Volumetric efficiency degradation prediction of axial piston pump based on friction and wear test

Abstract

The axial piston pump (APP) is being developed towards higher pressure and higher rotational speeds to enhance operational power density. The piston-cylinder friction pair is a critical component of the APP. Due to its lack of self-compensation capability, the leakage of the piston-cylinder friction pair escalates rapidly under increasingly severe wear conditions. An innovative method for predicting the performance degradation and lifespan of APPs based on friction and wear tests has been proposed. This method can effectively predict the performance degradation trends of APPs under different operating conditions. The actual contact force on the piston pair (PP) during operation is determined through dynamic analysis. Friction and wear tests were conducted on 38CrMoAl piston and ZCuPb15Sn8 cylinder materials under various conditions using a testing apparatus. Utilizing friction and wear theory, the volumetric efficiency of APP under various operating conditions was derived as a function of operational time. The reliability of the theoretical analysis was validated through leakage tests on the APP. The results indicate that volumetric efficiency decreases exponentially with increasing working pressure at rated speed. This research provides theoretical guidance and an experimental foundation for the failure prediction of volumetric efficiency degradation in APP.

Highlights

• •Predicting piston pump volumetric efficiency degradation and failure.
• •The friction and wear characteristics of plunger pair materials were obtained.
• •The relationship between plunger wear, pump leakage, and volumetric efficiency.

1. Introduction

The axial piston pump (APP) is an essential power component in fluid power systems, featuring a compact design, ease of variable control, high efficiency, long service life, and the capability to operate under high pressures. It is widely used in fields such as aerospace, construction machinery, and marine defense applications [[1], [2], [3]]. The development of high speed and high pressure APPs has the advantages of improving the equipment manufacturing level, saving the installed space, reducing the installed weight and realizing the high integration of the system. So increasing the speed and pressure of APPs to achieve higher power density is a critical direction for their development [4]. The APPs in large construction machinery are mainly to improve its operating pressure. In the process of the combination of hydraulic system and electrification, the gradual high-speed APPs is an important development process. Stricter operating conditions lead to performance degradation and reduced lifespan of APPs. Therefore, predicting the operational lifespan under various working conditions is crucial for ensuring their reliable operation.

Statistics indicate that wear-related issues account for approximately 80 % of failures in APPs, leading to reduced operational efficiency, increased leakage, shortened lifespan, and significant economic losses, as well as potential catastrophic injuries or fatalities [5]. During operation, APPs involve multiple pairs of friction components. These friction components operate under high stress and high relative velocity conditions, which makes tribological control challenging due to the harsh internal environment. Researchers have conducted relevant studies on the friction pairs of APPs. The relative friction surface between the valve plate and the cylinder block is referred to as the flow distribution pair (FDP). Huang et al. [6] investigated the effects of different heat treatment methods and various rotational speeds on the friction and wear performance of the FDPs. The results indicated that adhesive wear is more likely to occur in the FDP under high-speed conditions. Chen et al. [7] proposed a method combining surface micro-texturing and wet micro-explosive treatment to enhance the tribological performance of the FDPs. Danilo et al. [8] analyzed the friction failure of cylinder body anti-friction coatings and found that the failure lifetime of the coating is primarily attributed to the uneven distribution of lead caused by casting cooling temperatures. The relative friction surface between the slipper and the swashplate is referred to as the slipper pair (SP). Liu et al. [9] established a mixed lubrication model for the SPs, focusing on the microscopic surface changes during the wear process and analyzing the influence of wear depth on the oil film degradation behavior. Wu et al. [10] improved the dry friction performance of the SPs by exploring different pairing materials. Chao et al. [11] summarized the existing research on SP test rigs and proposed that novel sensors and non-invasive measurement techniques are important future development directions for SP testing platforms. The relative friction surface between the piston and the cylinder block is referred to as the piston pair (PP). Zhang et al. [12] developed a coupled model of thermal flow structure for the PP. Zhang et al. [13] derived the wear profile at the minimum wear rate based on the wear degradation model, providing guidance for the design of machined surface profiles. Lyu et al. [14] developed a wear prediction method for the PP to forecast the time-varying wear process. Zhang et al. [15] focused on ultra-high-pressure APPs and proposed a lubrication film design method for the PP. In summary, researchers have investigated the wear failure mechanisms and performance enhancement strategies of friction pairs in APP through lubrication improvement, material selection, and surface treatment approaches.

APPs are classified as degradation-type failure products, and unanticipated failures can lead to serious incidents and hazards, including equipment damage and potential casualties. These events have a significant effect on the progress of construction projects and public safety. Researchers have investigated the performance degradation and fault diagnosis of APPs through real-time condition monitoring. These studies are generally founded on the monitoring and analysis of data collected during the operational processes of APPs. Vibration signals are the most common data for identifying faults in APPs. Chao et al. [16] collected vibration signals from multiple locations during the operation of the APP and proposed a decision fusion strategy, which enhanced the accuracy of multi-fault identification in APPs. Du et al. [17] suggested a hierarchical clustering algorithm that enables the simultaneous diagnosis of five common faults in aircraft APPs. Tang et al. [18] proposed a diagnostic method for diagnosing loose shoe faults under load conditions using vibration signals. Zhu et al. [19] applied particle swarm optimization to optimize the hyperparameters of an improved Lenet-5 model, achieving a recognition accuracy of 98.71 % for faults such as swashplate wear. Pressure and flow signals, which are less susceptible to environmental influences, can also be utilized as data for identifying the operational status of APPs. Lu et al. [20] defined a degradation state index for quantitatively assessing the performance deterioration of APPs by monitoring the pressure signals at the APP outlet. Jiang et al. [21] introduced a DTW-RCK-IF approach for detecting anomalies in APPs utilizing pressure signals, demonstrating the effectiveness of the method with publicly available full lifetime datasets from CWRU and XJTU-SY bearings. Wang et al. [22] described the performance degradation of APPs and predicted their remaining life based on return flow rate signals and the Wiener process. Guo et al. [23] investigated the degradation of the valve plate material and utilized fitting curves of flow rate and wear amount to predict the performance degradation and faults of the APP. Acoustic signals are also one of the indicators reflecting the operational state of APPs. Gao et al. [24] employed an enhanced clustering segmentation method to extract weak fault features of APPs from background noise and natural impulses. Zhu et al. [25] applied a particle swarm optimization-based convolutional neural network model to the standard LeNet architecture for identifying five common faults in APPs using acoustic signals. The performance of the model was validated by comparing it with several classical models. Additionally, researchers extracted multiple signals based on the performance of different failure modes to jointly predict the occurrence of faults [26]. The complex structure of APPs and the obscurity of fault characteristics present significant challenges for fault identification. This complexity and invisibility complicate the accurate diagnosis of issues within APPs [27].

Friction and wear are the primary causes of APPs failure. Researchers have studied anti-wear and friction reduction methods for the key friction pairs in APPs. Additionally, they have employed signal detection techniques to diagnose the operational status of the APP in real time, allowing them to infer performance degradation and potential failure. The lack of inherent self-compensation capability within the piston/cylinder block friction interface represents a critical vulnerability in the design of APPs, constituting a significant point of failure within the system. This study innovatively proposes a performance degradation and lifespan prediction method that uses volumetric efficiency as the evaluation criterion, based on friction and wear experiments of PP materials in APPs. This method can predict the performance degradation of APPs under various operating conditions. It provides a fundamental basis for the lifespan design and predictive maintenance of the app.

2. Model and method

2.1. Structure and principle

The structure diagram of the rotary assembly of the swashplate APP is shown in Fig. 1a. Inclined piston structure and spherical flow distribution are used to improve the compact and overturning resistance of the APP structure. The main parts include swashplate, slipper, piston, piston sleeve, valve plate, cylinder block, etc. The main shaft drives the cylinder in continuous rotation. This rotational motion, in conjunction with the swashplate, drives the pistons and slippers to reciprocate within the cylinder bores. The valve plate enables the APP to perform the suction and discharge of oil. The swashplate plays a role in adjusting the displacement of the APP. The swashplate APP rotating assembly dimensions diagram is shown in Fig. 1b. The cylinder piston hole diameter is d. The distribution circle radius of the piston is R. The inclination angle of the swashplate is α. The inclination angle of the piston is β.

Fig. 1.

a) The swashplate APP rotating assembly structure diagram b) The swashplate APP rotating assembly dimensions diagram.

2.2. Leakage analysis

The structural characteristics of APPs necessitate the presence of matching gaps and working pressure differences during operation. Friction and wear during operation increase leakage gaps, which then reduce volumetric efficiency. Ultimately, the operational performance and longevity of the APPs are affected. The leakage of APPs mainly occurs in the PP, FDP, and SP. The PP is most affected by friction and wear because it does not have the ability to compensate for the leak gap.

• •Leakage of inclined PP

Clearance between PP is minimal, allowing for the flow state to be characterized as laminar. By conducting a comprehensive analysis of the motion dynamics of the inclined piston, it is inferred that the piston comes into contact with both the front and back ends of the cylinder hole, leading to complete eccentricity. Conversely, the piston achieves perfect concentric alignment with the cylinder hole at the juncture of the two contact stress lines and the piston axis. The immediate leakage flow of an individual PP is described in Equation (1).

$$q=\frac{\mathrm{\pi }d{\delta }_c^3\Delta p}{8.68\mu l_i}-\frac{\mathrm{\pi }d{\delta }_c{v}_{pi}}{2}$$ (1)

where q represents the leakage quantity of an individual piston, d denotes the piston diameter, δ_C is the unilateral clearance of the PP, Δp signifies the pressure difference of the piston cavity, μ stands for the dynamic viscosity of the oil, l_i indicates the piston cylinder length, v_pi is the piston axial speed.

• •Leakage of spherical FDP

The spherical FDP possesses characteristics such as a compact structure, a large bearing area, and a strong anti-overturning moment. It is one of the common structures found in heavy-duty and large-flow APP. The leakage of the spherical FDP can be divided into internal leakage and external leakage. By establishing boundary conditions for the sealing zone and integrating the separate variables, the calculation equation of external leakage at the sealing area can be obtained as shown in Equation (2).

$$Q_{1i}=\frac{\Delta p{e}^3{\phi }_f{B}_1}{3\mu C_e}$$ (2)

where Q_1i represents the leakage quantity from the sealing belt to the exterior, C_e denotes the flow coefficient, B₁ signifies the correlation angle coefficient for the spherical FDP, e is the oil film gap of spherical FDP, the initial design value is 10.5 μm, and φ_f is the envelope angle of the valve plate, φ_f = 159.95°.

The leakage expression in the spherical FDP is shown in Equation (3).

$$Q_{2i}=b\left[\frac{e^3{\left(\cos \theta \right)}^3}{12\mu l}\Delta p\pm \frac{e{v}_e{\left(\cos \theta \right)}^2}{2}\right]$$ (3)

where Q_2i is the leakage amount in the spherical FDP, b denotes the width of the waist curve of the valve plate, b = 16.02 mm, v_e is the average oil flow speed in the transition zone, and l is the average length of the FDP clearance in the transition zone.

• •Leakage of SP

The slipper supports the compressive force from the piston and the opposing thrust from the oil film within the SP. The compressive force generally exceeds the support provided by the oil film, ensuring an adequate residual compression force on the surface of the SP. During this period, leakage can be minimized while reducing the friction and wear of the SP. Operating under high-pressure and high-speed conditions, the sliding SP must be well-designed to avoid excessive friction, wear, and leakage, which could otherwise compromise the reliability of the APPs. Assuming that the oil film is evenly distributed and the fluid in the gap of the SP exhibits laminar flow, the leakage amount of the SP can be represented by Equation (4).

$$Q_4=\frac{\mathrm{\pi }{h_1}^3}{6\mu \ln \left(r_2/r_1\right)}\Delta p$$ (4)

where Q₄ is the leakage amount of a single slipper, h₁ is the oil film thickness, r₂ represents the radius of the outer sealing band, and r₁ denotes the radius of the inner sealing band.

According to Equation (4), the leakage of the SP is dependent on various factors including the oil film thickness, the oil discharge pressure, the radius of the outer sealing belt, and the radius of the oil chamber. As the oil discharge pressure and oil film thickness in the piston cavity increase, so does the leakage. The larger the radius of the outer sealing belt, the smaller the leakage.

2.3. Dynamic characteristics

To ascertain the wear patterns of the PP under actual operating conditions, it is imperative to correlate the loading force applied to the test specimens with the contact force. Therefore, prior to conducting friction and wear tests within the PP, it is necessary to obtain the results of the contact force through dynamic analysis. The force diagram of the piston at the top dead center is provided in Fig. 2. The equilibrium equations of force and moment are obtained, as shown in Equation (5) to Equation (7).

$$F_n\sin \left(\beta +\alpha \right)+F_{cf2}\cos \beta +F_{R2}-F_{R1}=0$$ (5)

where, F_n indicates the support force of the piston, F_cf is the centrifugal force caused by the acceleration, F_cf1 and F_cf2 are the components of centrifugal force along the x and y axes, and F_R1 and F_R2 are the reaction force of the cylinder hole.

$$F_n\cos \left(\beta +\alpha \right)-F_{cf1}\sin \beta -f{F}_{R2}-f{F}_{R1}-F_p-F_g=0$$ (6)

where fF_R1 and fF_R2 are the friction force caused by F_R1 and F_R2, F_p denotes the force caused by liquid pressure, and F_g is the inertia force.

$$f{F}_{R1}\frac{d}{2}+l_c{F}_{cf}\cos \beta +F_{R2}\left(l_p-\frac{l_2}{3}\right)-F_{R1}\left(l_p-l_o+\frac{l_1}{3}\right)-f{F}_{R2}\frac{d}{2}=0$$ (7)

where l₀ is the minimum cylinder length at the top dead point of the piston, l_p denotes the distance between the bottom end and the center of the piston ball head, and l₁ and l₂ are the force arm sizes.

Fig. 2.

Force diagram of the piston at top dead center.

To determine the contact force of the piston and the cylinder block, a dynamic analysis of the relevant components was conducted. These components include the piston, slipper, piston sleeve, cylinder block, and swashplate. Rotating components are maintained at the maximum inclination angle. Table 1 presents the simulation conditions and structural parameters used in the dynamic analysis of the APP. Through numerical simulation, the variation curves of the PP contact force at 2200 r/min under different load pressures were obtained. The resulting contact force change curve is depicted in Fig. 3. The contact force of the PP exhibits periodic fluctuations. The contact force of the PP decreases as the working pressure decreases, the corresponding relationship is shown in Table 2. When the piston transitions into and out of the oil discharge area, sudden connections with the suction tank occur, resulting in abrupt changes in piston speed direction and the generation of inertial forces. Consequently, the contact force of the PP rises to a stable state, often accompanied by an overshoot.

Table 1.

Dynamic simulation parameter table.

Structure parameter	Number
Piston number	9
Nominal pressure (MPa)	35
Swashplate inclination (deg)	16
Piston Tilt Angle (deg)	5
Piston Diameter (mm)	27.9
Piston radius (mm)	56.75
Speed (r/min)	2200
Simulation time (s)	0.5
Simulated steps	15000

Fig. 3.

2200 r/min contact force change curve of PP under different pressure conditions.

Table 2.

Contact forces under different operating conditions corresponding table.

Working pressure (MPa)	10	15	20	25	30	35
Average contact force (N)	985	1971	1479	2464	2957	3450

2.4. Test method for friction and wear

The wear test of the friction pair was carried out by MMD-5A standard end friction and wear testing machine, as shown in Fig. 4. Specimen mounting device is composed of a main shaft, a lower column, a medium groove, etc. The upper specimen is mounted on the spindle through the tooling and rotated at a fixed speed under computer control. The lower specimen is fixed on the lower column, and the hydraulic pump supplies the system oil. Driven by a servo hydraulic cylinder, the specimen moves vertically up along the main shaft and provides the experimental setting load. The test piece is in a medium tank containing 46# anti-wear hydraulic oil to achieve hydraulic oil immersion lubrication. The medium groove is made of plexiglass material, and its strength and heating capacity can meet the experimental requirements, and it is installed on the lower column. Pour in 46 # anti-wear hydraulic oil before the experiment to submerge the specimen. The real-time friction coefficient of the friction specimen can be obtained by calculating the measurement data of the tension sensor, and the friction-time curve and temperature-time curve of each friction specimen can be obtained. The temperature sensor is installed on the bottom surface of the lower specimen to reflect the temperature of the friction surface in real-time.

Fig. 4.

MMD-5A standard end friction and wear testing machine.

According to product parameters of heavy-duty APP, the lower specimen is piston material 38CrMoAl advanced nitriding steel. After tempering and nitriding treatment, the material has good wear resistance, strength, and fatigue strength. The upper specimen is ZCuPb15Sn8, a cylinder block piston sleeve material, which is made by metal casting. It has high hardness good, yield strength, and tensile strength. The chemical composition of 38CrMoAl and ZCuPb15Sn8 material are listed in Table 3. The mechanical properties of 38CrMoAl and ZCuPb15Sn8 material are shown in Table 4.

Table 3.

Main chemical composition table.

Material composition	C	Si	Mn	S	Mo	Cr	Al	Cu	Ag	Zn	Fe	Sn	Pb
38CrMoAl	0.35-0.42	0.20-0.45	0.30-0.60	residual content≤0.35	0.15-0.25	0.135	0.7-0.75	–	–	–	–	–	–
ZCuPb15Sn8	–	–	–	0.0009	–	–	–	other	0.001	≤0.02	0.008	0.07-0.09	0.13-0.17

Table 4.

Mechanical properties table.

Mechanical parameter	Yield strength (MPa)	Tensile strength (MPa)	Elongation (%)	Hardness (HB)	Density (kg/m3)
38CrMoAl	≥835	≥980	≥14	908–1028	7850
ZCuPb15Sn8	≥100	≥200	≥6	≥635	8900

The procedure for the friction and wear test is illustrated in Fig. 5. Before the test, specimens were continuously cleaned by an ultrasonic cleaning instrument for 40 min to remove surface debris of the friction specimen and broken particles left by sandpaper polishing. Following cleaning, the test component was weighed five times using an electronic balance. The accuracy of the electronic balance is 0.00001 g. The average of these measurements represented the pre-test weight. Olympus laser confocal electron microscope was employed to inspect the surface shape and surface roughness of the test piece before the test. MMD-5A was used for friction and wear experiments under different pressure, speed, and time. The experiment duration was 2 h under different pressure conditions and 3 h under different speed conditions. The friction specimen was subjected to friction and wear in 46 # anti-wear hydraulic oil, and the friction and wear test was carried out after the applied load and rotational speed were input on the industrial computer. After the friction and wear test is completed, the test piece is cleaned and weighed again, and the weight of the test piece before and after wear is compared to obtain the wear amount, and the change of surface morphology and roughness of the test piece before and after wear is measured. Difference in the wear mechanism of test parts under varying pressure and speed conditions is obtained.

Fig. 5.

Friction and wear test flowchart.

3. Experimental results

3.1. Experimental results under different speed conditions

In order to explore the wear conditions at different rotational speeds, the loading force of the friction and wear testing machine was set at 150 N, and the upper and lower specimens were worn for 3 h under the working conditions of 1000, 1800, and 2300 r/min respectively. The results of friction surface temperature, surface topography, wear amount, and surface roughness before and after wear of the test pieces were obtained.

• •Surface topography analysis of test parts

In order to analyze the surface topography of the specimen before and after wear under different speed conditions, the specimen were grouped and numbered as shown in Table 5, and the surface topography of each group was observed using QLS3100 electron microscope.

Table 5.

Specimens group under different speed conditions.

Number	Specimens group
a	Original upper specimen
b	the upper specimen after wear at 1000 r/min
c	the upper specimen after wear at 1800 r/min
d	the upper specimen after wearing at 2300 r/min
e	Original lower specimen
f	the lower specimen after wear at 1000 r/min
g	the lower specimen after wear at 1800 r/min
h	the lower specimen after wearing at 2300 r/min

Fig. 6 depicts the two-dimensional morphology of the test specimen before and after wear under different rotational speeds. Fig. 6(a–d) shows the wear diagram of the copper sleeve material of the upper specimen cylinder block. The original morphology is relatively flat, the processing marks are uniform, and the roughness is low (Fig. 6a). Fig. 6(b–d) show the surface morphology after wear of the upper specimen. At 1000 r/min, the grooves are shallow and uniform, and the friction scratches are evenly distributed, which corresponds to the situation of low and stable friction coefficient. Most of the troughs are filled and the processing marks remain more (Fig. 6b). Under the working condition of 1800 r/min, the surface crest was basically worn down, some shallow troughs were also worn down, and some deep grooves appeared. The friction marks on the surface were chaotic and the wear was serious (Fig. 6c). At 2300 r/min operating speed, the specimen exhibited extensive wear with uneven surface wear depth, resulting in scratches, grooves, and numerous small-diameter spots of spalling, accompanied by partial oxidation and adhesive wear marks (Fig. 6d). The above phenomena indicate insufficient support from the oil film on the friction surface. Certain areas are in boundary lubrication conditions. Significant noise accompanies the wear process. As the rotational speed increases, the grooves and scratches resulting from friction and wear on the specimen become more pronounced. The wear forms of specimens under different speed conditions are abrasive wear and mixed friction.

Fig. 6.

Two-dimensional morphology of test parts before and after wear under different speed conditions a) Original morphology of the upper specimen b) The morphology of the upper specimen after wear at 1000 r/min c) The morphology of the upper specimen after wear at 1800 r/min d) The morphology of the upper specimen after wearing at 2300 r/min e) Original morphology of the lower specimen f) The morphology of the lower specimen after wear at 1000 r/min g) The morphology of the lower specimen after wear at 1800r/min h) The morphology of the lower specimen after wear at 2300 r/min.

Fig. 6(e–h) shows the wear diagram of the piston material in the lower specimen. The machining marks on the lower specimen before wear are observed to be fairly consistent (Fig. 6e). The friction marks of the specimen under 1000 r/min condition are relatively flat as a whole, some shallow grooves appear, most of the wave peaks are worn out, and the degree of friction and wear is slight (Fig. 6f). There are many grooves on the surface of the specimen at 1800 r/min speed, and the whole is smooth (Fig. 6g). The friction mode at this speed is mixed friction. The surface of the specimen at 2300 r/min speed has some deep pits and obvious friction grooves, and the surface is more flat than that at other speed conditions (Fig. 6h). At the same time, the adhesive part of the specimen is brass debris.

• •Friction surface temperature analysis

Fig. 7 illustrates the variation in friction surface temperature of the test specimen over time at different rotational speeds. As wear time increases, the surface friction temperature continues to elevate. At 1800 and 2300 r/min, the temperature rises sharply. This is due to the high friction coefficient between the test pieces at high speeds, resulting in fast heat production.

• •Analysis of specimen wear

Fig. 7.

Temperature change curve of friction surface under different speed conditions.

When subjected to a load of 150 N and worn for 3 h under varying speed conditions, the variation curve of the wear amount of the test piece with speed is depicted in Fig. 8. It is evident that the wear on the test piece rises as speed increases, with the wear amount on the upper specimen being greater than that on the lower specimen. This is because the piston sleeve material of the upper specimen is soft and more prone to material loss. Among the speeds tested, the specimen wear at 2300 r/min is the highest, amounting to 0.013 g. As the speed increases, the relative linear speed between the test pieces also increases, resulting in more severe wear conditions. As a result, the micro-protrusions on the friction surface become more susceptible to wear.

• •Surface roughness analysis of specimen before and after wear

Fig. 8.

Wear the amount of specimens under various rotational speeds.

To thoroughly examine the friction and wear on the specimen surface, the change of friction surface roughness Ra was quantitatively analyzed by OLS3100 laser confocal electron microscope. The Ra calculation expression is shown in Equation (8). The surface roughness of the test piece photographed by confocal electron microscope is shown in Fig. 9. Seven measurement lines are uniformly selected from the photographed surface to extract roughness. The average value of the linear roughness is taken as the surface roughness value of the specimen. This approach ensures the accuracy and scientific validity of the roughness measurement.

$$R_a=\frac{1}{l_6}{\int }_0^{l_6}\left|y\left(x\right)\right|\mathrm{d}x$$ (8)

where 1 is the sampling length, R_a is the arithmetic average deviation of surface profile deviation, and y(x) is the deviation of surface profile.

Fig. 9.

Roughness measurement diagram.

Fig. 10a displays the roughness of the upper specimen under various speed conditions. The roughness before wear is stable between 0.29 and 0.32. With the increase of friction and wear speed, the roughness after wear gradually decreases, and the surface roughness under the 2300 r/min speed condition decreases the most, reaching 0.125 μm.

Fig. 10.

Comparison of surface roughness before and after wear of specimen under different speed conditions a) Upper specimen b) Lower specimen.

Fig. 10b illustrates the roughness of the lower specimen across different speed conditions. The roughness changes before and after wear are minimal due to the composition of relatively hard piston material. Under the rotational speed of 1800 r/min, the surface roughness shows the highest increase, measuring 0.03 μm. Under various rotational speed conditions, the specimen exhibits abrasive wear characterized by abrasive particles. Debris generated from the wear of the upper specimen material adheres to the lower specimen, forming irregular pits and protrusions. The peaks of the lower specimen continuously rub against the upper specimen, intensifying the friction of the wearing pair. This severe friction exacerbates the wear of the softer upper specimen.

3.2. Experimental results under different pressure conditions

The friction and wear testing machine, operating at 500 rpm, was used to investigate the wear behavior of the tribological pair under various loading conditions. The wear tests were conducted for 2 h under applied loads of 200, 600, 1000, and 1400 N, respectively. Dynamic analysis was used to determine the contact force patterns of the piston. The experimental loading forces corresponding to the working pressures of the APP were 2.06, 6.18, 10.29, and 14.41 MPa, respectively. The results of friction surface temperature, surface topography, wear amount, and surface roughness before and after wear of the test part were obtained.

• •Surface morphology analysis

In order to analyze the surface topography of the specimen before and after wear under different pressure conditions, the specimen were grouped and numbered as shown in Table 6, and the surface topography of each group was observed using QLS3100 electron microscope.

Table 6.

Specimens group under different pressure conditions.

Number	Specimens group
a	The upper specimens experienced a loading force of 200 N
b	The upper specimens experienced a loading force of 600 N
c	The upper specimens experienced a loading force of 1000 N
d	The upper specimens experienced a loading force of 1400 N
e	The lower specimens experienced a loading force of 200 N
f	The lower specimens experienced a loading force of 600 N
g	The lower specimens experienced a loading force of 1000 N
h	The lower specimens experienced a loading force of 1400 N

Fig. 11 illustrates the two-dimensional shape of the test specimen following wear under varying load conditions. The original morphology is relatively flat as a whole and the processing marks are uniform (Fig. 6). Fig. 11a-d depicts the shape of the upper specimen after 2 h of wear under loads of 200, 600, 1000, and 1400 N. Under 200 N condition, the overall wear degree is relatively light, and more small parts of the upper specimen are worn off, resulting in more spot spalling. The initial machining marks on the wear surface are obvious, the friction and wear marks are relatively chaotic, and slight plastic deformation occurs, forming a shallow groove with a longer length and a narrower width in the same direction as the rotation of the specimen (Fig. 11a). Under a load of 600 N, the friction surface of the upper specimen exhibited significant delamination of the metal layers. The wear marks were relatively uniform, accompanied by black oxide traces produced by high-temperature oxidation (Fig. 11b). Under the condition of 1000 N, oil and air oxidized, large oxidation marks were produced on the specimen surface, and the grooves were wide and deep, resulting in severe oxidative wear and adhesive wear (Fig. 11c). During the friction process of the specimen under 1400 N condition, large plastic deformation occurs, accompanied by large black friction marks, the metal layer is peeled off, and the degree of friction and wear is severe (Fig. 11d). Because the specimen is oxidized at high temperature, there are large oxidation traces on the whole, forming different forms of oxides. At this time, the flaky grinding chips are reddish-brown, while the filamentary grinding chips are grayish-black. Therefore, with the increase of load, adhesion will occur on some worn surfaces, forming pits, and the plastic deformation of the specimen surface will increase, while the adhesive wear will be aggravated.

Fig. 11.

2D wear morphologies of test parts after wear under different loading conditions. The upper specimens: a) 200 N loading force b) 600 N loading force c) 1000 N loading force d) 1400 N loading force. The lower specimens: e) 200 N loading force f) 600 N loading force g) 1000 N loading force h) 1400 N loading force.

During the sliding wear process between test specimens, abrasive dust accumulates and compacts in the hotspot areas of the friction surface. A friction transfer layer is formed, enhancing the shear force of the abrasive particles. This ultimately leads to the work hardening of the metal surface. The experimental results confirm that the contact area of the PP is affected by thermal extrusion deformation, abrasive particles, and frictional heat.

The surface morphology of the lower specimen after 2 h wear under different loads is shown in Fig. 11(e–h). Because the 200 N loading force is small and the lubrication between the specimens is sufficient, the surface scratches and grooves of the specimens are shallow and the metal is less spalling (Fig. 11e). The specimen under 600 N condition has plastic deformation pits, and the depth of grooves is larger than that under 200 N condition. The reason for this phenomenon is that the surface of the upper specimen in this working condition is seriously bruised (Fig. 11f). Under the action of transverse shear force and longitudinal load, the surface of the friction pair produces cutting and extrusion effects. The whole specimen under 1000 N condition is smooth and flat. Under this condition, some wear marks and micro-spikes produced by low loading force are re-worn, and adhesion of brass particles appears, accompanied by severe oxidative wear and adhesion wear marks (Fig. 11g). Due to the softer material of the upper specimen, the surface of the lower specimen exhibits stronger adhesion to the brass of the upper specimen under a load of 1400 N. Under these conditions, a significant portion of the specimen material adheres to the contact surface (Fig. 11h).

• •Friction surface temperature analysis

Fig. 12 illustrates the temperature curve of the friction surface under different loading forces. The temperature of the friction surface continuously increases with wear time, eventually stabilizing at a constant value. Under applied loads of 1000 and 1400 N, the friction surface heats up more rapidly due to the higher friction coefficient and frictional force under high pressure, resulting in faster heat generation. At a load of 1400 N, the final temperature of the friction surface exceeds 100 °C.

• •Analysis of specimen wear

Fig. 12.

Temperature curve of friction surface under different loading forces.

After 2 h wear at 500 r/min and under different loading forces, the change curve of the wear amount of the test piece with the loading force is shown in Fig. 13. The wear of the test specimens increases gradually with the applied load. The wear of the upper specimen is greater than that of the lower specimen. This is because the upper test piece is a piston sleeve material with soft performance and easy to fall off after friction. At an applied load of 1400 N, the wear of the test specimens is at its maximum. The upper specimen exhibits a wear amount of 0.0062 g, while the lower specimen shows a wear amount of 0.0016 g.

• •Surface roughness analysis of specimen before and after wear

Fig. 13.

Specimen wear under different loading conditions.

Fig. 14a depicts the comparison of the roughness of the upper specimen before and after wear under various loading conditions. Due to the softer nature of the upper specimen, the peaks are worn down, and the valleys are filled during the wear process. Consequently, the roughness of the upper specimen decreases after wear. Under the loading condition of 1400 N, the surface roughness decreases the most, reaching 0.11 μm. Fig. 14b presents the comparison of the roughness of the lower specimen before and after wear under different loading conditions a comparison of the roughness of the lower specimen before and after wear across various loading conditions. As the lower specimen grinds the upper specimen, coiled abrasive chips are generated, and the shape of the abrasive chips is extremely irregular. Therefore, the roughness of the lower specimen tends to increase. The surface roughness of the specimen under 1000 N loading condition increases the most, reaching 0.11 μm.

Fig. 14.

Comparison of surface roughness before and after wear of specimen under different loading conditions a) Upper specimen b) Lower specimen.

4. Volumetric efficiency

As a crucial metric for assessing APP performance, volumetric efficiency gradually deteriorates with increasing operational time. When the volumetric efficiency is below the threshold, the APP is considered to be invalid. Based on the friction and wear test and the contact wear theory, the corresponding relationship between contact wear and geometric loss of the PP under different operating conditions has been derived in this section. This study assumes that the oil film leakage in the FDP and SP remains stable under self-compensation conditions. The impact of cumulative wear on PP leakage and APP volumetric efficiency is investigated.

Through dynamic analysis, it was found that the contact force between the piston and the cylinder bore varies periodically. The contact force in the oil discharge region is relatively high, reaching several thousand newtons, while the contact force in the oil suction region is approximately zero. Therefore, the operating time of the APP is twice that of the wear time in the PP.

4.1. Friction pair wear theory

The actual wear is affected by working conditions, environmental factors, medium factors, lubrication conditions, and material characteristics. The wear can be divided into the running-in stage, stable wear stage, and intense wear stage. In practical engineering applications, the service life and wear performance depends on the steady-state wear stage of the friction pair. The wear performance is primarily evaluated based on the wear rate of the material, defined as shown in Equation (9). The wear rate reflects the amount of material worn per unit load and unit sliding distance. When the wear mechanism remains unchanged, the material wear rate remains constant.

$$W=\frac{\Delta m}{s\rho F_N}$$ (9)

where W denotes material wear rate, Δm represents wear amount, s stands for wear stroke, ρ denotes material density, and F_N represents positive force between specimens.

4.2. The corresponding relationship between the wear amount of the specimen and the wear amount of PP

From Equation (9), it can be observed that, under constant frictional contact force, the wear amount is directly proportional to the sliding distance of frictional wear. It is essential to derive the quantitative relationship between the test PP and the actual wear distance, establishing how the wear amount of the PP changes over time. Considering that the piston material in the PP is harder than the cylinder bore material and the piston is replaceable, the focus of the study is on investigating the wear amount of the cylinder bore material.

The contact force of the PP in the absence of an oil film is determined via dynamic analysis. The structural characteristics of the studied APP are the same as those in the literature0. The contact area and deformation of the PP under oil film conditions were referenced. Ultimately, the total contact force of the PP was obtained.

This study disregards changes in contact area caused by elastic deformation, thus ensuring a consistent contact area between the piston and the cylinder bore under different operating conditions. The wear pattern of the PP exhibits periodic variations. The operating speed is 2200 r/min. Table 7 illustrates the evolution of PP wear over 2 h.

Table 7.

Piston sub-wear table.

Wear time: 2 h
Wear parameter	Test speed (r/min)	Test line speed (m/s)	Test wear stroke (mm)	Actual speed (r/min)	Actual piston travel (mm)
Number	500	0.7	5047911	2200	462000

4.3. Wear amount and wear depth

Based on the frictional wear test results of the PP material under different operating conditions, the relationship between PP wear (cylinder bore wear) and APP operating time is deduced, as shown in Equation (10). Combined with the cylinder bore density (8900 kg/m³), the relationship between cylinder bore wear and time at 2200 rpm is determined.

$$V_w=k_{w}t\times {10}^{-2}$$ (10)

where V_w denotes the wear volume of the cylinder hole, k_w represents the wear coefficient, and the corresponding relationship between different pressures and the wear coefficient is shown in Table 8, and t is the time.

Table 8.

Working pressure and wear coefficient corresponding table.

Working condition	10 MPa	15 MPa	20 MPa	25 MPa	30 MPa	35 MPa
Coefficient	1.106	1.67	2.313	2.571	3.341	3.85

According to the structure and wear characteristics, it can be seen that the worn shape formed by the hole wall of the piston wear cylinder is a chamfered prism structure, which is surrounded by two arcs and is approximately elliptical. Therefore, the cylinder bore wear volume is calculated as shown in Equation (11).

$$V=\frac{\mathrm{\pi }{h}_2{b}_1}{2}\times a_1+\frac{\mathrm{\pi }{h}_2{b}_2}{2}\times a_2=133h_2$$ (11)

In the equation, b₁ and b₂ are the length of the long axis and short axis of the ellipse, a₁ and a₂ are the wear axial length of the two ends, and h₂ is the maximum wear depth of the cylinder block.

4.4. Change the rule of leakage of PP

By bringing Equation (11) into Equation (1), the correlation between PP leakage and elapsed time can be established. The average value of the retaining cylinder length of the piston is the minimum value of 53.24 mm and the maximum value of 84.98 mm. Simultaneously, the leakage varies with the dynamic viscosity of the oil. The expression for the oil under different pressures is given by Equation (12).

$${\mu }_i={\mu }_0{e}^{\alpha \Delta p_i}$$ (12)

where μ_i is the oil viscosity under different pressures, μ₀ denotes the initial dynamic viscosity of the oil, α represents the change coefficient of the dynamic viscosity, and ΔP_i denotes the oil pressure.

Substituting the expressions for oil viscosity and PP wear depth over time into PP leakage expression (Equation (1)), the relationship between PP leakage and time under different pressures at 2200 rpm cylinder speed is obtained, as depicted in Fig. 15.

Fig. 15.

Piston leakage curve with working time.

As the operating time of the APP increases, the leakage of the PP continuously rises. Moreover, with increasing operating pressure, the leakage of the PP increases even more significantly. In the initial stages of operation, within 251.5 h without pressure, the leakage of the PP is less than 3 L/min.

4.5. Volumetric efficiency variation

Besides the leakage from the PP, there are also leaks from the spherical FDPs and SPs. The design of FDPs and SPs of the APP in this study is based on the residual compression force method. The clearance value can be compensated for wear during operation, so the leakage amount changes little.

Based on the structural parameters of the APP and the method for calculating the spherical oil film thickness, the thickness of the spherical FDP central oil film is 10.5 μm. Equation (13) shows the calculation expression for the volumetric efficiency of the APP. At the rated speed of 2200 r/min, the APP has a theoretical flow rate of 319 L/min.

$$\eta =1-\frac{Q_2+Q_3+Q_4}{Q_6}\times 100\%$$ (13)

where η denotes the volumetric efficiency, Q₂ represents the leakage of the spherical FDP, Q₃ represents the leakage of the PP, Q₄ represents the leakage of the SP, and Q₆ represents the theoretical flow of the APP.

From Equation (13), it can be deduced that the volumetric efficiency of the APP varies over time under different operating pressures at a speed of 2200 rpm, as illustrated in Fig. 16. It can be inferred that the volumetric efficiency of the APP decreases progressively with increasing operating time, and higher working pressures exacerbate this decline in volumetric efficiency. The volumetric efficiency of the APP under all pressure conditions decreased by more than 4 % in the first 251.5 h. According to the results of volumetric efficiency degradation, the failure life of the PP and the whole pump can be predicted under different discharge pressure conditions.

Fig. 16.

Change curve of volumetric efficiency of APP over time.

4.6. Leakage of APP and volumetric efficiency test

To validate the accuracy of the theoretical analysis, the volumetric efficiency of the APP was measured under various operating conditions using an APP test bench for comparison and verification. Fig. 17 depicts the 200 W hydraulic pump and motor comprehensive test bench, where the test system is loaded via the overflow valve.

Fig. 17.

200 kW pump motor integrated test bed.

Firstly, the no-load displacement of the APP was tested and verified. The measured no-load displacement was 143.96 ml/r, and the error compared with the theoretical displacement was only 0.72 %, which verified the accuracy of the test. The volumetric efficiency testing was conducted on the 200 kW hydraulic pump and motor comprehensive test bench. Based on the leakage and operational flow, the leakage and volumetric efficiency after 251.5 h of testing under various operating pressures at 2200 rpm were obtained and compared with the theoretical analysis results, depicted in Fig. 18. The small difference between the theoretical analysis and experimental results confirms the validity of the theoretical analysis.

Fig. 18.

Leakage and volumetric efficiency test comparison curve.

5. Conclusion

The leakage model for the SP, PP, and FDP of the APP was investigated and developed. The contact force results of the PP during movement were obtained through dynamic simulation analysis. Friction and wear experiments were conducted on the PP material using an end-face wear testing machine under various combinations of rotational speeds and pressures. The following conclusions are obtained.

• (1)The fluctuation of the contact force of the PP during the operation of the APP is determined. Simulation results indicate that the contact force of the PP varies periodically with the formation of alternating oil suction and discharge zones.
• (2)Based on the friction and wear characteristics of the PP material at various speeds, the correlation between wear volume and speed is determined. The results indicate that the coefficient of friction and the wear volume of the specimens increases with rotational speed, the specimen wear at 2300 r/min is the highest, the upper specimen is 0.013 g, and the lower specimen is 0.007 g. The surface roughness of the upper specimen (ZcuPb15Sn8) decreases with increasing rotational speed, the surface roughness under the 2300 r/min speed condition decreases the most, measuring 0.125 μm. Conversely, the surface roughness of the lower specimen (38CrMoAl) increases with increasing rotational speed, the rotational speed of 1800 r/min, the surface roughness shows the highest increase, measuring 0.03 μm. The wear forms under different speed conditions are abrasive wear and mixed friction, accompanied by a small part of adhesive wear and oxidation wear.
• (3)Friction and wear properties of the PP material were investigated under various loading conditions. The correlation between wear volume and applied load was established. The results indicate that the coefficient of friction and wear volume of the specimens increase with the applied load. At an applied load of 1400 N, the wear of the test specimens is at its maximum, the upper specimen is 0.0062 g, and the lower specimen is 0.0016 g. The surface roughness of the upper specimen decreases with increasing applied load, under the loading condition of 1400 N, the surface roughness decreases the most, reaching 0.11 μm, whereas the surface roughness of the lower specimen increases with increasing applied load, the surface roughness of the specimen under 1000 N loading condition increases the most, reaching 0.11 μm. The wear forms under different loading conditions are adhesive wear and abrasive wear.
• (4)Using the experimental friction and wear data, the relationship between PP wear, PP leakage, and the decline in APP volumetric efficiency is established. The greater the operating pressure of the APP, the larger the increase in leakage of the PP over time, the maximum leakage rate exceeds 45 L/min. The volumetric efficiency decreases with PP wear, exhibiting a decay pattern similar to a quadratic function. As the operating pressure increases, the decrease in APP volumetric efficiency intensifies. At its most severe, the volumetric efficiency is less than 85 %.

Funding statement

This work was funded by the National Key Research and Development Program of China (No.2023YFB3406701).

Data availability

Data will be made available on request.

Additional information

No additional information is available for this paper.

CRediT authorship contribution statement

Wenlong Yin: Writing – original draft, Methodology, Data curation, Conceptualization. Jin Zhang: Writing – review & editing, Supervision, Funding acquisition, Conceptualization. Xu Wang: Visualization, Investigation, Formal analysis. Qiyao Zhang: Resources, Investigation. Ying Li: Data curation, Conceptualization.

Declaration of competing interest

The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper.