Gecho 210 step multiplier, was Re: [CAD_CAM_EDM_DRO] Stepper Math

Paul,

Mid-band stabilization (parametric resonance) is an entirely
different animal. Here's the cause and the cure:

THE CAUSE:

A step motor is a first-order resonant system, also called a mass-
spring system. What characterizes first-order systems is (in
mechanical systems) a 90 degree phase lag between force and velocity.
Velocity is at maximum when force is zero and visa versa in a
resonating mass-spring system.

Now enter the drive. At low speeds the drive is a current source
(infinite impedence) and effectively is an open circuit to the
winding back EMF. The drive contributes 0 degrees phase shift to the
system.

Above some speed (corner speed), the drive transitions from a current
source to a voltage source. A voltage source has (ideally) 0
impedence and effectively shorts the winding back EMF. This adds an
additional 90 degree phase shift, making the total 180 degrees now.
This is a setup for undamped oscillation and that is exactly what
happens. The motor will break out into an oscillation that builds in
amplitude until the motor stalls (+/- 2 full steps mechanical).

THE CURE:

Reduce the system phase lag by adding a phase lead component.
Everyone has seen what a car does with bad/missing shock absorbers.
More properly called rate or viscous dampers, they introduce second-
order damping to quickly damp out oscillation. Adding a phase lead
requires a derivative component and "rate" is the derivative of
position. A rate damper provides a resistive force proportional to
velocity.

A cheaper way to the same goal is to do it electronically. The rate
of motor load change (acceleration) is sensed and bandpass amplified.
This signal then phase modulates the step pulses by retarding or
advancing their timing in the drive. This prevents the motor from
resonating, so all of its torque is now available for the load.

Mariss


--- In CAD_CAM_EDM_DRO@y..., "Paul R. Hvidston" <paul_hvidston@y...>
wrote:

> I'm impressed! That's one heck (or should I say, Geck) of a lot of

stuff

> going on in that little package. So is this how the mid-band

stabilization

> is performed?
>
> Thanks for the detailed description.
>
> Paul R. Hvidston, N6MGN
> ACKSYS Engineering
> Upland, CA