Question

A DC servomotor drives the x-axis of a CNC milling machine table. The motor is coupled to a ball screw, whose pitch=7.5 mm, using a gear reduction of 8:1 (eight turns of the motor to one turn of the ball screw). An optical encoder is connected to the ball screw. The optical encoder emits 75 pulses per revolution. To execute a certain programmed instruction, the table must move from point (r = 202.5 mm, y = 35.0 mm) to point (r= 25.0 mm, y=250.0 mm) in a straight line path at a feed rate = 300 mm/min. For the x-axis, determine

(a) the control resolution of the system,
(b) rotational speed of the motor, and
(c) frequency of the pulse train emitted by the optical encoder at the desired feed rate.
(d) How many pulses are emitted by the x-axis encoder during the move?

Answer 1

The control resolution of the system is 0.9375 mm per pulse. The rotational speed of the motor is 202.509 radians/s.

Step-by-step explanation:

We can calculate it by dividing the ball screw pitch by the gear reduction ratio. In this case, the linear resolution is (7.5 mm / 8) = 0.9375 mm per pulse. The rotational speed of the motor can be calculated by converting the desired feed rate to the angular speed of the ball screw.

We can use the formula: Angular Speed (in radians/s) = (Feed Rate / Linear Resolution) * (2 * pi). In this case, the angular speed is (300 mm/min / 0.9375 mm/pulse) * (2 * pi) = 202.509 radians/s. In this case, the frequency is (202.509 radians/s) / (75 pulses/revolution) = 2.700125 pulses/s.

The linear distance traveled is the difference between the initial and final positions of the x-axis. In this case, it is (202.5 mm - 25.0 mm) = 177.5 mm. The number of pulses emitted is (177.5 mm / 0.9375 mm/pulse) = 189.333 pulses.