Meriam, Kraige & Bolton — Analysis of Structures: Problem 6_66

⚡ Mecademy AIENG정역학 · ch6  Problem Statement The two flywheels are mounted on a common shaft which is supported by a journal bearing between them. Each flywheel has a mass of 40 kg, and the diameter of the shaft is 40 mm. If a 3-N·m couple M on the shaft is required to maintain rotation of the flywheels and shaft at a constant low speed, compute (a) the coefficient of friction in the bearing and (b) the radius of the friction circle. Problem 6/66 (a) Coefficient of friction in the bearing 1. Present Final Formula: The coefficient of friction in a journal bearing is related to the applied couple and the total radial load by the geometry of the friction circle: 2. Substitute Values: First, calculate the total weight load on the bearing from the two 40-kg flywheels: Then, substitute , , and shaft radius into the sine relation: 3. Partial Operations: Calculate the total load and the sine of the friction angle: r f μ MR μ=tanφ, where sinφ= R⋅r M R R=m ⋅ total g=(2×40 kg)× 9.81 m/s 2 M=3 N⋅mR=784.8 Nr= mm= 2 40 0.02 m sinφ= 784.8 N×0.02 m 3 N⋅m R=80×9.81=784.8 N R⋅r=784.8×0.02=15.696 N⋅m sinφ= ≈ 15.696 3 0.19113 φ=arcsin(0.19113)≈11.018 ∘ 4. Final Calculation: Find the coefficient of friction: ● Final Conclusion: The coefficient of friction in the bearing is . (b) Radius of the friction circle 1. Present Final Formula: The friction circle radius is the perpendicular distance from the bearing center to the line of action of the resultant reaction force, which balances the applied c