电液伺服阀压电双晶片力马达组件数学建模

凌杰; 彭洪涛; 李蕴琪; 张文星; 康佳豪; 朱玉川

doi:10.13224/j.cnki.jasp.20250241

电液伺服阀压电双晶片力马达组件数学建模

doi: 10.13224/j.cnki.jasp.20250241

1.
南京航空航天大学机电学院，南京 210016
2.
中国航空工业集团公司西安飞行自动控制研究所，西安 710065

基金项目: 航空科学基金（20220007052001）

详细信息

作者简介:
凌杰（1990-），男，副教授，博士，研究方向为精密驱动与控制。E-mail：meejling@nuaa.edu.cn

中图分类号: V241
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- 被引次数: 0
出版历程
- 收稿日期: 2025-05-21
- 网络出版日期: 2025-09-08

Mathematical modeling of piezoelectric bimorph actuated force motor assembly for electrohydraulic servo valve

1.
College of Mechanical and Electrical Engineering，Nanjing University of Aeronautics and Astronautics，Nanjing 210016，China
2.
Xi’an Flight Automatic Control Research Institute，Aviation Industry Corporation of China，Limited，Xi’an 710065，China

摘要

摘要:
压电双晶片替代力矩马达，能够提升电液伺服阀的响应速度，简化先导级结构，提高系统的零位稳定性和可靠性。目前压电性电液伺服阀力马达组件模型无法从物理机理层面解释不同约束条件对输出特性的影响。针对压电型射流偏转板电液伺服阀先导级设计了等效力马达组件，基于分段建模思想与等效原理开展数学建模研究，并开展不同约束条件下输出特性测试。结果显示：静态输出方面，当伸出长度减小4 mm时，前置级力马达组件位移减小幅值最大，为27.7 μm；动态输出方面，当伸出长度减小4 mm时，前置级力马达组件谐振幅值下降最多，为1.9 dB；谐振频率增幅最大，为15.9%。建立了包含迟滞模型、线性动力学模型及液动力模型3部分的数学模型，进行了静/动态输出特性仿真。通过仿真与实验对比分析可知：静态输出特性方面，仿真迟滞为11.6%，实验迟滞为11.2%，两者方均根误差为2.5 μm；动态输出特性方面，在驱动频率为600 Hz且不同约束条件下，仿真与实验最大方均根误差为5.7 μm，说明数学模型准确。研究为力马达组件结构设计与优化提供理论指导。
- 电液伺服阀 /
- 压电双晶片 /
- 线性动力学 /
- 液动力 /
- 迟滞非线性 /
- 数学模型
Abstract:
Replacing the torque motor with a piezoelectric bimorph can improve electrohydraulic servo valve response, simplify the pilot stage, and enhance the stability. Yet existing actuator models fail to explain constraint effects on output. A mathematical model using piecewise and equivalent principles was developed. An equivalent actuator was designed for the jet-deflector stage, and tests under different constraints were conducted. Results showed that a 4 mm reduction in extension led to the largest static displacement decrease of 27.7 μm, the maximum dynamic resonance amplitude drop of 1.9 dB, and resonance frequency increase of 15.9%. A model including hysteresis, linear dynamics, and hydrodynamics was then built, with static/dynamic simulations validated against experiments. In static output, simulated hysteresis was 11.6% vs. experimental hysteresis 11.2% (RMS error 2.5 μm); in dynamic output at 600 Hz, the maximum RMS error was 5.7 μm, confirming the accuracy. This study can offer theoretical guidance for actuator design and optimization.
- electrohydraulic servo valve /
- piezoelectric bimorph /
- linear dynamics /
- hydrodynamics /
- hysteresis nonlinearity /
- mathematical model

HTML

图 1 压电型射流偏转板电液伺服阀^[23]

Figure 1. Piezoelectric jet deflection plate electrohydraulic servo valve^[23]

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图 2 压电型射流偏转板电液伺服阀力马达组件

Figure 2. Piezoelectric jet deflection plate electrohydraulic servo valve force motor assembly

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图 3 压电双晶片执行器结构与工作原理

Figure 3. Configuration and operating principle of piezoelectric bimorph actuators

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图 4 力马达组件构型

Figure 4. Piezoelectric bimorph-feedback rod assembly configuration

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图 5 力马达组件控制策略验证试验平台

Figure 5. Experimental platform for validating the control strategy of piezoelectric bimorph-feedback rod assembly

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图 6 不同约束条件示意图

Figure 6. Schematic diagram of different boundary conditions

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图 7 建模整体框架图

Figure 7. Overall framework diagram of the model

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图 8 振型函数求解结果

Figure 8. Mode shape function solution results

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图 9 迟滞模型辨识结果

Figure 9. Hysteresis model identification results

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图 10 变反馈杆质量仿真与实验对比结果

Figure 10. Simulation and experimental comparison results under variable feedback rod mass

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图 11 变反馈杆长度仿真与实验对比结果

Figure 11. Simulation and experimental comparison results under variable feedback rod length

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图 12 变夹持位置仿真与实验对比结果

Figure 12. Simulation and experimental comparison results under variable clamping positions

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图 13 变油液环境仿真与实验对比结果

Figure 13. Simulation and experimental comparison results under variable oil environments

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表 1 不同约束条件下力马达组件输出特性实验结果

Table 1. Test results of the output characteristics of the force motor assembly under different constraint conditions

阻尼环境	伸出长度/ mm	压片个数	反馈杆长度/ mm	位移幅值/ μm	谐振幅值/ dB	谐振频率/ Hz
非浸油	18	2	24	81.4	15.1	685
液压油				81.7	14.1	647
硅酮油				81.5	13.4	641
非浸油	18	2	24	81.4	15.1	685
	16			72.8	14.3	717
	14			53.7	13.2	794
非浸油	18	2	24	81.4	15.1	685
		4		81.4	15.8	674
		6		81.9	16.4	662
非浸油	18	2	20	81.3	15.4	687
			24	81.4	15.1	685
			26	81.7	15.1	684

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表 2 等效动力学参数

Table 2. Equivalent dynamic parameters

参数	数值	辨识方法
$ {m}_{11} $/10⁻⁴ kg	3.42	等效质量求解函数
$ {j}_{12} $/10⁻⁸ （kg·m³）	1.4	解析建模计算
$ {c}_{11} $	0.178	最小二乘法辨识
$ {c}_{12} $	0.244	最小二乘法辨识
$ {k}_{11} $/10⁴ （N/m）	4.41	解析建模计算
$ {I}_{12} $/10³ （N·m/rad）	2.91	解析建模计算
$ {m}_{21} $/10⁻³ kg	1.7	解析建模计算
$ {j}_{22} $/10⁻⁸ （kg·m³）	8.3	解析建模计算
$ {c}_{21} $	0.173	最小二乘法辨识
$ {c}_{22} $	0.122	最小二乘法辨识
$ {m}_{31} $/10⁻⁵ kg	4.71	等效质量求解函数
$ {j}_{32} $/10⁻⁹ （kg·m³）	4.97	解析建模计算
$ {c}_{31} $	0.166	最小二乘法辨识
$ {c}_{32} $	0.143	最小二乘法辨识
$ {k}_{31} $/10³ （N/m）	3.62	解析建模计算
$ {I}_{32} $/10⁻⁹ （kg·m³）	5.7	解析建模计算
$ {d}_{\mathrm{e}} $	0.0162	最小二乘法辨识

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表 3 液动力模型和迟滞模型参数

Table 3. Hydrodynamic model parameters and hysteresis model parameters

参数	数值	参数	数值
$ {\kappa }_{1} $	0.0238	$ {\kappa }_{2} $	0.0630
$ {\kappa }_{3} $	0.0014	$ {\kappa }_{4} $	0.0019
$ {\kappa }_{5} $	0.1493	$ {\kappa }_{6} $	0.0748
$ {\kappa }_{7} $	0.0108	$ {\kappa }_{8} $	0.0092
$ \alpha $/$ {10}^{9} $（m/F）	7.364	$ a $/$ {10}^{7} $（V/m）	6.13
$ c $	0.839	$ k $/$ {10}^{7} $（V/m）	6.48
$ {P}_{\mathrm{s}} $/（C/m²）	0.0192

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