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Aiming at the existing problems of traditional water piston pump used in the naval ship, such as low efficiency, high noise, large vibration, and nonintelligent control, a new type of linear-motor-driven water piston pump is developed and its vibration characteristics are analyzed in this research. Based on the 3D model of the structure, the simulation analyses including static stress analysis, modal analysis, and harmonic response analysis are conducted. The simulation results reveal that the mode shape under low frequency stage is mainly associated with the eccentricity swing of the piston rod. The vibration experiment results show that the resonance frequency of linear-motor-driven water piston pump is concentrated upon 500 Hz and 800 Hz in the low frequency range. The dampers can change the resonance frequency of the system to a certain extent. The vibration under triangular motion curve is much better than that of S curve, which is consistent with the simulation conclusion. This research provides an effective method to detect the vibration characteristics and a reference for design and optimization of the linear-motor-driven water piston pump.

High-pressure water pump is one of important piece of equipment in ship engineering [

Previously, several researchers studied the vibration characteristics of hydraulic piston pump/motor. Shin [

Actually, the conventional rotary-motor-driven piston pump would produce unbalanced loading force and moment on the axis and cylinder body and is prone to causing large mechanical vibration and noise. With the rapid development of linear motor technology, more and more researchers have paid attention to the application of linear motor in the field of fluid transmission and control field. Early, the linear motor was used in artificial heart, single piston pump, pumping unit, air compressor, and so on. Yamada et al. [

Aiming at the existing problems of traditional piston pump used in the naval ship, such as low efficiency, high noise, large vibration, and nonintelligent control, a new type of linear-motor-driven water piston pump is developed and its vibration characteristics are analyzed in this research. Based on the 3D model of the structure, the simulation analysis including static stress analysis, modal analysis, and harmonic response analysis will be conducted, and then the stress diagram, the natural frequency, and the harmonic response spectrum of the pump system can be obtained. In order to optimize the linear motor motion, the motion characteristics under different motion curves and modes are explored. The vibration response characteristics of linear-motor-driven water piston pump will be investigated so as to avoid the resonance and reduce the system vibration.

The developed linear-motor-driven water piston pump is composed of four-group permanent magnet linear synchronous motor, two sets of highly integrated valve type piston pump units, and one set of servo control system. The schematic diagram of linear-motor-driven water piston pump is illustrated as in Figure

Schematic diagram of linear-motor-driven piston pump system.

Theoretically, the constant flow output of the linear-motor-driven water piston pump could effectively relieve the flow pulsation and pressure impact and lower the vibration of the pump. To achieve constant flow rate, the precise velocity property of single linear motor and the synchronization of multilinear motors are of significance. Therefore, four axes motion control strategy should be specifically investigated based on operation plan and numerical simulation to coordinate the operation phases of linear motors.

Furthermore, the piston pump only has one friction pair, which can improve the volumetric efficiency and is driven directly by linear motor, which can avoid the intermediate transmission mechanism and increase the mechanical efficiency. By means of the servo control system, the linear-motor-driven water piston pump can get good vibration characteristics and a sound flow output performance in comparison with the traditional water piston pump which can only regulate the movement by means of rotor speed control.

The linear-motor-driven water piston pump (as shown in Figure

Linear-motor-driven water piston pump system.

The water hydraulic piston pump section is comprised of two large cylinders, eight distributing valves, and eight pistons. The simplified 3D model of the water hydraulic piston pump is built by the software SolidWorks. As shown in Figure

Simplified 3D model of hydraulic piston pump section.

In the case of normal operation condition, the rated pressure of linear-motor-driven water piston pump is 6 MPa and the thrust output of each linear motor reaches 5 KN. The results of static analysis are illustrated in Figure

Stress and deformation diagram.

Stress diagram

Deformation diagram

Modal is the natural characteristics of the mechanical structure. Each modal has its special characteristics including natural frequency, mode shape, and damping ratio [

Generally, for a relatively simple system, the modal parameters and system response could be obtained by mathematical method; for a complex system studied in this paper, excessive simplification will lead to the results of calculation not being consistent with actual. For the complex vibration analysis, many methods such as finite element analysis, operational modal analysis, and experimental modal analysis could be applied. While in traditional experimental modal analysis, the forces exciting test sample is controlled, and the testing is conducted in the laboratory. In operational modal analysis, the forces are just the ones which are naturally presented during the operation of the structure [

For a multidegree of freedom forced vibration system, the motion equation can be expressed as

In the case of proportional damping, there is

Make the

Back to (

Therefore, the response expression of the system can be obtained:

Similarly, the response of any coordinates

Substitution into (

The fore ten-order mode shapes and natural frequencies.

The 1st-order vibration mode diagram

The 2nd-order vibration mode diagram

The 3rd-order vibration mode diagram

The 4th-order vibration mode diagram

The 5th-order vibration mode diagram

The 6th-order vibration mode diagram

The 7th-order vibration mode diagram

The 8th-order vibration mode diagram

The 9th-order vibration mode diagram

The 10th-order vibration mode diagram

Table

The fore ten modes of vibration.

Modes | Frequency (Hz) | Modal deformation (mm) |
---|---|---|

1 | 166.19 | 18.339 |

2 | 166.38 | 14.080 |

3 | 166.50 | 17.310 |

4 | 166.59 | 18.448 |

5 | 166.87 | 17.263 |

6 | 167.27 | 18.570 |

7 | 167.46 | 19.287 |

8 | 167.84 | 19.253 |

9 | 380.25 | 43.912 |

10 | 382.62 | 44.080 |

Harmonic response analysis (including frequency response analysis and frequency sweep analysis) is mainly used to analyze the steady state response of linear structure according to the harmonic loading. The vibration harmonic response analysis method could reveal the relationships between the frequency, displacement, velocity, and acceleration under different frequency [

In order to evade the resonance and fatigue, avoiding the excitation frequency is one of effective ways. The input load of the harmonic response analysis is a sinusoidal load which is changing by the time. The primary characteristic values of the load are frequency and amplitude, while the load form can be defined as force, pressure, and the displacement. Generally, the simulation results are usually the displacement, stress, and strain. By analyzing the output curve, the peak response frequency and amplitude can be obtained, which can be used as the basis of the vibration mechanism analysis and vibration reduction design.

In a typical multiple degree of freedom system, the dynamic equation is given by

For different research purposes, it can be used to solve the different problem based on formula (

Deformation-frequency diagrams.

Deformation of cylinder wall in axial direction

Deformation of cylinder wall in radial direction

Deformation of cylinder wall in vertical direction

The three figures present the modal deformation of axial direction (the motion direction of linear motor), radial direction (perpendicular to the linear motor motion direction in the horizontal plane), and vertical direction, respectively. From Figure

On the other hand, the simulation results demonstrate that the resonance frequencies of the linear-motor-driven water piston pump mainly concentrated under 500–800 Hz. Because the motion frequency of the pump is about 3 Hz and the mass is large, the resonance does not easily occur under the low frequency stage. Thus, when debugging the parameters of linear motor, the resonance frequency should also be avoided. The harmonic analysis provides a method to predict the dynamic characteristic of structure, which can help to overcome the harmful effects caused by fatigue, resonance, and other forced vibration. Before the system vibration testing, the PID parameter adjustment of linear motor should be carried out. In the next section, the experiment will be conducted to verify the harmonic response analysis.

The vibration characteristics of the linear-motor-driven water piston pump are affected by several factors, such as mechanical structure and servo control system. Compared with the single control mode of traditional piston pump, the servo control system of the linear-motor-driven water piston pump is able to perform a variety of servo control modes. The spline (i.e., spline interpolation algorithm) and PVT (i.e., location-time interpolation algorithm) motion mode are the most widely used motion modes of the linear motor. In the spline motion mode, the movement distance is divided into equal segments by the time and only needs to define the position of the coordinate points at the time of operation. The advantage of this method is that it can reduce the workload and facilitate the calculating. The PVT motion mode needs to define the distance, velocity, and move time at the end of each step. Therefore, it has higher request for computing performance of the servo control system in comparison with the spline motion mode.

Since the piston is directly connected with the linear motor, the instantaneous flow rate of the system is proportional to the piston instantaneous effective velocity. Thus, the property parameters of linear motor, such as the following errors, will eventually affect the performance of linear-motor-driven water piston pump. In order to make the pump get steady flow output and achieve the goal of low vibration and noise, it should set the servo control characteristic parameters of linear motor appropriately. The influencing factors of servo control characteristics include not only the motion mode but also the movement curve. Usually the motion curves are triangular wave and S wave curve.

The velocity mathematic model of triangle wave planning in the time domain of

The velocity mathematic model of S wave planning in the time domain of

For the sake of obtaining the best running state, the dynamic response characteristics of the linear motor under different motion modes and motion curves have been conducted in the simulation system. The debugging results of the linear motor in simulation mode under different motion modes and curves are shown in Figure

Debugging diagram under different motion modes and curves.

Triangle velocity curves of linear motor at PVT mode

S velocity curves of linear motor at PVT mode

Triangle velocity curves of linear motor at spline mode

S velocity curves of linear motor at spline mode

In the coordinate system, the horizontal axis represents time and the unit is the second, while the longitudinal axes represent the velocity and following error, and the measuring units are cts/s and cts (cts is the counting unit of grating, and it depends on the resolution of grating; here one cts is equal to 0.5

The following errors under different modes and curves.

Maximum following errors (cts) | Average following errors (cts) | |
---|---|---|

PVT/triangle curve | 148.1 | 51.0 |

PVT/S curve | 155.3 | 54.6 |

Spline/triangle curve | 149.6 | 51.5 |

Spline/S curve | 150.0 | 56.3 |

Note: 1 cts = 0.5

The vibration source of the linear-motor-driven water piston pump mainly comes from the motion of mechanism and the flow pulsation noise. The main effect factors of the vibration response characteristics in this pump are the response lag of distributing valve and synchronous phase error of linear motor. Therefore, under the certain system structure parameters, the control strategy of linear motor has become the key factor for influencing the system vibration characteristics. On the basis of the above simulation analysis, the vibration experiment is conducted to obtain the vibration and noise information.

As shown in Figure

Vibration test point.

Though Coinv DASP software, the acceleration, velocity, and displacement of the vibration signal are collected in real time. According to previous dynamic characteristic simulation analysis of the linear motor, the vibration response test of triangle curve and S curve under PVT motion mode have been conducted. The motion period is set as 0.6 seconds, and the stroke is 205 mm. Four groups of linear motor are moving at the phase difference of 90 degrees. After the calculus processing of the collected vibration data, the amplitude distribution in the time domain of the

Vibration amplitude distribution in the time domain of the

Triangle curve, PVT motion mode

S curve, PVT motion mode

It can be seen from Figure

Vibration amplitude of each channel under the triangle wave motion curve.

Signal channel | Maximum amplitude ( |
Minimum amplitude ( |
---|---|---|

1 | 413.2 | −454.0 |

2 | 2673.6 | −2972.2 |

3 | 742.4 | −655.8 |

Vibration amplitude of each channel under the S wave motion curve.

Signal channel | Maximum amplitude ( |
Minimum amplitude ( |
---|---|---|

1 | 634.6 | −423.7 |

2 | 6706.8 | −7312.9 |

3 | 903.5 | −1071.4 |

From the previous parameters debugging of simulation system, it can be known that the following errors of linear motor under triangle curve are lesser than that of S curve. The following error was ultimately reflected in the vibration amplitude of test results. Comparing the vibration amplitudes (as shown in Tables

Random vibration is the most common type of vibration, and it should be studied when carrying out a vibration-proof design. Power spectrum density (PSD) is an effective method to describe random vibration. Generally, the random vibration is characterized by the power spectral density function, for a time series

The PSD is widely used because the modes could be indicated clearly by spectral peaks. Power spectrum is the concept of statistical average random process that is expressed by the signal power with the change of frequency. The horizontal axis unit of power spectrum density plot is Hz, and the vertical axis is

Power spectrum of linear-motor-driven water piston pump system under triangle and S motion curve.

Triangle curve, PVT motion mode

S curve, PVT motion mode

Compared to the graphs of signal channel in the different motion mode, it can be observed that the trend of power spectrum is basically identical. Like the previous analysis, the power spectrum only reserves the amplitude information and lost the phase information. So, the difference lies in the amplitude at the resonance frequency. The amplitudes of each channel under triangular curve are 0.025, 0.082, and 0.078

It can be seen from Figure

Based on the prototype and three-dimensional model of the linear-motor-driven water piston pump, this paper has carried out the vibration characteristic analysis. The finite element analysis software has been employed to perform a static stress, modal, and harmonic analysis. The maximum deformation and equivalent stress of the mechanical structure were measured at the rated working condition. From the results presented in this paper, the important conclusions obtained can be drawn as follows:

The research provides an effective method to detect the vibration characteristics of the linear-motor-driven water piston pump and also a reference for design and optimization of the piston pump.

The authors declare that they have no competing interests.

The authors would like to thank the National Natural Science Foundations of China (nos. 51375018 and 11572012), National High-Tech R&D (863) Program (no. 2012AA091103), Beijing Natural Science Foundation (no. 3164039), and China Postdoctoral Science Foundation (no. 2015M580946) for their funding for this research.