# Speed of position servo control

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#### Bulent UNALMIS

I have DC motors, shaft encoders, screws and nuts.
I want to build home made CNC using this parts.
I ask, if I use this motors what can be my cnc's bandwidth?

Yes Electrical time constants, servo controller, Friction and mass of axis plays importand role on BW. Lets forget these parameters.

I will use this motor and other parts (screw, nuts..)
Now i want to know if i use this motors what happens the max axis speed of my cnc? I find an answer for this question but i am not sure, I want learn your ideas.

Motor labels says 3000rpm and screws has 4 mm/rev. (p=4)

We can calculate the maximum velocity of lineer motion.

n=3000/60 = 50 rev.per sec.

vmax = p * n = 4 * 50 = 200 mm/sec.

My machine working area 300x300mm

Now I ask this question: If i want to draw circle with this motors what happens the max speed?

Max radius is 150 mm. (Machine limits)

we know sin and cos functions draw circle.

Function of X axis position
Px = 150 * sin(wt)

Function of Y axis position function
Py = 150 * cos(wt)

we can calculate the velocity functions

Vx=150 * w * cos(wt)

Vxmax = 150 * w = 200 mm/sec

w = 2pi/T T=2pi/w = 4.7 sec. Appox. 5 sec.

F = 1/T = 1/5 = 0.2Hz

My machine can draw circle (r=150mm) in 5 seconds.

My cnc's position control servo bandwidth must be minimum 02 * 10 = 2 Hz

Am I wrong? I am waiting your responses.

Thanks.

S

#### Simon Choi

Your estimations seems O.K. But in real world, you need to consider two important facts:
1. Friction related force of the system. This can influence your estimation up to 15% easily.
2. In controls, even a simple positioning control, when you set PID setting of the system, there is always overshoot/ undershoot, or even unstability of the system settings. To get the untimate settings, experiences and engineering judgements are more important than your calculation. In other words, your calculation can be used to get some approximate original system setup, however, the real speed of the system would be quite different unless you add or modify the system until you get the speed you want.

Just a thought.

C

#### Curt Wuollet

Let's think about the upper boundery by inspection:

50 RPS X encoder counts per revolution. X 2 axis. For full resolution you would need (by Nyquist) a sample rate twice that with interleaved reads. This should be your highest
frequency requirement. Real World equipment often cheats and interpolates as one encoder count is a fairly small distance.

Regards

cww

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#### oj

> n=3000/60 = 50 rev.per sec.
>
> vmax = p * n = 4 * 50 = 200 mm/sec.
This is the shaft speed.

> My machine working area 300x300mm
>
> Now I ask this question: If i want to draw circle with this motors what happens the max speed?
>
> Max radius is 150 mm. (Machine limits)
>
> we know sin and cos functions draw circle.
>
> Function of X axis position
> Px = 150 * sin(wt)
>
> Function of Y axis position function
> Py = 150 * cos(wt)
>
> we can calculate the velocity functions
>
> Vx=150 * w * cos(wt)
>
> Vxmax = 150 * w = 200 mm/sec
>
>
> w = 2pi/T T=2pi/w = 4.7 sec. Appox. 5 sec.
>
> F = 1/T = 1/5 = 0.2Hz
This is the hard way, the easy way is circumference = 2*pi*radius/200mm = 4.7sec.

> My machine can draw circle (r=150mm) in 5 seconds.
>
> My cnc's position control servo bandwidth must be minimum 02 * 10 = 2 Hz
>
> Am I wrong? I am waiting your responses.
are correct if you are rolling the motor shaft
on a surface and doing a circular to linear motion.
Typically, cnc's I believe use 2 or 3 axes, x, y,
& z. So you'll need at least 3 motors for motion and one for drilling or milling. The motion is usually gear reduced and slow so that your cnc head does not fly off. If you need high
speed, the materials have to be able to support all that inertia.

oj

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#### Bulent UNALMIS

Have all of us same idea for 2 Hz Band width? This point is very critic.

(Yes Nyquist says Ts = T/2 but this is maximum sample time.)

I want to learn,

Can I use this type relation for Bandwidth?

Regards.

C

#### Curt Wuollet

Yes, it's where I'd start. And then you have to deal with reality. How you sample, alternate reads or burst mode for minimum skew. Can the encoders truly be sampled in parallel,latencies, yada, yada. How the machine really performs, the actual task, what is needed to stop your inertial load, etc. most of this is pretty logical but your bandwidth is always related to the fastest event you need to process. History is full of approaches and techniques that compensate for insufficient speed. Today, that's much less of a problem.

Regards

cww

J

#### J. M. Tirabasso

Hello,
I think that your estimation is only valid for the sine-cosine drive in the X-Y axis.
What do you really need to know? Sample time or analog bandwidth?

Best regards

J. M. Tirabasso
Sistemas DACS S.A.

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#### Bulent UNALMIS

I have more question but i must solve this question.

I am looking analog bandwidth also sample time...