With clear measurements, the issues are also much clearer.
For the conditions specified, the power supply is performing pretty much as you might expect. The problem is that this power supply is
not appropriate for the need.
When you look at the transformers, the voltages are given as 12V and 24V - which are AC voltages. AC voltages like this are typically given as RMS. If I skip quickly through the math, this means that you should only expect DC voltages of 12V and 24V when your power supply is operating at its rated load. Considering diode voltage drops and other circuit parameters, this supply is actually operating within reasonable expectations.
The first point of understanding is that the "no load" voltage of V
JK = 55.2V @ 0A relates to the
peak voltage. The capacitors will charge up to this and keep the voltage high - but it is meaningless. It's like a weightlifter lifting only the bar - with no weights on it.
The under load measurement of V
JK = 37V @ 2.6A is a more realistic reflection on the demands of the load and the capabilities of the supply. However, as you have observed, at this voltage, the controller has a problem.
This is the obvious solution -
If you want to supply enough voltage to the motor and controller you will need a 48 V supply instead of a 36 V supply, which means you will need to put two 24 V transformer secondaries in series rather than 24 V and 12 V.
but with one
significant caveat...
But if you do this with the capacitors you will get nearly 70 V unloaded. You have to be careful about not exceeding the maximum voltage on the controller.
The answer is that your power supply needs to be
voltage regulated. The regulator must keep the voltage to a respectable level across a range of current - and allow the required current to pass.
You might be asking yourself ...
So why is this so hard? - and the answer lies in the normal mode of operation for which the scooter equipment was designed to operate - batteries. Four 12V, high capacity batteries will produce a reasonably stable 48V (nominal) over the range of current drawn by the motor. A simple unregulated supply will not do this (unless it was
massively overrated).
To continue your project, you will need to regulate your supply - or run off batteries.