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Applications of Proportional Valves T
here are many applications for proportional solenoids in the control of hydraulic pressure and flow in both mobile and industrial applications. The terms pressure differential and pressure drop indicate the same entity – a difference in pressure – and are often used interchangeably. In this discussion on proportional valves, we'll use the term pressure differential. Proportional valves are typically catalog rated for a nominal flow at a 5 bar (72.5 psi) pressure differential per flow path for a total 10 bar (145 psid), and a total loop differential across the valve equal to system pressure minus load and return line pressure or ΔpV = pS - pL - pT. In reality, however, very few systems have such an exact pressure differential. Therefore, it is necessary to determine the size of valve, based on the requirements of the system that it will be controlling. To maximize the performance characteristics of a proportional valve, a more thorough examination must be conducted of not only the required actuator flow but also of the available pressure to drive flow through the valve. In most applications using industrial type proportional valves, flow is simultaneously metered in and out of the actuator (much like a pair of interconnected flow controls with sharp-edged orifices) in some proportion to the magnitude of the electric input signal, to provide precise control. And for a sharp-edged orifice of a given size, a mathematical relationship exists between the flow rate through and the pressure differential across the orifice such that: Flow is proportional to the square root of the pressure differential and is expressed as:
Q :: Δp
Meaning, that if the pressure differential is increased by a factor of 4, the flow will double. For example, with a given size valve: If QRATED = 10 lpm at ΔpRATED = 10 bar, what is QACTUAL if ΔpACTUAL = 40 bar?
QACTUAL =
ΔpACTUAL ΔpRATED
• Qrated =
40 •10 = 20 lpm 10
Where: ΔpACTUAL is the actual (or required) pressure differential across the valve ΔpRATED is the catalog rated pressure differential across the valve QACTUAL is the actual (or required) flow passing through the valve QRATED is the catalog rated flow through the valve at a given pressure differential Conversely, pressure differential is proportional to the square of the flow and is expressed as: Δp::Q2 Meaning that, if the flow is reduced by half, the pressure differential is reduced to 1/4. For example, with a given size valve: If ΔpACTUAL = 40 bar and QACTUAL = 20 lpm, what must ΔpRATED be if QRATED = 10 lpm? 2
ΔpRATED
24
2 ⎛Q ⎞ ⎛ 10 ⎞ RATED ⎟ • Δp = ⎜⎜ = ⎜⎜ ⎟⎟ 40 = 10 bar ACTUAL ⎟ Q ⎝ 20 ⎠ ⎝ ACTUAL ⎠
JULY 2022
Initially, increasing the pressure differential will increase the power available to the actuator and the higher flow will outweigh the power lost by the increased differential across the valve. Beyond a certain point, however, the power lost due to the increasing pressure differential becomes larger than the power gained by higher flow to the actuator, as shown in figure 1.
Figure 1: Pressure drop across valve (ΔPV ).
Experience has shown that this point occurs at approximately 1/3 of the maximum available system pressure and can be calculated as: Where: ΔpV = Total valve pressure differential pS = Available system pressure. 1
Δpv =
3
• ps
For example, if applying this to a system with a maximum system pressure of 150 bar (2,175 psi), if the sum of the pressures acting on the load (including acceleration, friction, and pressure losses across other connected components and plumbing) and return line back-pressures add up to 100 bar (1,450 psi), 50 bar (725 psi) remains and is the differential that will drive flow across the valve. Assume that the system has a 200 lpm (53 gpm) flow requirement. The graph in figure 2 is for a valve that at 100% command, passes 220 lpm (58 gpm) at a 10 bar (145 psi) differential (flow curve 1). On the surface, this seems like a reasonable, energy-efficient choice because the valve can pass the required flow at a low-pressure differential. The reality is, however, the system has up to 50 bar (725 psi) available to drive flow and at 95% command, this valve can pass over 400 lpm (105 gpm) (flow curve 4), far in excess of the 200 lpm (53 gpm) required. To limit the flow this proportional valve can pass at a 50 bar (725 psi) differential, the spool command would have to be set to about 63% of its full stroke – effectively a 37% reduction in its available control range. The graph in figure 3 is for a valve that at 100% command produces approximately 100 lpm (26 gpm) at a 10 bar (145 psi) differential (flow curve 1) which compared to the 220 lpm (58 gpm) valve is, on the surface, too small.
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