BIZOMAT MAKEOS · Power Transmission
RMS Torque for a Motor Duty Cycle
What is the RMS torque of this duty cycle, and can the motor carry it continuously?
Root-mean-square (thermal) torque and peak torque over a repeating duty cycle of up to five segments, compared with a motor’s continuous and peak torque ratings.
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How this tool works
Inputs, units and where to find them
| Input | Unit | Typical source |
|---|---|---|
| Segment 1 | ||
| Torque | N·m | Torque in segment 1 (accelerating, for example). |
| Duration | s | Duration of segment 1. |
| Segment 2 | ||
| Torque | N·m | Torque in segment 2 (constant speed). |
| Duration | s | Duration of segment 2. |
| Segment 3 | ||
| Torque | N·m | Torque in segment 3 (decelerating, negative if braking). |
| Duration | s | Duration of segment 3. |
| Segment 4 | ||
| Torque | N·m | Torque in segment 4 (dwell, 0 if standing). |
| Duration | s | Duration of segment 4. |
| Segment 5 | ||
| Torque | N·m | Torque in segment 5 (0 if not used). |
| Duration | s | Duration of segment 5. |
| Motor | ||
| Continuous rated torque | N·m | Motor continuous (rated) torque at the operating speed. |
| Peak torque rating | N·m | Motor or drive peak torque. |
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.
Segment 1
What this means: Torque
- What it is
- The motor torque needed during the first segment of the repeating cycle, often the acceleration segment: load torque plus inertia torque.
- Units and format
- Enter a number in N·m: newton-metres. The form accepts -1000000 N·m to 1000000 N·m. Required: the tool does not calculate until every input is valid.
- Example
- The form opens with 12 N·m as a worked example. It is an illustration, not a recommended value: replace it with your own figure.
- Get it right
- Torque from the load side must be referred to the motor shaft through the gear ratio and efficiency first.
What this means: Duration
- What it is
- How long the first segment of the cycle lasts. A segment with zero duration is left out.
- 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 0.2 s as a worked example. It is an illustration, not a recommended value: replace it with your own figure.
- Get it right
- Enter seconds, not milliseconds.
Segment 2
What this means: Torque
- What it is
- The motor torque needed during the second segment of the cycle, often running at constant speed against friction and process load.
- Units and format
- Enter a number in N·m: newton-metres. The form accepts -1000000 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.
What this means: Duration
- What it is
- How long the second segment of the cycle lasts.
- 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.
Segment 3
What this means: Torque
- What it is
- The motor torque during the third segment, often deceleration. Braking torque is entered as negative; its sign does not change the result because torque is squared.
- Units and format
- Enter a number in N·m: newton-metres. The form accepts -1000000 N·m to 1000000 N·m. Required: the tool does not calculate until every input is valid.
- Example
- The form opens with -10 N·m as a worked example. It is an illustration, not a recommended value: replace it with your own figure.
What this means: Duration
- What it is
- How long the third segment of the cycle lasts.
- 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 0.2 s as a worked example. It is an illustration, not a recommended value: replace it with your own figure.
Segment 4
What this means: Torque
- What it is
- The motor torque during the fourth segment, often a dwell. A standstill with no holding load is zero torque but still counts as time.
- Units and format
- Enter a number in N·m: newton-metres. The form accepts -1000000 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
- Keep dwell time in: it lets the motor cool and lowers the RMS torque.
What this means: Duration
- What it is
- How long the fourth segment of the cycle lasts, including any dwell at standstill.
- 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 s as a worked example. It is an illustration, not a recommended value: replace it with your own figure.
Segment 5
What this means: Torque
- What it is
- The motor torque during an optional fifth segment of the cycle. Leave its duration at zero if there is no fifth segment.
- Units and format
- Enter a number in N·m: newton-metres. The form accepts -1000000 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.
What this means: Duration
- What it is
- How long the optional fifth segment lasts. Zero leaves it out of the 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 0 s as a worked example. It is an illustration, not a recommended value: replace it with your own figure.
Motor
What this means: Continuous rated torque
- What it is
- The torque the motor can deliver continuously without overheating at the operating speed, from the motor data sheet or torque-speed curve.
- 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
- Read it at the actual operating speed; continuous torque often falls at higher speeds.
What this means: Peak torque rating
- What it is
- The highest torque the motor and drive together can deliver for short periods, from the motor or drive data sheet, whichever is lower.
- 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 current limit often sets the peak torque below the motor’s own rating.
Method and formulas
- T_rms = √(Σ Tᵢ² tᵢ ÷ Σ tᵢ), including dwell time at zero torque.
- Peak = largest |Tᵢ|.
- Motor acceptable when T_rms ≤ continuous rating and peak ≤ peak rating.
- Example: the default cycle has T_rms = 5.2058 N·m and a peak of 12 N·m.
Limitations
- Torque only; speed and the motor’s thermal time constant also matter for long cycles.
- Dwell segments help cooling only if the motor is actually at zero torque.
- Example values are illustrations. Replace them with values for your actual task.
Typical uses
- Size a servo or VFD motor for an indexing or reciprocating cycle
- Check that a motor will not overheat
- Compare motion profiles
Who it is for
- Automation engineers
- Electrical engineers
What you get
- RMS torque
- Peak torque
- Utilisation of continuous and peak ratings
Interpreting the result
- Keep a margin (often 20%) below the continuous rating for ambient temperature and ageing.
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
The motor at low and high speed
In Variable-Speed Drives by the Numbers
What it covers: How load torque changes with speed for conveyors, fans and pumps, why a self-cooled motor overheats at low speed under constant torque, and what field weakening gives above rated speed.
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