Summarizing last month’s discussion, Figure 1 serves as a starting point for explaining the test method used by manufacturers and users of unloading compensator valves and for the development of its math model. The basic test parameters are the 4-way spool position, or spool shift (KVPL in Figure 1), and the load pressure. With bias spring precompression adjusted to the desired value, the procedure involves setting the pump output flow, setting the 4-way spool at a starting position, then changing the variable load pressure. This is done while measuring flows through the compensator spool metering land, to the load, and from the pump. We also measure the compensator inlet pressure, the outlet pressure, and the differential pressure across the 4-way powered land.

Modelling from data
After adjusting the load pressure through its full range, we reduce it, and the 4-way spool is shifted to a new position and held there while the load pressure is again adjusted through the desired range. The result is a set of graphs that displays how well the load pressure remains constant as the load pressure is varied. The simulated results of this test are shown in Figure 2.

A computer program conforming to the above outline was written and has been run many times to explore those parameter values that produce better performance from the valve type in question. The output is the source for the data in Figure 2. Results are a reasonable approximation of actual test data for valves with the same parametric values.

The input data describe the valve that was simulated. It has a spool diameter of 34 in., and the pump is delivering 150 in.3/sec, which is just under 40 gpm. The bias spring has a stiffness coefficient of 250 lb/in., and precompression has been adjusted so that 40 psid is needed to just crack open the compensator spool’s metering land. Total spool travel from end to end is 0.45 in.

An additional parameter is used for investigating the use of notches on the compensator spool: circumference percentage, which is the amount of compensator spool circumference that is notched, expressed as a percentage. It is set to 40%, meaning that the notches occupy 40% of the spool’s circumference without regard to geometric details, except that they are rectangular. Triangular or circular notches cannot be investigated with this model.

The powered land coefficient will iterate from a minimum of 0.1 hole to 18.1 holes in 5 “treads.” As the spool position is iterated from full open toward valve closure, the compensator pressure, PC, will increase. The last parameter sets the exit pressure to 4000 psig. When that pressure is reached, spool position decrease ends, the program increments the powered land coefficient, and spool position is again stepped off from maximum to minimum. There is a special algorithm in the program that causes the spool potion to change more quickly at the large openings (low pressures) and more slowly at the small openings (high pressures). This ensures good data sampling in regions with the most rapid pressure changes.

Results of the simulation
The data graph in Figure 2 is a display of the results of a simulated test on the valve model just described. The graph is a simulation of the conventional test in order to determine the degree to which the valve can maintain the flow to the load for any given setting of the 4-way valve, KVPL. The 4-way setting goes from 0.1 hole to 18.1 hole in four steps.

 Figure 1. A combination analytical schematic, cutaway diagram, and ISO symbols illustrates an unloader system that has been reduced to its most minimal form without sacrificing essential features.

Clearly, the flow is not constant for each of the 4-way settings. For maximum KVPL , 18.1 hole, the flow ranges from 134 to 139 in.3/sec, but flow has a wider range for the mid-range value of 9.1 hole, where the flow varies from 85 to 96 in.3/sec. The least amount of variation occurs at the lowest 4-way setting and is almost zero. The reason for the variations is because the pressure drop across the 4-way valve does not stay constant. This can be seen in Figure 2.

For the maximum setting of the 4-way valve — that is, when the valve is set to the minimum amount of opening (KVPL = 0.1) — its differential pressure drop variation is the greatest, ranging from 141 to 156 psid. However, pressure drop is lowest when the 4-way valve is fully opened; in this case, the pressure variation ranges from 55 to 59 psid.

Flow and force interactions
A kind of inverse relationship exists between what is happening to the load flow and to the compensator spool. That is, when the 4-way spool is at its minimum opening, the bypass flow is at its maximum. Therefore, the compensator spool has its maximum opening. It follows, then, that with maximum 4-way opening, there must be commensurately smaller compensator opening. At the same time, the flow force on the compensator spool is varying widely as well. The flow force acts to influence the position of the compensator spool.

 Figure 2. These simulated results illustrate how well the load pressure is maintained at a constant value as load pressure is varied.

The short explanation for why the flow metering characteristics appear as they do in Figure 2 is the interaction of the flow and bias spring forces with the differential pressure as the load pressure is changed. At zero load pressure, the load pressure increase results in a drop in load flow. This is the reaction of the compensator spool position (compensator valve opening) to the differential pressure and the spring force because the flow force is very low,.

Recall that flow force acts to close the compensator spool, which means it adds to and aids the spring force. This makes the spring seem to be non-linear and become stiffer as pressure increases. The flow force is so pronounced (it reaches about 48 lb in this instance) that it over compensates the load flow! In Figure 2, the output flow at 4000 psi is higher than the flow at pressures less than 500 psi! This can result in a load speed that increases with load pressure — a counter-intuitive consequence of flow force. Changing the engineering parameters can worsen or improve these behaviors.

 Figure 3. Simulated differential pressure drop across the 4-way powered land as a function of load pressure.

Flow force can be the bane of valve designers. However, in this case, it can be to the designer’s benefit. First, it helps to correct for the expected flow dropoff with pressure increase and improves the flow regulation. Perhaps more importantly, the high flow forces are confined to the compensator spool and are removed from the 4-way valve. This means the 4-way spool is easier to shift, relieving the effort needed by any solenoid or human operators.

Conclusions
The simulation program calculates several other variables that are not included in this discussion in the interest of conserving space. Other important issues that could be covered include details and quantification of the flow force, and in simulation, it is easy to explore the effects of having no flow force. This is interesting because it clearly exposes an effect that cannot be accomplished in the lab and is one of many powerful uses of mathematical models.

Math models as design aids cannot be overestimated. Toward that end, then, the following are important:

• The unloading pressure compensated flow control valve does not perfectly regulate the output flow because the valve cannot regulate the pressure drop across the 4-way metering land.

• The reasons for the imperfect regulation is the complex interactions involving pressure, spring, and flow force.

• The flow force results in over-compensation of output flow so that output speed can undergo an increase as load pressure increases. In the best case, it may be possible to counteract the effects of the inevitable dropoff in pump flow as pressure increases, but that requires tuning the system.

• Although the lift-off pressure was set to 40 psi, the lowest differential pressure in the simulation never dropped below 50 psi, while the maximum exceeded 185 psi, consequences of the imperfect regulation.

• The mathematical model is a powerful tool for exploring the myriad what ifs of valve and system design. Some of the possibilities are the effects of changing bias spring precompression, spring stiffness coefficient, spool diameter, spool stroke length, spool notching effects, and pump output flow. All can be assessed before committing to any hardware.

• The mathematical model will never perfectly simulate the real hardware. However, it can take much of the guesswork out of prototype design and testing.

• Because so many variations in performance can be investigated quickly, the models can aid the user and, with a knowledge of the variations that are possible, can lead to much more intelligent and economically achievable performance specifications of the final system.

• Flow forces are relegated to the compensator spool, not the 4-way spool, and become the friend of both the valve designer and the valve operator.

The next issue will take a similar look at the math modeling and simulation of the pressure reducing pressure compensated flow control valve.

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