Cycling is usually due to low refrigerant charge....it may cycle when it is overcharged also.
The triple pressure switch (TP switch) acts on both too much and too little refrigerant.
When you have too little, the TP switch will stop the current going to the clutch in order, to save the compressor.
When you have too much it does the same thing.
When the system is at equilibrium, the pressures on both sides are equal. Usually there is enough pressure in the system so the the TP switch will turn on the compressor.
The suction and discharge lines, referred to as the HI and LO sides are just that, HI and LO pressure lines.
When you run the A/C, the suction (LO) line has gaseous (cold) refrigerant, so the pressure is Low. The discharge (HI) side has liquid (hot) refrigerant, so the presure is Hi.
If you don't know what I am talking about look up Boyles law pv=t
When the A/C is running you should get pressures around 25psi for LO and 225psi for HI.
Now when your A/C is chugging along, the pressure on one side may drop or rise, so that the TP switch says "hey that's too low or that's too high, I'm killing the compressor".
So the system runs a little bit and the pressure drops down to within the specs and now the TP switch allows the compressor to turn on again. Repeat that, and you have cycling.
The gist of all of that, is, you may be close to one of the cut off points when your A/C is running and when it actually operates, it creates the situation of the compressor cycling.
You may also have air in the system.
When you let out the R-134a, you needed to pull a vacuum and boil out all the water in the system, then charge into the vacuum.
R-134 systems need 26.5oz of refrigerant.
How much did you put in ?
If more than 26oz, you may blow your relief valve or worse your compressor.
