Jian-hua ZHAO, Hang LIU, Xin-wei WANG, You-zhi PEI, Yong YANG, Zhao-hua WU, Jin WANG,, Jun-bo CAO,, Lan-chun XING,, Guo-jun DU

(1College of Civil Engineering and Mechanics, Yanshan University, Qinhuangdao 066004, China) (2Shijiazhuang Haishan Industrial Development Co.,Ltd., Shijiazhuang 050200, China) (3Fluid Power Transmission and Control Laboratory, Yanshan University, Qinhuangdao 066004, China) (4The State Key Lab of Fluid Power Transmission and Control, Zhejiang University, Hangzhou 310027, China)

Abstract: Axial plunger pump is considered as the core component of hydraulic system, and its performance directly determines the safety and reliability. The complicated symptoms, such as pressure pulsation, substandard flow rate, large amount of oil leakage, abnormal shell vibration and so on caused by the faults of three friction pairs and bearing can improved the difficulties of accurately identifying the source of the faults for the researcher. However, the abnormal vibration time-frequency curve of the shell in the different fault modes of axial plunger pump is inconsistent. Therefore, this paper analyzes the generation mechanism and transfer law of fluid vibration in the normal and various fault modes of axial plunger pump. The fluid vibration transfer path model and vibration differential equation of axial plunger pump are established. The vibration response curves in time/frequency domain of the front, middle and rear shell under various modes are presented by MATLAB, and typical fault characteristic signals are extracted. This paper provides theoretical basis for diagnosis of axial plunger pump in various fault modes.

Key words: Axial plunger pump, Fluid vibration, Transfer path, Shell vibration, Fault analysis

1 Introduction

As the power component of the hydraulic system, the axial plunger pump can continuously convert the mechanical energy into the pressure energy of the liquid to ensure the normal and stable work of the hydraulic system.

The complicated symptoms, such as pressure pulsation, substandard flow rate, large amount of oil leakage, abnormal shell vibration etc. caused by the faults of three friction pairs and bearing can increase the level of difficulty of accurately identifying the source of the faults for the researcher. However, the abnormal vibration time-frequency curve of the shell in different fault modes of axial plunger pump is inconsistent. Therefore, it is very necessary to study the generation, transfer and influence of the vibration of the plunger pump under the condition of fault.

The vibration of axial plunger pump is mainly composed of fluid vibration and mechanical vibration[1-2]. The fluid vibration is caused by natural flow pulsation, pressure impact, flow backflow and pressure impact in the oil-trapped area of the valve plate[3].

Many scholars have done a lot of research on plunger pump fault diagnosis and fluid vibration.

Wang[4] summarized the research on pump fault diagnosis. Wang[5-6] studied information fusion algorithm for hydraulic pump fault diagnosis. Yamauchi[7-8] solved the pressure in the plunger cavity by used the difference method. Paoloc[9] studied the influence of oil characteristics of buffer slot on flow pulsation of axial plunger pump. Yang[10-12] conducted an axial plunger pump vibration experiment, which proves that the main vibration source of the plunger pump is the “swash plate-variable mechanism”, and flow backflow and pressure impact in the oil-trapped area of the valve plate. Zhang[13-15] solved the problem of uncertain vibration transfer path better through random response analysis of vibration transfer path system in time domain. The research above are of great significance to reveal the vibration mechanism of axial plunger pump.

Previous research are mostly confined to the vibration of the normal plunger pump, and then there are few report on the abnormal vibration of plunger pump under different failure modes. Therefore, the generation mechanism and transfer law of fluid vibration in the normal and various fault modes of axial plunger pump are analyzed in the paper. The fluid vibration transfer path model and vibration differential equation of axial plunger pump are established. The vibration response time/frequency domain curves of front, middle and rear shell under various modes of axial plunger pump are obtained by MATLAB, and typical fault characteristic signals are extracted. It provides the theoretical basis for diagnosis of axial plunger pump in various fault modes.

2 Fluid vibration model of swash-plate axial plunger pump

2.1 Conditions of physical model of fluid vibration transfer path

A swash-plate axial plunger pump is taken as the research object of the fluid vibration of the plunger pump, and some assumptions can be shown as follows:

(1) The unbalance and eccentricity of the rotor system are ignored.

(2) The source of fluid vibration is the flow impact, pressure pulsation and flow backflow of the front shell.

(3) The source of fluid vibration excitation force is the plunger cavity pressure, and then the front, middle and rear shell of the pump are the final acceptors.

(4) Cylinder block and drive shaft are assumed as the whole rotating components.

(5) The ball hinge movement between plunger and slipper is ignored.

(6) The rotation and swing motion of the plunger is ignored.

(7) The quality of the connection element is equivalent to the vibration body, the supporting oil film between the contact surfaces is considered as rigid elastomer, at the same time, there is viscous damping between Port Plate Pair and Slipper Pair.

(8) The axial damping of the bearing is ignored.

2.2 Physical model of fluid vibration transfer path

There are three transfer paths in physical model of fluid vibration transfer path as Fig.1.

Path 1: plunger cavity oil → plunger slipper assembly → swash plate → cylindrical roller bearing → rear shell.

Path 2: plunger cavity oil → plunger slipper assembly → swash plate → variable mechanism → middle shell.

Path 3: plunger cavity oil → cylinder block and drive shaft → front shell.

Fig.1 Physical model of transfer path of fluid vibration shell of axial piston pump

In Fig.1,Fis the exciting force on the oil in the plunger cavity;xb、xm、xf、xvm、xsp、xp、xoandxcbare respectively the vibration displacement of the rear shell, middle shell, front shell, variable mechanism, swash plate, plunger slipper component, plunger cavity oil, cylinder block, drive shaft and valve plate under the action of excitation forceF;mb、mm、mf、mvm、msp、mp、moandmcbare the actual mass of the rear shell, middle shell, front shell, variable mechanism, swash plate, slipper, plunger, plunger cavity oil, cylinder block and drive shaft respectively;k1is axial stiffness between the rear shell and the middle shell;k2is stiffness between the middle shell and the front shell;k3is axial stiffness of cylindrical roller bearing;k4is axial stiffness of deep groove ball bearing;kb1is axial stiffness of cylindrical roller bearing;kb2is axial stiffness of deep groove ball bearing;kspis axial stiffness between the rear shell and the variable mechanism;ksbandcsbare stiffness and damping of oil film supported by slipper;kowandcoware stiffness and damping of the oil film of No.w plunger cavity;cvmis damping of oil film of variable mechanism;kmfandcmfare stiffness and damping of oil film of Port Plate Pair support. There are nine plungers in the axial plunger pump in the paper.

2.3 Mathematical model of fluid vibration

The fluid vibration transfer path of axial plunger pump is establish and the functional relationship between components is determined in order to get Lagrange Equation of plunger pump as follows:

(1)

Where,Tis work done by inertial forces;Uis work done by elastic forces;Dis work done by damping forces;qjis generalized coordinates,Ωis generalized force.

By combining with the fluid vibration transfer path model, the fluid vibration motion differential equation of each body is obtained as follows:

kb1(xsp-xb)-kb2(xcb-xb)=0

(2a)

(2b)

kmf(xcb-xf)=0

(2c)

kspcosβ(xspcosβ-xvm)=0

(2d)

ksp(xsp-xspcosβ)-

kb1(xsp-xbcosβ)-

(2e)

ksbcosβ(xp1-xspcosβ)=0

(2f)

ksbcosβ(xp9-xspcosβ)=0

(2g)

ko1(xo1-xcb)+ko1(xo1-xp1)=Fn

(2h)

ko9(xo9-xp9)=Fn

(2i)

(2j)

Where,Fn=F0sin(2πn/60)t,nis rotate speed of axial plunger pump,F0represents the amplitude of excitation force,trepresents the action time of excitation force.

3 Analysis on transfer path model of fluid vibration

3.1 Parameters of plunger pump model

The assumptions are shown as follows[16-19]:

(1) Stiffness and damping are constant, and nonlinear and time-varying characteristics are ignored.

(2) The effects of roughness and friction force are ignored in the finite element modeling process.

3.2 Model solution of vibration transfer path of healthy plunger pump

Due to the complex structure of Equation (2), it is difficult to calculate the analytical solution. Therefore, Runge-Kutta Method[20] is proposed to solve the time/frequency domain diagram of vibration acceleration of the front shell, middle shell and rear shell of the plunger pump.

The vibration response curves of the front shell, middle shell and rear shell of healthy plunger pump are shown as Fig.2～Fig.4.

Fig.2 Vibration response curve of front shell under healthy state

Fig.3 Vibration response curve of middle shell under healthy state

Fig.4 Vibration response curve of rear shell under healthy state

According to Fig.2～Fig.4, the time domain response of shell includes the transient state and the steady state. In the transient state stage, the amplitude of the shell is large and it can be arranged as: rear shell> front shell> middle shell.

The initial maximum amplitude of front shell, middle shell and rear shell are 5.7 m/s2, 4.9 m/s2, 12.3 m/s2respectively, and the stable amplitude are 0.3 m/s2, 2.3 m/s2, 4.9 m/s2.

Due to the damping effect of axial piston pump, the shell vibrates periodically in the steady state stage. The sum of acceleration amplitude of front shell, middle shell and rear shell are 3.75 m/s2, 9.85 m/s2and 12.5 m/s2respectively. The fundamental frequency of the shell is 135 Hz. And the frequency of each order harmonic is the integral number of the fundamental frequency, which is consistent with the excitation frequency of axial piston pump. The first order response frequency of vibration acceleration is 1 350 Hz, the second order is 2 430 Hz and the third order is 3 375 Hz. The shell is easy to occur the strong resonance in the vicinity of 2 430 Hz.

4 Analysis and simulation of common fault mechanism

4.1 Wear-out failure of slipper pair

The wear of slipper pair is mainly composed of adhesive wear and abrasive wear, which are characterized by eccentric wear of the oil sealing surface of slipper as Fig.5 and Fig.6. The thickness of oil-film of slipper pair will increase when it is worn eccentrically (The changing thickness is assumed to 0.3 mm in this paper).

Fig.5 Eccentric Wear of Slipper

Fig.6 Flow Field of Gap of parallel disc

The oil-film dampingcsband stiffnessksb[3] of the slipper pair are calculated and substituted into equation (2) to obtain the time/frequency domain diagrams of the vibration of the front shell, middle shell and rear shell under the wear of the slipper pair.

The time/frequency domain response curves of the front shell, middle shell and rear shell under the wear of slipper pair can be shown as Fig.7～Fig.9.

According to Fig.7～Fig.9, the initial maximum amplitudes of axial plunger pump are arranged as: 18.3 m/s2(rear shell) > 7.8 m/s2(middle shell) > 6.6 m/s2(front shell). And the stable amplitude are 4.7 m/s2(rear shell), 4.9 m/s2(middle shell) and 0.4 m/s2(front shell).

Fig.7 Vibration Response Curve of Front Shell under Wear of Slipper Pair

Fig.8 Vibration Response Curve of Middle Shell under Wear of Slipper Pair

Fig.9 Vibration Response Curve of Rear Shell under Wear of Slipper Pair

Compared with the healthy plunger pump (Fig.2～Fig.4), the acceleration amplitudes of front shell of plunger pump with wear-out failure of slipper pair in time/frequency domain change little. The maximum acceleration amplitudes of the middle shell and the rear shell increase by 2.8 m/s2and 2.3 m/s2respectively. The sum of frequency amplitude of middle shell is 17.17 m/s2, which increases by 7.32 m/s2while the rear shell is 20.93 m/s2, which increases by 5.68 m/s2. It can be seen that the wear of slipper pair has a great impact on the vibration of the middle shell and the rear shell.

4.2 Wear-out failure of port plate pair

The wear of port plate pair is also mainly adhesive wear and abrasive wear, and its wear pattern is uniform circumferential friction marks, such as peeling of the zinc coating. (The surface wear of Port Plate is set as 0.15 mm in this paper.)

The oil-film stiffnesskmfand dampingcmf[3] of the port plate pair are substituted into equation (2) to obtain the time/frequency domain diagrams of the vibration of the front shell, middle shell and rear shell under the wear of the port plate pair.

The time/frequency domain response curves of the front shell, middle shell and rear shell under the wear of port plate pair can be shown as Fig.10～Fig.12.

According to Fig.10～Fig.12, the initial maximum amplitudes of axial plunger pump are arranged as: 12.3 m/s2(rear shell) > 7.8 m/s2(front shell) > 4.6 m/s2(middle shell). And the stable amplitude are 5.6 m/s2(rear shell), 0.4 m/s2(front shell) and 2.6 m/s2(middle shell).

Compared with the healthy plunger pump (Fig.2～Fig.4), the acceleration amplitudes of middle shell and rear shell of plunger pump with wear-out failure of Port Plate Pair in time/frequency domain change little. The acceleration amplitude of front shell increases by 2.1 m/s2. The sum of frequency amplitudes of front shell is 7.74 m/s2, which increases by 3.99 m/s2. It can be seen that the wear of port plate pair has a great impact on the vibration of front shell.

Fig.10 Vibration Response Curve of Front Shell under Wear of Port Plate Pair

Fig.11 Vibration Response Curve of Middle Shell under Wear of Port Plate Pair

Fig.12 Vibration Response Curve of Rear Shell under Wear of Port Plate Pair

4.3 Failure of bearing

The failure of bearing is mainly composed of wear marks and scratches of the rollers. (It is set as 0.2 mm in this paper.)

The stiffnesskb1of the failed bearing is simulated and substituted into equation (2), and the time/frequency domain diagram of the vibration of the front shell, middle shell and rear shell is obtained.

The time/frequency domain response curves of the front shell, middle shell and rear shell of the plunger pump with the failed bearing can be shown as Fig.15～Fig.17.

Fig.13 Failure of Bearing RollerFig.14 Finite Element Analysis of Bearing

Fig.15 Vibration Response Curve of Front Shell under Failure of Bearing

Fig.16 Vibration Response Curve of Middle Shell under Failure of Bearing

Fig.17 Vibration Response Curve of Rear Shell under Failure of Bearing

According to Fig.15～Fig.17, the initial maximum amplitudes of axial plunger pump are arranged as: 13.3 m/s2(rear shell) > 5.8 m/s2(front shell) > 5.6 m/s2(middle shell). And the stable amplitude are 6.43 m/s2(rear shell), 0.4 m/s2(front shell) and 3.8 m/s2(middle shell).

Compared with the healthy plunger pump (Fig.2～Fig.4), the acceleration amplitudes of front shell and rear shell of plunger pump with the failed bearing in time/frequency domain change little. The acceleration amplitude of rear shell increases by 15.25 m/s2. The sum of frequency amplitudes of rear shell is 22.87 m/s2, which increases by 7.62 m/s2. It can be seen that the failed bearing has a great impact on the vibration of rear shell.

5 Conclusion

When the slipper pair is worn, the acceleration amplitudes in time/frequency domain of front shell change little while middle shell and rear shell both increase significantly.

When the port plate pair is worn, the acceleration amplitudes in time/frequency domain of middle shell and rear shell change little while front shell increase significantly.

When the bearing fails, the acceleration amplitudes in time/frequency domain of front shell and middle shell change little while rear shell increase significantly.