Can someone please confirm my calculation.
I am designing an indexing toolmount out of a rectangular frame that has a shaft going through the center of each end of the frame. The shaft is mounted on bearings on each end. The tool is well balanced and total mass including the shaft is 600lbs. The tool width is 40 inches. I want to be able to rotate the tool to 15 RPM in 5 seconds. With friction out of the equation, the question is will a servo motor with a 14 Nm output torque rated at 5000 rpm attached to a 4:1 worm gear work?
Mass = 600lbs = 272.16kg
Distance to center = 20 in = .508m
RPM = 15
Time (t) = 5 sec
Here are formulas I am using.
Find central axis moment of inertia = 1/2 *M( R * R)
I = 1/2 * 272.16 * .258
I = 35.11kg m2
Convert RPM to radians/s = 2Pi(RPM/60)
Radians/s = 1.57 rad/s
Find Angular Acceleration
a = acceleration, V1 = Initial velocity, V2 = Final velocity
a = (V2-V1)/t
a = (1.57 - 0)/t
a = .314 rad/s/s or round up in degrees to 18 deg/s/s
Torque = i * a
Torque = 35.11 * .314
Torque = 11.02 Nm
So using a worm gear would be more than enough since my the minimum Torque requirement is 11.02 Nm?