Acceleration is defined as the rate that a
velocity changes. The acceleration that we are most concerned with is
how fast an XY movement goes from 0 to the selected feedrate (F) once the
controller tells the motors to start moving. In the graph below, the
acceleration (also known as ΔV/ΔT) is the slope of the ramp of the red
velocity plot. The steeper the ramp (higher acceleration), the quicker the
axes get up to speed. The shallower the ramp (low acceleration), the
longer it takes to get to "F" (F is the Gcode command that sets the feedrate).
From the point of view of higher
performance, higher acceleration means shorter cycle times and snappier
customer demos. Unfortunately, as acceleration is increased, more
transient transverse stress is exerted on the bit. If the stress exceeds a
certain threshold (transverse rupture point), the bit will break. This is
like whacking something brittle with a hammer (or your boss's head with a
new idea). A little tap might not be a big deal, but a resounding smack
will send shrapnel flying. In the case of cutting soft media with small diameter
carbide tools, it turns out that there is a pretty good compromise between
higher performance and longer tool life.
20 inches per
second per second, or
0.51m per second per second
At this acceleration, your bit will think that you are
coddling it like a wee baby and not break as soon as it starts to
move. This is especially important as the bit starts to get dull and
cutting resistance increases. Of course, if you set the feedrate (F) too
high, the rupture point will eventually be exceeded and the bit will break
anyway. Do not think for a minute that this acceleration is so low that your performance will suffer. At 20
in/sec/sec, you tool can get to 720 in/min in just 1 second.
Axis acceleration is set using the controller software (e.g. Mach 3, EMC2, FlashCut) that was supplied with your CNC router. In the case of larger CNC machining centers, the hardware control panel (e.g. Fanuc, Fagor) is used to configure each axis. In virtually all cases, you will need to set the acceleration parameters for each axis individually.
Setting Up a Rotary Axis
Rotary axes present a particularly challenging case since the LINEAR acceleration of the material relative to the cutting tool will change with the distance from the rotary axis. The further out from the center of rotation you are, the higher the LINEAR acceleration is for a fixed ANGULAR acceleration. To make sure that the linear acceleration never gets too high, it is best to determine the angular acceleration necessary to result in 20 in./sec/sec (0.51m/sec/sec) at the surface of your material.
The linear acceleration L_{a} on the surface of a cylinder with radius r (same units as L) rotating under the influence of an angular acceleration Φ_{a} is determined by:
L_{a} = r * Φ_{a}
Since L_{a} is fixed, the maximum angular acceleration is determined by:
Φ_{a}(max) = L_{a} / r
For example, if L_{a} = 20 in./sec/sec (0.51m/sec/sec) and r = 2.5 in. (0.0635 m), the maximum angular acceleration is determined by:
Φ_{a} = (20 in./sec/sec) / 2.5 in. = 8 rad/sec/sec
or for those of a metric persuasion:
Φ_{a} = (0.51m/sec/sec) / 0.0635 m = 8 rad/sec/sec
where "rad" is short for "radians, the dimensionless unit of angle.
"Note: If your software needs angular acceleration in terms of "degrees/sec/sec", just multiply the result above by 57.3
