Motors and transformers (and chokes) are all wound devices but they use quite different mechanisms, so changing the frequency has different effects.
A 50Hz transformer will work OK on 60Hz as the magnetising current will be lower, hence less peak flux in the core (although 20% more hysteresis loss). A 60Hz transformer may saturate on 50Hz especially if it is not generously designed, which can lead to much greater heat dissipation. Any transformer supplied for use at either frequency will be designed for 50Hz. Many 60Hz transformers will survive fine on 50Hz provided the voltage is at the low end of the intended voltage range. 50Hz induction motors and vibratory devices will run fast and may lack power on 60Hz, while 60Hz versions will run slow and develop more heat on 50Hz. Whether they function correctly will depend both on the design, quality of manufacture and more than anything on the application to which they are put. Universal (brush) motors are much less affected and will run at their correct speed so long as the voltage is correct. Heat dissipation may be affected as with transformers. Anything that rectifies the AC and uses a permanent magnet motor, such as most hairdryers (other than the 'silent' type with induction motors) will work equally well on either frequency. Devices with choke ballasting (e.g. switchstart fluorescents) will be overrun with a 60Hz ballast on 50Hz and underrun with a 50Hz ballast on 60Hz, but the ballast itself might be fine.
Incidentally we don't know for certain what is inside your engraver. If it hums then it is a magnetic vibrator, but if it whirrs like a motor, it won't be an induction motor so might not be affected by frequency.