﻿ GO-FLOW法在飞机EHA可靠性分析中的应用<sup>*</sup>
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GO-FLOW法在飞机EHA可靠性分析中的应用

Application of GO-FLOW methodology in reliability analysis of aircraft EHA
LAN Xue, DUAN Fuhai, SANG Yong
School of Mechanical Engineering, Dalian University of Technology, Dalian 116023, China
Received: 2016-05-24; Accepted: 2016-06-24; Published online: 2016-11-23 09:11
Foundation item: Aeronautical Science Foundation of China (20150863003)
Corresponding author. DUAN Fuhai, E-mail:duanfh@dlut.edu.cn
Abstract: The GO-FLOW methodology is applied in the reliability analysis of aircraft electro-hydrostatic actuator (EHA). Firstly, based on the reasonable division of unit function, GO-FLOW reliability analysis model of EHA was established. In order to solve the difficult problem that GO-FLOW chart cannot contain feedback loops, Boolean algebra was used to solve the Boolean equations that describe the feedback loops. Secondly, the GO-FLOW calculation was finished and the system reliability at each time point was obtained. Thirdly, compared with the results of GO methodology, the feasibility and accuracy of GO-FLOW methodology were clearly verified. Finally, the system reliability changing rule with time was obtained through the MATLAB curve fitting so that the system can be repaired and maintained timely. The results show that the GO-FLOW methodology can easily obtain the system reliability at each time point with only one operation and has more advantages than GO methodology in reducing computational complexity.
Key words: electro-hydraulic actuator (EHA)     GO-FLOW methodology     GO methodology     Boolean algebra     reliability analysis

1 EHA系统分析

EHA系统通常由控制器、电机驱动模块、270 V直流无刷电机、双向定量泵、储能罐及辅助液压阀组、作动筒等组成[10]，结构原理如图 1所示。

 图 1 EHA系统结构原理图[10] Fig. 1 Structural schematic diagram of EHA system[10]

EHA工作过程中，控制器和伺服驱动模块接受上位机的指令，驱动直流无刷电机转动，电机带动双向定量泵作旋转运动，继而控制泵输出到作动筒的高压油的流量，以容积调速方式完成对作动筒的控制。储能罐通过单向阀为系统进行补油增压，保持系统的最低压力，并防止油液中发生气穴现象，定量泵通过单向阀回油到储能罐。过滤器用来过滤液压油中的杂质，保证系统液压管道和其他设备的正常运行。

2 GO-FLOW法分析EHA可靠性

GO-FLOW法的主要分析过程包括建立GO-FLOW模型和完成定量计算。作动杆部件按照控制指令要求输出相应位移代表EHA系统成功工作，结合模型图和运算规则计算系统成功工作的概率，即系统的可靠度。

2.1 求解EHA反馈环

EHA带有反馈环的部分系统结构如图 2所示。

 图 2 EHA带有反馈环的结构图 Fig. 2 EHA structure diagram with feedback loops

A部件为例，将t时刻成功输出的事件集合表示为AqAs，其中Aq代表A部件成功起动的事件集合，As代表A部件的全部状态集合，其余部件的表示方法同A部件。X(=Bout)和Y(=Eout)分别表示BE部件的成功输出事件集合，那么布尔关系式可表示为

 (1)

 (2)

 (3)

 (4)

GO-FLOW法以成功为导向，系统所有部件在t时刻成功起动，因此As=Bs=Cs=Ds=Es=Bs=Es=Es=1.0，即

 (5)

 (6)

 (7)
 (8)

 图 3 求解反馈环的GO-FLOW图 Fig. 3 GO-FLOW chart of solving feedback loops
2.2 构建EHA的GO-FLOW模型

GO-FLOW模型主要由操作符和信号流两部分组成[15]。结合EHA结构模型图 1和求解反馈环模型图 3，在单元功能合理划分的基础上，建立EHA系统GO-FLOW模型如图 4所示。

 图 4 EHA系统的GO-FLOW图 Fig. 4 GO-FLOW chart of EHA system

2.3 GO-FLOW可靠性运算

GO-FLOW法在确定成功准则和定义时间点后，从信号发生器开始，沿信号线序列，按运算规则，逐个对操作符计算，直到得到最终输出信号在各时间点的“强度”，即系统的可靠性。图 4中关键信号流的表达式如下，其中Ii(t)表示信号i在时间点t的强度。

1) 信号流18：或门

 (9)

 编号 类型 参数 含义 1 25 R(1)=0, R(t)=1(t≠1) 电源信号 2 25 R(1)=0, R(t)=1(t≠1) 控制指令信号 3 25 R(2)=1, R(t)=0(t≠2) 电机运行信号 4 25 R(3)=1, R(t)=0(t≠3) 泵运转信号 5 25 R(4)=300 h, R(t)=0(t≠4) 时间间隔信号 23 25 R(1)=0, R(t)=1(t≠1) 油液信号 6, 7 21, 35 Pg=0.999 997 9, λ=2.1×10-6/h 控制器 8, 9 26, 35 Pp=12.0×10-6, Pg=0.999 973 0, λ=15.0×10-6/h 电机 10, 11 30 与门 12, 13 21, 35 Pg=0.999 999 5, λ=0.5×10-6/h 速度传感器 14, 15 21, 35 Pg=0.999 999 5, λ=0.5×10-6/h 位移传感器 16, 17 21, 35 Pg=0.999 999 5, λ=0.5×10-6/h 压力传感器 18 22 或门 19, 20 26, 35 Pp=0.0, Pg=0.999 988 0, λ=12.0×10-6/h 泵 21, 24, 30 21 Pg=0.999 998 8 单向阀 22, 25, 31 35 λ=1.27×10-6/h 单向阀 26, 32 21 Pg=0.999 992 0 过滤器 27, 33 35 λ=8.0×10-6/h 过滤器 28, 34 21 Pg=0.999 996 2 安全阀 29, 35 35 λ=3.8×10-6/h 安全阀 36, 37 30 与门 38, 39 21, 35 Pg=0.999 999 6, λ=0.4×10-6/h 作动筒

 (10)

2) 信号流36：与门

 (11)

3) 信号流38

 (12)

4) 信号流39

 (13)

I39(1)=I38(1)=0.000 00

I39(2)=I38(2)=0.000 00

I39(3)=I38(3)=0.999 79

I39(4)=I38(4)·exp(-λI5(4)×1.0)=0.983 48

 操作符编号 操作符类型 输出信号在各时间点的强度 1 2 3 4 22 35 0.000 00 0.000 00 0.999 96 0.991 51 36 30 0.000 00 0.999 83 0.999 83 0.992 02 39 35 0.000 00 0.000 00 0.999 79 0.983 48

3 与GO法比较

 图 5 EHA系统GO图 Fig. 5 GO chart of EHA system

4 系统可靠度的变化规律

 时间/h 信号强度 操作符22 操作符36 操作符39 0 0.999 96 0.999 83 0.999 79 50 0.998 55 0.998 52 0.997 05 100 0.997 13 0.997 22 0.994 32 150 0.995 73 0.995 92 0.991 60 200 0.994 32 0.994 62 0.988 89 250 0.992 92 0.993 32 0.986 18 300 0.991 51 0.992 02 0.983 48

 图 6 EHA系统可靠度变化规律 Fig. 6 System reliability changing rule of EHA

MATLAB拟合得到曲线的函数表达式为R(t)=-5.435 70×10-5t+0.999 77。由该表达式可以快速而准确地计算出EHA系统在任意时刻的工作可靠度，以便及时对系统进行检修和维护。

5 结论

1) 研究了GO-FLOW法在EHA系统可靠性分析中的应用。采用布尔代数求解描述反馈环的布尔方程，解决了模型中不允许存在循环的难题，并将计算结果与GO法的结果相比较，验证了GO-FLOW法的可行性与准确性，得到了系统在各时间点的可靠度以及随时间的变化规律，便于及时对系统进行检修和维护。

2) 充分挖掘了GO-FLOW法分析系统可靠性的优势，只需进行一次运算，就可得到系统最终信号在所有时间点的强度，完成对有复杂运行时序且状态随时间变化的系统可靠性分析。若采用GO法对大型的复杂系统进行分析计算，由于需要庞大的内存支持，往往难以获取最终信号存在概率的精确值。因此，GO-FLOW法能凭借其独特的优势为可靠性工程的深入研究提供重要支持。

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#### 文章信息

LAN Xue, DUAN Fuhai, SANG Yong
GO-FLOW法在飞机EHA可靠性分析中的应用
Application of GO-FLOW methodology in reliability analysis of aircraft EHA

Journal of Beijing University of Aeronautics and Astronsutics, 2017, 43(6): 1264-1270
http://dx.doi.org/10.13700/j.bh.1001-5965.2016.0444