Transmission and Motors
Understanding Motor Torque–Speed Curves
See why usable torque changes with speed and when reduction gearing helps.
You need to size or verify a real system using “Understanding Motor Torque–Speed Curves”, with units, duty and limits that match the application.
Read motor torque-speed envelopes, compare every cycle point with continuous and intermittent limits, and understand how a real gearbox changes speed, torque, inertia and control behavior.
- Select or check first
- 1. Describe the load cycle. Create speed-time and load-force or load-torque profiles including gravity, friction, process load, inertia, dwell and reversal.
- Controlling assumption
- Load, motion profile, geometry, alignment, duty, lubrication and environment match the selected mechanism and ratings.
- Top risk
- Stall torque is not full-speed torque. A brushed DC motor's idealized torque-speed line often begins at stall torque and falls toward no-load speed, but neither endpoint is a normal continuous operating point. A stepper holding-torque rating is measured at standstill under defined excitation.
- Proof
- 6. Commission and measure. Test worst defined cycles and record current or torque estimate, temperature, following error, vibration and regenerative behavior.
Start with the basics Optional foundation before “Understanding Motor Torque–Speed Curves”
Mechanical-design basics
Mechanical parts must carry loads, guide motion and remain aligned; similar-looking components can behave very differently under real force and duty.
- Force and torque
- Force pushes or pulls along a line. Torque is a turning effect equal to force multiplied by its perpendicular lever arm.
- Speed and acceleration
- Speed describes how fast position changes. Acceleration describes how fast speed changes and often creates the highest inertial load.
- Strength and stiffness
- Strength concerns permanent damage or failure. Stiffness concerns elastic deflection under load; a part can be strong enough yet too flexible for accurate motion.
- Load path
- The load path is the complete route by which force travels through shafts, bearings, fasteners, frames and foundations. Every interface on that route must be checked.
- Tolerance, clearance and alignment
- Tolerance permits controlled variation, clearance provides intentional space, and alignment keeps interacting axes or surfaces in the required relationship.
How to use this article: Sketch the load path and motion direction first, then attach units, worst-case loads, duty and acceptance limits to every calculation.
On this page
A motor does not have one usable torque value. It has a range of permissible torque-and-speed combinations, shaped by electromagnetic limits, drive voltage and current, heat removal and mechanical speed limits. The application also has a torque demand at each speed. A valid selection keeps every operating point inside the appropriate motor-drive envelope and keeps the repeating thermal demand inside the continuous region.
Read the axes, boundaries and test conditions first
Diagram description
The available torque remains near four newton-metres to about 3000 revolutions per minute and then falls toward one newton-metre at 5000 revolutions per minute. An example demand rises with speed. Their marked operating point at 3000 revolutions per minute and about 1.6 newton-metres sits below the available limit.
| Read | Question | Why it matters |
|---|---|---|
| Axes and units | Is speed rpm, rad/s or linear speed? Is torque N·m, mN·m, oz·in or another unit? | A correct shape with a wrong conversion still produces a wrong selection |
| Continuous boundary | Which region is permitted continuously under stated thermal conditions? | The cycle's equivalent heating must remain acceptable here |
| Intermittent boundary | How long and how often may the higher torque be used? | Peak capability is time-, speed-, drive- and temperature-limited |
| Supply and drive | Which voltage, current limit, amplifier and control method created the curve? | The same motor can have different high-speed capability with different electrical conditions |
| Thermal conditions | What ambient, mounting plate, heatsink or cooling method is assumed? | Reduced heat removal can shrink the continuous envelope |
| Mechanical limit | Is there a maximum motor, bearing, brake, gearbox or screw speed? | A torque-capable point can still be mechanically prohibited |
| Tolerance and derating | Are the curves typical, guaranteed or reference values? Are altitude or temperature factors required? | Catalogue lines may not be worst-case acceptance boundaries |
Graph orientation varies. Some catalogues put speed on the horizontal axis and torque on the vertical; others reverse them. Shade may indicate continuous and intermittent zones, or separate curves may represent different supply voltages. Read the legend rather than relying on the familiar appearance of the graph.
Why available torque often falls as speed rises
As a motor turns faster, its electrical and magnetic conditions change. In a stepper, winding inductance limits how quickly phase current reaches the commanded value; less current is established before commutation advances, so available torque usually falls. A higher compatible drive voltage can improve current rise and high-speed torque, but only within the motor-drive ratings. Resonance, load inertia and acceleration can further reduce the reliable operating region.
In a permanent-magnet servo, back electromotive force rises with speed and leaves less voltage available to force current through winding resistance and inductance. The drive eventually reaches a voltage limit. Some systems use field weakening above base speed, trading available torque for speed while respecting current, voltage and thermal constraints. An induction motor under variable-frequency control has its own constant-torque, base-speed and possibly constant-power regions. These general patterns never replace the exact curve.
Mechanical power explains the constant-power shape
P = T × ω
If available mechanical power is approximately constant above a base speed, torque must decrease as angular speed increases. At zero speed, mechanical output power is zero even when a motor develops stall or holding torque and produces substantial heat.
- P
- mechanical output power, W
- T
- shaft torque, N·m
- ω
- shaft angular speed, rad/s
A constant 2 kW mechanical output corresponds to about 6.37 N·m at 3000 rpm but only about 3.18 N·m at 6000 rpm. Real boundaries also reflect voltage, current, loss and speed limits.
Overlay the complete motion cycle—not one nominal point
| Interval | Speed and torque question | Common oversight |
|---|---|---|
| Start and acceleration | Can the system produce load, friction, gravity and inertia torque at each rising speed? | Checking peak torque only at zero speed |
| Constant-speed travel | Does process plus friction torque remain inside the continuous envelope? | Using motor rated power without checking actual shaft speed |
| Deceleration | What torque is needed to slow the inertia and what energy returns to the drive? | Assuming deceleration torque is simply the negative of acceleration when friction and gravity act |
| Dwell or holding | Is torque required at zero speed and can the motor reject that heat? | Treating zero mechanical power as zero electrical heating |
| Reversal | Are backlash, lost motion, peak torque and coupling or gearbox reversal limits acceptable? | Ignoring the change in contact and transient load |
| Disturbance and recovery | Is a brief overload inside the intermittent region and allowed duration? | Assuming the drive will provide unlimited peak current |
| Repeated cycle | Does RMS or manufacturer-equivalent torque remain in the continuous region at relevant speeds? | Using arithmetic-average torque for thermal sizing |
Check maximum torque at the speed where it occurs, then check the full repeating cycle with the manufacturer's thermal method. RMS torque is useful because winding heating broadly follows current squared, but a single RMS number cannot detect an out-of-envelope peak, excessive overload duration, excessive regeneration or a mechanical overspeed. All checks must pass.
What margin should look like
Margin is the documented distance between a requirement and a relevant limit after tolerances, load variation, friction change, voltage variation, ambient temperature, wear and modelling uncertainty are included. It is not one unexplained percentage copied onto every calculation. Too little margin risks trips or overheating; excessive motor and gearbox size can add inertia, cost, current, structure and tuning difficulty.
Record which curve and revision were used, whether it is guaranteed or typical, and which worst-case operating point sets each margin. Verify the commissioned system with current or torque estimates, speed, following error and temperature measurements.
A gearbox moves the operating point—but adds its own limits
Diagram description
A servo or DC gearmotor and a stepper with gearbox are shown on precision screw axes and slow chain drives. Notes explain higher output torque, lower output speed, positioning and backlash considerations, and that a gearbox does not automatically provide braking or self-locking.
Idealized speed and torque through a reduction gearbox
n_out = n_motor ÷ i, T_out ≈ T_motor × i × η
Here the reduction ratio i is greater than one and efficiency η is less than one. Starting efficiency, direction, temperature and load can differ from a catalogue nominal value. Verify both the gearbox's permissible continuous and peak output torque and the motor operating point.
- n_out
- gearbox output speed
- n_motor
- motor speed
- i
- reduction ratio, input speed divided by output speed
- T_out
- available output torque
- T_motor
- motor input torque
- η
- gearbox efficiency as a decimal
With a 10:1 reduction and 90% assumed efficiency, 1 N·m at the motor gives about 9 N·m at the output while output speed is one tenth of motor speed. The exact gearbox may have additional start, reversal and thermal limits.
Reduction also changes reflected inertia
J_load→motor = J_load ÷ i²
This ideal relationship can make a high-inertia load easier for the motor to accelerate and control. Add gearbox and coupling inertia at the correct shafts, and follow the motor and drive manufacturer's permissible inertia guidance.
- J_load→motor
- load inertia reflected to the motor shaft, kg·m²
- J_load
- load inertia at gearbox output, kg·m²
- i
- reduction ratio
A 10:1 reduction ideally reflects one hundredth of the external load inertia to the motor. It does not remove backlash, compliance, friction or output-bearing loads.
| Potential benefit | Added consequence | Verification |
|---|---|---|
| More output torque for a given motor torque | Efficiency loss and gearbox heating | Continuous, peak and thermal ratings in both directions |
| Lower output speed | Motor and gearbox maximum input speed | Every cycle point, lubrication and overspeed case |
| Lower reflected external inertia | Added gearbox, coupling and motor-side inertia | Complete inertia model and control response |
| Finer theoretical output increment | Backlash, lost motion, compliance and transmission error | Loaded reversal and final load-position measurements |
| Compact motor for a slow load | Added mass, length, noise, service and cost | Envelope, mounting, bearing loads and lifecycle comparison |
| Possible resistance to backdriving in some designs | Behavior varies with gear geometry, efficiency, wear and vibration | Never assume self-locking or safety holding without explicit verified design data |
A reliable curve-based selection check
- 1. Describe the load cycle.Create speed-time and load-force or load-torque profiles including gravity, friction, process load, inertia, dwell and reversal.
- 2. Choose a candidate transmission.Translate output speed, torque and inertia to the motor shaft using ratio and realistic efficiency.
- 3. Plot the motor-side points.Place maximum and representative cycle points on the exact torque-speed curves for the intended drive and supply.
- 4. Check continuous and intermittent rules.Verify RMS or equivalent thermal demand, every peak, overload duration, repetition and drive-current limit.
- 5. Check the complete drivetrain.Confirm motor, brake, coupling, gearbox, screw, bearings and load all pass their speed, torque, thrust, life and environmental limits.
- 6. Commission and measure.Test worst defined cycles and record current or torque estimate, temperature, following error, vibration and regenerative behavior.
Use Reading Motor Specs Before Buying Components to identify the conditions behind each curve, and Gear Ratio, Speed and Torque in Real Machines for the transmission calculations. If the chosen curve does not contain every required operating point with explainable margin, change the motor, drive, supply, ratio or motion—not the meaning of the curve.
One-minute questions
Questions to answer before you apply this lesson
What should I select or check first for Understanding Motor Torque–Speed Curves?
1. Describe the load cycle. Create speed-time and load-force or load-torque profiles including gravity, friction, process load, inertia, dwell and reversal.
Which assumption can change the conclusion?
Load, motion profile, geometry, alignment, duty, lubrication and environment match the selected mechanism and ratings.
What can go wrong if I copy the example directly?
Stall torque is not full-speed torque. A brushed DC motor's idealized torque-speed line often begins at stall torque and falls toward no-load speed, but neither endpoint is a normal continuous operating point. A stepper holding-torque rating is measured at standstill under defined excitation.
How do I verify the result in the real system?
6. Commission and measure. Test worst defined cycles and record current or torque estimate, temperature, following error, vibration and regenerative behavior.
Sources and further reading
- Servo Motor Sizing ConceptsYaskawa America, Inc. · 2026-10-12Primary technical document reviewed for continuous and intermittent speed-torque regions, maximum torque at application speed, motion profiles and RMS torque.
- All Servos Are Not Created EqualYaskawa America, Inc. · 2026-10-12Primary manufacturer paper reviewed for continuous versus intermittent torque, overload-time variation and thermal duty.
- Speed / Torque Curves — SGM Sigma Servo SystemYaskawa Electric America, Inc. · 2026-10-12Product-family curves reviewed as evidence that continuous and intermittent envelopes vary by exact model and supply class.
- 0.36° Geared Stepper Motor and Driver PackageOriental Motor U.S.A. Corp. · 2026-10-12Primary catalogue reviewed for supply-dependent speed-torque curves, permissible versus instantaneous torque, gear ratio, speed range and temperature conditions.
- How to Address Increased Loads in Size and Weight with a Stepper MotorOriental Motor U.S.A. Corp. · 2026-10-12Manufacturer education reviewed for the approximate relationship between motor torque, reduction ratio, efficiency and gearbox speed limits.
- S200 Servo Motors CatalogSiemens · 2026-10-12Primary catalogue reviewed for model-specific torque-speed curves, rated and maximum values, inertia and matched system conditions.