The moment of inertia of the 2-inch cube is 32 times greater than that of the 1-inch cube, meaning it is 32 times harder to spin the 2-inch cube compared to the 1-inch cube of the same material. This significantly greater resistance is due to the cube's size (side length) affecting the moment of inertia exponentially, as indicated by the \( a^5 \) dependency.

Correct. I work it out this way: The mass increases by 8 so that's cubed. The particles of mass are at double the radius so it takes double the torque to apply the same force to the particle. Also the double radius makes the particles move double the speed for the same RPM so need double the acceleration. So 3+1+1=5th order.

So regarding a lathe with something like a solid cylinder for stock the moment of inertial is linear with the length but 4th order with radius.

So the geometry of a 100lb rotational mass is important.

Regarding the Plot: With such low Jerk and Acceleration and with a relatively short move the velocity is only getting up to ~10,000 counts/s. No where near the 200,000 limit that is specified. If you would have plotted velocity you could have seen this. If you zip and attach the raw data then we can plot velocity or error or zoom to see things however we wish.

The TripsWPF is a tool we provide for plotting acceleration and velocity for a set of parameters. Here is a plot for your settings

Notice the Acceleration is triangular because it is completely Jerk limited and only ramps up to 30,000counts/sec2 before it needs to start ramping back down to avoid overshooting the target move size. Its like driving a car but only being allowed to move the accelerator or brake very very slowly, you wont spill your coffee, but will take a long distance to accelerate or stop. So the 50,000counts/sec2 of acceleration is never used.

For a Spindle Jerk limit is probably not very important. You might set it to infinity (1e7).

Notice the Output (green) peaks at about 400 DAC counts which is about 1/5th of the 2000 counts available. So you could probably accelerate several times faster that the 30,000counts/s2 in this test.

The output shows some oscillation which might mean it is borderline unstable. You might decrease P or increase D to try to stabilize it.

The Output has 50 DAC Count "spikes". I assume all the IIR Filters are cleared (you didn't show us). Without any Filters and a D gain of 50 each time the encoder changes by 1 count the output will jump 50 counts. Adding a 2nd order low Pass filter in the last stage at 500Hz and Q of 1.4 should reduce the spikes. The Amplifier might ignore the spikes but it is better to attenuate them.

Try a larger move to test higher velocities. This is difficult with very slow axes like that due to the 3.5sec plot limitation. But maybe with the higher acceleration and Jerk it may show us what we need.

HTH