Modeling of Self-expanding Elastic Pressurized Reservoir Considering Hysteresis Characteristics

doi:10.3969/j.issn.1004-132X.2026.02.002

Abstract

Abstract:

To meet the demands for high-pressure， lightweight hydraulic reservoirs in high-end mobile equipment， a self-expanding elastic pressurized reservoir （SEPR） was proposed. The rubber-woven composite material was used to replace the traditional metal reservoir shell. The system achieved oil volume compensation and pressure output through the flexible deformations of rubber and the reinforcement provided by the external woven fiber. Based on the geometric characteristics of the woven fiber and the force analysis of the shell， the ideal static mathematical model of the SEPR was established， and the Maxwell hysteresis model was introduced to modify the model. The relationships among SEPR structural parameters， volume， and pressure were obtained. Based on the flow equation， force balance equation， and volume formula， the dynamic nonlinear mathematical model of the SEPR was established. Based on the tests of displacement/pressure hysteresis characteristics of the SEPR， the model parameters were identified. The results show that the SEPR may reach a maximum pressure of 530 kPa while weighing only 950 g. The SEPR exhibits strong motion-tracking behavior with the hydraulic cylinder under sinusoidal excitation. As the step amplitude increases， both of the pressure rise time and the pressure change amplitude increases under the oil inlet conditions.

Key words: hydraulic component, lightweight, pressurized reservoir, mathematical model, hysteresis characteristic, woven fiber

摘要：

为满足高端移动装备对液压油箱高承压、轻量化的需求，提出一种自增容弹性压力油箱。采用橡胶-编织组合材料代替传统金属油箱壁面，利用橡胶柔性变形和外置编织纤维防护增强特性，实现系统中油液体积补偿并输出压力油液。基于编织纤维几何特性、壳体受力分析，建立油箱理想静态数学模型，并引入Maxwell迟滞模型进行修正，得到其结构参数与体积、压力的关系。基于流量方程、受力平衡方程和容积公式得到油箱动态非线性数学模型。在油箱位移/压力迟滞特性试验的基础上进行模型参数辨识。研究结果表明：所设计油箱样机最大压力为530 kPa，质量仅950 g。正弦响应下油箱跟随液压缸运动特性良好。随着阶跃幅值的增大，进油工况下压力增大时间和变化幅值逐渐增大。

关键词: 液压元件, 轻量化, 压力油箱, 数学模型, 迟滞特性, 编织纤维

CLC Number:

TH137

YAO Jing, WANG Dingyu, LIANG Dong, HAO Jinlu, HE Aiwen. Modeling of Self-expanding Elastic Pressurized Reservoir Considering Hysteresis Characteristics[J]. China Mechanical Engineering, 2026, 37(2): 264-274.

姚静, 王定煜, 梁栋, 郝金鹿, 何蔼雯. 考虑迟滞特性的自增容弹性压力油箱建模研究[J]. 中国机械工程, 2026, 37(2): 264-274.

Figures/Tables 27

Fig.1 Structure of the SEPR

Fig.2 Comparison of the SEPR deformation

Fig.3 Geometric relationship of single fiber

Fig.4 Diagram of force analysis of the SEPR shell

Fig.5 The influence of elastic modulus of rubber on static properties of the SEPR

Fig.6 The influence of shell thickness on static properties of the SEPR

Fig.7 The influence of the initial woven angle on static properties of the SEPR

Fig.8 Element of Maxwell-slip

Fig.9 Parallel Maxwell models

Fig.10 A simplified model of the SEPR

Fig.11 Single degree of freedom system for the SEPR

Tab.1 Structural parameters of the reservoir prototype

参数	初始值	最大压力状态时
长度L/m	0.17	0.14
弹性壳体外半径R/m	0.029	0.041
弹性壳体厚度t/mm	1.50	1.05
油箱结构容积V_Δ/L	0.4	0.6
油箱压力p/kPa	0	530
编织角θ/（°）	36.0	51.5
弹簧刚度K/（N·m $- 1$ ）	2000
工作容积V_Δ/L	0.2
质量m/g	950

Tab.1 Structural parameters of the reservoir prototype

参数	初始值	最大压力状态时
长度L/m	0.17	0.14
弹性壳体外半径R/m	0.029	0.041
弹性壳体厚度t/mm	1.50	1.05
油箱结构容积V_Δ/L	0.4	0.6
油箱压力p/kPa	0	530
编织角θ/（°）	36.0	51.5
弹簧刚度K/（N·m $- 1$ ）	2000
工作容积V_Δ/L	0.2
质量m/g	950

Fig.12 Diagram of the SEPR prototype

Tab.2 Parameters of hydraulic testing system

参数	数值
系统压力/MPa	10
系统流量/（L·min $- 1$ ）	2.4
液压缸缸径/mm	25
液压缸杆径/mm	16
液压缸行程/mm	200

Tab.2 Parameters of hydraulic testing system

参数	数值
系统压力/MPa	10
系统流量/（L·min $- 1$ ）	2.4
液压缸缸径/mm	25
液压缸杆径/mm	16
液压缸行程/mm	200

Fig.13 Schematic of static performance testing of the SEPR

Fig.14 Reservoir hysteresis characteristic curve fitted by Maxwell’s model

Tab.3 Parameters of Maxwell unit

参数	阶段1	阶段2	阶段3
K	$-$ 0.0529	0.645	$-$ 0.577
w	$-$ 1.058	17.415	$-$ 16.3291

Tab.3 Parameters of Maxwell unit

参数	阶段1	阶段2	阶段3
K	$-$ 0.0529	0.645	$-$ 0.577
w	$-$ 1.058	17.415	$-$ 16.3291

Fig.15 Displacement-pressure curve of the SEPR at oil absorption condition

Fig.16 Displacement-pressure hysteresis characteristic curve of the SEPR at oil absorption and discharging condition

Fig.17 Simulation curve in a step input condition with an amplitude of 20 mm

Fig.18 Simulation curve in a step input condition with an amplitude of 40 mm

Fig.19 Simulation curve in a step input condition with an amplitude of 50 mm

Tab.4 Results of the step response

阶跃幅值/mm	20	40	50
上升时间/s	0.362	0.672	0.808
压力变化幅值/kPa	88	227	328

Fig.20 Simulation curve in a sinusoidal input condition with 0.1 Hz±50 mm

Fig.21 Schematic of dynamic performance testing

Fig.22 Pressure curve of the SEPR in a step input condition with an amplitude of 30 mm

Fig.23 Displacement curve of the SEPR in a sinusoidal input condition with 0.1 Hz±50 mm

References 18

[1]	孔祥东，朱琦歆，姚静，等. 高端移动装备液压元件与系统轻量化发展综述［J］. 燕山大学学报， 2020， 44（3）： 203-217.
	KONG Xiangdong， ZHU Qixin， YAO Jing， et al. Reviews of Lightweight Development of Hydraulic Components and Systems for High-level Mobile Equipment［J］. Journal of Yanshan University， 2020， 44（3）： 203-217.
[2]	孔祥东，朱琦歆，姚静，等. “液压元件与系统轻量化设计制造新方法” 基础理论与关键技术［J］. 机械工程学报， 2021， 57（24）： 4-12.
	KONG Xiangdong， ZHU Qixin， YAO Jing， et al. Basic Theory and Key Technology of “New Method for Lightweight Design and Manufacturing of Hydraulic Components and Systems”［J］. Journal of Mechanical Engineering， 2021， 57（24）： 4-12.
[3]	张垚，温育明，王山. 多功能航空液压油箱研究与试验［J］. 液压与气动， 2018， 42（11）： 104-107.
	ZHANG Yao， WEN Yuming， WANG Shan. Research and Experiment of Multifunction Aero Hydraulic Tank［J］. Chinese Hydraulics & Pneumatics， 2018， 42（11）： 104-107.
[4]	OUYANG Xiaoping， FAN Boqian， YANG Huayong， et al. A Novel Multi-objective Optimization Method for the Pressurized Reservoir in Hydraulic Robotics［J］. Journal of Zhejiang University： Science A， 2016， 17（6）： 454-467.
[5]	SEGUIN C. Variable Volume Reservoir： US6981523［P］. 2006-01-03.
[6]	WANG Pei， YAO Jing， FENG Baidong， et al. Modelling and Dynamic Characteristics for a Non-metal Pressurized Reservoir with Variable Volume［J］. Chinese Journal of Mechanical Engineering， 2022， 35（1）： 39.
[7]	钱胜，陆益民，杨咸启，等. 橡胶材料超弹性本构模型选取及参数确定概述［J］. 橡胶科技， 2018， 16（5）： 5-10.
	QIAN Sheng， LU Yimin， YANG Xianqi， et al. Overview of Selection and Parameter Determination for Hyperelastic Constitutive Model of Rubber Material［J］. Rubber Science and Technology， 2018， 16（5）： 5-10.
[8]	VO-MINH T， TJAHJOWIDODO T， RAMON H， et al. A New Approach to Modeling Hysteresis in a Pneumatic Artificial Muscle Using the Maxwell-slip Model［J］. IEEE/ASME Transactions on Mechatronics， 2011， 16（1）： 177-186.
[9]	GAYLORD R H. Fluid Actuated Motor System and Stroking Device： US2844126［P］. 1958-07-22.
[10]	FERRARESI C， FRANCO W， BERTETTO A M. Flexible Pneumatic Actuators： a Comparison between the McKibben and the Straight Fibres Muscles［J］. Journal of Robotics and Mechatronics， 2001， 13（1）： 56-63.
[11]	KOTHERA C S， JANGID M， SIROHI J， et al. Experimental Characterization and Static Modeling of McKibben Actuators［J］. Journal of Mechanical Design， 2009， 131（9）： 091010.
[12]	DAVIS S， CALDWELL D G. Braid Effects on Contractile Range and Friction Modeling in Pneumatic Muscle Actuators［J］. The International Journal of Robotics Research， 2006， 25（4）： 359-369.
[13]	COLBRUNN R W， NELSON G M， QUINN R D. Modeling of Braided Pneumatic Actuators for Robotic Control［C］∥Proceedings 2001 IEEE/RSJ International Conference on Intelligent Robots and Systems. Expanding the Societal Role of Robotics in the the Next Millennium. Maui， 2002： 1964-1970.
[14]	ITTO T， KOGISO K. Hybrid Modeling of McKibben Pneumatic Artificial Muscle Systems［C］∥2011 IEEE International Conference on Industrial Technology. Auburn， 2011： 65-70.
[15]	ZANG Kejiang， MA Yan， SUN Ning， et al. Study on Finite Element Model of Pneumatic Artificial Muscle［J］. Advanced Materials Research， 2012， 430/431/432： 383-386.
[16]	郭振武，黄继清，王飞洋，等. McKibben型气动肌肉模型改进与性能测试［J］. 中国机械工程， 2019， 30（19）： 2313-2318.
	GUO Zhenwu， HUANG Jiqing， WANG Feiyang， et al. Improvement and Performance Testing of McKibben Pneumatic Muscle Model［J］. China Mechanical Engineering， 2019， 30（19）： 2313-2318.
[17]	王启好，蔡小培，常文浩，等. 考虑枕下胶垫超弹性本构的弹性长枕轨道动力仿真［J］. 中南大学学报（自然科学版）， 2020， 51（7）： 2021-2027.
	WANG Qihao， CAI Xiaopei， CHANG Wenhao， et al. Dynamic Simulation of Long Elastic Sleeper Track Based on Hyperelastic Constitutive Models of Ruber Cushion under Sleeper［J］. Journal of Central South University （Science and Technology）， 2020， 51（7）： 2021-2027.
[18]	ASCHEMANN H， SCHINDELE D. Comparison of Model-based Approaches to the Compensation of Hysteresis in the Force Characteristic of Pneumatic Muscles［J］. IEEE Transactions on Industrial Electronics， 2014， 61（7）： 3620-3629.