[cjchands]

Hi guys,
Does anyone know how to calculate Power Rating and RPM from the specification of Stepper?
I was told that formula:
Power (KW) = (Torque in N-m) x RPM/ 9.55

What I got is NEma 34, holding Torque 3N-m, Current 2A

Assume i use 35Vdc supply, then P = IxV = 70Watt (That's tooooo small??)
Then RPM = Power (KW) x 9.55 / Torque = 0.2 RPM????

That's again seem strange??
Best way might be to look at performanace curve, but any idea to get general number?

Thanks in advance.

[davidmb]

Not sure what your asking, but if it's to find the fastest rpm that you can drive the motor then the following may help. If it's for sizing the psu then each motor usually has a maximum power rating, depending on how you drive them then the voltage is a bit of a red herring as most motor drivers run the current through the motor windings in a controlled manner, usually at a much higher voltage that the motor specs dictate. ( Gives a much faster motor response ).

Unfortunately it's not the holding torque that you need, for each stepper motor that is manufactured there is usually a speed/torque curve, what you need to do is calculate the cutting forces ( push ) that you require, convert this into torque needed to drive it ( differs depending on drive mechanism whether ballscrew, acme leadscrew or toothed belt/gear train - all have different efficiencies and losses ), once you know the minimum torque you can get away with that will drive the system then you go to your speed/torque curve and that will give you the maximum rpm that you cannot go above. This is a very simplistic approach since you really need to figure in the masses involved that you want to accelerate and decelerate.

Stepper motors behave differently to most other motors the maximum torque is developed when the motor is stationary and falls off with increasing speed. I guess that's why they are sold by 'holding torque'.

Hope this helps.

[Mariss Freimanis]

Hi,

I think I have derived some useful equations which allows you to calculate
motor corner speed, power output and its speed-torque curve using only
the motor's datasheet and your operating parameters. Perhaps some of
the more analytically inclined here can criticize it.


1) Corner speed Hz = Vs / (2pi * I * L)
Or:
Corner speed RPM = (1.2 * Vs) / (2pi * I * L)
Or:
2) Corner speed RPM = (0.191 * Vs) / (L * Is)

Where:
RPM = the motor's corner speed
Vs = supply voltage
L = winding inductance in Henries
Is = drive's set phase current in Amperes


The corner speed of a motor is where the motor transitions from
constant torque to inverse torque with speed. That is also the speed
the motor reaches its maximum available power output (see green
'power' curve).

By extension from (2), this power is:

Output Watts = Low-speed torque in-oz * corner-speed RPM / 1351
Or:
3) W = (Vs * Th) / (10 * mH * Ir)

Where:
W = motor power output in Watts mechanical
Vs = supply voltage
Th = rated holding torque in in-oz
mH = winding inductance in milli-henries
Ir = rated phase current in Amperes


Low-speed torque can be calculated from the motor datasheet or
measured directly with a torque wrench. The tests were run with
microstepping drives. The low-speed torque is:

T = (Th * Is) / (SQRT 2 * Ir)
Where Th is the holding torque at the rated current Ir and Is is the
set current of the drive.

For calculating the speed-torque curve, rearrange (3) for torque:

4) T = W * 1351 / RPM
Where T = in-oz, W = Watts and RPM = for motor speeds > corner RPM.

-----------------------------------------------
Results:


Please refer to MS23_4A_24V.gif and Gearing.gif. The Gearing.gif dyno measured speed vs. torque data was taken with a G201 drive, the MS23_4A_24V.gif data (red curve) was taken with a G203V drive. Refer to the Gearing.gif "4A / phase, 24VDC" (green curve and table). There is no substantial difference except that the G203V doesn't have a dip in the low-speed portion of the torque curve.

For the motor in MS23_4A_24V.gif, the corner speed is 662 RPM using
(2). From (3) the output power calculates to 53.9 Watts. The
CALCULATED values in the table below are from (4), the MEASURED values
are from dynamometer results for the motor.

SPEED_______CALC.______MEASURED

0.000 KRPM___110 in-oz___110 in-oz
0.100 KRPM___110 in-oz___110 in-oz
0.200 KRPM___110 in-oz___110 in-oz
0.300 KRPM___110 in-oz___110 in-oz
0.400 KRPM___110 in-oz___110 in-oz
0.500 KRPM___110 in-oz___110 in-oz
0.600 KRPM___110 in-oz___104 in-oz
0.700 KRPM___104 in-oz___095 in-oz
0.800 KRPM___091 in-oz___087 in-oz
0.900 KRPM___081 in-oz___080 in-oz
1.000 KRPM___073 in-oz___073 in-oz
1.250 KRPM___058 in-oz___058 in-oz
1.500 KRPM___048 in-oz___048 in-oz
2.000 KRPM___036 in-oz___035 in-oz
2.500 KRPM___029 in-oz___027 in-oz
3.000 KRPM___024 in-oz___022 in-oz

The equation gives a good fit to experimental (measured) data. The
biggest divergence error is at the corner speed because the equation
assumes an abrupt transition from current mode to voltage mode
operation while in reality the transition is somewhat more gradual.
The other divergence is at the high-speed end. This is due to the
equation not factoring in the effect of detent torque on power output.
This is an easy term to add.

Mariss

[Oldmanandhistoy]

Hi,

I think I have derived some useful equations which allows you to calculate
motor corner speed, power output and its speed-torque curve using only
the motor's datasheet and your operating parameters. Perhaps some of
the more analytically inclined here can criticize it.

I know this reply was not directed at me personally but I would like to thank you for another excellent highly informative post. Finding a post like this is like finding a gold nugget while sifting silt where you are expecting to find some grains only. I for one will be using your formulas for my own calculations and adding this thread to my cnczone favourites.

Best regards,
John

[Mariss Freimanis]

Well, think of it as serendipity then. A few days ago I began to wonder why if brush-type PM servomotor characteristics can be derived from the motor's datasheet, why not step motor characteristics? So I sat down with a pencil, paper and a calculator and began to puzzle it all out. The results are these preliminary equations and about 10 pages of scribbled notes and calculations. Luckily the dynamometer agrees with the equations so far.

Mariss

[Madclicker]

I'm having a tough time getting past the first 2 equations.

I notice that the coil resistance is conspicuously absent. Except for the missing R, I can see a pretty believable V/I transfer function. Maybe you dropped the resistance because it is, or is nearly 1?

[Mariss Freimanis]

Good point. This is a first cut at describing the relationship so second-order effects were neglected.

R is missing because it contributes only slightly, the main effect being (Is * R) subtracts from Vs. This term drops rapidly in magnitude with increasing speed, its contribution is under 2%.

Detent torque effects are also neglected. Detent torque is a constant and is always present whether the motor is turning or not. It is a loss that is proportional to speed (Td * RPM) that subtracts from the power output.

The equation assumes constant power output past the corner frequency. Detent torque effects modifies the power output curve from a constant to a negative slope line. See the measured torque table (green) in Gearing.gif and note power output is 54W at 1,000RPM and 49W at 3,000RPM. The 5W drop is caused by detent torque losses. Detent torque effects contribute under 5% to the results.

Mariss

[Madclicker]

This occurred to me after I posted. I always did like first order approximations to second order systems. After all, the object is to find the corner frequency, ie dominant pole.

[H500]

Very interesting post. However, I done the calculations on a different motor but the numbers did not agree with the vendor's torque curve.

Motor: Keling kl23h276-30-8b
Vendor's torque curve: http://www.kelinginc.net/KL23H276-30-8BT.pdf

test voltage: 30v
test current: 4 amps
rated holding oz-in: 282
rated current: 4.2 amps
inductance: 2.2 mH

low speed torque = 282 * 4 /sqrt(2) / 4.2 = 190 oz in
corner RPM = .191 * 30/2.2/4.2*1000 = 620 rpm

power = 190*620/1351 = 87 watts


87 watt is much higher than the ~53 watts shown in their torque curve. I realize they done their test using half stepping, but the discrepancy seems rather large.

Any insights?

[Mariss Freimanis]

Actually it's remarkably close considering the speed-torque curve looks a little flakey. I took the curve values to get measured power:

0.15KRPM__22W
0.30KRPM__40W
0.45KRPM__49W
0.60KRPM__56W
0.75KRPM__59W
0.90KRPM__61W
1.05KRPM__54W
1.20KRPM__50W
1.35KRPM__50W
1.50KRPM__47W

The above data was plotted and a best-fit spline was generated. See thumbnail. The peak power was measured as 58.5W.

I'm not familiar with their drive so I'll assume it uses a classic half-step sequence: strong-step, weak-step (both windings on, one winding on). This averages to a 67% utilization of the motor giving 0.67 * 87W or 58W calculated versus 58.5W measured.

The power curve has a negative slope equal to -17.3W / KRPM due to dentent torque. This suggests a detent torque of 23 in-oz. The value isn't published in the datasheet. Maybe someone can measure it to see if it matches the calculated value. It seems a little high.

Mariss

[H500]

Mariss,
Thanks for the explanation. The calculated output for the motor seems surprisingly high for a nema23. I calculated 137 watts at 45V! Perhaps the heat from the apparently high detent losses will be the limiting factor on the output.

I will try to do some measurements when the motors arrive.