Wednesday, October 17, 2012

CNC the math

Here is the math, as I see it, for calculating the max mass that a NEMA 32 ( ) can lift in a vertical plane using a 1/2 inch diameter threaded rod ( ).  First, I calculated the circumference of the rod and labeled that x. Then used the known distance up for one turn as y.  Calculated the degrees tangent O using opposite over adjacent. 

Using the formula Force = mass * gravity * cosO and Work = Force * distance.  I substituted Force into the work equation. Input the knowns, degrees = 17.7, distance = 1.2 m, max work capable per the specs of the motor = 4.6 Nm, and gravity = 9.8 m/s^2.  Re-wrote the equation to solve for mass (kg).

The result is a gearing for a 1:1 ratio.  I then calculated the result for other gearing ratios to find a larger mass.  Unfortunately, the best gearing for a 14 lbs is set at 1:6 which means that for each rotation of the stepper motor, the threaded rod will move an object up a little over a 1/16 of an inch.

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