Engineering Reference
Motor Electrical and Mechanical Parameters Reference
Quick-reference motor torque, speed, power, Kv, Kt, back EMF, stall current, copper loss, efficiency, PWM, gearing, units, and engineering boundaries.
- Reading Time
- 14 min
- Format
- Parameter lookup
- Updated
- September 27, 2026
Motor Parameter Lookup
| Parameter | Symbol | Unit | Meaning | Boundary |
|---|---|---|---|---|
| Torque | τ | N·m | Rotational effort at a stated shaft and operating point | Distinguish motor-shaft, gearbox-output, continuous, peak, and stall torque |
| Speed | n, ω | rpm, rad/s | Mechanical rotational rate | ω = 2πn/60 |
| Mechanical power | Pmech | W | Shaft output power | Pmech = τω; zero at ideal zero speed even when stall current is high |
| Terminal voltage | V | V | Applied motor-terminal voltage | Driver drop and PWM waveform can differ from supply voltage |
| Armature current | I | A | Current producing torque and copper loss | Continuous and transient thermal limits differ |
| Winding resistance | R | Ω | DC phase or terminal resistance at a stated temperature | Copper resistance rises with temperature |
| Back EMF | E | V | Speed-proportional generated voltage opposing applied voltage | E ≈ Keω under the adopted SI model |
| Torque constant | Kt | N·m/A | Torque per ampere under stated current convention | Peak, RMS, phase, and line-current conventions must match |
| Speed constant | Kv | rpm/V | No-load-like speed per effective volt under stated convention | Not a voltage rating; inverse relation to Kt requires consistent SI conventions |
| Copper loss | Pcu | W | Resistive winding loss | Pcu = I²R for the same winding/current convention |
| Efficiency | η | % | Useful output divided by input | State motoring/generating direction and included losses |
| Stall current | Istall | A | Ideal initial current at zero speed | Istall ≈ V/R; often destructive if sustained |
| PWM duty cycle | D | ratio, % | Fraction of switching period commanded on | Average-voltage model does not predict ripple, torque dynamics, or driver losses |
| Gear ratio | G | ratio | Input speed divided by output speed in this reference | Ideal torque multiplies by G; real output includes gearbox efficiency |
Core Relationship Index
| Relationship | Ideal expression | Conditions |
|---|---|---|
| Speed conversion | ω = 2πn/60 | n in rpm; ω in rad/s |
| Mechanical power | Pmech = τω | Torque and speed at the same shaft and operating point |
| DC terminal model | V ≈ E + IR | Steady-state brushed DC boundary; add driver/brush drops as needed |
| Back EMF | E ≈ Keω | Ke and speed units must match |
| Torque | τ ≈ KtI | Current convention and loss torque must be stated |
| Stall current | Istall ≈ V/R | Zero speed, ideal initial electrical boundary |
| Copper loss | Pcu = I²R | Same winding and current convention |
| Efficiency | η = Pout/Pin | Use consistent power direction and included losses |
| PWM average voltage | Vavg ≈ DVdc | Ideal switching boundary, not a dynamic speed law |
| Gearbox | nout = nin/G; τout ≈ τinGηg | G = input/output speed ratio |
Operating-Point Interpretation
| Condition | Speed | Current / torque | Power and thermal note |
|---|---|---|---|
| No load | Near maximum for applied voltage | Enough current for friction and internal loss | Output power is small; no-load speed is not a loaded rating |
| Rated continuous | Specified operating speed | Within continuous current/torque and temperature-rise limits | Preferred thermal comparison point |
| Peak / transient | Load-dependent | Above continuous level for limited duration | Duration and starting temperature matter |
| Stall | Zero | Maximum ideal current and torque | Mechanical output is zero while copper heating is severe |
| Regeneration | Driven by load | Power can flow back toward the bus | Controller and supply must accept or dissipate energy |
Worked Reference Examples
| Case | Inputs | Ideal result | Interpretation |
|---|---|---|---|
| Shaft power | τ = 0.5 N·m, n = 3000 rpm | ω = 314.159 rad/s; P = 157.08 W | Both values must refer to the same shaft |
| Stall current | V = 12 V, R = 0.6 Ω | 20 A | This is an initial ideal estimate, not a safe continuous current |
| Copper loss | I = 5 A, R = 0.4 Ω | 10 W | Hot-winding resistance raises loss for the same current |
| PWM voltage | 24 V bus, D = 40% | 9.6 V average | Ripple and driver drops are outside the average model |
| Gearbox | 3000 rpm, 0.2 N·m, 10:1, 85% | 300 rpm, 1.7 N·m | Power falls by gearbox loss |
| Efficiency | 200 W electrical input, 160 W shaft output | 80% | The missing 40 W becomes electrical/mechanical loss and heat |
Common Parameter Mistakes
- Using rpm directly in P = τω without converting to rad/s.
- Treating Kv as a maximum voltage rating.
- Mixing rpm/V and rad/s/V when relating Kv and Kt.
- Mixing phase, line, peak, RMS, and DC current conventions.
- Using cold winding resistance for a hot operating point without qualification.
- Treating stall current as a continuous rating.
- Assuming high stall torque means useful stall power.
- Equating PWM duty cycle directly with speed.
- Ignoring driver, brush, switching, iron, friction, and windage losses.
- Combining motor and gearbox torque without ratio convention or efficiency.
- Comparing efficiency values measured at different operating points.
- Applying ideal formulas without checking controller, thermal, and mechanical limits.
Support reference
FAQ
How are motor torque, speed, and power related?
Mechanical shaft power is torque multiplied by angular speed: P = τω, with ω = 2πn/60 when speed n is in rpm.
What is motor back EMF?
Back EMF is the speed-proportional generated voltage that opposes the applied terminal voltage while the motor rotates.
What is motor Kv?
Kv is a speed constant commonly stated in rpm/V. It is not a maximum voltage rating and its test convention must be checked.
What is motor Kt?
Kt is torque produced per ampere under a specified current convention, commonly expressed in N·m/A.
Are Kv and Kt exact inverses?
They have an inverse relationship in a consistent ideal SI model, but rpm/V versus rad/s/V and phase, line, peak, or RMS conventions must be reconciled.
How is DC motor stall current estimated?
At zero speed, back EMF is zero, so the ideal initial estimate is Istall = V/R. Driver resistance, wiring, brush drop, and temperature change the real value.
Why is stall dangerous?
Current and copper loss can be very high while mechanical output power is zero, causing rapid winding and driver heating.
How is motor copper loss calculated?
For a stated winding and current convention, resistive copper loss is I²R. Multi-phase totals require the correct phase currents and winding arrangement.
Does PWM duty cycle set motor speed directly?
Duty cycle sets an average-voltage boundary under an ideal switching model. Actual speed depends on load, back EMF, resistance, control strategy, ripple, and losses.
How does a gearbox affect speed and torque?
Under the ratio convention G = input speed/output speed, ideal output speed is input speed/G and output torque is input torque × G; real torque includes gearbox efficiency.
Is motor efficiency constant?
No. Efficiency changes with speed, torque, current, voltage, temperature, controller loss, and mechanical loss.
Does this reference cover BLDC commutation timing?
No. Pole pairs, electrical RPM, commutation, encoder counts, and detailed step timing are reserved for the timing reference.
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