Stepper power-supply sizing

How it is worked out

Every number below the drive limits is a rule of thumb: a quick, safe starting point that works for most chopper-driven stepper machines. Each one is stated with its assumption, so you can see where your machine might differ. The drive limits come from the published Tiny Controls product data.

1. The bus voltage

V(motor)   = 32 × √L          L = phase inductance in mH          rule of thumb
V(ceiling) = drive maximum × 90%   regulated SMPS
           = drive maximum × 85%   linear supply
V(bus)     = lowest over all motors of  min( V(motor), V(ceiling) )

• 32 × √L is a widely used rule of thumb for chopper drives. Below it a motor loses torque sooner as speed rises. Above it the chopping current heats the motor iron with little extra benefit.
• The lowest motor governs because every drive on the machine shares one bus, and the motor with the lowest inductance is the one that overheats first.
• The 90% SMPS margin leaves room for energy returned by the motors while braking. A regulated output does not rise with the mains.
• The 85% linear margin is tighter. An unregulated bus follows the mains, and at +10% mains it reaches about 93.5% of the drive maximum before braking energy is added.
• For an SMPS the tool picks the largest standard output of 24, 36, 48, 60 or 72 V that is at or below the bus voltage and inside the drive range.

2. Supply current and SMPS wattage

I(supply) = 2/3 × Σ ( motors × rated phase current )     rule of thumb
P(load)   = V(bus) × I(supply)
SMPS      ≥ 1.25 × P(load), rounded up to 50, 100, 150, 200, 320, 350, 400, 480, 600, 800 or 1000 W

A chopper drive is itself a switch-mode converter. It connects the winding to the full bus voltage in short pulses and lets the winding inductance smooth them. The current in the winding is the set phase current, but the current drawn from the supply is roughly the power the motor uses divided by the bus voltage, and that is much less. The two phases are driven 90° apart, a stationary motor runs at reduced current, and several axes rarely accelerate hard at the same moment. Together these give the usual figure of two thirds. The Tstep-087 and Tstep-484 manuals give the same limit: a motor wired for high performance (parallel) draws no more than 2/3 of its rated phase current from the supply. The 25% SMPS headroom keeps the supply out of its current limit during simultaneous rapids.

3. Linear supply: transformer, bridge and capacitor

V(secondary, V AC)  = ( V(bus) + 1.4 ) / 1.414       rounded down to a whole volt
V(bus, no load)     = V(secondary) × 1.414 − 1.4
V(bus, mains +10%)  = V(secondary) × 1.10 × 1.414 − 1.4     must stay under the drive maximum
Transformer VA      = V(secondary) × I(supply) × 1.8
Reservoir C (µF)    = 80000 × I(supply) / V(bus)            rule of thumb
Capacitor voltage   ≥ 1.25 × V(bus, mains +10%)

• 1.4 V is two silicon bridge diodes conducting at about 0.7 V each. Unloaded, the capacitor charges to the peak of the secondary minus those drops. Under load the bus sags, which only adds margin.
• The secondary is rounded down so the bus lands at or below the target. Mains is assumed to rise up to 10% above nominal. That +10% check is the one that protects the drive.
• Form factor 1.8. A capacitor-input bridge draws current from the transformer in short, tall pulses near each peak, so the RMS current is about 1.4 to 1.8 times the DC current. The tool uses 1.8, the top of that range, because a large reservoir makes the pulses shorter and heats the winding more.
• 80000 × I / V gives a ripple of roughly 10% at 50 Hz mains, where the capacitor carries the load for up to 10 ms between charging peaks. The Tstep manuals ask for unregulated supply ripple of at most 10% of the DC voltage. Standard sizes run 1000, 1500, 2200, 3300, 4700 and 6800 µF in each decade.
• The Tstep-117X and Tstep-168X also accept AC. Their product pages list 18–80 V AC and 18–110 V AC, so a transformer secondary inside that range at +10% mains can be wired to the drive directly.

Worked example: the page as it opens

Four NEMA 23 motors, T57H76-2804 (2.8 A and 3.6 mH per phase on its product page): three on X, Y and Z and one on a slave axis, each on a Tstep-087X (18–80 V DC).

32 × √3.6               = 60.7 V     the same for all four motors
SMPS ceiling            = 0.90 × 80 = 72 V      so the target stays 60.7 V
Standard SMPS voltage   = 60 V       largest of 24/36/48/60/72 at or below 60.7 V
Phase currents          = 4 × 2.8 = 11.2 A
Supply current          = 2/3 × 11.2 = 7.47 A
Load                    = 60 × 7.47 = 448 W
With 25% headroom       = 560 W      so a 60 V, 600 W SMPS (10 A)

Linear ceiling          = 0.85 × 80 = 68 V      the target stays 60.7 V
Secondary               = (60.7 + 1.4) / 1.414 = 43.9 V AC, so 43 V AC
Bus, no load            = 43 × 1.414 − 1.4 = 59.4 V
Bus at mains +10%       = 43 × 1.10 × 1.414 − 1.4 = 65.5 V      under 80 V
Transformer             = 43 × 7.47 × 1.8 = 578 VA, so 600 VA
Reservoir               = 80000 × 7.47 / 59.4 = 10054 µF, so 15000 µF
Capacitor voltage       ≥ 1.25 × 65.5 = 81.9 V, so 100 V

Why more voltage buys speed, not holding torque

Torque follows winding current. At standstill the drive chopper holds the current at its setting whatever the bus voltage, so a motor holds exactly the same torque on 24 V as on 72 V. Once it turns, every step asks the current to reverse through the winding inductance. The current rises at a rate of roughly (V(bus) − back-EMF) / L, and back-EMF grows with speed. When a step lasts less time than the current needs to reach its setting, the motor never gets its full current and torque falls away. A higher bus voltage makes the current rise faster, so full current, and full torque, holds to a higher step rate. The cost is heat from the faster, harder chopping, which is why the voltage is capped at 32 × √L.

Braking energy

A motor slowing a heavy load, or lowering a vertical axis, works as a generator, and the drive passes that energy back to the supply. The Tstep-087 and Tstep-484 manuals warn that if the supply cannot absorb it, the voltage can climb past the drive limit and damage the drive and the supply. A linear supply stores some of it in the reservoir capacitor. An SMPS cannot take current back, so its output rises until something trips. For heavy or vertical axes, keep the bus well under the drive maximum, add bulk capacitance near the drives, or fit a shunt (braking) regulator.

From the Tstep manuals

• With an SMPS, fit a 470 µF / 100 V capacitor across the drive supply terminals, as close to the drive as possible.
• If the supply leads are longer than 12 inches (about 300 mm), fit a 100 µF capacitor across the supply terminals at the drive.
• Several drives can share one supply if its filter capacitor is sized for the combined load. Run a separate pair of leads from each drive back to the supply.
• Switch the supply on its AC side, never on the DC side. A loose DC lead acts like a switch and can trip the drive.
• Do not share the motor supply with low-level logic circuitry. Power the controller and I/O from their own supply, at the voltage their manuals give.

Drive limits used

These are the supply-voltage and output-current rows on each product page. The Tstep-087 and Tstep-484 operation manuals give the same voltage ranges. One Tstep-484 manual lists current settings up to 4.2 A; the tool keeps to the 4 A on the product page.

What this tool does not cover

• Series-wired 6- and 8-lead motors, closed-loop and servo drives, spindles and VFDs.
• The controller and I/O supply. Size that separately from the controller manual.
• Duty cycle, enclosure temperature and derating. The rules of thumb assume an ordinary machine tool at room temperature.