A Novel Servovalve Pilot Stage Actuated by a Piezo-electric Ring Bender: A Numerical and Experimental Analysis
Abstract
:1. Introduction
- (1)
- The pilot stage requires a quiescent flow rate to work, to be referred to as the internal leakage of the pilot stage (note that the overall internal leakage is the sum of this contribution and a second contribution given by the internal leakage in the main stage). Although it is small compared to the nominal flow rate of a valve, the internal leakage in the pilot stage is continuous and constant regardless of the opening degree of the main stage, thus causing unwanted power consumption during operation [1,2].
- (2)
- The electromagnetic torque motor assembly is also a major issue associated with these valves because it is composed of many sensitive mechanical and electrical parts that penalise simplicity, set-up, duration of manufacture and manufacturing costs. Of these components, the flexure tube, used to support the flapper while separating the torque motor from the hydraulic fluid, is the most critical. Indeed, it needs to be manufactured very accurately to ensure the stiffness required [1,2]. Moreover, the flapper-flexure tube system is very sensitive to vibration, and a valve may experience fatigue failure of the flexure tube due to excessive bending under vibration, in addition to the fact that the oscillations of the flapper caused by external noise may result in a change of the valve output [1,2].
2. Materials and Methods
2.1. Novel Servovalve Concept
2.2. Valve Prototype and Hydraulic Test Rig
2.3. Numerical Model of the Piezo-Valve
3. Results
3.1. Experimental Results and Comparison with the Numerical Model
3.2. Numerical Analysis of the Piezo-Valve
4. Conclusions
Author Contributions
Funding
Conflicts of Interest
Nomenclature
Ar | Restriction area [mm2] |
C | Capacitance [nF] |
CD | Discharge coefficient |
Crb | Damping coefficient of the moving parts [Ns/m] |
Cstop | Damping coefficient hard stop [Ns/m] |
D | Diameter of the hydraulic chamber [mm] |
D0 | Diameter of the hydraulic chamber of the prototype [mm] |
d | Diameter of the piezo valve orifice [mm] |
E | Bulk modulus [N/m2] |
E0 | Pure liquid bulk modulus [N/m2] |
Fflow | Flow force [N] |
Frb | Actuation force of the ring bender [N] |
Imax | Maximum current [A] |
K | Proportional factor |
Ka | Gain of the amplifier |
Kd,v | Ring bender conversion factor [N/V] |
Krb | Spring stiffness of the ring bender [N/m] |
Kstop | Stiffness of the hard stop [N/m] |
L | Length of the hydraulic chamber [mm] |
L0 | Length of the hydraulic chamber of the prototype [mm] |
m | Mass of the moving parts [kg] |
m0 | Mass of the moving parts of the prototype [kg] |
n | Hysteresis non-linear term [V] |
p | Absolute pressure [N/m2] |
p0 | Atmospheric pressure [N/m2] |
q | Volumetric flow rate [m3/s] |
Vamp | Voltage from the amplifier [V] |
Vc | Control voltage [V] |
x | Ring bender displacement [mm] |
xmax | Maximum displacement of the ring bender [mm] |
xmin | Minimum displacement of the ring bender [mm] |
x0 | Pre-compression [mm] |
α | Parameter for the hysteresis formula |
β | Parameter for the hysteresis formula |
γ | Ratio of the specific heats |
δ | Parameter for the hysteresis formula |
ε | Relative gas content at atmospheric pressure |
ξ | Damping factor of the amplifier |
Fluid density at atmospheric conditions [kg/m3] | |
ωn | Natural frequency of the amplifier [rad/s] |
ωn,0 | Natural frequency of the experimental amplifier [rad/s] |
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Parameter | Value |
---|---|
Outer diameter of the ring bender | 40 mm |
Inner diameter of the ring bender | 8 mm |
Height of the ring bender | 0.7 mm |
Maximum theoretical displacement of the ring bender | ±185 µm |
Maximum theoretical force of the ring bender | ±13 N |
Operating voltage of the ring bender | ±100 V |
Diameter of the nozzle (10) | 1 mm |
Equivalent length of the oil chamber between the restriction (6) and the nozzle (10) | 60 mm |
Equivalent diameter of the oil chamber between the restriction (6) and the nozzle (10) | 20 mm |
Area of the restriction (6) | Variable |
Mass of the moving parts of the piezo-valve (closure member, ring-bender, o-rings) | 90 g |
Component | Parameter | Symbol | Value |
---|---|---|---|
Oil | Density | 851 kg/m3 | |
Relative gas content | ε | 0.01 | |
Supply line (from accumulator 4 to point 5) | Supply pressure | p4 | 71 bar/51 bar |
Fictitious restriction area | 4 mm2 | ||
Discharge coefficient | CD,4-5 | 0.7 | |
Variable restrictor (6) | Restriction area | Ar,6 | 0.42 mm2 |
Discharge coefficient | CD,6 | 0.7 | |
Oil chamber volume (from restriction 6 to nozzle 10) | Equivalent diameter | Do | 20 mm |
Equivalent length | Lo | 60 mm | |
Piezo valve | Ring bender conversion factor (force over voltage) | Kd,v | 0.13 N/V |
Diameter of the nozzle (10) | d | 1 mm | |
Discharge coefficient | CD,v | 0.65 | |
Mass of the moving parts | m0 | 90 g | |
Damping coefficient | Crb | 26 Ns/m | |
Ring bender stiffness | krb | 70,000 N/m | |
Pre-compression of the ring bender | x0 | 50 μm | |
Stop damping coefficient | 500 Ns/m | ||
Stop stiffness | 107 N/m | ||
Maximum displacement of the ring bender | None | ||
Minimum displacement of the ring bender | 0 | ||
Discharge line | Pressure | pT | 1 bar |
Amplifier | Natural frequency | ωn,0 | 1400 rad/s |
Damping factor | ξ | 1.5 | |
Maximum current | Imax | 1A | |
Capacitance | 2 × 1740 nF | ||
Gain of the amplifier | 20 |
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Tamburrano, P.; Plummer, A.R.; De Palma, P.; Distaso, E.; Amirante, R. A Novel Servovalve Pilot Stage Actuated by a Piezo-electric Ring Bender: A Numerical and Experimental Analysis. Energies 2020, 13, 671. https://doi.org/10.3390/en13030671
Tamburrano P, Plummer AR, De Palma P, Distaso E, Amirante R. A Novel Servovalve Pilot Stage Actuated by a Piezo-electric Ring Bender: A Numerical and Experimental Analysis. Energies. 2020; 13(3):671. https://doi.org/10.3390/en13030671
Chicago/Turabian StyleTamburrano, Paolo, Andrew R. Plummer, Pietro De Palma, Elia Distaso, and Riccardo Amirante. 2020. "A Novel Servovalve Pilot Stage Actuated by a Piezo-electric Ring Bender: A Numerical and Experimental Analysis" Energies 13, no. 3: 671. https://doi.org/10.3390/en13030671
APA StyleTamburrano, P., Plummer, A. R., De Palma, P., Distaso, E., & Amirante, R. (2020). A Novel Servovalve Pilot Stage Actuated by a Piezo-electric Ring Bender: A Numerical and Experimental Analysis. Energies, 13(3), 671. https://doi.org/10.3390/en13030671