Non-synchronous data
Torque, speed, and input power sampled at different times can create a false loss or an apparent efficiency above 100%.
Engineering
Shaft Efficiency Calculator
Convert measured shaft torque and speed into output power, compare it with upstream input power, and separate declared auxiliary loss from the unexplained balance.
SHAFT EFFICIENCY
Reconcile torque-speed output with the power that entered the shaft train
Efficiency is only credible when input and output measurements refer to the same operating point. The calculator derives mechanical output from torque and rpm, removes separately measured auxiliary loss, and exposes any remaining energy imbalance instead of hiding it inside a single percentage.
Torque-speed output (kW)-
Measured efficiency-
Total input-output loss (kW)-
Unexplained balance (kW)-
Input less auxiliary loss (kW)-
ENGINEERING DECISION VIEW
Follow power across the measurement planes
A material unexplained balance is a measurement and boundary problem before it is an efficiency conclusion. Check timestamp alignment, sensor location, torque sign, speed basis, and whether auxiliaries sit inside or outside the stated boundary.
| Balance item | Torque / input | Speed / comparison | Power (kW) | Evidence meaning |
|---|
LIVE CALCULATION PROCESS
Formula, substitution, and reconciliation
Pout = 2*pi*N*T / 60,000; efficiency = Pout / Pin x 100%; unexplained loss = Pin - Pout - declared auxiliary loss
Torque in newton-metres multiplied by angular speed gives watts; division by 1,000 gives kilowatts. The input-output loss is then split between the separately entered auxiliary loss and the unexplained balance. No efficiency value is clipped to look plausible.
HOW TO USE
Build an efficiency result that can be reconciled later
- Define the system boundary first: identify exactly where input power is measured and where torque and speed are measured.
- Enter torque and rpm from the same steady operating interval; do not pair a peak torque with an average speed.
- Enter only auxiliary loss supported by a separate measurement or documented estimate, and keep its method with the record.
- Review output power and the unexplained balance before accepting the efficiency percentage.
- Save synchronized raw samples and the measurement-plane sketch so a later reviewer can reproduce the residual instead of seeing only the efficiency percentage.
SUBJECT FUNDAMENTALS
Power-measurement concepts behind shaft efficiency
- Angular speed
- Rotational speed expressed in radians per second; omega equals 2*pi*rpm/60.
- Torque-speed power
- Instantaneous mechanical power produced by torque acting at angular speed.
- Measurement plane
- Physical section of the drivetrain where a sensor or inferred quantity applies.
- System boundary
- Declared equipment included in the input-output balance, such as couplings, bearings, seals, or gearbox stages.
- Auxiliary loss
- A separately evidenced loss that sits inside the chosen boundary but is not part of useful output.
- Energy residual
- Input minus accounted output and known losses; a diagnostic for missing loss or inconsistent measurements.
CALCULATION METHOD
Use a power balance that preserves the unexplained residual
Pout = 2*pi*N*T / 60,000; efficiency = Pout / Pin x 100%; unexplained loss = Pin - Pout - declared auxiliary loss
Torque in newton-metres multiplied by angular speed gives watts; division by 1,000 gives kilowatts. The input-output loss is then split between the separately entered auxiliary loss and the unexplained balance. No efficiency value is clipped to look plausible.
DEFAULT CASE AUDIT TRAIL
Symbols, units, substitution, and independent check
| Symbol | Meaning | Unit |
|---|---|---|
| Pin | Measured power entering the chosen boundary | kW |
| T | Measured output torque | N*m |
| N | Output rotational speed | rpm |
| omega | Output angular speed | rad/s |
| Pout | Torque-speed output power | kW |
| Paux | Separately evidenced auxiliary loss | kW |
Default values
- Pin = 75 kW, T = 225 N*m, and N = 2,950 rpm.
- Paux = 2.2 kW inside the declared measurement boundary.
Unit conversion
- omega = 2 x pi x 2,950 / 60 = 308.923 rad/s.
- Torque times rad/s gives watts; divide by 1,000 to report kilowatts.
Numerical substitution
- Pout = 225 x 308.923 / 1,000 = 69.508 kW.
- Measured efficiency = 69.508 / 75 x 100 = 92.677%.
- Total input-output loss = 75 - 69.508 = 5.492 kW.
- Unexplained balance = 5.492 - 2.2 = 3.292 kW.
Named intermediate results
- Angular speed: 308.923 rad/s.
- Declared auxiliary share: 2.200 kW.
- Unexplained residual: 3.292 kW.
Independent check:69.508 kW output + 2.200 kW declared auxiliary loss + 3.292 kW unexplained balance equals the 75.000 kW input within display rounding.
DEEPER ANALYSIS
Why plausible percentages can still be wrong
Sensor and plane mismatch
A motor electrical input, coupling torque, and downstream speed do not describe the same boundary unless intervening losses are explicitly included.
Transient operation
Acceleration stores kinetic energy in the rotating inertia. A steady-state input-output balance cannot be applied blindly during run-up or coast-down.
WORKED DECISION CASES
Two practical efficiency investigations
Commissioning a driven pump
A technician compares motor-side input power with downstream shaft torque and rpm. A 4 kW residual leads to a review of coupling alignment and the location of the auxiliary oil-pump load.
Post-maintenance comparison
The same operating point is recorded before and after a seal replacement. Output power is unchanged but declared seal loss falls, providing a traceable maintenance benefit.
Shaft power-balance terminology
- Dynamometer
- Instrument that measures torque, often together with rotational speed.
- Mechanical power
- Rate of work transmitted through rotation.
- Parasitic loss
- Power consumed by friction, windage, seals, auxiliaries, or other non-useful paths.
- Steady state
- Interval in which stored rotational energy is not materially changing.
- Calibration
- Documented relationship between sensor indication and reference values.
- Residual
- Unexplained difference remaining after known balance terms are applied.
EVIDENCE AND DATA LINEAGE
Retain synchronized measurements and the physical boundary
Keep instrument IDs, calibration status, sampling interval, averaging method, torque sign convention, rpm source, input-power method, measurement-plane diagram, included equipment, declared auxiliary-loss evidence, ambient and lubrication condition, raw data, and unrounded balance.
LIMITS AND EXCLUSIONS
What this steady-state balance does not establish
- No transient inertia, torsional vibration, electrical harmonics, thermal soak, uncertainty propagation, or efficiency-map interpolation is included.
- The calculator does not validate sensor calibration, torque sign, measurement synchrony, or the chosen system boundary.
- Efficiency does not demonstrate shaft strength, coupling capacity, bearing life, alignment, or acceptable operating temperature.
RELIABLE SOURCES
References for the method and its boundaries
FREQUENTLY ASKED QUESTIONS
Questions about torque-speed efficiency
Why can the calculator reject output above input?
A small difference can come from uncertainty, but a material excess usually means mismatched units, signs, timestamps, or measurement planes.
Should motor efficiency be entered?
Only if you are converting electrical motor input to shaft input. This page expects the input power already defined at the selected shaft boundary.
Can auxiliary loss be zero?
Yes when no separate internal loss is being claimed, but the unexplained residual then carries all unaccounted loss.
Does the result include gearbox efficiency?
Only if the gearbox lies inside the boundary between the entered input and measured output.
What rpm should I use for variable speed?
Use the speed synchronized with the torque and input-power sample or integrate a time-resolved balance.
Is the unexplained balance automatically friction?
No. It may reflect heat, windage, measurement bias, timing mismatch, or a boundary definition error.
RELATED CALCULATORS
Continue the engineering review
Shaft Loss Calculator
Break bearing, seal, and windage losses into an explicit heat balance.
Shaft Capacity Calculator
Check whether the same shaft section can carry the entered torque and bending action.
IMPORTANT NOTE
Do not use a reconciled power balance as a mechanical integrity approval
Use calibrated, synchronized measurements and a defined system boundary. Equipment selection and acceptance still require the governing manufacturer procedures, design standard, uncertainty analysis, and competent engineering review.