How to estimate life from an application duty cycle
The mechanism runs a repeating cycle. How do you turn that cycle into a statement about how long the motor will last, and what part of that statement can only come from a test?
A duty cycle is the sequence of loads and rests the mechanism repeats. It decides two different things, on two different clocks, and the mistake that makes life estimates useless is treating them as one.
The thermal clock is fast and calculable. It asks whether the winding reaches an acceptable temperature, and it resets whenever the motor cools. The wear clock is slow and cumulative. It counts revolutions, starts, reversals and stalled seconds, and it never resets. Both have to be evaluated, and only the first can be closed with arithmetic.
Start by writing the cycle down
| Phase | Torque mN·m | Duration s | Motor current A |
|---|---|---|---|
| accelerate | 18.0 | 0.15 | 1.165 |
| run | 6.0 | 1.20 | 0.415 |
| decelerate | 12.0 | 0.15 | 0.790 |
| dwell | 0.0 | 2.50 | 0 (unpowered) |
The thermal clock
Trms = √( Σ Ti² · ti / Σ ti )
- Trms
- root mean square torque over one whole cycle
- Ti
- torque during phase i
- ti
- duration of phase i, including the rest phases
RMS torque is a convenient proxy, but the quantity that actually heats the winding is RMS current, and the two are not proportional because current carries the no-load offset. For this cycle the current-weighted result is 0.355 A, which gives a copper loss of 0.57 W and, at an illustrative 10 K/W thermal resistance, a steady rise of about 6 K. Comfortable, and comfortably calculable.
That calculation is the part of a life estimate that can be done honestly at a desk. It answers whether the motor will overheat. It says nothing about how long it will last.
The wear clock
Wear accumulates against counters, not against hours. Converting the cycle into counters is arithmetic, and it is the step most life discussions skip.
At 6 mN·m the illustrative motor turns at about 6047 rpm, so the 1.2 second run phase is roughly 121 motor revolutions. Add the ramps and one cycle is on the order of 130 motor revolutions, one start, one deceleration and no stalled seconds.
| Counter | Per cycle | Over 100,000 cycles | What it wears |
|---|---|---|---|
| Motor revolutions | about 130 | about 13 million | Brush sliding distance, bearing revolutions, gear tooth contacts |
| Starts | 1 | 100,000 | Brush and commutator erosion from inrush current |
| Reversals or braking events | 1 | 100,000 | Brush contact, endplay impacts, gear backlash impacts |
| Stalled seconds | 0 | 0 | Nothing here, and this row is the one to check first |
| Powered hours | 0.0004 h | about 42 h | Very little. This is why quoting life in hours misleads |
| Elapsed hours | 0.0011 h | about 111 h | Grease oxidation and evaporation, which run on elapsed time and temperature |
The last two rows are the argument against hour-based life figures. This mechanism accumulates 13 million revolutions in 42 powered hours. A different mechanism could accumulate 42 powered hours at a tenth of the speed and do a tenth of the sliding. The same "hours" figure describes both.
What limits life, and what closes each one
| Mechanism | Counter it runs on | Can it be calculated? |
|---|---|---|
| Brush and commutator wear | Revolutions, starts, current density, contamination | No. Ordering between candidates can be reasoned; the number requires a life test at the real duty |
| Bearing life | Revolutions under a stated radial and axial load | Partly. Standard bearing life models apply when the loads are known, and small-motor bearings are frequently below the range those models were built for |
| Gear tooth wear and fatigue | Tooth contacts and load per contact | Partly, for metal gears with published material data. For small molded gears, test |
| Grease degradation | Elapsed time at temperature | Directionally, using an oxidation rule of thumb. Not to a number |
| Winding insulation | Cumulative time at temperature | Yes, once the temperature rise is measured, using published insulation class data |
| Connections and leads | Flex cycles, if the lead moves with the mechanism | No. This is a mechanical fatigue test on the harness, and it is regularly forgotten |
Designing the life test
-
Reproduce the counters, not the hours
The test has to deliver the same number of starts, reversals and revolutions as the field. A continuous-running test with the same total hours understates brush wear severely.
-
Compress dwell, carefully
Shortening rest periods is the legitimate way to accelerate. Verify that the compressed cycle does not raise the steady temperature above the field case, because that changes the failure mechanism rather than accelerating it.
-
Do not accelerate by raising the load
Higher torque changes current density, temperature and contact behavior at once. The result is a different failure mode, tested faster.
-
Measure continuously, not at the end
Log current, speed and temperature throughout. The trend curve tells you the mechanism. A pass or fail at the end tells you almost nothing.
-
Define the end-of-life criterion first
A percentage change from each unit's own initial measurement, agreed before the test starts. Deciding afterwards what counts as failure is how a life test produces an argument instead of a result.
-
Tear down the units when the test ends
Including the ones that passed. The wear distribution on a survivor tells you how much margin the design actually had.
A life test run this way produces something more useful than a number. It produces a curve of degradation against counted cycles, which can be extrapolated to a different duty with defensible assumptions. A single pass or fail at one duration cannot.
Where the cycle data comes from
A duty table written from the design intent is a starting point. The one that predicts life is measured on the real mechanism, because mechanisms do things the design did not describe.
-
Put a shunt in series with the motor
A low-value resistor and an oscilloscope give current against time for the whole cycle. Current converts to torque through the torque constant, so this single trace produces the torque column of the duty table directly.
-
Capture the whole sequence, including what happens between cycles
Homing moves at power-up, retries after an error, jog moves during service and cleaning cycles all add starts. They are usually absent from the design duty and present in the field.
-
Capture the worst unit, not the nominal one
Mechanism friction varies across a production population and rises over life. The duty that matters is the one at the high end of that distribution, at the end of its service interval.
-
Record the ambient the mechanism actually sits in
Enclosed instruments run warmer inside than the room they stand in, and the temperature inside is what sets both winding rise and lubricant life.
The difference between the designed cycle and the measured cycle is often a factor of two or more in start count, and start count is the dominant wear counter for a brushed machine. Measuring it is a day of work that changes the life answer more than any component selection.