CN116257948A - Axial plunger pump analysis method and system containing bearing faults under liquid-carrying working condition - Google Patents
Axial plunger pump analysis method and system containing bearing faults under liquid-carrying working condition Download PDFInfo
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Abstract
The invention provides an analysis method of an axial plunger pump with bearing faults under a liquid-carrying working condition, which comprises the steps of constructing a geometric structure model of a rotor system of a vertical axial plunger pump so as to obtain a fluid acting force equation; the working medium mass is equivalently decomposed into a rotor additional mass, a shell additional mass and a liquid coupling mass, and an axial plunger pump rotor dynamics equation is constructed by combining a fluid acting force equation and a friction force, centrifugal force and mass unbalance force equation of a cylinder assembly; constructing a dynamic model of local defect faults of the roller bearing to calculate the angular position of the roller motion, and acquiring time-varying displacement excitation and time-varying contact stiffness excitation to be assembled into the dynamic equation when the roller enters the defect to obtain a dynamic model containing the bearing faults; and analyzing the dynamic model containing the bearing faults to obtain the critical rotation speed of each fault element. By implementing the invention, the analysis and calculation result is closer to the actual value, and the vibration characteristic analysis and dynamic design work can be better carried out.
Description
Technical Field
The invention relates to the technical field of axial plunger pumps, in particular to an axial plunger pump analysis method and an axial plunger pump analysis system containing bearing faults under a liquid-carrying working condition.
Background
The axial plunger pump is widely applied to industries such as engineering machinery, aerospace, marine equipment and the like, and along with the continuous improvement of the requirement on the operation efficiency, the axial plunger pump increasingly tends to develop in the high-speed, high-pressure and high-flow directions in recent years. The axial plunger pump rotor system has a complex structure and is generally composed of a cylinder body assembly (a cylinder body, a swash plate, a valve plate, a plunger and a sliding shoe), a bearing, a main shaft, a shell and other parts, and the working rotation speed is more than 3000rpm, so that on the basis of traditional mechanical strength design, the surface damage, abrasion and other fault dynamics characteristics of the bearing are always considered. In recent years, bearing friction damage faults of the axial plunger pump occur, stable operation of the axial plunger pump is seriously endangered, and huge economic loss is caused for serious national equipment. The traditional axial plunger pump fault prediction and operation and maintenance are mainly based on experimental tests and experience maintenance, lack of direct evidence of key component fault tracing, and prolong the design research and development period. Therefore, the common practice is that the working speed range of the plunger pump and the critical speed area containing the defective cylindrical roller bearing meet a certain isolation margin dynamic design requirement, otherwise, the designed axial plunger pump is easy to have strong vibration, noise and other problems in the actual operation process, the fault characteristic frequency of the defective cylindrical roller bearing is obtained, the corresponding relation between the vibration characteristic frequency of the defective cylindrical roller bearing and the vibration characteristic of the rotor system of the axial plunger pump is established, and the accurate tracing of the local fault of the axial plunger pump is realized. In the working operation process of the axial plunger pump, as the liquid working medium has certain mass, the flowing process is very complex under the action of the rotation centrifugal force of the pump rotor, and certain mutual coupling action exists between the liquid working medium and the cylinder assembly. When the axial plunger pump rotor assembly vibrates, liquid media contacted with the axial plunger pump rotor assembly also vibrate, on one hand, the rotating cylinder assembly can influence the distribution of a liquid media flow field, so that the distribution and the size of fluid load are changed; on the other hand, the cylinder assembly deforms under the pressure load of the flow field. Based on the influence of the factors in various aspects, the critical rotating speed and vibration mode of the axial plunger pump which is operated by the fault defects of the liquid working medium and the bearing can be changed, so that the vibration characteristic of the rotor of the axial plunger pump becomes more complex, and the dynamic design difficulty is greatly increased. Therefore, in the dynamic design of the axial plunger pump, it is necessary to consider the influence of the liquid working medium on the vibration characteristics of the axial plunger pump, accurately analyze the local fault characteristics, the critical rotation speed and the vibration mode of the axial plunger pump, and provide basis and reference for the structural dynamic design and the vibration analysis of the axial plunger pump.
At present, a great deal of research work is carried out on the aspects of pump rotor dynamics modeling and analysis by a great number of scholars at home and abroad. For example, the device and the method derive a pump wet rotor dynamics equation by analyzing the coupling effect of an axial plunger pump rotor and surrounding working media, and calculate the vibration mode of the pump rotor by adopting a spectrum analysis method, but because the actual operation working condition under the working media with liquid is complex in site, fundamental frequency signals cannot be effectively extracted from stirring containing a plurality of interference frequency components, and the critical rotation speed and vibration mode of the axial plunger pump are difficult to accurately estimate and analyze through responses at a limited number of measuring points. For another example, most domestic manufacturers perform dynamic modeling and critical rotation speed analysis on the rotor of the axial plunger pump under normal working conditions, but the influence of the fault of the liquid working medium and the bearing on the vibration characteristics of the rotor of the axial plunger pump is not considered, so that the built dynamic model is not matched with the actual working conditions, the vibration characteristic value calculated by the dynamic model analysis is greatly different from the actual value, a large number of single and multiple fault samples of different types reflecting the actual working conditions cannot be obtained, the axial plunger pump designed and produced is excessively vibrated and has reduced performance, and the safe production and the healthy operation of the axial plunger pump are seriously influenced.
Therefore, it is necessary to analyze the axial plunger pump by using a new axial plunger dynamics modeling method, so that the analysis calculation result (such as the vibration characteristic value and the like) is closer to the actual value, and the vibration characteristic analysis and the dynamic design work can be better performed.
Disclosure of Invention
The technical problem to be solved by the embodiment of the invention is to provide the method and the system for analyzing the axial plunger pump with the bearing fault under the working condition of liquid, so that the analysis and calculation result is closer to the actual value, the vibration characteristic analysis and dynamic design work can be better carried out, and the service life of the axial plunger pump is prolonged.
In order to solve the technical problems, the embodiment of the invention provides an axial plunger pump analysis method containing bearing faults under a liquid-carrying working condition, which comprises the following steps:
s1, constructing a geometric structure model among a rotor, a cylinder assembly, a shell and a working medium of the vertical axial plunger pump according to the actual space positions and the actual dimensions of a component shell, the cylinder assembly and a rotating shaft structure of the axial plunger pump so as to obtain a fluid acting force equation between the working medium and the cylinder assembly;
s2, decomposing the mass equivalent of a working medium into a rotor additional mass, a shell additional mass and a liquid coupling mass, determining calculation expressions of the rotor additional mass, the shell additional mass and the liquid coupling mass, and further combining a fluid acting force equation, a friction force equation, a centrifugal force equation and a mass unbalance force equation of a cylinder assembly to respectively carry out stress analysis on a disc, a shaft section and a support of the axial plunger pump rotor so as to construct an axial plunger pump rotor dynamics equation under a liquid carrying working condition;
S3, constructing a partial defect fault dynamics model of the cylindrical roller bearing considering time-varying excitation, calculating the angular position of roller motion in the cylindrical roller bearing, acquiring time-varying displacement excitation and time-varying contact stiffness excitation according to a load deformation relation when the roller is judged to enter the defect based on the calculated angular position, and further assembling the acquired time-varying displacement excitation and time-varying contact stiffness excitation into an axial plunger pump rotor dynamics equation under the liquid-carrying working condition by a matrix operation method to obtain an axial plunger pump rotor system fault dynamics model containing bearing faults under the liquid-carrying working condition;
s4, analyzing a fault dynamic model of the axial plunger pump rotor system containing the bearing fault under the working condition with the liquid to obtain the critical rotation speed of each fault element under the corresponding fault characteristic frequency; wherein the failure element comprises a bearing outer ring, a bearing inner ring and rolling elements.
The step S1 specifically includes:
according to the actual space positions and the actual dimensions of a component shell, a cylinder assembly and a rotating shaft structure of the axial plunger pump, and by combining the fluid acting force between a working medium and the cylinder assembly, adopting regular cylinders to respectively perform equivalent modeling on a shell, a rotor and the working medium; wherein, the working medium fills the annular space between the rotor and the shell;
Determining the inner radius and the outer radius of the annular space according to the diameters of the rotor, the cylinder assembly and the shell, and constructing a geometric structure model among the rotor, the cylinder assembly, the shell and the working medium of the vertical axial plunger pump;
based on the constructed geometric model, the pressure vector value on each grid node of the cylinder assembly is solved by utilizing Fluent software to obtain a fluid acting force equation between the working medium and the cylinder assembly.
Wherein the specific steps of solving the pressure vector values at each grid node of the cylinder assembly to obtain the fluid force equation between the working medium and the cylinder assembly include:
let the area of the node i in the main flow field be Deltas, the fluid acting force F of the node i i ＝p i ΔS i Then the node i fluid force F i In the x, y direction components are
Wherein a is F i An angle with the x-axis; i=1, 2,. -%, n;
based on node i fluid force F i The total acting force component of the main flow field on the cylinder body assembly is obtained as
The step S2 specifically includes:
equivalent splitting of the mass of the working medium into a rotor-attached mass, a housing-attached mass and a liquid-coupled mass, and determining the rotor-attached mass, the housingA computational expression of the volume-added mass and the liquid-coupled mass; wherein the calculated expression of the additional mass of the rotor is 
The calculated expression of the additional mass of the shell is +.>
The calculated expression of the liquid coupling quality is m 21 ＝ρπL 1 (R 2 -R 1 ) 2 ；m 11 Adding mass to the rotor; m is m 12 Adding mass to the housing; m is m 21 A mass for said liquid coupling; ρ is the density of the working medium; r is R 1 A disc inner radius that is the annular space; r is R 2 A housing outer radius for the annular space; l is the disc length of the annular space;
based on the calculated expressions of the rotor additional mass, the shell additional mass and the liquid coupling mass, respectively carrying out stress analysis on a disc, a shaft section and a support of the axial plunger pump rotor by combining the fluid acting force equation, a friction force equation, a centrifugal force equation and a mass unbalance force equation of a cylinder assembly so as to construct an axial plunger pump rotor dynamics equation under a liquid-carrying working condition; the expression of the dynamic equation of the axial plunger pump rotor under the working condition with liquid is as follows
wherein ,
and M is the rotor system inertia matrix; />
And C is a system damping matrix taking into account fluid effects; />
And K is * A system stiffness matrix for consideration of fluid effects;
G 1 a damping matrix for consideration of gyroscopic effects; m is M 1 From an axis segment unit inertia matrix M s Disk unit inertia matrix M d Forming; c (C) 1 Damping matrix C by shaft section unit s Disc unit damping matrix C d Forming; k (K) 1 From the axle segment unit stiffness matrix K S Stiffness matrix K of disc unit d Forming a dynamic characteristic coefficient of the bearing;
F e is an unbalanced force of the cylinder assembly, and F e ＝J p meω 2 ；F s Is the centrifugal force of the slipper pair; f (F) fs Friction force of the slipper pair; f (F) p Is the centrifugal force of the cylinder assembly, and F p ＝m sp ω 2 R；F v1 and Fv2 Friction forces of cylinder assemblies respectively, and
F z friction force of the flow distribution pair; />
And u is the acceleration vector, velocity vector and displacement vector of the system respectively; j (J) p The rotary inertia of the rotary assembly is represented by m, the mass of the cylinder assembly is represented by e, the eccentric amount is represented by ω, and the angular velocity of the disc is represented by ω; ms of p Is the diameter of the cylinder assembly; mu is hydrodynamic viscosity, R c For cylinder assembly radius, l c For the length of the cylinder assembly>
t is the width of the gap between the cylinder assembly outer surface and the housing inner surface.
The step S3 specifically includes:
defining geometric parameters, rotating speed and load of the bearing and geometric parameters and position parameters of the local defect;
by the formula
Calculating the ratio eta of the diameter d of the bearing to the minimum dimension L of the local defect b And pass through the formula
Calculating the ratio eta of the length L and the width B of the local defect d ；
According to the ratio eta of the diameter d of the bearing to the minimum dimension L of the local defect b And the ratio eta of the local defect length dimension L to the width dimension B d Constructing a local defect model based on a piecewise function; wherein the piecewise function is composed of half sine and rectangle functions, and the expression of the time-varying displacement excitation induced by the local defect is as follows:
wherein mod () is a remainder function; t is t dl1 、t dl2 、t j Respectively different time periods; 0 to t dl1 The time period represents a half sine function; t is t dl1 ～t dl2 The time period represents a rectangular function; t is t dl1 ～(t dl1 +t dl2 ) The time period represents a piecewise function consisting of half sine functions; Δd is the ratio η b Or ratio eta d ；
Determining a time-varying contact stiffness equation between the friction members; wherein the expression of the time-varying contact stiffness equation between the friction parts is
K is Hertz contact stiffness between friction pairs; k (K) 1 、K 2 and K3 The contact rigidity between the friction part and the defect edge under different conditions is shown;
determining a nonlinear contact stiffness equation between friction parts, wherein the expression of the nonlinear contact stiffness equation between friction parts is F (t) =K (t) delta n(t) The method comprises the steps of carrying out a first treatment on the surface of the F (t) is a time-varying contact force; k (t) is the time-varying contact stiffness between the sphere and the local defect edge; n (t) is the time-varying load-deformation coefficient between the sphere and the local defect edge;
Calculating time-varying displacement excitation and time-varying contact stiffness excitation between the rolling bodies and the defect edges according to a time-varying contact stiffness equation between the friction parts and a nonlinear contact stiffness equation between the friction parts;
acquiring a bearing dynamics model, and solving the bearing dynamics model to acquire the angular position of each rolling body of the rolling bearing; wherein the expression of the bearing dynamics model comprises
And
and after determining that the roller enters the defect according to the angular position of each rolling body, assembling the calculated time-varying displacement excitation and time-varying contact stiffness excitation between the rolling bodies and the defect edge into an axial plunger pump rotor dynamics equation under the liquid-carrying working condition by a matrix operation method to obtain a fault dynamics model of the axial plunger pump rotor system containing the bearing fault under the liquid-carrying working condition.
The specific step of solving the bearing dynamics model to obtain the angular position of each rolling element of the rolling bearing comprises the following steps:
solving the bearing dynamics model by adopting a fixed-step length 4-order Dragon lattice tower method, and ending the solution when the solution time is determined to be longer than the set time; otherwise, when the solving time is smaller than the set time, continuing to solve;
And after the solving is finished, obtaining time domain and frequency domain vibration signals of each rolling body in the rolling bearing so as to determine the angular position of each rolling body in the rolling bearing.
The step S4 specifically includes:
the first step, a second order differential equation of motion is given:
wherein M is a structural mass matrix, C is a structural damping matrix, and K is a structural rigidity matrix;
secondly, determining a Newmark method, wherein the Newmark method adopts a finite differential expansion mode over a time step delta t, and is expressed by the following formulas (2) and (3):
wherein alpha and beta are Newmark integral parameters; Δt=t n+1 -t n For the integration step size,
and un Respectively t n Acceleration vector, velocity vector, displacement vector of moment; />
and un+1 Respectively t n+1 Acceleration vector, velocity vector, displacement vector of moment;
the third step, since the main purpose of solving equation (1) is to obtain t n+1 The displacement of the moment, therefore, is converted from equations (2) and (3), t n+1 The velocity and acceleration vectors at time are denoted as t n+1 Time displacement vector u n+1 Is a functional form of:
in the formula ,
α 6 ＝Δt(1-β),α 7 ＝βΔt
the fourth step, from equation (1), can be found as follows:
fifth step, simultaneous equations (4) - (6) can obtain t n+1 Time displacement vector u n+1 Is represented by the expression:
sixth step, according to displacement vector u n+1 And combining equations (4) and (5), then determining t n+1 Acceleration vector of moment of time
And velocity vector->
Seventh step, according to t n+1 Acceleration vector of moment of time
And velocity vector->
A critical rotational speed is determined.
The embodiment of the invention also provides an axial plunger pump analysis system containing bearing faults under the working condition with liquid, which comprises the following components;
the fluid acting force equation acquisition unit is used for constructing a geometric structure model among the rotor, the cylinder assembly, the shell and the working medium of the vertical axial plunger pump according to the actual space positions and the actual dimensions of the component shell, the cylinder assembly and the rotating shaft structure of the axial plunger pump so as to obtain a fluid acting force equation between the working medium and the cylinder assembly;
the system comprises a fault-free pump rotor dynamics equation construction unit, a hydraulic pump rotor dynamics equation analysis unit and a hydraulic pump rotor dynamics equation analysis unit, wherein the fault-free pump rotor dynamics equation construction unit is used for decomposing the mass equivalent of a working medium into a rotor additional mass, a shell additional mass and a liquid coupling mass, determining the calculation expressions of the rotor additional mass, the shell additional mass and the liquid coupling mass, and further respectively carrying out stress analysis on a disc, a shaft section and a support of the axial plunger pump rotor by combining a fluid acting force equation, a friction force equation, a centrifugal force equation and a mass unbalance force equation of a cylinder assembly so as to construct the axial plunger pump rotor dynamics equation under the working condition with liquid;
The pump rotor dynamic equation construction unit with faults is used for constructing a partial defect dynamic model of the cylindrical roller bearing considering time-varying excitation, calculating the angular position of the roller motion in the cylindrical roller bearing, acquiring time-varying displacement excitation and time-varying contact stiffness excitation according to a load deformation relation when the roller is judged to enter the defect based on the calculated angular position, and further assembling the acquired time-varying displacement excitation and time-varying contact stiffness excitation into the axial plunger pump rotor dynamic equation under the working condition with liquid by a matrix operation method to obtain the axial plunger pump rotor system fault dynamic model with the bearing faults under the working condition with liquid;
the pump rotor power failure analysis unit is used for analyzing the failure dynamic model of the axial plunger pump rotor system containing the bearing failure under the working condition of liquid carrying so as to obtain the critical rotation speed of each failure element under the corresponding failure characteristic frequency; wherein the failure element comprises a bearing outer ring, a bearing inner ring and rolling elements.
The embodiment of the invention has the following beneficial effects:
according to the invention, through combining the characteristic that faults of working medium and bearing defects in the pump are not negligible under the working condition of liquid carrying, the structural relation of the vertical shaft to the rotor of the plunger pump, the bearing and the working medium is analyzed, the mass of the working medium is decomposed into three parts of additional mass of the rotor, additional mass of the shell and liquid coupling mass, so that an axial plunger pump rotor system dynamics model with the bearing defects of the liquid working medium is accurately built, and further, the calculation and analysis of the critical wet rotating speed and the fault characteristic frequency are carried out according to the built dynamics model, so that the vibration faults of the axial plunger pump rotor in the actual running process are effectively reduced.
Drawings
In order to more clearly illustrate the embodiments of the invention or the technical solutions of the prior art, the drawings which are required in the description of the embodiments or the prior art will be briefly described, it being obvious that the drawings in the description below are only some embodiments of the invention, and that it is within the scope of the invention to one skilled in the art to obtain other drawings from these drawings without inventive faculty.
FIG. 1 is a flow chart of an analysis method of an axial plunger pump with bearing faults under a liquid-carrying working condition provided by an embodiment of the invention;
fig. 2 is a schematic diagram of axial plunger pump rotor system engineering in an application scenario of an analysis method of an axial plunger pump with bearing failure under a liquid-carrying working condition provided by an embodiment of the invention;
FIG. 3 is a schematic diagram of an axial plunger pump rotor system model under a liquid-carrying condition in an application scenario of an analysis method of an axial plunger pump with bearing faults under the liquid-carrying condition provided by an embodiment of the invention;
FIG. 4 is a schematic diagram of a piecewise function-based local defect model in an application scenario of an axial plunger pump analysis method with bearing faults under a liquid-carrying working condition provided by an embodiment of the invention;
FIG. 5 is a vibration response diagram of an axial plunger pump under different rotation speeds in an application scenario of an analysis method of an axial plunger pump with bearing failure under a liquid-carrying working condition provided by an embodiment of the invention; wherein, (a) is a campbell diagram; (b) is a frequency chart;
fig. 6 is a schematic structural diagram of an axial plunger pump analysis system containing bearing faults under a hydraulic working condition according to an embodiment of the present invention.
Detailed Description
The present invention will be described in further detail with reference to the accompanying drawings, for the purpose of making the objects, technical solutions and advantages of the present invention more apparent.
Referring to fig. 1, in an embodiment of the present invention, an analysis method for an axial plunger pump with bearing failure under a hydraulic working condition is provided, where the method includes the following steps:
s1, constructing a geometric structure model among a rotor, a cylinder assembly, a shell and a working medium of the vertical axial plunger pump according to the actual space positions and the actual dimensions of a component shell, the cylinder assembly and a rotating shaft structure of the axial plunger pump so as to obtain a fluid acting force equation between the working medium and the cylinder assembly;
firstly, according to the actual space positions and sizes of a component shell, a cylinder assembly and a rotating shaft structure of an axial plunger pump, and by combining the fluid acting force between a working medium and the cylinder assembly, adopting a regular cylinder to respectively perform equivalent modeling on a shell, a rotor and the working medium; wherein the working medium is liquid and fills the annular space between the rotor and the shell;
Secondly, determining the inner radius and the outer radius of the annular space according to the diameters of the rotor, the cylinder assembly and the shell, and constructing a geometric structure model among the rotor, the cylinder assembly, the shell and the working medium of the vertical axial plunger pump;
finally, based on the constructed geometric model, the pressure vector value on each grid node of the cylinder assembly is solved by utilizing Fluent software, so as to obtain a fluid acting force equation between the working medium and the cylinder assembly. Wherein the specific step of solving the pressure vector values at each grid node of the cylinder assembly to obtain a fluid force equation between the working medium and the cylinder assembly comprises: (1) Let the area of the node i in the main flow field be Deltas, the fluid acting force F of the node i i ＝p i ΔS i Then the node i fluid force F i In the x, y direction components are
Wherein a is F i An angle with the x-axis; i=1, 2,. -%, n; (2) Based on node i fluid force F i The total force component of the main flow field on the cylinder assembly is obtained as +.>
In one example, as shown in fig. 2, according to an engineering schematic diagram of an axial plunger pump rotor system, the structural size of the pump rotor system is determined, and the key parts of the rotating shaft, the cylinder assembly and the bearing are simplified by combining preset physical parameters of all parts, so that an axial plunger pump rotor system model under the working condition with liquid is constructed, as shown in fig. 3.
At this time, the specific modeling steps of the axial plunger pump rotor system are as follows:
(a) And selecting the left end face of the left end shaft as a reference plane, dividing corresponding shaft sections by setting nodes, and discretizing the shaft system into cylinders.
(b) For non-cone components such as cylinder assemblies, rotating shafts, sleeves and the like, mass, rotational inertia and gravity center position parameters of the non-cone components can be obtained through Pro/E software analysis, the specific positions of the non-cone components on the shafts are determined according to the gravity center positions of the non-cone components, and equivalent mass and rotational inertia parameters are applied in the form of rigid discs; the node 14 in this model is the cylinder assembly center of gravity position.
(c) Since the clearance between the inner race of the rolling bearing and the journal is very small, the bearing oil film force can be expressed linearly as:
in the formula ,Fx0 and Fy0 Is the static component of oil film force; [ K ]]Is a rigidity matrix of the bearing; [ C]Is a damping matrix of the bearing. In the dynamic analysis of the bearing, the oil film bearing is simplified into an elastic damping bearing, and then the oil film rigidity coefficient and the oil film damping coefficient are
By the above formula, 8 dynamic characteristic coefficients of the bearing can be obtained.
(d) Let the area of the node i in the main flow field be Deltas, the fluid acting force F of the node i i ＝p i ΔS i Then the node i fluid force F i In the x, y direction components are
Wherein a is F i An angle with the x-axis; i=1, 2,. -%, n; (2) Based on node i fluid force F i The total force component of the main flow field on the cylinder assembly is obtained as +.>
S2, decomposing the mass equivalent of a working medium into a rotor additional mass, a shell additional mass and a liquid coupling mass, determining calculation expressions of the rotor additional mass, the shell additional mass and the liquid coupling mass, and further combining a fluid acting force equation, a friction force equation, a centrifugal force equation and a mass unbalance force equation of a cylinder assembly to respectively carry out stress analysis on a disc, a shaft section and a support of the axial plunger pump rotor so as to construct an axial plunger pump rotor dynamics equation under a liquid carrying working condition;
the method comprises the steps of firstly, considering that working medium in an axial plunger pump flows along with the rotation of a cylinder body assembly of the pump, the working medium causes inconsistent speeds of liquid particles at different radial positions in an annular shape under the action of centrifugal force due to viscosity, decomposing the mass of the working medium in a simplified annular space into three parts of mass of rotor additional mass, shell additional mass and liquid coupling mass according to the speed difference, and determining the calculation expressions of the rotor additional mass, the shell additional mass and the liquid coupling mass. Wherein the calculated expression of the additional mass of the rotor is 
The calculated expression of the additional mass of the housing is +.>
The calculated expression of the liquid coupling quality is m 21 ＝ρπL 1 (R 2 -R 1 ) 2 ；m 11 Adding mass to the rotor; m is m 12 Adding mass to the shell; m is m 21 Is the liquid coupling quality; ρ is the density of the working medium; r is R 1 A disc inner radius that is an annular space; r is R 2 A housing outer radius that is an annular space; l is the disc length of the annular space.
Secondly, determining a friction force equation, a centrifugal force equation and a mass unbalance force equation of the cylinder assembly by considering external loads of factors such as main flow field acting force, friction force, centrifugal force, mass unbalance force and the like; wherein the cylinder assembly unbalance force F e The equation expression of (2) is F e ＝J p meω 2 The method comprises the steps of carrying out a first treatment on the surface of the Centrifugal force F of cylinder assembly p The equation expression of (2) is F p ＝m sp ω 2 R is R; friction force F of cylinder assembly v The equation expression of (2) is
J p The rotary inertia of the rotary assembly is represented by m, the mass of the cylinder assembly is represented by e, the eccentric amount is represented by ω, and the angular velocity of the disc is represented by ω; ms of p Is the diameter of the cylinder assembly; mu is hydrodynamic viscosity, R c For cylinder assembly radius, l c For the length of the cylinder assembly>
t is the width of the gap between the cylinder assembly outer surface and the housing inner surface.
Finally, on the basis of the calculation expressions of the additional mass of the rotor, the additional mass of the shell and the liquid coupling mass, respectively carrying out stress analysis on a disc, a shaft section and a support of the axial plunger pump rotor by combining a fluid acting force equation, a friction force equation of a cylinder assembly, a centrifugal force equation and a mass unbalance force equation so as to construct an axial plunger pump rotor dynamics equation under a liquid-carrying working condition; wherein,
The expression of the dynamic equation of the axial plunger pump rotor under the working condition with liquid is
wherein ,
and M is the rotor system inertia matrix; />
And C is a system damping matrix taking into account fluid effects; />
And K is * A system stiffness matrix for consideration of fluid effects;
G 1 a damping matrix for consideration of gyroscopic effects; m is M 1 From an axis segment unit inertia matrix M s Disk unit inertia matrix M d Forming; c (C) 1 Damping matrix C by shaft section unit s Disc unit damping matrix C d Forming; k (K) 1 From the axle segment unit stiffness matrix K S Stiffness matrix K of disc unit d Forming a dynamic characteristic coefficient of the bearing;
F s is the centrifugal force of the slipper pair; f (F) fs Friction force of the slipper pair; f (F) v1 and Fv2 Friction of cylinder assemblies, respectively, can be calculated by the formula
Performing corresponding calculation to obtain; f (F) z Friction force of the flow distribution pair; />
And u is the acceleration vector, velocity vector and displacement vector of the system, respectively.
S3, constructing a partial defect fault dynamics model of the cylindrical roller bearing considering time-varying excitation, calculating the angular position of roller motion in the cylindrical roller bearing, acquiring time-varying displacement excitation and time-varying contact stiffness excitation according to a load deformation relation when the roller is judged to enter the defect based on the calculated angular position, and further assembling the acquired time-varying displacement excitation and time-varying contact stiffness excitation into an axial plunger pump rotor dynamics equation under the liquid-carrying working condition by a matrix operation method to obtain an axial plunger pump rotor system fault dynamics model containing bearing faults under the liquid-carrying working condition;
Firstly, defining geometric parameters, rotating speed and load of the bearing and geometric parameters and position parameters of the local defect.
Second, by the formula
Calculating the ratio eta of the diameter d of the bearing to the minimum dimension L of the local defect b And is>
Calculating the ratio eta of the length L and the width B of the local defect d 。
Then, according to the ratio eta of the diameter d of the bearing to the minimum dimension L of the local defect b And the ratio eta of the local defect length dimension L to the width dimension B d Constructing a local defect model based on a piecewise function; the piecewise function consists of half sine and rectangle functions, and the expression of the time-varying displacement excitation induced by the local defect is as follows:
wherein mod () is a remainder function; t is t dl1 、t dl2 、t j Respectively different time periods; 0 to t dl1 The time period represents a half sine function; t is t dl1 ～t dl2 The time period represents a rectangular function; t is t dl1 ～(t dl1 +t dl2 ) The time period represents a piecewise function consisting of half sine functions; Δd is the ratio η b Or ratio eta d 。
Next, determining a time-varying contact stiffness equation between the friction members; wherein the expression of the time-varying contact stiffness equation between the friction parts is
K is Hertz contact stiffness between friction pairs; k (K) 1 、K 2 and K3 The contact rigidity between the friction part and the defect edge under different conditions is shown;
Next, a nonlinear contact stiffness equation between the friction members is determined, wherein the expression of the nonlinear contact stiffness equation between the friction members is F (t) =k (t) δ n(t) The method comprises the steps of carrying out a first treatment on the surface of the F (t) is a time-varying contact force; k (t) is the time-varying contact stiffness between the sphere and the local defect edge; n (t) is the time-varying load-deformation coefficient between the sphere and the local defect edge;
then, according to a time-varying contact stiffness equation between the friction parts and a nonlinear contact stiffness equation between the friction parts, calculating time-varying displacement excitation and time-varying contact stiffness excitation between the rolling bodies and the defect edges;
then, a bearing dynamics model is obtained, and the bearing dynamics model is solved to obtain the angular position of each rolling body of the rolling bearing; wherein the expression of the bearing dynamics model comprises
And
it should be noted that the specific steps of solving the bearing kinetic model to obtain the angular position of each rolling element of the rolling bearing include: solving the bearing dynamics model by adopting a fixed-step length 4-order Dragon lattice tower method, and ending the solution when the solution time is determined to be longer than the set time; otherwise, when the solving time is smaller than the set time, continuing to solve; and after the solving is finished, obtaining time domain and frequency domain vibration signals of each rolling body in the rolling bearing so as to determine the angular position of each rolling body in the rolling bearing.
And finally, after determining that the roller enters the defect according to the angular position of each rolling body, assembling the calculated time-varying displacement excitation and time-varying contact stiffness excitation between the rolling body and the edge of the defect into an axial plunger pump rotor dynamics equation under the working condition with liquid by a matrix operation method to obtain a fault dynamics model of the axial plunger pump rotor system containing the bearing fault under the working condition with liquid.
In one example, (1) the local defects of different types are characterized by adopting a piecewise function form consisting of a rectangular function and a half sine function according to the actual surface contour form of the local defects, and the load deformation relation between the friction part and the edges of the local defects is deduced according to the Hertz elastic contact theory. Defining geometric parameters, rotating speed and load of the friction part, and geometric parameters and position parameters of the local defect;
(2) Calculating the ratio of the diameter of the bearing component to the minimum size of the local defect and the ratio of the length size of the local defect to the width size;
(3) A piecewise function model is constructed based on the ratio of the friction member diameter to the local defect minimum size and the local defect length to width ratio, as shown in fig. 4.
(4) Calculating time-varying displacement excitation and time-varying contact stiffness excitation between the rolling bodies and the defect edge;
(5) Calculating the angular position of each rolling element of the rolling bearing;
(6) Judging whether the friction part enters a local defect position, if so, considering time-varying displacement excitation and time-varying contact stiffness excitation between the friction part and the local defect edge, otherwise, not considering time-varying displacement excitation and time-varying contact stiffness excitation between the friction part and the local defect edge;
(7) Solving a bearing dynamics model by adopting a fixed-step 4-order Dragon-Gregory tower method, judging whether the solving time is longer than the set time, and ending the solving if the solving time is longer than the set time; otherwise, continuing to solve; finally obtaining time domain and frequency domain vibration signals of the rolling bodies to determine the angular positions of the rolling bodies;
(8) It is determined whether the bearing component thereof enters a defect. If the bearing component enters a defect, time-varying displacement excitation and time-varying contact stiffness excitation are obtained according to a load deformation relation, and are assembled on an axial plunger pump rotor dynamic equation under a liquid-carrying working condition which is subjected to matrix and constraint by a matrix operation method, so that a fault dynamic model of the axial plunger pump rotor system containing bearing faults under the liquid-carrying working condition is established.
S4, analyzing a fault dynamic model of the axial plunger pump rotor system containing the bearing fault under the working condition with the liquid to obtain the critical rotation speed of each fault element under the corresponding fault characteristic frequency; wherein the failure element comprises a bearing outer ring, a bearing inner ring and rolling elements.
The specific process is that a second-order motion differential equation is given in the first step:
wherein M is a structural mass matrix, C is a structural damping matrix, and K is a structural rigidity matrix;
secondly, determining a Newmark method, wherein the Newmark method adopts a finite differential expansion mode over a time step delta t, and is expressed by the following formulas (2) and (3):
wherein alpha and beta are Newmark integral parameters; Δt=t n+1 -t n For the integration step size,
and un Respectively t n Acceleration vector, velocity vector, displacement vector of moment; />
and un+1 Respectively t n+1 Acceleration vector, velocity vector, displacement vector of moment;
the third step, since the main purpose of solving equation (1) is to obtain t n+1 The displacement of the moment, therefore, is converted from equations (2) and (3), t n+1 The velocity and acceleration vectors at time are denoted as t n+1 Time displacement vector u n+1 Is a functional form of:
in the formula ,
α 6 ＝Δt(1-β),α 7 ＝βΔt
The fourth step, from equation (1), can be found as follows:
fifth step, simultaneous equations (4) - (6) can obtain t n+1 Time displacement vector u n+1 Is represented by the expression:
sixth step, according to displacement vector u n+1 And combining equations (4) and (5), then determining t n+1 Acceleration vector of moment of time
And velocity vector->
Seventh step, according to t n+1 Acceleration vector of moment of time
And velocity vector->
A critical rotational speed is determined.
It can be seen that by analyzing the critical rotation speed and the failure characteristic frequency of the axial plunger pump rotor dynamics model containing the bearing defects under the fluid-carrying working condition established in the step S2, it is possible to obtain the analysis conclusion that the bearing failure (outer ring, inner ring and rolling element failure) excitation force is regarded as the external excitation of the rotor action, the failure excitation frequency is proportional to the rotor speed, so that the failure excitation tends to excite the rotor resonance, and the service life of the piston pump mechanical system is reduced.
In order to study the response of different bearing fault excitations to rotor resonance, a vibration response diagram of an axial plunger pump at different rotational speeds is given in fig. 5, comprising a campbell diagram (a) and a frequency diagram (b). As shown in fig. (a), the fault excitation frequency scale line intersects the rotor order natural frequencies, and the rotor speed (forward rotation) at the intersection corresponds to the peak speed in (b). In a healthy state, the critical rotor speed of rotor resonance is 3200rpm, and the rotor is excited by unbalanced excitation force. In the event of a bearing failure, the critical rotor speed is expected to decrease significantly because the product relationship between the bearing failure excitation frequency and the rotor speed is greater than 1.
This multiplication is reflected in the slope of the bearing failure excitation frequency scale line, with a large slope of the curve meaning a low critical speed. From this relationship, it can be concluded that: the critical rotational speeds (320 rpm, 1180rpm and 2230 rpm) at which the inner race of the bearing fails are at a minimum, while the rotational speeds (590 rpm, 2180rpm and 4200 rpm) at which the rolling elements fail are at a maximum. The critical speeds (460 rpm, 1700rpm and 3203 rpm) at which the bearing outer race fails are in the middle.
FIG. 6 shows an embodiment of the present invention, which provides an axial plunger pump analysis system with bearing failure under hydraulic working conditions, comprising;
a fluid acting force equation obtaining unit 110, configured to construct a geometric model between the rotor, the cylinder assembly, the housing and the working medium of the vertical axial plunger pump according to the actual spatial positions and dimensions of the component casing, the cylinder assembly and the rotating shaft structure of the axial plunger pump, so as to obtain a fluid acting force equation between the working medium and the cylinder assembly;
the pump rotor dynamics equation construction unit 120 is configured to decompose the mass equivalent of the working medium into a rotor additional mass, a shell additional mass and a liquid coupling mass, determine a calculation expression of the rotor additional mass, the shell additional mass and the liquid coupling mass, and further combine the fluid force equation, the friction force equation, the centrifugal force equation and the mass unbalance force equation of the cylinder assembly to perform stress analysis on the disc, the shaft section and the support of the axial plunger pump rotor respectively, so as to construct an axial plunger pump rotor dynamics equation under the working condition with liquid;
The pump rotor dynamic equation construction unit 130 with faults is used for constructing a partial defect dynamic model of the cylindrical roller bearing considering time-varying excitation, calculating the angular position of the roller motion in the cylindrical roller bearing, acquiring time-varying displacement excitation and time-varying contact stiffness excitation according to a load deformation relation when the roller is judged to enter the defect based on the calculated angular position, and further assembling the acquired time-varying displacement excitation and time-varying contact stiffness excitation into the axial plunger pump rotor dynamic equation under the working condition with liquid by a matrix operation method to obtain an axial plunger pump rotor system fault dynamic model with the bearing faults under the working condition with liquid;
the pump rotor power failure analysis unit 140 is configured to analyze a failure dynamic model of the axial plunger pump rotor system including a bearing failure under a hydraulic condition, so as to obtain a critical rotation speed of each failure element under a corresponding failure characteristic frequency; wherein the failure element comprises a bearing outer ring, a bearing inner ring and rolling elements.
The embodiment of the invention has the following beneficial effects:
according to the invention, through combining the characteristic that faults of working medium and bearing defects in the pump are not negligible under the working condition of liquid carrying, the structural relation of the vertical shaft to the rotor of the plunger pump, the bearing and the working medium is analyzed, the mass of the working medium is decomposed into three parts of additional mass of the rotor, additional mass of the shell and liquid coupling mass, so that an axial plunger pump rotor system dynamics model with the bearing defects of the liquid working medium is accurately built, and further, the calculation and analysis of the critical wet rotating speed and the fault characteristic frequency are carried out according to the built dynamics model, so that the vibration faults of the axial plunger pump rotor in the actual running process are effectively reduced.
It should be noted that, in the above system embodiment, each unit included is only divided according to the functional logic, but not limited to the above division, so long as the corresponding function can be implemented; in addition, the specific names of the functional units are also only for distinguishing from each other, and are not used to limit the protection scope of the present invention.
Those of ordinary skill in the art will appreciate that all or a portion of the steps in implementing the methods of the above embodiments may be implemented by a program to instruct related hardware, where the program may be stored in a computer readable storage medium, such as ROM/RAM, a magnetic disk, an optical disk, etc.
The above disclosure is only a preferred embodiment of the present invention, and it is needless to say that the scope of the invention is not limited thereto, and therefore, the equivalent changes according to the claims of the present invention still fall within the scope of the present invention.
Claims (8)
1. An analysis method of an axial plunger pump containing bearing faults under a liquid-carrying working condition is characterized by comprising the following steps:
s1, constructing a geometric structure model among a rotor, a cylinder assembly, a shell and a working medium of the vertical axial plunger pump according to the actual space positions and the actual dimensions of a component shell, the cylinder assembly and a rotating shaft structure of the axial plunger pump so as to obtain a fluid acting force equation between the working medium and the cylinder assembly;
S2, decomposing the mass equivalent of a working medium into a rotor additional mass, a shell additional mass and a liquid coupling mass, determining calculation expressions of the rotor additional mass, the shell additional mass and the liquid coupling mass, and further combining a fluid acting force equation, a friction force equation, a centrifugal force equation and a mass unbalance force equation of a cylinder assembly to respectively carry out stress analysis on a disc, a shaft section and a support of the axial plunger pump rotor so as to construct an axial plunger pump rotor dynamics equation under a liquid carrying working condition;
s3, constructing a partial defect fault dynamics model of the cylindrical roller bearing considering time-varying excitation, calculating the angular position of roller motion in the cylindrical roller bearing, acquiring time-varying displacement excitation and time-varying contact stiffness excitation according to a load deformation relation when the roller is judged to enter the defect based on the calculated angular position, and further assembling the acquired time-varying displacement excitation and time-varying contact stiffness excitation into an axial plunger pump rotor dynamics equation under the liquid-carrying working condition by a matrix operation method to obtain an axial plunger pump rotor system fault dynamics model containing bearing faults under the liquid-carrying working condition;
S4, analyzing a fault dynamic model of the axial plunger pump rotor system containing the bearing fault under the working condition with the liquid to obtain the critical rotation speed of each fault element under the corresponding fault characteristic frequency; wherein the failure element comprises a bearing outer ring, a bearing inner ring and rolling elements.
2. The method for analyzing the axial plunger pump with bearing faults under the working condition with liquid according to claim 1, wherein the step S1 specifically comprises the following steps:
according to the actual space positions and the actual dimensions of a component shell, a cylinder assembly and a rotating shaft structure of the axial plunger pump, and by combining the fluid acting force between a working medium and the cylinder assembly, adopting regular cylinders to respectively perform equivalent modeling on a shell, a rotor and the working medium; wherein, the working medium fills the annular space between the rotor and the shell;
determining the inner radius and the outer radius of the annular space according to the diameters of the rotor, the cylinder assembly and the shell, and constructing a geometric structure model among the rotor, the cylinder assembly, the shell and the working medium of the vertical axial plunger pump;
based on the constructed geometric model, the pressure vector value on each grid node of the cylinder assembly is solved by utilizing Fluent software to obtain a fluid acting force equation between the working medium and the cylinder assembly.
3. The method for analyzing the axial piston pump with bearing faults under the hydraulic working condition according to claim 2, wherein the specific step of solving the pressure vector value on each grid node of the cylinder assembly to obtain the fluid acting force equation between the working medium and the cylinder assembly comprises the following steps:
let the area of the node i in the main flow field be Deltas, the fluid acting force F of the node i i ＝p i ΔS i Then the node i fluid force F i In the x, y direction components are
Wherein a is F i An angle with the x-axis; i=1, 2,. -%, n;
based on node i fluid force F i The total acting force component of the main flow field on the cylinder body assembly is obtained as
4. The method for analyzing the axial plunger pump with bearing faults under the working condition with liquid according to claim 3, wherein the step S2 specifically comprises the following steps:
decomposing the mass equivalent of the working medium into a rotor additional mass, a shell additional mass and a liquid coupling mass, and determining a calculation expression of the rotor additional mass, the shell additional mass and the liquid coupling mass; wherein the calculated expression of the additional mass of the rotor is
The calculated expression of the additional mass of the shell is +.>
The calculated expression of the liquid coupling quality is m 21 ＝ρπL 1 (R 2 -R 1 ) 2 ；m 11 Adding mass to the rotor; m is m 12 Adding mass to the housing; m is m 21 A mass for said liquid coupling; ρ is the density of the working medium; r is R 1 A disc inner radius that is the annular space; r is R 2 A housing outer radius for the annular space; l is the disc length of the annular space;
based on the calculated expressions of the rotor additional mass, the shell additional mass and the liquid coupling mass, respectively carrying out stress analysis on a disc, a shaft section and a support of the axial plunger pump rotor by combining the fluid acting force equation, a friction force equation, a centrifugal force equation and a mass unbalance force equation of a cylinder assembly so as to construct an axial plunger pump rotor dynamics equation under a liquid-carrying working condition; the expression of the dynamic equation of the axial plunger pump rotor under the working condition with liquid is as follows
wherein ,
and M is the rotor system inertia matrix; />
And C is a system damping matrix taking into account fluid effects; />
And K is * A system stiffness matrix for consideration of fluid effects;
G 1 a damping matrix for consideration of gyroscopic effects; m is M 1 From an axis segment unit inertia matrix M s Disk unit inertia matrix M d Forming; c (C) 1 Damping matrix C by shaft section unit s Disc unit damping matrix C d Forming; k (K) 1 From the axle segment unit stiffness matrix K S Stiffness matrix K of disc unit d Forming a dynamic characteristic coefficient of the bearing;
F e is an unbalanced force of the cylinder assembly, and F e ＝J p meω 2 ；F s Is the centrifugal force of the slipper pair; f (F) fs Friction force of the slipper pair; f (F) p Is the centrifugal force of the cylinder assembly, and F p ＝m sp ω 2 R；F v1 and Fv2 Friction forces of cylinder assemblies respectively, and
F z friction force of the flow distribution pair; />
And u is the acceleration vector, velocity vector and displacement vector of the system respectively; j (J) p The rotary inertia of the rotary assembly is represented by m, the mass of the cylinder assembly is represented by e, the eccentric amount is represented by ω, and the angular velocity of the disc is represented by ω; ms of p Is the diameter of the cylinder assembly; mu is hydrodynamic viscosity, R c For cylinder assembly radius, l c For the length of the cylinder assembly>
t is the width of the gap between the cylinder assembly outer surface and the housing inner surface.
5. The method for analyzing the axial plunger pump with bearing faults under the working condition with liquid according to claim 4, wherein the step S3 specifically comprises the following steps:
defining geometric parameters, rotating speed and load of the bearing and geometric parameters and position parameters of the local defect;
by the formula
Calculating the ratio eta of the diameter d of the bearing to the minimum dimension L of the local defect b And is>
Calculating the ratio eta of the length L and the width B of the local defect d ；
According to the ratio eta of the diameter d of the bearing to the minimum dimension L of the local defect b And the ratio eta of the local defect length dimension L to the width dimension B d Constructing a local defect model based on a piecewise function; wherein the piecewise function is composed of half sine and rectangle functions, and the expression of the time-varying displacement excitation induced by the local defect is as follows:
wherein mod () is a remainder function; t is t dl1 、t dl2 、t j Respectively different time periods; 0 to t dl1 The time period represents a half sine function; t is t dl1 ～t dl2 The time period represents a rectangular function; t is t dl1 ～(t dl1 +t dl2 ) The time period represents a piecewise function consisting of half sine functions; Δd is the ratio η b Or ratio eta d ；
Determining a time-varying contact stiffness equation between the friction members; wherein the expression of the time-varying contact stiffness equation between the friction parts is
K is Hertz contact stiffness between friction pairs; k (K) 1 、K 2 and K3 For friction under different conditionsThe stiffness of contact between the part and the defective edge;
determining a nonlinear contact stiffness equation between friction parts, wherein the expression of the nonlinear contact stiffness equation between friction parts is F (t) =K (t) delta n(t) The method comprises the steps of carrying out a first treatment on the surface of the F (t) is a time-varying contact force; k (t) is the time-varying contact stiffness between the sphere and the local defect edge; n (t) is the time-varying load-deformation coefficient between the sphere and the local defect edge;
calculating time-varying displacement excitation and time-varying contact stiffness excitation between the rolling bodies and the defect edges according to a time-varying contact stiffness equation between the friction parts and a nonlinear contact stiffness equation between the friction parts;
Acquiring a bearing dynamics model, and solving the bearing dynamics model to acquire the angular position of each rolling body of the rolling bearing; wherein the expression of the bearing dynamics model comprises
And
/>
and after determining that the roller enters the defect according to the angular position of each rolling body, assembling the calculated time-varying displacement excitation and time-varying contact stiffness excitation between the rolling bodies and the defect edge into an axial plunger pump rotor dynamics equation under the liquid-carrying working condition by a matrix operation method to obtain a fault dynamics model of the axial plunger pump rotor system containing the bearing fault under the liquid-carrying working condition.
6. The method for analyzing the axial plunger pump with bearing faults under the working condition with liquid according to claim 5, wherein the specific step of solving the dynamic bearing model to obtain the angular position of each rolling element of the rolling bearing comprises the following steps:
solving the bearing dynamics model by adopting a fixed-step length 4-order Dragon lattice tower method, and ending the solution when the solution time is determined to be longer than the set time; otherwise, when the solving time is smaller than the set time, continuing to solve;
and after the solving is finished, obtaining time domain and frequency domain vibration signals of each rolling body in the rolling bearing so as to determine the angular position of each rolling body in the rolling bearing.
7. The method for analyzing the axial plunger pump with bearing faults under the working condition with liquid according to claim 6, wherein the step S4 specifically comprises the following steps:
the first step, a second order differential equation of motion is given:
wherein M is a structural mass matrix, C is a structural damping matrix, and K is a structural rigidity matrix;
secondly, determining a Newmark method, wherein the Newmark method adopts a finite differential expansion mode over a time step delta t, and is expressed by the following formulas (2) and (3):
wherein alpha and beta are Newmark integral parameters; Δt=t n+1 -t n For the integration step size,
and un Respectively t n Acceleration vector, velocity vector, displacement vector of moment; />
and un+1 Respectively t n+1 Acceleration vector, velocity at timeVector, displacement vector;
the third step, since the main purpose of solving equation (1) is to obtain t n+1 The displacement of the moment, therefore, is converted from equations (2) and (3), t n+1 The velocity and acceleration vectors at time are denoted as t n+1 Time displacement vector u n+1 Is a functional form of:
in the formula ,
α 6 ＝Δt(1-β)，α 7 ＝βΔt
the fourth step, from equation (1), can be found as follows:
fifth step, simultaneous equations (4) - (6) can obtain t n+1 Time displacement vector u n+1 Is represented by the expression:
sixth step, according to displacement vector u n+1 And combining equations (4) and (5), then determining t n+1 Acceleration vector of moment of time
And velocity vector->
Seventh step, according to t n+1 Acceleration vector of moment of time
And velocity vector->
A critical rotational speed is determined.
8. An axial plunger pump analysis system containing bearing faults under a liquid carrying working condition is characterized by comprising the following components;
the fluid acting force equation acquisition unit is used for constructing a geometric structure model among the rotor, the cylinder assembly, the shell and the working medium of the vertical axial plunger pump according to the actual space positions and the actual dimensions of the component shell, the cylinder assembly and the rotating shaft structure of the axial plunger pump so as to obtain a fluid acting force equation between the working medium and the cylinder assembly;
the system comprises a fault-free pump rotor dynamics equation construction unit, a hydraulic pump rotor dynamics equation analysis unit and a hydraulic pump rotor dynamics equation analysis unit, wherein the fault-free pump rotor dynamics equation construction unit is used for decomposing the mass equivalent of a working medium into a rotor additional mass, a shell additional mass and a liquid coupling mass, determining the calculation expressions of the rotor additional mass, the shell additional mass and the liquid coupling mass, and further respectively carrying out stress analysis on a disc, a shaft section and a support of the axial plunger pump rotor by combining a fluid acting force equation, a friction force equation, a centrifugal force equation and a mass unbalance force equation of a cylinder assembly so as to construct the axial plunger pump rotor dynamics equation under the working condition with liquid;
The pump rotor dynamic equation construction unit with faults is used for constructing a partial defect dynamic model of the cylindrical roller bearing considering time-varying excitation, calculating the angular position of the roller motion in the cylindrical roller bearing, acquiring time-varying displacement excitation and time-varying contact stiffness excitation according to a load deformation relation when the roller is judged to enter the defect based on the calculated angular position, and further assembling the acquired time-varying displacement excitation and time-varying contact stiffness excitation into the axial plunger pump rotor dynamic equation under the working condition with liquid by a matrix operation method to obtain the axial plunger pump rotor system fault dynamic model with the bearing faults under the working condition with liquid;
the pump rotor power failure analysis unit is used for analyzing the failure dynamic model of the axial plunger pump rotor system containing the bearing failure under the working condition of liquid carrying so as to obtain the critical rotation speed of each failure element under the corresponding failure characteristic frequency; wherein the failure element comprises a bearing outer ring, a bearing inner ring and rolling elements.
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| CN117570013A (en) * | 2024-01-11 | 2024-02-20 | 浙江大学高端装备研究院 | Fault diagnosis monitoring method, device and system for axial plunger pump |
| CN117570013B (en) * | 2024-01-11 | 2024-04-05 | 浙江大学高端装备研究院 | Fault diagnosis monitoring method, device and system for axial plunger pump |
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