Technology / Technical guide
Loaded Generator Torque Ripple & Cogging Contributions
A generator can have a nonzero mean electromagnetic torque with periodic variation around it. That loaded torque ripple can contain several contributions. Cogging torque, associated with magnetic geometry even without external winding current in its ideal definition, is one contribution rather than another name for every loaded variation.
Separate the mean torque from the mechanisms that modulate it.
A periodic component needs an angular or time reference; one ripple percentage cannot identify its physical source.
01 / Mean and variation
Torque ripple describes variation around an operating result.
Represent a steady periodic torque waveform as its mean plus a zero-mean varying component over the same interval.
Represent a steady periodic torque waveform as its mean plus a zero-mean varying component over the same interval. The mean contributes to average mechanical loading, while the changing part can excite dynamic behaviour. A stable mean alone does not describe the waveform’s peaks.
A peak-to-peak range, RMS varying component and harmonic amplitude are different measures. Each uses a particular interval and convention. Labelling a value simply ripple without defining its denominator or statistic makes comparisons between operating points ambiguous.
02 / Cogging boundary
No-current geometry is not the whole loaded waveform.
In a permanent-magnet machine model, cogging torque can arise from the rotor magnets interacting with a position-dependent magnetic reluctance.
In a permanent-magnet machine model, cogging torque can arise from the rotor magnets interacting with a position-dependent magnetic reluctance. Its ideal no-external-current definition separates that geometrical contribution from torque created through winding-current interaction.
The cogging and start-up guide concerns that no-current contribution and rotation onset. Under load, the total torque additionally depends on current and field relationships. A cogging waveform cannot automatically be relabelled as the complete loaded torque waveform.
03 / Loaded components
Current and magnetic spatial patterns can interact.
Current waveforms, induced-field harmonics and position-dependent machine behaviour can contribute to varying electromagnetic torque.
Current waveforms, induced-field harmonics and position-dependent machine behaviour can contribute to varying electromagnetic torque. Their phases can reinforce or partly cancel contributions at a stated operating point. Component amplitudes alone therefore do not always add into the total peak-to-peak range.
COMSOL’s permanent-magnet model evaluates time-dependent torque separately from a stationary angle-dependent result. It is an example of distinct model quantities, not evidence for a MARSTON geometry, winding pattern, converter algorithm or specified ripple magnitude.
04 / Waveform example
State the ripple measure before calculating a percentage.
Consider the invented waveform T(θ) = 10 + cos(θ) N·m over complete angular cycles.
Consider the invented waveform T(θ) = 10 + cos(θ) N·m over complete angular cycles. Mean torque is 10 N·m, the varying component’s peak amplitude is 1 N·m, and total peak-to-peak range is 2 N·m.
Using peak-to-peak range divided by the positive mean gives 20% for that hypothetical definition. Using peak amplitude divided by mean gives 10%. Both calculations are correct for their declared measures; neither is a product result or an allowable torque-quality threshold.
05 / Angular order
A spatial periodicity becomes a time frequency through speed.
A component with k cycles per mechanical revolution has time frequency k times mechanical rotational frequency when speed is constant.
A component with k cycles per mechanical revolution has time frequency k times mechanical rotational frequency when speed is constant. If speed changes, that time frequency changes even if its angular order stays fixed. Electrical-cycle and mechanical-revolution references must also remain distinct.
Measured motion can respond differently from the original torque because inertia and structural dynamics intervene. The shaft-dynamics guide concerns mechanical response; a vibration peak alone is not a unique identification of cogging or one current harmonic.
06 / Model scope
Do not turn a waveform concept into a quality claim.
Comparing loaded waveforms requires the same torque boundary, operating condition and statistic.
Comparing loaded waveforms requires the same torque boundary, operating condition and statistic. A rotor’s aerodynamic driving torque, electromagnetic resisting torque and shaft response have related but distinct meanings. The torque-power guide retains that boundary distinction.
No MARSTON cogging amplitude, loaded-ripple percentage, harmonic order or balancing result is specified. The page provides no current-shaping algorithm, speed change, rotor modification or test procedure, and the illustrative cosine waveform is entirely hypothetical.
Related technical guides: Generator Core Loss: Magnetic Hysteresis & Eddy Currents · Three-Phase Space Vectors & Ideal Inverter States · Converter Instantaneous Power, Storage & Dissipation.
General background: COMSOL: angle-dependent and time-dependent torque in a permanent-magnet model · McIntosh: original study of distinct cogging components. These references explain industry concepts; they are separate from the applicable MARSTON product and project documents.
Key concepts and conditions.
Read each quantity with its reference, units and stated conditions. A general relation does not establish a model-specific value.
| Concept / quantity | Meaning / relation | Conditions / limits |
|---|---|---|
| Mean torque | Average over a defined complete period | Same boundary and operating condition. |
| Cogging contribution | Position-dependent no-current term | Not the entire loaded electromagnetic torque. |
| Peak-to-peak range | Maximum minus minimum in N·m | Different from one-sided amplitude or RMS variation. |
| Ripple percentage | Declared measure/declared reference | A nonzero applicable denominator is required. |
| Angular order | Cycles per mechanical revolution | Constant speed maps it into time frequency. |
Engineering questions.
Are cogging and loaded torque ripple interchangeable?
No. Cogging is one defined geometrical contribution; loaded torque can contain other terms.
Does equal mean torque imply equal torque peaks?
No. The varying waveform can differ.
Why can the example have both 10% and 20% ripple?
They use peak amplitude and peak-to-peak range respectively, with the same mean denominator.
Does angular order stay at a fixed hertz value?
Only if the relevant rotational speed stays fixed.
Can a vibration peak alone identify a torque cause?
No. Mechanical response and several exciting mechanisms can contribute.
Does the cosine example describe MARSTON torque quality?
No. It is an invented waveform with no actual quality threshold.
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