In the motorized rackandpinion system in a milling machine t

In the motorized rack-and-pinion system in a milling machine, the pinion has 50 teeth and a pitch radius of 0.75in. Over a certain range of its motion, the motor rum at 800rpm, (a) Determine the horizontal velocity of the rack. (b) If a peak torque of 10ft-lb is supposed by the motor, determine the pulling force that is produced in the rack and transferred to the milling machine.

Solution

N= 800rpm

Radius = .75 inches or (.75/.039320 )= 19 mm

Horizontal velocity = 2×3.14×N×radius

Horizontal velocity = 2×3.14×800×19= 95456 mm/min

Or

Horizontal velocity = 95456/60= 1590.93mm/sec