Re: [CAD_CAM_EDM_DRO] Z-Axis Knee Woes

I would like to offer a few simple formulas that might be
useful for calculating the requirements of driving heavy
loads like a conventional acme screw driven knee on
a vertical mill.

First consider we are raising a lot of weight - perhaps
hubdreds of pounds. With tight gibs the friction can also
be very very high.

The first thing I would consider is to measure the torque
at the Z axis handwheel. This can be done with a fish scale
attached to the handle pulling circumferentially until the wheel
moves. The values will tend to be higher to get it moving due
to static friction. Even though one can only turn the wheel a little
way with the scale attached it is still not too hard to see the running
torque required after some motion begins.

Do this in the knee up direction with the gibbs as tight as you
would ever have them.

That scale force multiplied by the distance from the handle to the
centerline of the wheel or crank is the torque required.

Let's take an example. Say it takes 15 lb of circumferential force
on a handwheel with the handle 5 in from the wheel centerline to
keep it moving slowly.

The required torque is 5in x 15lb or 75 in lb.

Many motor torque specs are in in oz, so let's convert.
To do that we simply multiply by 16 oz/lb and get:

75 in lb x 16 oz/lb = 1200 in oz continuous!

I tried to use numbers folks had mentioned so the first observation
is that this is a LOT of torque! No wonder it can be a problem.

Ok, so we will probably want some reduction on the drive.
But how much?

Well the motor torque will increase by a simple factor
of the reduction ratio.

Let's say we have a motor/amp that can do 300 in oz continuous
and 1000 in oz peak. If the 1000 in oz occured at a typical 20A
amp current the 300 in oz would use about 5 amps continuous.

In this case we would have to use a 4:1 gear reduction.

If the no load max speed of the motor/amp combination was a
typical 1800 rpm, our rate of travel with a 5tpi jack screw goes
to 1800/(4*5) = 90 in/min. We might approach this in the
down direction where the weight is on our side. In the up
(hard) direction the motor winding resistance might limit us
to about 3/4 of that value... perhaps 60 or 70 ipm.
If the crank mechanism has gear reduction it will be
proportionally less. On my Index Mill it would be about
20 ipm. Actually the well-worn bevel gears in it have too
much backlash for a cnc control.

How much power are we using?

Well let's consider the power needed just to raise a weight at
a certain speed. That is just mass x gravity constant x velocity.

Another example... this time in mks because the units are convenient.

Lets run a heavy 200 kg knee load at 0.025 meters per sec. That is about
60ipm.
The gravity constant in this case is about 10.

So the power is 200 x 10 x .025 = 50 watt

Not very much!

So most of the energy must be going into friction rather than raising the
weight because our original handle torque required on the order of

75 in lb x 5N/lbf x .025 m/in x 5 s^-1 = 300 watt (at 60ipm)

... a little under half a horsepower.

That makes sense to me....otherwise the thing would freewheel down
if you let go of the handle.

This suggests the following conclusions:

With a typical vertical mill acme screw knee as our examples

1) a typical NEMA 56 frame dc motor can easily handle this application
with proper reduction giving speeds in the 60 ipm range if the crank
is geared 1:1 and the motor is 4:1 reduced. 20 ipm might be typical
if the crank bevel gears are like mine.

2) A counterbalance or spring will help only a little as much of the torque
required is to overcome acme screw and gib friction

3) A brake probably will not be required

4) The acceleration will often be limited by the rotor inertia of the motor
rather than the mass of the knee.

5) replacing the acme screw with a ballscrew would reduce the motor
requirements by perhaps half to two thirds, but would cost more than
the difference. (a brake / counterforce also might have to be added).

Les







Leslie Watts
L M Watts Furniture
Tiger, Georgia USA
http://www.alltel.net/~leswatts/wattsfurniturewp.html
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