Say a motor is rated for 20 N·m continuous torque, and 35 N·m peak (peak = for no more than 30 seconds). Alternatively it may be specified at with continuous/peak currents, but if the motor efficiency is good overall, then this is almost an equivalent definition.
Say that I want to run the motor producing 25 N·m for some time. Is there a general mathematical model that approximates the safe run-time at that level? It's certainly more than 30 seconds, but I'm unsure how to derive an approximate value.
More specifics: it's a 3-phase brushless motor, and it does have a temperature sensor. However using the temperature alone (and disregarding the specs) does not seem to be a good approach. E.g. 30 seconds at 35 N·m does not heat it very much, and it doesn't get even close to the max temperature per specifications. I'm also constraining myself to the typical application RPM ranges, e.g. 50 to 100% of the rated speed.