Meriam, Kraige & Bolton — Analysis of Structures: Problem 6_73

⚡ Mecademy AIENG정역학 · ch6  Problem Statement The 10-Mg crate is lowered into an underground storage facility on a two-screw elevator designed as shown. Each screw has a mass of 0.9 Mg, is 120 mm in mean diameter, and has a single square thread with a lead of 11 mm. The screws are turned in synchronism by a motor unit in the base of the facility. The entire mass of the crate, screws, and 3-Mg elevator platform is supported equally by flat collar bearings at A, each of which has an outside diameter of 250 mm and an inside diameter of 125 mm. The pressure on the bearings is assumed to be uniform over the bearing surface. If the coefficient of friction for the collar bearing and the screws at B is 0.15, calculate the torque M which must be applied to each screw (a) to raise the elevator and (b) to lower the elevator. Problem 6/73 (a) Torque required to raise the elevator 1. Formula: The total torque required to turn each screw is the sum of the torque to overcome friction in the screw threads at B and the friction in the collar bearing at A: Where for raising: And . 2. Substitution: Mass of crate Mass of platform Mass of each screw Total load on each bearing A: M M=M + threads M collar M = threads W r B ( 1−μtanα μ+tanα ) M = collar μ W 3 2 cA ( R −R o 2 i 2 R −R o 3 i 3 ) tanα= 2πr L m = c 10 Mg=10,000 kg m = p 3 Mg=3,000 kg m = s 0.9 Mg=900 kg W= A (10000+ 2 1 3000+2×900)× 9.81=72,594 N Load on each screw thread B: Mean radius of screw: Lead of screw: Coefficient of friction: