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     Self-excited oscillations, caused by variable displacement hydraulic pump and motor controls are the one topic I could discuss for hours, and I surely will devote a number articles to this very interesting, but also extremely extensive subject. Not the theory and math, but rather some (the key word is some) practical stuff taken from my personal experience, like what can be attempted to "fix" them controls when they go swingy on you.

      I would like to begin the first chapter of my self-oscillating chatter with focusing on the control fluid leakage as a factor, that can condition self-oscillations in pump and motor displacement controls. By control fluid I mean - hydraulic fluid, that is directed from a control spool to the servo-cylinder, and by the leakage I mean the controlled (with a calibrated orifice) leak of this fluid to tank (or pump case).

     You will find this in many pump control assemblies - that tiny orifice that creates a leak in the servo-pressure line. It is there for a reason, in case you wondered, for several reasons actually. For one - the leakage flow helps cooling the pump, especially in stand-by or dead-head modes. But there is another benefit to its presence - the control fluid leakage can often resolve control instability issues, because it shifts the working position of the control spool to a more stable zone, since it "forces" the spool to supply more oil. The drawback of the efficiency losses due to the added leakage comes with the benefit of a stable behavior.

    From theory to practice! Below IH is presenting a practical example of how controlling the amount of servo-fluid leakage solved the problem of unwanted self-oscillation of high pressure cut-off control in a Rexroth A7VO open circuit pump (extensively used and reasonably warn-out). I also created a video that contains the pressure readings at different stages of the "experiment", but you should read the description before watching it, otherwise it won't make much sense.

    The problem - Rexroth A7VO55LR3E/61L open circuit pump, equipped with torque limiter and high pressure cut off control, both with hydraulic overrides (I placed a detailed description of this model in the back-engineering section, also you can find the schematics and the detailed cut view of the main control spool to the left), was presenting self-oscillating behavior in the dead-head condition, when the cut-off was kicking in (seen at the beginning of the video). The self-oscillation was present both with and without the cut-off setting override pilot. In the video the 400 bar pressure gauge is connected to the A1 port (the outlet pressure), and the 250 bar gauge is connected to the  X3 port (servo-pressure).

    In such situations many people assume that these self-sustained oscillations can be fixed by means of strangulation/dampening of the control flow with a "strategically placed"orifice, but despite seeming like a perfectly logical next step, it often doesn't work or even brings undesirable consequences - like the increase of the control response time. This pump actually has a thread in the control fluid passage (cut-view), so this theory was easy to test. Placing a 0.8mm orifice in this passage didn't solve the self-oscillation issue, and also resulted in an unacceptably slow response time of the cut-off control, which can be seen by the 350 bar pressure peak, easily visible even on the analogical pressure gauge in the second part of the video.

    If you check the schematics, you'll see that there is a small orifice in the T1 port, that provides the control fluid leakage to an external tank line. Since these pumps have no drain line (the case is internally connected to the suction line) - the first thing that comes in mind is - it is there to allow the pump to dead-head for longer periods of time before overheating like hell, as the T1 flow carries away some of the heat, generated by the pump. However, by looking at the schematics, one might assume that, aside from the overheating rate,  this control should behave in the same manner with the T1 plugged.  Well, if you try it - you will see that the cut-off does cut-off, but it self-oscillates even more violently than before. (seen in the third part of the video)

    What we got so far is - no control fluid leakage - violent outlet pressure self-oscillation, some control fluid leakage - less self-oscillation. Let us  play around this tendency a little, shall we? Let us take out the 0.8mm orifice the T1 port was carrying, and connect it to the tank line via an adjustable restrictor valve to be able to infinitely control the control fluid leakage. The result can be seen in the fourth part of the video - two things happen as the rate of the leakage increases - the dead head pressure rises (slightly), and the behavior of the control becomes more and more stable, with the self-oscillations eventually disappearing.

   So, we are finally getting somewhere - increasing the amount of the control fluid leakage results in a more stable dead-head condition of our pump. By the way,  a "filed" variant of the added leakage experiment can be easily performed by means of a gauge test hose, connected to the  X3 port (which already has the conveniently placed test fitting there), with the other end disconnected (I would point it to an adequate vessel, though...). The behavior of the control with this "improvised" added leakage is seen in the next scene - again - no self oscillations here.

   In case you wonder how much leakage the disconnected test hose added to the already existing one - observe the next part, where you can see a one liter volume, filled by the test hose with the pump dead-headed at 230 bar. The added leakage is around 4-5 liters per minute.

   Several orifice sizes were tested in the T1 port, and in the end the original 0.8mm orifice was replaced with a 0.9mm orifice, which didn't remove the oscillations completely, but reduced them to an acceptably low level, with a relatively small increase of the leakage flow. The final result can be seen in the last part of the clip.

   Conclusions:

   1) Control fluid leakage, along with the obvious benefits of creating an additional cooling flow, can solve control stability issues and reduce self-oscillations.

   2) A 0.9 mm orifice is different from a 0.8 mm orifice, although the difference is barely seen with the naked eye.

   3)  In filed conditions, gauge connecting hoses can serve as a rough replacement of an orifice or a restrictor valve.

   And now (finally!!!) the so promised video:
A7VO55LR3E hydraulic diagram
A7VO55LR3E Control Spool Detail
O.8mm and 0.9mm orifices