H-bridge (L298N DUAL FULL-BRIDGE DRIVER) gets very hot - help!

We do not have the L298N attached to a heatsink. Can you recommend a link sayng how to do this?

I'm assuming you have the L298N in the through-hole package (not the surface-mount). You will need to get something that looks like this:

http://www.aavidthermalloy.com/cgi-bin/stdisp_print.pl?Pnum=530510b00000g

This bolts on to the package using a nut and bolt, and you should also apply thermal grease between the two to fill in any air gaps and improve thermal conduction:

If you have a machine shop you can just make yourself a big block of aluminum to bolt on instead of trying to find a proper heatsink (it's not a standard package so finding a heatsink for it could be challenging).

We thought that when the datasheet said: Rated Voltage: 3,96 V, that we should feed the motor with 3,96 volt from the adjustable DC powersupply.

That is just the maximum steady voltage you should be applying, and really it's a sideways way of telling you the maximum current, which is more important (I=V/R). You can always operate a motor at a lower voltage/current to get lower torque.

Now for steppers, it is common to use a higher voltage but just not leave it on all the time. That is, use pulse-width modulation (PWM) to deliver an effective average current that is within the motor specifications but turn it on and off quickly so that the current does not rise beyond the rated current.

In the datasheet for the motors we read that the rated current is: 2,2 amp. So can we run it at a lower current?

Absolutely. The lower the current you run at the less hot your driver will get, and the less torque you will get from your motors.

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