I'm an EE, but I don't know code in Denmark. Assuming this machine is installed somewhere near a sink, and that Denmark may also require ground-fault interrupt breakers on any receptacle within 2 meters of a plumbing fixture (eg. sink), there could be two causes for those breaker trips:

1. Overcurrent. In the USA, residential breakers have two trip mechanisms: thermal and magnetic. The magnetic trip is fast, designed to catch a short circuit, and typically set around 10,000 amps in the USA. You would be able to easily detect a short circuit with an ohmmeter, measuring between each pair of the three pins on your power cord (unplugged, of course). The thermal trip is slow, from tens of seconds to tens of minutes, depending on how far you load the circuit above the rated current. So, a 15 amp circuit loaded to 17 amps might take 1 to 15 minutes to trip, depending on other factors (breaker cabinet temperature, adjacent circuit loads, etc.). I would imagine the same two mechanisms are employed in residential breakers used in Denmark, it only makes sense, although the numbers are surely different.

2. Ground fault. In the USA, residential outlets installed in kitchens, bathrooms, garages, and basements require a ground fault interruption feature. This is designed to shut off power if current above a given threshold (5 mA, if I recall) is detected between line (110VAC) and ground. Historically, these mechanisms resided inside the breaker (GFI or GFCI breaker type), but folks found that too much a hassle, so most installations put this mechanism inside the outlet today. If you are tripping a GFI outlet, you have a current path from line to ground, not a circuit overload.

If you tell us the type of outlet and breaker you have, we may be able to lead you through a debug process, to find the source of the trouble. Also, do keep in mind that breakers installed in damp basements do go bad over time, it's possible it is tripping below its rated current. It's also likely a loose wiring connection in the path from machine to breaker could be generating sufficient heat to cause a trip, when there is nothing actually wrong with your machine. My mother once replaced an air conditioner due to this loose wire problem, only to have the new air conditioner trip the same circuit.

Flitzgordon wrote:If I get my hand on a insulation tester aka megger, would that be useful for such diagnosis?

An insulation tester / megger in the right hands can find a ground fault that may not be detected with a multimeter. It does that by applying a much higher voltage to the test leads than a multimeter would. This voltage could be hazardous to you or to the equipment you are checking. If you find a qualified electrical repair person with a megger, let the electrician do the testing. They will best know how to use their test equipment safely and effectively.