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peteroznewman
Subscriber

Let's assume there is a bearing on the shaft close to the gear and the shaft is 200 mm long. Assume the same on the other side of the mesh for the pinion. The first natural frequency of that system is probably the shaft twisting and the gear and pinion rotating against each other with the teeth in mesh. Now make the shafts 300 mm long, the first natural frequency goes lower, or reduce the shaft length to 100 mm and the twisting mode natural frequency goes higher, but maybe that is no longer the first natural frequency. Do you see that you need to look at the system and not just the gear and pinion?