Volume ration is strictly a characteristic of the machine: Even if nothing was flowing through it, it would still have a volume ratio. If the tips and grooves were actually sealed without motion or oil: you could pour water in the suction port to just fill one thread and no more: that would be the volume available to the suction port. Flip the machine over and bring the same thread to just accessible via the discharge port and fill that with water and you would measure the volume of the thread when it is just exposed to the discharge port. If the suction volume were 3 meters cubed and the discharge volume were 1 meter cubed, the machine's volume ratio would be 3.0.

Compression ratio is determined by both the fluid properties and the machine geometry.....If you measure the suction cavity pressure and (if you could) measure the pressure of the thread just as it was first exposed to the discharge port you would have the pressures of the compression process. THIS NOT THE SAME as a recip. which forms part of the confusion. Divide the internal thread pressure near discharge by the suction cavity pressure (in absolute units....) and you will have the compression ratio. The compression ratio is predictable from the compressor volume ratio, the characteristics of the gas being pumped, and the extent of cooling incorporated as the gas is being compressed...

Pressure ratio is a characteristic of the circuit: and is simply discharge pressure divided by suction pressure, both in absolute units. In testing a compressor alone, this number will not include any pressure looses due to suction strainer, suction check valve, discharge check valve, coalescing elements and the like.

So the compressor manufacturer's pressure ratio will not quite be the same as the circuit pressure ratio if the circuit pressure ratio is for instance, discharge header pressure divided by suction header pressure.....but they should be close. The compressor is always going to develop a slightly lower suction cavity pressure than that of the header and a slightly higher discharge port pressure than that measured at the header; so the machine's pressure ratio will be higher than the "header" ratio.

Variable Vi addresses the departure of the compression ratio within the machine from the pressure ratio of the system. If the machine is over compressing, say making an internal P-ratio of 8, where the actual port cavity pressures have a ratio of 6: the machine is overcompressing by a factor of .33. This requires more power input per unit of mass flow: so the Variable Vi arrangement adjusts the machine's seal point for the suction fllow so that the discharge port is exposed earlier in the compression process, so the compression ratio decreases to match the pressure ratio....