All switch contacts arc when opened or closed. The data sheet for the relay indicates that the contacts has a tendency to tack-weld if precautions are not taken. The contact current rating is much lower for inductive loads like a motor.
The contacts will bounce so increasing that chance of welding. during that time the voltage can easily exceed the 12V specification. Operating at 57V (even if, as you say, "pre-charged" is dodgy. It provides an opportunity for sustained transient voltages that can generate sustained arcing.
The transient voltages can be a damped oscillation. You should look at the switching with an oscilloscope.
The data sheet warns that a resistance in parallel with the coil can increase the chance of tact-welding.
The diode suppression across the coil is extending release time enhancing tack-welding. The 2N7000 may not be the best choice for this. The current is near the maximum.
- Place a resistor in series with the diode to allow the voltage across the inductor to rise to at least 12V during turn off. It can go higher if the FET can tolerate it.
- Pick a more robust FET that can absorb a transient through the body diode. Pay attention to the transient coupling to the gate through the Miller capacitance. Use an oscilloscope. Don't assume anything. This choice can allow the coil to be unsuppressed. Make sure that there is a large value ceramic between the 12V at the coil and the source of the FET to control the transient current path.
- Take steps to reduce transients associated with the motor with the focus on arc suppression. Use an oscilloscope to see the transients on the contacts.
- Use a different relay. You are operating this one out of the range of the specifications.
Clarification edit: The 12 rating on the contacts is an arcing specification. Most welders used for fabrication have a strike voltage of about 30V. During the arc, the voltage is transferred to the equivalent source resistance. The higher the source voltage is, the more current there is in the arc, raising the temperature and making it easier to sustain the arc. I think this welding in this case is happening when the contacts break and bounce. The arc starts at the tiniest gap then is maintained as the gap gets bigger. The maximum gap depends on the available voltage. The gap is designed for 12V. The circuit can provide 57V almost 5 times the spec. Also, the switch will bounce before fully retracting, so the hot arc, due to the high voltage, will have melted the surfaces. When they touch they weld. The diode across the coil will slow down the release, maintaining a longer arc and allowing more bounce events.
Edit2: When the relay opens, the motors will still demand current through the controller. This will maintain an arc longer than with other loads. You say that there is a capacitor. This may help, but its voltage will likely fall very quickly when the relay opens. I still think my comments above apply.
EDIT 3:
The datasheet for the controller has no information about its internal circuitry. We can only speculate.
Measurement 1- triggered on coil being energised (30 s after powering on system):
The oscillograph indicates a 36.2A spike of current through the switch ~4ms after the relay coil is energized. This is near the limit for the switch with a capacitive load. The battery voltage drops an it appears that the motor is starting to turn. I speculate that this is the motors' starting current. The pulse starts to decrease very fast then oscillates a bit before decaying. I speculate that this is a switch bounce followed by an arc as the switch closes. This would seem the culprit for the damage. This may exceed the contact current rating from pulse to pulse.
Measurement 2 - Triggered on coil de-energised (system turned off)
The blue battery trace makes no sense.
When the relay is de-energized the coil current flows through the diode, shown by the small negative voltage just after the trigger. About 1/2 way through this region a 5A peak oscillation occurs (pink line) indicating an arc while the switch is opening. The switch should be able to handle this current level.
Based on this latest information:
- The motor controller has speed control. Turn on the relay then ramp up the speed using the controller, then ramp down the speed to stop then deenergize.
- Use a better relay or replace with solid state switch, optically isolated or otherwise. Point 1 should probably always be used to control the start and stop currents.
EDIT4: @mbrig links an app note from TE indicates that the make current rating is limited to 20 ms. This is for a 12 volt system. Even though a step was taken to make the 57 volt system look like a 12 volt system, when the switch bounces, all bets are off. 57 volts across the gap will increase the gap length that will sustain the arc and decrease the duration max time to about 4ms.
Arc suppression for capacitive loads is difficult because current must be diverted around sensitive parts while maintaining a closed loop. That is why the AgSnO2 contacts are used for very high currents and capacitive loads. A short search on Google finds a lot of information on these alloys. The AgNi.15 (which is the contact plating in use)is more "weldable" than AgSnO2 which also has a higher resistance to erosion. The datasheets also indicate that these contacts should be used with suitable arc suppression, which should be added here.
So the root cause of this relay failure is:
It is the wrong relay which several answers have stated.
A better solution is a FET switch providing a controlled soft turn on. The high turn on surge currents can shorten the life of the big capacitors due to internal magnetic forces.
Best I can do. Cheers.