Formula for a particular tool move

The formula for the time estimate for a particular tool move is:

time = dist/fpm + fpm * (1 + zdist/dist * (1/z-accln - 1)) / xy-accln

where:

• fpm is feed per minute (Rapid Travers for rapids, feed rate for cutting moves).
• xy-accln is XY Acceleration.
• z-accln is Z Acceleration.
• dist is the total distance of tool move.
• zdist is the total distance that the tool moves in the Z-direction.

Acceleration conversions

If the acceleration rates for your machine are reported in different units, use the following conversions:

Current Units	Desired Units	Multiply by
Meter per second squared	Millimeters per minute squared	3,600,000
Feet per second squared	Inches per minute squared	43,200
Inches per second squared	Inches per minute squared	3,600

Assumptions used

Most often, because of change of direction (and/or several other factors), the tool must effectively accelerate to final fpm from a stop. So the acceleration is calculated as if the tool head must always accelerate to final fpm from 0.

Also, most mills take longer to accelerate in the Z-direction than in either X or Y (and that X and Y acceleration are equal).