The deflector jet servo valve driven by multilayer bimorph achieves exceptional performance for advanced aerospace applications, with critical advantages of fast response, high precision and compact structure. The valve output characteristics is fundamentally determined by the output characteristics of its multilayer bimorph and deflector-feedback rod assembly, where existing models fail to accurately predict behavior under limited working conditions. This study develops a mathematical model to precisely characterize the output characteristics of assembly, incorporating adjustable clamping length and reduction of effective driving force. With finite element analysis and experiments, static characteristics of the assembly are analyzed. Experimental validation demonstrates the accuracy of model, reducing maximum relative errors by 50.5% in assembly end feedback force prediction and 66% in deflector displacement estimation compared to conventional approaches. This work provides not only essential theoretical support for multilayer bimorph applications in complex structural load, but also provides theoretical support for developing precise control algorithms with mechanical feedback. The improved model enables optimization of servo valve design and assembly precision while maintaining system performance.
ChenZGeSJiangY, et al. Mathematical modeling of pressure characteristics of the deflector-jet pilot stage considering boundary layer flow. Flow Meas Instrum2023; 90: 102312.
2.
LvXYangJQiQ, et al. Mathematical modeling of an armature assembly in a flapper–nozzle servo valve based on the finite element method. IEEE/ASME Trans Mechatron2024; 29: 3684–3695.
3.
KarunanidhiSSingaperumalM.Mathematical modelling and experimental characterization of a high dynamic servo valve integrated with piezoelectric actuator. Proc Inst Mech Eng Part I-J Syst Control Eng2010; 224: 419–435.
4.
ChenZGeSJiangY, et al. Refined modeling and experimental verification of a torque motor for an electro-hydraulic servo valve. Chin J Aeronaut2023; 36: 302–317.
5.
Al-DweikatMZhangGLiuY, et al. A comparison of two piezoelectric actuator concepts for fast mechanical switching in dc hybrid circuit breakers. Rev Sci Instrum2024; 95: 074709.
6.
JiHWLinLMLiuY, et al. Achieving smooth motion in displacement amplification piezoelectric stick-slip actuator. Rev Sci Instrum2024; 95: 105002.
7.
XuZLiuTLiX, et al. An impact inertial piezoelectric actuator with high thrust-weight ratio driven by coupling the inertial force and friction force. IEEE Trans Ind Electron2024; 71: 16275–16285.
8.
QiJWangL.Development of a stick-slip piezoelectric actuator using bending deformation based on hammer-type driving foot. Rev Sci Instrum2025; 96: 025004.
9.
ZhangYPanWChenS, et al. Mathematical modeling and experimental characterization of the piezoelectric servo valve system. J Tribol Trans2024; 146: 014601.
10.
BertinMPlummerABowenC, et al. A dual lane piezoelectric ring bender actuated nozzle-flapper servo valve for aero engine fuel metering. Smart Mater Struct2019; 28: 115015.
11.
TamburranoPSciattiFPlummerAR, et al. A review of novel architectures of servo valves driven by piezoelectric actuators. Energies2021; 14: 4858.
12.
PlummerA.Electrohydraulic servo valves – past, present, and future. In: Proceedings of the 10th international fluid power conference, Dresden, Germany, 8–10 March, 2016.
13.
LingMWangJ.Nonlinear coupled dynamic effects in flexure-amplified piezoelectric valve with an analytical transfer function. Proc Inst Mech Eng C J Mech Eng Sci2023; 237: 359–373.
14.
HanCChoiSBHanYM.A piezoelectric actuator-based direct-drive valve for fast motion control at high operating temperatures. Appl Sci2018; 8: 1806.
15.
TamburranoPDe PalmaPPlummerAR, et al. Simulation of a high frequency on/off valve actuated by a piezo-ring stack for digital hydraulics. E3S Web Conf2021; 312: 05008.
16.
TamburranoPPlummerARDe PalmaP, et al. A novel servovalve pilot stage actuated by a piezo-electric ring bender: a numerical and experimental analysis. Energies2020; 13: 671.
17.
SedziakDMinorowiczBStefańskiF, et al. Modelling and investigations of piezobender used in control of electrohydraulic servo valve. In: 17th international Carpathian control conference (ICCC), 2016, pp.651-656.
18.
GuiSZhangSFuB, et al. Fluid-dynamic analysis and multi-objective design optimization of piezoelectric servo valves. Flow Meas Instrum2022; 85: 102157.
19.
BanerjeeABeraKKSinghaAK.Enhanced vibration control using non-reciprocal piezoelectric beam having sensing and actuating bimorph: spectral element formulation. Compos Struct2024; 329: 117793.
20.
SongJ.Research on design and characteristics of servo valve actuated by piezoelectric ceramics. Master’s Thesis, Harbin Institute of Technology, China, 2019.
21.
BraunSHaaslSSadoonS, et al. Small footprint knife gate microvalves for large flow control. In: International conference on solid-state sensors, actuators and microsystems, 2005, pp. 329-332.
22.
ChengMWuJGuanM, et al. A high-resolution electric field sensor based on piezoelectric bimorph composite. Smart Mater Struct2022; 31: 025008.
23.
SmitsJGDalkeSICooneyTK.The constituent equations of piezoelectric bimorphs. Sens Actuator A-Phys1991; 28: 41–61.
24.
ZhuLESZhuX, et al. Development of hydroelectric servo-valve based on piezoelectric elements. In: 2010 international conference on mechanic automation and control engineering, 2010, pp. 3330-3333.
25.
MileckiARybarczykD.Investigations of applications of smart materials and methods in fluid valves and drives. J Mach Eng2019; 19: 122–134.
26.
ChenXZhuYGaoQ, et al. Simulation research for fluid-solid interaction performance of a piezoelectric bimorph actuator applied in servo valves. In: 2019 IEEE 8th international conference on fluid power and mechatronics (FPM), 2019, pp.236–242.
27.
SangiahDKPlummerARBowenCR, et al. A novel piezohydraulic aerospace servo valve. Part 1: design and modelling. Proc Inst Mech Eng I J Syst Control Eng2013; 227: 371–389.
28.
SalmaniHHankeUHalvorsenE.Competing anticlastic and piezoelectric deformation at large deflections. Smart Mater Struct2021; 30: 035019.
29.
IshiharaDChigahalli RamegowdaPAikawaS, et al. Importance of three-dimensional piezoelectric coupling modeling in quantitative analysis of piezoelectric actuators. Comput Model Eng Sci2023; 136: 1187–1206.
30.
DeVoeDLPisanoAP.Modeling and optimal design of piezoelectric cantilever microactuators. J Microelectromech Syst1997; 6: 266–270.
31.
KiouaHMirzaS.Multilayer laminated piezoelectric bending actuators: design and manufacturing for optimum power density and efficiency. Smart Mater Struct2000; 9: 476–484.
32.
ZhangTTShiZF.Bending behavior of 2–2 multi-layered piezoelectric curved actuators. Smart Mater Struct2007; 16: 634–641.
33.
SkrzypaczPNurakhmetovDWeiD.Generalized stiffness and effective mass coefficients for power-law Euler–Bernoulli beams. Acta Mech Sin2020; 36: 160–175.
ZhangZXiaCQiG, et al. Multi-step state-based opacity for unambiguous weighted machines. Sci China Inf Sci2024; 67: 212204.
37.
TianFYangCZhangE, et al. Design optimization of hydraulic machinery based on ISIGHT software: a review of methods and applications. Water2023; 15: 2100.
38.
ZhangZXiaCFuJ, et al. Initial-state observability of mealy-based finite-state machine with nondeterministic output functions. IEEE Trans Syst Man Cybern Syst2022; 52: 6396–6405.
