Meriam, Kraige & Bolton — Internal Forces and Moments: Problem 7_12

⚡ Mecademy AIENG정역학 · ch7  Problem Statement The speed reducer shown is designed with a gear ratio of 40:1. With an input torque , the measured output torque is . Determine the mechanical efficiency of the unit. Problem 7/12 (a) Mechanical Efficiency of the Speed Reducer ● Calculation Process 1. Present Final Formula: The mechanical efficiency of a gear system is defined as the ratio of the output power to the input power. For a steady-state system, this can be expressed in terms of torques and the gear ratio : Alternatively, , where is the output torque in the absence of friction. 2. Substitute Values: Given values are: Input torque: Actual output torque: Gear ratio: (since it is a 40:1 speed reducer, the ideal torque multiplication is 40) Substituting into the formula: 3. Partial Operations: Calculate the ideal output torque: M = 1 30 N⋅mM = 2 1180 N⋅m e e n e= = P in P out = M ω 11 M ω 22 = M 1 ( ω 2 ω 1 ) M 2 M ⋅n 1 M 2 e= M 2,ideal M 2 M = 2,ideal n⋅M 1 M = 1 30 N⋅m M = 2 1180 N⋅m n=40 e= 30 N⋅m×40 1180 N⋅m M = 2,ideal 30×40=1200 N⋅m Now calculate the ratio: 4. Final Calculation: As a percentage: ● Final Conclusion: The mechanical efficiency of the speed reducer is or . ✨ Final Answer Summary (a) (or ) Mecademy AI Solution · ENGProblem 7/12 e= 1200 1180 e= = 120 118 0.98333... e=98.3% 0.98398.3% e=0.98398.3%