CN113255220A - Gear pump maintenance method based on digital twinning - Google Patents

Gear pump maintenance method based on digital twinning Download PDF

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CN113255220A
CN113255220A CN202110605998.8A CN202110605998A CN113255220A CN 113255220 A CN113255220 A CN 113255220A CN 202110605998 A CN202110605998 A CN 202110605998A CN 113255220 A CN113255220 A CN 113255220A
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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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Abstract

本公开揭示了一种基于数字孪生的齿轮泵维护方法，方法包括：测量并实时接收齿轮泵工况参数，基于工况参数计算齿轮泵容积效率和极限转速以评定齿轮泵的运行状态并对失效作出预估，计算齿轮泵的主、从动齿轮的中心位置和摩擦副磨损量，齿轮泵内流场中，基于集中参数法建立齿轮泵压力脉动模型，建立齿轮泵的数字孪生模型，以齿轮泵出口压力脉动为预测维护模型的监测信号。

Figure 202110605998

The present disclosure discloses a gear pump maintenance method based on digital twin. The method includes: measuring and receiving gear pump working condition parameters in real time; Make an estimate, calculate the center position of the main and driven gears of the gear pump and the wear amount of the friction pair. In the flow field of the gear pump, the pressure pulsation model of the gear pump is established based on the centralized parameter method, and the digital twin model of the gear pump is established. The pump outlet pressure pulsation is the monitoring signal for the predictive maintenance model.

Figure 202110605998

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 already known in this country to a person 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 working condition parameters of the gear pump in real time, wherein the working condition parameters comprise working pressure p, flow Q, rotating speed n and torque MpAnd a temperature T;
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 BDA0003093248120000021
Figure BDA0003093248120000022
in the formula: omegaminIs the limit rotation speed; p is the working pressure; mu is the dynamic viscosity of the oil liquid; c is the clearance between the bearing and the bearing bush; raIs the bearing radius; etaVIs volume efficiency; v2，eIs the displacement at the working pressure; v2，iDisplacement at no load pressure; q. q.sV2，eIs the flow at the working pressure; q. q.sV2，IIs the flow at no load pressure; n iseIs the rotation speed under the working pressure; n isiIs 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 BDA0003093248120000023
Figure BDA0003093248120000024
Figure BDA0003093248120000025
Figure BDA0003093248120000026
Figure BDA0003093248120000027
Figure BDA0003093248120000028
in the formula: m is1Is the mass of the gear 1; f. ofb1Is the bearing counter force borne by the gear 1; f. ofp1Is the pressure to which the gear 1 is subjected; f. ofmgThe meshing force applied to the gear; j. the design is a square1Is the moment of inertia of gear 1; theta1Is the angle of rotation of the gear 1; mp1Torque generated by the pressure to which the gear 1 is subjected; mmTorque generated for the motor; r isb1Is the radius of the meshing point of the gear 1; m is2Is the mass of the gear 2; f. ofb2Is the bearing counter force borne by the gear 2; f. ofp2Is the pressure to which the gear 2 is subjected; j. the design is a square2Is the moment of inertia of gear 2; theta2Is the angle of rotation of the gear 2; mp2Torque generated by the pressure to which the gear 2 is subjected; r isb2Is the radius of the meshing point of the gear 2,
the wear amount of the friction pair comprises the end face of the gear and the floatingThe abrasion loss among the movable shaft sleeve, 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 determine 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 determine 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 BDA0003093248120000031
in the formula: q is the abrasion loss of the friction pair; e is the energy consumed by wear per stroke; n is the number of strokes; s is the sliding distance of each stroke; c is the wear system constant; tau ismaxThe 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 BDA0003093248120000032
Figure BDA0003093248120000033
in the formula: b is the tooth width; omega is the gear pump rotating speed; r isextIs the addendum circle radius; bfIs the tooth height; r ismIs the average tooth height; mu is dynamic viscosity of oil liquid; ltThe tooth crest thickness; lfThe tooth thickness of the pitch circle; p is a radical ofiIs the ith chamber pressure; p is a radical ofi-1Is the i-1 th chamber pressure; qh，iThe tooth crest clearance flow is obtained; qf，iIs the tooth flank clearance flow;
under adiabatic, isentropic conditions, and pi+1＞piThe pressure in the ith control body can be obtained according to the continuity equation:
Figure BDA0003093248120000034
ΔQi＝Qi+1-Qi，
in the formula: b isoilIs the bulk modulus of elasticity; omega is the gear pump rotating speed; viIs the ith control volume; theta is a gear rotation angle; delta QiIs the amount of change in the flow in the ith control fluid; qi+1The flow rate of the ith +1 th control body flowing into the ith control body through the gap is set; qiThe 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, and obtaining the pressure of the whole internal flow field by using M, wherein the model is as follows:
Figure BDA0003093248120000041
Figure BDA0003093248120000042
Figure BDA0003093248120000043
Figure BDA0003093248120000044
Figure BDA0003093248120000045
Figure BDA0003093248120000046
Figure BDA0003093248120000047
Figure BDA0003093248120000048
Figure BDA0003093248120000049
in the formula: p is a radical ofn(θ)|1The pressure of the nth chamber of the gear 1; p is a radical ofm(θ)|2Pressure of the mth cavity of the gear 2; p is a radical oft(theta) is the pressure of the gear pump sealed cavity; p is a radical ofout(θ) is gear pump outlet pressure; p is a radical ofin(θ) is 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 BDA0003093248120000051
in the formula: a. theoLIs a direct current component; a. the1Lcos(ωoLt+ψ1) Is the fundamental component of the frequency conversion; n is not less than 2, AnLcos(nωoLt+ψn) Is a harmonic component of the frequency conversion; n-1 … 6; a. theoHIs a constant; a. themHGenerating a pressure pulsation signal amplitude for the tooth frequency; k is a radical ofamIs an amplitude modulation coefficient; k is a radical offmIs a frequency modulation coefficient; zetamIs a phase angle; omegaoHIs the tooth frequency; m is 1 … 6; p'outL(t) is an amplitude modulated signal; p ″)outL(t) is 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 four-order and five-order Runge-Kutta single-step algorithm 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 BDA0003093248120000061
Figure BDA0003093248120000062
in the formula: b is the tooth width; omega is the gear pump rotating speed; r isextIs the addendum circle radius; bfIs the tooth height; r ismIs the average tooth height; mu is dynamic viscosity of oil liquid; ltThe tooth crest thickness; lfThe tooth thickness of the pitch circle; p is a radical ofiIs the ith chamber pressure; p is a radical ofi-1Is the i-1 th chamber pressure; qh，iThe tooth crest clearance flow is obtained; qf，iIs the 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.
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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 by 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 present 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 working condition parameters of the gear pump in real time, wherein the working condition parameters comprise working pressure p, flow Q, rotating speed n and torque MpThe temperature T;
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 BDA0003093248120000071
Figure BDA0003093248120000072
in the formula: omegaminIs the limit rotation speed; p is the working pressure; mu is the dynamic viscosity of the oil liquid; c is the clearance between the bearing and the bearing bush; raIs the bearing radius; etaVIs volume efficiency; v2，eIs the displacement at the working pressure; v2，iDisplacement at no load pressure; q. q.sV2，eIs the flow at the working pressure; q. q.sV2，IIs the flow at no load pressure; n iseIs the rotation speed under the working pressure; n isiIs 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 BDA0003093248120000081
Figure BDA0003093248120000082
Figure BDA0003093248120000083
Figure BDA0003093248120000084
Figure BDA0003093248120000085
Figure BDA0003093248120000086
in the formula: m is1Is the mass of the gear 1; f. ofb1Is the bearing counter force borne by the gear 1; f. ofp1Is the pressure to which the gear 1 is subjected; f. ofmgThe meshing force applied to the gear; j. the design is a square1Is the moment of inertia of gear 1; theta1Is the angle of rotation of the gear 1; mp1Torque generated by the pressure to which the gear 1 is subjected; mmTorque generated for the motor; r isb1Is the radius of the meshing point of the gear 1; m is2Is the mass of the gear 2; f. ofb2Is the bearing counter force borne by the gear 2; f. ofp2Is the pressure to which the gear 2 is subjected; j. the design is a square2Is the moment of inertia of gear 2; theta2Is the angle of rotation of the gear 2; mp2Torque generated by the pressure to which the gear 2 is subjected; r isb2Is the radius of the meshing point of the gear 2,
the abrasion loss of the friction pair comprises abrasion among the gear end, the floating shaft sleeve, the tooth top and the inner wall of the pump shell, and the abrasion loss of the friction pair is as follows:
Figure BDA0003093248120000087
Figure BDA0003093248120000088
in the formula: q is the abrasion loss of the friction pair; e is the energy consumed by wear per stroke; n is the number of strokes; s is the sliding distance of each stroke; c is the wear system constant; tau ismaxThe 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 isometric control body, an outlet control body and a closed cavity control body are respectively modeled,
Figure BDA0003093248120000091
Figure BDA0003093248120000092
Figure BDA0003093248120000093
Figure BDA0003093248120000094
Figure BDA0003093248120000095
Figure BDA0003093248120000096
Figure BDA0003093248120000097
Figure BDA0003093248120000098
Figure BDA0003093248120000099
in the formula: p is a radical ofn(θ)|1The pressure of the nth chamber of the gear 1; p is a radical ofm(θ)|2Pressure of the mth cavity of the gear 2; p is a radical oft(theta) is the pressure of the gear pump sealed cavity; p is a radical ofout(θ) is gear pump outlet pressure; p is a radical ofin(θ) is 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 BDA00030932481200000910
Figure BDA00030932481200000911
in the formula: a. theoLIs a direct current component; a. the1Lcos(ωoLt+ψ1) Is the fundamental component of the frequency conversion; n is not less than 2, AnL cos(nωoLt+ψn) Is a harmonic component of the frequency conversion; n-1 … 6; a. theoHIs a constant; a. themHGenerating a pressure pulsation signal amplitude for the tooth frequency; k is a radical ofamIs an amplitude modulation coefficient; k is a radical offmIs a frequency modulation coefficient; zetamIs a phase angle; omegaoHIs the tooth frequency; m is 1 … 6; p'outL(t) is an amplitude modulated signal; p ″)outLAnd (t) 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 simulation 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 differential equation system of the pressure pulsation is solved by ODE45 in the gear pump internal flow field.
In the preferred embodiment of the method, in the gear pump external flow field, a homogeneous turbulence spectrum analysis method is adopted, and 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, so that a basis function coefficient of a tentative function space is corrected, and parameters of a 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 the pressure sensor, the flow sensor and the rotating speed-torque sensor are arranged on the physical experiment table, and the temperature sensor respectively obtains the pressure p, the flow Q, the rotating speed n and the torque MpTemperature T, etc.
Constructing a state evaluation module, wherein the volumetric efficiency eta of the gear pump is calculated according to the actually measured flow of the flow sensorVAnd obtaining the limit rotation speed omega by an expression between the pressure and the rotation speedminAnd 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 BDA0003093248120000111
And (2) 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 the differential equation set of pressure pulsation is solved through ODE45 to obtain the 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 module, wherein a gear pump performance test bench is constructed according to the requirements of the gear pump performance test with reference to national standards.
FIG. 2 is a schematic diagram of a human-computer interaction interface based on the digital twin gear pump prediction maintenance method, as shown in FIG. 2, a working condition parameter module on the interface constantly reflects parameters such as pressure p, flow Q, rotating speed n, temperature T and the like of the operation of the gear pump; the performance evaluation module mainly displays the volumetric efficiency eta of the gear pumpVLimit rotation speed omegaminThe 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 graph of characteristic signal pressure pulsation based on the digital twin gear pump predictive maintenance method according to the present invention, in which the gear pump speed was 2466.6r/min, the load was 10MPa, the temperature was 22 ℃, and the flow rate was 9866.4 mL/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 plot of the characteristic signal pressure pulsation of the predictive maintenance method based on the digital twin gear pump according to the present invention, the gear pump speed was 2466.6r/min, the load was 10MPa, the temperature was 22 deg.C, and the flow rate was 9866.4mL/min during the experiment. 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 technical solutions of the present disclosure are not limited to two operating conditions of different rotation speeds and different loads, and 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 (7)

1.一种基于数字孪生的齿轮泵维护方法，其特征在于，所述方法包括以下步骤：1. a gear pump maintenance method based on digital twin, is characterized in that, described method comprises the following steps: 测量并实时接收齿轮泵工况参数，工况参数包括工作压力p、流量Q、转速n、扭矩Mp和温度T；Measure and receive gear pump working parameters in real time, including working pressure p, flow Q, speed n, torque M p and temperature T; 基于工况参数计算齿轮泵容积效率和极限转速以评定齿轮泵的运行状态并对失效作出预估，其中，
Figure FDA0003093248110000011
Figure FDA0003093248110000012
式中：ωmin为极限转速；p为工作压力；μ为油液的动力粘度；c为轴承和轴瓦的间隙；Ra为轴承半径；ηV为容积效率；V2，e为工作压力下的排量；V2，i为空载压力下的排量；qV2，e为工作压力下的流量；qV2，I为空载压力下的流量；ne为工作压力下的转速；ni为空载压力下的转速，Calculate the volumetric efficiency and limit speed of the gear pump based on the working condition parameters to evaluate the operating state of the gear pump and predict the failure, among which,
Figure FDA0003093248110000011
Figure FDA0003093248110000012
In the formula: ω min is the limit speed; p is the working pressure; μ is the dynamic viscosity of the oil; c is the clearance between the bearing and the bearing bush; R a is the bearing radius; η V is the volumetric efficiency; V2 , i is the displacement under no-load pressure; q V2, e is the flow under working pressure; q V2, I is the flow under no-load pressure; n e is the speed under working pressure; n i is the rotational speed under no-load pressure, 计算齿轮泵的主、从动齿轮的中心位置和摩擦副磨损量，其中，中心位置为：Calculate the center position and friction pair wear amount of the main and driven gears of the gear pump, where the center position is:
Figure FDA0003093248110000013
Figure FDA0003093248110000013
 式中：m1为齿轮1的质量；fbx1为齿轮1所受的轴承反力在x轴方向分力；fpx1为齿轮1所受的压力在x轴方向分力；fby1为齿轮1所受的轴承反力在y轴方向分力；fpy1为齿轮1所受的压力在y轴方向分力；fmg为齿轮所受的啮合力；J1为齿轮1的转动惯量；θ1为齿轮1的转角；Mp1为齿轮1所受压力产生的转矩；Mm为电机产生的转矩；rb1为齿轮1啮合点的半径；m2为齿轮2的质量；fbx2为齿轮2所受的轴承反力在x轴方向分力；fpx2为齿轮2所受的压力在x轴方向分力；fby2为齿轮2所受的轴承反力在y轴方向分力；fpy2为齿轮2所受的压力在y轴方向分力；J2为齿轮2的转动惯量；θ2为齿轮2的转角；Mp2为齿轮2所受压力产生的转矩；rb2为齿轮2啮合点的半径，In the formula: m 1 is the mass of gear 1; f bx1 is the component force of the bearing reaction force on gear 1 in the x-axis direction; f px1 is the pressure component of gear 1 in the x-axis direction; f by1 is the gear 1 The component force of the bearing reaction force in the y-axis direction; f py1 is the component force of the pressure on the gear 1 in the y-axis direction; f mg is the meshing force on the gear; J 1 is the moment of inertia of the gear 1; θ 1 is the rotation angle of gear 1; M p1 is the torque generated by the pressure on gear 1; M m is the torque generated by the motor; r b1 is the radius of the meshing point of gear 1; m 2 is the mass of gear 2; f bx2 is the gear 2 is the component force of the bearing reaction force on the x-axis; f px2 is the component force of the pressure on the gear 2 in the x-axis direction; f by2 is the component force of the bearing reaction force on the gear 2 in the y-axis direction; f py2 is the force component of the pressure on the gear 2 in the y-axis direction; J 2 is the moment of inertia of the gear 2; θ 2 is the rotation angle of the gear 2; M p2 is the torque generated by the pressure on the gear 2; r b2 is the meshing of the gear 2 the radius of the point, 摩擦副磨损量包括在齿轮端面与浮动轴套、齿顶和泵壳内壁之间的磨损量，齿轮端面与浮动轴套之间的磨损量决定齿轮端面与浮动轴套之间间隙hf的大小，齿顶和泵壳内壁之间的磨损量决定齿轮泵泵壳与轮齿齿顶间隙hi的大小；摩擦副磨损量为：
Figure FDA0003093248110000021
式中：Q为摩擦副磨损量；E为每次行程中磨损所消耗的能量；N为行程次数；s为每一行程滑动距离；c为磨损系统常数；τmax为零件所受的最大剪切力；The wear amount of the friction pair includes the wear amount between the end face of the gear and the floating sleeve, the tooth tip and the inner wall of the pump casing. The amount of wear between the end face of the gear and the floating sleeve determines the size of the gap h f between the end face of the gear and the floating sleeve , the wear amount between the tooth tip and the inner wall of the pump casing determines the size of the gap hi between the gear pump casing and the gear tooth tip; the wear amount of the friction pair is:
Figure FDA0003093248110000021
In the formula: Q is the wear amount of the friction pair; E is the energy consumed by wear in each stroke; N is the number of strokes ; s is the sliding distance of each stroke; c is the wear system constant; cutting force; 根据压差和间隙的大小得到通过间隙的流量，其中，According to the pressure difference and the size of the gap, the flow through the gap is obtained, where,
Figure FDA0003093248110000022
Figure FDA0003093248110000022
Figure FDA0003093248110000023
Figure FDA0003093248110000023
 式中：b为齿宽；ω为齿轮泵转速；rext为齿顶圆半径；bf为齿高；rm为平均齿高；μ为油液动力粘度；lt为齿顶厚度；lf为节圆处齿厚；pi为第i腔压力；pi-1为第i-1个腔压力；Qh，i为齿顶间隙流量；Qf，i为齿侧间隙流量；Where: b is the tooth width; ω is the speed of the gear pump; r ext is the radius of the tooth tip; b f is the tooth height; r m is the average tooth height; μ is the oil dynamic viscosity; l t is the tooth tip thickness; l f is the tooth thickness at the pitch circle; p i is the pressure of the i-th cavity; p i-1 is the i-1-th cavity pressure; Q h, i is the tooth tip clearance flow; Q f, i is the tooth side clearance flow; 在绝热、等熵的条件下，且pi+1＞pi，根据连续性方程可得第i个控制体中的压力：Under adiabatic and isentropic conditions, and p i+1 > p i , the pressure in the i-th control volume can be obtained according to the continuity equation:
Figure FDA0003093248110000031
Figure FDA0003093248110000031
 ΔQi＝Qi+1-Qi，ΔQ i =Q i+1 −Q i , 式中：Boil为体积弹性模量；ω为齿轮泵转速；Vi为第i个控制体体积；θ为齿轮转角；ΔQi为第i个控制体中流量的变化量；Qi+1为第i+1个控制体通过间隙流入第i个控制体的流量；Qi为第i个控制体通过间隙流出的流量；In the formula: B oil is the bulk modulus of elasticity; ω is the speed of the gear pump; Vi is the volume of the ith control body; θ is the gear angle; ΔQ i is the change of the flow in the ith control body; Q i+1 is the flow of the i+1th control body flowing into the i-th control body through the gap; Q i is the flow rate of the i-th control body flowing out through the gap; 利用上式对进口控制体、等体积控制体、出口控制体、密闭腔控制体依次进行建模，从而得到整个内流场压力的大小，模型如下式：Use the above formula to model the inlet control body, equal volume control body, outlet control body, and closed cavity control body in turn, so as to obtain the pressure of the entire internal flow field. The model is as follows:
Figure FDA0003093248110000032
Figure FDA0003093248110000032
 式中：pn(θ)|1为齿轮1第n个齿腔的压力；pm(θ)|2为齿轮2第m个齿腔的压力；pt(θ)为齿轮泵密闭腔的压力；pout(θ)为齿轮泵出口压力；pin(θ)为齿轮泵进口压力；In the formula: p n (θ)| 1 is the pressure of the n-th tooth cavity of gear 1; p m (θ) | 2 is the pressure of the m-th tooth cavity of gear 2; p t (θ) is the pressure of the closed cavity of the gear pump. pressure; p out (θ) is the gear pump outlet pressure; p in (θ) is the gear pump inlet pressure; 齿轮泵外流场中，测点处压力脉动信号的傅里叶展开为：In the external flow field of the gear pump, the Fourier expansion of the pressure pulsation signal at the measuring point is:
Figure FDA0003093248110000041
Figure FDA0003093248110000041
 式中：A1Lcos(ωoLt+ψ1)为转频的基波分量；n≥2，AnLcos(nωoLt+ψn)为转频的谐波分量；n＝1…6；ωoL为转频；AnL为转频产生压力脉动信号幅值；C为常数；AmH为齿频产生压力脉动信号幅值；kam为调幅系数；kfm为调频系数；ζm，ψn为相位角；ωoH为齿频；m＝1…6；p′outL(t)为调幅信号；p″outL(t)为调频信号，In the formula: A 1L cos(ω oL t+ψ 1 ) is the fundamental component of the rotational frequency; n≥2, A nL cos(nω oL t+ψ n ) is the harmonic component of the rotational frequency; n=1…6 ;ω oL is the rotation frequency; A nL is the amplitude of the pressure pulsation signal generated by the rotation frequency; C is a constant; AmH is the amplitude of the pressure pulsation signal generated by the tooth frequency; k am is the amplitude modulation coefficient; k fm is the frequency modulation coefficient; ζ m , ψ n is the phase angle; ω oH is the tooth frequency; m=1…6; p′ outL (t) is the amplitude modulation signal; p″ outL (t) is the frequency modulation signal, 建立齿轮泵的数字孪生模型，以齿轮泵出口压力脉动为预测维护模型的监测信号。A digital twin model of the gear pump is established, and the pressure pulsation at the outlet of the gear pump is used as the monitoring signal for the predictive maintenance model. 2.根据权利要求1所述的方法，其特征在于，优选的，齿轮泵外流场测点处压力脉动信号的展开中，对实测数据和仿真数据进行时域分析、频域分析、小波分析、泛函分析或矩阵分析。2. method according to claim 1 is characterized in that, preferably, in the unfolding of pressure pulsation signal at measuring point of gear pump outer flow field, time domain analysis, frequency domain analysis, wavelet analysis are carried out to measured data and simulation data , functional analysis or matrix analysis. 3.根据权利要求2所述的方法，其特征在于，时域分析包括时域统计分析或相关性分析，频域分析包括FFT、相干分析、倒频谱分析或自回归谱分析。3. The method according to 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.根据权利要求1所述的方法，其特征在于，通过解微分方程组计算主、从动齿轮的中心位置以及摩擦副的磨损量。4 . The method according to claim 1 , wherein the center positions of the main and driven gears and the wear amount of the friction pair are calculated by solving the differential equation system. 5 . 5.根据权利要求1所述的方法，其特征在于，齿轮泵内流场中，通过四阶，五阶Runge-Kutta单步算法求解压力脉动的微分方程组。5 . The method according to claim 1 , wherein, in the flow field in the gear pump, the differential equation system of pressure pulsation is solved by the fourth-order and fifth-order Runge-Kutta single-step algorithm. 6 . 6.根据权利要求1所述的方法，其特征在于，齿轮泵外流场中，采用均质湍流谱分析方法，通过神经网络来学习不同工况下齿轮泵测点处湍流中各种不同尺度涡的能量分布，来修止试探函数空间的基函数系数，从而优化压力脉动数学模型的参数。6. The method according to claim 1, wherein, in the external flow field of the gear pump, a homogeneous turbulent spectrum analysis method is used to learn various scales in the turbulent flow at the measuring points of the gear pump under different working conditions through a neural network The energy distribution of the vortex is used to modify the basis function coefficients of the heuristic function space, thereby optimizing the parameters of the mathematical model of pressure pulsation. 7.根据权利要求1所述的方法，其特征在于，齿轮泵端面间隙和齿顶间隙之间的流动等效为平板间的库埃特-泊肃叶流动，通过间隙的流量为：7. The method according to claim 1, wherein the flow between the gear pump end face clearance and the tooth tip clearance is equivalent to the Couette-Poiseuille flow between the plates, and the flow through the clearance is:
Figure FDA0003093248110000051
Figure FDA0003093248110000051
Figure FDA0003093248110000052
Figure FDA0003093248110000052
 式中：b为齿宽；ω为齿轮泵转速；rext为齿顶圆半径；bf为齿高；rm为平均齿高；μ为油液动力粘度；lt为齿顶厚度；lf为节圆处齿厚；pi为第i腔压力；pi-1为第i-1个腔压力；Qh，i为齿顶间隙流量；Qf，i为齿侧间隙流量。Where: b is the tooth width; ω is the speed of the gear pump; r ext is the radius of the tooth tip; b f is the tooth height; r m is the average tooth height; μ is the oil dynamic viscosity; l t is the tooth tip thickness; l f is the tooth thickness at the pitch circle; pi is the pressure of the i-th cavity; p i -1 is the i-1-th cavity pressure; Q h, i is the tooth tip clearance flow; Q f, i is the tooth side clearance flow.
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