Does it trigger the arc-fault right when it turns the relay on or off, or is it just random while it is running?
The arc-fault breakers will always sense at least some fraction of any kind of arc, including those that are expected, like a universal motor would create. It may be as simple as just adding some suppression capacitance either across the relay contacts if that is that causes it or across the load side to suppress transients from motor I would guess...
Sometimes one breaker will become extra twitchy, if you have several you could try swapping them around and see if one is at least more tolerant if it remains an issue, I suppose...