Choosing stepper for a delta

What is specific in delta robots ?

Delta printer have a kinematic very different from Cartesian printers as due to the geometry, while one carriage is in low position, the speed and acceleration of this carriage is nearly three times higher than the effector speed. So, at maximum printable diameter, the stepper shall run three times faster than for a Cartesian printer.

Speed up coefficient for given arm angle
 arm angle/bed plane speed multiplier 25° 2.14 20° 2.75 15° 3.73

Stepper characteristics

Steppers have their torque decreasing significantly while their speed increase and above some speed, the torque became so low it can barely turn the motor. The capability of a stepper to run fast is related to its construction and the resistance to changing current in a stepper is translated in a parameter called Inductance, expressed in mH (millihenry).

How to have a stepper run fast: The speed limit is related to the electrical characteristics of the stepper, which makes the electrical current change of direction more or less difficult. To ease the change of current in the stepper, there are two solutions:

• Increase the voltage supply, which is fairly efficient. This is one of the reason you see more high end machines supplied in 24V (there are other motives).
• Have a different winding for the same form factor, say use less turns on the coils, which reduce the inductance, but increase the nominal current.

There is no alternative, stepper faster speed require either higher voltage or higher current (or both, e.g. for CNC machine). See Stepper_torque.

The market

High inductance motors

You find on the market steppers sold for 3D printers, with a torque ranging from 2.6 tof 4.4 kg.cm and a current of 0.4A. This low current appeal builders as it make the electronic driver heating much less.

However, it came at a cost, which is a very high inductance which varies from 30 to 35mH. That means these motors are totally incapable of any speed. They are unusable for a delta and a bad choice for another printer. As an example, a 4.4 kg.cm motor wired for this low current, while having a static torque twice the Fisher motors, simply cannot reach the maximum speed used by the Fisher, effectively having a near zero torque over a given speed. Same motors with a winding giving a nominal current of 1.5 to 2A will be more usable.

Highest usable current

Most drivers cannot practically reach 2A. There is no problem to use a current lower than the nominal current (and you shall, indeed). That will slightly reduce the static torque, but as the high current motors have a low inductance, their effective torque at speed may be higher than for motors designed for lower current and supplied at their maximum. A current lower than the nominal will significantly reduce generated heat.

Don't be fooled by the big torque on the plate, which is the static torque, for the movement motors, what counts is the torque at maximum speed (an info which is rarely supplied, anyway).

Low current high torque stepper may be used for direct drive extruders, as the speed of extruder is very low. But that will reduce the possible retracting speed, which is not good, especially with 'Bowden' tube extruder.

A good practical setup

The Fisher, a small delta printer was designed by late RRP company. As for all their printers, they were using small and compact steppers with a torque of 2.2 kg.cm. This is lower than most repraps but is sufficient if there is no mechanical problem (friction).

These small motors have a low nominal static torque, but they also have a low inductance (2.5 mH), while due to their small size, the nominal current remains reasonable (1.2A).

The Fisher is supplied by an external power supply with a voltage of 19V. With low inductance and a higher voltage than most printers, RRP get the best of these small motors and the maximum speed of the Fisher is fair with 180 mm/s at maximum diameter, 250mm/s if diameter is slightly reduced. This is with a geometry where the arm angle at maximum diameter is 12.5°, lower than usual (inducing a carriage speed 4.7 times the effector speed).

Speed, torque and acceleration.

The torque required by a printer movement is due to:

• Mechanical friction (most notable being the belt)
• Acceleration
• Gravity

The first one may be limited by careful construction and assembly, and the belt tension shall be sufficiently high for good stiffness, but not too much to limit friction.

However, you can (and shall) play with the acceleration to decrease the torque requirements. While high end machines demonstrated accelerations above 10000 mm/s^2, a more common value is 4000 mm/s^2. Few software allow different acceleration for travel and printing, which is wise, as larger acceleration may reduce printing time, especially for some infill type as honeycomb. For comparison, the gravitational acceleration is 9810 mm/s^2 (on earth).

The only way to play with gravity is going in space (which was done in space station, anyway)...

Bigger is better ?

NO

• A bigger motor will generate more heat, which will be difficult to dissipate, as large stepper external area is not much higher than for a small stepper, and not in proportion of the generated heat
• A bigger stepper will makes more noise
• And the biggest problem is that you may experience vibrations with the bigger stepper, which are difficult to fight
• For a given current, a bigger stepper may not have a bigger torque at speed, it is fairly possible that the torque at maximum speed will be indeed, lower. So, the good choice of current is the current which could be reasonably handled by your board without heating too much (from 1.2 to 1.5A, depending the board), considering the set current may not exceed 85~90% of the stepper nominal current.

Using NEMA23 stepper motors for printers

For large machines, there are questions of the interest to use larger size steppers for movement or extruder, say Nema23 sized motors. However, Nema23 steppers are less optimised than Nema17 for micro-steps so there will be loss of precision. In addition, the rotating inertia is larger, so rapid change capacities may be reduced, driving to difficulties at corners. All steppers will have an increase of vibrations at medium step rates. This is called 'mid-band resonance'. NEMA 23 steppers may be more prone to have this problem, at a lower frequency than NEMA 17 stepper motors. So, it is preferable to use long NEMA 17 stepper motors than NEMA23. Electrically, larger motors will need more current, whatever their size.

I want it big !

For ceramic printer, multi-purpose printers or really big machines, you may want the most powerful setup.

Staying with Nema17 stepper, the larger one are 60mm long and could deliver 6.5 kg.cm torque. Those who could easily be found are intended for extruders with current 1.5A and inductance 6.5mH. However you could find the same dimensions with more appropriate winding for movement, with nominal current 2.1A and inductance 3mH. They could be driven by a thermally well designed board based on A4988 at 1.8A (like a genuine Smoothieboard), which is 86% of nominal current, good setup for reasonable stepper heat control.

For high current, the new Duet WiFi could effectively be used at 2A and future firmware revision may allow more current. The RDS(on) resistance of their driver is five time lower than A49xx series, generating a lot less heat.

Panucatt propose independent drivers BigFoot with nominal current of 3A in a new form factor, different from the Pololu. However, the only board (sept 2016) Gradus M1 which accept this form factor is for CNC, not for printers.

Going to larger steppers will drive you entering another world, with high end CNC drivers, higher voltage (36V to 70V), maybe feedback driven steppers and a much higher overall cost.

To use the highest possible current, you need well-cooled drivers, so you may want to use an 'integral' board with drivers soldered on the main board, sharing a much larger cooling area than 'pololu' style drivers. In this case, all drivers contribute to the overall board heating, and in order to limit the heat generation, you may use geared extruder instead of direct drive extruders, as steppers on geared extruder could be smaller and requires less current.

Another solution to handle high current is to use higher duty independent drivers as those used for CNC, like the 'Gecko' drivers or the Chinese M542.

Vibration insulators

It is a common experience to get vibrations from the steppers, generating noise and sometimes, transmitting the vibration to the whole printer structure.

You can find on the market vibration insulators under the reference Astrosyn MY17RMDAMP. Experience shows that they effectively decouple the stepper from its support. They possibly could introduce a slight imprecision in the movement.

You also find cork gaskets sold as vibration insulators, at a much lower cost than the Astrosyn. They are a good thermal insulator, but if they are installed with all 4 screws, the screws transmit the vibrations to the support and there is no vibration decoupling.

However, it is possible to have them acting as real vibration insulator if you un-tight the two screws that are not in tension. While the belt is in tension, you effectively only need two screw to maintain the motors. Removing the unneeded screws may effectively reduce the stepper motor noise and vibration, the stepper somewhat 'articulating' on the remaining two screws. These cork insulators are quite flexible and the stepper support shall be slightly reclined to take into account the angle due to belt tension.

Using 0.9° stepper (400 step per rotation)

There is a recurring question of the benefit of using 0.9° stepper for delta, as in some position, the delta geometry drive to a loss of precision in some axis.

Indeed, a stepper with twice the steps will be stiffer, as the mechanical stiffness of micro-step is not very high. Experiences show that for light effector and carriage as found in Kossel, there is a benefit, but limited. Larger machine with heavier effectors (dual metal hotend or extruder on effector) may benefit more of 0.9° steppers. While bought new, the price of such steppers is not much higher, so the extra-cost for the stepper is limited.

There is a significant drawback, then. To have the same speed, you need twice the steps. So, your stepper behave nearly like a 1.8° at twice the speed (not completely, as mechanical inertia is unmodified).

So, you are back to the speed problem as explained above and using 0.9° steppers may generally be associated with a 24V power supply. Note that at this voltage, the steppers will be 'singing' at low speed.

It is important to note that as the stepper behaviour is more stiff, the jerk values shall be reduced for 0.9° steppers to avoid loosing steps at corners.

Doubling the steps required for a given displacement implies the steps rate is doubled and some software running upon 8 bits processors may not be capable of such output. For a delta using 8 bits board, the choice of a well optimized software is critical, more so if you are using 0.9° steppers.

Using 24V with DRV8825 Drivers

The drivers we use in 3D printers are all PWM controlled, which means that the current is controlled by switching it off at frequent intervals, which makes the steppers behave like they are supplied with a voltage controlled driver. The frequency of switching, which may not be constant, is usually over 20kHz to not be audible by most humans.

In operation, the current is measured continuously to shut down the supply when the current set point is reached. However, the driver chips do have a minimum time while the current flow is 'open'.

With a 24V power supply, the current increases much more quickly than with 12V (this is the reason for using the higher voltage - it allows faster speeds) and on the DRV8825 the minimum on-time is too long and the current will overshoot the target, making the stepper miss microsteps, overheat, and making hissing/squealing noises. So drivers based upon DRV8825 should be avoided for any voltage over 12V and are generally not good drivers for 3D printers. The problem is less serious if you have high inductance stepper motors. However, using high inductance stepper is a poor choice for a printer as explained above.

There is an excellent article about the problems with this driver: This article details the use of diodes inline with the stepper motors to help solve this problem.

The traditional A4988 chip used in a lot of controllers does not suffer from that problem and is a good solution for printer if properly cooled by its bottom, the heat being dissipated by the bottom of the printed circuit board, which is where a heat-sink is most efficient.