Our sizing walkthrough takes you from a load to a part number. This is the step that decides whether that part number survives its first year, and it is the one most often done by eye.
The question is simple to state: your axis sees a torque that varies through its cycle, and the datasheet gives you one rated torque. What single number do you compare against it?
Two averages that feel right and are not
The peak. Sizing so that rated torque exceeds your worst transient is conservative to the point of being wrong. Peak torque is a separate published limit and it exists precisely so you do not have to do this. Size this way and you buy mass and cost you did not need.
The time-average. Add up torque × time, divide by cycle time. This is the intuitive answer and it is the dangerous one, because it treats a four-second dwell at low torque as cancelling out a three-tenths-of-a-second acceleration transient. It does not, and the reason is physical rather than statistical.
Why the cube
Published life for a strain wave gear is governed by its wave generator bearing, as we covered in rated life is a coin flip. Rolling-element bearing life goes with roughly the cube of load. Double the torque and you do not halve the life, you cut it to about an eighth.
So the average that matters weights each phase by its torque cubed, and by the number of input revolutions it turns through rather than by wall-clock time:
where n is input speed in rpm, t is the duration of the phase, and T is the output torque during it.
Two consequences fall straight out of that form. A phase at zero input speed contributes nothing at all, because the bearing is not turning. And a brief hard transient contributes far more than its share of the clock, because it enters cubed.
A worked cycle
Take a rotary indexing axis: accelerate, index, decelerate, then hold the position while something else in the machine does the work.
| Phase | Input speed | Duration | Output torque |
|---|---|---|---|
| Accelerate | 3,000 rpm | 0.3 s | 200 N·m |
| Index | 4,000 rpm | 1.2 s | 60 N·m |
| Decelerate | 3,000 rpm | 0.3 s | 180 N·m |
| Hold | 0 rpm | 4.0 s | 25 N·m |
A 5.8-second cycle, average input speed 1,138 rpm. Now the three answers:
| Method | Result | Smallest frame that passes |
|---|---|---|
| Time-average over the whole cycle | 49 N·m | AS-GS-51 — and it fails on peak |
| Peak transient only | 200 N·m | AS-GS-63 — and it fails on duty |
| Cube-weighted average | 127 N·m | AS-GS-81 |
Three methods, three frames, one duty cycle. The time-average is optimistic by a factor of 2.6 and points at a frame whose 120 N·m peak rating cannot even absorb the transient. Sizing on the peak alone picks AS-GS-63, whose 229 N·m peak clears the transient comfortably — but whose 87 N·m rated torque is well under the 127 N·m the duty actually averages to, so it runs its bearing above rating for the life of the machine.
AS-GS-81 is the answer: 178 N·m rated clears 127 N·m, 484 N·m peak clears 200 N·m. It is a bigger part than either shortcut suggested, and that is the useful result rather than an unwelcome one — the alternative is finding out at eighteen months.
The dwell is not free, it is just free of bearing wear
The four-second hold drops out of the calculation entirely because the wave generator is stationary. That is correct for bearing life and it is not permission to ignore the phase. A static holding torque still loads the tooth mesh, and it has to clear the allowable static torque rating, which is a separate published figure for exactly this reason. A drive can be perfectly sized on duty and still be damaged by what it holds when it is doing nothing.
What to take from this
- Get the duty cycle before the part number. Torque, input speed and duration for each phase. Without those three columns, any sizing is a guess with a decimal point.
- Check both limits independently. Cube-weighted average against rated torque; worst transient against peak torque. Passing one does not imply the other, and this example fails a different check in each direction.
- Re-run it when the cycle time changes. Speeding up a machine usually shortens the dwell and leaves the transients where they are, which raises the cube-weighted average even though nothing about the loads changed.
Send us the four columns above and we will run this against the range rather than leaving you to it. It takes minutes, and it is the difference between a frame that makes its published life and one that was always going to be replaced early.
Related: How to size a harmonic drive · Your rated life is a coin flip.