Question

Consider a CNC work table driven by a closed-loop control system consisting of a servomotor, lead screw and optical encoder. The lead screw has a pitch, p = 5.08 mm and is coupled to the motor shaft with a screw to motor gear ratio of 1 : 4. The encoder generates 150 pulses per revolution of the lead screw. If the number of pulses and the pulse rate received by the control system are 2250 and 200 Hz respectively, then the
Distance traveled by the table (mm) respectively _________.

• A. 79.5
• B. 76.2
• C. 71.2
• D. 72.6

Answer 1

The correct option is B 76.2

$V=p\left(RPM\right)=5.08\left(RPM\right)$

$=\left(5.08\right)\left(60f/N\right)$

$=\left(5.08\right)\left(60\right)\left(200\right)/150$

$=406.4mm/min$

$\text{RPM of the lead screw}=\left(60\right)\left(200\right)/\left(150\right)=80$

$\text{RPM of the motor}=320$

$x=p\left(n/N\right)=\left(5.08\right)\left(2250\right)/\left(150\right)$

$=76.2mm$