Simulation of a Hydraulic Load Sensing Proportional Valve

Nowadays energy saving is a topical issue due to increasing fuel costs and this aspect is amplified by more stringent emissions regulations that impact on vehicle development. A recent study conducted by the U.S. Department of Energy shows that about five percent of the U.S. energy consumption is transmitted by fluid power equipment. Nevertheless, this study also shows that the efficiency of fluid power averages 21 percent. This offers a huge opportunity to improve the current state-of-the-art of fluid power machines, in particular to improve the energy consumption of current applications. These facts dictate a continuous strive toward improvements and more efficient solutions: to accomplish this objective a strong reduction of hydraulic losses and better control strategies of the hydraulic systems are needed. In fluid power, there exist many techniques to reduce/recover energy losses of the conventional layouts, e.g. load sensing, electrohydraulic flow matching, independent metering, etc. One of the most efficient ways to analyze these different layouts and identify the best hydraulic solution is done through virtual simulations instead of prototyping, since the latter involves higher investment costs to deliver the product into the market. However, to build a fluid power machine virtual model, some problems arise relative to different aspects, for instance: loads on actuators (both linear and rotational) are not constant and pumps are driven by a real engine whose speed depends on required torque. Furthermore, it is important to achieve higher level of detail to simulate each component in the circuit: the greater detail, the better the machine behavior is portrayed, but it obviously entails heavy impact on simulation time and computational resources. Therefore, there is a need to create mathematical model of components and systems with sufficient level of detail to easily acquire all those phenomena necessary to correctly evaluate machine performance and make modifications to the fluid power component design. In this context, a hydraulic proportional valve PVG 32 by Danfoss is taken as an object of study, its performance is analyzed with suitable mathematical model and simulation is done to observe closeness of a model to the laboratory experiment.


Introduction
There are many fluid power machines in the industry. An example from material handling equipment is a forklift truck. Hydraulic circuit of it consists of load sensing variable displacement pump in the flow generation unit, a block of PVG32 valve in the control unit and number of actuators as users. As a single flow generation unit feeds different actuators to steer the wheels, lift the load and incline the forks, this paper focuses on a control valve PVG32 involved in fluid power transfer.
An example of the load sensing pre-compensation technique is a block of PVG32 made by Danfoss. There is a PVB module for each user followed by inlet module PVP. Each PVB module comes with electro-hydraulic actuation PVE and manual drive PVM for safety. The flow rate controlled by each PVB is exclusively a function of the available command signal. In fact, the load-sensing PVG32 makes the flow independent of each user, while there is a variability of the load between users. Working principle of PVG32 is present in the manual of the valve [1] and Mirzaliev [2] studied the valve with different types of spools.
Cross section of the PVB module is seen in Figure 1. Flow passing through the local compensator LC feeds port A or B depending on the main spool MS position, which is controlled by the operator via PVE or PVM.

Experimental tests
Flow rate versus spool position. To start the steady state analysis of the block PVG32, it is possible to assume that local compensator is fixed in its regulating condition. By design, one can assume that its fixed position during regulation is such to have maximum opening and this position doesn't vary considerably at steady state operating condition. Therefore, in the experimental tests, the spacers are machined and mounted on the local compensator to fix its position in PVB block. As there are many configurations of the spool in the PVB module, such as floating center (serial no 9782) or closed center (serial no 9721), in the laboratory test, floating center spool is chosen.     As seen from the figure above, an upper graph shows two repititions of pressure vs flow measurements at port P to observe repeatability. In the lower part of the figure, graphs of pressure vs flow rate of port A and B (with two repititions) are seen.

SoildWorks Flow Simulation
Solidworks Flow simulation is a convenient CFD tool. As it is mentioned above, spool position and flow rate are taken as boundary conditions. As an output of CFD simulation, the pressure drop across the PVB module ∆p is computed. The outlet pressure can be set to ambient atmospheric pressure. It is also necessary to consider mesh sensitivity analysis to find the minimum number of cells able to accurately represent fluid-     In summary, it is seen that discharge coefficients at the P-A and B-T connections fluctuates around 0.7.
Regarding Cd at local compensator, CFD simulation demonstrated insignificant pressure drop across LC.
Therefore, it is possible to set Cd =0.7 at the metering edges of the mathematical model of PVB module.

Amesim modeling
Below is the mathematical model of the PVB. It is composed two components, namely, the local pressure compensator on the left and the main spool on the right. Ports A and B are interconnected via restrictor. As input parameters, position of the spool and pressure is given. As an output, flow rate through the valve is computed. As the experimental simulation is performed with fixed LC, mass component of the local compensator model has upper displacement limit.  The answer lies in the most important part of the main spool, i.e. the notch connecting power port with the working port. Therefore with great attention, flow area versus displacement data should be calculated for the notch connecting working port, 3D of which is given below. Orthogonal area has the shape of rectangle. From 3D drawing as above, it is possible to obtain the following information: = 13.4° and ℎ 0 = 0.29 ; 0 = 1.27 and = 6.37°; (2) is the plane perpendicular to spool axis and = 1 + 2 , where 1 is the area of the rectangle of width 2 and ℎ; and 2 is the area of the segment between arc and rectangle. Let us assume that the latter 2 is negligible. Let ℎ 1 be the height of the rectangle at displacement . Then ℎ 1 = × . Analogously, we relate with spool position . ℎ = ℎ 0 + ℎ 1 = ℎ 0 + × ; = 0 + 1 = 0 + × Frontal area (aka radial) is the sum of the trapezoid 2 and a half circle 1 .
1 is calculated with reference to [3]. Finally, by choosing minimum between frontal and orthogonal areas and minimum is imposed to Amesim.

Conclusions
The hydraulic proportional load sensing valve PVB was discussed through the simulation and experimental analysis. These useful conclusions are obtained: (1) The mathematical model made in Amesim of the PVB module of the PVG32 block correctly describes the real valve.
(2) Considerable throttling losses are observed at the connection between B and T when connection P and A is open, since the spool valves are designed with over-running loads in mind.
(3) Further research will concentrate on energy saving techniques by using independent metering, electronic flow matching, etc.