Meriam, Kraige & Bolton — Analysis of Structures: Problem 6_65

⚡ Mecademy AIENG정역학 · ch6  Problem Statement A torque of must be applied to the -diameter shaft of the hoisting drum to raise the load at constant speed. The drum and shaft together have a mass of . Calculate the coefficient of friction for the bearing. Problem 6/65 (a) Calculation of the coefficient of friction 1. Formula: To solve for the coefficient of friction in the journal bearing, we must first establish the equilibrium of moments and forces acting on the drum and shaft assembly. Tension in the cable: Weight of the drum and shaft: Total vertical reaction force at the bearing: Equilibrium of moments about the shaft center: Friction moment relation for a journal bearing: , where 2. Substitution: Given values: Load mass, Drum/shaft mass, Applied torque, Drum radius, Shaft diameter, Shaft radius, Acceleration due to gravity, First, calculate the tension and weights: M1510 N⋅m50-mm 500-kg 100 kgμ μ T=m g L W = D m g D R=T+W D M =∑ O 0⇒M−T⋅ R − drum M = f 0 M = f R⋅r sinφ j μ=tanφ m = L 500 kg m = D 100 kg M=1510 N⋅m R = drum 300 mm=0.3 m d=50 mm⇒r = j 0.025 m g= 9.81 m/s 2 T=500×9.81=4905 N W = D 100×9.81=981 N The total bearing reaction is: 3. Calculation: 1. Calculate the required friction moment : 2. Determine the friction angle using the journal bearing friction circle relation: 3. Calculate the coefficient of friction : 4. Result: ● Final Conclusion: The coefficient of friction required for the journal bearing to maintain the constant speed raising of the load is . ✨