CN113255220B - Gear pump maintenance method based on digital twinning - Google Patents

Gear pump maintenance method based on digital twinning Download PDF

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CN113255220B
CN113255220B CN202110605998.8A CN202110605998A CN113255220B CN 113255220 B CN113255220 B CN 113255220B CN 202110605998 A CN202110605998 A CN 202110605998A CN 113255220 B CN113255220 B CN 113255220B
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gear pump
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CN113255220A (en
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严如强
许文纲
周峥
孙闯
田绍华
王志颖
梁清华
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Xian Jiaotong University
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    • F—MECHANICAL ENGINEERING; LIGHTING; HEATING; WEAPONS; BLASTING
    • F04—POSITIVE - DISPLACEMENT MACHINES FOR LIQUIDS; PUMPS FOR LIQUIDS OR ELASTIC FLUIDS
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Abstract

The disclosure discloses a gear pump maintenance method based on digital twinning, which comprises the following steps: measuring and receiving working condition parameters of the gear pump in real time, calculating the volumetric efficiency and the limiting rotation speed of the gear pump based on the working condition parameters to evaluate the running state of the gear pump and estimate failure, calculating the central positions of a driving gear and a driven gear of the gear pump and the abrasion loss of a friction pair, establishing a pressure pulsation model of the gear pump based on a centralized parameter method in an internal flow field of the gear pump, establishing a digital twin model of the gear pump, and taking the pressure pulsation at the outlet of the gear pump as a monitoring signal for predicting and maintaining the model.

Description

Gear pump maintenance method based on digital twinning
Technical Field
The invention belongs to the field of gear pump operation and maintenance, and particularly relates to a gear pump maintenance method based on digital twinning.
Background
The gear pump has compact structure, small volume, light weight, low price, low sensitivity to oil pollution and good self-absorption performance, and is widely applied to mechanical industries such as electric power, automobiles, metallurgy, military industry, aviation, aerospace, chemical engineering and the like. The most significant failure mode of gear pumps during use is the reduction in volumetric efficiency caused by leakage. Gear pump leaks include internal and external leaks, external leaks being visible to the naked eye and which can be addressed by replacing seals; the leakage causing the reduction of the volume efficiency is mainly internal leakage, is a process that oil in a high-pressure cavity flows to a low-pressure cavity through a friction pair gap, and mainly comprises end surface leakage between a gear end surface and a side plate, radial leakage between a tooth top and a shell and meshing leakage at the meshing position of two gears.
In the past, the fault monitoring and performance degradation research of the gear pump mainly adopts the diagnosis and prediction technology of multi-source signal fusion. However, the early weak fault of the gear pump cannot be well diagnosed and predicted, and meanwhile, the performance degradation of the gear pump cannot be evaluated and predicted in time, so that the pressure and the flow of the whole hydraulic system are insufficient, the overall performance of the system is seriously influenced, and especially when the gear pump is used in an aircraft engine fuel system, the insufficient pressure and the insufficient flow are fatal faults, so that a digital twin model of the gear pump based on physical knowledge is established, the degradation performance and the faults of the gear pump are mirrored in time, and the self vital signs of the gear pump in the life cycle are dynamically reflected. The method has great potential in gear pump fault monitoring and predictive maintenance.
The above information disclosed in this background section is only for enhancement of understanding of the background of the invention and therefore it may contain information that does not form the prior art that is well known to those of ordinary skill in the art.
Disclosure of Invention
Aiming at the problems in the prior art, the invention provides a gear pump maintenance method based on digital twins.
The purpose of the invention is realized by the following technical scheme.
In one aspect of the invention, a predictive maintenance method based on a digital twin gear pump comprises the following steps:
measuring and receiving gear pump working condition parameters in real time, wherein the working condition parameters comprise working pressure
Figure 858843DEST_PATH_IMAGE001
Flow rate of
Figure 90367DEST_PATH_IMAGE002
Rotational speed of the motor
Figure 680617DEST_PATH_IMAGE003
Torque of the motor
Figure 1877DEST_PATH_IMAGE004
And temperature
Figure 54409DEST_PATH_IMAGE005
；
Calculating volumetric efficiency and limit speed of the gear pump based on the operating condition parameters to assess the operating condition of the gear pump and make a prediction of failure, wherein,
Figure 119317DEST_PATH_IMAGE006
，
Figure 705019DEST_PATH_IMAGE007
in the formula:
Figure 666022DEST_PATH_IMAGE008
is the limit rotation speed;
Figure 471429DEST_PATH_IMAGE001
is the working pressure;
Figure 74449DEST_PATH_IMAGE009
the dynamic viscosity of the oil is adopted;
Figure 249078DEST_PATH_IMAGE010
the clearance between the bearing and the bearing bush;
Figure 912140DEST_PATH_IMAGE011
is the bearing radius;
Figure 927546DEST_PATH_IMAGE012
is volume efficiency;
Figure 334256DEST_PATH_IMAGE013
is the displacement at the working pressure;
Figure 894551DEST_PATH_IMAGE014
displacement at no load pressure;
Figure 462935DEST_PATH_IMAGE015
is the flow at the working pressure;
Figure 242935DEST_PATH_IMAGE016
is the flow at no load pressure;
Figure 187757DEST_PATH_IMAGE017
is the rotation speed under the working pressure;
Figure 336979DEST_PATH_IMAGE018
is the rotation speed at the no-load pressure,
calculating the central positions of a driving gear and a driven gear of the gear pump and the abrasion loss of a friction pair, wherein the central positions are as follows:
Figure 341844DEST_PATH_IMAGE019
in the formula:
Figure 343560DEST_PATH_IMAGE020
is the mass of the gear 1;
Figure 826494DEST_PATH_IMAGE021
is the bearing counter force borne by the gear 1;
Figure 95801DEST_PATH_IMAGE022
is the pressure to which the gear 1 is subjected;
Figure 271568DEST_PATH_IMAGE023
the meshing force applied to the gear;
Figure 760580DEST_PATH_IMAGE024
is the moment of inertia of gear 1;
Figure 906260DEST_PATH_IMAGE025
is the angle of rotation of gear 1;
Figure 436598DEST_PATH_IMAGE026
torque generated by the pressure to which the gear 1 is subjected;
Figure 783266DEST_PATH_IMAGE027
torque generated for the motor;
Figure 759574DEST_PATH_IMAGE028
is the radius of the meshing point of the gear 1;
Figure 584311DEST_PATH_IMAGE029
is the mass of the gear 2;
Figure 828210DEST_PATH_IMAGE030
bearing counter force borne by the gear 2;
Figure 345779DEST_PATH_IMAGE031
by pressure exerted on gear wheel 2；
Figure 809384DEST_PATH_IMAGE032
Is the moment of inertia of gear 2;
Figure 296866DEST_PATH_IMAGE033
is the angle of rotation of the gear 2;
Figure 395272DEST_PATH_IMAGE034
torque generated by the pressure to which the gear 2 is subjected;
Figure 319628DEST_PATH_IMAGE035
is the radius of the meshing point of the gear 2,
the abrasion loss of the friction pair comprises the abrasion loss between the end surface of the gear and the floating shaft sleeve, between the tooth top and the inner wall of the pump shell, the abrasion loss between the end surface of the gear and the floating shaft sleeve determines the size of a gap hf between the end surface of the gear and the floating shaft sleeve, and the abrasion loss between the tooth top and the inner wall of the pump shell determines the size of a gap hi between the pump shell of the gear pump and the tooth top of the gear; the abrasion loss of the friction pair is as follows:
Figure 503485DEST_PATH_IMAGE036
，
Figure 201182DEST_PATH_IMAGE037
in the formula:
Figure 419674DEST_PATH_IMAGE002
the abrasion loss of the friction pair is obtained;
Figure 780510DEST_PATH_IMAGE038
the energy consumed for wear on each stroke;
Figure 592609DEST_PATH_IMAGE039
the number of strokes;
Figure 562839DEST_PATH_IMAGE040
a sliding distance for each stroke;
Figure 635837DEST_PATH_IMAGE041
is the wear system constant;
Figure 931689DEST_PATH_IMAGE042
the maximum shear force to which the part is subjected;
obtaining a flow rate through the gap based on the pressure differential and the size of the gap, and obtaining a pressure for each chamber based on a relationship between the gap and the flow rate, wherein,
Figure 603321DEST_PATH_IMAGE043
，
Figure 377242DEST_PATH_IMAGE044
，
in the formula:
Figure 304747DEST_PATH_IMAGE045
is the tooth width;
Figure 505921DEST_PATH_IMAGE046
the gear pump rotating speed;
Figure 387552DEST_PATH_IMAGE047
is the addendum circle radius;
Figure 965164DEST_PATH_IMAGE048
is the tooth height;
Figure 278333DEST_PATH_IMAGE049
is the average tooth height;
Figure 650409DEST_PATH_IMAGE009
the dynamic viscosity of the oil is adopted;
Figure 19336DEST_PATH_IMAGE050
the tooth crest thickness;
Figure 400638DEST_PATH_IMAGE051
the tooth thickness of the pitch circle;
Figure 302735DEST_PATH_IMAGE052
is as follows
Figure 845712DEST_PATH_IMAGE053
A cavity pressure;
Figure 233093DEST_PATH_IMAGE054
is as follows
Figure 886929DEST_PATH_IMAGE055
Individual chamber pressure;
Figure 909111DEST_PATH_IMAGE056
the tooth crest clearance flow is obtained;
Figure 357410DEST_PATH_IMAGE057
is the tooth flank clearance flow;
under adiabatic, isentropic conditions, and
Figure 966508DEST_PATH_IMAGE058
the pressure in the ith control body can be obtained according to the continuity equation:
Figure 158455DEST_PATH_IMAGE059
，
Figure 300723DEST_PATH_IMAGE060
，
in the formula:
Figure 919924DEST_PATH_IMAGE061
is the bulk modulus of elasticity;
Figure 750739DEST_PATH_IMAGE062
the gear pump rotating speed;
Figure 11956DEST_PATH_IMAGE063
is the ith control volume;
Figure 743151DEST_PATH_IMAGE064
is the gear rotation angle;
Figure 798832DEST_PATH_IMAGE065
is the amount of change in the flow in the ith control fluid;
Figure 116943DEST_PATH_IMAGE066
the flow rate of the ith +1 th control body flowing into the ith control body through the gap is set;
Figure 181851DEST_PATH_IMAGE067
the flow rate of the ith control body flowing out through the gap is measured;
the inlet control body, the isometric control body, the outlet control body and the closed cavity control body are sequentially modeled by utilizing the above formula, so that the pressure of the whole internal flow field is obtained, and the model is as follows:
Figure 33132DEST_PATH_IMAGE068
in the formula:
Figure 994135DEST_PATH_IMAGE069
the pressure of the nth chamber of the gear 1;
Figure 65122DEST_PATH_IMAGE070
pressure of the mth cavity of the gear 2;
Figure 668141DEST_PATH_IMAGE071
the pressure of a sealed cavity of the gear pump;
Figure 108350DEST_PATH_IMAGE072
is the gear pump outlet pressure;
Figure 771412DEST_PATH_IMAGE073
is the gear pump inlet pressure;
in an external flow field of the gear pump, fourier expansion of a pressure pulsation signal at a measuring point is as follows:
Figure 521239DEST_PATH_IMAGE074
in the formula:
Figure 927949DEST_PATH_IMAGE075
is a direct current component;
Figure 222664DEST_PATH_IMAGE076
is the fundamental component of the frequency conversion;
Figure 56628DEST_PATH_IMAGE077
is a harmonic component of the frequency conversion; n =1 …;
Figure 836628DEST_PATH_IMAGE078
is a constant;
Figure 781450DEST_PATH_IMAGE079
generating a pressure pulsation signal amplitude for the tooth frequency;
Figure 196251DEST_PATH_IMAGE080
is an amplitude modulation coefficient;
Figure 201116DEST_PATH_IMAGE081
is a frequency modulation coefficient;
Figure 842313DEST_PATH_IMAGE082
is a phase angle;
Figure 92291DEST_PATH_IMAGE083
is the tooth frequency; m =1 …;
Figure 361598DEST_PATH_IMAGE084
is an amplitude-modulated signal;
Figure 537364DEST_PATH_IMAGE085
in order to be a frequency-modulated signal,
and establishing a digital twin model of the gear pump, and taking the outlet pressure pulsation of the gear pump as a monitoring signal of the predictive maintenance model.
In the method, during the expansion of the pressure pulsation signal at the measuring point of the gear pump external flow field, time domain analysis, frequency domain analysis, wavelet analysis, functional analysis or matrix analysis is carried out on the measured data and the simulation data.
In the method, the time domain analysis comprises time domain statistical analysis or correlation analysis, and the frequency domain analysis comprises FFT, coherent analysis, cepstrum analysis or autoregressive spectrum analysis.
In the method, the central positions of the driving gear and the driven gear and the abrasion loss of the friction pair are calculated by solving a differential equation system.
In the method, a differential equation set of pressure pulsation is solved through a Runge-Kutta single-step algorithm of four orders and five orders in an internal flow field of the gear pump.
In the method, in the external flow field of the gear pump, a homogeneous turbulence spectrum analysis method is adopted, energy distribution of vortexes of various scales in turbulence at a measuring point of the gear pump under different working conditions is learned through a neural network, and a basis function coefficient of a heuristic function space is corrected, so that parameters of a pressure pulsation mathematical model are optimized.
In the method, the flow between the gear pump end surface gap and the gear crest gap is equivalent to the Couett-Poiseuille flow between the flat plates, and the flow passing through the gap is as follows:
Figure 524912DEST_PATH_IMAGE086
，
Figure 313002DEST_PATH_IMAGE087
，
in the formula:
Figure 561449DEST_PATH_IMAGE088
is the tooth width;
Figure 783483DEST_PATH_IMAGE062
the gear pump rotating speed;
Figure 258327DEST_PATH_IMAGE089
is the addendum circle radius;
Figure 115687DEST_PATH_IMAGE090
is the tooth height;
Figure 359586DEST_PATH_IMAGE091
is the average tooth height;
Figure 877155DEST_PATH_IMAGE009
the dynamic viscosity of the oil is adopted;
Figure 573716DEST_PATH_IMAGE092
the tooth crest thickness;
Figure 703608DEST_PATH_IMAGE093
the tooth thickness at the pitch circle;
Figure 67593DEST_PATH_IMAGE094
is as follows
Figure 756064DEST_PATH_IMAGE095
A cavity pressure;
Figure 939920DEST_PATH_IMAGE096
is a first
Figure 873503DEST_PATH_IMAGE097
Individual chamber pressure;
Figure 91995DEST_PATH_IMAGE098
the tooth top gap flow is measured;
Figure 951367DEST_PATH_IMAGE099
is the tooth flank clearance flow.
The above description is only an overview of the technical solutions of the present invention, and in order to make the technical means of the present invention more clearly apparent, and to make the implementation of the content of the description possible for those skilled in the art, and to make the above and other objects, features and advantages of the present invention more obvious, the following description is given by way of example of the specific embodiments of the present invention.
Drawings
Various other advantages and benefits of the present invention will become apparent to those of ordinary skill in the art upon reading the following detailed description of the preferred embodiments. The drawings are only for purposes of illustrating the preferred embodiments and are not to be construed as limiting the invention. It is obvious that the drawings described below are only some embodiments of the invention, and that for a person skilled in the art, other drawings can be derived from them without inventive effort. Also, like parts are designated with like reference numerals throughout the drawings.
In the drawings:
FIG. 1 is a schematic step diagram of a digital twin gear pump based predictive maintenance method according to one embodiment of the present invention;
FIG. 2 is a schematic diagram of a human-machine interaction control screen based on a digital twin gear pump predictive maintenance method according to one embodiment of the invention;
FIG. 3 is a time domain diagram of pressure pulsation based on a digital twin gear pump predictive maintenance method according to one embodiment of the invention;
FIG. 4 is a frequency domain plot of pressure pulsations for a digital twin gear pump based predictive maintenance method in accordance with one embodiment of the present invention.
The invention is further explained below with reference to the figures and examples.
Detailed Description
Specific embodiments of the present invention will be described in more detail below with reference to the accompanying drawings fig. 1 to 4. While specific embodiments of the invention are shown in the drawings, it should be understood that the invention may be embodied in various forms and should not be construed as limited to the embodiments set forth herein. Rather, these embodiments are provided so that this disclosure will be thorough and complete, and will fully convey the scope of the invention to those skilled in the art.
It should be noted that certain terms are used throughout the description and claims to refer to particular components. As one skilled in the art will appreciate, various names may be used to refer to a component. This specification and claims do not intend to distinguish between components that differ in name but not function. In the following description and in the claims, the terms "include" and "comprise" are used in an open-ended fashion, and thus should be interpreted to mean "include, but not limited to. The description which follows is a preferred embodiment of the invention, but is made for the purpose of illustrating the general principles of the invention and not for the purpose of limiting the scope of the invention. The scope of the present invention is defined by the appended claims.
For the purpose of facilitating understanding of the embodiments of the present invention, the following description will be made by taking specific embodiments as examples with reference to the accompanying drawings, and the drawings are not to be construed as limiting the embodiments of the present invention.
For better understanding, fig. 1 is a schematic diagram of a digital twin based gear pump predictive maintenance, and as shown in fig. 1, a digital twin based gear pump maintenance method comprises the following steps:
measuring and receiving gear pump working condition parameters in real time, wherein the working condition parameters comprise working pressure
Figure 622520DEST_PATH_IMAGE001
Flow rate of
Figure 94214DEST_PATH_IMAGE002
Rotational speed of the motor
Figure 167213DEST_PATH_IMAGE003
Torque of the motor
Figure 197486DEST_PATH_IMAGE100
Temperature of
Figure 621514DEST_PATH_IMAGE005
；
Calculating volumetric efficiency and limit speed of the gear pump based on the operating condition parameters to assess the operating condition of the gear pump and make a prediction of failure, wherein,
Figure 908618DEST_PATH_IMAGE101
，
Figure 836123DEST_PATH_IMAGE102
in the formula:
Figure 37297DEST_PATH_IMAGE103
is the limit rotation speed;
Figure 683042DEST_PATH_IMAGE001
is the working pressure;
Figure 762119DEST_PATH_IMAGE009
the dynamic viscosity of the oil is adopted;
Figure 544130DEST_PATH_IMAGE010
the clearance between the bearing and the bearing bush;
Figure 916206DEST_PATH_IMAGE011
is the bearing radius;
Figure 49247DEST_PATH_IMAGE012
is volume efficiency;
Figure 666435DEST_PATH_IMAGE013
displacement at operating pressure;
Figure 568532DEST_PATH_IMAGE104
displacement at no load pressure;
Figure 377088DEST_PATH_IMAGE105
is the flow at the working pressure;
Figure 997425DEST_PATH_IMAGE106
is the flow at no load pressure;
Figure 152725DEST_PATH_IMAGE107
is the rotation speed under the working pressure;
Figure 909329DEST_PATH_IMAGE108
is the rotation speed at the no-load pressure,
calculating the central positions of a driving gear and a driven gear of the gear pump and the abrasion loss of a friction pair, wherein the central positions are as follows:
Figure 623207DEST_PATH_IMAGE109
in the formula:
Figure 730840DEST_PATH_IMAGE020
is the mass of the gear 1;
Figure 424252DEST_PATH_IMAGE110
bearing counter force borne by the gear 1;
Figure 566520DEST_PATH_IMAGE111
is the pressure to which the gear 1 is subjected;
Figure 451300DEST_PATH_IMAGE023
the meshing force applied to the gear;
Figure 780650DEST_PATH_IMAGE024
is the moment of inertia of gear 1;
Figure 543332DEST_PATH_IMAGE112
is the angle of rotation of the gear 1;
Figure 415473DEST_PATH_IMAGE113
torque generated by the pressure to which the gear 1 is subjected;
Figure 471153DEST_PATH_IMAGE114
torque generated for the motor;
Figure 287800DEST_PATH_IMAGE115
is the radius of the meshing point of the gear 1;
Figure 87128DEST_PATH_IMAGE116
is the mass of the gear 2;
Figure 174295DEST_PATH_IMAGE117
is the bearing counter force borne by the gear 2;
Figure 666457DEST_PATH_IMAGE118
is the pressure to which the gear 2 is subjected;
Figure 235978DEST_PATH_IMAGE119
is the moment of inertia of gear 2;
Figure 573419DEST_PATH_IMAGE120
is the angle of rotation of the gear 2;
Figure 780671DEST_PATH_IMAGE121
torque generated by the pressure to which the gear 2 is subjected;
Figure 178155DEST_PATH_IMAGE122
is the radius of the meshing point of the gear 2,
the friction pair abrasion loss comprises abrasion between the end face of the gear and the inner walls of the floating shaft sleeve, the tooth top and the pump shell, and the friction pair abrasion loss is as follows:
Figure 969393DEST_PATH_IMAGE123
，
Figure 110524DEST_PATH_IMAGE124
in the formula:
Figure 160565DEST_PATH_IMAGE002
the abrasion loss of the friction pair is obtained;
Figure 994529DEST_PATH_IMAGE038
the energy consumed for wear on each stroke;
Figure 7484DEST_PATH_IMAGE039
the number of strokes;
Figure 952306DEST_PATH_IMAGE125
a sliding distance for each stroke;
Figure 868572DEST_PATH_IMAGE126
is the wear system constant;
Figure 873437DEST_PATH_IMAGE042
the maximum shear force to which the part is subjected;
in the internal flow field of the gear pump, a gear pump pressure pulsation model is established based on a centralized parameter method, an inlet control body, an isovolumetric control body, an outlet control body and a closed cavity control body are respectively modeled,
Figure 639268DEST_PATH_IMAGE127
，
in the formula:
Figure 122202DEST_PATH_IMAGE069
the pressure of the nth chamber of the gear 1;
Figure 158553DEST_PATH_IMAGE128
pressure of the mth cavity of the gear 2;
Figure 334319DEST_PATH_IMAGE129
the pressure of a sealed cavity of the gear pump;
Figure 587446DEST_PATH_IMAGE130
is the gear pump outlet pressure;
Figure 874071DEST_PATH_IMAGE131
is the gear pump inlet pressure;
in the gear pump external flow field, the Fourier expansion of the pressure pulsation signal at the measuring point is as follows:
Figure 138830DEST_PATH_IMAGE132
，
in the formula:
Figure 986963DEST_PATH_IMAGE075
is a direct current component;
Figure 461807DEST_PATH_IMAGE133
is the fundamental component of the frequency conversion;
Figure 552122DEST_PATH_IMAGE077
is a harmonic component of the frequency conversion; n =1 …;
Figure 61601DEST_PATH_IMAGE134
is a constant;
Figure 815056DEST_PATH_IMAGE135
generating a pressure pulsation signal amplitude for the tooth frequency;
Figure 777196DEST_PATH_IMAGE136
is an amplitude modulation coefficient;
Figure 671202DEST_PATH_IMAGE137
is a frequency modulation coefficient;
Figure 769608DEST_PATH_IMAGE138
is a phase angle;
Figure 693964DEST_PATH_IMAGE139
is the tooth frequency; m =1 …;
Figure 143400DEST_PATH_IMAGE140
is an amplitude-modulated signal;
Figure 575518DEST_PATH_IMAGE141
is a frequency modulated signal.
In a preferred embodiment of the method, time domain analysis, frequency domain analysis, wavelet analysis, functional analysis or matrix analysis is performed on the measured data and the simulated data.
In a preferred embodiment of the method, the time domain analysis comprises time domain statistical analysis or correlation analysis, and the frequency domain analysis comprises FFT, coherence analysis, cepstral analysis or autoregressive spectral analysis.
In the preferred embodiment of the method, the central positions of the driving gear and the driven gear and the abrasion amount of the friction pair are calculated by solving a differential equation system.
In the preferred embodiment of the method, the system of differential equations for the pressure pulsations is solved by the ODE45 in the gear pump internal flow field.
In the preferred embodiment of the method, in the external flow field of the gear pump, a homogeneous turbulence spectrum analysis method is adopted, and the energy distribution of various scale vortexes in turbulence at the measuring point of the gear pump under different working conditions is learned through a neural network, so that the basis function coefficient of a tentative function space is corrected, and the parameters of the pressure pulsation mathematical model are optimized.
In one embodiment, a digital twin based gear pump maintenance method comprises:
constructing a working condition parameter updating module, wherein pressure is respectively obtained by a pressure sensor, a flow sensor, a rotating speed-torque sensor and a temperature sensor which are arranged on a physical experiment table
Figure 528431DEST_PATH_IMAGE001
Flow rate of
Figure 623688DEST_PATH_IMAGE002
Rotational speed of the motor
Figure 294841DEST_PATH_IMAGE143
Torque of the motor
Figure 530650DEST_PATH_IMAGE144
Temperature of
Figure 603648DEST_PATH_IMAGE005
And the like.
Constructing a state evaluation module, wherein the volumetric efficiency of the gear pump is calculated according to the actually measured flow of the flow sensor
Figure 135386DEST_PATH_IMAGE012
And through between pressure and speedExpression to obtain the limit speed
Figure 293835DEST_PATH_IMAGE145
And the gear pump operation can be guided.
Constructing a model dynamic parameter calculation module, wherein a dynamic model of the gear pump is established, and the central positions of the driving gear and the driven gear are calculated by solving a differential equation set; the gear pump tooth crest and end surface abrasion mainly refers to abrasive wear, tooth crest and end surface abrasion amount is obtained according to an abrasion amount calculation formula and through combination of experimental measurement, and basic parameters of the gear pump are shown in table 1.
TABLE 1
Figure 67756DEST_PATH_IMAGE146
And constructing a gear pump internal flow field module, wherein a gear pump control body pressure pulsation equation set is established by adopting a centralized parameter method, the flow of tooth tops and end surfaces is assumed to be laminar flow between plates in the model, the influence of turbulent flow is considered by an inlet, an outlet and a closed cavity control body, and then a differential equation set of pressure pulsation is solved through ODE45 to obtain a pressure pulsation value in each control body.
And constructing a gear pump outflowing flow field module, wherein a homogeneous turbulence spectrum analysis method is adopted, pressure pulsation at a measuring point is approximately considered to be a stable random process, and the pressure pulsation is considered to be the superposition of vortexes with various different scales, and the energy distribution of the vortexes with various different scales in turbulence at the measuring point of the gear pump under different working conditions is learned through a neural network to correct a basis function coefficient of a heuristic function space, so that parameters of a pressure pulsation mathematical model are optimized.
And constructing a physical entity model, wherein a gear pump performance test bench is constructed by referring to the requirements on the gear pump performance test.
FIG. 2 is a schematic diagram of a human-computer interaction interface based on a predictive maintenance method of a digital twin gear pump, as shown in FIG. 2, and a working condition parameter module on the interface constantly reflects the operating pressure of the gear pump
Figure 260840DEST_PATH_IMAGE001
Flow rate of
Figure 709618DEST_PATH_IMAGE002
Rotational speed of the motor
Figure 355363DEST_PATH_IMAGE143
Temperature of
Figure 667396DEST_PATH_IMAGE005
The like; the performance evaluation module mainly displays volumetric efficiency of the gear pump
Figure 714987DEST_PATH_IMAGE012
Limit rotation speed
Figure 854106DEST_PATH_IMAGE147
The total working time h and the volumetric efficiency make a prediction evaluation on the failure of the gear pump, and the minimum rotating speed mainly prompts an operator to the minimum rotating speed at which the lubricating oil film of the gear pump bearing is damaged and abraded under a certain load, for example, when the load is 14MPa, the minimum rotating speed is 2000r/min, so that the abrasion of the gear pump bearing is reduced by increasing the rotating speed or reducing the load; the characteristic signal module mainly displays the information of the selected characteristic signals, such as pressure pulsation signals, flow signals, vibration signals and the like, and the change information of the characteristic signals can reflect the performance degradation and the occurrence of faults of the gear pump.
FIG. 3 is a time domain diagram of the characteristic signal pressure pulsation based on the digital twin gear pump predictive maintenance method according to the present invention, in the experiment, the gear pump rotation speed is 2466.6r/min, the load is 10MPa, the temperature is 22 ℃, and the flow rate is 9866.4mL/min. The figure shows that the obvious periodic fluctuation of the pressure pulsation signal is mainly caused by the periodic motion of the gear pump, and 12 small fluctuations are included in a large fluctuation, wherein the small fluctuation represents outlet pressure pulsation caused by oil removal when one tooth is rotated, and the large fluctuation represents pulsation caused by periodic change of leakage when the gear pump rotates for one circle. The amplitude of the pulsation is influenced by the rotating speed and the outlet pressure, and if the pulsation is worn and broken, the leakage amount is increased, so that the influence factor of large fluctuation is increased.
FIG. 4 is a frequency domain graph of characteristic signal pressure pulsation based on the digital twin gear pump predictive maintenance method according to the present invention, in the experiment, the gear pump rotational speed is 2466.6r/min, the load is 10MPa, the temperature is 22 ℃, and the flow rate is 9866.4mL/min. The figure shows that obvious periodic fluctuation components of the pressure pulsation signal mainly comprise gear rotating frequency, gear pump meshing frequency (tooth frequency) and frequency multiplication of the tooth frequency. The frequency conversion component is influenced most obviously by the rotating speed, the proportion of the frequency conversion component is gradually smaller along with the increase of the rotating speed, the tooth frequency gradually becomes the main pulse frequency, but the absolute amplitude of the frequency conversion basically keeps unchanged, the relative amplitude changes obviously, and the frequency conversion is reflected in a frequency domain graph to modulate the tooth frequency.
The method establishes a digital twin model of the gear pump, and takes the outlet pressure pulsation of the gear pump as a monitoring signal of a predictive maintenance model. Firstly, establishing a pressure pulsation model of an internal flow field of the gear pump by adopting a centralized parameter method to obtain the pressure in each control body inside the gear pump; secondly, a local homogeneous turbulence pulsation model is established for the position of a pressure sensor measuring point on an outlet pipeline of the gear pump, a mathematical model of pressure pulsation at the measuring point is obtained by adopting a homogeneous turbulence spectrum analysis method, energy distribution of various scale vortexes in turbulence at the measuring point of the gear pump under different working conditions is learned through a neural network, a basis function coefficient of a heuristic function space is corrected, high-fidelity simulation of the virtual model on a physical entity model is realized, and meanwhile, the virtual model makes an instructive strategy on the operation condition of the physical entity by calculating the volumetric efficiency and the limit rotating speed of the gear pump. By adopting the method, the real-time interaction between the gear pump virtual model and the physical entity can be realized, so that the composition of turbulence at the outlet measuring point of the gear pump is disclosed, and a new thought is provided for the performance monitoring and maintenance of the gear pump.
Although the embodiments of the present disclosure are described above with reference to the drawings, the embodiments of the present disclosure are not limited to two operating conditions of different rotation speeds and different loads, and may also include other kinds of operating conditions. The particular embodiments disclosed above are illustrative and explanatory only and are not restrictive. Those skilled in the art, having the benefit of this disclosure, may effect numerous modifications thereto and changes may be made without departing from the scope of the disclosure as set forth in the claims that follow.

Claims (6)

1. A method of digital twinning based gear pump maintenance, the method comprising the steps of:
measuring and receiving gear pump working condition parameters in real time, wherein the working condition parameters comprise working pressure
Figure DEST_PATH_IMAGE001
Flow rate of
Figure 161996DEST_PATH_IMAGE002
Rotational speed, torque
Figure DEST_PATH_IMAGE003
And temperature
Figure 519028DEST_PATH_IMAGE004
；
Calculating volumetric efficiency and limit speed of the gear pump based on the operating condition parameters to assess the operating condition of the gear pump and make a prediction of failure, wherein,
Figure DEST_PATH_IMAGE005
，
Figure 651194DEST_PATH_IMAGE006
in the formula:
Figure DEST_PATH_IMAGE007
is the limit rotation speed;
Figure 726467DEST_PATH_IMAGE001
is the working pressure;
Figure 936868DEST_PATH_IMAGE008
the dynamic viscosity of the oil is adopted;
Figure 587555DEST_PATH_IMAGE010
the clearance between the bearing and the bearing bush;
Figure DEST_PATH_IMAGE011
is the bearing radius;
Figure 920316DEST_PATH_IMAGE012
is volume efficiency;
Figure DEST_PATH_IMAGE013
is the displacement at the working pressure;
Figure 984349DEST_PATH_IMAGE014
displacement at no load pressure;
Figure DEST_PATH_IMAGE015
is the flow at the working pressure;
Figure 529600DEST_PATH_IMAGE016
is composed of
Figure DEST_PATH_IMAGE017
Flow at no load pressure;
Figure 628268DEST_PATH_IMAGE018
is the rotation speed under the working pressure;
Figure DEST_PATH_IMAGE019
is the rotation speed at the no-load pressure,
calculating the central positions of a driving gear and a driven gear of the gear pump and the abrasion loss of a friction pair, wherein the central positions are as follows: ,
Figure 600772DEST_PATH_IMAGE020
in the formula:
Figure DEST_PATH_IMAGE021
is the mass of the gear 1;
Figure 152102DEST_PATH_IMAGE022
the component of the bearing reaction force borne by the gear 1 in the direction of the x axis is formed;
Figure DEST_PATH_IMAGE023
the component force of the pressure applied on the gear 1 in the direction of the x axis;
Figure 235464DEST_PATH_IMAGE024
the component of the bearing reaction force borne by the gear 1 in the y-axis direction;
Figure DEST_PATH_IMAGE025
the component of the pressure applied on the gear 1 in the y-axis direction;
Figure 176920DEST_PATH_IMAGE026
the gear is subjected to meshing force;
Figure DEST_PATH_IMAGE027
is the moment of inertia of gear 1;
Figure 585905DEST_PATH_IMAGE028
is the angle of rotation of the gear 1;
Figure DEST_PATH_IMAGE029
torque generated by the pressure to which the gear 1 is subjected;
Figure 358951DEST_PATH_IMAGE030
torque generated for the motor;
Figure DEST_PATH_IMAGE031
the radius of the meshing point of the gear 1;
Figure 246004DEST_PATH_IMAGE032
is the mass of the gear 2;
Figure DEST_PATH_IMAGE033
the component of the bearing reaction force borne by the gear 2 in the direction of the x axis;
Figure 53686DEST_PATH_IMAGE034
the component force of the pressure applied on the gear 2 in the direction of the x axis;
Figure DEST_PATH_IMAGE035
the component of the bearing reaction force borne by the gear 2 in the y-axis direction;
Figure 633572DEST_PATH_IMAGE036
the component of the pressure applied to the gear 2 in the y-axis direction;
Figure DEST_PATH_IMAGE037
is the moment of inertia of gear 2;
Figure 425072DEST_PATH_IMAGE038
is the angle of rotation of the gear 2;
Figure DEST_PATH_IMAGE039
torque generated by the pressure to which the gear 2 is subjected;
Figure 850237DEST_PATH_IMAGE040
is the radius of the meshing point of the gear 2,
the abrasion loss of the friction pair comprises the abrasion loss between the end face of the gear and the floating shaft sleeve, between the tooth top and the inner wall of the pump shell, and the abrasion loss between the end face of the gear and the floating shaft sleeve determines the clearance between the end face of the gear and the floating shaft sleeve
Figure DEST_PATH_IMAGE041
The abrasion amount between the tooth crest and the inner wall of the pump shell determines the space between the pump shell and the tooth crest of the gear teeth of the gear pumpGap
Figure 512425DEST_PATH_IMAGE042
The size of (d); the abrasion loss of the friction pair is as follows:
Figure DEST_PATH_IMAGE043
，
Figure 263212DEST_PATH_IMAGE044
in the formula:
Figure 712648DEST_PATH_IMAGE002
the abrasion loss of the friction pair is obtained;
Figure DEST_PATH_IMAGE045
the energy consumed for wear on each stroke;
Figure 442969DEST_PATH_IMAGE046
the number of strokes;
Figure 661461DEST_PATH_IMAGE048
a sliding distance for each stroke;
Figure 786412DEST_PATH_IMAGE050
is the wear system constant;
Figure DEST_PATH_IMAGE051
the maximum shear force to which the part is subjected;
the flow between the tooth flank clearance and the tooth crest clearance is equivalent to couette-poisson flow between the plates, and the flow through the clearance is obtained according to the pressure difference and the size of the clearance, wherein,
Figure 21346DEST_PATH_IMAGE052
，
Figure DEST_PATH_IMAGE053
，
in the formula:
Figure 319472DEST_PATH_IMAGE054
is the tooth width;
Figure DEST_PATH_IMAGE055
the gear pump rotating speed;
Figure 956252DEST_PATH_IMAGE056
is the addendum circle radius;
Figure DEST_PATH_IMAGE057
is the tooth height;
Figure 48842DEST_PATH_IMAGE058
is the average tooth height;
Figure 454895DEST_PATH_IMAGE008
the dynamic viscosity of the oil is adopted;
Figure DEST_PATH_IMAGE059
the tooth crest thickness;
Figure 291133DEST_PATH_IMAGE060
the tooth thickness of the pitch circle;
Figure DEST_PATH_IMAGE061
is as follows
Figure 47999DEST_PATH_IMAGE062
A cavity pressure;
Figure DEST_PATH_IMAGE063
is a first
Figure 311490DEST_PATH_IMAGE064
Individual chamber pressures;
Figure DEST_PATH_IMAGE065
the tooth top gap flow is measured;
Figure 521017DEST_PATH_IMAGE066
is the tooth flank clearance flow;
under adiabatic, isentropic conditions, and
Figure DEST_PATH_IMAGE067
the pressure in the ith control body can be obtained according to the continuity equation:
Figure 895366DEST_PATH_IMAGE068
，
Figure DEST_PATH_IMAGE069
，
in the formula:
Figure 772318DEST_PATH_IMAGE070
is the bulk modulus of elasticity;
Figure 878814DEST_PATH_IMAGE055
the gear pump rotating speed;
Figure DEST_PATH_IMAGE071
is the ith control volume;
Figure 74172DEST_PATH_IMAGE072
is the gear rotation angle;
Figure DEST_PATH_IMAGE073
is the amount of change in the flow in the ith control fluid;
Figure 753677DEST_PATH_IMAGE074
for the flow rate of the (i + 1) th control body flowing into the ith control body through the gap；
Figure DEST_PATH_IMAGE075
The flow rate of the ith control body flowing out through the gap is measured;
modeling an inlet control body, an equal-volume control body, an outlet control body and a closed cavity control body in sequence by using the above formula so as to obtain the pressure of the whole internal flow field, wherein the model is as follows:
Figure 718091DEST_PATH_IMAGE076
in the formula:
Figure DEST_PATH_IMAGE077
the pressure of the nth tooth chamber of the gear 1;
Figure 824849DEST_PATH_IMAGE078
the pressure of the mth tooth chamber of the gear 2;
Figure DEST_PATH_IMAGE079
the pressure of a sealed cavity of the gear pump;
Figure 241924DEST_PATH_IMAGE080
is the gear pump outlet pressure;
Figure DEST_PATH_IMAGE081
is the gear pump inlet pressure;
pressure pulsation signal P at measuring point in external flow field of gear pump out The Fourier expansion of (t) is:
Figure 725121DEST_PATH_IMAGE082
in the formula: when n =1, the ratio of n to n is set to 1,
Figure DEST_PATH_IMAGE083
is the fundamental component of the frequency conversion;
Figure 544041DEST_PATH_IMAGE084
is a harmonic component of the frequency conversion; n =1 …;
Figure DEST_PATH_IMAGE085
is the frequency conversion;
Figure 821701DEST_PATH_IMAGE086
generating a pressure pulsation signal amplitude for frequency conversion;
Figure DEST_PATH_IMAGE087
is a constant;
Figure 991651DEST_PATH_IMAGE088
generating a pressure pulsation signal amplitude for the tooth frequency;
Figure DEST_PATH_IMAGE089
is the amplitude modulation coefficient;
Figure 735661DEST_PATH_IMAGE090
is a frequency modulation coefficient;
Figure DEST_PATH_IMAGE091
is a phase angle;
Figure 409088DEST_PATH_IMAGE092
is the tooth frequency; m =1 …;
Figure DEST_PATH_IMAGE093
is an amplitude-modulated signal;
Figure 123228DEST_PATH_IMAGE094
in order to be a frequency-modulated signal,
and establishing a digital twin model of the gear pump, and taking the outlet pressure pulsation of the gear pump as a monitoring signal of the predictive maintenance model.
2. The method of claim 1, wherein the time domain analysis, frequency domain analysis, wavelet analysis, functional analysis, or matrix analysis is performed on the measured data and the simulated data during the expansion of the pressure pulsation signal at the test point of the gear pump external flow field.
3. The method of claim 2, wherein the time domain analysis comprises time domain statistical analysis or correlation analysis, and the frequency domain analysis comprises FFT, coherence analysis, cepstral analysis, or autoregressive spectral analysis.
4. The method of claim 1, wherein the center positions of the driving and driven gears and the amount of wear of the friction pair are calculated by solving a system of differential equations.
5. The method as set forth in claim 1, wherein the differential equation set of the pressure pulsation is solved by a four-order, five-order Runge-Kutta one-step algorithm in the gear pump internal flow field.
6. The method as claimed in claim 1, wherein in the gear pump external flow field, a homogeneous turbulence spectrum analysis method is adopted to learn the energy distribution of various scale vortexes in turbulence at the gear pump measuring point under different working conditions through a neural network, so as to modify the basis function coefficient of a heuristic function space, thereby optimizing the parameters of the pressure pulsation mathematical model.
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