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[[cha:stepper-info]]
= Stepper Information

== Stepper Motor Operation

Stepper motors operate by sequentially energising and de-energising several coils surrounding the rotor in such a
way that the shaft is magnetically forced to rotate around in discrete steps. Steps of 0.9 - 1.8 degrees are quite
common, giving 400 - 200 steps per full revolution of the shaft.

As in real life, nothing can change from one state to another with absolutely no time delay. In the case of the
stepper motor, the current passing through each coil, and thus the magnetic field that pulls the rotor around to
each step of rotation takes some time to take effect. This is due to the coil having inductance (expressed in
Henries, abbreviated to the letter H) which has a natural tendency to resist the flow of a rapidly changing
current. More coil inductance results in a slower rate of current change and thus a slower rate of magnetic field
expansion and contraction.

The maximum torque that the stepper motor can achieve is when the motor is stationary with one winding energised.
This figure may be quoted on a stepper motor datasheet as the 'holding torque'. As the rate at which each coil is
energised and de-energised increases to induce rotation in the shaft, the time that each coil can exert its full
magnetic attraction on the rotor reduces, thereby reducing the overall torque. This relationship between speed and
torque is largely inversely proportional.

In the below example, the charging time for three coils is shown when the applied voltage is stepped from 0V to
40V. While all three coils can easily reach the full current limit of 5 amps, the time taken varies for each
coil. The 4 milli-Henry coil (blue trace) takes twice as long to reach full current than the 2mH coil (green
trace), and the 8mH (red trace) coil takes twice as long again:

image::images/inductance-step-response.png[align="center"]

If the rate at which step changes are applied to the coils is significantly shorter than the rise time, it's easy
to see that the winding has less time to attain full magnetic attraction on the rotor, and thus maximum torque is
curtailed. In the below example the 2mH coil can achieve the full 5A limit before the step voltage is removed, but
the 4mH and 8mH coils cannot:

image::images/inductance-pulse-response-slow-charge.png[align="center"]

The accepted way of improving motor speed while maintaining torque is to increase the speed at which the magnetic
field of the motor coils can expand and collapse. The easiest way to accomplish this is to increase the supply
voltage to force the current in each winding to rise and fall much more rapidly. A quicker magnetising time
equates to faster step rates while improving torque at higher speeds, both of which are obviously desirable in a
CNC system.

Using the same example as above, but increasing the step voltage to 80V it can be seen that all three coils can
now reach the 5A maximum quite easily:

image::images/inductance-pulse-response-fast-charge.png[align="center"]

However, careful management of a higher drive voltage is required, as a higher voltage will increase current
flowing in each coil with a corresponding increase in temperature of the winding. Excessive temperature rise in
the winding will lead to eventual overheating and failure of the motor.

In most stepper-based CNC systems the voltage of the supply feeding the stepper driver is several orders of
magnitude greater than the voltage of the motor itself. A typical NEMA23 stepper motor may have a rating of only a
handful of volts, yet the power supply and driver could be operating at 48 VDC or more.

Nearly all modern stepper motor drivers on the market today are constant-current types. That is, the current being
applied to each winding is fixed irrespective of how much voltage is being applied. Most drivers accomplish this
by monitoring the current being drawn through the motor windings and rapidly switching the outputs on and off at a
very high frequency to maintain this current. Depending on the drivers being used, it may even be possible to hear
this high frequency whistling in the motors themselves when stationary. Because the voltage is rapidly switched on
and off to maintain the winding current at an approximate fixed value, these types of drivers are also known as
'chopper drive'.

== Selecting a Stepper Power Supply

While a higher voltage is directly related to more speed and torque, obviously there comes a limit where
increasing supply voltage is no longer beneficial. The first limitation to the maximum power supply voltage is
likely to be what the stepper driver itself is capable of withstanding. This value should be provided in the
datasheet for the stepper driver, and exceeding this voltage will result in the destruction of the driver. Ideally
the power supply voltage should be chosen with a degree of headroom that falls under this maximum voltage limit of
around 10%. If, for example a stepper driver has a V~max~ rating of 80 VDC, the maximum power supply voltage should
be limited to 72 VDC.

As mentioned above, excessive motor supply voltage also leads to excessive heat rise in the motor windings which
can lead to eventual failure of the motor through overheating. A commonly used equation for providing a guideline
in determining the maximum voltage to prevent excessive heat rise is to take the square-root of the winding
inductance quoted in the motor datasheet (expressed in mill-Henries) and multiply by 32. For example, choosing a
stepper with a coil inductance of 4mH will result in a maximum power supply voltage of 32 x SQRT (4) = 64 VDC.

Many stepper motor datasheets will also provide speed/torque curves, often plotted using different supply
voltages. By studying the graphs it may be determined that increasing the supply voltage by a factor of two will
not result in a corresponding improvement in speed/torque by the same degree. If there is little to be gained in
running a stepper motor at 64 VDC, this may help in narrowing down the proposed power supply to 32 VDC which will
also help minimise excessive heat rise in the motor windings.

The other factor to consider is the current rating of the power supply. This is based from the motor's winding
current ratings and whether the motor windings are wired in series or parallel, both of which should be listed in
the motor's datasheet. A good rule of thumb is to size the power supply current rating at 2/3 of the rated phase
current of the stepper motor if the windings are in parallel, or 1/3 of the rated current if wired in series.
Thus, for a stepper motor rated at 4 A wired in parallel, the power supply needs to have a current rating of at
least 2.7 A, or 1.3 A if wired in series.
The total current rating of the complete system is then the sum of all stepper motors' current requirements.

== Resonance

Motor resonance occurs when the rate at which the steps are applied to the windings matches the natural frequency
of the motor itself. Applying steps for a prolonged period of time at this rate results in the torque dropping
dramatically, and the motor may stall or even rotate in random directions. Some stepper motor datasheets provide
plots of the torque/speed relationship and show a dip in the graph where resonance is likely to occur. It should
be noted that this resonant peak provided in the datasheet is only for the motor itself - as soon as the motor is
coupled to other components (ie, installed in a CNC system) the resonant frequency may be altered, or even
multiple new resonances introduced.

Several methods exist to help control the effects of resonance, all with varying degrees of complexity,
effectiveness and side effects:

* Microstepping can help reduce resonance by using smaller step changes in current between each step.
  These smaller step changes cause less ringing in the motor and windings and thus cause less excitation at the point of resonance.
* Ensuring the motor is never operated at a particular frequency for a sustained period is a very basic method of
  reducing resonance, always accelerating or decelerating through the resonant peak.
* Increasing inertial load will damp unwanted resonances at the expense of some torque and potentially some accuracy.
  Elastomeric motor mounts, shaft couplings or bearing mounts can be employed.
* More advanced stepper motor drives may have the ability to switch between stepping modes such that the resonant
  peak is managed at certain rates of operation.
  Other systems exist to place electrical load on the windings, which has a similar effect to mechanical damping, above.

== Microstepping

A stepper motor operating with each winding being fully energised in a sequential fashion is operating in
full-step mode. That is, the maximum rotation resolution possible for that motor is the same as the number of
whole steps that motor is manufactured to perform at (eg, 200 steps per revolution for a 1.8 degree/step motor).
As each winding is energised the rotor clocks around fully from one detent to the next.

Additional rotational resolution from a stepper motor can be obtained by performing microstepping, whereby the
current being driven into each winding can essentially be 'ramped' in discrete intermediate steps. This then
causes the rotor to gradually straddle across each rotational detent rather than making the full jump from one
step to the next.

Microstepping is commonly performed in multiples of 2 (4x, 8x, 16x, 32x etc). For example, a drive set to 4x
microstepping will divide each step into four discrete current levels in the motor windings, thus affording an
improvement in rotational resolution by a factor of four. This obviously means that for a typical step/direction
control interface there will need to be four times as many step pulses generated to make the motor move the same
amount had it been operating in full-step mode. To make the motor rotate at the same speed the rate at which
pulses need to be applied to the drive also needs to be four times as fast.

At low rotational speeds, microstepping actually results in slightly higher torque than when full stepping. This
is due to the smaller changes in current between intermediate steps resulting in less energy being wasted exciting
natural resonances in the motor. As RPM increases however, torque tends to fall off at a similar rate as full
stepping.

However, continuing to increase the degree of microstepping will eventually lead to some real-life limitations.
Step pulse generation, particularly when using the parallel port, is limited in frequency. This will inevitably
limit the maximum speed at which the drive can be commanded to step at. With high degrees of microstepping this
will result in unacceptably slow RPM of the motor.

Excessively-high rates of microstepping have no real benefit if the resultant accuracy is too small to be
mechanically useful. A 1.8 degree per step motor running at 16x microstepping is theoretically capable of 0.1125
degrees per step. Coupled with a 20TPI leadscrew this should result in a positional resolution of 0.000016” or
0.0004 mm. In reality it is incredibly difficult to achieve such fine degrees of control. All components in the CNC
system will contain tolerances and countering forces (backlash in leadscrews, flex in gantries, runout in the
spindle and cutting tool, static friction in the stepper motor itself, stepper detent error etc) that will render
such small amounts of resolution completely meaningless. In practice, microstepping at rates in excess of 4x or 8x
on a CNC machine fitted with leadscrews serves little purpose. In some cases it may even be more beneficial to run
at lower degrees of microstepping or even full steps, and operate the stepper motor through a gear reduction to
obtain the necessary resolution and torque gains.

== Open and Closed Loop

In the simplest CNC systems employing stepper motors, the host computer and/or stepper driver receives no feedback
from the motor that it has achieved the desired outcome when commanded to begin stepping. The assumption by the
software, driver and end user is that the motor operated correctly and the axis has moved to the expected new
position. A system operating in this fashion is said to be running in 'open loop', where the device at the end of
the signal chain (the stepper motor) does not provide any indication to the device at the start of the chain (the
computer) that the target was reached.

A further enhancement to the basic stepper motor is to run the system in a 'closed loop'. This is achieved by
equipping the stepper motor with a rotary encoder whose positional signal is returned back to a device higher up
in the signal chain. In this way the motors' actual position can be compared to the expected position at all
times, and the drive parameters adjusted in real time to ensure that the motor does not fall behind. This enables
closed loop stepper systems to be able to achieve better speed and torque performance than open loop systems, due
to the system constantly compensating for any deviation to the stepper's performance under varying loads.

Basic systems operating in this fashion may only close the loop between the motor and the driver, leaving the
software on the host computer out of the loop. The software issues step/direction pulses to the downstream driver
as it would normally when running in open loop. In these situations the drivers usually include an alarm output
which signals the software to halt when the load placed on the stepper becomes too great for the driver to
compensate without losing steps.

More advanced implementations of closed loop operation bring the encoder signal all the way back to the host
computer, but require that a much higher hardware and software overhead be installed to manage the encoder
feedback and calculation and delivery of drive compensation.

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