BIZOMAT MAKEOS · Power Transmission
Servo or Motor Duty Cycle Check (Move Profile, RMS and Peak)
For this move profile, what torque does the motor need to accelerate, run and stop the load, and is it within the motor’s continuous and peak ratings?
Duty-cycle sizing of a motor for a repeated trapezoidal move: acceleration, running, deceleration and dwell segments from the inertia at the motor, the top speed and the segment times, segment torques including friction or load torque, the RMS torque over the cycle (as the RMS torque tool) against the continuous rating, the peak torque against the peak rating, the inertia ratio and the energy returned on each deceleration.
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How this tool works
Inputs, units and where to find them
| Input | Unit | Typical source |
|---|---|---|
| Load inertia at the motor shaft | kg·m² | Inertia of the load and transmission referred to the motor shaft (divide load inertia by the ratio squared). |
| Motor rotor inertia | kg·m² | Inertia of the motor rotor (and brake, if fitted). |
| Top speed | rpm | Top speed of the move at the motor. |
| Acceleration time | s | Time to accelerate from rest to top speed. |
| Running time at top speed | s | Time at top speed. |
| Deceleration time | s | Time to decelerate to rest. |
| Dwell time | s | Rest time before the next move. |
| Friction or load torque while moving | N·m | Torque for friction and load while the axis moves (positive, opposing motion). |
| Holding torque during dwell | N·m | Torque the motor holds at rest (for a vertical axis without a brake). |
| Motor continuous (rated) torque | N·m | Continuous torque rating of the motor (from the maker). |
| Motor peak torque | N·m | Peak torque rating of the motor and drive (from the maker). |
| Motor maximum speed | rpm | Maximum speed of the motor. |
| Largest load-to-rotor inertia ratio | Largest inertia ratio you accept for good servo tuning (your value). |
What each input means
Open an input to see what it is, its units, the worked example and the common mistakes, with a small diagram.
What this means: Load inertia at the motor shaft
- What it is
- The rotating inertia of everything the motor drives (load, couplings, pulleys, screws, gearbox), all referred to the motor shaft.
- Units and format
- Enter a number in kg·m²: kilogram square metres (mass moment of inertia). The form accepts 0.000001 kg·m² to 10000 kg·m². Required: the tool does not calculate until every input is valid.
- Example
- The form opens with 0.006 kg·m² as a worked example. It is an illustration, not a recommended value: replace it with your own figure.
- Effect on the result
- More load inertia raises the acceleration torque and the inertia ratio.
- Get it right
- Refer load inertia to the motor by dividing it by the gear ratio squared; forgetting this overstates it hugely.
What this means: Motor rotor inertia
- What it is
- The inertia of the motor’s own rotor, plus any holding brake fitted, from the motor catalogue.
- Units and format
- Enter a number in kg·m²: kilogram square metres (mass moment of inertia). The form accepts 0 kg·m² to 10000 kg·m². Required: the tool does not calculate until every input is valid.
- Example
- The form opens with 0.002 kg·m² as a worked example. It is an illustration, not a recommended value: replace it with your own figure.
- Effect on the result
- It adds to the inertia the motor must accelerate; a larger rotor lowers the inertia ratio.
- Get it right
- Check whether the catalogue value includes the brake; add it if not.
What this means: Top speed
- What it is
- The highest speed the motor reaches in the move, at the motor shaft (after referring the load speed through any gearing).
- Units and format
- Enter a number in rpm: revolutions per minute. The form accepts 0.000001 rpm to 100000 rpm. Required: the tool does not calculate until every input is valid.
- Example
- The form opens with 3000 rpm as a worked example. It is an illustration, not a recommended value: replace it with your own figure.
- Effect on the result
- The inertia part of the acceleration and deceleration torques rises in proportion to the speed reached.
What this means: Acceleration time
- What it is
- The time the axis takes to speed up from rest to top speed at constant acceleration.
- Units and format
- Enter a number in s: seconds. The form accepts 0.000001 s to 600 s. Required: the tool does not calculate until every input is valid.
- Example
- The form opens with 0.2 s as a worked example. It is an illustration, not a recommended value: replace it with your own figure.
- Effect on the result
- A shorter acceleration time raises the acceleration torque and the peak.
- Get it right
- Seconds, not milliseconds.
What this means: Running time at top speed
- What it is
- The time the axis runs at constant top speed between accelerating and decelerating.
- Units and format
- Enter a number in s: seconds. The form accepts 0 s to 100000 s. Required: the tool does not calculate until every input is valid.
- Example
- The form opens with 0.6 s as a worked example. It is an illustration, not a recommended value: replace it with your own figure.
- Get it right
- Enter 0 for a triangular move with no constant-speed section.
What this means: Deceleration time
- What it is
- The time the axis takes to slow from top speed to rest at constant deceleration.
- Units and format
- Enter a number in s: seconds. The form accepts 0.000001 s to 600 s. Required: the tool does not calculate until every input is valid.
- Example
- The form opens with 0.2 s as a worked example. It is an illustration, not a recommended value: replace it with your own figure.
- Effect on the result
- A shorter deceleration time makes the braking torque larger.
What this means: Dwell time
- What it is
- The rest time at standstill before the next move starts, completing one full cycle.
- Units and format
- Enter a number in s: seconds. The form accepts 0 s to 100000 s. Required: the tool does not calculate until every input is valid.
- Example
- The form opens with 1.4 s as a worked example. It is an illustration, not a recommended value: replace it with your own figure.
- Effect on the result
- A longer dwell at zero holding torque lowers the RMS torque.
What this means: Friction or load torque while moving
- What it is
- The torque at the motor shaft that opposes motion while the axis moves: friction, process force and steady load, referred through any gearing.
- Units and format
- Enter a number in N·m: newton-metres. The form accepts 0 N·m to 1000000 N·m. Required: the tool does not calculate until every input is valid.
- Example
- The form opens with 3 N·m as a worked example. It is an illustration, not a recommended value: replace it with your own figure.
- Effect on the result
- It adds to the acceleration and running torque and reduces the braking torque.
- Get it right
- Enter it as a positive value at the motor shaft, not at the load.
What this means: Holding torque during dwell
- What it is
- The torque the motor must keep producing while stopped during the dwell, for example to hold a vertical axis without a brake.
- Units and format
- Enter a number in N·m: newton-metres. The form accepts 0 N·m to 1000000 N·m. Required: the tool does not calculate until every input is valid.
- Example
- The form opens with 0 N·m as a worked example. It is an illustration, not a recommended value: replace it with your own figure.
- Get it right
- Enter 0 for a horizontal axis or when a brake holds the load.
What this means: Motor continuous (rated) torque
- What it is
- The torque the motor can deliver continuously without overheating, from the maker’s data. The RMS torque of the cycle is compared with it.
- Units and format
- Enter a number in N·m: newton-metres. The form accepts 0.000001 N·m to 1000000 N·m. Required: the tool does not calculate until every input is valid.
- Example
- The form opens with 6 N·m as a worked example. It is an illustration, not a recommended value: replace it with your own figure.
- Get it right
- Use the continuous rating, not the stall or peak value.
What this means: Motor peak torque
- What it is
- The highest short-time torque the motor and its drive together can deliver, from the maker’s data. The largest torque in the cycle is compared with it.
- Units and format
- Enter a number in N·m: newton-metres. The form accepts 0.000001 N·m to 1000000 N·m. Required: the tool does not calculate until every input is valid.
- Example
- The form opens with 18 N·m as a worked example. It is an illustration, not a recommended value: replace it with your own figure.
- Get it right
- The drive’s peak current often limits this below the motor’s own peak.
What this means: Motor maximum speed
- What it is
- The highest speed the motor is rated for, from the motor data sheet.
- Units and format
- Enter a number in rpm: revolutions per minute. The form accepts 0.000001 rpm to 100000 rpm. Required: the tool does not calculate until every input is valid.
- Example
- The form opens with 3000 rpm as a worked example. It is an illustration, not a recommended value: replace it with your own figure.
What this means: Largest load-to-rotor inertia ratio
- What it is
- The largest ratio of load inertia to rotor inertia you accept for responsive servo tuning, from your practice or the drive maker’s guidance.
- Units and format
- Enter a plain number with no unit. The form accepts 0.5 to 100. Required: the tool does not calculate until every input is valid.
- Example
- The form opens with 10 as a worked example. It is an illustration, not a recommended value: replace it with your own figure.
- Get it right
- It only triggers a warning; it does not change the torques.
Method and formulas
- ω = 2π n ÷ 60; total inertia J_t = J + J_m.
- Acceleration torque = J_t ω ÷ t_a + T_f; running = T_f; deceleration = T_f − J_t ω ÷ t_d (negative = braking); dwell = holding torque.
- RMS = √(Σ T² t ÷ Σ t) (as the RMS torque tool); peak = the largest |T|.
- Inertia ratio = J ÷ J_m; energy returned per stop ≈ J_t ω² ÷ 2 − T_f ω t_d ÷ 2.
- Example: the move needs 15.566 N·m to accelerate; the RMS torque is 5.4835 N·m against 6 N·m continuous.
Limitations
- Trapezoidal profile with constant acceleration; S-curves lower the peak slightly.
- Motor heating also depends on speed; check the maker’s speed-torque curve.
- Example values are illustrations. Replace them with values for your actual task.
Typical uses
- Size a servo motor for an indexing or pick-and-place axis
- Check a motor for a faster cycle
- Estimate the braking resistor energy per stop
Who it is for
- Automation engineers
- Machine designers
- Controls engineers
What you get
- Segment torques
- RMS and peak torque against the ratings
- Inertia ratio and energy returned per stop
Interpreting the result
- Longer dwell lowers RMS torque; shorter acceleration raises the peak sharply.
References
- Machinery’s Handbook, 29th edition (Industrial Press, 2012), printed pp. 2569–2580, 180–186. Topic reference; no source tables or recommended settings are reproduced.
Learn the Concepts Behind This Tool
These BIZOMAT Library readings explain the method this tool uses, with worked examples.
Method explained here · BIZOMAT original book
Move profiles and RMS torque
In Inertia and Flywheels by the Numbers
What it covers: How to turn a repeated move into acceleration, run, deceleration and dwell torques, check RMS torque against a motor's continuous rating and peak torque against its peak, and choose the profile shape.
Method explained here · BIZOMAT original book
Permanent-magnet servo motors
In Permanent Magnets in Machines by the Numbers
What it covers: How magnets set a servo's torque constant, RMS and peak torque from the duty cycle, why hot magnets mean more current and heat, the drive's current limit, demagnetisation and back-EMF checks.
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Open the Servo or Motor Duty Cycle Check (Move Profile, RMS and Peak) calculator