Reliability Analysis of Hydraulic Steering System with DICLFL Considering Shutdown Correlation Based on GO Methodology

Transcription

1 2015 ICRSE&PHM-Beijing Reliability Analysis of Hydraulic Steering System with DICLFL Considering Shutdown Correlation Based on GO Methodology YI Xiaojian, SHI Jian, MU Huina, DONG Haiping, GUO Shaowei BEIJING INSTITUTE OF TECHNOLOGY

2 Contents Introduction (DICLFL) Dual Input Closed-Loop Feedback Link Method Dealing with DICLFL Considering Shutdown Correlation System Analysis of Hydraulic Steering System Reliability Analysis of Hydraulic Steering System Based on GO Methodology Results Verified by FTA (qualitative analysis) and Monte-Carlo Simulation(quantitative analysis)

3 1 Introduction Profile 1 (DICLFL) are widely applied in repairable systems FTA is difficult to conduct DICLFL system reliability analysis accurately. GO methodology is a success-oriented method for system reliability analysis. 2 GO methodology is initially applied in safety and reliability analysis of weapons and missile systems, safety and availability analysis of nuclear power plant. Now it is also applies in reliability analysis of transportation, water supply systems, manufacturing systems, military industry, nuclear industry, power systems, etc. 3 GO methodology GO model operator signal flow a unit itself logical relationship of input and output links operators a specific fluid or logical process GO operation

4 1 Introduction Background LI He-qing and TAN Qing used GO methodology to make reliability quantitative calculation and qualitative analysis for hydraulic system of 25t type crane. DING Su-fang and HUANG Hua-liang established GO model based on flow chart of transmission of ZL50 loader hydraulic system and used GO method to analyze reliability of hydraulic system. However, they did not consider maintenance correlation problem in these systems. DENG Ya-xiong and XU Fei-yun conducted reliability analysis of a hydraulic system based on GO methodology and used Type 14 operator to deal with problem of multi-state output of the system, however, they also neglected correlation problem in the system. ZHENG Wen-jie etc. used GO method to analyze system steady-state reliability of Ship Anchor Hydraulic System. YI Xiao-jian etc. presented a new method to deal with the multiple failure modes based on GO methodology and used this method to analyze reliability of Hydraulic Transmission Oil Supply System of Power-shift Steering Transmission. Then they conducted steady-state availability analysis and qualitative analysis for Hydraulic Transmission Oil Supply System of Power-shift Steering Transmission with maintenance correlation of parallel structure with the same elements. However, the DICLFL is usually taken as a whole component and represented by an existing operator and this often leads to inaccuracy for reliability analysis of systems with DICLFL, and study on reliability analysis of DICLFL considering shutdown correlation has not been seen. Because of its advantages, GO methodology can be improved to solve reliability analysis problems for systems with DICLFL considering shutdown correlation.

5 1 Introduction What we do? A new GO operator, named type 9C operator, is created to describe the DICLFL considering shutdown correlation, whose number is 1 in this paper. And its steady state probability quantification formulas are derived based on Markov process theory. The new method is adopted to conduct the reliability analysis of a hydraulic steering system of a Power-Shift Steering Transmission for the first time. The success rule of hydraulic steering system is defined according to system analysis. The operator type and reliability parameters of each component are determined through system analysis. GO model of the system is built. Then, success probability of the system is calculated by the exact algorithm with shared signals. And all system minimum cut sets are obtained by GO method. Compared with Fault Tree Analysis and Monte Carlo simulation, the results show that this new GO method is correct and suitable for reliability analysis of repairable systems with the DICLFL considering shutdown correlation. It is more advantageous in the aspects of system model building and quantitative analysis.

6 2 Method Dealing with DICLFL Considering Shutdown Correlation Creation of New GO Operator Representing DICLFL Considering Shutdown Correlation Assumptions: Two input signals of DICLFL are denoted as S1, S2 respectively, and the output signal is denoted as R. All components included in the feedback path and output path can be equivalent to component C, which is described by Type 1 operator. All components included in the output path can be equivalent to component F, which is also described by Type 1 operator. The shutdown correlation is existed among S1, S2, C and F, and the number of shutdown correlation is one. I.e. as long as there is one broken among S1, S2, C and F, the system will stop working. A new operator, named Type 9C operator whose reliability parameters are those of the above equivalent component C and F, is defined to describe DICLFL considering shutdown correlation. The quantification formulas of Type 9C Operator are the steady state probability quantification formulas of Type 9C operator. 1-F S C R S 1 9C R S 2 S 2 Figure 1 Equivalent diagram of DICLFL and its corresponding type 9C operator

7 2 Method Dealing with DICLFL Considering Shutdown Correlation Quantification Formulas of Type 9C Operator Table 1 The State Combination Table of Type 9C Operator State S 1 S 2 C F R represents the state of success, and 2 represents the state of failure. 3 λ C t μ C t λ S2 t λ S1 t μ S2 t μ S1 t μ F t λ F t 4 Figure 2 The State Transition Diagram of Type 9C Operator S1 S 2 C F S1 S 2 C F S1 S A S2 0 S2 0 0 C 0 0 C 0 F F A P A 0 4 i1 = S 2 C F S1 S1 S1 F S 2 C S 2 C F S1 S 2 C 9C S1 S 2 C F 9C P i S1S 2CF ( ) ( ) S1 S2 S1S 2CF S 2S1CF C S1S 2F F S1S 2C ( ) ( ) S 2 C F S1 S1 S1 F S 2 C C S 2 F S1 S 2 C 9C S1 S 2 C F C F S 2 S1 C F C S1 S 2 F F S1 S 2 C

8 3 System Analysis of Hydraulic Steering System P B C E LF3 A D P2 RV3 Pressure oil tank Figure 3 Diagram of hydraulic steering system Working principle of hydraulic steering system Open system of hydraulic steering system analysis Closed system of hydraulic steering system analysis Success rule of hydraulic steering system Success rule can be defined that the system could control two kinds of steering working condition on the right and left without considering overload protection, and the system can change oil of closed circuit.

9 4 Reliability Analysis of Hydraulic Steering System Based on GO Methodology Assumed that: The availability of tube and interface of the hydraulic steering system is set 1. The correlation of stopping work of DICLFL is only considered. Assumption that device only has grass-roots level maintenance, and the maintenance work is mainly the replacements of components, and the maintenance time is generally no more than 2 h. Building GO model Table 2 operator type and its reliability parameters No. component Operator type Failure rate(/h -1 ) Maintenance rate (/h -1 ) Availability 1 Directional signal Manual servo valve C Swash plate servo cylinder Swash plate of pump Double-action variable displacement pump Back pump oil Pump power sources Pressure oil tank Coarse filter

10 4 Reliability Analysis of Hydraulic Steering System Based on GO Methodology Continued from table 2 No. component Operator type Failure rate(/h -1 ) Maintenance rate (/h -1 ) Availability 10 Integrative fixed displacement pump P Constant pressure valve RV Refined filter power source of P Pump P Filter LF Relief valve B Relief valve A Check valve I Shuttle valve set E and D Fixed displacement motor Relief valve C Check valve II

11 4 Reliability Analysis of Hydraulic Steering System Based on GO Methodology When being at the situation of right steering, GO model of hydraulic steering system is built, as showed in Fig. 4. When being at the situation of left steering, GO model of hydraulic steering system is built, as showed in Fig. 5. In operators of all above GO models, the former number is the type of operator, and the latter number is a serial number. The number on a signal flow is serial number of signal flow. Signal flow 23-1 and 23-2 are system output of Fig.4 and Fig.5 respectively C C Figure 4 GO model of hydraulic steering system at situation of right steering Figure 5 GO model of hydraulic steering system at situation of left steering

12 4 Reliability Analysis of Hydraulic Steering System Based on GO Methodology Quantitative analysis of hydraulic steering system based on GO method Calculation of success probability of DICLFL Calculation of success probability of hydraulic steering system based on exact algorithm with shared signal The formula on success probability of system output with shared signal is P P [ 1 P 1 K P K ] R RK1K 2KL SL L SL K10 K20 KL 0 L1 l Table 3 GO Operation on Different Combination of Shared Signals and Calculation Results of System Success Probability State of shared signal P S7 P S8 P S17 State probability of combination L Success probability of system e e Accurate success probability of system

13 4 Reliability Analysis of Hydraulic Steering System Based on GO Methodology Qualitative analysis of hydraulic steering system based on GO method When success probability of one not-logical operator in system GO model is set 0 and success probabilities of other operators is kept constant. The operator is a one-order minimum cut set if the success probability of the system is 0. In the same way, two-order and more minimum cut sets can be determined. The results of qualitative analysis of the hydraulic steering system based on GO method are that all components except Power source of P2, P2 and LF3 in Table II are one-order minimum cut sets. Because it is difficult to get the exact failure probability of system from all minimum cut sets by using Boolean algebra method and probabilities of minimum cut sets are generally small, meanwhile all minimum cut sets can be assumed to be independent, the approximate failure probability of system can be obtained from the sum of all probability of minimum cut sets on engineering application. The sum can be taken as the upper limit of the failure probability of system and the corresponding success probability of the system can be taken as the lower limit. The sum of probability of all minimal cut sets of the hydraulic steering system is , and the success probability of hydraulic steering system is

14 5 Results Verified by FTA and Monte-Carlo Simulation Results Verified by FTA (qualitative analysis) and Monte-Carlo Simulation(quantitative analysis) Table 4 System Success Probability Calculated Through Different Methods Method Success probability of hydraulic steering system Exact algorithm with shared signal Qualitative analysis based on GO method FTA Monte Carlo The Results in Table 4 show that: Because qualitative analysis results by GO method and FTA can be thought as the lower limit of success probability of system, and results of exact algorithm with shared signal is larger than the lower limit, we can get that GO method is correct for reliability analysis of system with DICLFL considering shutdown correlation. The result by the exact algorithm considering shared signal is closer to the result by Monte Carlo simulation, and it indicates that GO methodology is suitable for reliability analysis of systems with DICLFL considering shutdown correlation.

15 6 Conclusions Works: This paper provides a reliability analysis method for repairable systems with DICLFL considering shutdown correlation, whose number is 1. A new operator which can be used to represent DICLFL considering shutdown correlation, whose number is 1, is created and named as Type 9C operator, and its steady state probability quantification formulas are deduced based on Markov process theory. To verify the correctness and feasibility of the new method presented in this paper, take a hydraulic steering system as an example to conduct the reliability analysis, and the analysis result is compared with that of FTA and Monte-Carlo simulation. Significance: The comparison results show that the new method is correct and feasible for the reliability analysis of system with DICLFL considering shutdown correlation. It is more advantageous in the aspects of system model building and quantitative analysis. This paper provides guidance for reliability analysis of repairable systems with DICLFL considering shutdown correlation.

16