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摘 要:针对水电站液压启闭机,研究了数字液压缸换向阀结构、工作参数对其流场分布特征的影响规律,通过计算流体动力学理论,建立了三种典型节流口形式的换向阀流场分析模型,获得了不同阀口形式、进出口压差以及阀口开度下的稳态流场特征。研究结果表明:阀芯具有明显的二级节流特征;相比于 U 形、三角形阀口,方形阀口下流速峰值最低,负压区压力值为 -0.22MPa,能有效避免气穴、气蚀等现象;随着进出口压差的增大,流场中最低负压值逐渐减小,流速峰值由 39.60m/s 增大至 95.79m/s;随着阀口开度的变大,流场最低负压值逐渐变大,压力梯度分布更加均匀,射流角降低了 15°。研究结果为数字液压缸的结构设计和性能优化提供理论依据。
关键词:数字液压缸;换向阀;流场;阀口形式
0 引言
液压启闭机绝大多数安装到水利枢纽项目中的关键位置。它们的可靠性与安全性对工程质量至关重要 [1-2]。液压缸作为液压系统主要的执行结构,其高水平的定位精度和高品质的动态特性是学者的研究重点,并由此产生了典型的比例、伺服控制技术。但是,传统液压系统依靠阀口的节流、溢流作用实现液压缸的方向、位移等控制,不仅增加了系统的复杂程度,而且能量利用率低下。与比例、伺服液压系统相比,采用机械闭环反馈调节与控制的数字液压系统将复杂的速度控制和位置控制变成了单一的脉冲控制,不仅具有结构紧凑、控制简单、定位精度高等特性,而且成本低、环境适应性强 [3]。
数字液压缸作为数字液压系统的典型元件,国内外研究学者针对其设计与应用进行了大量研究 [4-6]。 宋 飞 等 [6] 通 过 建 立 数 字 液 压 缸 的AMESim 仿真分析模型,研究发现螺母与丝杠的减速比过大是导致系统低速稳定性差的主要原因。张乔斌 [8] 等采用控制变量的方法,对比分析了输入信号的类型、幅值以及频率对数字液压缸跟踪误差影响规律,研究结果表明数字液压缸跟踪误差随着输入信号的幅值、频率的增加而增大。颜晓辉 [9] 等提出了改变脉冲频率系数控制数字液压缸的稳态误差的方法,并通过试验对分析结果进行了验证。陈佳 [10] 等在充分考虑功率匹配和非对称结构的基础上,建立了数字液压缸传递函数模型,通过参数匹配设计优化了系统响应特性,并结合具体参数进行了仿真验证。刘有力 [11] 等建立了数字液压缸 Simulink 仿真分析模型,研究了供油压力、滑阀死区、芯径向泄漏等非线性因素对其动态特性的影响,揭示了液压缸定位误差与步进电机的频率成正相关。
由于数字液压缸具有复杂而独特的内部结构,使得系统特性在很大程度上由其本身结构参数决定。换向阀是数字液压缸重要的液压控制元件,其在运行过程中会一直受到液动力的作用,并且阀内局部区域在油液高压、高速流动下也会形成负压区而产生气穴等现象,种种因素都会改变换向阀的控制性能,并进一步影响着数字液压缸的精度与性能。因此,本文通过建立三种典型节流口形式的换向阀仿真模型,对比分析其稳态流场特征,为数字液压缸的结构设计和性能优化提供理论依据。
1 数字液压缸基本结构和工作原理
图 1 为数字液压缸结构简图,主要由步进电机、三位四通换向阀、缸体和反馈机构组成,其具体工作原理如下:数字液压缸通过电机驱动器接收调制好的脉冲信号,使得步进电机按照预期运动并带动四通换向阀阀芯同步旋转。由于阀芯一侧螺杆螺母副的存在,阀芯旋转的同时产生轴向位移导致阀口开启,形成液压通路。通过改变阀芯移动的方向和开度即可控制回路中液压油的流向和流量,从而改变活塞运动的方向和速度。高压油进入液压缸腔后,推动活塞杆作直线运动,与活塞杆连成一体的反馈螺母带动滚珠丝杆旋转,最后经螺杆螺母副的作用旋转推动换向阀芯反向移动,直至阀口关闭,活塞杆运行至预期位置,实现位置负反馈。
图 1 数字液压缸结构简图
2 数字液压缸换向阀流场分析模型建模
2.1 阀体结构几何模型
根据数字液压缸换向阀实际尺寸,在合理简化阀套与阀芯配合间隙、阀体内部倒角、圆角的基础上,采用三维建模软件 SolidWorks 建立了换向阀阀体、阀芯几何模型,为了研究换向阀阀芯开口形式对其内部流场特性的影响规律,按照正投影面积相等的原则,设计了方形、U 形、三角形三种阀口结构的阀芯几何模型,如图 2 所示。方形节流口阀芯和阀体的组合装配示意图如 3 所示。
图 3 中阀芯处于中位,进口处节流口与回油处节流口均为负开口正遮盖形式,遮盖量为 0.1mm,换向阀阀口开度可以通过在 SolidWorks 软件中设置阀芯与阀体的相对位置而实现。
图 2 换向阀物理模型结构图
2.2 阀体流场模型抽取及网格划分
常用的流体计算域建模方法有直接建模与几何抽取两种。由于阀体内部结构较为复杂,采用直接建模的方式建模过程复杂,且不宜于阀口开度的更改,因此,本文将 2.1 节建立的阀芯、阀体装配模型导入到 ANSYS Workbench 的DesignModeler 模块中,采用几何抽取的方式建立流体计算域。由于阀腔结构具有对称性,根据相似原理,阀内各腔流场分布具有相似性,所以本文以换向阀其中一腔为研究对象进行流场仿真,分析阀体内部流场特征。流场模型网格划分包括结构网格、非结构网格两种形式。考虑到数字液压缸换向阀内部流道较为复杂,采用适应性较好的非结构四面体网格进行划分。对于流速、压力变化梯度较大的阀口区域,为了增加求解精度,对该处网格进行了加密处理,并且添加膨胀层实现从边界层到内部网格的平滑过渡,以便更加真实的模拟实际流体模型。图 4为方形阀口的流体计算域网格划分结果,其中,网格数量 836504 个,网格平均正交质量为 0.88。
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