Re: stepper motor inertia

Dan,
Thanks for the link. I picked the IH23014 motor, digitized the
torque/speed curve, and fitted it to a quadratic equation. It fits a
quadratic very closely out to 20,000 step/s.


The next thing was to play with some motion games.
The first case was to assume that torque was constant, the value it
would have at 10,000 step/s. The distance it would travel in a fixed
time was then calculated.
The second case assumed that torque decreased with velocity per the
fitted curve. The distance traveled in a constant time was
calculated, this is a double integral of the acceleration (derived
from the torque).
The distance traveled in the second case was 3X larger than in the
first case.

The conclusion drawn is that if the acceleration curve is matched to
the torque curve of the motor, greatly improved rapids could be
obtained, compared to simple constant acceleration models of the
stepping speed.

If this is of interest to the motor tweakers out there, I'll make a
PDF of the math and plots.

This comparison could be refined to include a model where the
acceleration is constant up to a certain speed and then decreases to
zero. This is what Mach3 does, isn't it? I suspect that a
substantial increase in speed could still be obtained.

A further feature of an analytic technique is that it would permit
some stepper tuning, knowing the motor torque curve, the screw (and
stage?) friction, screw pitch, stage mass, moment of intertia of this
and that, the maximimum rates of acceleration could be calculated.

regards-
Elliot



--- In CAD_CAM_EDM_DRO@yahoogroups.com, "Dan Mauch" <dmauch@...>
wrote:

>
> Here is a link to the MCG web site that has the Torque curves http:/

/www.mcg-net.com/electric_motors/downloads/step_motors/
IH23_step_motor.pdf

> Dan Mauch
> economical 3D scanner software and kits
> low cost stepper and servo motors.
> cases for Gecko drives
> kits and assembled 3-4 axis drives
> www.camtronics-cnc.com
> www.seanet.com/~dmauch
> ----- Original Message -----
> From: optics22000
> To: CAD_CAM_EDM_DRO@yahoogroups.com
> Sent: Friday, May 11, 2007 8:00 AM
> Subject: [CAD_CAM_EDM_DRO] stepper motor inertia
>
>
> Thanks to Dan Mauch and Alan KM6W I have rotor inertia for some
> steppers, I'l use the MCG IH23014 252 oz-in one in this example.
> moment of inertia = 340 g cm^2
>
> the moment of inertia of a cylinder rotated around its axis is
> I= m r^2
> m= pi r^2 l density
> density steel is about 7.8 g cm^-2
> so I=12.2 r^4 l
>
> Conside a 1/2" diameter leadscrew 1' long,
> I=60 gm cm^2 ; this is much less than the rotor inertia
>
> there are some coupling bits of larger diameter, about 1"

diameter

> and 2" long altogether,
> these have I=160 gm cm^2 by the same formulas,
> so total is 220 g cm^2 ; this is still less than the motor

inertia.

>
> The stage mass has some inertia too, this is coupled to the motor

via

> the screw thread. Using a bit of algebra (does anyone want to see
> this?) I get
>
> I = p^2 m/2pi , where p is the screw pitch and m is the mass

moved by

> the stage.
>
> The Taig in my example has a 20 pitch screw and I guess a 5 lb

mass

> (too lazy to weight it).
>
> therefore I = 36 g cm^2
>
> added to the screw and coupling intertia we get I=256 g cm^2,

still

> less than the motor inertia.
>
> It wouldn't take much for the screw inertia to increase very

rapidly,

> it goes by the fourth power of the radius.
> A coarser lead screw would increase the inertia load of the stage
> mass radidly, for example a 5 pitch screw would quadruple it

compared

> to the 20 pitch.
>
> Screw friction adds a constant load which should just be

subtracted

> from the motor torque.
>
> Dan, can you suggest a URL for a motor torque curve? If this can

be

> put into a simple form, it should be possible to write an

equation

> that will describe the maximum attainable acceleration for any
> condition of screw size, pitch, stage mass and screw friction.
>
> This may be of some small use in setting up acceleration curves

in

> software. Acceleration could be reduced as speed increased,

allowing

> the greatest possible acceleration at low speeds.
>
> regards-
> Elliot
>
>
>
>
>
> [Non-text portions of this message have been removed]
>