Analysis of pressure pulsation mechanism and dynamic characteristics of axial piston pump

ZHAO Baojian, GU Lichen, LIU Jiamin, GENG Baolong, SHI Yuan, WU Haoyu, YANG Sha

(School of Mechatronic Engineering， Xi’an University of Architecture and Technology, Xi’an 710055, China)

Abstract： The pressure pulsation of axial piston pump is not only an important cause of rotation speed fluctuation, vibration noise and output stability of the hydraulic system, but also the main information source for obtaining fault information. Hydraulic system is characterized by strong noise interference, which leads to low signal-to-noise ratio (SNR) of detection signals. Therefore, it is necessary to dig deep into the system operating state information carried by pressure signals. Firstly, based on flow loss mechanism of the plunger pump, the mapping relationship between flow pulsation and pressure pulsation is analyzed. After that, the pressure signal is filtered and reconstructed based on standard Gabor transform. Finally, according to the time-domain waveform morphology of pressure signal, four characteristic indicators are proposed to analyze the characteristics of pressure fluctuations under different working conditions. The experimental results show that the standard Gabor transform can accurately extract high-order harmonics and phase frequencies of the signal. The reconstructed time-domain waveform of pressure pulsation of the axial piston pump contains a wealth of operating status information, and the characteristics of pulsation changes under various working conditions can provide a new theoretical basis and a method support for fault diagnosis and health assessment of hydraulic pumps, motors and key components.

Key words： axial piston pump； pressure pulsation； standard Gabor transform； appearance characteristics； operating conditions

0 Introduction

The axial piston pump has the characteristics of compact structure, high power density and high volumetric efficiency. It is the most important component in hydraulic equipment[1]. Due to the special structure of the axial piston pump itself, oil backflow and impact occur during the working process, and its output flow and pressure are cyclically pulsating. The high-frequency pressure pulsation of system will cause pipes and shell vibrations, which increases the noise of axial piston pump, reduces working quality and overall performance of the plunger pump, and even causes the damage to the pump. The pressure pulsation signal of pump results from of dynamic coupling of the multi-energy domain of the hydraulic system. It is an important information source for system operation status monitoring because it carries dynamic operating information of the equipment. The pressure pulsation signal can be used as one of the information sources for pump fault diagnosis[2-4]. The revelation of the characteristics of pressure pulsation mechanism in the normal working condition of hydraulic pump is a necessary condition for the follow-up condition monitoring and fault analysis. Yan et al.[5]used the ITI-SimulationX software package to establish a simulation model of variable displacement and variable speed pumps, so as to predict pressure pulsation under different working conditions. Ma et al.[6]analyzed the hysteresis characteristics of the reciprocating multi-phase pump suction and discharge valve under different working conditions, and further studied the influence of the hysteresis angle on pressure pulsation of the pump. Bergada et al.[7]put forward a new flow pulsation calculation model by analyzing the leakage of the plunger pump to analyze the general pressure/flow fluctuation characteristics of the pump. Liu et al.[8]used fluid dynamic simulation software CFX to numerically simulate the internal flow field of a high-speed centrifugal pump, and analyzed the pressure fluctuation characteristics under different flow rates. Sun[9]obtained the pressure pulsation characteristics at different monitoring points on the back of the axial flow pump by calculating the non-constant value of the axial flow pump. Wang et al.[10]studied the pressure pulsation characteristics of centrifugal pumps by numerical simulation turbulence model, and obtained the pressure pulsation characteristic curves of each calculation domain through non-dimensional data processing. Based on AMEsim software, Yan et al.[11]studied the pulsation characteristics and noise of variable speed and variable displacement dual-control axial piston pumps. Gu et al.[12]proposed a stochastic dynamic expression to simulate the stochastic dynamic characteristics of pressure fluctuations in the piston pump piping system. Qian et al.[2]proposed a feature extraction method based on variational modal decomposition (VMD), which accurately extracts the pressure beat vibration component from the pressure frequency domain signal of high-pressure oil circuit of hydraulic system. At present, research on the pressure pulsation dynamic characteristics of axial piston pump only consideres the amplitude of fundamental frequency of pressure pulsation signal while the energy and phase information of pressure pulsation signal has not been studied in detail.

This study takes pressure signal as monitoring object. According to flow loss mechanism of internal friction pair of plunger pump, pressure pulsation is traced to the source. Based on standard Gabor transform, pressure signal is analyzed on time-frequency. Based on principle of inaction, main characteristic components are accurately reconstructed. From the time-domain waveform characteristics, the pressure fluctuation characteristics under different working conditions are analyzed, which provides a new theoretical basis and a method for fault diagnosis of plunger pump.

1 Causes of flow pulsation

The plunger pump has a phenomenon of backflow as well as a phenomenon of oscillation caused by oil impact, which are the main causes of flow pulsation of elastic fluid. The flow pulsation caused by backflow and leakage of fluid is the most important form of pump pressure pulsation. Therefore, before analyzing the dynamic characteristics of pressure pulsation under different working conditions, pressure pulsation needs to be traced from the flow leakage mechanism.

The fluid inside the axial piston pump leaks in three friction pairs： leakage of port pairQgp, gap leakage of slipper pairQxh, and gap leakage between cylinder block and plunger pairQgz. Gu et al.[13]revealed the flow and pressure pulsation mechanism of piston equipment according to variation law of internal leakage and flow shock with operating parameters.

1.1 Flow leakage between plate and cylinder

There is leakage and pressure distribution between the plate and the cylinder. The distribution is used to determine the integral of the lubrication Reynolds number equation in polar coordinates. Assuming that flow field is laminar, oil is incompressible, and oil moves radially[9], the leakage of the valve plate is expressed as

(1)

whereαais the angle of valve plate groove;δLis the leakage gap between cylinder block and valve plate;μis the hydrodynamic viscosity;pzis the pressure in high pressure chamber;phis the pressure in low pressure chamber;r1is the outer diameter of inner seal;r2is the inner diameter of inner seal;r3is the inner diameter of outer seal; andr4is the outer diameter of outer seal.

Fig.1 Structural size of port plate

According to Eq.(1), leakage of the valve plate depends on the difference between high pressure and low pressure, geometry, leakage gap and groove angle of valve plate. Meanwhile, the timing leakage caused by triangular groove should also be considered. However, the analysis by Bergada[7]. shows that the leakage at triangular groove can be neglected compared with that of main groove.

1.2 Flow leakage between swash plate and slipper

The leakage flow of the plunger flows out through the center hole of the piston, the center hole of the slide block, and the gap between the slide block section and the swash plate. The static pressure support is formed. Assuming that the speed of slipper relative to that of swash plate is ignored and there is no gap leakage between the piston head and the groove, according to laminar flow theory between the gaps of parallel discs[10], the leakage equation of the swash plate-slide shoe can be expressed as

(2)

whereμis the hydrodynamic viscosity;δxhis the thickness of oil film between the shoe and the swash plate；R1is the inner diameter of slipper seal oil belt；R2is the outer diameter of slipper seal oil belt；dis the diameter of the orifice in piston； andlis the length of the orifice in plunger.

It can be seen from Eq.(2) that the leakage between the shoe and the swash plate is related toR1,R2,dandl.

1.3 Flow leakage between piston and cylinder [11]

During the rotation of the cylinder, the piston is subjected to centrifugal force. There is flow leakage between the cylinder and the piston, which is mainly caused by centrifugal force. Due to the centrifugal force, the piston is pressed tightly on one side of the cylinder. The eccentric ring gap is formed. Under the action of internal and external pressures, the pump makes a pressure difference flow in the gap. At the same time, due to the relative movement of the piston and the cylinder, Carter flow appears in the oil in the gap. The size of Carter flow is related to the axial velocity of the piston, and the flow direction is opposite to the flow direction of the pressure flow difference. Therefore, under the combined action of the differential pressure flow and the Carter flow, the leakage between the piston and the cylinder is expressed as

(3)

whereδgzis oil film gap between the plunger and the cylinder;εis piston eccentricit;μis hydrodynamic viscosity;d1is piston diameter; andvis piston speed.

1.4 Compression loss of axial piston pump

In the transition process of high and low pressures of piston pump, compressibility of the oil causes piston pump to lose part of its volume[12]. There are oil trapped volume loss and compression volume loss[13]. Compression volume loss is mainly composed of backflow and return flow. The valve plate has an oil suction area and an oil discharge area. There is a pressure difference between the piston cavity and the oil suction area, and there is a pressure difference between the piston cavity and the oil discharge area. Due to these two pressure differences, the piston cavity cannot completely absorb and discharge oil, and oil trapping occurs. The flow loss caused by trapped oil and compression is calculated by

(4)

whereVdzis the volume of a single piston cavity; andEis the elastic modulus of oil volume.

1.5 Equilibrium equation of flow

Thekth piston moves in the cylinder block, and its instantaneous volume is calculated by

(5)

whereVkis the instantaneous volume of each piston;Rpois the piston pith radius;θis the instantaneous angular position;ε1is the angle of swash plate; andzis the number of pistons.

According to Eq.(5), it can be obtained thatVkis a periodic function ofθ.Then, the theoretical instantaneous flow of thekth piston is got as

(6)

whereωis the angular velocity.

In order to study the influence of 7 pistons on the overall pump dynamics, the output flows of all pistons in the high-pressure chamber at any time are combined, then we obtain

(7)

whereVvpis the volume of the pipeline between the throttle valve and the pump;Eis elastic modulus of oil volume; ∑Qkis outlet flow of the pump;Qoutis the flow through throttle valve;Cis the flow coefficient;Ais the discharge area of plunger cavity;ρis oil density; and theppis the pressure in the plunger chamber.

Since the instantaneous angle of the piston is related to angular velocity, that is,θ=ωt, Eq.(7) can be rewritten as

(8)

Eq.(8) is the flow pressure coupling equation of plunger pump, which describes the mapping relationship between the flow and the pressure pulsation and provides a theoretical basis for the traceability of pressure pulsation. At the same time, it can be inferred from Eq.(8) that the pressure pulsation is related to not only the structure of plunger pump, but also the leakage of each movement pair of plunger pump. As a result, the changes of characteristics in pressure pulsation occur, including changes in pulsation amplitude and phase. The pressure pulsation contains information about the operating status of plunger pump. Therefore, by mining this information, the characteristics of the pressure pulsation can be studied and the system health status can be initially judged.

2 Pressure signal extraction based on standard Gabor transform[18]

2.1 Standard Gabor transform

Supposing that a time signal isf(t)∈C, its linear time-frequency transform can be expressed as

(9)

(10)

where i is an imaginary unit, and∧is the Fourier transform operator.

If the Fourier transform of the time-frequency transform kernel of Eq.(10) satisfies Eq.(11), the linear time-frequency transform is defined as the normal time-frequency transform (NTFT), that is,

(11)

where |·| is the modulus operation.

The typical kernel function expression of NTFT is

(12)

(13)

whereσ>0 is the window width. Thus, the kernel function expression of NTFT corresponding to standard Gabor transform is

(14)

After the signal passes through NTFT, according to the result of time-frequency analysis, the interested component information is extracted and the transform from frequency domain to time domain is completed, which is the inverse transform of NTFT, and is also the basis of time-frequency filtering.

2.2 Inaction principle

Inaction principle is to extract automatically displayed harmonic signal from its standard time-frequency transform spectrum without inverse transform process. The proof process is as follows.

Let the harmonic signal whose frequency or amplitude fluctuates slightly over time be

h(t)=Aexp[i(βt+φ)],

(15)

whereAis the amplitude;βis the frequency;φis the initial phase;βt+φis the instantaneous phase. When NTFT is applied to this signal, there are some properties expressed as

(16)

ψh(τ,β)=h(τ)=Aexp[i(βt+φ)],∀τ∈R.

(17)

The proof process is as follows:

Lett-τ=x, then we get

(18)

3 Experimental platform and working principle

The test platform consists of hydraulic system, electrical system and control system. The schematic diagram is shown in Fig.2.

The asynchronous motor 2 drives the piston pump 6 (main pump) to rotate, and then the high pressure oil output directly enters the piston motor 14 (variable motor), which makes the piston motor rotate to work and then drive the load to work. The power source is composed of frequency converter 1 and asynchronous motor 2. Based on the LabVIEW measurement and control system, the frequency conversion speed regulation of the asynchronous motor 2 is realized by changing the control voltage of frequency converter 1. The closed transmission system is mainly composed of a piston pump 6 and a piston motor 14. The piston pump is a swash plate type slanting axial piston pump (SAPP), and the piston motor is a swash plate type axial piston motor. The specific technical parameters are shown in Table 1. The loading system is composed of a gear pump 16 and an electromagnetic proportional relief valve 18. The load system pressure and load torque can be controlled by changing the orifice opening of proportional relief valve 18. Because the load of the whole system is hydraulic motor and gear pump, both of them may have a certain impact on the study of oil pump pressure pulsation. Therefore, we use the standard Gabor transform linear filtering method to accurately filter out other interference components except pump frequency. The pressure sensor is installed at the pump outlet, and the A/D acquisition card is used to realize the signal acquisition of the sensor. The pressure sensor performance parameters are shown in Table 2. The platform is equipped with Advantech IPC,PCI-1715U analog acquisition card and PCI-1727U analog output card, and also equipped with NI industrial computer and PXI-6251 multifunction acquisition card to meet the high precision signal acquisition.

Table 1 Variable pump/motor and main component parameters

Table 2 HYDAC HDA4844-A-400-Y00 pressure sensor parameters

4 Spectrum traceability and method verification

4.1 Spectrum traceability

Set the displacement of variable piston pump to 55 mL/r, the displacement of motor to 55 mL/r, the speed of motor to 900 r/min, the pressure of system to 12.2 MPa, and the sampling frequency to 40 kHz.The original waveform of pump outlet is shown in Fig.3.

(a) Time domain waveform of pressure signal

(b) Spectrum diagram of pressure signal

As shown in Fig.3(a), the original pressure time domain signal becomes messy due to the influence of motors and noise. In Fig.3(b), in addition to the frequency components of pump and motor appearing in the spectrum, the pulsation caused by motor speed, load, environmental noise, flow and so on will also be mixed with the pressure pulsation signal because noise, pump rotor misalignment, oil compression will have an impact on pressure pulsation of the pump. In order to accurately extract the pressure signal of the pump and ensure that real-time frequency, real-time phase and real-time amplitude of the reconstructed signal and the original pressure signal do not deviate, we use the standard Gabor transform method to extract the pressure signal of the pump.

4.2 Standard Gabor transformation of pressure signals

The standard Gabor transform is a linear filtering method, which has high resolution for the signal, and can accurately extract the interested pressure fluctuation process and frequency components of the oil pump. As shown in Figs.4(a) and (b), for the pressure time-frequency signal after filtering and reconstruction, the real-time phase, real-time amplitude and real-time frequency do not deviate. Compared with ensemble empirical mode decomposition (EEMD) and wavelet packet method[13], the time-domain fluctuation process of pump pressure pulsation and the accuracy of frequency component analysis are benefit to fault analysis of oil pump.

(a) Time domain waveform of pressure signal

(b) Spectrum diagram of pressure signal

The flow chart of pressure signal extraction method is shown in Fig.5.

Fig.5 Flow chart of pressure signal extraction method

First, the original pressure signal is extracted from the pump outlet through pressure sensor， then the frequency components of original signal are analyzed by spectrum traceability， The reasonable frequency component is selected according to the working mechanism of piston pump. Then, the required oil pump pressure signal is accurately extracted by the standard Gabor transform linear filtering method. Finally, the proposed four characteristic indexes are used to analyze the pressure pulsation characteristics under different working conditions.

5 Pressure pulsation characteristics under different working conditions

5.1 Characteristic indexes of pressure pulsation

The reconstructed pressure signal waveform in Fig.4 shows that there are seven pulsating cycles in one revolution of the piston in the cylinder, and the pressure pulsating waveform in each cycle consists of three peaks: the first pulsation waveform characteristic value (PK1), the second pulsation waveform characteristic value (PK2) and the third pulsation waveform characteristic value (PK3). The difference between the pressure mean values with PK1, PK2 and PK3 are defined as characteristics index to measure the pressure pulsation. The root mean square (Var) of the peak statistics is used to describe the stability of the pulsation. Therefore, these four characteristic indexes can be defined to describe the influence of different working conditions on the profile of pressure pulsation, as shown in Fig.6.

Fig.6 Characteristic indexes of pressure pulsation

5.2 Pressure pulsation characteristics at different speeds

Set the pump speed to 600 r/min, 900 r/min, 1 200 r/min, respectively, the system pressure to 17 MPa, the pump displacement to 55 mL/r, and the motor displacement to 55 mL/r. The filtered pressure signal of pump outlet is extracted, as shown in Fig.7. It is clearly exhibited that the waveform of pressure pulsation changes with the speed, and the period of pressure pulsation is consistent with that of piston suction and discharge. While other parameters remain constant, when the speed is in the range of 600 r/min-900 r/min, the absolute pump amplitude of pressure pulsation gradually decreases with the increase of speed. When the speed is in the range of 900 r/min-1 200 r/min, the absolute pump amplitude of pressure pulsation gradually increases with the increase of speed. To study the waveform changing trend of pressure pulsation in the range of 600 r/min-1 200 r/min more comprehensively, four groups of working condition experiments of 700 r/min, 800 r/min, 1 000 r/min and 1 100 r/min are added to further discuss the relationship between speed and pressure pulsation.

Fig.7 Amplitude histogram of pressure pulsation at different speeds

Fig.8 shows the characteristic values of pump outlet pressure pulsation waveforms PK1, PK2, PK3 and variance at different speeds, and three sets of experiments are repeated at the same working condition.

Fig.8 Amplitude histogram of pressure pulsation at different speeds

Experimental results show that the variance value (Var) of each group is small, indicating that this pulsation phenomenon can be repeated and stably exists. It is observed that with the increase of speed, PK1 and PK2 show nonlinear trends which decrease first and then increase, and it is easy to produce ambiguity as a pulsation quantitative indicator. PK3 increases mono-tonously with the speed, and the different speeds correspond to the pulsation degree one by one.

5.3 Pressure pulsation characteristics under different loads

Set the pump speed to 1 200 r/ min, the pump displacement to 55 mL/r, the motor displacement to 55 mL/r, and the load to 8 MPa, 10 MPa, 12 MPa, 14 MPa and 16 MPa. The filtered pressure signal of pump outlet is extracted, as shown in Fig.9. It can be seen that with the increase of load, the amplitude of pulsation increases significantly.

Fig.9 Pump outlet pressure pulsation under different loads

Fig.10 shows the statistics of pump outlet pressure pulsation amplitudes PK1, PK2, PK3 and variance under different loads, and three sets of experiments are repeated at the same working condition.

Fig.10 Amplitude histogram of pressure pulsation under different loads

Experimental results show that the variance value (Var) of each group is small, indicating that this pulsation phenomenon can be repeated and stably exists. With the increase of load pressure, the pump outlet pressure pulsation amplitudes PK1, PK2, and PK3 all increase steadily, indicating that the change of load has an effect on all three waveforms and is positively related. The results of coupling by the internal subsystem of the piston pump show that the higher the output pressure of the piston pump, the more obvious the pressure shock of the piston cavity, which causes the greater fluctuation of the pump outlet pressure[15].

5.4 Pressure pulsation characteristics under different displacements

Set the pump speed to 800 r/min, the pump displacement to 15 mL/r, 25 mL/r， 35 mL/r， 45 mL/r， 55 mL/r, and the motor displacement to 55 mL/r. The filtered pressure signal of pump outlet is extracted, as shown in Fig.11.

Fig.11 Pump outlet pressure pulsation at different displacements

It is illustrated that the bigger the displacement, the greater the waveform of pressure pulsation changes. Fig.12 shows statistics of PK1, PK2, PK3 and variance under different displacements, and three sets of experiments are repeated at the same working condition.

Fig.12 Amplitude histogram of pressure pulsation under different displacements

Experiments show that theVarof each group is small, indicating that this pulsation phenomenon can be repeated and stably exists. It is observed that with the increase of displacement, PK1 and PK3 show nonlinear trends, and it is easy to produce ambiguity as a pulsation quantitative indicator. PK2 increases monotonously with the displacements, and the different displacement corresponds to the pulsation degrees one by one.

6 Conclusions

1) The standard Gabor transform method is used to filter and reconstruct the pressure signal. The results show that compared with the traditional band-pass filter, the standard Gabor transform has the characteristics of line-pass and zero phase shift for high frequency signal, which effectively improves the signal-to-noise ratio of the oil pump pressure signal fluctuation process and the accuracy of fault analysis.

2) Piston pump leakage and compression flow loss have a serious impact on pressure pulsation, which directly causes the amplitude of pressure pulsation to change with the displacement, speed and load. The waveform characteristic PK3 of pressure pulsation is taken as the index of the rotating speed change, the waveform characteristic PK1 of pressure pulsation is taken as the index of load fluctuation change, and the waveform characteristic PK2 of pressure pulsation is taken as the index of pulsation change under different displacement conditions. Several groups of experiments show that PK1, PK2, PK3 can fully reflect the morphology characteristics of pressure pulsation and more accurately reveal the running state of the piston pump.

3) The hydraulic system PK under different working conditions contains abundant information of operating state. PK is used as a characteristic index to study the influence of different system faults on the shape characteristics of pressure pulsation, which lays a theoretical foundation for further study on the application of pump pressure pulsation in fault diagnosis and operation reliability.

4) The causal relationship between flow and pressure pulsation is qualitatively explained by flow leakage formula, and the generation of pressure pulsation is traced. However, in the derivation process of the formula, the influence of various parameters and the structure of piston pump on pressure pulsation needs further study. At the same time, the weakening degree of hydraulic circuit with accumulator on peak pressure fluctuation also needs further study.