Servo Drive Selection and Sizing: Power, Regeneration and Cable

Key Takeaway

Servo drive selection is arithmetic done backwards from the load: force at the process, torque at the screw, torque at the motor, RMS over the real duty cycle, then 3:1 peak headroom, then regeneration and cable sizing from the same numbers. Size the drive on RMS torque and everything else follows.

1. Start From the Load, Not the Catalogue

The wrong way to do servo drive selection is to open a catalogue, find a 1.5 kW drive in a good price band, and then look for a motor that fits it. That approach works until the first part is cut, and it fails in one of three ways: the motor saturates during the cut, the drive trips on overcurrent, or the axis runs beautifully empty and stutters under load. Servo drive selection is a sequence with a fixed order, and the sequence matters more than any single catalogue number.

The right way is to work backwards from the load. Every number in servo drive selection comes from the process: how much force the process needs, how fast, how often, and for how long. From that you get the torque at the motor, the RMS torque over the real duty cycle, the peak torque for the transient, the electrical power, the regeneration duty, and finally the cable. The catalogue comes in at the end, when the numbers are already known.

The five numbers you need before you shop

Servo drive selection is a sequence with a fixed order, and the sequence matters more than any single catalogue number. The servo motor sizing calculator on this site does the arithmetic from these five inputs. The rest of this article shows the arithmetic so that you can check it. Servo drive selection starts with these five numbers and nothing else, and a quotation built without them is a guess with a price attached.

2. Converting Force into Torque

Torque at the shaft is the only currency that matters in servo drive selection. A process force becomes a torque through the mechanical transmission, and the transmission is either a screw or a pulley. Every servo drive selection ends at a conversion like this one, because force is what the process knows about and torque is what the motor understands.

Ball screw drive

Every servo drive selection ends at a conversion like this one, because force is what the process knows about and torque is what the motor understands. For a screw drive, the force at the nut becomes a torque at the motor:

T = F x L / (2 x pi x efficiency)

where F is the process force in newtons, L is the lead in metres per revolution, and efficiency accounts for the friction in the nut and the screw. Ball screws are typically 90 to 95 percent efficient, so use 0.90 for a plain service axis and 0.95 for a preloaded ball screw with a return nut.

Work a real example. A vertical axis lifts a 50 kg workpiece, so F = 50 x 9.81 = 490.5 N. Add 20 percent for friction and cable drag on the carriage: F = 490.5 x 1.2 = 588.6 N. The screw has a 20 mm lead, so L = 0.020 m. With 90 percent efficiency:

T = 588.6 x 0.020 / (2 x 3.14159 x 0.90) = 11.77 / 5.6549 = 2.08 Nm

That 2.08 Nm is the static holding torque at the motor. The dynamic torque is higher because of acceleration, which is calculated in the next section.

Timing belt drive

A 40 mm pitch belt on a 30 mm radius pulley: T = 588.6 x 0.030 = 17.66 Nm. Belts are much cheaper than screw drives and much faster, but they have no positional accuracy, they stretch, and they need a tensioner. On a conveyor or a rotary indexer that is the correct trade. On a positioning axis it usually is not. A belt is chosen for cost and speed rather than for positioning accuracy, and servo drive selection has to accept that difference rather than pretend it is not there.

Do not forget gravity and the direction of travel

The vertical axis example above is a lifting load. A descending load makes the gravity term negative: the motor has to brake rather than push, and the regeneration comes back into the DC bus on every cycle. A horizontal axis has no gravity term, which is why horizontal axes are the easy case and vertical axes are where servo drive selection goes wrong. If the load can be driven into the floor by a jam, add a holding brake and size the motor to hold it with the brake released. The same problem appears in the motion control troubleshooting guide as an unexplained overcurrent fault on a Z axis.

3. Acceleration Torque and the Inertia Term

Torque is not only for holding the load. It is also for accelerating it, and this is the term most often left out of a servo drive selection calculation. A vertical axis is the case where servo drive selection most often goes wrong, because gravity is a continuous term and not a transient. In servo drive selection the acceleration term is where axes are usually undersized, because the static torque is what gets written down and the inertia term is what gets forgotten.

The force needed to accelerate a mass m at acceleration a is:

F_acc = m x a

The equivalent torque at the motor for a screw drive is:

T_acc = m x a x L / (2 x pi)

Continue the vertical axis example. The carriage plus workpiece is 70 kg, the axis must reach 1.5 m/s in 0.3 s, so a = 1.5 / 0.3 = 5 m/s^2. F_acc = 70 x 5 = 350 N. Through the 20 mm lead screw:

T_acc = 70 x 5 x 0.020 / (2 x 3.14159) = 7.0 / 6.2832 = 1.11 Nm

Add that to the static torque: T = 2.08 + 1.11 = 3.19 Nm peak. Add 20 percent for friction variation and for the transient when the load is not exactly at the commanded position, and the motor must produce 3.8 Nm peak.

The inertia ratio check

In servo drive selection the inertia term is where axes are usually undersized, because the static torque is what gets written down and the inertia term is what gets forgotten. Inertia ratio is the load inertia reflected to the motor divided by the motor rotor inertia. For a screw drive the reflected inertia of a translating mass is:

J_reflected = m x (L / (2 x pi))^2

For 70 kg and a 20 mm lead: (0.020 / 6.2832) = 0.003183 m, so J_reflected = 70 x 0.003183^2 = 70 x 1.0133e-5 = 7.09e-4 kg m^2. A typical 750 W servo motor has a rotor inertia of about 0.31e-4 kg m^2, giving an inertia ratio of 7.09e-4 / 0.31e-4 = 22.9:1. That is above the 10:1 limit for general work, which means the axis will need either a larger motor or a gearbox. The inertia ratio and servo oscillation guide explains what to do about it.

The practical rule: if the inertia ratio comes out above 10:1, step up one motor size and check again. A bigger motor has more rotor inertia, so this converges, but it costs money. If it comes out above 20:1, put a 10:1 gearbox on, which divides the reflected inertia by 100.

4. RMS Torque, Peak Torque and the Duty Cycle

This is the part of servo drive selection that separates a correctly sized drive from an oversized one, and it is where real money is saved or wasted. The RMS calculation and the peak headroom check are the two halves of servo drive selection that separate a correctly sized drive from one that is 20 percent too big.

The motor rating on the nameplate is the torque the motor can deliver continuously without exceeding its temperature rise limit. Peak torque is a short-duration rating, typically 3 times rated for 3 seconds. The drive has to be sized on the continuous number and checked against the peak number.

The RMS torque over a repeating cycle is:

T_rms = sqrt( (T1^2 x t1 + T2^2 x t2 + T3^2 x t3) / (t1 + t2 + t3) )

Take the vertical lift axis with this duty: 2 s of rapid traverse at 1.5 m/s, 1 s of dwell with the brake clamped, 1 s of controlled descent. The traverse needs the full 3.8 Nm. The dwell needs no torque. The descent needs the static torque minus the acceleration term, which is 2.08 – 1.11 = 0.97 Nm, plus a small amount for friction, so about 1.3 Nm.

Over a 4 second cycle:

T_rms = sqrt( (3.8^2 x 2 + 1.3^2 x 1) / 3 ) = sqrt( (14.44 x 2 + 1.69) / 3 ) = sqrt( 30.57 / 3 ) = sqrt(10.19) = 3.19 Nm

The motor must be rated at 3.19 Nm or more, and must produce 3.8 Nm peak. A motor rated 3.3 Nm with 10 Nm peak is the right choice. Had the axis been sized on the 3.8 Nm peak alone, it would be oversized by 19 percent, which means a bigger drive, a bigger cabinet, a bigger power supply and more heat to remove, for no benefit at all.

Quantity	Value	Where it comes from
Process force	588.6 N	50 kg load plus 20 percent friction
Static torque	2.08 Nm	F x L / (2 pi x efficiency)
Acceleration torque	1.11 Nm	m x a x L / (2 pi)
Peak torque	3.8 Nm	Static plus acceleration plus 20 percent
RMS torque	3.19 Nm	Over the real 4 s duty cycle
Reflected inertia	7.09e-4 kg m^2	m x (L / 2 pi)^2
Inertia ratio	22.9:1	Too high, needs a bigger motor or a gearbox

Peak headroom rule

The RMS calculation and the peak headroom check are the two halves of servo drive selection that separate a correctly sized drive from one that is 20 percent too big. After the RMS calculation, check that the peak torque fits inside the motor’s peak rating with margin. The standard rule is that peak torque should not exceed 85 to 90 percent of the motor’s peak rating, so that the drive does not sit at its limit during a transient that happens to coincide with a cold start or a high friction event. A 3:1 peak to rated ratio on the motor and a 90 percent utilisation limit gives you roughly 2.7:1 usable headroom over the RMS torque.

5. Electrical Power and Drive Current

Torque and speed give mechanical power. Mechanical power gives electrical power, and the electrical power sizes the drive, the supply and the cabinet. Once the numbers are settled, servo drive selection converts them into the electrical quantities that actually get ordered.

P_mech = 2 x pi x N x T / 60

At the traverse speed of 1.5 m/s with a 20 mm lead, the motor speed is N = 1.5 / 0.020 = 75 rpm. At the peak torque of 3.8 Nm:

P_mech = 2 x 3.14159 x 75 x 3.8 / 60 = 2 x 3.14159 x 285 / 60 = 1790.8 / 60 = 29.85 W

That is the peak mechanical power. The continuous power is set by the RMS torque: P = 2 x pi x 75 x 3.19 / 60 = 2 x 3.14159 x 239.25 / 60 = 1503.3 / 60 = 25.06 W. This is a small axis, and that is exactly why the drive should be small.

Current from power

Once the numbers are settled, servo drive selection converts them into the electrical quantities that actually get ordered. The drive current for a three phase 415 V supply with a servo drive power factor near 1 and 95 percent efficiency is:

I = P_elec / (1.732 x V x pf x eff)

With P_elec = 25.06 / (0.90 x 0.95) = 29.3 W, I = 29.3 / (1.732 x 415 x 0.98 x 0.95) = 29.3 / 668.8 = 0.044 A. That is a tiny drive, and it is the correct one. The peak of 3.8 Nm at 75 rpm needs 29.85 W mechanical and about 35 W electrical, so a 0.1 A drive would do. Most people would have specified a 1.5 kW drive here and paid four times the price for it.

Single phase versus three phase

For a 1 kW servo motor and drive pair, budget roughly Rs 65,000 to Rs 110,000 for the drive alone depending on the brand and the protocol, and Rs 18,000 to Rs 35,000 for the motor with an incremental encoder. Absolute encoders add about 25 to 40 percent to the motor price. A 3 kW pair runs from about Rs 1.6 lakh for the drive and Rs 55,000 to Rs 90,000 for the motor. Local brands such as Estun, Inovance and Step should be considered first for cost-driven builds, and the international names for the axes where the process value is high. On a single phase installation the current is roughly double for the same power, which changes the cable, the breaker and the transformer, and servo drive selection has to carry that through every line.

Motor and drive pricing moves with the brand, the protocol and the encoder, and servo drive selection has to price the axis as a system rather than as two items.

During deceleration the motor becomes a generator and the energy returns to the DC bus. If the drive has no regenerative unit and no brake chopper, that energy has nowhere to go: the DC bus voltage rises, the drive trips on overvoltage, and the axis stops. The three ways to handle it are a brake resistor, a regenerative unit that pushes the energy back to the supply, or a mechanical brake that absorbs it in friction.

6. Regeneration and the Brake Resistor

Regeneration is where servo drive selection turns into a cabinet decision and a heat removal problem. There are two distinct regeneration cases and they need different answers.

Two different calculations

Case 1: decelerating a moving mass. The kinetic energy is:

E = 0.5 x J x (omega2^2 – omega1^2)

With the 70 kg carriage through the 20 mm lead, the inertia at the motor is 7.09e-4 kg m^2. The motor omega at 1.5 m/s is 1.5 / 0.0031831 = 471.2 rad/s. Decelerating to zero:

E = 0.5 x 7.09e-4 x 471.2^2 = 0.5 x 7.09e-4 x 222,029 = 78.7 J

Decelerating at 5 m/s^2 takes 1.5 / 5 = 0.3 s, so the peak regeneration power is 78.7 / 0.3 = 262 W. But this is a transient that lasts 0.3 s out of a 4 second cycle, so the average regeneration power is 78.7 / 4 = 19.7 W. A brake resistor only has to handle the peak for the duration, and most drive brake choppers are rated for a duty cycle, not a continuous power.

Case 2: lowering a load against gravity. This is a continuous power and it does not go away. The static power needed to lower the load is:

P_regen = F x v = 588.6 x 1.5 = 883 W

and if the axis lowers continuously the drive is generating 883 W of heat that has to be removed from the cabinet for as long as the axis runs. A brake resistor for this case must be rated for 883 W continuous, not for the transient. This is the mistake that shows up as a drive that trips on overvoltage every time the axis goes down, or as a cabinet that cannot be closed because the resistor is too big to fit.

Sizing the resistor

A regenerative unit is the better answer when the axis regenerates continuously, or when the machine has several axes that are never all decelerating at once. It costs roughly Rs 35,000 to Rs 90,000 for a 5 kW unit and it needs a supply that can absorb the power, which usually means a 3-phase regenerative supply or a resistor bank on the supply side. The resistor is sized from the peak power and the duty cycle, and servo drive selection has to state both, because a resistor rated for the average will burn out in the first fast move.

The relation between torque and regeneration on a vertical axis is simple and worth memorising: with a screw lead of L metres and an efficiency of 0.9, a 588.6 N load regenerates 588.6 x L x 0.9 x v watts, which is 588.6 x 0.02 x 0.9 x 1.5 = 15.9 W per metre per second of speed.

7. The Cable, the Encoder and the Installation

The last part of servo drive selection is the part that determines whether the axis works reliably for five years or intermittently for five months. The cable is the last step in servo drive selection and the one most often skipped, which is why axes trip on undervoltage only at full speed.

Voltage drop

Work it: the vertical axis needs 0.044 A RMS, which is trivial, so the drop is not the issue there. But take a 3 kW axis at 8 A running 50 m on a 1.5 mm^2 cable. Loop resistance = 2 x 50 x 0.0175 / 1.5 = 1.167 ohm. Drop = 8 x 1.167 = 9.33 V. On a 415 V supply that is 2.25 percent, within the 3 percent guideline, so the cable passes. Now the same 3 kW axis at 40 m on 1.0 mm^2: R_loop = 2 x 40 x 0.0175 / 1.0 = 1.4 ohm, drop = 8 x 1.4 = 11.2 V = 2.70 percent. Still passes, but there is no margin for the motor drawing more current at low speed where the torque is highest. The feedback cable is a servo drive selection item even though it appears on a different purchase order, and a marginal feedback cable produces an axis that fails intermittently for years.

The rule that keeps this simple: use 1.5 mm^2 for motor power up to 16 A, 2.5 mm^2 up to 25 A, 4 mm^2 up to 40 A, and add a 3 to 5 percent margin for ambient temperature, since copper resistance rises about 0.39 percent per degree C. An Indian shop floor at 45 degrees C adds 2 percent to the resistance and therefore to the drop.

Encoder feedback cable

Use differential line driver (RS-422) encoder outputs on any machine with a spindle VFD. Single-ended HTL outputs will pick up noise from the drive output cables, and that noise appears as a following error spike that looks exactly like a tuning problem. The earth and shield arrangement belongs in servo drive selection because it is the difference between an axis that runs for five years and one that haunts the maintenance department.

Earth and shield

Bond the drive, the motor and the machine frame to a common earth bar with dedicated straps. Do not rely on the cable tray as an earth path. A servo system with multiple ground points is a servo system with a common mode voltage that the encoder signal has to fight, and that is what turns into a hunting axis two years after commissioning.

The broader installation detail is in the industrial motion control guide, and the coupling between the motor and the screw is covered in the shaft coupling guide.

8. The Servo Drive Selection Checklist and the Cost Roll-up

Work through this list before the parts order goes out. Every line is a number you can put in front of a customer. Putting servo drive selection and Indian prices together is the only way to quote an axis honestly.

1. Process force in newtons, with the friction and gravity allowance included.
2. Torque at the motor, from force and lead or radius, with the efficiency in the denominator.
3. Acceleration torque, from moving mass and required acceleration.
4. Peak torque, and the motor’s peak rating, with 10 to 15 percent unused.
5. RMS torque over the real duty cycle, and the motor’s continuous rating.
6. Inertia ratio, and the action if it exceeds 10:1 or 5:1.
7. Mechanical power at the traverse speed, and the electrical power with efficiencies.
8. Drive continuous current, and the peak current against the drive’s rating.
9. Regeneration: peak power and average power, and the brake resistor or regenerative unit.
10. Cable cross-section from the voltage drop calculation, and the encoder cable type.
11. Ambient derating for a 40 to 45 degree C shop floor and a sealed cabinet.

What it costs in India

Item	1 kW axis	3 kW axis	Notes
Servo motor with incremental encoder	Rs 18,000 to 35,000	Rs 55,000 to 90,000	Absolute encoder adds 25 to 40 percent
Servo drive, pulse train	Rs 65,000 to 110,000	Rs 1,60,000 to 2,60,000	EtherCAT or Profinet adds 20 to 40 percent
Motor power cable, per 10 m	Rs 3,500 to 7,000	Rs 6,000 to 12,000	Shielded, oil resistant
Encoder and feedback cable, per 10 m	Rs 4,000 to 9,000	Rs 5,000 to 11,000	Differential, shielded
Brake resistor 330 ohm 500 W	Rs 3,500 to 7,000	Rs 6,000 to 13,000	With thermal switch
Contactor, breaker and MCB	Rs 4,000 to 9,000	Rs 8,000 to 18,000	Not included in most quotes
Total axis, bare	Rs 95,000 to 1,65,000	Rs 2,45,000 to 4,05,000	Excludes cabinet and labour

Putting servo drive selection and Indian prices together is the only way to quote an axis honestly. The last row is the number to quote. Most axis quotations leave out the cable, the brake resistor and the protective devices, and then the machine builder finds them later at a markup. Every one of these three failures is an arithmetic error, and every one of them is prevented by servo drive selection being done in the right order.

What usually goes wrong

Three failures dominate. First, sizing on peak instead of RMS, which over-sizes the drive by 15 to 25 percent and wastes money on every axis. Second, forgetting that a vertical axis regenerates continuously, which produces a drive that trips on overvoltage on the way down. Third, an inertia ratio above 10:1 that makes the axis hunt, and then the fix applied is more gain rather than a bigger motor or a gearbox.

None of these three are difficult to avoid. All three are arithmetic, and the arithmetic is in the sections above.

Related Reading

• Industrial Motion Control: Complete Guide to Servo, Stepper and Axis Design
• Inertia Ratio and Servo Oscillation: Causes, Limits and Fixes
• Harmonic Drive Gearbox Selection: Ratio, Repeatability and Life
• Stepper Motor Sizing: Torque, Speed and Holding Torque Calculations

Sources

1. Yaskawa, Sigma-7 Servo Drive Series Operation Manual (rated and peak torque, regeneration)
2. Nidec, Servo Motor Sizing and Motor Selection Guide
3. IEC 61800-5-1, Adjustable speed electrical power drive systems: Safety requirements
4. IEC 60034-1, Rotating electrical machines: Rating and performance
5. Rockwell Automation, Regenerative Drive Systems and Braking Resistor Selection

Key Takeaways

• Servo drive selection means sizing the drive on RMS torque over the real duty cycle, not on the peak torque of the fastest move. On a typical 10 second machining cycle the difference is 15 to 25 percent.
• Keep at least 3:1 of peak headroom over rated torque. A drive that saturates its torque limit during a cut is a drive that will trip on the next part.
• Constant-speed regeneration is a continuous power, not a transient. A 490 W vertical load needs a brake resistor rated for 490 W continuous, not for the 5 J of kinetic energy in the moving mass.
• Cable voltage drop is a design calculation. For copper, loop resistance is 2 x length x 0.0175 / cross-section, and the drop is that resistance times the motor current.
• On a 40 degree C Indian shop floor, derate the drive for ambient and the cabinet. A 1 kW servo drive derated 15 percent still needs a 200 W heat exchanger in a sealed cabinet.