# A Critical Analysis of Valve-Compensated Hydrostatic Actuators: Qualitative Investigation

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## Abstract

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## 1. Introduction and Problem Definition

## 2. Basic Designs

_{1}and R

_{2}, are placed in the circuit for pressure spike protection. These valves are mandatory for every hydrostatic actuator, although they will not be represented in the remaining circuits of this paper for the sake of clarity. The check valves C

_{1}and C

_{2}connect both sides of the cylinder to the tank, keeping the circuit pressure above a minimum value.

_{2}, sensing the cap-side pressure, connects the rod-side to the tank.

_{1}and C

_{2}, sense the rod and cap-side pressures, respectively, connecting the cap and rod-sides to the charge circuit whose pressure is limited by the relief valve R. When the cap-side pressure is higher than the rod-side pressure, valve C

_{2}opens, connecting the rod-side to the charge circuit. When the rod-side pressure is higher than the cap-side pressure, valve C

_{1}opens, connecting the charge circuit to the cap-side. This is an example of a motored circuit because the pump absorbs energy from the load in both quadrants II and IV.

_{C}) compensates for the uneven cap and rod-side flows (the cracking pressures at each side of the valve, ${p}_{\mathrm{crp}}$ and ${p}_{\mathrm{cra}}$, are different). Two externally activated 2 × 2 valves are added to dampen out pressure oscillations. The circuit in Figure 7b, proposed in [12], is almost identical to the one in Figure 7a; the only difference being in the central position of the 3 × 3 directional valve, which allows for a limited leakage between the high-pressure line and the charge circuit. The addition of leakage in the central position of the directional valve in Figure 7b aims to correct some pressure oscillations caused by commuting between the charge circuit and the two sides of the cylinder.

_{1}, V

_{2}, C

_{1}, C

_{2}and V

_{C}) are switched by directly sensing the pressure on the cap and rod sides. We therefore think it is appropriate to coin the term direct sensing (DS) to categorize circuits using this kind of compensation as opposed to indirect sensing (IS) circuits, where the compensation valve is activated by means of an external stimulus, as in Figure 5. DS systems have also been termed type A switched systems, following the nature of the system dynamics [13]. Likewise, IS systems can be identified as type B switched systems.

## 3. Flow Commutation in Valve-Compensated Circuits

_{1}and C

_{2}in Figure 6 need information from pressures ${p}_{\mathrm{a}}$, ${p}_{\mathrm{p}}$ and ${p}_{\mathrm{c}}$, simultaneously, when operating in pilot mode, i.e., when valves C

_{1}and C

_{2}are opened by the pressure acting on their pilot ports. On the other hand, they need information from ${p}_{\mathrm{a}}$ and ${p}_{\mathrm{c}}$ or from ${p}_{\mathrm{p}}$ and ${p}_{\mathrm{c}}$ when operating in normal mode, i.e., when valves C

_{1}and C

_{2}are opened due to the pressure differential between their input and output ports. Likewise, valves V

_{1}and V

_{2}in Figure 4 need information from pressures ${p}_{\mathrm{a}}$ and ${p}_{\mathrm{p}}$ independently. Finally, the circuits shown in Figure 7 need information from $\left({p}_{\mathrm{p}}-{p}_{\mathrm{a}}\right)$ to connect the charge circuit to the main lines. Out of the three sources of pressure information, ${p}_{\mathrm{a}}$, ${p}_{\mathrm{p}}$ and ${p}_{\mathrm{c}}$, only the charge circuit pressure, ${p}_{\mathrm{c}}$, can be known in advance.

#### 3.1. New Definition of Operational Quadrants

#### 3.2. Instability during Flow Commutation

## 4. Flow Compensation Using Pilot-Operated Check Valves

_{1}and C

_{2}in the circuit shown in Figure 6, reproduced in Figure 13. Let us disregard conduit losses in the circuit and study the behaviour of these valves when subjected to the pilot pressures ${p}_{\mathrm{p}}$ (valve C

_{2}) and ${p}_{\mathrm{a}}$ (valve C

_{1}). Assuming an on-off operation for the check valves, it is possible to write that valve C

_{2}opens when [14]

_{1}

_{1}and C

_{2}change their status according to the pressures on the cap- and rod-sides of the cylinder. We do this in the following section.

_{1}and C

_{2}in pilot operation (inequalities 1P and 2P, respectively) and normal operation (inequalities 1N and 2N, respectively)

_{1}, A

_{2}and B, indicate instabilities in the circuit, where both valves are open or closed at the same time. According to (7), valve C

_{1}is open in the region above line 1P and to the left of line 1N. On the other hand, valve C

_{2}is open in the region below lines 2P and 2N.

_{1}and C

_{2}, are simultaneously closed. The situation is also unfavourable when the cap and rod-side pressures are high, causing both valves to open. This may well be the case during motoring quadrants if a higher than usual pressure is chosen for the charge circuit.

_{1}must remain closed while C

_{2}is open during the whole operation. However, given that ${p}_{\mathrm{p}}$ continuously changes from zero to a maximum value, this ideal situation is not likely to happen. Figure 16 shows three possible paths to be taken by the pressure, ${p}_{\mathrm{p}}$, when the same settings used for the diagram in Figure 14 are applied. Depending on the charge pressure value (note that ${p}_{\mathrm{a}}={p}_{\mathrm{c}}$ during operation), the cap-side pressure might change along lines L

_{1}, L

_{2}or L

_{3}. In the first case, represented by line L

_{1}, region A

_{1}is crossed and, for a moment in time, both valves C

_{1}and C

_{2}are simultaneously open. If line L

_{2}is chosen, region B is reached and, for a moment, valves C

_{1}and C

_{2}are closed. If we choose to increase the charge pressure even more (line L

_{3}), we cross region A

_{2}, where C

_{1}and C

_{2}are open. In summary, there is absolutely no way to obtain a sound operation of the circuit in Figure 15. This circuit does not work anyway, regardless of how you operate the valves; one way or another, they fail.

_{1}and C

_{2}do not operate as expected, we might still be able to improve the circuit performance. Figure 17 shows one solution to shift the operation zone to the right during the first and fourth quadrants [14].

_{1}and V

_{2}, is to set a minimum pressure at both sides of the cylinder, below which no motion takes place. This way, we can shift the operation zone to the right. Take, for example, line L

_{2}in Figure 16, represented again in Figure 18. If the minimum cap-side pressure is set to 15 bar, the circuit operates along the zone where C

_{1}is closed and C

_{2}is open, which fulfils the requirement for a sound circuit operation. The minimum cap-side pressure is set by sensing the rod-side pressure, ${p}_{\mathrm{a}}$. Since the cylinder will not move before the opening of valves V

_{1}and V

_{2}(Figure 17), we can write that ${p}_{\mathrm{p}}={p}_{\mathrm{a}}/\alpha $. Thus, when ${p}_{\mathrm{a}}$ reaches a minimum value, valve V

_{2}opens, unblocking the flow coming from the rod-side during the first quadrant. A similar situation happens in the fourth quadrant. Figure 18 shows the operation in the first and fourth quadrants of the circuit shown in Figure 17.

_{3}in Figure 16. In that case, ${p}_{\mathrm{min}}$ should increase to escape the region where both valves, C

_{1}and C

_{2}, are open. Furthermore, depending on the value of the external force, $F$, the cylinder may not complete its stroke during the fourth quadrant of operation. In fact, at some point during the pendulum swing in Figure 15, the external force, $F\left(\theta \right)$, becomes low enough to render ${p}_{\mathrm{p}}<{p}_{\mathrm{min}}$. As a result, the piston stops before completing its stroke.

## 5. Flow Compensation Using Directional Valves

_{1}and V

_{2}as ${p}_{\mathrm{cr}1}$ and ${p}_{\mathrm{cr}2}$, respectively. The following conditions must be fulfilled for each valve to be activated

_{1}and V

_{2}, are identical (${p}_{\mathrm{cr}1}={p}_{\mathrm{cr}2}={p}_{\mathrm{cr}}$). We also consider that ${p}_{\mathrm{cr}}=6\text{}\mathrm{bar}$, a typical cracking pressure for this type of valve. Lines L

_{1}and L

_{2}represent two possible variations of the cap-side pressure, ${p}_{\mathrm{p}}$, as the circuit operates between the first and fourth quadrants. Note that the only operation path acceptable is the one along line L

_{1}, crossing a large region where valve V

_{2}is open, connecting the rod-side to the charge circuit, and valve V

_{1}is closed. However, for smaller values of ${p}_{\mathrm{p}}$, both valves are closed. In the first quadrant, the cylinder extends anyway because of the check valve C

_{2}, connecting the rod-side to the charge circuit. In the fourth quadrant, since valve C

_{2}remains closed, the cylinder will stop moving at point A, where the cap-side pressure reaches 6 bar. As a result, the weight will move in a full swing to the left (first quadrant) but will stop before returning to the upright position on its way back (fourth quadrant).

_{1}and I

_{2}, are placed at the cap and rod-side of the cylinders, dividing the pump-cylinder lines into two parts. The inline check-valve concept resembles the counterbalance valves of the circuit shown in Figure 17.

_{1}and C

_{2}, and a relief valve, R, were added to keep the lowest circuit pressure within acceptable levels. First quadrant operation only requires that the cap-side pressure becomes high enough to open valve I

_{2}. As soon as the cylinder starts extending, the low pressure created at the rod-side opens the anti-cavitation valve C

_{2}. In the third quadrant, the 2 × 2 valve, V, is activated by the pressure differential between the pump ports, ${p}_{\mathrm{pi}}$ and ${p}_{\mathrm{po}}$, so that the cap-side pressure is set by the relief valve, R, when the following inequality is satisfied

_{0}, replaces valves V and R in Figure 21, to make third quadrant operation possible. Although there is practically no conceptual difference between the designs in Figure 21 and Figure 22, we note that the circuit in Figure 22 allows for motoring operation in the second quadrant. In that case, the counterbalance valve V

_{2}opens directly by the rod-side pressure. According to our previous classification, this circuit is partially motored, since it cannot operate in the fourth quadrant.

## 6. Flow Compensation Using Single-Directional Valve

_{1}and L

_{2}, along the first and fourth quadrants. In both cases, there is a region where communication between the charge circuit and the cylinder is either blocked (Figure 23a) or partially opened (Figure 23b). Such region has been called “critical” [11] and, apparently, should be minimized for a smooth circuit operation. As seen in this paper, although such condition improves the circuit performance, the instabilities are not completely eliminated even when the critical region is reduced to zero.

_{0}, which does not have either a central position or a spring element whose cracking force needs to be overcome.

_{1}is poor. In fact, as the circuit operates between points A and B, the rod-side is disconnected from the charge circuit and, since we do not know for sure where the borderline between quadrants II and I is located, it is possible to have the rod-side disconnected from the charge circuit in the first quadrant with the risk of pump starvation. In fact, the only guarantee of a smooth operation with no ambiguous shift between quadrants would be along line L

_{2}in Figure 26, for which the rod-side pressure, ${p}_{\mathrm{a}}$, is zero. This would be achieved by connecting the compensation valve to the tank, as opposed to the accumulator in Figure 25. However, such arrangement would result in a considerably low rod-side pressure, with an inherent risk of cavitation.

## 7. Solving the Flow Distribution Problem

- (a)
- Neither the individual values of pressures ${p}_{\mathrm{p}}$ and ${p}_{\mathrm{a}}$ nor the pressure differential $\left({p}_{\mathrm{p}}-{p}_{\mathrm{a}}\right)$ can be correctly used as an indicator for the operational quadrant;
- (b)
- The only correct indicator for the operational quadrant is the cylinder force, $\left(\alpha {p}_{\mathrm{p}}-{p}_{\mathrm{a}}\right)$.

_{a}, otherwise the pressure at port a is set to zero. A similar reasoning can be applied to port b.

_{1}and V

_{2}, must be smaller than the charge pressure, ${p}_{\mathrm{c}}$, so that they are fully open as soon as the triggering pressure signal is received. Although it is not shown in the figure, there is absolutely no need for the charge circuit to feed both the compensation valves and the signal circuit simultaneously, as they work independently from one another.

_{1}and V

_{2}in Figure 8 change with the cap and rod-side pressures. For instance, following line L, suppose that the load is initially pulling the cylinder rod in such a way that ${p}_{\mathrm{p}}>\alpha {p}_{\mathrm{a}}$ (operating point 1). In this case, we have that ${F}_{\mathrm{R}}<0$ and $v>0$, which means that the actuator operates in the second quadrant (Figure 10). Valve V

_{1}then opens up, connecting the cap-side to the charge circuit while valve V

_{2}remains closed, as expected. As the cap-side pressure rises past point 2, ${F}_{\mathrm{R}}$ becomes positive and the circuit enters into pumping mode. As a result, valve V

_{1}closes while valve V

_{2}opens, as is expected for first quadrant operation.

_{1}in Figure 26 could not be altogether smooth. Observe that line L in Figure 29 coincides with line L

_{1}in Figure 26. Thus, if we follow line L in Figure 29, we see that, in the stretch between operating points 2 and 3, we would have had the cap-side connected to the charge circuit in Figure 26 (note the dashed line ${p}_{\mathrm{a}}={p}_{\mathrm{p}}$ is the same line dividing the two regions in Figure 26). However, the cap-side connection between points 2 and 3 would have happened in the first quadrant, causing the circuit to misbehave. This is why eliminating the “critical region”, as defined in Section 6, does not solve the problem.

## 8. Conclusions

## Author Contributions

## Funding

## Conflicts of Interest

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**Figure 1.**The problem of unmatched flows in single-rod actuators: (

**a**) pump starvation during extension; (

**b**) cap-side pump overflow during retraction.

**Figure 8.**Circuit with signal processing and flow compensation modules [15].

**Figure 11.**Critical zones and quadrant division [14].

**Figure 19.**Circuit with two 2 × 2 compensation valves and external force on the cylinder rod (first and fourth quadrants).

**Figure 24.**Circuit connections for: (

**a**) ${p}_{crp}=\alpha {p}_{cr}$; (

**b**) ${p}_{cra}={p}_{cr}/\alpha $.

**Figure 29.**Compensation flow connections for the circuit in Figure 8.

© 2019 by the authors. Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (http://creativecommons.org/licenses/by/4.0/).

## Share and Cite

**MDPI and ACS Style**

Koury Costa, G.; Sepehri, N.
A Critical Analysis of Valve-Compensated Hydrostatic Actuators: Qualitative Investigation. *Actuators* **2019**, *8*, 59.
https://doi.org/10.3390/act8030059

**AMA Style**

Koury Costa G, Sepehri N.
A Critical Analysis of Valve-Compensated Hydrostatic Actuators: Qualitative Investigation. *Actuators*. 2019; 8(3):59.
https://doi.org/10.3390/act8030059

**Chicago/Turabian Style**

Koury Costa, Gustavo, and Nariman Sepehri.
2019. "A Critical Analysis of Valve-Compensated Hydrostatic Actuators: Qualitative Investigation" *Actuators* 8, no. 3: 59.
https://doi.org/10.3390/act8030059