How to Size a Servo Drive for Multi-Axis Loads

Why Multi-Axis Sizing Differs From Single-Axis Design

Sizing a servo drive for a single axis is straightforward. You match the motor torque to the load torque. Multi-axis systems are different. Each axis operates independently, but the power supply, cooling, and control bus share resources. A mis-sized drive in one axis can starve power from another, causing communication errors or position drift.

Consider a packaging line with three synchronized axes. If the first axis initiates a rapid acceleration, it draws a large current spike from the shared power supply. If the supply is undersized or the bus voltage droops, the second axis may fail to maintain its tracking error. The controller detects a loss of synchronization and halts the line. The root cause is not a mechanical fault in the second axis. It is a sizing mismatch in the shared power architecture.

The goal of servo drive sizing is to find the smallest drive that handles peak acceleration, continuous load, and environmental stress without triggering thermal or current faults. Over-sizing wastes capital and increases system cost. Under-sizing leads to stalling, missed moves, or permanent damage.

Before starting calculations, gather the mechanical drawings and motion profiles. You need the inertia of all moving parts, the load torque, the gear ratios, and the acceleration requirements. Without these numbers, any sizing estimate is a guess. You must also account for the specific control environment. A drive operating in a high-vibration environment requires different thermal margins than one housed in a climate-controlled cabinet. The mechanical layout dictates the heat dissipation path. If the drive is mounted in a tight enclosure, the effective thermal rating is lower than the datasheet value suggests.

Prerequisites: Data Required for Accurate Calculation

Do not begin sizing until you have the following data in hand:

1. Motor specifications: Rated torque, peak torque, rated speed, and thermal constants.
2. Load specifications: Static friction, dynamic friction, and external load torque.
3. Inertia data: Rotational inertia of the motor, gearbox, and load.
4. Mechanical advantages: Gear ratios and belt pulley ratios between the motor and load.
5. Motion profile: Maximum acceleration and deceleration values, and the duty cycle.

If you do not have the exact inertia of the load, estimate it conservatively. An under-estimated inertia leads to an under-sized drive. A motor that cannot accelerate the load within the specified time will stall, regardless of its continuous torque rating.

Inertia estimation is often the source of error in early-stage designs. If the load is a rotating drum, you need its mass distribution. A solid cylinder has a different inertia than a hollow tube of the same mass. Use the parallel axis theorem if the center of rotation is not at the geometric center. For belt-driven systems, do not forget the inertia of the pulleys. They rotate at the motor speed and add directly to the reflected inertia. A small pulley may seem negligible, but if it has a large mass, its contribution to the acceleration torque can be significant.

Friction data is equally critical. Static friction is the torque required to start motion. Dynamic friction is the torque required to maintain constant speed. If the load includes a conveyor belt, friction increases with belt tension. If the load includes a vertical lift, gravity is a constant load torque that changes sign during retraction. You must model these forces as functions of position or direction. A simplified constant torque model may fail for high-precision positioning systems where friction variation causes steady-state errors.

Step 1: Reflect Load Torque to the Motor Shaft

The first step in servo load calculation is converting the load torque to the motor shaft. This accounts for mechanical advantages and losses.

Use the formula:
Reflected Load Torque = Load Torque x Gear Ratio / Efficiency

Efficiency is typically between 80% and 95% for gearboxes. Use the lower end for conservative sizing. If the system uses belts or chains, use the efficiency of the specific transmission type.

Reason: The drive must overcome friction and mechanical losses. Ignoring efficiency results in a drive that is too small for the actual torque demand at the motor shaft.

Gearbox efficiency varies with speed and torque. At low speeds, lubrication is thicker, and efficiency drops. At high loads, gear meshing forces increase, reducing efficiency further. A planetary gearbox may operate at 95% efficiency under light load but drop to 90% under maximum torque. Use the minimum expected efficiency for the operating range.

For belt drives, the efficiency depends on the belt type and tension. V-belts and toothed belts have different loss characteristics. Toothed belts generally offer higher efficiency and less slippage. If the system uses a harmonic drive, the efficiency is highly dependent on the load torque. These reducers can be very efficient at low torque but lose efficiency significantly as the load approaches the rated torque. Always check the manufacturer’s efficiency curve, not just a single nominal value.

Step 2: Calculate Inertial Torque Demand

Torque required for acceleration is separate from load torque. This is the inertial component.

Use the formula:
Inertial Torque = (Total Reflected Inertia) x (Angular Acceleration)

Total reflected inertia is the sum of the motor inertia and the load inertia reflected to the motor shaft. The load inertia must be divided by the square of the gear ratio.

Reason: Acceleration is where torque demand spikes. A drive that is sized only for continuous load will drop speed when the system must accelerate rapidly.

Angular acceleration is derived from the linear acceleration or the required change in position over time. If the motion profile specifies a move of 100 mm in 0.5 seconds with a trapezoidal profile, you can calculate the maximum acceleration phase. The peak acceleration occurs during the ramp-up phase. This peak acceleration determines the maximum inertial torque demand.

A common mistake is using the average acceleration for the entire move. Servo drives must handle the peak instantaneous demand, not the average. A short, high-acceleration burst requires significantly more torque than a slow, steady ramp. If the motion profile includes a jerk limit, the acceleration profile is smoother, and the peak torque is lower. However, if the profile is a step command or a fast ramp, the torque demand is much higher.

Step 3: Sum Continuous and Peak Torque Requirements

Add the reflected load torque and the inertial torque. This gives you the torque required at any point in the motion cycle.

Total Torque Demand = Reflected Load Torque + Inertial Torque

Identify the peak value. This occurs during acceleration. The continuous value occurs during constant speed. The drive must handle the peak without tripping its overcurrent protection.

Reason: Peak torque determines the current limit of the drive. The drive controller adjusts current based on the commanded acceleration. If the peak torque exceeds the drive’s capability, the axis will not reach the target speed.

The total torque demand is not constant. It changes as the load torque varies and as acceleration transitions to constant speed. You must identify the maximum instantaneous sum. This maximum value is the peak torque requirement. The continuous torque requirement is the average torque during the constant speed phase, or the RMS value if the load is variable.

If the load torque is negative during a phase of the cycle (for example, when lowering a weight), it reduces the total torque demand. However, the drive must still be capable of handling the braking torque to prevent the load from accelerating uncontrollably. This is where regenerative braking comes into play, which is addressed in the common mistakes section.

Step 4: Apply a Safety Margin for Friction and Shock

Add a safety margin to your calculated torque. A standard practice is to add 20% to 30% to the peak torque calculation.

Sized Torque = Total Torque Demand x 1.2

Reason: Friction coefficients change with temperature and lubrication. Mechanical shock from external forces or loose components creates transient torque spikes. A margin prevents the drive from hitting its current limit during normal operation.

The safety margin is not just for theoretical uncertainties. It accounts for real-world variations. Lubrication can thicken in cold start conditions. Bearings can degrade over time, increasing friction. A loose coupling can introduce mechanical shock during acceleration. These factors create torque spikes that are not captured in the ideal motion profile.

A 20% margin is often sufficient for well-designed, well-maintained systems. A 30% margin is recommended for harsh environments or systems with unknown friction characteristics. Do not exceed 50% without a clear justification, as this leads to significant over-sizing and cost increases.

Step 5: Check Power and Voltage Constraints

Torque is not the only factor. Check the power requirements.

Power = Torque x Angular Velocity

Ensure the drive can supply the required voltage and current. High-speed, low-torque axes demand high current at low speeds. Low-speed, high-torque axes demand high voltage.

Reason: A drive may have sufficient torque capability but insufficient voltage headroom. If the drive voltage is too low, the motor will not reach its rated speed, causing position errors.

The power rating of the drive must be sufficient to sustain the maximum power demand. This often occurs during acceleration at high speed. Check the power curve of the motor. A motor may have a constant torque region and a constant power region. Beyond the base speed, the torque capability drops as speed increases. The drive must be able to supply the voltage required to reach the target speed.

Voltage drop in the power cables is a practical concern. If the power supply is far from the drive, the voltage at the drive terminals may be lower than the supply voltage. A low voltage causes the drive to limit current to protect the motor, reducing torque capability. This can cause missed moves or tracking errors. Ensure the power supply has enough headroom to maintain the required voltage under full load.

Step 6: Verify Thermal Duty Cycle

Servo drives have thermal limits. A drive that can handle a peak torque for one second may overheat if that peak is repeated every few seconds.

Calculate the RMS torque over the motion cycle.

RMS Torque = sqrt((Torque1^2 x Time1 + Torque2^2 x Time2) / Total Time)

Compare the RMS torque to the drive’s continuous torque rating.

Reason: Thermal protection trips the drive when internal temperature rises. RMS calculation ensures the drive does not overheat during repetitive operation. If the RMS torque exceeds the rating, the drive will reduce output or shut down.

The RMS torque is a measure of the average heating effect over the entire motion cycle. It accounts for the time spent at each torque level. A drive operating at 50% torque for 10 seconds and 100% torque for 2 seconds has a different thermal load than one operating at 100% torque for 12 seconds. The RMS value captures this average.

Check the drive’s thermal derating curve. Many drives reduce their continuous torque rating as the ambient temperature increases. If the drive is in a hot enclosure, the effective continuous torque may be 80% of the rated value. You must size for the actual ambient conditions, not the nominal datasheet value.

Step 7: Select the Drive and Motor Combination

Choose a drive whose rated torque exceeds your calculated RMS torque. Ensure its peak torque exceeds your calculated peak torque plus the safety margin.

Check the motor’s current capability. The motor must be able to handle the peak current commanded by the drive.

Reason: The drive and motor must be matched. A drive that commands more current than the motor can handle will damage the windings. A motor that cannot sustain the commanded torque will stall.

The drive and motor are a system. The drive provides the electrical power, and the motor converts it to mechanical torque. They must be compatible in terms of voltage, current, and thermal characteristics. A high-power drive with a low-inertia motor may overheat the motor during peak acceleration. A low-power drive with a high-inertia motor will not be able to accelerate the load quickly enough.

Check the current rating of the motor. The peak current commanded by the drive must not exceed the motor’s peak current rating for the duration of the peak torque. If the peak torque is required for more than a few seconds, the motor’s thermal rating becomes the limiting factor, not the instantaneous current capability.

Common Mistakes in Multi-Axis Sizing

• Ignoring reflected inertia: Calculating torque based only on load torque misses the acceleration demand.
• Using ideal efficiency: Assuming 100% gearbox efficiency underestimates required torque.
• Neglecting deceleration: Regenerative braking during deceleration can overload the DC bus, requiring a larger drive or braking resistor.
• Oversizing for peak only: Selecting a drive based solely on peak torque leads to high cost and poor efficiency.
• Ignoring bus voltage: Mismatched voltage between the drive and power supply causes communication errors or immediate faults.

Regenerative braking is a critical factor often overlooked. When the load is decelerated, it acts as a generator and sends power back to the DC bus. If the power supply cannot absorb this energy, the bus voltage rises. The drive will trip on overvoltage if the voltage exceeds the limit. You must calculate the regenerative power during deceleration. If the average regenerative power exceeds the power supply’s absorption capability, you need a braking resistor or a DC bus capacitor bank.

Bus voltage mismatches are a common cause of system failures. If the power supply is 400V and the drive is rated for 230V, the drive will fault immediately. Even small mismatches can cause problems. A 230V drive may not tolerate a 260V supply without damage. Check the voltage tolerance of the drive and ensure the power supply is within that range.

Final Verification Step

After selecting the drive, run a simulation or a test with the mechanical load. Verify the following:

1. Check the drive’s current profile during a full motion cycle. Ensure it does not hit the overcurrent limit.
2. Monitor the DC bus voltage. It should remain within the drive’s specified range.
3. Measure the motor temperature after a full duty cycle. It should remain below the rated temperature.
4. Verify position accuracy. If the axis drifts, the torque may be insufficient for friction compensation.

Reason: Calculations are estimates. Physical testing confirms the drive handles the real-world load. If the test shows faults, revisit the torque calculations and increase the drive size.

Simulation is a valuable tool before physical testing. It can predict thermal behavior and current profiles. However, simulation models rely on accurate parameters. If the friction model is wrong, the simulation will be misleading. Physical testing is the final validation.

During testing, use a thermal camera to monitor the motor and drive. Hot spots can indicate poor mounting or inadequate cooling. Check the bus voltage under load. A droop of more than 5% can cause issues. Verify position accuracy by running a long cycle and measuring the cumulative error. Drift indicates that the torque is insufficient to overcome friction or that the encoder is misaligned.

If the test reveals faults, do not simply increase the drive size. Identify the root cause. Is the friction higher than expected? Is the inertia underestimated? Is the power supply undersized? Fixing the root cause is more effective than over-sizing the drive.

Table: Torque Calculation Reference

Parameter	Formula	Typical Range
Reflected Load Torque	Load Torque x Gear Ratio / Efficiency	0.5 Nm to 500 Nm
Inertial Torque	Total Inertia x Angular Acceleration	0.1 Nm to 50 Nm
Peak Torque	Reflected Load + Inertial Torque	1.0 to 1.5 x Continuous
RMS Torque	Square Root of Mean Square Torque	Close to Continuous Rating
Safety Margin	1.2 to 1.3 x Peak Torque	Standard Engineering Practice
Power Rating	Torque x Angular Velocity	10 W to 5 kW