A DC motor is used to drive a winch in a vending machine The

A DC motor is used to drive a winch in a vending machine. The load has a mass of 2kg and is lifted vertically by a cable wrapped around a drum of radius 2.5cm. The mechanism is not operated continuously.

a) Draw a free body diagram for the drum at zero acceleration. Calculate and show forces and torques.

b) The load is to be lifted a distance of 0.7m in a time of 2 seconds. Assume overall drivetrain efficiency of 70%. Calculate approximate output power in requirement of the motor.

c) Calculate what speed should the drum rotate at in RPM.

d) The DC motors you are considering all have a no lolad speedof around 6000RPM. Approximately what motor speed should you design for if you want to oeprate at peak efficiency?

e) If you expect the motor to run at 4000RPM, what gear ratio should you choose (round to multiple of 5)?

f) Using a x25 gear reduction, what torque is required at the motor?

g) Using the attached data sheet, what speed in RPM ill the motor spin at with a load of 25mN.m?

h) Using part (g) calculate the speed at which the load will rise in m/s.

i) At 25mN.m what current will be required?

j) What system issues would you expect if the load were doubled?

Solution

The diameter of rod produced in a lathe (X) during mass production of nominal dia 20 mm, is known to follow the following distribution: fX(x) = o when x<20 mm = 15 exp(-15*(x-20)) when x>=20 mm Determine the following: 2.1 probability distribution function of diameter of rod (5 points) (1 Point) 2.2 if rods with diameter larger than 20.2 mm are not acceptable, determine the proportion of rods that are accepted and rejected (10 points) (1 Points) 2.3 Find mean and standard deviation of X (5 points) (2 Points)