Meriam, Kraige & Bolton — Rigid Bodies: Equivalent Systems of Forces: Problem 3_96

⚡ Mecademy AIENG정역학 · ch3  Problem Statement A large symmetrical drum for drying sand is operated by the geared motor drive shown. If the mass of the sand is 750 kg and an average gear-tooth force of 2.6 kN is supplied by the motor pinion A to the drum gear normal to the contacting surfaces at B, calculate the average offset of the center of mass G of the sand from the vertical centerline. Neglect all friction in the supporting rollers. Problem 3/96 (a) Determination of the average offset ● Calculation Process 1. Present Final Formula: To determine the offset , we consider the equilibrium of moments for the drum about its center . The reactions from the supporting rollers at the bottom pass through , and the weight of the symmetrical drum also acts through , so they do not contribute to the moment. The only forces producing moments are the weight of the sand and the gear-tooth force. where: is the weight of the sand. is the horizontal offset of the sand's center of mass. is the force from the pinion on the drum gear. is the pressure angle of the gear teeth. is the pitch radius of the drum gear. 2. Substitute Values: Mass of sand, Acceleration due to gravity, Gear-tooth force, Pressure angle, xˉ xˉ xˉ O O O M = ∑ O 0⟹W⋅=xˉ(Fcosφ)⋅R W xˉ F φ R m=750 kg g= 9.81 m/s 2 F=2.6 kN=2600 N φ=20 ∘ Radius of drum gear, Substituting into the moment equation: 3. Partial Operations: Calculate weight of sand: Calculate the tangential component of the gear force: Calculate the moment of the