, increase Ρ² from 800 to 1800 in steps of 200. OBSERVATIONS Table 1: The variation of w2, with w1 for constant lap angle (Ρ² = 1800) w1/ kg w2/kg 0.50 8.00 0.75 8.85 1.00 9.70 1.25 11.95 1.50 13.00 1.75 14.75 Table 2: The variation of w2, with lap angle when w1 = 2.5kg Ρ²/deg w2/kg 80 7.70 100 9.50 120 10.70 140 14.40 160 18.20 180 20.00 DATA: Weight of the scale pan 1 (wsp1) Weight of the scale pan 2 (wsp2) The acceleration of gravity (g) = = = 0.295 kg 0.305 kg 9.81 ms-2 SPECIMEN CALCULATION PART 1 Consider the 4th set of readings from table 1. Tension in the slack side (T1) = (w1 + wsp1) * g = (1.25+0.295)*9.81 N = 15.156 N Tension in the tight side (T2) = (w2 + wsp2) * g = (11.95+0.305)*9.81 N = 120.222 N Lap angle (Ρ²) π = 180 * 180 = π rad PART 2 Consider the 4th set of readings from table 1. Tension in the slack side (T1) = (w1 + wsp1) * g = (2.5+0.295)*9.81 N = 27.419 N Tension in the tight side (T2) = (w2 + wsp2) * g = (14.40+0.305)*9.81 N = 144.256 N Lap angle (Ρ²) π = 140 * 180 = 7π/9 π2 144.256 ln ( ) = ln ( ) π1 27.419 =1.660 rad TABULATIONS Table 3: Variation of T2 with T1 for a constant lap angle (Ρ² = 180Λ) T1 (N) T2 (N) 7.799 10.251 12.704 15.156 17.609 20.061 81.472 89.811 98.149 120.222 130.522 147.690 Table 4: Variation of ln(T2/T1) with lap angle Ρ² when w1 = 2.5 kg Ρ² (rad) 4π/9 5π/9 2π/3 7π/9 8π/9 π ln(T2/T1) 1.052 1.255 1.371 1.660 1.890 1.983 Figure 05: Variation of T2 with T1 for a constant lap angle θ=180o Figure 06: Variation of ln(T2/T1) with lap angle θ when w1=2.5kg CALCULATIONS Part 1 From Figure 05 = (148.5 - 14)/(18.75 – 1.75) = 7.912 m1 = eμΡ² μ = ln m1 / Ρ² = ln(7.912) / π = 0.658 = (2.13 – 0.475) / (π - 2 π/9) = 0.677 The gradient of the graph m1 From (6), Part 2 From Figure 06 The gradient of the graph m2 RESULTS Table 5: Coefficient of friction For constant lap angle (Ρ² = 180Λ) For constant w1 = 2.5 kg Coefficient of friction (μ) 0.658 0.677 DISCUSSION Compare the coefficient of friction for the 2 scenarios and comment on the results. If the two coefficients do not tally comment on the possible reasons. Comment on the possible errors in the practical and give suggestions on the improvement of the accuracy of the practical. After conducting the experiment, the comparison of coefficients of friction obtained under two distinct scenarios reveals intriguing insights into the behavior of the belt and pulley system. A constant lap angle of 180Λ yields a coefficient of friction of 0.658, while under a constant weight of 2.5 kg, the coefficient slightly increases to 0.677. The observed differences in coefficients could be attributed to many factors. This discrepancy suggests that variations in weight may influence the frictional interaction, emphasizing the complex nature of friction in real-world applications. Potential sources of error include fluctuations in tension, belt deformation under load, and surface irregularities. Inaccuracies in measuring and maintaining consistent tension in the belt could have impacted the reliability of the errors. Also, the deformation of the belt under load can affect the contact area which may have altered the results. The surface condition of the belt and pulley if contaminated can cause irregularities in the result, thus regular cleaning and inspection are essential to mitigate this factor. Not only that but also the calibration issues with measurement devices or inaccuracies in load application could have contributed to the errors. To enhance accuracy, it is crucial to standardize experimental conditions, including tension, lap angle, and load application to enhance the accuracy of the results. By also improving the precision in tension measurements and load application through calibrated instruments most of the discrepancies can be rectified. It is also crucial to maintain surfaces meticulously since the friction is heavily dependant on the contact surface thus minimizing variations in friction. Also, by conducting multiple trials under each set of conditions can provide a comprehensive dataset and help identify and mitigate outliers. Finally, by considering a detailed analysis of belt properties we can enhance the accuracy of the predictions. By addressing these potential sources of error and implementing suggested improvements, the experimental accuracy and reliability can be significantly enhanced, leading to more robust and meaningful results. REFERENCES 1. Moore, J. (2021). 6.7: Belt Friction. [online] Engineering LibreTexts. Available at: https://eng.libretexts.org/Bookshelves/Mechanical_Engineering/Mechanic s_Map_(Moore_et_al.)/06%3A_Friction_and_Friction_Applications/6.07%3 A_Belt_Friction. 2. UKEssays. November 2018. Belt Friction Test Objective Engineering Essay. [online]. Available from: https://www.ukessays.com/essays/engineering/belt-friction-test-objectiveengineering-essay.php?vref=1 [Accessed 26 November 2023]. 3. Uicker, J.J., Pennock, G.R. and Shigley, J.E. (2023). Theory of Machines and Mechanisms. Cambridge University Press.
