The A320 PTU has an in-line variable displacement pump on one side and a bent-axis fixed displacement pump on the other connected directly by a shaft.
what would be needed to know how fast the shaft turns during PTU operation?
Source: eaton.ru (PDF)
From an A320 systems design document (own work from published on-line data):
Power Transfer Unit (PTU) Eaton MPHV3-115-1C
The PTU is a double hydraulic pump mounted on a common axis, one side connected to the Green hydraulic system and the other to the Yellow hydraulic system. This enables the Green system to be powered by the Yellow system and vice versa, without hydraulic fluid transfer between the two systems. The PTU enables the gear to be retracted upon engine 1 fail, and for the LH elevator to be powered upon engine 2 fail.
The PTU has the following characteristics:
- Each pump can function as a hydraulic motor for powering the pump at the other side.
- The Green side pump is a fixed displacement bent-axis type, delivering max. 90 l/min on the Green side and costing max. 120 l/min on the Yellow side. Delivered flow is a linear function of pump rotational speed.
- The Yellow side pump is a variable displacement type, delivering up to 50 l/min on the Yellow side at a cost of 60 l/min on the Green side.
- The PTU switches ON automatically when one side has a pressure that is 500 PSI lower than the other side. It switches OFF when pressures are close to equal.
- PTU function can be inhibited from a switch in the cockpit.
The PTU shaft RPM can be determined from the following:
There will be dynamic effects in RPM to to changes in power delivery.
The shaft speed is dependent on the flow rate through the fixed displacement side of the PTU. I am not sure what the size of the A320 PTU pumps are, but it will have some fixed amount of volume per revolution, such as 0.9 cubic inches (14.7 ml) per revolution. Therefore, if you know the flow rate into that pump (Green Side) you can easily calculate to the shaft speed.
Again, I am not familar with the A320 system specifically, but the PTUs I am familiar will all have a flow regulator upstream to control the maximum flow rate (and thus speed) of the PTU.
If you are not allowed to attach the measuring device to it, the two unobtrusive methods are by sound or by video.
Measuring by video would require the device to be visible, have some surface features to determine some particular rotation and the possibility to make probably video recording while in operation. The recorded video can be split into individual frames in the simplest case just estimating the rotation visually, as the time interval between the frames would be known. Otherwise, tools like OpenCV or fast.ai may help to analyse the images automatically. But these methods are limited by the number of frames per second you can capture. Most of the cameras would only do 30 frames per second or about but much faster cameras are available if you look on purpose. But the method can also capture slow or irregular movements.
Another approach is by sound - record the sound and plot the windowed spectrogram of recording. This can be done with less access possible, and work with higher frequencies, as long as the rotation sound is loud enough. Of course it will be a strong band from the engines on the spectrogram but it may fall far outside the reasonable frequency range of this "barking dog".