- Original Article
- Open Access
Noise Reduction of an Axial Piston Pump by Valve Plate Optimization
© The Author(s) 2018
Received: 16 October 2017
Accepted: 22 June 2018
Published: 5 July 2018
Current researches mainly focus on the investigations of the valve plate utilizing pressure relief grooves. However, air-release and cavitation can occur near the grooves. The valve plate utilizing damping holes show excellent performance in avoiding air-release and cavitation. This study aims to reduce the noise emitted from an axial piston pump using a novel valve plate utilizing damping holes. A dynamic pump model is developed, in which the fluid properties are carefully modeled to capture the phenomena of air release and cavitation. The causes of different noise sources are investigated using the model. A comprehensive parametric analysis is conducted to enhance the understanding of the effects of the valve plate parameters on the noise sources. A multi-objective genetic algorithm optimization method is proposed to optimize the parameters of valve plate. The amplitudes of the swash plate moment and flow rates in the inlet and outlet ports are defined as the objective functions. The pressure overshoot and undershoot in the piston chamber are limited by properly constraining the highest and lowest pressure values. A comparison of the various noise sources between the original and optimized designs over a wide range of pressure levels shows that the noise sources are reduced at high pressures. The results of the sound pressure level measurements show that the optimized valve plate reduces the noise level by 1.6 dB(A) at the rated working condition. The proposed method is effective in reducing the noise of axial piston pumps and contributes to the development of quieter axial piston machines.
Axial piston pumps are broadly applied in industrial and mobile applications to convert mechanical energy into fluid power energy . Axial piston pumps are advantageous in terms of their efficiency, compactness and reliability [2, 3]. The prominent disadvantage is a high noise level. The noise emitted from an axial piston pump can be divided into structure-borne noise, fluid-borne noise and airborne noise . The structure-borne noise is generated by various internal forces and moments, and the fluid-borne noise is produced by flow ripples in the inlet and outlet ports . Both structure-borne noise and fluid-borne noise contribute to the generation of airborne noise.
For an axial piston pump, the valve plate is the main component affecting the noise generation, especially the transition regions between the outlet and inlet ports. In many industrial applications, the pressure relief grooves are machined in the transition regions to smooth the piston chamber pressure. It is desirable to find the optimum type of pressure relief groove of those that can be manufactured. The effects of different types of cross-sectional grooves on the piston chamber pressure were investigated, and the results showed that a steeply sloping triangular cross-sectional groove was the optimal design to reduce the pressure overshoot in the piston chamber . Three different types of slot geometries were compared considering their effects on the pressure transient in the piston chamber, and the results indicated that the quadratic varying slot geometry had no clear advantages compared with the constant and linearly varying slot geometries . In addition to the type of pressure relief groove, the groove volume, slope and angular extent of the pressure relief groove also have great effects on the pressure ripple . The optimal match between the pre-compression angle and cylinder-kidney angle was determined based on a parametric analysis at one particular operating pressure level to maximize the outlet flow rate and minimize the pressure ripple . The valve plate parameters were found to affect the volumetric efficiency, fluid-borne noise sources, structure-borne noise sources and control characteristics of an axial piston pump [10, 11], and a multi-objective optimization method using genetic algorithm was proposed to optimize the parameters of valve plate [12–14]. The valve plate’s effect on the volumetric efficiency and pressure pulsations of an asymmetric axial piston pump was investigated , and the valve plate was designed for a dual-acting axial piston pump .
A dynamic pump model is developed, in which the fluid properties are carefully modeled to reflect the phenomena of air-release and cavitation.
The causes of and factors affecting the noise sources are identified based on the pump model.
A comprehensive parametric analysis is conducted to analyze the effects of the valve plate parameters on the generation of noise sources.
A multi-objective optimization method using a genetic algorithm is proposed to optimize the valve plate parameters.
It will be shown that the noise sources and noise level can be reduced at high pressure levels by a comparison between the original and optimized valve plates, and the noise level is reduced by 1.6 dB(A) at the rated working condition.
2 Pump Modeling
2.1 Description of the Pump
A loud noise is emitted by the pump from different noise sources, and the leakages across different friction interfaces, i.e., the piston/cylinder interfaces, slipper/swash-plate interfaces and cylinder/valve-plate interface, have impacts on the noise sources because the pressure build-up in the piston chamber depends on them . To fully capture the leakages across the friction pairs, special effort is required for the modeling of the piston/cylinder interfaces [19, 20], slipper/swash-plate interfaces [21, 22], and cylinder/valve-plate interface . However, the classical analytical equations used to describe the leakages are acceptable because they are easier and faster to solve .
2.2 Valve Plate
Damping hole three does not connect with the inlet port but instead links directly to the pump case. This design reduces the pressure in the piston chamber by bleeding off a small amount of fluid directly to the pump case. In many cases, air is released from the oil when the piston chamber pressure falls below the saturation pressure. With ordinary valve plate design using a pressure relief groove in the transition regions, the released air is stored in the piston chamber. In contrast, air is released directly into the pump case which enables the released air to dissolve into the fluid .
2.3 Dynamic Model
2.4 Fluid Properties
3 Generation of Noise
To understand the generation of noise from different sources in the axial piston pump, it is desirable to identify the factors contributing to the generation of flow ripples in the inlet and outlet ports and the fluctuation of the swash plate moment.
3.1 Outlet Flow Rate
3.2 Inlet Flow Rate
3.3 Swash Plate Moment
These analyses identify that the piston chamber pressure has a close relationship with the fluctuation of the swash plate moment, and the piston chamber pressure is determined by the flow exchanges between the piston chamber and inlet port, the outlet port and the pump case, which are greatly affected by the valve plate parameters.
4 Parametric Study
Values of the valve plate parameters
Name of structure variable
Starting location of outlet port \(\varphi\)s1 (°)
Ending location of outlet port \(\varphi\)e2 (°)
Starting location of inlet port \(\varphi\)s3 (°)
Ending location of inlet port \(\varphi\)e4 (°)
Location of damping hole one \(\varphi\)l5 (°)
Radius of damping hole one r1 (mm)
Location of damping hole two \(\varphi\)l6 (°)
Radius of damping hole two r2 (mm)
Location of damping hole three \(\varphi\)l7 (°)
Radius of damping hole three r3 (mm)
4.1 Effects of Damping Hole One
Second, the radius of the damping hole affects the pressure undershoot, as shown in Figure 11(b). The lowest pressure increases when the radius increases. The lowest pressure is 0.017 MPa when the damping hole is not used, and it increases to a value higher than 0.05 MPa (high saturated vapor pressure) when the radius is 0.3 mm. As the high saturated vapor pressure is 0.05 MPa, the cavitation occurs when the radius is too small. This implies that the damping hole is capable of maintaining a relatively higher lowest pressure at the start of the compression process, which is the main reason for employing the damping hole.
4.2 Effects of Damping Hole Two
4.3 Effects of Damping Hole Three
Effects of damping holes on the noise sources
pmin (10−2 MPa)
5 Multi-objective Optimization
Due to the limitations of the parametric study, an optimization methodology is required to optimize the valve plate parameters to reduce the pump noise. A multi-objective optimization genetic algorithm that accounts for both the structure-borne noise sources and fluid-borne noise sources is employed.
5.1 Definition of the Objective Functions
5.2 Definition of the Variables and Constraints
The ten structural parameters listed in Table 1 are variables used for the optimization. The parameters defining the starting and ending positions of the inlet and outlet ports result in four variables. The parameters defining each damping hole are the center of the location and the radius of the damping hole. There are six variables for the three damping holes in total. The ranges of the variables are also required to allow for the manufacturing of an actual valve plate, and their values are set according to the parametric analysis. In addition, different constraints are required to provide a reasonable and realistic optimization. The pressure overshoot and undershoot are limited, for which the smallest and largest piston chamber pressures are used as constraints to avoid unexpected phenomena. The upper limit of the piston chamber pressure is 3 MPa higher than the average outlet pressure, whereas the lower limit is 0.05 MPa to avoid air-release and cavitation.
5.3 Optimization Procedure
If the mutation amplitude is near 0, the speed of convergence increases. If the mutation amplitude is near 1, more time is required to obtain convergence because there are more designs to explore. After several generations, individuals converge to one or several best solutions.
5.4 Optimization Results
As shown in Figure 21(a), the amplitudes of the outlet flow rates are reduced when the pressure levels are larger than 15 MPa, and the amplitudes are nearly the same when the pressure levels are smaller than 15 MPa. The amplitudes of the inlet flow rates are reduced at 25 and 28 MPa, and the values increase as the pressure level gets smaller. The amplitude of the swash plate moment is reduced when the pressure level is higher than 10 MPa, and the values increase at 5 and 10 MPa. The main cause of the larger noise sources is that the optimization is carried out at the rated operating condition (28 MPa), and the optimal results obtained at this operating condition cannot reduce the noise sources at lower pressure levels. However, because the investigated pump is designated to be used at a high pressure, the increase in noise sources at low pressures is acceptable.
5.5 Noise Measurement
The inlet, outlet and leakage lines are all flexible hoses. The shortage is that no acoustic cladding has been done to them, and no acoustic cladding has been done to the shaft support either. This allows the noise emitted from these components to reach the microphones as well. However, the noise emitted from these components is smaller than that emitted by the pump, and the measured sound pressure level can be regarded as the sound pressure level emitted from the pump.
The positions of the microphones were defined according to ISO 3745-2003 , assuming that there is one reflecting plane in the sound-free field. As there are only five microphones available, and the sound power level (SWL) was calculated by averaging the sound pressure level (SPL) at ten microphone positions, the microphone positions were moved manually during the measurement. The measurement of SWL was divided into two steps. The first step was to measure the SPL at the first five microphone positions, and the second step was to measure the SPL at the other five microphone positions.
The microphones are type 4189-A-021 (Brüel & Kjær) with an error of 0.2 dB and a measurable frequency ranging from 6-20000 Hz. The signal acquisition equipment is PULSE LAN-XI 3050-A-060 with six channels. All microphones were calibrated with a B&K type 4231 sound calibrator.
Details of the hydraulics system
Inlet pressure sensor
NS-I1, 0-1 MPa, accuracy 0.3% FS
Inlet temperature sensor
SBWR/Z, range -25-120 °C, accuracy 0.25% FS
Y315L2-2, speed range 300-2980 r/min
Shaft speed sensor
JC2C, range 0-4000 r/min, accuracy ± 1 r/min
Shaft torque sensor
JC2C, range 0-2000 Nm, 0.2 class accuracy
Outlet pressure sensor
NSI1, range 0-40 MPa, accuracy 0.3% FS
Outlet flow meter
LC-A50, range 0-400 L/min, 0.2 class accuracy
Pressure relief valve
The pump model with carefully modeled fluid property is effective in analyzing the phenomena of air-release and cavitation. The noise of an axial piston pump is affected by the inlet and outlet flow ripples, and the pulsation of swash plate moment.
Valve plate parameters have great impacts on the generation of noise sources, both fluid-borne noise and structure-borne noise sources. A multi-objective optimization method is required to find the best valve plate parameters in order to reduce all the noise sources. The objective functions and constraints used in the optimization are adequate.
The noise sources and the noise levels are reduced at high pressure levels by a comparison between the original and optimized valve plates, and the noise is reduced by 1.6 dB(A) at the rated pressure level.
The optimization method is effective in optimizing the valve plate parameters to reduce the noise levels. The valve plate used in this study can also be applied to other kinds of axial piston pumps, and the method used here can be extended to other kinds of axial piston machines.
BX was in charge of the whole trial; S-GY and J-HZ wrote the manuscript; S-GY and J-HZ assisted with sampling and laboratory analyses. All authors read and approved the final manuscript.
Shao-Gan Ye, born in 1989, is currently a post-doctorial at Ocean College, Zhejiang University, China. His main research interest is noise control of axial piston machines
Jun-Hui Zhang, born in 1983, is currently a research associate at State Key Laboratory of Fluid Power Transmission and Control, Zhejiang University, China. His main research interests are fluid power transmission and control, and noise control of axial piston machines
Bing Xu, born in 1971, is currently a professor and a PhD candidate supervisor at State Key Laboratory of Fluid Power Transmission and Control, Zhejiang University, China. His main research interests are fluid power transmission and control, and noise control of axial piston machines.
The authors would like to express their appreciation to Professor Su-Mei Chen in Fuzhou University for providing the necessary assistant during the measurements of sound pressure levels.
The authors declare no competing financial interests.
Supported by National Basic Research Program of China (Grant No. 2014CB046403), and Zhejiang Provincial Natural Science Foundation of China (Grant No. LQ14E050005)
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