Reliability analysis and calculationof the drive hydraulic system group of combined transportation

Jian-jun WANG，Jing-yi ZHAO，Wen-lei LI，Wei CAI

（1 Hebei Provincial Key Laboratory of Heavy Machinery Fluid Power Transmission and Control，Yanshan University，Qinhuangdao 066004，China）

（2College of Mechanical Engineering，Anhui Technical College of Mechanical and Electrical Engineering，Wuhu 241000，China）

（3State Key Laboratory of Fluid Power and Mechatronic Systems，Zhejiang University，Hangzhou 310027，China）

（4 Key Laboratory of Advanced Forging＆Stamping Technology and Science，Yanshan University，Qinhuangdao 066004，China）

（5 Hebei Key Laboratory of Special Delivery Equipment，Yanshan University，Qinhuangdao 066004，China）

Abstract：In order to ensure the safety of transportation，the reliability of the drive hydraulic system group of two transport vehicles combined transportationare studied.The key of the safe transportation is synchronous control，which requires high reliability of the drive hydraulic system group and control system.It is necessary to study the life prediction and reliability growth of drive hydraulic system group.The reliability of the drive hydraulic system group of the two transport vehicles is taken as the research object.Firstly，the reliability model of one transport vehicle is studied，and the reliability block diagram model is established for the drive hydraulic system.At the same time，the corresponding mathematical model of reliability is established.The reliability curve of the drive hydraulic system is obtained by using the MATLAB software.On this basis，the reliability of the combined vehicles drive hydraulic system group is also obtained.Based on the analysis of the drive asynchronous problems in the engineering practice，the fault tree of the drive hydraulic system failure is established.The quantitative and qualitative analysis is carried out for the fault tree，and the weak links of the drive hydraulic system are found out.The prevention of the failure can be considered in the design process，and the design level of the system will be improved.The method can be used to improve the reliability of the hydraulic system group of multi-vehiclecombined transportation.

Key words：Reliability，Drive hydraulic system group，F(xiàn)ault tree，Combined transportation

For the large-scale transportation，the combined transportation of multiple transport vehicles has become inevitable［1-2］.The hydraulic system of the transport vehicle mainly consists of the drive system，suspension system and steer system.The combination of multiple transport vehicles will form a huge hydraulic system group［3］.The reliability of the hydraulic system group is related to the safety and stability ofthe combined transportation.Not only the single vehicle hydraulic system should have high reliability，but also the reliability research of multiple vehicle hydraulic system group should be studied in depth.

The steering，lifting and synchronous running of the combined transport vehicles depend on the coordinated control and reliability of the hydraulic system group.The synchronization of multiple vehicles is realized by closed-loop control of multi-sensor signals，and the formation must be unchanged during the combined transportation.One of the vehicles can be operated or remotely controlled by the driver，and the others will be driven automatically according to the signals of the first vehicle［4］.

Aiming at the reliability research of the drivehydraulic system，the FTA（fault tree analysis）method is introduced［5］.The FTA is a complex fault analysis system with good reliability and safety.It is an effective method for fault risk assessment［6-7］.Chengyu Yao proposed the Fuzzy Reliability Assessment Method Based on T-S Fault Tree and Bayesian Network［8］.Mentes A.used the fuzzy fault tree analysis to the spread mooring systems［9］.According to quantitative data，the cause of system fault and the probability of fault occurrence can be determined.And more accurate fault point results can be obtained，which has better practical significance for system fault diagnosis［10］.Hoseinie，Hadi has carried on the reliability analysis to the loading system of hydraulic excavator［11］.Feng Z.proposed a new operation method based on the universal grey number to overcome the shortcomings of typical interval operation in solving system fault trees［12］.And a promising driving plan of emergence extension is proposed in respect of the reliability sensitivity analyses with a mixture of models［13］.

In this paper，the reliability model and reliability growth of the hydraulic system group of two transport vehicles are studied.The drive hydraulic system is analyzed in Section 2.Based on the analysis，the reliability block diagrams are established in Section 3.In Section 4，the reliability mathematical model of drive hydraulic system is obtained，and the reliability of the drive hydraulic system group is calculated and obtained through the MATLAB software.In Section 5，the fault tree of the drivehydraulic system group is analyzed，and the weak links of the drive hydraulic system are obtained.Finally，the reliability growth of the hydraulic system is analyzed and summarized in the Section 6.

1 Analysis of the drive hydraulic system

The drivehydraulic system is the key part of the transport vehicle，which provides the drive force for the transport vehicle.According to the structural characteristics and operation requirements of the transport vehicle，the closed system of variable displacement pump and motor is adopted in the drivehydraulic system.In the drivehydraulic system of the transport vehicle，the hydraulic pump drives the motor through the hydraulic oil，and the motor drives the reducer，which can drive the wheel through the speed reduction.The schematic diagram of the drivehydraulic system is shown in Fig.1.

Fig.1 The drive hydraulic system

The drive system of the transport vehicle is mainly composed of the hydraulic system and electric control system.The drive hydraulic system is a part of the hydraulic system of the transport vehicle，which is supplied by the closed load sensitive pump.Therefore，other hydraulic systems of the transport vehicle need to be considered when analyzing the reliability of the drive hydraulic system.

2 Reliability block diagram of drive hydraulic system

In order to analyze the reliability of the system，it is necessary to establish the reliability model.The reliability block diagram is used in this project，which can directly reflect the failure characteristics of components or systems，and can also carry out quantitative allocation and estimation of the system［14］.

In the drive hydraulic system of the transport vehicle，the variable motor is driven by the closed variable pump.The closed variable pump inputs the hydraulic oil into the hydraulic system.Through the connectionbetween the steel pipes and rubber pipes in the hydraulic circuit，the hydraulic oil enters the hydraulic motor to realize the multiple wheels rotate.In order to study the reliability of the drivehydraulic system group of the two vehicles，the reliability block diagram of the closed load sensitive pump is established as shown in Fig.2，the reliability block diagram of the oil tank is established as shown in Fig.3，and the reliability block diagram of the drive hydraulic system group of the two vehicles is established as shown in Fig.4.

Fig.2 The reliability block diagram of the closed load sensitive pump

Fig.3 The reliability block diagram of the oil tank

Fig.4 The reliability block diagram of the hydraulic system group

3 Reliability calculation of the drive hydraulic system

Because the design of the hydraulic system has been completed in advance and the corresponding components have been selected，so the failure rate prediction method is used in the reliability calculation of the transport vehicle drive hydraulic system［15］.Considering the difference between the practical application and the ideal situation，the failure rate is modified accordingly，and it is obtained as follows.

whereλiis the failure rate of system i，πEis the environmental factor，πDis the derating factor，πRis the correction factor，λjis the failure rate of component j.

The reliability of each series branch is as follows.

where Riis reliability of the unit i，n is the number of system unit.

The transport vehicle belongs to the ground equipment，so in this case，πEis 10.In general，the actual use of hydraulic components is not always under rated conditions，so the actual failure rate of components is smaller than that under rated conditions.Therefore，reduction factor should be introduced to correct，soπDis 0.85.For the hydraulic system of the transport vehicle，the fine filter is usually used to reduce the failure rate caused by the oil pollution.The failure rate of the used fine filter is generally 93.5%of the failure rate of the unused fine filter.In this case，the correction factor should be 0.935.The failure rates of all hydraulic components and parts required for reliability calculation of the drive hydraulic system are shown in the Table 1［16］.

Table 1 The failure rate of all hydraulic components and parts of the drive hydraulic system

According to Fig.2，the reliability function of the closed load sensitive pump can be calculated as Equation 3.And according to Fig.3，the reliability function of the oil tank can be calculated as Equation 4.The reliability function of the single vehicle drivehydraulic system is calculated as Equation 5.

The reliability curve of the closed load sensitive pump is obtained by using the MATLAB software，as shown in Fig.5，and the reliability curve of the oil tank is obtained as shown in Fig.6.The reliability curve of the single vehicle drive hydraulic system is obtained as shown in Fig.7.

Fig.5 The reliability curve of the pump

Fig.6 The reliability curve of the oil tank

Fig.7 The reliability curve of the single vehicle drive hydraulic system

The reliability function expression of thesingle vehicle drive hydraulic system is obtained as Equation 6.

According to Equation 6，and the parameters of the two vehicles are the same，so the reliability function of the two transport vehicles drivehydraulic system group can be obtained as follows［17］.

The reliability curve of the drive hydraulic system group of the two vehicles is obtained by usingthe MATLAB software，as shown in Fig.8.

Fig.8 The reliability curve of the drive hydraulic system group of the two vehicles

It can be seen that the oil tank part，the pump source and the drive system are connected in seriesfrom Fig.5，F(xiàn)ig.6 and Fig.7.From Fig.8，it can be seen that the reliability of drivehydraulic system groupreduces by about 0.2 after 4000 hours，which has high reliability in this field and meets the design requirements of the hydraulic system.In the vehicle hydraulic system，the reliability of the oil tank is the highest and the reliability of the drivehydraulic system is the lowest.There are 16 sets of drivehydraulic systems in the two vehicles.Through calculation results of the reliability，it can be seen that the number of series components leads to the decrease of the reliability of the drivehydraulic system.

4 Fault tree of the drive hydraulic system

4.1 Top event selection

The fault tree is established for the hydraulic motor powerlessnessoccurred in thecombined transportation.As the executive component of the drivehydraulic system，whether in the process of forward or backward，if the hydraulic motor is powerlessness，it will directly affect the transportation，and even cause accident.The failure of the system components may lead to the hydraulic motorpowerlessness.Therefore，the failure is selected as the top event，the possible failure of the components can be found out in the drivehydraulic system through analysis.

4.2 Establishment of the fault tree

Before establishment of the fault tree，it is necessary to make assumptions on the system，so as to facilitate the fault analysis of the system［18］.The analysis results in the following reasons：the failure of the hydraulic motor；the failure of the balance valve；the insufficient oil pressure into the hydraulic motor.The status of these three cases in fault tree is the first level intermediate event.

After analyzing the first intermediate event，the next step is to analyze the next intermediate event.Through the motor fault and balance valve fault these two intermediate events can directly analyze the bottom event［19］.The reasons for the failure of the hydraulic motor may be：insufficient pressure at the outlet of the variable displacement pump；the failure of the proportional multi-way valve；pipeline leakage；check valve stuck.Among them，the pipeline leakage and check valve stuck can be regarded as the bottom event directly，while the insufficient outlet pressure of variable displacement pump and the failure of multi-way valve can be regarded as the second intermediate event.

When the pump outlet pressure is insufficient，it can continue to develop into the third intermediate events including overflow valve failure and pump performance failure.And multi-way valve failure can be divided into three levels of intermediate events including slow reversing and non reversing，and even the bottom events is the blocking of control pressure oil circuit.Three levels of intermediate events can be directly get their own bottom events.Therefor，the fault tree can be established as shown in Fig.9.And the meaning of each event code is shown in Table 2.

Fig.9 The fault tree of the hydraulic motor powerless

Table 2 The event of the fault tree

4.3 Fault tree analysis

There are only logicORgates in the fault tree，it can be obtained as follows by the Boolean algebra.It means that the top event will occur if any bottom event fails.

According to the references［20-21］，the failure probability of each bottom event in the fault tree is distributed exponentially.The transport vehicle needs to timelymaintenance after 1 500 h of use.After determining the failure rate of each bottom event，the calculation results of the events are shown in Table 3.

Table 3 Quantitative analysis data of the fault tree

Table 3 shows that reliability is 0.889 4，and the probability of fault is 0.112 9.But for the two transport vehicles combined transportation，the reliability is 0.791 0 and the probability of fault is 0.225 8.Since the value of probability importance can quantitatively explain the degree of influence of bottom event on top event［22］，the top event can also be solved according to the order of probability importance.And the probability importance of each bottom event is relatively large，the bottom events with great influence on the top event are x13，x15and x17，the influence of variable pump fault and multiplex valve fault on the top event is the larger influence on the top event.Because the critical importance indicates the status of the event，and also can reflect the degree of unreliability，it can objectively reflect the event to the system fault.According to the structural importance calculation formula of components［23］，the structural failure degree of each bottom event can be obtained as 0.517.From the structure of the fault tree，it can be seen that the bottom events are equal.

5 Conclusion

Based on the monitor data and reliability evaluation theory of large-scale hydraulic transport vehicle，the reliability analysis and calculation of the drivehydraulic system group of the combined transportation are carried out，and finally the reliability curve of the combined transportation driving hydraulic system is obtained，and the change rule of its reliability in the transportation can be observed from the reliability curve，which can realize the improvement of hydraulic system group and ensure the stable combined transportation of multiple large-scale transport vehicles.

From the fault tree of the hydraulic motor powerless，the weak links of the drive hydraulic system of the combined transportation are obtained.The reliability should be improved from the bottom event with high probability importance.At the same time，the criticality importance of the bottom event and the vulnerable part of the system should be considered，and the logic AND gates of the system should be increased，especially the links prone to failure should be designed for the system reserve.The high reliability hydraulic components can also be used to improve the reliability of the system.