Yep all sorts of wrong here.
First issue and the biggest by far. The potential relay is buzzing because it's not getting quite enough voltage for it to fully open.
You need to start to RPC up (and make sure it's ALWAYS run with the cover in place. ALWAYS) let the RPC run for a couple minutes, shut it down and see what is getting hot. Either the potential relay is getting hot, the caps are getting hot or they are both getting hot. The caps should NEVER get hot. They are only suppose to be in circuit for a few seconds to start the motor. If they are staying in (I don't believe they are or your 3rd leg voltage under no load would be around 400 volts with that much capacitance) they will get hot and then come apart, which is why you need to run the cover at all times. Of course when checking for heat, make damn sure that the power is OFF to all of it. And don't touch any of the wiring regardless as the caps can hold a charge and bite you even with no power connected. If you are not comfortable with using your hand, get a non-contact infrared thermometer.
Second issue and as stated by others, no run caps are why your 3rd leg voltages are low. Now, here's the thing with an RPC. Real honest to God 3 phase power is 3 legs of 230 volts that are 120 degree's opposed leg to leg. Single phase (in truth split phase) house power is two phases at 120 volts that are 180 degrees opposed leg to leg. You will NEVER generate true 3 phase with a phase converter. The split phase transformer feeding your house will not allow it and will force the two powered legs to be 180 degrees apart no matter what. So what you are doing with this design of static phase converter is using brute force (read that high current and big power bill) split phase to run a 3 phase motor that you are starting with start caps. It's not designed for that. In fact most factories and businesses that are running 3 phase 208 or 460 have special devices connected to the 3 phase feeds from the utility that monitor for whats called a phase out condition. This is where one of the 3 phases stops providing current to the building. When it senses this, it sets off an alarm and may even drop the switch gear out putting the building dark. Reason is that if you have running motors that are 3 phase and try to run them off 2 of the 3 phases they will overheat and burn up. Which is EXACTLY what your static phase converter is doing. How do I know this? Well I got to replace 13 exhaust fan motors in a warehouse that had a phase out condition for about 6 hours one day and that morning the fans were all started up. The phase loss happened about 9 AM and no one thought to shut them off until a couple of them started smoking. Building was built in 71 and the 3 phase monitoring stuff was not available at that time or was not deemed as needed. Now that's when you are running a 3 phase motor on 2 legs that are 120 degrees apart. This is running them 180 degrees apart. Which is a bit easier on them but still not good. It still draws tons of current (hi electric bill) and causes heating of the motor.
Enter the run capacitor phase converter.
So what does the run capacitor do in a RPC that cleans stuff up, lowers current draw and makes things smoother?
A motor is an inductor. Like any coil of wire. Gonna get into some basic AC electronics type stuff here so bear with me. What an inductor does is as current is applied to it, it builds a magnetic field around it. As the power is removed the magnetic field collapses in on the coils of wire inducing voltage across them. This causes current flow out of the inductor when it has something it's connected to. Now all of this can be calculated with the voltage and time. And remember that we are talking about AC power here. It starts at 0 volts, increases to 240 volts, then begins to go back to 0 volts. It then passes 0 volts and heads to a negative 240 volts. Then back to 0 and on to 240 positive volts. This cycle happens 60 times a second, or at 60 Hertz. You yanks got shorted 10 cycles per second and run at 50 Hertz, but you concept is the same. Now, the capacitor. It does the same thing. It will charge up and hold a charge as well. But it's different. Where an inductor has it's charge via a magnetic field. the Capacitor holds it electrostaticly via two plates that are seperated and partly insulated from one another. Now.... here's the cool part. And anyone that has a RPC without an output contactor and lights connected to their RPC will tell you that when they turn it off the light stays on for a time. But how is this possible? Because the combination of a capacitor and an inductor in parallel is called a tuned circuit. And that circuit will RING. By this I mean that the inductor will collapse it's magnetic field, and charge the capacitor for a certain amount of time. Then the capacitor will discharge into the inductor for a specific amount of time. and back and forth it will go. Now why is this important? Simple... the value of the inductance (measurement of the inductor) and the value of the capacitance can be mathematically figured to oscillate (RING) at 60 or whatever Hertz that you need it to. And then you have a third leg, that can generate current, that's oscillating it's happy self along creating the third leg. And the split phase power kicks the wheel a bit to keep it going. And it's why that you really need to have run capacitors in an RPC. It gives the RPC the ability to generate more usable power. To this point. I have started and run 20 HP motors that were just sitting on the floor with nothing connected to their output shafts with a 10 HP RPC. I do it all the time when I am testing idlers out before building them into full RPC units. So the capacitors do work, do help and will benefit you in the long run.
Now that you know WAY more about RPC's than any RPC manufacture will EVER tell you. I have some advice. If you can hook up an RPC to a motor and get it running you have enough smarts to build a full RPC with a bit of guidance. If you don't believe this, and want a box that will hang on the wall, and make your idler motor into a proper RPC there are a number of manufactures out there that will sell you just the box. The motor is your responsibility to provide and connect, which is sort of what you have tried to do here.
Ask questions. Message me, if you want. I actually prefer you ask right here. I promise that any question that you have someone else will also have and if the answer is here they can find it too.
