An analysis method and system for an axial plunger pump with bearing fault under a belt liquid working condition

Abstract

The application provides an analysis method for an axial plunger pump with bearing faults under a liquid working condition, comprising the following steps: constructing a geometric structure model of an equation axial plunger pump rotor system to obtain a fluid acting force equation; decomposing a working medium mass into a rotor additional mass, a shell additional mass and a liquid coupling mass, and combining the fluid acting force equation with a friction force, a centrifugal force and a mass unbalance force equation of a cylinder body assembly to construct an axial plunger pump rotor dynamics equation; constructing a local defect fault dynamics model of a roller bearing to calculate an angular position of roller movement, and when the roller enters a defect, acquiring a time-varying displacement excitation and a time-varying contact stiffness excitation to be assembled into the dynamics equation to obtain a dynamics model with bearing faults; and analyzing the dynamics model with bearing faults to obtain critical rotating speeds of each fault element. By implementing the application, the analysis and calculation results are closer to actual values, and the vibration characteristic analysis and dynamic design work can be better carried out.

Description

Technical Field

[0001] This invention relates to the field of axial piston pump technology, and in particular to an analysis method and system for axial piston pumps with bearing failures under liquid-carrying conditions. Background Technology

[0002] Axial piston pumps are widely used in industries such as engineering machinery, aerospace, and marine engineering equipment. With increasing demands for operational efficiency, axial piston pumps have increasingly trended towards high speed, high pressure, and high flow rate in recent years. The rotor system of an axial piston pump has a complex structure, generally composed of multiple components including the cylinder assembly (cylinder block, swashplate, distributor plate, pistons, and slippers), bearings, main shaft, and housing. Its operating speed is often above 3000 rpm. Therefore, in addition to traditional mechanical strength design, the surface damage and wear dynamics of the bearings must often be considered. In recent years, bearing friction damage failures in axial piston pumps have occurred frequently, seriously jeopardizing the stable operation of axial piston pumps and causing huge economic losses to major national equipment. Traditional axial piston pump fault prediction and maintenance rely mainly on experimental testing and experience-based repair, lacking direct evidence for tracing the source of key component failures, thus prolonging the design and development cycle. Therefore, a common practice is to ensure that the operating speed range of the plunger pump and the critical speed range of the defective cylindrical roller bearing meet certain isolation margin dynamic design requirements. Otherwise, the designed axial plunger pump is prone to strong vibration and noise problems during actual operation. It is crucial to obtain the fault characteristic frequencies of the defective cylindrical roller bearing and establish a correspondence between the vibration characteristic frequencies of the defective cylindrical roller bearing and the vibration characteristics of the axial plunger pump rotor system, thus achieving precise source tracing of local faults in the axial plunger pump. During the operation of the axial plunger pump, due to the mass of the liquid working medium, its flow process is very complex under the centrifugal force of the rotating pump rotor, and there is a certain degree of mutual coupling between the liquid medium and the cylinder assembly. When the axial plunger pump rotor assembly vibrates, the liquid medium in contact with it also vibrates. On the one hand, the rotating cylinder assembly affects the distribution of the liquid medium flow field, thereby changing the distribution and magnitude of the fluid load; on the other hand, the cylinder assembly will deform under the pressure load of the flow field. Due to the influence of the above factors, the critical speed and mode shape of an axial piston pump operating with liquid working medium and bearing failure defects may change, making the rotor vibration characteristics of the axial piston pump more complex and significantly increasing the difficulty of dynamic design. Therefore, in the dynamic design of axial piston pumps, it is necessary to consider the influence of liquid working medium on its vibration characteristics, accurately analyze the local fault characteristics, critical speed, and mode shape of the axial piston pump, and provide a basis and reference for its structural dynamic design and vibration analysis.

[0003] Currently, many scholars both domestically and internationally have conducted extensive research on pump rotor dynamics modeling and analysis. For example, Quan Lingxiao et al. derived the dynamic equations of the wet rotor of an axial piston pump by analyzing the coupling effect between the rotor and the surrounding working medium, and calculated the mode shape of the pump rotor using spectral analysis. However, due to the complexity of actual operating conditions under liquid working medium, it is impossible to effectively extract the fundamental frequency signal from the stirring containing numerous interfering frequency components. Therefore, it is difficult to accurately estimate and analyze the critical speed and mode shape of the axial piston pump using the response at a limited number of measuring points. Furthermore, most domestic manufacturers perform dynamic modeling and critical speed analysis on the rotor of axial piston pumps under normal operating conditions, but they do not consider the influence of the liquid working medium and bearing defects on the vibration characteristics of the axial piston pump rotor. This results in the established dynamic model not matching the actual operating conditions, leading to a significant difference between the vibration characteristic values ​​calculated by the dynamic model and the actual values. It is also impossible to obtain a large number of single and multiple fault samples reflecting different types of actual operating conditions, resulting in excessive vibration and performance degradation of the designed and manufactured axial piston pumps, seriously affecting the safe production and healthy operation of axial piston pumps.

[0004] Therefore, it is necessary to adopt a new axial piston dynamics modeling method to analyze axial piston pumps, so that the analysis and calculation results (such as vibration characteristic values) are closer to the actual values, so as to better carry out vibration characteristic analysis and dynamic design work. Summary of the Invention

[0005] The technical problem to be solved by the embodiments of the present invention is to provide an axial piston pump analysis method and system for bearing failure under liquid conditions, so that the analysis and calculation results are closer to the actual values, and the vibration characteristic analysis and dynamic design work can be carried out better, thereby extending the service life of the axial piston pump.

[0006] To address the aforementioned technical problems, embodiments of the present invention provide a method for analyzing an axial piston pump with bearing failure under liquid-carrying conditions, the method comprising the following steps:

[0007] S1. Based on the actual spatial position and dimensions of the components of the axial piston pump, such as the housing, cylinder assembly, and shaft structure, construct a geometric model of the rotor, cylinder assembly, housing, and working medium of the vertical axial piston pump to obtain the fluid force equation between the working medium and the cylinder assembly.

[0008] S2. The mass of the working medium is equivalently decomposed into rotor additional mass, shell additional mass and liquid coupling mass, and the calculation expressions for rotor additional mass, shell additional mass and liquid coupling mass are determined. Furthermore, combined with the fluid force equation and the friction force equation, centrifugal force equation and mass imbalance force equation of the cylinder assembly, the force analysis of the disk, shaft section and support of the axial piston pump rotor is carried out to construct the dynamic equation of the axial piston pump rotor under liquid conditions.

[0009] S3. Construct a dynamic model of local defects in cylindrical roller bearings considering time-varying excitation, calculate the angular position of the roller motion in the cylindrical roller bearing, and when the roller enters the defect based on the calculated angular position, obtain the time-varying displacement excitation and time-varying contact stiffness excitation according to the load deformation relationship. Further, use matrix operation to assemble the obtained time-varying displacement excitation and time-varying contact stiffness excitation into the dynamic equation of the axial piston pump rotor under liquid conditions to obtain the dynamic model of the axial piston pump rotor system with bearing fault under liquid conditions.

[0010] S4. Perform critical speed and fault characteristic frequency analysis on the fault dynamic model of the axial piston pump rotor system with bearing failure under liquid conditions to obtain the critical speed of each fault element at the corresponding fault characteristic frequency; wherein, the fault element includes the bearing outer ring, bearing inner ring and rolling element.

[0011] Specifically, step S1 includes:

[0012] Based on the actual spatial positions and dimensions of the components of the axial piston pump, including the housing, cylinder assembly, and shaft structure, and considering the fluid interaction between the working medium and the cylinder assembly, a regular cylinder is used to represent the housing, rotor, and working medium in an equivalent manner; wherein the working medium fills the annular space between the rotor and the housing.

[0013] Based on the diameters of the rotor, cylinder assembly, and housing, the inner and outer radii of the annular space are determined, and a geometric model of the vertical axial piston pump rotor, cylinder assembly, housing, and working medium is constructed.

[0014] Based on the constructed geometric model, the pressure vector value on each grid node of the cylinder assembly is solved using Fluent software to obtain the fluid force equation between the working medium and the cylinder assembly.

[0015] The specific steps for solving the pressure vector value at each grid node of the cylinder assembly to obtain the fluid force equation between the working medium and the cylinder assembly include:

[0016] Let the area of ​​node i in the main flow field be Δs, and the fluid force F acting on node i be... i =p i ΔS i Then the fluid force F at node i i The components in the x and y directions are Where a is F i Angle with the x-axis; i = 1, 2, ..., n;

[0017] Based on the fluid interaction force F at node ii The total force components of the main field on the cylinder block assembly are obtained as follows:

[0018] Specifically, step S2 includes:

[0019] The mass of the working medium is equivalently decomposed into rotor-added mass, housing-added mass, and liquid-coupled mass, and calculation expressions for rotor-added mass, housing-added mass, and liquid-coupled mass are determined; wherein, the calculation expression for the rotor-added mass is as follows: The formula for calculating the additional mass of the shell is as follows: The expression for calculating the liquid coupling mass is m. 21 =ρπL1(R2-R1) 2 ;m 11 Add mass to the rotor; m 12 Add mass to the shell; m 21 ρ is the mass of the liquid coupling; R1 is the inner radius of the disk in the annular space; R2 is the outer radius of the shell of the annular space; L is the length of the disk in the annular space.

[0020] Based on the calculated expressions for the rotor's added mass, the housing's added mass, and the fluid coupling mass, and combined with the fluid force equations and the friction force, centrifugal force, and mass imbalance force equations of the cylinder assembly, force analyses are performed on the disk, shaft segment, and support of the axial piston pump rotor to construct the axial piston pump rotor dynamics equation under fluid-laden conditions; wherein, the expression for the axial piston pump rotor dynamics equation under fluid-laden conditions is as follows:

[0021] in, And M* is the inertia matrix of the rotor system; And C* is the system damping matrix considering fluid effects; And K * The system stiffness matrix considering fluid interactions;

[0022] G1 is the damping matrix considering the gyroscope effect; M1 is the inertia matrix M of the shaft segment element. s and the inertia matrix M of the disk element d Formed by; C1 is formed by the damping matrix C of the shaft segment unit. s and the damping matrix C of the disk element d Formed by; K1 is formed by the stiffness matrix K of the shaft segment element. S Stiffness matrix K of disk element d and the formation of bearing dynamic characteristic coefficient;

[0023] F e For the unbalanced force of the cylinder block assembly, and Fe =J p meω 2 ;F s F is the centrifugal force of the shoe pair; fs F represents the friction force of the slipper pair; p Let F be the centrifugal force of the cylinder block assembly. p =m sp ω 2 R;F v1 and F v2 These are the frictional forces of the cylinder block assembly, and F z The friction force of the distribution pair; and u are the acceleration vector, velocity vector, and displacement vector of the system, respectively; J p Let m be the moment of inertia of the rotating component, e be the mass of the cylinder component, ω be the eccentricity, and ω be the angular velocity of the disk. p R is the diameter of the cylinder assembly; μ is the fluid dynamic viscosity. c For the cylinder block assembly radius, l c For the length of the cylinder block assembly, t is the gap width between the outer surface of the cylinder assembly and the inner surface of the housing.

[0024] Specifically, step S3 includes:

[0025] Define the bearing's geometric dimensions, speed, and load, as well as the geometric dimensions and location parameters of local defects;

[0026] Through formula Calculate the ratio η of the bearing diameter d to the minimum size L of the local defect. b And through the formula Calculate the ratio η of the length dimension L to the width dimension B of the local defect. d ;

[0027] Based on the ratio η of the bearing diameter d to the minimum size L of the local defect b The ratio η of the length dimension L to the width dimension B of the local defect d A local defect model based on a piecewise function is constructed; wherein the piecewise function is composed of a half-sine and a rectangular function, and the expression for the time-varying displacement excitation induced by the local defect is: Where mod() is the modulo function; t dl1 t dl2 t j These represent different time periods; 0~t dl1 The time interval represents the half-sine function; t dl1 ~t dl2 The time interval represents a rectangular function; t dl1 ~(t) dl1 +tdl2 The time interval represents a piecewise function composed of half-sine functions; Δd is the ratio η. b Or ratio η d ;

[0028] Determine the time-varying contact stiffness equation between the friction components; wherein, the expression for the time-varying contact stiffness equation between the friction components is: K represents the Hertz contact stiffness between the friction pairs; K1, K2, and K3 represent the contact stiffness between the friction components and the edge of the defect under different conditions.

[0029] The nonlinear contact stiffness equation between the friction components is determined, wherein the expression of the nonlinear contact stiffness equation between the friction components is F(t)=K(t)δ. n(t) F(t) is the time-varying contact force; K(t) is the time-varying contact stiffness between the sphere and the edge of the local defect; n(t) is the time-varying load-deformation coefficient between the sphere and the edge of the local defect.

[0030] Based on the time-varying contact stiffness equation and the nonlinear contact stiffness equation between the friction components, the time-varying displacement excitation and time-varying contact stiffness excitation between the rolling element and the defect edge are calculated.

[0031] Obtain the bearing dynamics model and solve it to obtain the angular position of each rolling element of the rolling bearing; wherein, the expression of the bearing dynamics model includes and

[0032]

[0033] Based on the angular position of each rolling element, after the roller enters the defect, the time-varying displacement excitation and time-varying contact stiffness excitation between the calculated rolling element and the defect edge are assembled into the axial piston pump rotor dynamic equation under the liquid-carrying condition by matrix operation, thus obtaining the fault dynamic model of the axial piston pump rotor system with bearing failure under the liquid-carrying condition.

[0034] The specific steps for solving the bearing dynamics model to obtain the angular position of each rolling element of the rolling bearing include:

[0035] The bearing dynamics model is solved using the fixed-step fourth-order Runge-Kutta method. The solution ends when the solution time is determined to be longer than the set time; otherwise, the solution continues when the solution time is determined to be shorter than the set time.

[0036] After the solution is completed, the time-domain and frequency-domain vibration signals of each rolling element in the rolling bearing are obtained to determine the angular position of each rolling element in the rolling bearing.

[0037] Specifically, step S4 includes:

[0038] Step 1: Given a second-order differential equation of motion:

[0039]

[0040] Where M is the structural mass matrix, C is the structural damping matrix, and K is the structural stiffness matrix;

[0041] The second step is to determine the Newmark method, which adopts a finite differential expansion over the time step Δt, specifically expressed by formulas (2) and (3):

[0042]

[0043]

[0044] In the formula, α and β are Newmark integration parameters; Δt = t n+1 -t n The integration step size is... and u n t n The acceleration vector, velocity vector, and displacement vector at each instant; and u n+1 t n+1 The acceleration vector, velocity vector, and displacement vector at each instant;

[0045] The third step is that the main purpose of solving equation (1) is to obtain t. n+1 The displacement at time t, therefore, formulas (2) and (3) are transformed to change t. n+1 The velocity and acceleration vectors at time t are expressed as t n+1 displacement vector u at time t n+1 Functional form:

[0046]

[0047]

[0048] In the formula, α6=Δt(1-β), α7=βΔt

[0049] Fourth step: From equation (1), we can obtain the following equation:

[0050]

[0051] Step 5: Solve equations (4) to (6) simultaneously to obtain t. n+1 displacement vector u at time t n+1 The expression:

[0052]

[0053] Step 6: Based on the displacement vector u n+1 By finding the solution and combining it with formulas (4) and (5), t can be determined. n+1 acceleration vector at time t and velocity vector

[0054] Step 7: Based on t n+1 acceleration vector at time t and velocity vector Determine the critical speed.

[0055] This invention also provides an axial piston pump analysis system for bearing failure under liquid-carrying conditions, comprising:

[0056] The fluid force equation acquisition unit is used to construct a geometric model of the rotor, cylinder assembly, housing and working medium of the vertical axial piston pump based on the actual spatial position and size of the components of the axial piston pump, such as the casing, cylinder assembly and shaft structure, so as to obtain the fluid force equation between the working medium and the cylinder assembly.

[0057] The fault-free pump rotor dynamics equation construction unit is used to decompose the mass of the working medium into the rotor additional mass, the shell additional mass and the liquid coupling mass, and determine the calculation expressions of the rotor additional mass, the shell additional mass and the liquid coupling mass. Furthermore, combined with the fluid force equation and the friction force equation, centrifugal force equation and mass imbalance force equation of the cylinder assembly, the unit performs force analysis on the disk, shaft section and support of the axial piston pump rotor to construct the axial piston pump rotor dynamics equation under liquid conditions.

[0058] The pump rotor dynamics equation construction unit with faults is used to construct a fault dynamics model of local defects in cylindrical roller bearings considering time-varying excitations, and calculate the angular position of the roller motion in the cylindrical roller bearing. When the roller enters the defect based on the calculated angular position, the time-varying displacement excitation and time-varying contact stiffness excitation are obtained according to the load deformation relationship. Furthermore, the time-varying displacement excitation and time-varying contact stiffness excitation are assembled into the axial piston pump rotor dynamics equation under liquid conditions through matrix operation, thus obtaining the fault dynamics model of the axial piston pump rotor system with bearing faults under liquid conditions.

[0059] The pump rotor dynamic fault analysis unit is used to perform critical speed and fault characteristic frequency analysis on the fault dynamic model of the axial piston pump rotor system with bearing faults under liquid conditions, so as to obtain the critical speed of each fault element at the corresponding fault characteristic frequency; wherein, the fault element includes the bearing outer ring, the bearing inner ring and the rolling element.

[0060] Implementing the embodiments of the present invention has the following beneficial effects:

[0061] This invention analyzes the structural relationship between the rotor, bearing, and working medium of a vertical axial piston pump by combining the characteristics of the internal working medium and bearing defects that cannot be ignored under liquid conditions. The mass of the working medium is decomposed into three parts: rotor added mass, shell added mass, and liquid coupling mass. This allows for the accurate establishment of a dynamic model of the axial piston pump rotor system with liquid working medium and bearing defects. Furthermore, based on the constructed dynamic model, the critical speed and fault characteristic frequency of the "wet state" are calculated and analyzed, effectively reducing vibration faults in the actual operation of the axial piston pump rotor. Attached Figure Description

[0062] To more clearly illustrate the technical solutions in the embodiments of the present invention or the prior art, the drawings used in the description of the embodiments or the prior art will be briefly introduced below. Obviously, the drawings described below are only some embodiments of the present invention. For those skilled in the art, obtaining other drawings based on these drawings without creative effort still falls within the scope of the present invention.

[0063] Figure 1 A flowchart of an analysis method for an axial piston pump with bearing failure under liquid-carrying conditions provided by an embodiment of the present invention;

[0064] Figure 2 A schematic diagram of the axial piston pump rotor system in an application scenario of an axial piston pump analysis method with bearing failure under liquid conditions provided in this embodiment of the invention;

[0065] Figure 3 A schematic diagram of the rotor system model of an axial piston pump under liquid conditions in an application scenario of an analysis method for an axial piston pump with bearing failure under liquid conditions provided in an embodiment of the present invention.

[0066] Figure 4 This is a schematic diagram of a piecewise function-based local defect model in an application scenario of an axial piston pump analysis method with bearing failure under liquid conditions provided in an embodiment of the present invention.

[0067] Figure 5 Vibration response diagrams of an axial piston pump under different speed conditions in an application scenario of an analysis method for an axial piston pump with bearing failure under liquid conditions provided in an embodiment of the present invention; wherein, (a) is a Campbell diagram; (b) is an amplitude-frequency diagram;

[0068] Figure 6 This is a schematic diagram of the structure of an axial piston pump analysis system with bearing failure under liquid conditions, provided in an embodiment of the present invention. Detailed Implementation

[0069] To make the objectives, technical solutions, and advantages of the present invention clearer, the present invention will be further described in detail below with reference to the accompanying drawings.

[0070] like Figure 1 As shown in the figure, an axial piston pump analysis method for bearing failure under liquid-carrying conditions is proposed in an embodiment of the present invention. The method includes the following steps:

[0071] Step S1: Based on the actual spatial position and dimensions of the components of the axial piston pump, such as the housing, cylinder assembly, and shaft structure, construct a geometric model of the rotor, cylinder assembly, housing, and working medium of the vertical axial piston pump to obtain the fluid force equation between the working medium and the cylinder assembly.

[0072] The specific process is as follows: First, based on the actual spatial position and size of the components of the axial piston pump, such as the housing, cylinder assembly, and shaft structure, and combined with the fluid interaction force between the working medium and the cylinder assembly, a regular cylinder is used to perform equivalent modeling of the housing, rotor, and working medium respectively; wherein, the working medium is in liquid form and fills the annular space between the rotor and the housing.

[0073] Secondly, based on the rotor, cylinder assembly, and housing diameter, the inner and outer radii of the annular space are determined, and a geometric model of the vertical axial piston pump rotor, cylinder assembly, housing, and working medium is constructed.

[0074] Finally, based on the constructed geometric model, the pressure vector value on each grid node of the cylinder assembly is solved using Fluent software to obtain the fluid force equation between the working medium and the cylinder assembly. The specific steps for solving the pressure vector value on each grid node of the cylinder assembly to obtain the fluid force equation between the working medium and the cylinder assembly include: (1) Assuming the area of ​​node i in the main flow field is Δs, and the fluid force F at node i is... i =p i ΔS i Then the fluid force F at node i i The components in the x and y directions are Where a is F i Angle with x-axis; i = 1, 2, ..., n; (2) Based on the fluid force F at node i i The total force components of the main field on the cylinder block assembly are obtained as follows:

[0075] In one example, such as Figure 2As shown, based on the engineering schematic diagram of the axial piston pump rotor system, the structural dimensions of the pump rotor system are determined. Combining the pre-set physical parameters of each component, the key components such as the shaft, cylinder assembly, and bearings are simplified to construct a model of the axial piston pump rotor system under liquid-carrying conditions. Figure 3 As shown.

[0076] At this point, the specific modeling steps of the axial piston pump rotor system are as follows:

[0077] (a) Select the left end face of the left end shaft as the reference plane, and divide the corresponding shaft segments by setting nodes to discretize the shaft system into cylinders.

[0078] (b) For non-conical components such as cylinder block assemblies, shafts, and sleeves, their mass, moment of inertia, and center of gravity position parameters can be obtained through Pro / E software analysis. Based on their center of gravity position, their specific positions on the shaft can be determined, and equivalent mass and moment of inertia parameters can be applied in the form of a rigid disk. Node 14 in this model is the center of gravity position of the cylinder block assembly.

[0079] (c) Due to the very small clearance between the inner ring of the rolling bearing and the journal, when the journal undergoes a small-amplitude whirl around its static equilibrium position, the bearing oil film force can be linearly expressed as:

[0080]

[0081] In the formula, F x0 and F y0 Let [K] be the static component of the oil film force; [C] be the bearing stiffness matrix; and [K] be the bearing damping matrix. In bearing dynamics analysis, the oil film bearing is simplified to an elastically damped support, then the oil film stiffness coefficient and oil film damping coefficient are:

[0082]

[0083]

[0084] The above formula can be used to obtain the eight dynamic characteristic coefficients of the bearing.

[0085] (d) Let the area of ​​node i in the main flow field be Δs, and the fluid force F acting on node i be... i =p i ΔS i Then the fluid force F at node i i The components in the x and y directions are Where a is F i Angle with x-axis; i = 1, 2, ..., n; (2) Based on the fluid force F at node i i The total force components of the main field on the cylinder block assembly are obtained as follows:

[0086] S2. The mass of the working medium is equivalently decomposed into rotor additional mass, shell additional mass and liquid coupling mass, and the calculation expressions for rotor additional mass, shell additional mass and liquid coupling mass are determined. Furthermore, combined with the fluid force equation and the friction force equation, centrifugal force equation and mass imbalance force equation of the cylinder assembly, the force analysis of the disk, shaft section and support of the axial piston pump rotor is carried out to construct the dynamic equation of the axial piston pump rotor under liquid conditions.

[0087] The specific process is as follows: First, considering that the working medium in the axial piston pump flows with the rotation of the pump's cylinder assembly, and that the working medium, due to its viscosity, causes inconsistent velocities of liquid particles at different radial positions within the annular space under centrifugal force, the simplified annular space working medium mass is decomposed into three parts: rotor-added mass, shell-added mass, and liquid-coupled mass. The calculation expressions for these three masses are then determined. The calculation expression for the rotor-added mass is as follows: The formula for calculating the added mass of the shell is as follows: The expression for calculating the fluid coupling mass is m. 21 =ρπL1(R2-R1) 2 ;m 11 Add mass to the rotor; m 12 Add mass to the shell; m 21 R1 is the liquid coupling mass; ρ is the density of the working medium; R2 is the inner radius of the disk in the annular space; R2 is the outer radius of the shell in the annular space; L is the length of the disk in the annular space.

[0088] Secondly, considering external loads such as the main force, friction, centrifugal force, and mass imbalance force, the friction force equation, centrifugal force equation, and mass imbalance force equation of the cylinder block assembly are determined; among them, the unbalance force F of the cylinder block assembly... e The equation is expressed as F e =J p meω 2 Centrifugal force F of the cylinder block assembly p The equation is expressed as F p =m sp ω 2 R; Friction force F of the cylinder block assembly v The equation is expressed as follows: J p Let m be the moment of inertia of the rotating component, e be the mass of the cylinder component, ω be the eccentricity, and ω be the angular velocity of the disk. p R is the diameter of the cylinder assembly; μ is the fluid dynamic viscosity. c For the cylinder block assembly radius, l c For the length of the cylinder block assembly, t is the gap width between the outer surface of the cylinder assembly and the inner surface of the housing.

[0089] Finally, based on the calculated expressions for the rotor's additional mass, the housing's additional mass, and the fluid coupling mass, and combining the fluid force equations and the friction force, centrifugal force, and mass imbalance force equations of the cylinder assembly, force analyses are performed on the disk, shaft segment, and support of the axial piston pump rotor to construct the axial piston pump rotor dynamic equations under fluid-laden conditions; among which,

[0090] The expression for the rotor dynamics equation of an axial piston pump under liquid-carrying conditions is as follows:

[0091] in, And M* is the inertia matrix of the rotor system; And C* is the system damping matrix considering fluid effects; And K * The system stiffness matrix considering fluid interactions;

[0092] G1 is the damping matrix considering the gyroscope effect; M1 is the inertia matrix M of the shaft segment element. s and the inertia matrix M of the disk element d Formed by; C1 is formed by the damping matrix C of the shaft segment unit. s and the damping matrix C of the disk element d Formed by; K1 is formed by the stiffness matrix K of the shaft segment element. S Stiffness matrix K of disk element d and the formation of bearing dynamic characteristic coefficient;

[0093] F s F is the centrifugal force of the shoe pair; fs F represents the friction force of the slipper pair; v1 and F v2 The frictional forces of the cylinder block components can be expressed by the formula... The corresponding calculations were performed to obtain F. z The friction force of the distribution pair; Let u and y be the acceleration vector, velocity vector, and displacement vector of the system, respectively.

[0094] S3. Construct a dynamic model of local defects in cylindrical roller bearings considering time-varying excitation, calculate the angular position of the roller motion in the cylindrical roller bearing, and when the roller enters the defect based on the calculated angular position, obtain the time-varying displacement excitation and time-varying contact stiffness excitation according to the load deformation relationship. Further, use matrix operation to assemble the obtained time-varying displacement excitation and time-varying contact stiffness excitation into the dynamic equation of the axial piston pump rotor under liquid conditions to obtain the dynamic model of the axial piston pump rotor system with bearing fault under liquid conditions.

[0095] The specific process involves first defining the bearing's geometric dimensions, speed, and load, as well as the geometric dimensions and location parameters of local defects.

[0096] Secondly, through the formula Calculate the ratio η of the bearing diameter d to the minimum size L of the local defect. b And through the formula Calculate the ratio η of the length dimension L to the width dimension B of the local defect. d .

[0097] Next, based on the ratio η of the bearing diameter d to the minimum size L of the local defect... b The ratio η of the length dimension L to the width dimension B of the local defect d A local defect model based on a piecewise function is constructed; wherein the piecewise function is composed of a half-sine and a rectangular function, and the expression for the time-varying displacement excitation induced by the local defect is: Where mod() is the modulo function; t dl1 t dl2 t j These represent different time periods; 0~t dl1 The time interval represents the half-sine function; t dl1 ~t dl2 The time interval represents a rectangular function; t dl1 ~(t) dl1 +t dl2 The time interval represents a piecewise function composed of half-sine functions; Δd is the ratio η. b Or ratio η d .

[0098] Next, the time-varying contact stiffness equation between the friction components is determined; wherein, the expression for the time-varying contact stiffness equation between the friction components is: K represents the Hertz contact stiffness between the friction pairs; K1, K2, and K3 represent the contact stiffness between the friction components and the edge of the defect under different conditions.

[0099] Next, the nonlinear contact stiffness equation between the friction components is determined, where the expression for the nonlinear contact stiffness equation between the friction components is F(t)=K(t)δ n(t) F(t) is the time-varying contact force; K(t) is the time-varying contact stiffness between the sphere and the edge of the local defect; n(t) is the time-varying load-deformation coefficient between the sphere and the edge of the local defect.

[0100] Next, based on the time-varying contact stiffness equation between the friction components and the nonlinear contact stiffness equation between the friction components, the time-varying displacement excitation and time-varying contact stiffness excitation between the rolling element and the defect edge are calculated.

[0101] Next, the bearing dynamics model is obtained and solved to obtain the angular position of each rolling element of the rolling bearing; wherein, the expression of the bearing dynamics model includes and

[0102] It should be noted that the specific steps for solving the bearing dynamics model to obtain the angular position of each rolling element of the rolling bearing include: solving the bearing dynamics model using the fixed-step fourth-order Runge-Kutta method, and ending the solution when it is determined that the solution time is greater than the set time; otherwise, continuing the solution when it is determined that the solution time is less than the set time; after the solution is completed, the time-domain and frequency-domain vibration signals of each rolling element in the rolling bearing are obtained to determine the angular position of each rolling element in the rolling bearing.

[0103] Finally, based on the angular position of each rolling element, after the roller enters the defect, the calculated time-varying displacement excitation and time-varying contact stiffness excitation between the rolling element and the defect edge are assembled into the axial piston pump rotor dynamics equation under liquid conditions using matrix operations, thus obtaining the fault dynamics model of the axial piston pump rotor system with bearing fault under liquid conditions.

[0104] In one example, (1) based on the actual surface contour of the local defects, a piecewise function composed of rectangles and half-sine functions is used to characterize different types of local defects, and based on Hertz elastic contact theory, the load-deformation relationship between the friction component and the edge of the local defect is derived. Define the geometric dimensions, rotational speed and load of the friction component, and the geometric dimensions and position parameters of the local defects;

[0105] (2) Calculate the ratio of the diameter of the bearing component to the minimum size of the local defect, and calculate the ratio of the length of the local defect to the width of the local defect;

[0106] (3) Based on the ratio of the friction component diameter to the minimum size of the local defect and the ratio of the length to the width of the local defect, a piecewise function model is constructed, such as... Figure 4 As shown.

[0107] (4) Calculate the time-varying displacement excitation and time-varying contact stiffness excitation between the rolling element and the defect edge;

[0108] (5) Calculate the angular position of each rolling element of the rolling bearing;

[0109] (6) Determine whether the friction component has entered the position of the local defect. If the friction component has entered the position of the local defect, consider the time-varying displacement excitation and time-varying contact stiffness excitation between the friction component and the edge of the local defect. Otherwise, do not consider the time-varying displacement excitation and time-varying contact stiffness excitation between the friction component and the edge of the local defect.

[0110] (7) The bearing dynamic model is solved by the fixed step size fourth-order Runge-Kutta method. It is determined whether the solution time is greater than the set time. If it is greater than the set time, the solution is terminated; otherwise, the solution is continued. Finally, the time domain and frequency domain vibration signals of the rolling element are obtained to determine the angular position of the rolling element.

[0111] (8) Determine whether the bearing components have entered the defect. If the bearing components have entered the defect, obtain the time-varying displacement excitation and time-varying contact stiffness excitation according to the load deformation relationship, and assemble the time-varying displacement excitation and time-varying contact stiffness excitation into the axial piston pump rotor dynamic equation under liquid conditions by matrix operation and applying constraints, thereby establishing the fault dynamic model of the axial piston pump rotor system with bearing failure under liquid conditions.

[0112] S4. Perform critical speed and fault characteristic frequency analysis on the fault dynamic model of the axial piston pump rotor system with bearing failure under liquid conditions to obtain the critical speed of each fault element at the corresponding fault characteristic frequency; wherein, the fault element includes the bearing outer ring, bearing inner ring and rolling element.

[0113] The specific process is as follows: First, a second-order differential equation of motion is given:

[0114]

[0115] Where M is the structural mass matrix, C is the structural damping matrix, and K is the structural stiffness matrix;

[0116] The second step is to determine the Newmark method, which adopts a finite differential expansion over the time step Δt, specifically expressed by formulas (2) and (3):

[0117]

[0118]

[0119] In the formula, α and β are Newmark integration parameters; Δt = t n+1 -t n The integration step size is... and u n t n The acceleration vector, velocity vector, and displacement vector at each instant; and u n+1 t n+1 The acceleration vector, velocity vector, and displacement vector at each instant;

[0120] The third step is that the main purpose of solving equation (1) is to obtain t. n+1The displacement at time t, therefore, formulas (2) and (3) are transformed to change t. n+1 The velocity and acceleration vectors at time t are expressed as t n+1 displacement vector u at time t n+1 Functional form:

[0121]

[0122]

[0123] In the formula, α6=Δt(1-β), α7=βΔt

[0124] Fourth step: From equation (1), we can obtain the following equation:

[0125]

[0126] Step 5: Solve equations (4) to (6) simultaneously to obtain t. n+1 displacement vector u at time t n+1 The expression:

[0127]

[0128] Step 6: Based on the displacement vector u n+1 By finding the solution and combining it with formulas (4) and (5), t can be determined. n+1 acceleration vector at time t and velocity vector

[0129] Step 7: Based on t n+1 acceleration vector at time t and velocity vector Determine the critical speed.

[0130] Therefore, by analyzing the critical speed and fault characteristic frequency of the axial piston pump rotor dynamics model with bearing defects under liquid conditions established in step S2, we can obtain the following conclusions: the excitation force of bearing faults (outer ring, inner ring and rolling element faults) is regarded as the external excitation of the rotor. The fault excitation frequency is proportional to the rotor speed, which makes the fault excitation often induce rotor resonance, thereby reducing the service life of the piston pump mechanical system.

[0131] In order to study the response of rotor resonance to different bearing fault excitations, Figure 5The vibration response diagrams of the axial piston pump under different speed conditions are presented, including Campbell's plot (a) and amplitude-frequency plot (b). As shown in Figure (a), the fault excitation frequency scale line intersects with the rotor's natural frequencies, and the rotor speed (forward rotation) at the intersection point corresponds to the peak speed in (b). Under healthy conditions, the critical rotor speed for rotor resonance is 3200 rpm, and the rotor is excited by unbalanced excitation force. Under bearing failure conditions, since the product between the bearing failure excitation frequency and the rotor speed is greater than 1, the critical rotor speed is expected to decrease significantly.

[0132] This multiplicative relationship is reflected in the slope of the bearing failure excitation frequency scale line; a steeper slope indicates a lower critical speed. Based on this relationship, it can be concluded that the critical speeds for inner ring failure (320 rpm, 1180 rpm, and 2230 rpm) are the lowest, while the speeds for rolling element failure (590 rpm, 2180 rpm, and 4200 rpm) are the highest. The critical speeds for outer ring failure (460 rpm, 1700 rpm, and 3203 rpm) fall in the middle.

[0133] like Figure 6 As shown in the figure, an axial piston pump analysis system for bearing failure under liquid conditions is provided in an embodiment of the present invention, comprising:

[0134] The fluid force equation acquisition unit 110 is used to construct a geometric model of the rotor, cylinder assembly, housing and working medium of the vertical axial piston pump based on the actual spatial position and size of the components housing, cylinder assembly and shaft structure of the axial piston pump, so as to obtain the fluid force equation between the working medium and the cylinder assembly.

[0135] The fault-free pump rotor dynamics equation construction unit 120 is used to decompose the mass of the working medium into the rotor additional mass, the shell additional mass and the liquid coupling mass, and determine the calculation expressions of the rotor additional mass, the shell additional mass and the liquid coupling mass. Furthermore, it combines the fluid force equation and the friction force equation, centrifugal force equation and mass imbalance force equation of the cylinder assembly to perform force analysis on the disk, shaft section and support of the axial piston pump rotor, so as to construct the axial piston pump rotor dynamics equation under liquid conditions.

[0136] The pump rotor dynamic equation construction unit 130 with fault is used to construct a local defect fault dynamic model of cylindrical roller bearing considering time-varying excitation, and calculate the angular position of the roller movement in the cylindrical roller bearing. When the roller enters the defect based on the calculated angular position, the time-varying displacement excitation and time-varying contact stiffness excitation are obtained according to the load deformation relationship. Furthermore, the time-varying displacement excitation and time-varying contact stiffness excitation are assembled into the axial piston pump rotor dynamic equation under liquid conditions through matrix operation, so as to obtain the fault dynamic model of axial piston pump rotor system with bearing fault under liquid conditions.

[0137] The pump rotor dynamic fault analysis unit 140 is used to perform critical speed and fault characteristic frequency analysis on the fault dynamic model of the axial piston pump rotor system with bearing faults under liquid conditions, so as to obtain the critical speed of each fault element at the corresponding fault characteristic frequency; wherein, the fault element includes the bearing outer ring, the bearing inner ring and the rolling element.

[0138] Implementing the embodiments of the present invention has the following beneficial effects:

[0139] This invention analyzes the structural relationship between the rotor, bearing, and working medium of a vertical axial piston pump by combining the characteristics of the internal working medium and bearing defects that cannot be ignored under liquid conditions. The mass of the working medium is decomposed into three parts: rotor added mass, shell added mass, and liquid coupling mass. This allows for the accurate establishment of a dynamic model of the axial piston pump rotor system with liquid working medium and bearing defects. Furthermore, based on the constructed dynamic model, the critical speed and fault characteristic frequency of the "wet state" are calculated and analyzed, effectively reducing vibration faults in the actual operation of the axial piston pump rotor.

[0140] It is worth noting that the various units included in the above system embodiments are only divided according to functional logic, but are not limited to the above division, as long as the corresponding functions can be achieved; in addition, the specific names of each functional unit are only for easy differentiation and are not used to limit the scope of protection of the present invention.

[0141] Those skilled in the art will understand that all or part of the steps in the methods of the above embodiments can be implemented by a program instructing related hardware. The program can be stored in a computer-readable storage medium, such as ROM / RAM, disk, optical disk, etc.

[0142] The above description is merely a preferred embodiment of the present invention and should not be construed as limiting the scope of the invention. Therefore, any equivalent variations made in accordance with the claims of the present invention are still within the scope of the present invention.

Claims

1. A method for analyzing axial piston pumps with bearing failures under liquid-carrying conditions, characterized in that, The method includes the following steps: S1. Based on the actual spatial position and dimensions of the components of the axial piston pump, such as the housing, cylinder assembly, and shaft structure, construct a geometric model of the rotor, cylinder assembly, housing, and working medium of the vertical axial piston pump to obtain the fluid force equation between the working medium and the cylinder assembly. S2. The mass of the working medium is equivalently decomposed into rotor additional mass, shell additional mass and liquid coupling mass, and the calculation expressions for rotor additional mass, shell additional mass and liquid coupling mass are determined. Furthermore, combined with the fluid force equation and the friction force equation, centrifugal force equation and mass imbalance force equation of the cylinder assembly, the force analysis of the disk, shaft section and support of the axial piston pump rotor is carried out to construct the dynamic equation of the axial piston pump rotor under liquid conditions. S3. Construct a dynamic model of local defects in cylindrical roller bearings considering time-varying excitation, calculate the angular position of the roller motion in the cylindrical roller bearing, and when the roller enters the defect based on the calculated angular position, obtain the time-varying displacement excitation and time-varying contact stiffness excitation according to the load deformation relationship. Further, use matrix operation to assemble the obtained time-varying displacement excitation and time-varying contact stiffness excitation into the dynamic equation of the axial piston pump rotor under liquid conditions to obtain the dynamic model of the axial piston pump rotor system with bearing fault under liquid conditions. S4. Perform critical speed and fault characteristic frequency analysis on the fault dynamics model of the axial piston pump rotor system with bearing failure under liquid-carrying conditions to obtain the critical speed of each fault element at the corresponding fault characteristic frequency; wherein, the fault element includes the bearing outer ring, bearing inner ring and rolling elements. Step S3 specifically includes: Define the bearing's geometric dimensions, speed, and load, as well as the geometric dimensions and location parameters of local defects; Through formula Calculate the diameter of the bearing. d Minimum size of local defects L ratio And through the formula Calculate the length of local defects L With width dimension B ratio ; According to the bearing diameter d Minimum size of local defects L ratio and the length of local defects L With width dimension B ratio A local defect model based on a piecewise function is constructed; wherein the piecewise function is composed of a half-sine and a rectangular function, and the expression for the time-varying displacement excitation induced by the local defect is: Here, mod() is the modulo function; , , These represent different time periods; 0~ The time interval represents the half-sine function; ~ The time period represents a rectangular function; ~( + The time interval represents a piecewise function composed of half-sine functions; Ratio or ratio ; Determine the time-varying contact stiffness equation between the friction components; wherein, the expression for the time-varying contact stiffness equation between the friction components is: ; K For friction pairs Hertz Contact stiffness; K 1 、K 2 and K 3 The contact stiffness between the friction component and the defect edge under different conditions; Determine the nonlinear contact stiffness equation between the friction components, wherein the expression for the nonlinear contact stiffness equation between the friction components is: ; The contact force is time-varying. The time-varying contact stiffness between the sphere and the edge of the local defect; The time-varying load-deformation coefficient between the sphere and the edge of the local defect; Based on the time-varying contact stiffness equation and the nonlinear contact stiffness equation between the friction components, the time-varying displacement excitation and time-varying contact stiffness excitation between the rolling element and the defect edge are calculated. Obtain the bearing dynamics model and solve it to obtain the angular position of each rolling element of the rolling bearing; wherein, the expression of the bearing dynamics model includes and ; Based on the angular position of each rolling element, after the roller enters the defect, the time-varying displacement excitation and time-varying contact stiffness excitation between the calculated rolling element and the defect edge are assembled into the axial piston pump rotor dynamic equation under the liquid-carrying condition by matrix operation, thus obtaining the fault dynamic model of the axial piston pump rotor system with bearing failure under the liquid-carrying condition.

2. The method for analyzing axial piston pumps with bearing failures under liquid-carrying conditions as described in claim 1, characterized in that, Step S1 specifically includes: Based on the actual spatial positions and dimensions of the components of the axial piston pump, including the housing, cylinder assembly, and shaft structure, and considering the fluid interaction between the working medium and the cylinder assembly, a regular cylinder is used to represent the housing, rotor, and working medium in an equivalent manner; wherein the working medium fills the annular space between the rotor and the housing. Based on the diameters of the rotor, cylinder assembly, and housing, the inner and outer radii of the annular space are determined, and a geometric model of the vertical axial piston pump rotor, cylinder assembly, housing, and working medium is constructed. Based on the constructed geometric model, the pressure vector value on each grid node of the cylinder assembly is solved using Fluent software to obtain the fluid force equation between the working medium and the cylinder assembly.

3. The method for analyzing axial piston pumps with bearing failures under liquid-carrying conditions as described in claim 2, characterized in that, The specific steps for solving the pressure vector value at each grid node of the cylinder assembly to obtain the fluid force equation between the working medium and the cylinder assembly include: Assume nodes in the main field i The area of ​​this node is △s. i Fluid forces Then the node i Fluid forces exist x,y Directional components are ;in, a for F i and x Angle between axes; i = 1, 2, ..., n; Based on nodes i Fluid forces The total force components of the main field on the cylinder block assembly are obtained as follows: .

4. The method for analyzing axial piston pumps with bearing failures under liquid-carrying conditions as described in claim 3, characterized in that, Step S2 specifically includes: The mass of the working medium is equivalently decomposed into rotor-added mass, housing-added mass, and liquid-coupled mass, and calculation expressions for rotor-added mass, housing-added mass, and liquid-coupled mass are determined; wherein, the calculation expression for the rotor-added mass is as follows: The formula for calculating the additional mass of the shell is as follows: The expression for calculating the liquid coupling mass is as follows: ; Add mass to the rotor; Add mass to the housing; The mass of the liquid coupling; ρ The density of the working medium; R 1 represents the inner radius of the disk in the annular space; R 2 is the outer radius of the shell of the annular space; L The length of the disk in the annular space; Based on the calculated expressions for the rotor's additional mass, the housing's additional mass, and the fluid coupling mass, and combined with the fluid force equations and the friction force, centrifugal force, and mass imbalance force equations of the cylinder assembly, force analyses are performed on the disk, shaft segment, and support of the axial piston pump rotor to construct the axial piston pump rotor dynamics equation under fluid-laden conditions; wherein, the expression for the axial piston pump rotor dynamics equation under fluid-laden conditions is as follows: ; in, , and M* is the inertia matrix of the rotor system; And C* is the system damping matrix considering fluid action; And K * The system stiffness matrix considering fluid interactions; G 1 The damping matrix is ​​to take into account the effect of the gyroscope; M 1 Inertia matrix of shaft segment element M s and the inertia matrix of the disk element M d form; C 1 Damping matrix of shaft segment unit C s and the damping matrix of the disk element C d form; K 1 From the stiffness matrix of the shaft segment element K S Stiffness matrix of disk element K d and the formation of bearing dynamic characteristic coefficient; The unbalanced force of the cylinder block assembly, and ; F s The centrifugal force of the slipper pair; F fs The friction force of the slipper pair; The centrifugal force of the cylinder block assembly, and ; F v1 and F v2 These are the frictional forces of the cylinder block assembly, and ; F z The friction force of the distribution pair; , and These are the system's acceleration vector, velocity vector, and displacement vector, respectively. J p For the rotational inertia of the rotating component, m For the quality of cylinder block components, e For eccentricity, ω The disk's angular velocity; ms p The diameter of the cylinder block assembly; μ For fluid dynamic viscosity, R c The radius of the cylinder block assembly. l c For the length of the cylinder block assembly, , t This refers to the width of the gap between the outer surface of the cylinder block assembly and the inner surface of the housing.

5. The method for analyzing axial piston pumps with bearing failures under liquid-carrying conditions as described in claim 4, characterized in that, The specific steps for solving the bearing dynamics model to obtain the angular position of each rolling element of the rolling bearing include: The bearing dynamics model is solved using the fixed-step fourth-order Runge-Kutta method. The solution ends when the solution time is determined to be longer than the set time; otherwise, the solution continues when the solution time is determined to be shorter than the set time. After the solution is completed, the time-domain and frequency-domain vibration signals of each rolling element in the rolling bearing are obtained to determine the angular position of each rolling element in the rolling bearing.

6. The method for analyzing axial piston pumps with bearing failures under liquid-carrying conditions as described in claim 5, characterized in that, Step S4 specifically includes: Step 1: Given a second-order differential equation of motion: （1） in, M The structural mass matrix, C Here is the structural damping matrix. K For structural stiffness matrix; The second step is to determine the Newmark method, which employs a time step... Δt The finite differential expansion on the surface is specifically expressed by formulas (2) and (3): （2） （3） In the formula, α and β For Newmark integration parameters; Δt=t n+1 -t n The integration step size is... , and u n They are respectively t n The acceleration vector, velocity vector, and displacement vector at each instant; , and u n+1 They are respectively t n+1 The acceleration vector, velocity vector, and displacement vector at each instant; The third step is that the main purpose of solving equation (1) is to obtain... t n+1 The displacement at time t, therefore, formulas (2) and (3) are transformed to... t n+1 The velocity and acceleration vectors at time t are expressed as t n+1 displacement vector at time t u n+1 Functional form: （4） （5） In the formula, , , , , Fourth step: From equation (1), we can obtain the following equation: （6） Step 5: Solve equations (4) to (6) simultaneously to obtain... t n+1 displacement vector at time t u n+1 The expression: （7） Step 6: Based on the displacement vector u n+1 The solution, combined with formulas (4) and (5), determines the solution. t n+1 acceleration vector at time t and velocity vector ; Step 7, according to t n+1 acceleration vector at time t and velocity vector Determine the critical speed.

7. An axial piston pump analysis system for bearing failure under liquid-carrying conditions, used to execute the axial piston pump analysis method for bearing failure under liquid-carrying conditions as described in claim 1, characterized in that, include; The fluid force equation acquisition unit is used to construct a geometric model of the rotor, cylinder assembly, housing and working medium of the vertical axial piston pump based on the actual spatial position and size of the components of the axial piston pump, such as the casing, cylinder assembly and shaft structure, so as to obtain the fluid force equation between the working medium and the cylinder assembly. The fault-free pump rotor dynamics equation construction unit is used to decompose the mass of the working medium into the rotor additional mass, the shell additional mass and the liquid coupling mass, and determine the calculation expressions of the rotor additional mass, the shell additional mass and the liquid coupling mass. Furthermore, combined with the fluid force equation and the friction force equation, centrifugal force equation and mass imbalance force equation of the cylinder assembly, the unit performs force analysis on the disk, shaft section and support of the axial piston pump rotor to construct the axial piston pump rotor dynamics equation under liquid conditions. The pump rotor dynamics equation construction unit with faults is used to construct a fault dynamics model of local defects in cylindrical roller bearings considering time-varying excitations, and calculate the angular position of the roller motion in the cylindrical roller bearing. When the roller enters the defect based on the calculated angular position, the time-varying displacement excitation and time-varying contact stiffness excitation are obtained according to the load deformation relationship. Furthermore, the time-varying displacement excitation and time-varying contact stiffness excitation are assembled into the axial piston pump rotor dynamics equation under liquid conditions through matrix operation, thus obtaining the fault dynamics model of the axial piston pump rotor system with bearing faults under liquid conditions. The pump rotor dynamic fault analysis unit is used to perform critical speed and fault characteristic frequency analysis on the fault dynamic model of the axial piston pump rotor system with bearing faults under liquid conditions, so as to obtain the critical speed of each fault element at the corresponding fault characteristic frequency; wherein, the fault element includes the bearing outer ring, the bearing inner ring and the rolling element.

Images