Modeling and simulation of hydraulic systems with pressure inter-conditioning consumers.

Bucuresteanu, Anca

1. INTRODUCTION

Modeling and simulation of hydrostatic systems represent modern methods of research and engineering design that allow determining static and dynamic characteristics before making a prototype (Prodan, 2006). There are situations when the hydraulic consumers (cylinders) must perform a working cycle conditioned by reaching some pre-selected pressures (Prodan, 2004). Figure 1 presents such a kind of installation.

The pumps [P.sub.1] and [P.sub.2] feed the system with oil from the tank T. The flow [Q.sub.1] defines the pump [P.sub.1], while [Q.sub.2] defines [P.sub.2], and usually [Q.sub.1] > [Q.sub.2]. Absorption is made through suction filters [F.sub.1] and F2. Pressures [p.sub.1max] and [p.sub.2max] adjusted by means of the pressure valves [PV.sub.1] and [PV.sub.2] to the two pumps meet the condition [p.sub.1max] < [p.sub.2max]. The circuits of the two pumps are connected through the check valve [CV.sub.1]. The directional control valve DCV helps starting on the system and reversing the directions. The two hydraulic cylinders [C.sub.1] and [C.sub.2] represent the consumers. Two sequencing valves ([SV.sub.1] and [SV.sub.2]) equipped with check valves ([CV.sub.2] and [CV.sub.3]) ensure the desired working cycle based on two pre-adjusted pressures ([p.sub.1] and [p.sub.2]). The pilot operated check valve POCV prevents accidental charge failure of the cylinder [C.sub.2].

[FIGURE 1 OMITTED]

The pressure gauges [M.sub.1]--[M.sub.4] display the four adjusted pressures.

If considering the start positions of the cylinders as being those in the figure, then the system works as follows:

When powering the electromagnet [S.sub.1], cylinders [C.sub.1] moves to the left-hand side with the high speed resulted by summing of the flows [Q.sub.1] and [Q.sub.2]. The pressure required for the movement is lower then pressures [p.sub.1max] and [p.sub.1]. In this situation the sequencing valve [SV.sub.1] is closed and cylinder [C.sub.2] does not move. Moreover, the pilot operated check valve prevents its accidental failure (Bucuresteanu, 2003).

If cylinder [C.sub.1] reaches the end of the travel, then the pressure increases and exceeds the values [p.sub.1max] and [p.sub.1]. The valves [PV.sub.1], [SV.sub.1] and POCV get open and the cylinder [C.sub.2] starts descending. The flow supplied to this cylinder is [Q.sub.2] only, because the pump [P.sub.1] discharges to the tank through the pressure valve [PV.sub.1]. Therefore, the cylinder [C.sub.2] starts only when the pressure [p.sub.1] adjusted on [SV.sub.1] is reached.

If powering the electromagnet [S.sub.2], the cylinder [C.sub.2] ascends due to the oil that gets trough at the lower part of the pilot operated check valve POCV. The ascending is accomplished with the flows summed from the two pumps. When the pressure p2 adjusted on the check valve [CV.sub.3] is reached, the cylinder [C.sub.1] withdraws to the initial position. The pilot operated check valve POCV ensures the locking of the cylinder [C.sub.2] in case of accidental power failure.

2. MODELING AND SIMULATION OF THE SYSTEM

If the characteristics of the system components and the working parameters are known, then the modeling and simulation of the system can be done after having made the operating diagram. The cylinders have a significant influence from the dynamic point of view, among the components of the system. The mathematical model specific to the hydraulic cylinders working as those in Figure 1 is the one below (Oprean et al., 1998):

[Q.sub.HC] = [S.sub.1] x v + [a.sub.HC] * p + [V.sub.MHC] / [E.sub.0] x dp / dt (1)

M x dv / dt + [b.sub.HC] x v + [summation] F = p x [S.sub.1] (2)

where: [Q.sub.HC]--input flow of the hydraulic cylinder; [S.sub.1]--active surface of the cylinder; v--instant speed; [a.sub.HC]--linear coefficient of the flow loss in proportion with the pressure; p--pressure on the active surface of the cylinder; [V.sub.MHC]--average volume of pressured oil inside the active chamber; [E.sub.0]--elasticity module of the oil; t--time; M--weight of the moved assembly; [b.sub.HC] linearised coefficient of force losses in proportion with the speed; [summation]F--sum of resistant forces within the driving cylinder. Figure 2 shows the speed characteristics for [C.sub.1] during a working cycle.

[FIGURE 2 OMITTED]

When moving from the left-hand side to the right-hand side, by summing the flows, a speed of 0.1 m/s is ensured. When withdrawing, only the pump [P.sub.2] supplies oil, and a speed of only 0.05 m/s is reached. When actuating to the left-hand side, the pressure on the active surface develops according to the curve in Figure 3. The cylinder [C.sub.2] performs a cycle with the speed developing as shown in Figure 4. When descending, the useful flow comes only from pump [P.sub.2]. When returning, the speed is higher because of summing of the flows, at a pressure lower than the one adjusted on the pressure valve [PV.sub.1]. Figure 5 shows the development of the pressure on the active surface.

The simulation allows establishing the influence that each component has over the system working. Due to specialized software, optimal components can be selected and the dynamic balance of the system can be achieved (Oprean et al., 1989). Thus, by using the curve in Figure 6, one can study the transit flow of the pilot operated check valve during the whole cycle.

[FIGURE 3 OMITTED]

[FIGURE 4 OMITTED]

[FIGURE 5 OMITTED]

[FIGURE 6 OMITTED]

These curves/characteristics can be compared with those provided by the components manufacturer and, if necessary, modifications can be made from the design stage, so as the costs generated when making the prototype will decreased.

3. CONCLUSION

The hydraulic systems with pressure inter-conditioning are recommended for devices and presses actuation and for machine-tools. They are simple and reliable systems that can operate even in hazardous environment. The inter-conditioning being purely hydraulically, the electric installation is very simple. There is specialized software for the modeling and stimulation of those systems, which allows the optimization of the design and the selection of the components based on both technical and cost criteria. Modeling and simulation reduce the risks of a faulty working of the prototype, the test time and the costs, as well.

4. REFERENCES

Bucuresteanu, A. (2003). Hydraulic and Pneumatic Actuators, Printech Publishing House, ISBN 973-652-819-9, Bucharest

Oprean, A.; Ispas, C.; Olaru, A. & Prodan, D. (1989). Hydraulic Actuators and Automation, Technical Publishing House, ISBN 973-98652-2-4, Bucharest

Oprean, A.; Dorin, A.; Olaru, A. & Prodan, D. (1998). Hydraulic Actuators Equipments, Bren Publishing House, ISBN 973-98652-2-4, Bucharest

Prodan, D. (2004). Machine-Tools Hydraulics, Printech Publishing House, ISBN 973-718-109-3, Bucharest

Prodan, D. (2006). Elements and Hydrostatical Systems Modelling and Simulation, Printech Publishing House, ISBN (10)973-718-572-2, Bucharest