- Email: [email protected]
Erosion behavior and influence of solid particles in hydraulic spool valve without notches
Journal Pre-proofs Erosion behavior and influence of solid particles in hydraulic spool valve without notches Xinqiang Liu, Hong Ji, Wei Min, Zhi Zheng, Jinlin Wang PII: DOI: Reference:
S1350-6307(18)30982-8 https://doi.org/10.1016/j.engfailanal.2019.104262 EFA 104262
To appear in:
Engineering Failure Analysis
Received Date: Revised Date: Accepted Date:
9 August 2018 26 September 2019 4 November 2019
Please cite this article as: Liu, X., Ji, H., Min, W., Zheng, Z., Wang, J., Erosion behavior and influence of solid particles in hydraulic spool valve without notches, Engineering Failure Analysis (2019), doi: https://doi.org/ 10.1016/j.engfailanal.2019.104262
This is a PDF file of an article that has undergone enhancements after acceptance, such as the addition of a cover page and metadata, and formatting for readability, but it is not yet the definitive version of record. This version will undergo additional copyediting, typesetting and review before it is published in its final form, but we are providing this version to give early visibility of the article. Please note that, during the production process, errors may be discovered which could affect the content, and all legal disclaimers that apply to the journal pertain.
© 2019 Published by Elsevier Ltd.
Erosion behavior and influence of solid particles in hydraulic spool valve without notches Xinqiang Liu1,2,*, Hong Ji1,2, Wei Min1,2, Zhi Zheng1, Jinlin Wang3 1Energy
and Power Engineering College, Lanzhou University of Technology, Lanzhou, China Laboratory of Fluid Machinery and System, Gansu Province 3School of Aerospace Engineering, Tsinghua University, Beijing, China 2Key
Abstract Hydraulic spool valve without notches is used as a kind of important amplification component in hydraulic servo valve. Its static and dynamic properties have a significant impact on the performance of servo valve and hydraulic system. Under solid particles erosion in oil, the metering edges of spool valve were usually eroded and worn. This process was irreversible and induced serious control performance degradation of orifice and valve. In this paper, the erosive behavior and influence of solid particles in hydraulic spool valve without notches were investigated. By the surface microtopography measurement of the spool, erosion corners failure were present. The CFD simulation of solid-liquid two-phase flow was carried out by discrete phase model (DPM)to analyze the erosion failure. The migration route of the severe erosion region of hydraulic spool valve without notches was obtained and the mechanism of local erosion was revealed. An interesting phenomenon of erosion inflection point and face-back flow was found. The exact calculation method of the orifice area under erosion was discussed and put forward. This paper provides a reference for further study on the erosion damage and erosion resistance of hydraulic spool valve without notches.
Keywords Fluid power engineering，hydraulic spool valve without notches，erosion，microtopography，CFD simulation 1. Introduction 1.1 Objective Hydraulic servo valve was widely used in national defense and high-tech industries such as aerospace, navigation, industrial robotics for high-precision closed-loop control in fluid power engineering. As a typical hydraulic power amplifying unit in servo valve, sliding spool valve without notches has an important influence on the performance of hydraulic servo valve and system. Hydraulic spool valve without notches works by the principle of orifice throttle. By relative movement between the spool and body or sleeve to change the orifice, the flowrate and pressure were controlled. As long as the spool has a certain degree of opening, the fluid around the spool will immediately flow through the valve orifice. A four-sided hydraulic spool valve without notches mainly composed of spool and mating body or sleeve with supply port P, return port T, service port A and B was shown in Fig.1a. The valve orifice of hydraulic spool valve without notches is formed by the metering edge of the spool and sleeve as shown in Fig.1b. Corresponding author.Tel:+86 13679493196 E-mail address: [email protected]（Xinqiang Liu）
P
Sleeve
T
Body (Sleeve) Solid particles
Flow Metering edge Spool
A
B
Spool
（a）Hydraulic spool valve without notches
（b）Metering edge
Fig.1. Layout of hydraulic spool valve without notches and metering edge.
The microtopography and quality of metering edge of hydraulic spool valve without notches are crucial for valve performance. Based on the geometric accuracy of the metering edge detection method, two kinds of new examination methods of the valve metering edge were proposed by Wang et al[1]. Solid particles contamination in hydraulic oil often erode the corners of valve components [2]. When high-speed oil with solid particles flow through the orifice, the solid particles heavily impact the valve orifice metering edges repeatedly as if accelerated “cannonball”. This erosion process is irreversible, resulting in degraded control performance of orifice and hydraulic valve. Erosion behavior and influence of solid particles in hydraulic spool valve without notches were the focus in this paper. Firstly, a comprehensive and meticulous surface morphology measurement and analysis was conducted by the automatic zoom 3D surface profilometer on an used spool to find erosion failure microtopography of spool surface. Secondly, the computational fluid dynamic(CFD)simulation of solid-liquid two-phase flow was carried out by FLUENT discrete phase model (DPM).The paper presents the migration route of severe erosion in hydraulic spool valve without notches for the first time and the detailed mechanisms of local erosion wear was analyzed. Finally, based on the calculation and analysis of the pressure distribution near the orifice, the exact calculation formulas of the valve orifice area under erosion were discussed. From the perspective of “Erosion phenomenon-Internal mechanism-Influence”, a thorough and comprehensive study on the erosion of hydraulic spool valve without notches was carried out. This paper provides a useful reference for further study on the erosion damage and erosion resistance of hydraulic spool valve without notches. 1.2 Background The influence of the spool metering corner on the flow characteristics was studied by Wang and Ye [3] using FLUENT simulation and the results show that the metering corner aggravates the non-linearity of flowrate. The correlation between different types of metering edge geometry error and valve performance indicators such as flow characteristics, non-linearity were obtained[4]. They concentrate on the influence of the metering edge geometrical error on the valve external characteristics. In this paper, a comprehensive survey and analysis on the surface topography of the key parts of hydraulic spool valve without notches will be made. The internal mechanism of erosion formation will fully be explored to analyze the erosion behavior and influence of solid particles in hydraulic spool valve without notches.
Sample volume: 10ml
(a) Particle shapes
（c）Polluted spool
ISO:16/14/11
(b) Amount of different diameters(μm)
（d）Jet tube servo valve pre-stage erosion
Fig.2. Solid particles and erosion in hydraulic servo valve [12].
Solid particles are the most common and hazardous contaminant in hydraulic system. According to statistics, hydraulic system failures caused by solid particles accounted for more than 70% of the total failures[5]. Solid particles are substance-type contaminants, usually present in granular form in oil, mainly including sand, welding slag, fiber, dust, rust, packaging, painting, grinding debris, rubber abrasive grains, etc. The shapes of the particles in oil are various, such as polyhedron, spherical, flake and fibrous, and generally irregular shapes as shown in Fig.2a. Particle contaminant is composed of particles with different diameters as shown in Fig.2b. Fluid cleanliness test and analysis details are in MethodsX Part1. The literatures[6-7] suggested that the ratio of hardness of the particles in flowing medium to the hardness of the eroded material is about 1~1.2. A long-term experiment on relief valve under water emulsion was conducted and an erosion groove at the valve seat eventually leading to seal failure was found by British Coal Institute[8]. In order to obtain higher control accuracy, the valve orifice must be sharp and ideal arc in theory. Rounded corner radius generally would not exceed 0.5μm[9]. Solid particles and other pollutants will inevitably be produced in servo system. These particles carried in the working fluid flow in the system at a certain speed and angle causing the servo valve internal material surface problems, especially the pollution-sensitive parts such as valve metering edge erosion and severe equipment failures or even unsafe incidents. With the improvement of high reliability, long life requirement for hydraulic components, hydraulic valve erosion wear problem was gradually concerned. Under erosion, the performance changes of the hydraulic components were tested and the results found that erosion is an important factor in the failures of hydraulic equipment introduced by M.G.Talks et al[8] from the British Coal Research Institute of the Central Laboratory. Gas-solid erosion simulation of the needle type throttle valve was conducted and the easy erosion locations and erosion rate distribution were obtained[10]. Zhang et al [11]found that erosion and wear of water hydraulic planar valves caused by coal particles mainly occurred near the throttle orifice. The jet tube servo valve pre-stage erosion numerical simulation were done and erosion wear rate and theoretical life were obtained
by Yin et al[12] and Chu et al[13]as shown in Fig 2c and Fig.2d. It indicates that many particles accumulate on the spool and part of the pre-stage is missing under erosion. CFD simulation can track the trajectories of solid particles in multiphase flow and accurately predict erosion characteristics[14-16]. N.Barton et al[17]showed that CFD can be used to predict experimental erosion measurements to a high degree of accuracy and the best erosion prediction method is to treat gas, particle, and fluid as separate phase. Wong[18]found that the most erosion in the test section occurs on the forward-facing step. The above researches provide a useful reference for CFD simulation on the valve orifice solid particle erosion. This paper will focus on the local erosion mechanisms and the influence on valve orifice area. 2. Analysis of failure 2.1 Erosion microtopography 2.1.1 Measurement region
Spool
P
T
A
P
B
Sleeve
Fig.3. Sliding spool valve of hydraulic servo valve power stage
MOOG73-218 model double-nozzle flapper electrohydraulic servo valve power stage sliding spool valve composed of spool and sleeve is shown in Fig.3. The spool-sleeve is the key dual pair for high-precision control. The spool valve is simplified as shown in Fig.1. Supply port P is distributed at both ends of the valve spool and return port T is located in the middle. Service port A locates between the left supply port P and return port T. Service port B is between the right supply port P and return port T. When the spool moves toward left, service port B is open, right supply port P is connected to service port B and service port A is connected to return port T. Otherwise, when the spool shifted to the right, service port A is open and supply port P is connected to service port A, service port B is connected to return port T. 1
5 1
2 1
3 1
Metering edge
6 1
4 1
Metering edge
Fig.4. Measurement regions of the spool 1,4—P-A/B metering edge
2,3—A/B-T metering edge
5—P-A/B valve stem 6—A/B-T valve stem
This paper focuses on the surface microtopography of the metering edges of the spool such as P-A/B metering edge, A/B-T metering edge, P-A/B valve stem and A/B-T valve stem as shown in Fig.4. The measurement was carried out by the automatic zoom 3D surface profilometer as shown in Fig.A6 of MethodsX in Part2. By continuous automatic vertical scanning technology and advanced image processing technology, the complete surface of the sample 3D morphology will be obtained such as surface morphology, roughness, surface texture and so on. 2.1.2 Results and Analysis The valve metering edge, the spool shoulder face (face A) and the end surface (face B) morphology were measured by the P-A/B valve metering edge 4 in Fig. 5 and Fig. 6. Positive side
Metering corner
Z Y
O
Face A- Shoulder face
X
Face B-End face Negative side
Fig.5. Morphology of P-A/B metering edge . Face A—Shoulder face
Face B—End face
Face A
Face B
（a）YX-positive
（b）YX-negative
（c）ZX-positive
（d）ZX-negative Fig.6. Metering edge profiles of P-A/B
As show in Table 1，all the corner radiuses tested of edge 4 are far beyond 0.5μm[7] and are
unequal. Both the spool shoulder face and end face near the metering corner are uneven. Table 1 Corner radius of P-A/B metering edge. Corner radius(μm)
Edge4 Plane
Positive side
Negative side
YX
22.6214
46.9320
ZX
15.2103
16.2802
Metering corner
Z Face C Y T O
X Face D
Fig.7. Morphology of A/B-T metering edge. Face C—Shoulder face
Face D—End face
Face C
Face D
（a）YX-positive
（c）ZX-positive
（b）YX-negative
（d）ZX-negative Fig.8. Metering edge profiles of A/B-T Table 2 Corner radius of A/B-T orifice edge. Edge3
Corner radius(μm)
Plane
Positive side
Negative side
YX
12.1394
20.5407
ZX
26.2526
15.7244
The metering edge and the spool shoulder and the end surface morphology were measured by the A/B–T valve orifice edge 3 in Fig.7 and Fig. 8.
Flow direction Port P
Port A/B
Sa2=763.0830
Sa1=283.8021
Sa3=549.0287
Fig.9. Morphology of P-A/B valve stem
Flow direction Port T Sa4=71.9040
Port A/B Sa6=207.0900 Sa5=658.7854 Fig.10. Morphology of A/B –T valve stem
As show in Table 2, all the corner radiuses tested of edge 3 are far beyond 0.5μm and are unequal. Both the spool shoulder face and end face near the metering corner are uneven. In Fig.9 and Fig.10, valve stem surface 5 and 6 area does exist obvious erosion and erosion region surface roughness was significantly higher than the adjacent regions. The surface topography may be related to the flow of the valve orifice and details are in part2.2.2. 2.2 Numerical calculation 2.2.1 CFD model 2.2.1.1Calculation model Port A/B
3
Port P/T 6
5
5
Orifice
1
2
y x o
12 17
（a）Geometry
（b）Orifice mesh Fig.11. Calculation model
The flow field of hydraulic spool valve without notches is symmetrical with respect to the spool axis as shown in Fig.1a. In order to reduce the calculation amount, the uniform radial windows on the sleeve are simplified to an annular chamber [19-21]. As shown in Fig.11a, a two-dimensional hydraulic spool valve without notches CFD model axisymmetric geometry was built (unit: mm).
The left chamber is connect to the service port A/B of actuator, the right chamber is connect to the supply port P or return port T. Due to small size , the strong turbulent fluctuation and great pressure gradient, the valve orifice mesh is specially refined as shown in Fig.11b. 2.2.1.2 Calculation conditions The fluid dynamics software FLUENT was used to calculate the erosion of the wall exposed to flow field in the hydraulic spool valve without notches. With Euler-Lagrange method, the high-speed flow of oil was regarded as a continuous phase and the continuous phase flow simulation was done under Eulerian coordinate system. Solid particles were regarded as a discrete phase (discrete phase model (DPM))and the movement of solid particles trajectory were calculated[17]. In the Eulerian-Lagrangian simulation of the motion of discrete phase particles, the effect of particle volume fraction on the continuous phase and the interaction between particles and particles are not considered. Eulerian-Lagrangian simulation is applicable to multiphase flow when the volume fraction of discrete phase is less than10%~12%. The solid particle volume fraction of hydraulic oil in is much less than 10%. Eulerian-Lagrangian simulation is available for hydraulic spool valve without notches erosion calculation. In order to analyze the force of the solid particles, the equation of particle motion was established. To obtain the motion trajectory of discrete phase particles, the differential equation in Lagrange coordinate system was integrated as shown in equation (1).
d up dt
Fd (u up )
g x ( P )
P
Fx …
（1）
Where u is the liquid velocity (unit: m/s), up is the solid particle phase velocity (unit: m/s), ρp is the solid particle density(unit: kg/m3), and Fd（u-up） is the drag force of per unit mass particle in the x direction(unit: N), gx（ρp-ρ）/ρp for the mass of the unit mass in the x direction of the gravity (unit: N), Fx is additional force of per unit mass particles in the x direction, including the virtual mass force, Brownian force et al. The erosion wear model proposed by Edwards et al[22-24] by the grit and carbon steel and aluminum surface erosion test was used to calculate the internal erosion wear rate as shown in equation (2).
mPC (d P ) f ( ) b ( ) ……… Af n 1 N
Re
（2）
Where Re is the erosion rate (unit: kg/（m2∙s m/s)）, n is the number of particles, mp is the particle mass flow (unit: kg/s) , dp is the diameter of the particle(unit: m) , C(dp) is function of particle diameter, α is the erosion angle between the particle trajectory and the wall, f(α) is the erosion Table 3
Table 4
Erosion model parameters Parameter Flow Rate
mp
Particle diameter
dp
Diameter function C(dp)
Boundary conditions Valve
Unit
10-6
kg/s
5
μm
1.8×10-9
Erosion angle α
30
Erosion angle function f(α)
1
Relative velocity b(v)
2
°
Parameter
Valve
Unit
Pressure inlet (P→A/B)
21
MPa
Pressure outlet (P→A/B)
18
MPa
Pressure inlet (A/B→T)
18
MPa
Pressure outlet (A/B→T)
0
MPa
Oil density
889
kg/m3
Spool/Sleeve density
7850
kg/m3
Particle density
1500
kg/m3
angle function, v is the relative velocity of the particle, b(v) is the relative velocity of the particle, Af is the unit area of the particle erosion wall, as shown in Table 3. Solid particle
v
Wall Fig.12. Particles micro-cutting erosion model
This model (equation 2) is an erosion model based on the micro-cutting theory of rigid particle impact plastic materials proposed by Finnie [25]. The model is the first one to quantify the relationship between erosion rate and angle of attack under low attack angle. The theory is that abrasive particles such as a miniature tool, which cut off the material as it strikes the target surface and produce wear and tear as shown in Fig.12. 2.2.2 Results and analysis 2.2.2.1 Erosion wear distribution Inter flow passage
Sleeve edge Spool edge
End face Stem face x=0.01
x=0.07
x=0.5
x=0.05
x=0.03
x=0.09
x=0.1
x=1
Fig.13. P→A / B Erosion wear distribution with different openings ( x in mm)
M.S. Wallace et al [26] pointed out that CFD techniques hold the promise of delivering a design tool for the prediction of erosion conditions in engineering components and a typical requirement is to identify the potential location for erosion. Geometry changes have important influence to the prediction of erosion wear for that geometry changes lead to flow field changes. Valve opening x also can cause flow field changes especially for the movement of solid particles. With different valve openings, erosion wear distributions were investigated. Boundary conditions settings are in Table 4. As shown in Fig.13, with the increase opening of spool valve, when the flow direction of fluid is P to A/B, the erosion distribution is also constantly changing. The severe erosion distribution mainly located in inside of the inlet flow passage, the sleeve edge, the spool edge, end face and stem face. With the increase of opening, the severe erosion region gradually turns to the downstream of valve orifice. The erosion locations of the spool edge, end face, stem face and other regions are completely consistent with the measurement results of the microtopography in Fig.5, Fig.7, Fig.9, Fig.10 and literature [9]. Literature [9] indicates DPM erosions occur on the sharp edges of spool and sleeve. The accuracy of the erosion numerical calculation in the hydraulic spool valve without notches was verified.
x=0.01
x=0.03
x=0.05
x=0.07
x=0.09
x=0.1
α
x=0.5
x=1
Fig.14. P→A/B Velocity vector with different openings ( x in mm)
As shown in Fig.14, with the increase of opening, the flow velocity vector (arrows) distribution of the valve orifice region presents a great change. When the opening is extremely small (x=0.01), the flow area is quite small and approximate to a narrow gap. High-intensity vortex formed adjacent to the orifice, especially in the upstream region of the orifice. Due to strong vortex effect, the solid particles driven by a large centrifugal force repeatedly hit the inside of the passage, resulting in local erosion of the inter flow passage. With the increase of opening (x=0.03~0.1), the jet angle α of the main stream of valve orifice gradually decreases and the vortex located in upstream of the valve orifice gradually disappears, but the vortex located in downstream still exists. The severe erosion distributions mainly located in the spool end face, sleeve edge and spool edge downstream of the orifice. Unluckily, hydraulic servo valve just works near the zero position. The erosion of the spool edge and sleeve edge heavily threat the servo valve performance. With the further increase of the opening (x=0.5~1), a small vortex is formed on both sides of the main stream downstream of the valve orifice. The main stream directly impacts the valve stem and solid particles in the oil cut the valve stem surface at high speed. The erosion region is mainly concentrated in the valve stem downstream of the valve orifice at this opening rage. From x=0.01 to x=1, the main flow is initially attached to the wall flow, then gradually away from the spool end face and finally jet to the stem surface directly.
Port P
C
A B
Port A/B
D
E Fig.15. Severe erosion region migration route with increasing opening when P→A / B
40
AB
35 30 25 20 15
AB
10 5 0 -5
12
13
14
15
16
Axial position (mm) Fig.16. Erosion wear rate of location AB
17
Erosion wear rate（10-9）
Erosion wear rate（10-9）
As shown in Fig.15, when the flow direction of the oil is P→A/B, the severe erosion region shows the migration route of A→B→D→C→E as the valve opening increases (x=0.01~1).But the spool edge B always belongs to the more severe erosion region, where A is spool edge upstream region, B is spool edge region, C is sleeve edge region, D is spool end face, E is valve stem region. 100
C¦
80 60
C
40 20 0 4 .0
4 .2
4 .4
4 .6
4 .8
5 .0
Radial position (mm) Fig.17. Erosion wear rate of location C
8 6 4
D
2 0 2 .0
2 .5
3 .0
3 .5
4 .0
Erosion wear rate（10-12）
Erosion wear rate（10-9）
D
E¦
500 400 300
E
200 100
Radial position (mm)
0 0
2
4
6
8
10
12
Axial position (mm) Fig.19. Erosion wear rate of location E
Fig.18. Erosion wear rate of location D
Erosion wear rate changes along the wall ( opening x=0.05mm, the oil flow P→A/B) are showed in Fig.16~ Fig.19 under x-o-y coordinates in Fig.11a. From Fig.16, it can be clearly seen that the erosion wear rate at the upstream A and B of the spool reaches the maximum 3.5×10-8 near the spool metering edge and decreases almostly to 0 with the increase of axial position. As indicated in Fig.17, the erosion wear rate near the sleeve metering edge reaches the maximum 9×10-8 and then decreases gradually. The distribution of erosion rates at location A,B and C are very similar. The erosion wear rate of the spool end face D reaches the maximum 8×10-9 near the spool metering edge and decreases and increase alternately as shown in Figure 18. There is a large erosion wear rate near the spool end surface near the valve stem E as shown in Fig.19. In addition, the distribution of erosion rates at location D and E are also very similar and present peak-valley distribution. Severe erosion do occur on the metering edge of spool and sleeve which is completely consistent with literature[9] and microtopography measurement in part 2.1.
x=0.001
x=0.01
x=0.05
x=0.1
x=0.5
x=1
Fig. 20. A / B→T Erosion region distribution with different opening ( x in mm)
x=0.001
x=0.01
x=0.05
β x=0.5
x=0.1
x=1
Fig.21. A/B→T Velocity vector with different openings ( x in mm)
As shown in Fig.20 and Fig.21, when A/B→T and the valve opening is extremely small (x=0.001~0.01), the jet angle β of the main stream is close to 90°. One high-strength vortex develops respectively in the valve chamber upstream and downstream of the orifice. The solid particles driven by centrifugal force erode the valve stem and the inside of the passage near the inlet. As the orifice opening increases (x=0.05~0.1), the upstream vortex disappears and the downstream vortex below the main stream still exists. The jet angle β of the main stream becomes smaller and the erosion region mainly concentrates on the incoming flow face and the edge. With the further increase of the opening (x=0.5~1), the jet angle β of the main stream gradually decreases and the erosion region concentrates on the spool end face and the outlet of the valve body. Port A/B
Port T
J
H F
G
I
Fig. 22. Severe erosion region migration routes with increasing opening when A/B→T
As shown in Fig.22, when flow direction is A/B to T, as the opening of the valve increases, the severe region migration route change by F→G→H and G→I→J. At the very slight opening stage, there is a strong vortex respectively upstream and downstream of the valve orifice. Particles did not pass through the orifice but plunged into the upstream vortex. Not only stem, valve orifice but also valve body are eroded when A / B→T. However, the metering edges of the valve orifice always keeps in serious erosion. The erosion region gradually migrated to the downstream of the
orifice with the increase of opening when A/B to T. 2.2.2.2 Local erosion mechanism (P→A/B as an example)
Port P Sleeve
Solid particles
A
B
Spool
Port A/B （a）Location A
C
（c）Location C
（b）Location B
D
（d）Location D
E
（e）Location E
Fig.23. Local erosion mechanism schematic diagram
Different regions have different flow states, and therefore, the local erosion mechanism is different. The centrifugal action of the vortex and the main stream washing are considered as the main erosion power. 1. Location A -upstream of the spool shoulder face As shown in Fig.23a, when the opening is extremely small(x=0~0.01), a strong vortex forms in the valve chamber upstream of the valve orifice due to the tiny flow area. The solid particles driven by the centrifugal force in the oil repeatedly hit and cut the upstream region of spool shoulder face. 2. Location B-the spool metering corner As shown in Fig.23b, location B ,where the sharp corner of the metering side is designed to 90°, is the geometry singularity of flow field. In the vicinity of the edge of the valve orifice, the high-speed fluid carrying solid particles must keep a smooth flow at location B to maintain the flow inertia. Adjacent to the valve orifice, the flow area is sharply reduced and particles gathered. In this process a large numbers of solid particles impact and eroded the corner. This is fatal to the performance of the spool and servo valve. 3. Location C- Sleeve edge and metering corner As shown in Fig.23c, the valve sleeve edge and metering corner C is in the upper part of the main stream of the orifice and also belongs to the singularity geometry of the flow field. A vortex is easy to form around the corner. Solid particles driven by the vortex centrifugal force eroded the sleeve edge. In addition, valve orifice flow area reduced suddenly and the speed of mainstream increase drastically. The carrying particles with high kinetic energy eroded the metering corner. It
can be considered that the erosion at the sleeve edge and metering corner C is the combined result of the washing of the main stream of the valve orifice and particle erosion under the eccentric centrifugal force. This is also fatal to the performance of the servo valve. 4. Location D-Spool end face As shown in Fig.23d, location D is in the downstream of the orifice main stream. There is a strong wall flow, that’ to say the solid particles move along the wall. Solid particles with sharp edges and suitable angle cut the spool end face. 5. Location E-Valve stem face As shown in Fig. 23e, as the increase of the opening(x=0.5~1)location E directly faces the main stream of the valve orifice. The high speed solid particles flow impinge directly on the stem surface. The particle bounces twice to rebound and acts on the valve stem surface repeatedly resulting in erosion of the stem surface. The unwanted particles in the oil are the dominant factor in the erosion damage of the valve port when the geometric characteristics of the hydraulic spool valve are set for function. 2.2.2.3 Inflection point effect and Face-back flow phenomenon
Face flow region Inflection point 2
Inflection point 1
Back flow region （a）Erosion distribution
（b）Particle trajectory
Fig. 24. Inflection point effect and Face-back flow phenomenon
As shown in Fig. 24a, there are several severe regions of erosion in hydraulic spool valve without notches near the orifice. They are the spool metering edge (Inflection point 1), the spool shoulder face, the spool end face, the sleeve metering edge (Inflection point 2), the upstream area near the sleeve metering edge, the downstream area near the sleeve metering edge. The upstream area near the spool and the sleeve metering edge facing the incoming flow are known as the “Face-flow region”, the downstream area near the edge of the spool and the sleeve metering edge are referred to as “Back-flow region”. Erosion distribution in Fig.24a shows that erosion wear of the face-flow region is more severe than that of the back-flow region, which is called the “Face-back flow phenomenon”. The face-flow region is exposed to particles having a velocity comparable to that of the main stream. The erosion valve inflection point severe than the other region known as the “Inflection point effect”. With solid particles in the flow around the inflection point of the spool, particle trajectory should be smooth due to inertia is shown in Fig.24b. By the particles trajectory, it can be clearly seen that contacts between the particles and the valve wall really exist. There is a large differential pressure and small flow area near the valve orifice, the metering edge is slowly to be washed by the oil flow. Especially under micro opening and serious pollution, the particles move faster and
impact frequently, resulting in more severe erosion as shown in Fig.24b. “Inflection point effect” and “Face-back flow phenomenon” is consistent with the erosion in a pipe contraction [27]. 3. Discussion According to the“Inflection point effect”and “Face-back flow phenomenon” ，inflection points of the spool and sleeve near the valve orifice are easy to be eroded and worn. As a result, the spool valve null region characteristics, such as null leakage and overlap, which have an important influence on system operation and stability, will be degraded [18]. The essence of the hydraulic valve is the orifice and the orifice area which determines the control characteristics of the valve. The valve orifice is composed of metering edges of the spool and sleeve. Usually we just calculate the orifice area under the ideal contour. Therefore, it is very important to ascertain and calculate the orifice area after erosion to explore the sliding spool performance under erosion. 3.1 Valve orifice position Outlet Sleeve Spool Inlet （a）Square-Square
（b）Corner-Square Fig. 25.
（c）Square-Corner
（d）Corner-Corner
Models of eroded valve orifice
Based on CFD calculation of particle erosion, the“Inflection point phenomenon”of the spool metering edge, sleeve metering edge and the microtopography show that inflection point is the most vulnerable to erosion and the sharp edge of spool and sleeve turn into rounded corners. Thus, the following models of eroded valve orifice were established:Model1 Square-Square(Fig.25a),Model2Corner-Square(Fig.25b),model3Square-Corner(Fig.25c),model4 Corner-Corner (Fig.25d), Model 1 is for reference. Taking a two-dimensional hydraulic spool valve without notches with rounded corner radius of Unite: Pa
（a）Square-Square
（b）Corner-Square
（c）Square-Corner
（d）Corner-Corner
Fig.26. Pressure distributions of the orifice
0.25 mm as a model, flow field pressure distributions were obtained in Fig.26. For the sharp decrease of flow area, there is dense pressure gradient and a large pressure drop around the orifice. The valve orifice locats at the black line in Fig.26. Equivalent flow area is circular frustum side area formed by the black line as the bus and rotats around the spool axis as shown in Fig.27. 3.2 Eroded valve orifice area 3.2.1 Model2 Corner-Square
Round table up radius Round table bus
A H B
Flow Area
C x D H
A
Round table down radius
B F
I
G
C
D Fig. 27. Calculate diagram of Model 2
Set the spool-sleeve gap as h, spool diameter D, spool corner r, overlap x0 = 0, valve opening x, the origin of the coordinate O. Circular frustum bus BC: BC AC AB AC r
r 2 (r x)2 r ……………………………………
（3）
Circular frustum up radius CG：
D …………………………… 2 Circular frustum down radius BI:
（4）
CG=
BI (
D h r) r 2
r r 2 (r x)2
………………………………………
（5）
Circular frustum side area S: S CG BI BC (D h r
r2 r2 (r x)2
)( r2 (r x)2 r)
……
The orifice area is S (x) = f (x, D, h, r) where D=7.5mm, h=0.005mm, r=0.01mm. S (x) -x curve set h = 0 ,When x = -r, S(x) = 0.
（6）
15
Area(mm2)
10
Area(mm2)
1.5
A2(x) B2(x)
5
1
0.5
A2(x) B2(x)
0
0
0.1
0.2 0.3 Opening x (mm) (a) x=0~0.5 Fig.28.
0.4
0.5 0 0
0.01
0.02 0.03 0.04 Opening x (mm) (b) x=0~0.05
0.05
Erosive valve orifice area of model 2
A 2(x) is the valve area after erosion. B2 (x) is the traditional calculation formula B 2(x) = πd • x. 3.2.2 Model 3 Square -Corner
y A B O
G
B C
C
D E
D E
x
F Fig. 29.
Calculate diagram of Model 3
1.5
Area(mm2)
Area(mm2)
15
10
1
A3(x)
5
x
A3(x)
0.5
B3(x)
B3(x)
0 0
0.1 0.2 0.3 Opening x (mm) 1 (a) x=0~0.5 2 3
0.4
0.5
4
5
0
0
0.01
0.02 0.03 0.04 Opening x (mm)
Fig. 30. Erosive valve orifice area of model 3
Circular frustum Side area S:
(b) x=0~0.05
0.05
r h S D h r r (r h )2 (x r)2 (r h)2 (r x)2 r
……
（7）
Valve orifice area S (x) = f (x, D, h, r) where D, h, r are constants. D=7.5mm,h=0.005mm,r=0.01mm ,Set h = 0, then when x = -r, S (x) = 0 Note: A3 (x) is the valve area after erosion; B3(x) is the traditional calculation formula B 3(x)=πd•x 3.2.3 Model 4 Corner-Corner
A A H
K A
B C
K B
D G
O
F
E
X
C D O
I
X
M Fig. 31.
Calculate diagram of Model 4
1.5
10
1
Area(mm2)
15
Area(mm2)
F E
A4(x) B4(x)
5
A4(x)
0.5 B4(x)
0
0
0.2 0.4 Opening x (mm) (a) x=0~0.5
0.6
0
0
0.02 0.04 Opening x (mm) (b) x=0~0.05
0.06
Fig.32. Erosive valve orifice area of Model 4
Circular frustum Side area S: S (CJ BM ) BC
(r2 r1 )(r1 r2 h)
r1 r1
r2 h r1 r2 x 2
2
……………………………………（8） D h r1 r2
2 2 r2 h r1 r2 x r1 r2
Model 4 port area S (x) = f (x, D, h, r1, r2) where D, h, r1, r2 are constants. When h = 0 and r1 = r2, S(x) = 0 when x = -2r. Note: A4 (x) is the port area after erosion, B4 (x) is the traditional calculation formula
D=7.5mm,h=0.005mm,r1=0.01mm, r2=0.01mm. Valve orifice area characteristics of Model2, Model3,Model4 as shown in Fig. 28, Fig. 30, Fig. 32: (1)Within the opening range , the orifice area of the traditional calculation formula always smaller than that of the new calculation formula due to not consider the valve orifice erosion especially near the null position. (2) The new calculation formula at the null position x=0 calculates that the valve orifice area is not zero, which is consistent with the actual situation namely null leakage. (3)The valve orifice area after erosion has strong nonlinearity namely the “Bending phenomenon” near the null position, resulting in the control linearity deteriorated . 3.2.4 Differential area
Model 2 Model 3 Model 4
Differential area(mm2)
0.30 0.25 0.20 0.15 0.10
A4(x)-B4(x)
0.05
A3(x)-B3(x) A2(x)-B2(x)
0.00
0.00
0.01
0.02
0.03
0.04
0.05
Opening x (mm) Fig. 33. Opening-Differential area
As shown in Figure 33, the differential orifice area between Model 2, Model 3, and Model4 and conventional formula are calculated by selecting the valve opening x1 = 0, x2= 0.01, x3 = 0.03 and x4 = 0.05. (1) With the increase of valve opening, the differential orifice area between the new formula and the traditional formula gradually decreases and the largest difference locates at null position x=0. (2) The area difference of Model 3 is larger than that of Model 2, which shows that the edge erosion of the spool is more serious than the sleeve. (3) The area difference between Model 4 and Model 3 is larger than that of Model 2, which indicates that the influence of sleeve edge and spool edge erosion on the valve orifice area is obvious. According to the CFD calculation, both the metering edge of spool and sleeve are the most susceptible to erosion damage. Calculation formula of Model 4 is closest to actual working condition.
4. Conclusions Obviously erosion corner appearance at the metering edge:There are metering edge corners and the average radius of the valve orifice edge is 20.5818μm, which far beyond the servo valve spool
edge requirement. The valve orifice edge can easily cause valve flow control nonlinearity, which is consistent with numerical calculation and related experimental results. Severe erosion region migration path: When the oil flow direction is P→A/B, as the valve orifice opening increases migration path: spool shoulder face→ spool metering edge →spool end face →sleeve corner→ valve stem, but the metering edge of spool and sleeve are always in the more severe erosion region. Local erosion mechanism: Driven by the centrifugal force, the solid particles cut the upstream region of the valve orifice. A large numbers of solid particles impact and erode the corner to keep smooth flow. There is a strong wall flow leading to the spool end face erosion. The high speed solid particles flow impinge directly on the stem surface. Erosion inflection point effect and Face-backward flow phenomenon: “Inflection point effect”solid particles in the flow around the inflection point of the spool due to inertia and particle trajectory. “Face flow phenomenon”-the erosion area of the face-flow area is more severe than the back-flow area. Accurate calculation of erosive valve orifice area:The erosive valve orifice area curve in the small degree of openness has a curvature of the phenomenon that has a strong nonlinear, that is, the flow control of the linear degradation. The calculated results are in good agreement with related experiments. The predominant cause in the erosion damage of the valve: The unwanted particles in the oil are the dominant factor in the erosion damage of the valve port when the geometric characteristics of the hydraulic spool valve are set for function. Therefore, it is possible to reduce the erosion of the valve orifice by reducing the particles or change particles trajectory, which needs further study.
Acknowledgements This work is supported by the National China(51575254),(51565027)and (51465033).
Natural
Science
Foundation
of
References [1] Wang GL, Tao CD, Shao DX, et al. Research on geometric accuracy of servo valve orifice. J Journal of Harbin Institute of Technology 1999 ;05: 120-122. [2] Bent H.Nystad, Giulio Gola, John E.Hulsund,et al. Technical condition assessment and remaining useful life estimation of choke valves subject to erosion. Annual Conference of the Prognostics and Health Management Society. Oregon:Portlang.2010. [3] Wang DW and Ye ZM. Three-dimensional model simulation of the effect of the spool valve flange fillet on the flow characteristics. J Machine Tool & Hydraulics. 2013;41 (12): 6-9. [4] Zhang L. Valve edge geometry error on the performance of the slide valve simulation D Harbin Institute of Technology, 2007. [5] M.Singh· G.S.Lathkar· S.K.Basu. Failure prevention of hydraulic system based on oil contamination J Journal of The Institution of Engineers(India),2012;93(3):269-274. [6] Dong G, Zhang JY.
Research progress on erosion wear of solid particles[J]. Journal of Materials Science and
Engineering. 2003.21(2):307-312. [7] Shipway P H , Hutchings I M . The role of particle properties in the erosion of brittle materials[J]. Wear, 1996, 193(1):105-113. [8] M.G.Talks, A.R.M.Eedy, Zhu HW. Erosion and corrosion of mining hydraulic equipment J Mail mining
machinery, 1983;04: 44-46. [9] Zhang K., Yao J, Jiang T. Degradation assessment and life prediction of electro-hydraulic servo valve under erosion J wear. Eng. Fail. Anal., 2014;36:284-300. [10] Qian DL. Panyu 35-2 subsea gas pipeline erosion law. D Southwest Petroleum University, 2015. [11] Zhang H, Xiong SB, Liang YW, et al. Erosion wear characteristics analysis and structure discussion of hydraulic valves. J Journal of China Coal Society, 2008;02: 214-217 [12] Yan YB, Fu JH, Jin YL. Numerical simulation of pre-level erosion wear of jet tube servo valve. J Journal of Zhejiang University(Engineering Science), 2015;49(12): 2252-2260. [13] Chu YB, Yuan CH, Zhang Y. Erosion wear characteristics of jet pipe servo valve .J Acta Mechanica Sinica, 2015;36 (05): 1548-1555. [14]G.Haider,H.Arabnejad, S.A.Shiraz, et al.
A mechanistic model for stochastic rebound of solid particles with
application to erosion predictions. J Wear 376-377(2017)615-624. [15] Zhang JX，Kang J, Fan JC, et al.
Research on erosion wear of high-pressure pipes during hydraulic
fracturing slurry flow. J Journal of Loss Prevention in the Process Industries 2016; 43:438-448. [16] Peyman Zahedi, Jun Zhang, Hadi Arabnejad,et al. CFD simulation of multiphase flows and erosion preditions under annular flow and low liquid loading conditions. Wear 376-377(2017)1260-1270. [17] N.Barton, M.Lewis, P.Emmerson, CFD erosion prediction in gas-liquid-sand flow, Proceedings of SPE International Oilfield Corrosion Conference and Exhibition, Aberdeen, Scotland,UK,2016. [18] Chong Y.Wong, Christopher Solnordal, Anthony Swallow, et al. Experimental and computational modeling of solid particle erosion in a pipe annular cavity. J Wear 303(2013)109-129. [19] Yin YB, Yuan JY, Guo SG. Numerrical study of solid particle erosion in hydraulic spool valve. Wear 392-393(2017)174-189. [20] R.Yang, Hydraulic spool valve metering notch characterization using CFD. Procesdings of the ASME International Mechanical Engineering Congress and Exposition. American Society of Mechanical Engineers,11-17,2003. [21] R.Amirante, G.del Vescovo.A.Lippois. Flow forces analysis of an open center hydraulic directional control valve sliding spool,Energy Convers.Manag.47(1)(2006)114-131. [22] EDWARDS J k, MCLAURY B S,SHIRAZI S A. Evaluation of alternative pipe bend fittings in erosion service[C]//Proceedings of the 2000 ASME Fluid Engineering Division Summer Meeting, New York: American Society of Mechanical Engineers ,2000:956-966. [23] Edwards JK. Development, Validation and application of a three-dimensional, CFD-based erosion prediction procedure[dissertation].Tulsa:The University of Tulsa:2000. [24] Zhang YL. Application and improvement of computational fluid dynamics(CFD)in solid particle erosion modeling [dissertation].Tulsa: The University of Tulsa:2006. [25] Finnie,I.,1972.Some observations on the erosion of ductile metals. Wear 19(1),81-90. [26] M.S. Wallace, W.M. Dempster, T. Scanlon, et al. Prediction of impact erosion in valve geometries. J Wear,256(9)(2004), 927-936 . [27] B.S. McLaury,S.A. Shirazi, J.R. Shadley,E.F. Rybicki,Modeling erosion in chokes,ASME,Fluids Engineering Division(Publication)FED,vol.236,No.1,1996,pp.773-781.
Highlights 1. The measurement and analysis of the surface micro-morphology of the eroded spool. 2. The migration route of the severe erosion region of hydraulic spool valve without notches with the change of the valve opening and the mechanism of local erosion. 3. The phenomenon of erosion inflection point and face-back flow . 4. The exact calculation method of the orifice area after erosion .
Conflict of interest statement We declare that we have no financial and personal relationships with other people or organizations that can inappropriately influence our work, there is no professional or other personal interest of any nature or kind in any product, service and/or company that could be construed as influencing the position presented in, or the review of, the manuscript entitled, “Erosion behavior and influence of solid particles in hydraulic spool valve without notches” .
S1350-6307(18)30982-8 https://doi.org/10.1016/j.engfailanal.2019.104262 EFA 104262
To appear in:
Engineering Failure Analysis
Received Date: Revised Date: Accepted Date:
9 August 2018 26 September 2019 4 November 2019
Please cite this article as: Liu, X., Ji, H., Min, W., Zheng, Z., Wang, J., Erosion behavior and influence of solid particles in hydraulic spool valve without notches, Engineering Failure Analysis (2019), doi: https://doi.org/ 10.1016/j.engfailanal.2019.104262
This is a PDF file of an article that has undergone enhancements after acceptance, such as the addition of a cover page and metadata, and formatting for readability, but it is not yet the definitive version of record. This version will undergo additional copyediting, typesetting and review before it is published in its final form, but we are providing this version to give early visibility of the article. Please note that, during the production process, errors may be discovered which could affect the content, and all legal disclaimers that apply to the journal pertain.
© 2019 Published by Elsevier Ltd.
Erosion behavior and influence of solid particles in hydraulic spool valve without notches Xinqiang Liu1,2,*, Hong Ji1,2, Wei Min1,2, Zhi Zheng1, Jinlin Wang3 1Energy
and Power Engineering College, Lanzhou University of Technology, Lanzhou, China Laboratory of Fluid Machinery and System, Gansu Province 3School of Aerospace Engineering, Tsinghua University, Beijing, China 2Key
Abstract Hydraulic spool valve without notches is used as a kind of important amplification component in hydraulic servo valve. Its static and dynamic properties have a significant impact on the performance of servo valve and hydraulic system. Under solid particles erosion in oil, the metering edges of spool valve were usually eroded and worn. This process was irreversible and induced serious control performance degradation of orifice and valve. In this paper, the erosive behavior and influence of solid particles in hydraulic spool valve without notches were investigated. By the surface microtopography measurement of the spool, erosion corners failure were present. The CFD simulation of solid-liquid two-phase flow was carried out by discrete phase model (DPM)to analyze the erosion failure. The migration route of the severe erosion region of hydraulic spool valve without notches was obtained and the mechanism of local erosion was revealed. An interesting phenomenon of erosion inflection point and face-back flow was found. The exact calculation method of the orifice area under erosion was discussed and put forward. This paper provides a reference for further study on the erosion damage and erosion resistance of hydraulic spool valve without notches.
Keywords Fluid power engineering，hydraulic spool valve without notches，erosion，microtopography，CFD simulation 1. Introduction 1.1 Objective Hydraulic servo valve was widely used in national defense and high-tech industries such as aerospace, navigation, industrial robotics for high-precision closed-loop control in fluid power engineering. As a typical hydraulic power amplifying unit in servo valve, sliding spool valve without notches has an important influence on the performance of hydraulic servo valve and system. Hydraulic spool valve without notches works by the principle of orifice throttle. By relative movement between the spool and body or sleeve to change the orifice, the flowrate and pressure were controlled. As long as the spool has a certain degree of opening, the fluid around the spool will immediately flow through the valve orifice. A four-sided hydraulic spool valve without notches mainly composed of spool and mating body or sleeve with supply port P, return port T, service port A and B was shown in Fig.1a. The valve orifice of hydraulic spool valve without notches is formed by the metering edge of the spool and sleeve as shown in Fig.1b. Corresponding author.Tel:+86 13679493196 E-mail address: [email protected]（Xinqiang Liu）
P
Sleeve
T
Body (Sleeve) Solid particles
Flow Metering edge Spool
A
B
Spool
（a）Hydraulic spool valve without notches
（b）Metering edge
Fig.1. Layout of hydraulic spool valve without notches and metering edge.
The microtopography and quality of metering edge of hydraulic spool valve without notches are crucial for valve performance. Based on the geometric accuracy of the metering edge detection method, two kinds of new examination methods of the valve metering edge were proposed by Wang et al[1]. Solid particles contamination in hydraulic oil often erode the corners of valve components [2]. When high-speed oil with solid particles flow through the orifice, the solid particles heavily impact the valve orifice metering edges repeatedly as if accelerated “cannonball”. This erosion process is irreversible, resulting in degraded control performance of orifice and hydraulic valve. Erosion behavior and influence of solid particles in hydraulic spool valve without notches were the focus in this paper. Firstly, a comprehensive and meticulous surface morphology measurement and analysis was conducted by the automatic zoom 3D surface profilometer on an used spool to find erosion failure microtopography of spool surface. Secondly, the computational fluid dynamic(CFD)simulation of solid-liquid two-phase flow was carried out by FLUENT discrete phase model (DPM).The paper presents the migration route of severe erosion in hydraulic spool valve without notches for the first time and the detailed mechanisms of local erosion wear was analyzed. Finally, based on the calculation and analysis of the pressure distribution near the orifice, the exact calculation formulas of the valve orifice area under erosion were discussed. From the perspective of “Erosion phenomenon-Internal mechanism-Influence”, a thorough and comprehensive study on the erosion of hydraulic spool valve without notches was carried out. This paper provides a useful reference for further study on the erosion damage and erosion resistance of hydraulic spool valve without notches. 1.2 Background The influence of the spool metering corner on the flow characteristics was studied by Wang and Ye [3] using FLUENT simulation and the results show that the metering corner aggravates the non-linearity of flowrate. The correlation between different types of metering edge geometry error and valve performance indicators such as flow characteristics, non-linearity were obtained[4]. They concentrate on the influence of the metering edge geometrical error on the valve external characteristics. In this paper, a comprehensive survey and analysis on the surface topography of the key parts of hydraulic spool valve without notches will be made. The internal mechanism of erosion formation will fully be explored to analyze the erosion behavior and influence of solid particles in hydraulic spool valve without notches.
Sample volume: 10ml
(a) Particle shapes
（c）Polluted spool
ISO:16/14/11
(b) Amount of different diameters(μm)
（d）Jet tube servo valve pre-stage erosion
Fig.2. Solid particles and erosion in hydraulic servo valve [12].
Solid particles are the most common and hazardous contaminant in hydraulic system. According to statistics, hydraulic system failures caused by solid particles accounted for more than 70% of the total failures[5]. Solid particles are substance-type contaminants, usually present in granular form in oil, mainly including sand, welding slag, fiber, dust, rust, packaging, painting, grinding debris, rubber abrasive grains, etc. The shapes of the particles in oil are various, such as polyhedron, spherical, flake and fibrous, and generally irregular shapes as shown in Fig.2a. Particle contaminant is composed of particles with different diameters as shown in Fig.2b. Fluid cleanliness test and analysis details are in MethodsX Part1. The literatures[6-7] suggested that the ratio of hardness of the particles in flowing medium to the hardness of the eroded material is about 1~1.2. A long-term experiment on relief valve under water emulsion was conducted and an erosion groove at the valve seat eventually leading to seal failure was found by British Coal Institute[8]. In order to obtain higher control accuracy, the valve orifice must be sharp and ideal arc in theory. Rounded corner radius generally would not exceed 0.5μm[9]. Solid particles and other pollutants will inevitably be produced in servo system. These particles carried in the working fluid flow in the system at a certain speed and angle causing the servo valve internal material surface problems, especially the pollution-sensitive parts such as valve metering edge erosion and severe equipment failures or even unsafe incidents. With the improvement of high reliability, long life requirement for hydraulic components, hydraulic valve erosion wear problem was gradually concerned. Under erosion, the performance changes of the hydraulic components were tested and the results found that erosion is an important factor in the failures of hydraulic equipment introduced by M.G.Talks et al[8] from the British Coal Research Institute of the Central Laboratory. Gas-solid erosion simulation of the needle type throttle valve was conducted and the easy erosion locations and erosion rate distribution were obtained[10]. Zhang et al [11]found that erosion and wear of water hydraulic planar valves caused by coal particles mainly occurred near the throttle orifice. The jet tube servo valve pre-stage erosion numerical simulation were done and erosion wear rate and theoretical life were obtained
by Yin et al[12] and Chu et al[13]as shown in Fig 2c and Fig.2d. It indicates that many particles accumulate on the spool and part of the pre-stage is missing under erosion. CFD simulation can track the trajectories of solid particles in multiphase flow and accurately predict erosion characteristics[14-16]. N.Barton et al[17]showed that CFD can be used to predict experimental erosion measurements to a high degree of accuracy and the best erosion prediction method is to treat gas, particle, and fluid as separate phase. Wong[18]found that the most erosion in the test section occurs on the forward-facing step. The above researches provide a useful reference for CFD simulation on the valve orifice solid particle erosion. This paper will focus on the local erosion mechanisms and the influence on valve orifice area. 2. Analysis of failure 2.1 Erosion microtopography 2.1.1 Measurement region
Spool
P
T
A
P
B
Sleeve
Fig.3. Sliding spool valve of hydraulic servo valve power stage
MOOG73-218 model double-nozzle flapper electrohydraulic servo valve power stage sliding spool valve composed of spool and sleeve is shown in Fig.3. The spool-sleeve is the key dual pair for high-precision control. The spool valve is simplified as shown in Fig.1. Supply port P is distributed at both ends of the valve spool and return port T is located in the middle. Service port A locates between the left supply port P and return port T. Service port B is between the right supply port P and return port T. When the spool moves toward left, service port B is open, right supply port P is connected to service port B and service port A is connected to return port T. Otherwise, when the spool shifted to the right, service port A is open and supply port P is connected to service port A, service port B is connected to return port T. 1
5 1
2 1
3 1
Metering edge
6 1
4 1
Metering edge
Fig.4. Measurement regions of the spool 1,4—P-A/B metering edge
2,3—A/B-T metering edge
5—P-A/B valve stem 6—A/B-T valve stem
This paper focuses on the surface microtopography of the metering edges of the spool such as P-A/B metering edge, A/B-T metering edge, P-A/B valve stem and A/B-T valve stem as shown in Fig.4. The measurement was carried out by the automatic zoom 3D surface profilometer as shown in Fig.A6 of MethodsX in Part2. By continuous automatic vertical scanning technology and advanced image processing technology, the complete surface of the sample 3D morphology will be obtained such as surface morphology, roughness, surface texture and so on. 2.1.2 Results and Analysis The valve metering edge, the spool shoulder face (face A) and the end surface (face B) morphology were measured by the P-A/B valve metering edge 4 in Fig. 5 and Fig. 6. Positive side
Metering corner
Z Y
O
Face A- Shoulder face
X
Face B-End face Negative side
Fig.5. Morphology of P-A/B metering edge . Face A—Shoulder face
Face B—End face
Face A
Face B
（a）YX-positive
（b）YX-negative
（c）ZX-positive
（d）ZX-negative Fig.6. Metering edge profiles of P-A/B
As show in Table 1，all the corner radiuses tested of edge 4 are far beyond 0.5μm[7] and are
unequal. Both the spool shoulder face and end face near the metering corner are uneven. Table 1 Corner radius of P-A/B metering edge. Corner radius(μm)
Edge4 Plane
Positive side
Negative side
YX
22.6214
46.9320
ZX
15.2103
16.2802
Metering corner
Z Face C Y T O
X Face D
Fig.7. Morphology of A/B-T metering edge. Face C—Shoulder face
Face D—End face
Face C
Face D
（a）YX-positive
（c）ZX-positive
（b）YX-negative
（d）ZX-negative Fig.8. Metering edge profiles of A/B-T Table 2 Corner radius of A/B-T orifice edge. Edge3
Corner radius(μm)
Plane
Positive side
Negative side
YX
12.1394
20.5407
ZX
26.2526
15.7244
The metering edge and the spool shoulder and the end surface morphology were measured by the A/B–T valve orifice edge 3 in Fig.7 and Fig. 8.
Flow direction Port P
Port A/B
Sa2=763.0830
Sa1=283.8021
Sa3=549.0287
Fig.9. Morphology of P-A/B valve stem
Flow direction Port T Sa4=71.9040
Port A/B Sa6=207.0900 Sa5=658.7854 Fig.10. Morphology of A/B –T valve stem
As show in Table 2, all the corner radiuses tested of edge 3 are far beyond 0.5μm and are unequal. Both the spool shoulder face and end face near the metering corner are uneven. In Fig.9 and Fig.10, valve stem surface 5 and 6 area does exist obvious erosion and erosion region surface roughness was significantly higher than the adjacent regions. The surface topography may be related to the flow of the valve orifice and details are in part2.2.2. 2.2 Numerical calculation 2.2.1 CFD model 2.2.1.1Calculation model Port A/B
3
Port P/T 6
5
5
Orifice
1
2
y x o
12 17
（a）Geometry
（b）Orifice mesh Fig.11. Calculation model
The flow field of hydraulic spool valve without notches is symmetrical with respect to the spool axis as shown in Fig.1a. In order to reduce the calculation amount, the uniform radial windows on the sleeve are simplified to an annular chamber [19-21]. As shown in Fig.11a, a two-dimensional hydraulic spool valve without notches CFD model axisymmetric geometry was built (unit: mm).
The left chamber is connect to the service port A/B of actuator, the right chamber is connect to the supply port P or return port T. Due to small size , the strong turbulent fluctuation and great pressure gradient, the valve orifice mesh is specially refined as shown in Fig.11b. 2.2.1.2 Calculation conditions The fluid dynamics software FLUENT was used to calculate the erosion of the wall exposed to flow field in the hydraulic spool valve without notches. With Euler-Lagrange method, the high-speed flow of oil was regarded as a continuous phase and the continuous phase flow simulation was done under Eulerian coordinate system. Solid particles were regarded as a discrete phase (discrete phase model (DPM))and the movement of solid particles trajectory were calculated[17]. In the Eulerian-Lagrangian simulation of the motion of discrete phase particles, the effect of particle volume fraction on the continuous phase and the interaction between particles and particles are not considered. Eulerian-Lagrangian simulation is applicable to multiphase flow when the volume fraction of discrete phase is less than10%~12%. The solid particle volume fraction of hydraulic oil in is much less than 10%. Eulerian-Lagrangian simulation is available for hydraulic spool valve without notches erosion calculation. In order to analyze the force of the solid particles, the equation of particle motion was established. To obtain the motion trajectory of discrete phase particles, the differential equation in Lagrange coordinate system was integrated as shown in equation (1).
d up dt
Fd (u up )
g x ( P )
P
Fx …
（1）
Where u is the liquid velocity (unit: m/s), up is the solid particle phase velocity (unit: m/s), ρp is the solid particle density(unit: kg/m3), and Fd（u-up） is the drag force of per unit mass particle in the x direction(unit: N), gx（ρp-ρ）/ρp for the mass of the unit mass in the x direction of the gravity (unit: N), Fx is additional force of per unit mass particles in the x direction, including the virtual mass force, Brownian force et al. The erosion wear model proposed by Edwards et al[22-24] by the grit and carbon steel and aluminum surface erosion test was used to calculate the internal erosion wear rate as shown in equation (2).
mPC (d P ) f ( ) b ( ) ……… Af n 1 N
Re
（2）
Where Re is the erosion rate (unit: kg/（m2∙s m/s)）, n is the number of particles, mp is the particle mass flow (unit: kg/s) , dp is the diameter of the particle(unit: m) , C(dp) is function of particle diameter, α is the erosion angle between the particle trajectory and the wall, f(α) is the erosion Table 3
Table 4
Erosion model parameters Parameter Flow Rate
mp
Particle diameter
dp
Diameter function C(dp)
Boundary conditions Valve
Unit
10-6
kg/s
5
μm
1.8×10-9
Erosion angle α
30
Erosion angle function f(α)
1
Relative velocity b(v)
2
°
Parameter
Valve
Unit
Pressure inlet (P→A/B)
21
MPa
Pressure outlet (P→A/B)
18
MPa
Pressure inlet (A/B→T)
18
MPa
Pressure outlet (A/B→T)
0
MPa
Oil density
889
kg/m3
Spool/Sleeve density
7850
kg/m3
Particle density
1500
kg/m3
angle function, v is the relative velocity of the particle, b(v) is the relative velocity of the particle, Af is the unit area of the particle erosion wall, as shown in Table 3. Solid particle
v
Wall Fig.12. Particles micro-cutting erosion model
This model (equation 2) is an erosion model based on the micro-cutting theory of rigid particle impact plastic materials proposed by Finnie [25]. The model is the first one to quantify the relationship between erosion rate and angle of attack under low attack angle. The theory is that abrasive particles such as a miniature tool, which cut off the material as it strikes the target surface and produce wear and tear as shown in Fig.12. 2.2.2 Results and analysis 2.2.2.1 Erosion wear distribution Inter flow passage
Sleeve edge Spool edge
End face Stem face x=0.01
x=0.07
x=0.5
x=0.05
x=0.03
x=0.09
x=0.1
x=1
Fig.13. P→A / B Erosion wear distribution with different openings ( x in mm)
M.S. Wallace et al [26] pointed out that CFD techniques hold the promise of delivering a design tool for the prediction of erosion conditions in engineering components and a typical requirement is to identify the potential location for erosion. Geometry changes have important influence to the prediction of erosion wear for that geometry changes lead to flow field changes. Valve opening x also can cause flow field changes especially for the movement of solid particles. With different valve openings, erosion wear distributions were investigated. Boundary conditions settings are in Table 4. As shown in Fig.13, with the increase opening of spool valve, when the flow direction of fluid is P to A/B, the erosion distribution is also constantly changing. The severe erosion distribution mainly located in inside of the inlet flow passage, the sleeve edge, the spool edge, end face and stem face. With the increase of opening, the severe erosion region gradually turns to the downstream of valve orifice. The erosion locations of the spool edge, end face, stem face and other regions are completely consistent with the measurement results of the microtopography in Fig.5, Fig.7, Fig.9, Fig.10 and literature [9]. Literature [9] indicates DPM erosions occur on the sharp edges of spool and sleeve. The accuracy of the erosion numerical calculation in the hydraulic spool valve without notches was verified.
x=0.01
x=0.03
x=0.05
x=0.07
x=0.09
x=0.1
α
x=0.5
x=1
Fig.14. P→A/B Velocity vector with different openings ( x in mm)
As shown in Fig.14, with the increase of opening, the flow velocity vector (arrows) distribution of the valve orifice region presents a great change. When the opening is extremely small (x=0.01), the flow area is quite small and approximate to a narrow gap. High-intensity vortex formed adjacent to the orifice, especially in the upstream region of the orifice. Due to strong vortex effect, the solid particles driven by a large centrifugal force repeatedly hit the inside of the passage, resulting in local erosion of the inter flow passage. With the increase of opening (x=0.03~0.1), the jet angle α of the main stream of valve orifice gradually decreases and the vortex located in upstream of the valve orifice gradually disappears, but the vortex located in downstream still exists. The severe erosion distributions mainly located in the spool end face, sleeve edge and spool edge downstream of the orifice. Unluckily, hydraulic servo valve just works near the zero position. The erosion of the spool edge and sleeve edge heavily threat the servo valve performance. With the further increase of the opening (x=0.5~1), a small vortex is formed on both sides of the main stream downstream of the valve orifice. The main stream directly impacts the valve stem and solid particles in the oil cut the valve stem surface at high speed. The erosion region is mainly concentrated in the valve stem downstream of the valve orifice at this opening rage. From x=0.01 to x=1, the main flow is initially attached to the wall flow, then gradually away from the spool end face and finally jet to the stem surface directly.
Port P
C
A B
Port A/B
D
E Fig.15. Severe erosion region migration route with increasing opening when P→A / B
40
AB
35 30 25 20 15
AB
10 5 0 -5
12
13
14
15
16
Axial position (mm) Fig.16. Erosion wear rate of location AB
17
Erosion wear rate（10-9）
Erosion wear rate（10-9）
As shown in Fig.15, when the flow direction of the oil is P→A/B, the severe erosion region shows the migration route of A→B→D→C→E as the valve opening increases (x=0.01~1).But the spool edge B always belongs to the more severe erosion region, where A is spool edge upstream region, B is spool edge region, C is sleeve edge region, D is spool end face, E is valve stem region. 100
C¦
80 60
C
40 20 0 4 .0
4 .2
4 .4
4 .6
4 .8
5 .0
Radial position (mm) Fig.17. Erosion wear rate of location C
8 6 4
D
2 0 2 .0
2 .5
3 .0
3 .5
4 .0
Erosion wear rate（10-12）
Erosion wear rate（10-9）
D
E¦
500 400 300
E
200 100
Radial position (mm)
0 0
2
4
6
8
10
12
Axial position (mm) Fig.19. Erosion wear rate of location E
Fig.18. Erosion wear rate of location D
Erosion wear rate changes along the wall ( opening x=0.05mm, the oil flow P→A/B) are showed in Fig.16~ Fig.19 under x-o-y coordinates in Fig.11a. From Fig.16, it can be clearly seen that the erosion wear rate at the upstream A and B of the spool reaches the maximum 3.5×10-8 near the spool metering edge and decreases almostly to 0 with the increase of axial position. As indicated in Fig.17, the erosion wear rate near the sleeve metering edge reaches the maximum 9×10-8 and then decreases gradually. The distribution of erosion rates at location A,B and C are very similar. The erosion wear rate of the spool end face D reaches the maximum 8×10-9 near the spool metering edge and decreases and increase alternately as shown in Figure 18. There is a large erosion wear rate near the spool end surface near the valve stem E as shown in Fig.19. In addition, the distribution of erosion rates at location D and E are also very similar and present peak-valley distribution. Severe erosion do occur on the metering edge of spool and sleeve which is completely consistent with literature[9] and microtopography measurement in part 2.1.
x=0.001
x=0.01
x=0.05
x=0.1
x=0.5
x=1
Fig. 20. A / B→T Erosion region distribution with different opening ( x in mm)
x=0.001
x=0.01
x=0.05
β x=0.5
x=0.1
x=1
Fig.21. A/B→T Velocity vector with different openings ( x in mm)
As shown in Fig.20 and Fig.21, when A/B→T and the valve opening is extremely small (x=0.001~0.01), the jet angle β of the main stream is close to 90°. One high-strength vortex develops respectively in the valve chamber upstream and downstream of the orifice. The solid particles driven by centrifugal force erode the valve stem and the inside of the passage near the inlet. As the orifice opening increases (x=0.05~0.1), the upstream vortex disappears and the downstream vortex below the main stream still exists. The jet angle β of the main stream becomes smaller and the erosion region mainly concentrates on the incoming flow face and the edge. With the further increase of the opening (x=0.5~1), the jet angle β of the main stream gradually decreases and the erosion region concentrates on the spool end face and the outlet of the valve body. Port A/B
Port T
J
H F
G
I
Fig. 22. Severe erosion region migration routes with increasing opening when A/B→T
As shown in Fig.22, when flow direction is A/B to T, as the opening of the valve increases, the severe region migration route change by F→G→H and G→I→J. At the very slight opening stage, there is a strong vortex respectively upstream and downstream of the valve orifice. Particles did not pass through the orifice but plunged into the upstream vortex. Not only stem, valve orifice but also valve body are eroded when A / B→T. However, the metering edges of the valve orifice always keeps in serious erosion. The erosion region gradually migrated to the downstream of the
orifice with the increase of opening when A/B to T. 2.2.2.2 Local erosion mechanism (P→A/B as an example)
Port P Sleeve
Solid particles
A
B
Spool
Port A/B （a）Location A
C
（c）Location C
（b）Location B
D
（d）Location D
E
（e）Location E
Fig.23. Local erosion mechanism schematic diagram
Different regions have different flow states, and therefore, the local erosion mechanism is different. The centrifugal action of the vortex and the main stream washing are considered as the main erosion power. 1. Location A -upstream of the spool shoulder face As shown in Fig.23a, when the opening is extremely small(x=0~0.01), a strong vortex forms in the valve chamber upstream of the valve orifice due to the tiny flow area. The solid particles driven by the centrifugal force in the oil repeatedly hit and cut the upstream region of spool shoulder face. 2. Location B-the spool metering corner As shown in Fig.23b, location B ,where the sharp corner of the metering side is designed to 90°, is the geometry singularity of flow field. In the vicinity of the edge of the valve orifice, the high-speed fluid carrying solid particles must keep a smooth flow at location B to maintain the flow inertia. Adjacent to the valve orifice, the flow area is sharply reduced and particles gathered. In this process a large numbers of solid particles impact and eroded the corner. This is fatal to the performance of the spool and servo valve. 3. Location C- Sleeve edge and metering corner As shown in Fig.23c, the valve sleeve edge and metering corner C is in the upper part of the main stream of the orifice and also belongs to the singularity geometry of the flow field. A vortex is easy to form around the corner. Solid particles driven by the vortex centrifugal force eroded the sleeve edge. In addition, valve orifice flow area reduced suddenly and the speed of mainstream increase drastically. The carrying particles with high kinetic energy eroded the metering corner. It
can be considered that the erosion at the sleeve edge and metering corner C is the combined result of the washing of the main stream of the valve orifice and particle erosion under the eccentric centrifugal force. This is also fatal to the performance of the servo valve. 4. Location D-Spool end face As shown in Fig.23d, location D is in the downstream of the orifice main stream. There is a strong wall flow, that’ to say the solid particles move along the wall. Solid particles with sharp edges and suitable angle cut the spool end face. 5. Location E-Valve stem face As shown in Fig. 23e, as the increase of the opening(x=0.5~1)location E directly faces the main stream of the valve orifice. The high speed solid particles flow impinge directly on the stem surface. The particle bounces twice to rebound and acts on the valve stem surface repeatedly resulting in erosion of the stem surface. The unwanted particles in the oil are the dominant factor in the erosion damage of the valve port when the geometric characteristics of the hydraulic spool valve are set for function. 2.2.2.3 Inflection point effect and Face-back flow phenomenon
Face flow region Inflection point 2
Inflection point 1
Back flow region （a）Erosion distribution
（b）Particle trajectory
Fig. 24. Inflection point effect and Face-back flow phenomenon
As shown in Fig. 24a, there are several severe regions of erosion in hydraulic spool valve without notches near the orifice. They are the spool metering edge (Inflection point 1), the spool shoulder face, the spool end face, the sleeve metering edge (Inflection point 2), the upstream area near the sleeve metering edge, the downstream area near the sleeve metering edge. The upstream area near the spool and the sleeve metering edge facing the incoming flow are known as the “Face-flow region”, the downstream area near the edge of the spool and the sleeve metering edge are referred to as “Back-flow region”. Erosion distribution in Fig.24a shows that erosion wear of the face-flow region is more severe than that of the back-flow region, which is called the “Face-back flow phenomenon”. The face-flow region is exposed to particles having a velocity comparable to that of the main stream. The erosion valve inflection point severe than the other region known as the “Inflection point effect”. With solid particles in the flow around the inflection point of the spool, particle trajectory should be smooth due to inertia is shown in Fig.24b. By the particles trajectory, it can be clearly seen that contacts between the particles and the valve wall really exist. There is a large differential pressure and small flow area near the valve orifice, the metering edge is slowly to be washed by the oil flow. Especially under micro opening and serious pollution, the particles move faster and
impact frequently, resulting in more severe erosion as shown in Fig.24b. “Inflection point effect” and “Face-back flow phenomenon” is consistent with the erosion in a pipe contraction [27]. 3. Discussion According to the“Inflection point effect”and “Face-back flow phenomenon” ，inflection points of the spool and sleeve near the valve orifice are easy to be eroded and worn. As a result, the spool valve null region characteristics, such as null leakage and overlap, which have an important influence on system operation and stability, will be degraded [18]. The essence of the hydraulic valve is the orifice and the orifice area which determines the control characteristics of the valve. The valve orifice is composed of metering edges of the spool and sleeve. Usually we just calculate the orifice area under the ideal contour. Therefore, it is very important to ascertain and calculate the orifice area after erosion to explore the sliding spool performance under erosion. 3.1 Valve orifice position Outlet Sleeve Spool Inlet （a）Square-Square
（b）Corner-Square Fig. 25.
（c）Square-Corner
（d）Corner-Corner
Models of eroded valve orifice
Based on CFD calculation of particle erosion, the“Inflection point phenomenon”of the spool metering edge, sleeve metering edge and the microtopography show that inflection point is the most vulnerable to erosion and the sharp edge of spool and sleeve turn into rounded corners. Thus, the following models of eroded valve orifice were established:Model1 Square-Square(Fig.25a),Model2Corner-Square(Fig.25b),model3Square-Corner(Fig.25c),model4 Corner-Corner (Fig.25d), Model 1 is for reference. Taking a two-dimensional hydraulic spool valve without notches with rounded corner radius of Unite: Pa
（a）Square-Square
（b）Corner-Square
（c）Square-Corner
（d）Corner-Corner
Fig.26. Pressure distributions of the orifice
0.25 mm as a model, flow field pressure distributions were obtained in Fig.26. For the sharp decrease of flow area, there is dense pressure gradient and a large pressure drop around the orifice. The valve orifice locats at the black line in Fig.26. Equivalent flow area is circular frustum side area formed by the black line as the bus and rotats around the spool axis as shown in Fig.27. 3.2 Eroded valve orifice area 3.2.1 Model2 Corner-Square
Round table up radius Round table bus
A H B
Flow Area
C x D H
A
Round table down radius
B F
I
G
C
D Fig. 27. Calculate diagram of Model 2
Set the spool-sleeve gap as h, spool diameter D, spool corner r, overlap x0 = 0, valve opening x, the origin of the coordinate O. Circular frustum bus BC: BC AC AB AC r
r 2 (r x)2 r ……………………………………
（3）
Circular frustum up radius CG：
D …………………………… 2 Circular frustum down radius BI:
（4）
CG=
BI (
D h r) r 2
r r 2 (r x)2
………………………………………
（5）
Circular frustum side area S: S CG BI BC (D h r
r2 r2 (r x)2
)( r2 (r x)2 r)
……
The orifice area is S (x) = f (x, D, h, r) where D=7.5mm, h=0.005mm, r=0.01mm. S (x) -x curve set h = 0 ,When x = -r, S(x) = 0.
（6）
15
Area(mm2)
10
Area(mm2)
1.5
A2(x) B2(x)
5
1
0.5
A2(x) B2(x)
0
0
0.1
0.2 0.3 Opening x (mm) (a) x=0~0.5 Fig.28.
0.4
0.5 0 0
0.01
0.02 0.03 0.04 Opening x (mm) (b) x=0~0.05
0.05
Erosive valve orifice area of model 2
A 2(x) is the valve area after erosion. B2 (x) is the traditional calculation formula B 2(x) = πd • x. 3.2.2 Model 3 Square -Corner
y A B O
G
B C
C
D E
D E
x
F Fig. 29.
Calculate diagram of Model 3
1.5
Area(mm2)
Area(mm2)
15
10
1
A3(x)
5
x
A3(x)
0.5
B3(x)
B3(x)
0 0
0.1 0.2 0.3 Opening x (mm) 1 (a) x=0~0.5 2 3
0.4
0.5
4
5
0
0
0.01
0.02 0.03 0.04 Opening x (mm)
Fig. 30. Erosive valve orifice area of model 3
Circular frustum Side area S:
(b) x=0~0.05
0.05
r h S D h r r (r h )2 (x r)2 (r h)2 (r x)2 r
……
（7）
Valve orifice area S (x) = f (x, D, h, r) where D, h, r are constants. D=7.5mm,h=0.005mm,r=0.01mm ,Set h = 0, then when x = -r, S (x) = 0 Note: A3 (x) is the valve area after erosion; B3(x) is the traditional calculation formula B 3(x)=πd•x 3.2.3 Model 4 Corner-Corner
A A H
K A
B C
K B
D G
O
F
E
X
C D O
I
X
M Fig. 31.
Calculate diagram of Model 4
1.5
10
1
Area(mm2)
15
Area(mm2)
F E
A4(x) B4(x)
5
A4(x)
0.5 B4(x)
0
0
0.2 0.4 Opening x (mm) (a) x=0~0.5
0.6
0
0
0.02 0.04 Opening x (mm) (b) x=0~0.05
0.06
Fig.32. Erosive valve orifice area of Model 4
Circular frustum Side area S: S (CJ BM ) BC
(r2 r1 )(r1 r2 h)
r1 r1
r2 h r1 r2 x 2
2
……………………………………（8） D h r1 r2
2 2 r2 h r1 r2 x r1 r2
Model 4 port area S (x) = f (x, D, h, r1, r2) where D, h, r1, r2 are constants. When h = 0 and r1 = r2, S(x) = 0 when x = -2r. Note: A4 (x) is the port area after erosion, B4 (x) is the traditional calculation formula
D=7.5mm,h=0.005mm,r1=0.01mm, r2=0.01mm. Valve orifice area characteristics of Model2, Model3,Model4 as shown in Fig. 28, Fig. 30, Fig. 32: (1)Within the opening range , the orifice area of the traditional calculation formula always smaller than that of the new calculation formula due to not consider the valve orifice erosion especially near the null position. (2) The new calculation formula at the null position x=0 calculates that the valve orifice area is not zero, which is consistent with the actual situation namely null leakage. (3)The valve orifice area after erosion has strong nonlinearity namely the “Bending phenomenon” near the null position, resulting in the control linearity deteriorated . 3.2.4 Differential area
Model 2 Model 3 Model 4
Differential area(mm2)
0.30 0.25 0.20 0.15 0.10
A4(x)-B4(x)
0.05
A3(x)-B3(x) A2(x)-B2(x)
0.00
0.00
0.01
0.02
0.03
0.04
0.05
Opening x (mm) Fig. 33. Opening-Differential area
As shown in Figure 33, the differential orifice area between Model 2, Model 3, and Model4 and conventional formula are calculated by selecting the valve opening x1 = 0, x2= 0.01, x3 = 0.03 and x4 = 0.05. (1) With the increase of valve opening, the differential orifice area between the new formula and the traditional formula gradually decreases and the largest difference locates at null position x=0. (2) The area difference of Model 3 is larger than that of Model 2, which shows that the edge erosion of the spool is more serious than the sleeve. (3) The area difference between Model 4 and Model 3 is larger than that of Model 2, which indicates that the influence of sleeve edge and spool edge erosion on the valve orifice area is obvious. According to the CFD calculation, both the metering edge of spool and sleeve are the most susceptible to erosion damage. Calculation formula of Model 4 is closest to actual working condition.
4. Conclusions Obviously erosion corner appearance at the metering edge:There are metering edge corners and the average radius of the valve orifice edge is 20.5818μm, which far beyond the servo valve spool
edge requirement. The valve orifice edge can easily cause valve flow control nonlinearity, which is consistent with numerical calculation and related experimental results. Severe erosion region migration path: When the oil flow direction is P→A/B, as the valve orifice opening increases migration path: spool shoulder face→ spool metering edge →spool end face →sleeve corner→ valve stem, but the metering edge of spool and sleeve are always in the more severe erosion region. Local erosion mechanism: Driven by the centrifugal force, the solid particles cut the upstream region of the valve orifice. A large numbers of solid particles impact and erode the corner to keep smooth flow. There is a strong wall flow leading to the spool end face erosion. The high speed solid particles flow impinge directly on the stem surface. Erosion inflection point effect and Face-backward flow phenomenon: “Inflection point effect”solid particles in the flow around the inflection point of the spool due to inertia and particle trajectory. “Face flow phenomenon”-the erosion area of the face-flow area is more severe than the back-flow area. Accurate calculation of erosive valve orifice area:The erosive valve orifice area curve in the small degree of openness has a curvature of the phenomenon that has a strong nonlinear, that is, the flow control of the linear degradation. The calculated results are in good agreement with related experiments. The predominant cause in the erosion damage of the valve: The unwanted particles in the oil are the dominant factor in the erosion damage of the valve port when the geometric characteristics of the hydraulic spool valve are set for function. Therefore, it is possible to reduce the erosion of the valve orifice by reducing the particles or change particles trajectory, which needs further study.
Acknowledgements This work is supported by the National China(51575254),(51565027)and (51465033).
Natural
Science
Foundation
of
References [1] Wang GL, Tao CD, Shao DX, et al. Research on geometric accuracy of servo valve orifice. J Journal of Harbin Institute of Technology 1999 ;05: 120-122. [2] Bent H.Nystad, Giulio Gola, John E.Hulsund,et al. Technical condition assessment and remaining useful life estimation of choke valves subject to erosion. Annual Conference of the Prognostics and Health Management Society. Oregon:Portlang.2010. [3] Wang DW and Ye ZM. Three-dimensional model simulation of the effect of the spool valve flange fillet on the flow characteristics. J Machine Tool & Hydraulics. 2013;41 (12): 6-9. [4] Zhang L. Valve edge geometry error on the performance of the slide valve simulation D Harbin Institute of Technology, 2007. [5] M.Singh· G.S.Lathkar· S.K.Basu. Failure prevention of hydraulic system based on oil contamination J Journal of The Institution of Engineers(India),2012;93(3):269-274. [6] Dong G, Zhang JY.
Research progress on erosion wear of solid particles[J]. Journal of Materials Science and
Engineering. 2003.21(2):307-312. [7] Shipway P H , Hutchings I M . The role of particle properties in the erosion of brittle materials[J]. Wear, 1996, 193(1):105-113. [8] M.G.Talks, A.R.M.Eedy, Zhu HW. Erosion and corrosion of mining hydraulic equipment J Mail mining
machinery, 1983;04: 44-46. [9] Zhang K., Yao J, Jiang T. Degradation assessment and life prediction of electro-hydraulic servo valve under erosion J wear. Eng. Fail. Anal., 2014;36:284-300. [10] Qian DL. Panyu 35-2 subsea gas pipeline erosion law. D Southwest Petroleum University, 2015. [11] Zhang H, Xiong SB, Liang YW, et al. Erosion wear characteristics analysis and structure discussion of hydraulic valves. J Journal of China Coal Society, 2008;02: 214-217 [12] Yan YB, Fu JH, Jin YL. Numerical simulation of pre-level erosion wear of jet tube servo valve. J Journal of Zhejiang University(Engineering Science), 2015;49(12): 2252-2260. [13] Chu YB, Yuan CH, Zhang Y. Erosion wear characteristics of jet pipe servo valve .J Acta Mechanica Sinica, 2015;36 (05): 1548-1555. [14]G.Haider,H.Arabnejad, S.A.Shiraz, et al.
A mechanistic model for stochastic rebound of solid particles with
application to erosion predictions. J Wear 376-377(2017)615-624. [15] Zhang JX，Kang J, Fan JC, et al.
Research on erosion wear of high-pressure pipes during hydraulic
fracturing slurry flow. J Journal of Loss Prevention in the Process Industries 2016; 43:438-448. [16] Peyman Zahedi, Jun Zhang, Hadi Arabnejad,et al. CFD simulation of multiphase flows and erosion preditions under annular flow and low liquid loading conditions. Wear 376-377(2017)1260-1270. [17] N.Barton, M.Lewis, P.Emmerson, CFD erosion prediction in gas-liquid-sand flow, Proceedings of SPE International Oilfield Corrosion Conference and Exhibition, Aberdeen, Scotland,UK,2016. [18] Chong Y.Wong, Christopher Solnordal, Anthony Swallow, et al. Experimental and computational modeling of solid particle erosion in a pipe annular cavity. J Wear 303(2013)109-129. [19] Yin YB, Yuan JY, Guo SG. Numerrical study of solid particle erosion in hydraulic spool valve. Wear 392-393(2017)174-189. [20] R.Yang, Hydraulic spool valve metering notch characterization using CFD. Procesdings of the ASME International Mechanical Engineering Congress and Exposition. American Society of Mechanical Engineers,11-17,2003. [21] R.Amirante, G.del Vescovo.A.Lippois. Flow forces analysis of an open center hydraulic directional control valve sliding spool,Energy Convers.Manag.47(1)(2006)114-131. [22] EDWARDS J k, MCLAURY B S,SHIRAZI S A. Evaluation of alternative pipe bend fittings in erosion service[C]//Proceedings of the 2000 ASME Fluid Engineering Division Summer Meeting, New York: American Society of Mechanical Engineers ,2000:956-966. [23] Edwards JK. Development, Validation and application of a three-dimensional, CFD-based erosion prediction procedure[dissertation].Tulsa:The University of Tulsa:2000. [24] Zhang YL. Application and improvement of computational fluid dynamics(CFD)in solid particle erosion modeling [dissertation].Tulsa: The University of Tulsa:2006. [25] Finnie,I.,1972.Some observations on the erosion of ductile metals. Wear 19(1),81-90. [26] M.S. Wallace, W.M. Dempster, T. Scanlon, et al. Prediction of impact erosion in valve geometries. J Wear,256(9)(2004), 927-936 . [27] B.S. McLaury,S.A. Shirazi, J.R. Shadley,E.F. Rybicki,Modeling erosion in chokes,ASME,Fluids Engineering Division(Publication)FED,vol.236,No.1,1996,pp.773-781.
Highlights 1. The measurement and analysis of the surface micro-morphology of the eroded spool. 2. The migration route of the severe erosion region of hydraulic spool valve without notches with the change of the valve opening and the mechanism of local erosion. 3. The phenomenon of erosion inflection point and face-back flow . 4. The exact calculation method of the orifice area after erosion .
Conflict of interest statement We declare that we have no financial and personal relationships with other people or organizations that can inappropriately influence our work, there is no professional or other personal interest of any nature or kind in any product, service and/or company that could be construed as influencing the position presented in, or the review of, the manuscript entitled, “Erosion behavior and influence of solid particles in hydraulic spool valve without notches” .