Case study: stepper voltage selection

[cncrouterguy]

I'm trying to understand how voltage relates to a stepper's inductance.
This is a case study for selecting between two stepper voltage setups for a
CNC machine. Please pick apart my reasoning and clarify any
misunderstandings that I have or anything that I state that is not true.

Assume this setup will be used on a 48”x96” router with NEMA 34 steppers
and typical 48vdc power supplies.

I’ve found two rules for selecting a voltage for your stepper.

####################################################
Rule 1:

For optimum speed you want a supply at least 20 times and preferably 25
times the rated voltage of the motors. A value of 15 times the rated voltage
is the bare minimum.

####################################################
Rule 2:

Optimum Voltage = 32 x (square root of the inductance). Anything at this
voltage will not cause overheating and is the best voltage to run the stepper at.
####################################################

IMPORTANT: For both rules you must insure the selected voltage does not
cause the stepper to overheat.

####################################################
Stepper A calculations:

Volts 5.7
Amps 3.5
Resistance 1.9
Inductance 22mH
Torque 1600 oz/in

Required power supply using Rule 1:

Minimum voltage = 15 * 5.7vdc = 85.5vdc
Better 20 * 5.7vdc = 114vdc
Best 25 * 5.7vdc = 142.5vdc

Required power supply using Rule 2:

Optimum Voltage = 32 x (square root of the inductance)

( 32 * sqrt(22)) = (32 * 4.69041575982343) = 150.08vdc

####################################################
Stepper B calculations:

Volts 3
Amps 6.3
Resistance .30
Inductance 2.07mH
Torque 812 oz/in


Required power supply using Rule 1:

Minimum voltage = 15 * 3= 45vdc
Better 20 * 3 = 60vdc
Best 25 * 3 = 75vdc

Required power supply using Rule 2:

Optimum Voltage = 32 x (square root of the inductance)

( 32 * sqrt(22)) = (32 * 1.4387) = 46.0384vdc

####################################################
Both setups might perform similarly but the high inductance of stepper A
would require a much higher power supply than is normally possible. Using a
power supply with a maximum of 70vdc unregulated volts pared to stepper
drives rated at 80vdc max would allow the stepper A to run at half it’s
capacity.

Stepper B is sized almost perfectly to a 48 to 70vdc power supply and would
be a much better choice even at 48vdc.

Other facts I’ve found relating to voltage selection:

The voltage of a stepper power supply sets the ceiling for how fast a
stepper can spin. As the stepper spins it generates back EMF (voltage) as it
turns(acts as a generator). When this back EMF voltage nears the supplied
voltage, the stepper ceases to produce torque. Supplying too low of a
voltage also steepens the torque curve drop off as the stepper nears it's
limits and will cause the stepper to stall.

Useable speed increases proportionally as you increase voltage, so if you
double your voltage should double your speed up to the point of stepper overheating.

Increasing the voltage does two things, it speeds up the motor and
increases the torque at higher speeds. A stepper will always have torque
drop off as the RPM increases but running the appropriate voltage will flatten
the fall off curve.

Inductance limits how fast current can flow through a stepper, so high
inductance motors have a lower maximum top speed, due to reduced torque
at high RPM’s. Increasing voltage has the effect of forcing the current
through the stepper faster. To get the maximum performance from a stepper,
you increase the voltage to the max determined by one of the above rules.
You reach a point however, where increasing voltage only adds heat, and no
longer increases speed. That is the voltage greater than calculated by rule
number 2 above.

In summary Stepper A would barely perform at all on the typical 48vdc power
supply and would show a slower speed and similar torque compared to
Stepper B which is at or near it's optimum power and speed, even given that
Stepper B is rated at roughly half of Steppers A torque.

[ger21]

The 20-25x rule was basically a ballpark guess that people used to determine the maximum voltage to use, as there was no simple formula until gecko came out with the one below a few years ago.

And if you look at gecko's website, you'll see the 32 x sqrt(mH) is the maximum voltage. They don't say it's the optimum voltage. Keep in mind that while the motors won't overheat at this voltage, they can still run very, very hot. And in a lot of cases, the maximum voltage is not always required.

It's always been my understanding that the ideal voltage you need is the lowest voltage that gives you the performance you need.

Say the formula tells you the max voltage is 48V. Now, lets assume that 48V allows you to run your stepper at 1200rpm, but you never spin it faster than 800rpm. In that scenario, the optimum voltage would probably be closer to 36V. That will allow your motors to run much cooler, but still deliver the desired performance.

[cncrouterguy]

Great! That's the type feedback I was looking for. All this info is available but
it's spread all over the web.

[James Newton]

For more on finding the right combination of amps and volts for your motor to move a given load, see this page: techref.massmind.org/techref/io/steppers.htm#Estimating

[wildwestpat]

Hi There are a lot of actors that govern the voltage / current / inductance decisions on selecting the optimum conditions for driving a stepper motor.

There is a good interactive calculator on the Kollmorgen site

MOTIONEERING® | Kollmorgen

However there is a limit on the maximum voltage. The insulation break down voltage of the motor coils this also impacts on the allowable temperature. The voltage limits on the drive electronics including the ability to suppress the back emf from the coils. That said the electronic drivers are commercially available in several voltage ranges. Common ones are 48 volts and 80 volts.

The current is pulse width modulated by turning on and off the applied voltage to limit the current to the desired motor maximum at a high frequency compared to the full step rate. The current limit being adjustable on commercial drivers in steps. The current limit is normally stated on the motor's information plate and in the manufacturers data. Exceed this current and there is a high probability you will fuse the winding.

Now the inductance comes into play along with the source impedance of the power unit and any lead wire inductance. Normally only the motor inductance is used but I have seen some home brew power units that would limit the available current due to impeadance problems due to failure to consider the high ripple currents required.

Thus there is a complex relationship between the applied voltage the total circuit inductance and the switching rate used to control the motor winding during a single shot.

This I hope explains why the rules of thumb are often used in lieu of a mathematical approach. In any case the mechanical conditions imposed by the mechanism including cutting forces, weight of the work piece and axis acceleration involve approximations which make the use of excessive drive a necessity. (I have a background in light weight servos fro satellites where weight requires all factors to be pared down.)

The rules of thumb are relatively simple. Fix the torque required and the motor speed in terms of steps per revolution. This is easily done using the calculator in the above Kollmorgen link or something similar. From the torque and motor speed select a suitable motor taking into account any fall off in torque at the required shaft speed. You may have to reselect the torque shaft speed by changing the gearing of the mechanism.

The physical size of the motor then forms IMHO the next stage as a filter to select the candidate motor or motors. A safety factor needs to be assumed and taken into account or the motor will at some point be unable to shift the required load / mass and cause accuracy problems. At this point I would look to availability and price as there are industry preferred ranges within each family and these are often the best priced one. If you still have a bunch of suitable motors pick the one with the lowest inductance and highest maximum current as this should be the one that will achieve the best performance. The choice of power supply voltage and associated voltage rating of the electronics are down to cost consistent with motor maximum breakdown voltage. The breakdown voltage can be hard to find on the data sheets if indeed it is quoted. The plate voltage is the maximum safe voltage that can be applied to the winding due to the heating effect of the current that is caused to flow in the DC resistance of the coils. At this point many motors support both series and parallel connection of the coils. For speed torque the parallel connection is obviousl best as this minimises the inductance which limits the rate of rise time of the current in the coil to its maximum set value every high frequency pulse that goes to make up a full step.

Hope this gives you enough of a feel for both the calculations and the reason for the empirical so called rules for selecting motor size and drive conditions.

Good luck in making the right choices - regards - Pat

[RomanLini]

Beware of using too high a voltage, especially with low inductance motors and/or underdamped loads.

High voltage increases the excitation energy per microstep, in other words the motor moves from one microstep to the next much quicker so it violently "bangs" between steps and causes ringing and stress instead of rotating gently from one step to the next. An obvious symptom of too high a voltage will be that the motor "resonance" and noise is greatly increased at low speeds.

So a high voltage PSU allows very fast motor speeds (which is it's ONLY advantage), but at the cost of greatly increased vibration and resonance at ALL lower speeds, where the machine is commonly used. For many people this means using a higher voltage PSU will cause all general cutting jobs (which happen at low motor speeds) to have vibration issues like cutting finish and increased wear on tools, bearings etc.

It's my personal opinion that this forum has seen way too much emphasis on using high voltage PSUs that has encouraged a popular fashion of aiming for high speeds, but which comes at a very real cost to low speed performance.

As an example I lowered my PSU voltage from 44v back to 33v and got significantly reduced melting with troublesome plastics and much improved cutting finish, all due to reducing the per-microstep resonance. I cringe sometimes seeing people advise other people that they should go for a 70v PSU like that is just the "best" thing to do...

[ger21]

It's my personal opinion that this forum has seen way too much emphasis on using high voltage PSUs that has encouraged a popular fashion of aiming for high speeds, but which comes at a very real cost to low speed performance.

I agree with you 100%. You see way too many posts about hot motors.
And most people don't really use all the voltage anyway.

[H500]

It really depends on the system. On my mill, the 100lb head is giving my 280oz-in motor a strenuous workout on the Z axis. A higher voltage will allow me to avoid having to use bigger motors.

On the x and y, more power allows for tighter gibs, which improves the precision. Higher acceleration will also benefit circular moves where the table needs to reverse direction quickly.

[wildwestpat]

Starting out on a fresh design the question of voltage should not be one of the first parameters to consider. To state the obvious a stepper motor turns by making individual steps by switching currents in the motors coils. To make the motor rotate in a smooth fashion the current for each step is shaped by the drive electronics to look like a sine wave. This is where the pulse width modulation comes in and the search for low inductance windings. The higher the value of inductance the longer it takes to reach a particular current. The electronics in an ideal driver then balances the on off switching during each step so that the resulting drive is as near to an idealise sine wave. (It is possible to drive these motors with sine and cosine voltages using variable frequency to vary he speed but this is expensive and stepping is used to keep costs down.) Now the real life problem is the way the available torque falls away as the step rate increases due to the way the magnetic parts behave. This means that the high speed stepping represents a real barrier to the successful design of the actuator. The magnetic circuit in the motor also imposes limits on the microstep mode and this limits the useful torque. Consulting the Torque / RPM or stepping speed for motors will show a rapid fall in torque as the speed increases and the relationship to inductance with serial or parallel connection of the coils if the motor supports that choice of connection.

Given that stepper motors are primarily a high torque low speed devices there is a balance between using increased voltage and the need to avoid resonances in the mechanics to be addressed. There are threads on building dampers to smooth out these resonances or advocating friction to sort out minor resonance problems. In a new design the motor speed is best set by the gearing to achieve the required traverse speed and acceleration at motor speeds that do not approach the rapid fall off in available torque. Unfortunately stepper motors need a reserve of torque under all conditions so that each step is correctly translated into movement. The use of micro-stepping whilst attractive also reduces the available torque and may not achieve the improved accuracy as the step to shaft rotation accuracy is dependent on the accuracy of the 'teeth' on the stator. Good motor information will show the cyclic error between logic step and physical step but all too often this is not available. Again the use of micro-stepping reduces the available torque.

Boosting the applied voltage has for the above reasons limited impact unless the intention is to extract the last drop of acceleration and speed. If this is the aim then experimentation becomes the name of the game and any theoretical calculations become an academic exercise. Motor losses both in the winding resistance and the magnetic circuit cause power loss and this turns up as heat. With the torque falling as speed increases many driver circuits reduce the hold current when no stepping is demanded. A reduction of 50% is common but these motors will always run hot so initial testing needs to check that the motor maximum operating temperature is not exceeded under all operating conditions including being still.

Again the rules start to take over from calculation! Stepper designs are not as amenable as linear servo systems to analysis but they punch way above their cost and this makes them mighty attractive despite the snags and empirical way parts are selected for a design.

Hope this helps - regards - Pat

[James Newton]

I'm generally agreeing with what Pat says, but I want to clarify that it IS important to pick the right combination of voltage AND amperage (e.g. watts) with a fresh design. After you measure the torque required or know the weight of the load being moved, you can calculate the watts required to move it at a desired speed. Then you can break watts down into volts and amps, (watts = amps times volts) and start picking out your motors (amps and inductance to manage the max voltage), drivers (amps and volts) and power supply (volts and amps). The web site I posted above helps do that, and seems to have worked nicely for a number of people.

Of course, buying motors and drivers and supplies that can mange MORE than what you expect to need is always a wise choice for some of the reasons Pat listed.

[RomanLini]

It really depends on the system. On my mill, the 100lb head is giving my 280oz-in motor a strenuous workout on the Z axis. A higher voltage will allow me to avoid having to use bigger motors.
...

Sorry to disagree, but higher voltage does not increase motor torque, except during the very specific situation where the motor is rotating at a very high speed.

Modern steppers (the popular models people use) are generally quite low in inductance and will produce full torque with a 24v or 33v PSU even as high as 6 or 8 revs/second. After that speed the torque may drop off, depending on the PSU voltage and the motor characteristics. What I am saying is if your Z stepper is doing less than 6 revs/sec the increased PSU voltage will do nothing to "increase power".

...
Now the real life problem is the way the available torque falls away as the step rate increases due to the way the magnetic parts behave.
...

That is correct but I would add the point that the loss of torque does not happen at all during the lower speeds, it only starts to occur above a particular threshold. Most people making these motor/PSU decisions do not know where that threshold is.

Also, using a PSU which has a voltage too high increases the excitation energy to the point when it causes a loss of torque, so low speeds (where you do the cutting) can actually have LESS torque with a high voltage PSU than with a lower voltage PSU.

...
The use of micro-stepping whilst attractive also reduces the available torque...

Sorry that point is just plain wrong. It's a myth that comes from some badly written old white papers discussing torque vs per-step accuracy.

Motor torque (ie usable motor torque which is measured as torque vs displacement angle) is dependent on motor current at any point in time, not on step size. Microstepping gives greater usable torque than full or halfstepping torques (given similar currents) due to the decrease in excitation energy.

[wildwestpat]

Hi RomanLini

The theoretical design point I was labouring to point out was that for a motor with a given number of full steps of say 200 and a step to rotation inaccuracy of 2% using micro stepping can not improve on the 2% figure and that micro stepping reduces available torque hence the need to look at the curves on the data sheet. In addition that the available torque falls with rotational speed of the motor shaft. (This is why I kept banging on about consulting the data sheets for the candidate motors as the fall in torque with increasing step rate / shaft speed is a very important step in the design. The extra loss due to sub division of the basic step is a secondary effect and can for most purposes be ignored using electronics to give shaped drive wave forms. IMO too many builders expect too much in the way of speed failing to recognise the need to ensure steps are not lost relates to those torque curves. )

In my experience micro stepping shifts the resonance of the motor / driven mass and is helpful in achieving smooth operation and yes at low motor shaft speeds the motion is appreciably smoother and the torque loss is small. At high motor shaft speed the loss of torque by using micro stepping to achieve the same rotational speed become greater but it is the fall in torque that is the primary concern not any increase in micro step losses that limit the design. Stepper motors need to be operated well within their available torque capability under all conditions including maximum tooling loads and the design should ensure this. That is why I was stressing that the motor data sheets need to be consulted at an early stage in the design to ensure adequate motor torque is available.

From a theoretical designers view point calculation and perusing manufacturers data is fine but the resulting design has to be built and fettled into a fully operational bit of kit. Rules for selecting steppers are useful and the proven ones will work well but original request was for a theoretical reasoning on the selection. I personally advocate a quick ball park design based on calculation using worst case scenarios for speed - acceleration - tooling load - accuracy both absolute and incremental and then to select candidate components. After building the prototype fine tune as necessary to achieve the design parameters and test to establish that there is adequate torque in hand to prevent lost steps / stalling. The problem comes with those who will try and screw the proverbial last drop of performance and not pull back and operate well with in the capability of the motor but wonder why their machine performance becomes erratic. If high speed operation is required there are other systems that can provide the increased speed torque performance but at greatly increased cost.

Regards - Pat