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Dynamics Modeling and Bifurcation Analysis for Valve-Controlled Hydraulic Cylinder System Containing Counterbalance Valves
Journal of Vibration Engineering & Technologies ( IF 2.7 ) Pub Date : 2021-06-26 , DOI: 10.1007/s42417-021-00342-6
Hao Sun , Jianfeng Tao , Chengjin Qin , Honggan Yu , Chengliang Liu

Purpose

The pilot ratio is a critical parameter of the hydraulic system containing counterbalance valves, which has an important influence on the dynamic characteristics and energy consumption. Generally, these two aspects are contradictory. That is, a high pilot ratio is easy to cause the poor dynamic characteristics of the system, while a low pilot ratio leads to excessive energy consumption. Currently, there is still no effective method for determining the pilot ratio and analyzing the unstable dynamical behavior of the hydraulic system containing counterbalance valves.

Methods

This paper establishes a dynamics model for the valve-controlled hydraulic cylinder system containing counterbalance valves and investigates the bifurcation in detail. Firstly, the mathematical model, in which the pilot chamber and the spring chamber of counterbalance valves are considered, is established for the segment erector of a tunnel boring machine. Regarding load mass as the bifurcation parameter, the central manifold theorem and normal form method are then introduced to analyze Hopf bifurcation. Simultaneously, the interval of periodic solutions is further determined by the 0–1 test method. Due to the limitation of the quantitative result, a novel homotopy-based method is finally proposed for solving the periodic solution at the above interval.

Results

In the case of a high pilot ratio (kx = 8), the supercritical Hopf bifurcation occurs when the load mass exceeds 2352.5 kg. Moreover, the periodic solution exists at the interval (2352.5 kg, 3583 kg). Compared with the numerical solution, the homotopy series solution gives an analytical expression and has a good approximation for the periodic solution.

Conclusions

The qualitative results of bifurcation behaviors can be regarded as the basis for determining the pilot ratio of counterbalance valves. And the proposed method is adapted to analyze the unstable dynamical behavior introduced by counterbalance valves in a typical hydraulic circuit.



中文翻译:

含平衡阀的阀控液压缸系统动力学建模与分岔分析

目的

先导比是包含平衡阀的液压系统的关键参数,对动态特性和能耗有重要影响。一般来说,这两个方面是相互矛盾的。即高导频比容易导致系统动态特性差,而低导频比导致能耗过大。目前,还没有有效的方法来确定先导比和分析含平衡阀的液压系统的不稳定动力学行为。

方法

本文建立了包含平衡阀的阀控液压缸系统的动力学模型,并详细研究了分岔。首先,建立了考虑平衡阀先导腔和弹簧腔的隧道掘进机管片架的数学模型。以载荷质量为分岔参数,引入中心流形定理和范式方法对Hopf分岔进行分析。同时,周期解的区间由0-1检验法进一步确定。由于定量结果的限制,最终提出了一种新的基于同伦的方法来求解上述区间的周期解。

结果

在高先导比 ( k x  = 8) 的情况下,当负载质量超过 2352.5 kg 时发生超临界 Hopf 分叉。此外,周期解存在于区间 (2352.5 kg, 3583 kg)。与数值解相比,同伦级数解给出了解析表达式,并且对周期解有很好的逼近。

结论

分叉行为的定性结果可作为确定平衡阀先导比的依据。并且所提出的方法适用于分析典型液压回路中由平衡阀引入的不稳定动态行为。

更新日期:2021-06-28
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