1.Introduction

Integrated Electro-Hydrostatic Actuators(EHAs)have seen increased application in More-Electric Aircraft(MEA),due to their numerous advantages including high reliability,long lifetime,and high efficiency.1–4Traditional power-integrated Rotary Electro-Hydrostatic Actuators(REHAs)are facing many problems,such as severe heating,big inertia,low frequency response,and difficulty in redundancy con figuration.In order to solve these deficiencies,many researchers have proposed direct-drive EHAs.5–9Li et al.have presented a novel LEHA for the pump control system based on a collaborative rectification structure for linear pumps where the fundamental subsystem consists of two Direct Drive Pump Cells(DDPCs).10Their prototype has verified feasibility of the proposed actuator and flexibility of the dual-control strategy.Although the system has a number of advantages,its reliability characteristics,such as degradation and life prediction,need to be addressed and further improved.Applying the novel operating principle,the LEHA has improved these performance issues,but it has also introduced a problem due to the fact that it cannot integrate filters.The novel LEHA is also an integrated closed system which can increase the power-to-weight ratio.A linear resonance motor drives piston cylinder suction and discharges oil.The spool of a rectification slide valve is rigidly connected with the driving cylinder rod,resulting in the active rectification mechanism to be in a high-frequency condition.Due to non- filter design,contaminated particles will continuously cycle in an LEHA during its operation,which will precipitate further erosion and produce more contamination particles.Consequently,compared to a conventional hydraulic system with filters,the rectification mechanism in an LEHA can fail more rapidly,which can lead to a dominant progressive degradation process.

The rectification mechanism is commonly present in hydraulic systems,and when coupled with oil contamination,it can result in system failure.Some research results have indicated that contamination particles in oil wash out and wear the edges of valve components.11The resulting leakage increase caused by wear accounts for approximately 60%of cases of component failure.According to the research by Zhang et al.,the wear resulting from particulate contaminants causes an increase in the internal leakage,the output current hysteresis and null leakage,the input current threshold,and the pressure gain,as well as a decrease in the gain linearity of the electro hydraulic servo valve.12The Physics-of-Failure(PoF)models of particle erosion wear introduced by Fang et al.show that the erosion wear has significant impacts on the electro hydraulic servo valve’s service life and reliability.13Furthermore,the erosion of an LEHA is even more serious due to the particular type of motion and active rectification under relatively severe conditions.This paper is focused on the performance degradation of an LEHA induced by erosion wear.

Performance degradation analysis is extensively applied in numerous Engineering fields to evaluate safety of machine parts and equipment.14The associated theories can be divided into three categories:(a)failure physics,(b)probability statistics,and(c)artificial intelligence.The first approach studies the structural integrity of an object with respect to operating conditions and mechanical and physical properties of materials used to make the object.Probability statistics models are mainly suitable for analysis of degradation based on stress fatigue,which requires significant amount of test data.Alternately,the artificial intelligence approach is dependent on field performance degradation data.In the field of durability analysis and life prediction,numerous physical experiments are performed in order to evaluate the life and reliability of hydraulic components.Therefore,during the design stage,it is essential to analyze the overall LEHA system based on the physical nature of erosion.

A significant number of studies have been performed to analyze the effect of erosion on system performance degradation.Fitch and Hong investigated the effects of contaminated oil on erosion in pumps and contaminant lock in servo valves,and proposed a new method to predict service life.15The occurrence of contaminant lock is accidental whereas the erosion caused by contaminant particulates is a continuous process which takes place as long as the system is operational.Vaughan et al.examined the effects of the particle size and concentration,differential pressure across the metering land,spool opening,spool surface, flow direction,as well as fluid characteristics on erosion wear.16Yang et al.adopted a gamma process to describe the internal structure degradation under erosion for electrohydraulic servo valves.17Zhang et al.presented a degradation assessment and life prediction method for electrohydraulic servo valves based on the CFD method and hydraulicsimulation.12In addition,other researchers have predicted structural wear by CFD techniques.18–20The mechanism of erosion for a ductile metal material is a micro-cutting process,which was put forward by Finnie,who also presented an analytical erosion model to calculate erosion rates.21Tilly proposed that erosion of ductile materials could occur in two stages,where the first stage is micro-cutting whereas the second stage is surface fragmentation,and found that resulting estimates gave a good correlation with experimentaldata.22Recent theoretical and experimental studies explored the effects of particle properties,impacting speed and angle,and material properties on the severity of erosion.Among those studies,the Edwards model has been widely accepted to be applicable to erosion for gassolid,liquid-solid,or gas-liquid-solid flow,where particle properties,impacting speed and angle,and material properties are taken into account.23Therefore,the Edwards model is utilized in this study because of its extensive applicability and high prediction accuracy.In addition,erosion due to the rectification mechanism in an LEHA under the influence of contaminant particles in hydraulic oil falls within the model framework.

（3）将“套路”与新思路有效结合，实现解题效率的最大化。还有些情况下单一应用“套路”或构建新思路都难见成效，我们可以尝试将它们“融为一炉”。

This paper proposes a new method for analyzing performance degradation under dynamic erosion wear.The Edwards model is utilized to obtain erosion rates due to its broad applicability and high prediction accuracy.Furthermore,erosion rates of the rectification mechanism for different port openings and different degradation stages are estimated.In addition,in order to obtain the degradation curve under dynamic erosion wear,the concentration of contaminant particles is updated at different stages of degradation.Finally,the proposed degradation model is applied to simulate the wear degradation process in an LEHA under different flow conditions,and results are compared with results from traditional wear studies.

2.Problem description

2.1.Working principle of the LEHA

Fig.1 Hydraulic circuit diagram of the novel LEHA design.

Fig.2 Functional diagram and control loop of an REHA.

The schematic representation of the proposed LEHA architecture is shown in Fig.1,whereas Fig.2 represents the hydraulic circuit diagram and control loop of a traditional REHA.The REHA utilizes a motor and a pump to convert electrical energy to hydraulic energy,where the motor has reversible rotation in order to control the flow direction of hydraulic oil.Compared with the REHA,the proposed LEHA has the following distinct characteristics:(1)a linear resonance motor corresponding to the rotating electric machine,(2)a single direct drive piston cylinder corresponding to the traditional rotary piston pump,(3)a rectification model with passive reliance on a valve plate and active collaborative rectification dependence on a three-position four-way slide valve,and(4)direction control achieved through the phase difference between two DDPCs.The linear motor commonly operates in the resonant working mode in order to generate the maximum energy output.A Direct Drive Pump Module(DDPM)consists of DDPC1 and DDPC2,which are characterized with collaborative rectification.A DDPC consists of a cylinder and a valve,where a piston rod and a valve spool are integrated,and is driven directly by the linear resonating motor.X and Y are the interface ports of the DDPCs:one is the inlet and the other is the outlet.The deflection angle of aircraft’s control surface is θ.As a result,the novel pump is more compact and has better controllability.The theoretical research and experimental results conducted on the prototype valve have demonstrated that the DDPC-dis charged kinematic flow volume depends on the phase difference between the two cells.The output flow in one cycle from a DDPM port is represented by

The longitudinal cross section of the wear-free spool is assumed to be rectangular with square edges.As wear progresses,the spool edges start to develop a quarter-round geometry of radius r.The total wear volume of a valve’s orifice can be obtained by the following equation:

The kinematic volume efficiency is maximum for φ=±π/2,and zero for φ =0 or φ = ±π.

2.2.Dominant mode of gradual failure

At an earlier stage,a Failure Mode and Effect Analysis(FMEA)was performed for the LEHA.24The results show that resonant spring fatigue damage and rectification mechanism erosion are the two major progressive failure modes affecting the performance of the LEHA.The LEHA failure is defined as a condition when a performance indicator cannot be maintained within a specified range.The effect of rectification mechanism erosion is shown in Fig.3,where P,T,A,and B are the hydraulic oil ports of the three-position four-way valve.The figure indicates possible fluid flow patterns in the rectification slide valve when port P is connected with X and port T is connected with Y.It can be seen that the rectification valve is characterized by reciprocating flushing which is different from single-direction flushing which occurs in a traditional valve.The rectification valve at the middle position is equivalent to a piston pump at the upper or lower dead point.Consequently,wear of the internal structure can cause an increase in internal leakage and result in power loss.

脏器指数又称脏体比，是试验动物某脏器的重量与其体重的比值。脏器系数的变化可较好地反映化学毒物对该脏器的毒性综合情况。脏器系数下降表示萎缩、退行性变化；脏器系数加大，在一定范围内表示脏器机能增强，过大则可能是充血、水肿、增生肥大性变化等病变。

When particles impinge the valve wall at a certain angle and speed,they rebound at a certain angle and speed,as shownin Fig.7.The energy loss during collision can be determined from the impulse-momentum principle where normal and tangential restitution coefficients are employed,which are introduced as

精准农业是农业研究与应用的热点领域，是农业科技革命的方向。目前黑龙江垦区在精准农业应用方面走在全国前列，将来要进一步利用土地规模优势，大力发展以3G技术、自动控制技术为核心的精准农业，加大具有自主知识产权的技术、装备应用推广力度，减少投入成本，发挥垦区在现代农业发展中的引领示范作用。

Fig.3 Fluid flow in the rectification slide valve when P is connected with X and T is connected with Y.

The major impact of erosion is reflected on the performance of the LEHA.Namely,there are two ways in which the power/weight ratio of the LEHA can be affected:one is a change in the resonant frequency and the other one is a change in the amplitude.The resonant amplitude is subject to the size of the DDPM,which makes modification in the frequency become the most effective method.The initial clearance between the valve spool and sleeve in new valves is generally in the range of 3–5 μm,and the corner radius of edges is generally below 0.5 μm.Throughout their lifecycles,valves will undergo erosion which will cause an increase in internal leakage,which,on the other hand,will ultimately degrade the system performance.

3.Mathematical model of the degradation process

The erosion-induced performance degradation process can be analyzed in three consecutive steps:(1)identification of the potential erosion location and determination of the fluid dynamic boundary,(2)determination of the structural degradation after erosion,and(3)prediction of the erosion rate.

3.1.Stress-strain equation of the dynamic boundary

The erosion wear is analyzed in both valve and piston regions as indicated in Fig.4.Pv1,Tv1,Av1,and Bv1are the hydraulic oil ports of the valve in DDPC1.Ap2and Bp2are the cylinder chambers in DDPC2.The displacement of the mover is x1in DDPC1,and the velocity is v1.Similarly,the displacement of the mover is x2in DDPC2,and the velocity is v2.The positive direction is the cylinder pointing to the valve.When the spool in DDPC1 or DDPC2 is at the zero displacement,i.e.,x1=0 or x2=0,there is no connection between P,T and A,B.The piston determines the flow velocity and flow rate through the valve inlet,and in turn,the valve transfers the load pressure to the piston.

随着生产力的发展，奴隶主土地的开垦面积越来越大，从前的“井田制”遭到破坏，许多奴隶主一方面使用奴隶开垦公田同时又大量招收“隐民”、“私属徒”进行开荒，扩大自己的私田面积。有些贵族为了增加自己的收入大量开发荒芜的上地，就成为拥有大量私田的地主。另一方面，从事大规模集体生产的奴隶，由于不堪忍受奴隶主的残酷剥削和压迫，则纷纷选择逃亡，这样就使井田逐渐荒芜。井田制的破坏，就说明奴隶制社会的经济基础开始崩溃。私田的不断增多，促进了封建生产关系的产生和新兴地主阶级势力的发展，最终打破了奴隶社会“工商食官”社会分工体系。

The continuity equations of hydraulic chambers Ap2and Bp2can be written as

where PdA2is the hydraulic pressure in the left chamber,PdB2is the hydraulic pressure in the right chamber,βeis the effective bulk modulus(including hydraulic oil,connecting pipes,and the cylinder’s mechanical flexibility),VdA2is the volume of the left chamber(including valves and connecting pipes),VdB2is the volume of the right chamber(including valves and connecting pipes),Cipis the cylinder’s internal leakage coefficient,Cepis the cylinder’s external leakage coefficient,qdA2outis the out flow from the cylinder’s left chamber,qdB2inis the in flow to the cylinder’s right chamber,VdA02is the initial volume of the left chamber,and VdB02is the initial volume of the right chamber.

Fig.4 Schematic diagram of the reciprocating system.

The fluid flow rate Q from the driven hydraulic cylinder chamber to the valve entrance can be described by the following orifice flow equation:

where Cdis the flow coefficient of the orifice,Aeis the effective area of the orifice,Pfis the hydraulic pressure in front of the orifice,Pbis the hydraulic pressure behind the orifice,ρ is the fluid density,vpais the average velocity of fluid at the valve inlet,and Apis the cross-sectional area of the valve inlet.

3.2.Continuous flow model

The continuous phase modeling uses Reynolds averaged Navier-Stokes equations.Because of enhanced accuracy for rapidly strained and swirling flows,the RNG k-ε model is selected for turbulence,where the continuity equation is described as

公元前449年颁布的《十二铜表法》标志着罗马平民获得法律的基本保护，但依然存在“有产者(adsidui) ”和“无产者(proletarii) ”之分。[注]参见谢邦宇等编：《罗马法》，北京：群众出版社，1983年，第364-371页。这说明当时还有许多人是几乎没有地产的“无产者”。然而，无产者在身份上并不是奴隶，而是属于平民阶层，只是地位岌岌可危，随时都有可能丧失自由，沦为债奴。

where v is the velocity of fluid.

3.3.Structural degradation model

According to a significant number of published results,erosion has the greatest impacts on the radial clearance between the spool and the sleeve,and on the throttle edge radii.An ideal geometry calls for the throttle edges to be perfectly square with no rounding.11–13,25,26The erosion process will cause the throttle edges to wear and develop radii,resulting in an increase of the radial clearance between the spool and the sleeve,as shown in Fig.5.The radial clearance between the spool and the sleeve has a small initial value because of the fluid’s lubrication.

According to the Pythagorean theorem,the gap between the spool and the sleeve can be determined as

前文已经提到了，目前轧制加热过程需要的燃料一般是高炉煤气、转炉煤气等工业制气，该部分燃料大多是使用煤不完全燃烧产生的，而煤资源是不可再生的一次能源，所以加强轧钢加热过程的温度控制，不仅可以降低生产成本、减少污染，同时还可以减少一次能源的使用，所以，控制轧制温度的重要意义还有节省一定量的能源和资源。

where δ1is the radial clearance between the spool and the sleeve,δ2is the flow clearance between the spool and the sleeve,r1is the radius of the spool’s throttle edge,r2is the radius of the sleeve’s throttle edge.

It is assumed that r=r1=r2,since the difference between r1and r2is relatively small.

Fig.5 Throttle edge after wear.

3.4.Wear volume model

The geometry of the cylindrical spool changes during erosion wear as indicated in Fig.6.Assuming the same wear conditions between contact surfaces,then the degrees of wear of the spool and the sleeve can be assumed to be equal.In addition,it is assumed that the wear rate of each orifice is the same.Since the edge radius,r,is small compared to the spool radius,Rs,the radius of the spool,Rs,is considered to remain constant throughout the process.

where V is the output flow in one cycle from a DDPM port,Acis the piston’s effective area,Spis the resonance amplitude of a DDPC,and φ is the phase difference between the two cells.

where Vois the total wear volume of a valve’s orifice,Vsis the wear volume of a single throttle edge,r is the equivalent radius of the throttling edge,c is the perimeter of the throttle edge,and Rsis the radius of the spool’s boss.

The total wear volume of the valve can be obtained by the time integration of the erosion wear rate as follows:

where ρpis the contaminated particle’s density,seis the eroded area,and ρe(t)is the erosion rate function.

3.5.Contaminant particle concentration model

During a lifetime of LEHA operation,metal particles generated by wear end up in hydraulic oil.Since the LEHA is a closed system,it is reasonable to assume that all particles produced by wear are accumulated in the working hydraulic oil.The contaminant particulate concentration can be expressed by the following mass conservation equation:

where η0is the initial particle mass flow rate,η is the particle mass flow rate with the corresponding wear volume Vo,and Vhis the hydraulic oil volume in the LEHA.

Fig.6 Geometries of worn throttle edges.

3.6.Discrete phase model

The dynamics equation of a particle in a Lagrangian reference frame can be expressed as

where u is the fluid velocity,upis the particle velocity,and upis the scalar form of the particle velocity.FD(u-up)represents the force load on unit particle mass,g is the acceleration of gravity,and Fxis the additional force including Saffman’s lift force,the virtual mass force,the pressure gradient force,the thermophoretic force,the forces in moving reference frames,and the Brownian Force.

where dpis the particle’s diameter,Re is the relative Reynolds number,μ is the dynamic viscosity of the fluid,and CDis the drag coefficient,which is defined by Haider and Levenspiel27as

where Φ is the particle shape factor,s is the surface area of a sphere with the same volume as the particle,and S is the actual surface area of the particle,and b1,b2,b3,and b4are coefficients related to Φ.

It can be assumed that the particle volume fraction or concentration is very low and that the collision between particles can be neglected.

3.7.Particle-wall collision-rebound model

The major sources of initial contamination include particulates resulting from the manufacturing process,dust inclusions from storage,and contaminant particles mixed in oil.These contaminants can impact the system in three different ways:(a)three-body abrasion,(b)particle impingement erosion,and(c)motion impediment.15Motion impediment is rare in practice and caused by relatively large particles.However,the erosion problem is common,and can become serious as the process has a tendency of having positive feedback.

Fig.7 Schematic diagram of particle-to-wall collision-rebound.

where εNis the normal restitution coefficient,εTis the tangential restitution coefficient,vp1,nand vp1,tare the particle’s normal and tangential velocities with respect to the wall prior to collision,and vp2,nand vp2,tare the particle’s normal and tangential velocities after collision.

从某种意义上讲，兰博基尼Huracán Performante不过是意大利版的奥迪R8。然而，当打开车门坐进其中时，我便意识到，它的运动气息要比奥迪R8浓郁得多。

3.8.Semi-empirical material removal model

The Edwards model is commonly used to determine the erosion rate for certain particle concentration and wall boundaries,and can be expressed as follows:

where Npis the number of particles that impact the area represented by Aface,mpis a particle’s mass,C(dp)is the function of a particle’s diameter,vpis the particle velocity relative to the wall,b(vp)is the function of the relative particle velocity,Afaceis the area of the cell face on the wall,and f(αp)is the function of the impact angle,which is determined as

4.Simulation of erosion wear

7.Jänker P,Claeyssen F,Grohmann B,Christmann M,Lorkowski T,LeLetty R,et al.New actuators for aircraft and space applications.11th International conference on new actuators;2008 June 9–11;Bremen,Germany.Bremen:ACTUATOR Interest Group;2008 p.325–30.

综上所述,凶险型前置胎盘的临床特征具有显著的危险性,并对妊娠结局与新生儿结局造成严重影响,临床上应给予高度重视。具体可通过一下几方面来达成:(1)早发现,早干预。前期诊断前置胎盘,能够有效改善母婴预后;当前前期诊断主要通过超声检查来时间,如果诊断中出现不明状况,可通过MRI检查进一步确诊;(2)对于凶险型前置胎盘患者,要充分考虑患者实际状况给予个性化治疗,必要的情况下终止妊娠,保证患者生命甘泉;(3)严格管控剖宫产,降低剖宫产实施率。

The model of fluid flow is based on the Reynolds averaged Navier-Stokes equations,while the RNG k-ε model,due to its enhanced accuracy for rapidly strained and swirling flows,is used to describe turbulence.The particle trajectory and its velocity are determined by solving a set of ordinary differential equations formed by the Lagrangian method.A simulation is performed with ANSYS Workbench 15.0.

The simulation is based on the implementation of the flow chart shown in Fig.8.Firstly,the spool position and the concentration of contaminant particles are determined.A dimensional fluid domain model is established next,followed by meshing,parameter initialization,and calculation of erosion wear.The erosion wear is recalculated when the spool position or contaminated particles’concentration changes.Finally,an erosion degradation curve is obtained by integrating the erosion rate with respect to time.

It has been demonstrated by Grant and Forder et al.that restitution coefficients are dependent on the particle impingement angle,αp.28,29Furthermore,Forder et al.provided the expressions of restitution coefficients as follows:

The main structural parameters of the LEHA’s rectification mechanism are given in Table 1.The initial flow rate of hydraulic oil with contaminant particles can be obtained by 7th level.12It is assumed that the particles are pure iron,the reciprocating frequency is 100 Hz,and the opening size is±3 mm.The dynamic fluid boundary conditions can be obtained from Eqs.(7)and(8).In order to achieve high computational effectiveness,an optimal algorithm is used to balance the grid quality and calculation time.The resulting computational domain mesh is shown in Fig.9.The standard case simulation parameters are given in Table 2.

Fig.8 Algorithm for erosion prediction.

Table 1 Main structural parameters of the LEHA.

Structural parameters Value Diameter spool dsp7 mm Diameter cylinder’s rod dcr7 mm Diameter cylinder’s piston dcp10.5 mm Valve stroke Sv3 mm Diameter hydraulic pipe dp3 mm Hydraulic oil volume Vh0.5 L

Fig.9 Computational domain and mesh(when the valve opening is 50%).

In addition,the conventional SIMPLE algorithm is applied to couple pressure and velocity via a second-order upwind scheme for the momentum.The convergence criterion is set so that the residual is smaller than 10-3.

帕金森病痴呆患者在临床上发病率较高,可包括运动症状及非运动症状,发病原因尚未在临床上进行准确阐述,相关性影响因素包括环境因素、年龄因素及遗传因素等,病理改变是纹状体中减少多巴胺含量[2],占据相对优势的是胆碱能系统活动,可导致患者出现脑损害,可导致患者生活质量严重下降。

对照组患者采用X线检查的方式进行摄片,采取仰卧位的前后位片和胸部立位的正位和斜位片,在曝光时嘱咐患者注意屏气,以保证拍摄效果。实验组的患者采用DR检查的方式进行摄片,与对照组采用同样的体位和要求进行曝光拍摄。两组患者的检查结果均有资深影像学医生进行阅片给出诊断,对照组的结果在观片灯下观察,实验组患者的结果由于需要经过计算机处理的到标准图像、软组织像和骨组织像,共同观察确定结果,所以在PACS系统进行阅片,对比两组患者的诊断结果。

The simulation results representing the erosion rate contours of the spool valve are shown in Fig.10.The results indicate that the edge of the throttle orifice is experiencing the most serious erosion.The results are consistent with the published results focused on erosion of EHSVs,throttle valves,and needle valves.11–13,17,25,30,31The particle path lines and associated velocity magnitudes are shown in Fig.11.The areas with high-speed pro files are evident in the orifice edge region,where the particle velocity can be in excess of 100 m/s.Having a large number of particles with significant kinetic energy,directly impinging the orifice,will result in a severe erosion of the surface.

5.Results and discussion

5.1.Effect of the opening gap on the erosion rate

The average erosion rate of a sharp edge as a function of the valve opening(dop),during the early stage of degradation,is shown in Fig.12.Correspondingly,Fig.13 depicts the erosion rate distribution in the throttling edge for different valve opening sizes.The results are for valve port opening between 0 mm and 3 mm.It can be observed that the maximum average erosion rate occurs when the EHSV opening is 0.5 mm,and that the average erosion rate decreases rapidly for opening sizes between 0.5 mm and 1.0 mm.

Table 2 Standard case simulation parameters.

Case Valve opening Inlet velocity Inlet pipe diameter Load pressure Particle concentration Particle diamete Standard 0.5 mm 55 m/s 3.0 mm 3 MPa 1.78 × 10-7kg/s 5 μm r

Fig.10 Erosion rate contours of the valve.

Fig.11 Particles’path lines of the velocity magnitude.

Fig.12 Erosion wear rate under different valve opening sizes.

5.2.Effect of the inlet velocity on the erosion rate

2.MarÉJ-C,Fu J.Review on signal-by-wire and power-by-wire actuation for more electric aircraft.Chin J Aeronaut 2017;30(3):857–70.

The maximum erosion rate on the spool occurs at an inlet velocity of 65 m/s and is about 8.9 times higher than that at an inlet velocity of 45 m/s,while the maximum erosion rate along the sleeve throttle side for an inlet velocity of 65 m/s is 6.1 times higher than that for an inlet velocity of 45 m/s.

2.3 精密度与准确度实验 精密度用 RSD 表示，如表2 所示，5-羟色胺和 5-HIAA 日内精密度 RSD 均≤10.08%、日间精密度 RSD 均≤8.82%；准确度以相对回收率表示，结果表明5-羟色胺和 5-HIAA 日内、日间准确度范围在97.83%～113.00%。

5.3.Effect of the inlet pipe diameter on the erosion rate

The erosion rates for different inlet pipe diameters but for constant pressure and opening are shown in Fig.15.It can be observed that the maximum erosion wear rate initially increases and then decreases with an increase of the inlet diameter.The magnitude of the maximum erosion rate,for both the spool and the sleeve,is largest at din=4 mm.The erosion rate of the valve spool for an inlet pipe diameter of din=2.5 mm is approximately 8%,whereas for din=4 mm,it is 7.5%.

The results indicate that increasing the diameter of the inlet pipe results in an increase of the flow through the gap between the spool and the sleeve,which ultimately leads to an increase in the erosion severity.

5.4.Effect of the load pressure on the erosion rate

The results indicating the erosion rate distribution on the valve spool and along the sleeve for different levels of load pressure(Pl)are shown in Fig.16.When the load pressure increases from 0 MPa to 5 MPa,the erosion wear rate decreases slowly,whereas the erosion rate decreases rapidly with the load pressure increasing from 5 MPa to 8 MPa.The maximum erosion rates on the spool and along the sleeve throttling edges for a load pressure of 0 MPa are respectively 3.21 times and 3.46 times higher than those for a load pressure of 5 MPa.The erosion rate decreases rapidly when the load pressure increases to 8 MPa.

A lower load pressure causes a greater pressure drop on the valve path,resulting in a greater velocity of particles impinging on the valve wall,which increases erosion wear.

5.5.Effect of the particle concentration on the erosion rate

Fig.13 Erosion rate distribution in the throttling edge under different valve opening sizes.

The results indicate that the particle concentration (cp),expressed as the particle mass flow rate,plays a significant role in affecting the erosion,as shown in Fig.17.In addition,increasing the particle mass flow rate results in an increase of the erosion-dominated zone as well as the severity of erosion.As the mass flow rate increases from 1.78×10-7kg/s to 3.56×10-7kg/s,the erosion zone extends to the entire throttling edge.The peak erosion rate of the spool at a particle mass flow rate of 3.56×10-7kg/s is approximately 2.64 times of that at a flow rate of 1.78×10-7kg/s.Whereas,the maximum erosion rate along the sleeve at a particle mass flow rate of 3.56×10-7kg/s is about 2.21 times of that at a flow rate of 1.78×10-7kg/s.

The higher the particle mass flow rate is,the more particles impinge on the spool and the sleeve per unit time.The result is that the same region is impacted by a larger number of particles.

5.6.Effect of the particle diameter on the erosion rate

The results indicate that the particle diameter clearly affects the erosion rates of both the spool and the sleeve,as illustrated in Fig.18.As the particle diameter increases from 1 μm to 3 μm,the erosion rate increases rapidly;however,as the particle diameter increases from 3 μm to 20 μm,the erosion rate decreases slowly.The maximum erosion rates of the spool and along the sleeve at a particle diameter of 3 μm are respectively 2.41 and 2.35 times higher than those for a particle diameter of 1 μm.Furthermore,the maximum erosion rates of the spool and along the sleeve for a particle diameter of 3 μm are respectively 16.23 and 15.64 times of those for a particle diameter of 15 μm.The results indicate that the particle diameter has a significant effect on erosion.

Fig.14 Erosion rate distribution in the throttling edge under different inlet velocities.

Fig.15 Erosion rate distribution in the throttling edge under different inlet pipe diameters.

The underlying assumption is that the mass flow rate of particles is constant.Consequently,the larger the diameter of a single particle,the greater the mass of a single particle,and the smaller the number of particles.When the number of particles in the unit volume decreases,the probability of the particles impacting the spool or the sleeve is reduced with the number of particles passing through the gap between the valve spool and the sleeve.For the same velocity,a particle of a larger mass has greater kinetic energy than that of a particle of a smaller mass.As a result,assuming the same incidence angle,a particle of a larger mass causes more severe erosion than a particle of a smaller mass.As the particle diameter increases from 1 μm to 3 μm,the particle inertial force plays a dominant role in the erosion process,while for particle sizes between 3 μm and 15 μm,the number of particles plays a primary role.

近日，湖北省南漳县盘龙、新生、辉煌、李湾、群力等5座小（1）型水库，安乐堰、白龙滩、郭家棚等11座小（2）型水库除险加固工程，黑河治理工程，云台山灌区等工程全面推进，掀起了2012年水利工程建设高潮。

Fig.16 Erosion rate distribution in the throttling edge under different load pressures.

Fig.17 Erosion rate distribution in the throttling edge under different particle concentrations.

6.Conclusions

The paper introduces the working principle of a novel LEHA design,which is an integrated closed system without filters.A study was performed to analyze the effects of contaminant particles,caused by the system erosion wear,on the internal leakage of the valve and ultimately on its performance.According to failure analysis,erosion is the dominant progressive failure mode of the LEHA.Since the system does not include filters,the mass of contaminant particles accumulates over the life of the valve,which can lead to progressive failure of the system.Simulation results provide insight into the effects of valve opening on the erosion rate and the relationship between the erosion rate and structural degradation.A comparison between the simulation results and published wear erosion results for EHSVs indicates that the proposed analysis approach is effective.The following conclusions can be made based on the simulation results:(1)the erosion wear dominates the service life of the LEHA(not considering accidental failure),(2)the throttle edge erodes fastest,caused by dissipation of the kinetic energy of a large number of high-speed particles at that location,and(3)the erosion of the LEHA is an accelerated degradation process.The proposed approach can be used to evaluate the service life of the LEHA and to further guide the design of the LEHA’s rectification valve structure.An experimental setup is under construction,which will provide verification of the proposed analysis model,and enable further studies of erosion phenomena in the LEHA and their effects on performance degradation of the LEHA.

Fig.18 Erosion rate distribution in the throttling edge under different particle diameters.

Acknowledgements

This work was supported by the National Natural Science Foundation of China (Nos. 51620105010, 51675019,51575019),the National Basic Research Program of China(No.2014CB046402),and the Program 111 of China.The authors would also like to thank the reviewers and the editor for their comments and suggestions that led to significant improvement in the quality of the paper.

Appendix A.Supplementary material

Supplementary data associated with this article can be found,in the online version,at https://doi.org/10.1016/j.cja.2017.12.002.

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