Calculation
η = (U·Ia − Ia²·Ra − Pv,mech) / (U·Ia)
Resistive armature loss and mechanical loss are subtracted from input electrical power before power is available at the shaft.
Busch 2006, Abschnitt 8.2.3.1 Leistungsbilanz
DC motor overall efficiency
Resistive armature loss and mechanical loss are subtracted from input electrical power before power is available at the shaft.
MINTSI
02
Result
Select a target and calculate.
Understand the inputs
- Overall efficiency η (0 to 1) — Ratio of delivered shaft power to consumed electrical power at the operating point.
- Armature voltage U — DC voltage directly at the armature terminals at the steady operating point.
- Armature current Ia — Measured armature current, excluding separately supplied field current.
- Armature-circuit resistance Ra — Hot resistance of armature winding, brushes and permanent connection path.
- Mechanical loss power Pv,mech — Friction, windage and other mechanical losses between converted electromagnetic power and shaft output.
Example
U=230 V, Ia=20 A, Ra=0.5 Ω and Pv,mech=150 W give Pel=4,600 W, PCu=200 W, Pab=4,250 W and η≈0.924 or 92.4%.
Assumptions and limits
Steady motoring, constant field flux and temperature-constant Ra; field power, commutation/brush loss and starting transients are excluded.
Understand DC motor overall efficiency
This calculator extends the DC motor power balance to the shaft: it subtracts both resistive armature loss and mechanical loss from consumed electrical power, giving the actual overall efficiency.
What does this quantity describe?
From input power Pel=U·Ia, copper loss Ia²·Ra is subtracted first, giving converted electromagnetic power E·Ia. Subtracting mechanical loss power Pv,mech from that leaves shaft power Pab, and η=Pab/Pel.
Formula and variables
η = (U·Ia − Ia²·Ra − Pv,mech) / (U·Ia)
Pel = U·IaPCu = Ia²·Raη = (Pel−PCu−Pv,mech)/Pel
| Symbol / input | Meaning |
|---|---|
| Overall efficiency η (0 to 1) | Ratio of delivered shaft power to consumed electrical power at the operating point. |
| Armature voltage U | DC voltage directly at the armature terminals at the steady operating point. |
| Armature current Ia | Measured armature current, excluding separately supplied field current. |
| Armature-circuit resistance Ra | Hot resistance of armature winding, brushes and permanent connection path. |
| Mechanical loss power Pv,mech | Friction, windage and other mechanical losses between converted electromagnetic power and shaft output. |
Choose the inputs correctly
U and Ia are armature-circuit voltage and current at the same operating point. Ra is the hot armature-circuit resistance. Pv,mech bundles bearing, brush and windage friction and other mechanical losses, and must be known separately, e.g. from a no-load test.
How to use the calculator
Record U, Ia and Ra at the same steady operating point as for the back-EMF calculator. Determine Pv,mech from a no-load test at the same speed, where all supplied power turns into mechanical loss.
Worked example
U=230 V, Ia=20 A, Ra=0.5 Ω and Pv,mech=150 W give Pel=4,600 W, copper loss 200 W, shaft power Pab=4,250 W and η≈0.924 or 92.4%.
Understand the result and units
Low overall efficiency despite small copper loss points to dominant mechanical losses, such as bearing friction or an oversized fan.
U is a voltage, Ia a current, Ra a resistance and Pv,mech a power. η is dimensionless, shown as a ratio between 0 and 1.
Typical applications
Evaluating test-bench measurements, comparing operating points of the same motor and estimating energy demand for a known useful power.
Assumptions, limits and common mistakes
Steady operation with constant field flux and temperature-constant Ra. Field power, commutation/brush voltage loss and starting or load-change transients are excluded.
Common mistake: Do not confuse Pv,mech with copper loss Ia²·Ra; both loss types must be captured separately and both subtracted from Pel. Do not equate the pure back-EMF power E·Ia with shaft power Pab.
Frequently asked questions
What is “DC motor overall efficiency” used for?
Evaluating test-bench measurements, comparing operating points of the same motor and estimating energy demand for a known useful power.
Where do the input values come from?
U and Ia are armature-circuit voltage and current at the same operating point. Ra is the hot armature-circuit resistance. Pv,mech bundles bearing, brush and windage friction and other mechanical losses, and must be known separately, e.g. from a no-load test.
What does the result not cover?
Steady operation with constant field flux and temperature-constant Ra. Field power, commutation/brush voltage loss and starting or load-change transients are excluded.