Method for Establishing a Multi-Degree-of-Freedom Coupled Dynamic Model of a Plunger Pump Rotor System

Abstract

The method for establishing a multi-degree-of-freedom coupled dynamic model of a plunger pump rotor system includes the following steps: First, by determining the translational degrees of freedom of the cylinder block's center of mass along x, y, and z in the global coordinate system, and its rotational degrees of freedom around x and y, the kinetic energy expression of the cylinder block is obtained. Second, by determining the mutual kinematic relationships between the cylinder block and the main shaft, the cylinder block and the plunger, and the cylinder block and the distributor plate, expressions for potential energy and dissipated energy are obtained. Third, a dynamic analysis of the cylinder block is performed to obtain the forces acting on the cylinder block by components connected to it. Fourth, Hamilton's theorem is used to obtain the differential equations of motion for the cylinder block. Fifth, a kinematic analysis of the plunger, main shaft, and slide shoe is performed to obtain the kinetic energy expressions of the plunger, main shaft, and slide shoe. Sixth, a dynamic analysis of the plunger, main shaft, and slide shoe is performed to obtain the forces acting on the plunger, main shaft, and slide shoe by components connected to each component. Finally, Hamilton's theorem is used to obtain the differential equations of motion for the plunger, main shaft, and slide shoe.

Description

Technical Field

[0001] This invention relates to the field of plunger pumps, and more particularly to a method for establishing a multi-degree-of-freedom coupled dynamic model of a plunger pump rotor system. Background Technology

[0002] Piston pumps, due to their compact structure, high power-to-weight ratio, and convenient variable displacement control, are widely used as core power components in the hydraulic transmission systems of various heavy machinery and defense equipment. They are key components determining the reliability and lifespan of hydraulic systems. The internal coupling interface of a piston pump is a prerequisite for the energy conversion between mechanical and hydraulic energy, and also the root cause of singularities, disturbances, and failures. Under extreme operating conditions, it can easily induce a decline in the overall system function and performance degradation. The interaction of multiple internal components in a piston pump has a significant impact, resulting in complex dynamic characteristics.

[0003] Currently, the analysis of the dynamic characteristics of plunger pump rotor systems is not in-depth enough. Traditional modeling methods lack the ability to analyze coupling characteristics and do not consider the microscopic vibration of each component. Therefore, based on the analysis of the structural relationships and coupling between subsystems, this invention proposes a new method for establishing a multi-degree-of-freedom coupled dynamic model of a plunger pump rotor system. Summary of the Invention

[0004] The purpose of this invention is to solve the above-mentioned problems in the prior art and to provide a method for establishing a multi-degree-of-freedom coupled dynamic model of a plunger pump rotor system. By analyzing the interaction effects of the cylinder block, plunger, main shaft, and slipper that constitute the plunger pump rotor system, a multi-degree-of-freedom coupled dynamic model of the plunger pump rotor system is established. This deepens the understanding of the operating law of the plunger pump rotor system, allows for the early detection of design defects, optimization of parameters, significant improvement in development efficiency and quality, reduction of repeated physical testing, reduction of R&D risks, and acceleration of the development process, resulting in significant economic benefits.

[0005] To achieve the above objectives, the present invention adopts the following technical solution:

[0006] Firstly, this invention provides a model-building method applied to solving the globally coupled dynamic characteristics of a plunger pump, including:

[0007] 1) Perform kinematic analysis of the cylinder block assembly, establish a local coordinate system on the cylinder block, solve for the displacement and velocity of the mass points on the cylinder block, thereby obtaining the kinetic energy expression between the cylinder block and other components, perform coupling analysis, obtain the potential energy expression and dissipated energy expression of the cylinder block, combine with the Lagrange equation to obtain the differential equation of motion of the cylinder block, use an implicit solution method and another explicit solution method to perform integral solution, thereby obtaining the vibration response of the system;

[0008] 2) Perform kinematic analysis of the main shaft assembly. Establish a local coordinate system on the main shaft and solve for the displacement and velocity of the mass points on the main shaft. This will yield the kinetic energy expression between the main shaft and other components. Perform coupling analysis to obtain the potential energy expression and dissipated energy expression of the main shaft. Combined with the Lagrange equation, obtain the differential equation of motion of the main shaft. Use an implicit solution method and another explicit solution method to perform integration and solve the equation to obtain the vibration response of the system.

[0009] 3) Perform kinematic analysis of the plunger, establish a local coordinate system on the plunger, solve for the displacement and velocity of the particles on the plunger, thereby obtaining the kinetic energy expression between the plunger and other components, perform coupling analysis, obtain the potential energy expression and dissipated energy expression of the plunger, combine with the Lagrange equation to obtain the differential equation of motion of the plunger, and use an implicit solution method and another explicit solution method to perform integral solution to obtain the vibration response of the system;

[0010] 4) Perform kinematic analysis of the skid assembly. Establish a local coordinate system on the skid and solve for the displacement and velocity of the particles on the skid. This will yield the kinetic energy expression between the skid and other components. Perform coupling analysis to obtain the potential energy expression and dissipated energy expression of the skid. Combined with the Lagrange equation, obtain the differential equation of motion of the skid. Use an implicit solution method and another explicit solution method to perform integration and solve the equation to obtain the vibration response of the system.

[0011] In a second aspect, the present invention also provides an electronic device, including a memory, a processor, and a computer program stored in the memory and executable on the processor, wherein the processor executes the computer program to implement the steps of the method described in the first aspect above.

[0012] Thirdly, the present invention also provides a computer-readable medium having processor-executable non-volatile program code that causes the processor to perform the method described in the first aspect above.

[0013] Compared with the prior art, the beneficial effects achieved by the technical solution of this invention are:

[0014] 1. This invention employs a novel explicit two-step algorithm to solve for the periodic force during the rotational operation of a plunger pump, exhibiting damping characteristics similar to the implicit solution method.

[0015] 2. Since traditional plunger pump coupling models often use Newton's iteration method for calculation, the model of this invention uses an implicit solution method combined with another explicit solution method to correct and calculate the periodic force of the system.

[0016] 3. While accelerating the solution of vibration response, the model of this invention improves the accuracy of dynamic characteristic simulation results by correcting the response at each step. Attached Figure Description

[0017] Figure 1 A flowchart is provided for establishing a multi-degree-of-freedom coupled dynamic model of the plunger pump rotor system.

[0018] Figure 2 This is a schematic diagram of the coupled dynamics model of the plunger pump rotor system.

[0019] Figure 3 This is a schematic diagram showing the torque exerted by other components on the cylinder block in the x-direction in this embodiment.

[0020] Figure 4 This is a schematic diagram showing the forces exerted on the cylinder body in the x-direction by other components in this embodiment.

[0021] Figure 5 This is a schematic diagram showing the forces exerted on the cylinder body in the y-direction by other components in this embodiment.

[0022] Figure 6 This is a schematic diagram showing the torque exerted on the cylinder body in the y-direction by other components in this embodiment.

[0023] Figure 7 This is a schematic diagram showing the forces exerted on the cylinder body in the z-direction by other components in this embodiment.

[0024] Figure 8 This is a schematic diagram of the vibration acceleration response of each degree of freedom of the cylinder in this embodiment.

[0025] Figure 9 This is a schematic diagram of the vibration velocity response of each degree of freedom of the cylinder in this embodiment.

[0026] Figure 10 This is a schematic diagram of the vibration displacement response of each degree of freedom of the cylinder in this embodiment. Detailed Implementation

[0027] This embodiment provides a dynamic modeling of the cylinder subsystem of the plunger pump rotor system, combined with the accompanying drawings, to further illustrate the present invention and present the implementation results of the cylinder subsystem dynamic model.

[0028] This invention provides a method for establishing a multi-degree-of-freedom dynamic model of a plunger pump rotor system. Since the plunger pump system is a coupled dynamic process, the model essentially solves for the force state and motion parameters at each progress step. Figure 1 The process shown is used to construct the dynamic model of the plunger pump rotor system.

[0029] S1. Establish a global coordinate system O-XYZ, where O is the swashplate center, the Z-axis is the cylinder block center axis, the X-axis points from the inner dead center to the outer dead center, and the Y-axis is perpendicular to the OXZ plane. Based on the kinematic and dynamic analysis of each component, perform a coupled force analysis to obtain the forces acting on the cylinder block and piston, according to... Figure 1 The flowchart shown illustrates the construction of a multi-degree-of-freedom dynamic model for a plunger pump rotor system.

[0030] By analyzing the motion and force of the cylinder in the embodiments, force diagrams and torque diagrams of the cylinder and its adjacent components can be obtained. Figure 4 , Figure 5 , Figure 7 This is a schematic diagram showing the forces acting on the cylinder block and other adjacent components in various directions. Figure 3 , Figure 6 This is a schematic diagram showing the torques exerted on the cylinder block by other components in the x and y directions; from Figure 3 It can be seen that the torque on the cylinder block in the x-direction mainly originates from the distributor and the plunger cavity. The cylinder block is primarily subjected to the forces of the plunger, the main shaft, and the distributor plate. Specifically, a local coordinate system O1-x is established for the slipper. si y si z si Where O1 is the centroid of the skate, z si The axis is the axis perpendicular to the swashplate, x si The axis points from the inner dead point to the outer dead point. Local coordinate system O2-x of the cylinder block. c y c z c O2 is the cylinder block's center of mass z c The axis is the central axis of the cylinder block, x c The axis points from the inner dead point to the outer dead point, y c The axis is perpendicular to O2x c z c Plane. Local coordinate system O3-x for the plunger. pi y pi z pi O3 is the cylinder block's center of mass z pi The axis is the central axis of the cylinder block, x pi The axis points from the inner dead point to the outer dead point, y pi The axis is perpendicular to O3x pi z pi Planar. Regarding cylinder block dynamics analysis, the main considerations are the influence of plunger chamber pressure, centrifugal acceleration, and inertial acceleration on dynamic modeling, with centrifugal acceleration and inertial acceleration being related.

[0031] S2. Perform kinematic analysis on the cylinder block assembly, considering the positional change of the cylinder block's center of mass under the applied forces as the main shaft rotates. Cylinder vibration speed, X c Cylinder vibration displacement, M c The cylinder mass is given by equation (2.2). Differentiating the cylinder vibration displacement yields the velocity and acceleration of the cylinder's center of mass during periodic motion. Through analysis of the cylinder's motion state, the kinetic energy expression for the cylinder mass point can be obtained as follows:

[0032]

[0033]

[0034] Where T c The vibrational kinetic energy of the cylinder, m c For cylinder block mass, X represents the cylinder vibration velocity. c M represents the cylinder vibration displacement. c Let x be the cylinder mass matrix, ω be the angular velocity of the cylinder mass about the z-axis, and x be the mass matrix. c y c z c Let l be the displacement of the cylinder in the x, y, z directions. co This represents the distance of the cylinder block mass in the z-direction of the coordinate system. Let be the vibration velocity of the cylinder in the x, y, and z directions. I is the square of the angular acceleration of the cylinder mass rotating about the x and y axes; cx I cy I cz Let x be the moment of inertia of the cylinder about the x, y, and z axes.

[0035] The cylinder block assembly is analyzed to determine its potential energy and dissipated energy. The forces between the cylinder block and the spindle / plunger are considered equivalent to stiffness damping, with the points of application as shown in the figure. Figure 2 As shown, with the rotation of the spindle, the cylinder body is subjected to forces from the spindle and the plunger. The cylinder body is in direct contact with the plunger and the spindle. With the rotation of the spindle, both generate potential energy and dissipated energy. The expression for the potential energy is as follows:

[0036]

[0037] Among them U c For the cylinder block potential energy, K pc K cf These are the correction coefficient matrices for the potential energy changes between the cylinder block, piston, and spindle, respectively. pcx K pcy K pcz K is the correction factor for the changes in potential energy between the cylinder block and the plunger in x, y, z. cfx K cfy K cfz X is a correction factor for the changes in potential energy between the cylinder block and the spindle in the x, y, and z axes. pc1i and X pc2i X represents the vibration displacement of the cylinder block, piston, and spindle relative to the coordinate system. cf The displacement between the cylinder block mass and the main shaft is given by the following parameters:

[0038]

[0039] Among them l pc1i l is the distance from the plunger's center of mass to the plunger's bottom surface in the x, y, and z directions of stiffness damping; pc2i l is the distance from the plunger's center of mass to the z-direction of the contact surface between the plunger and the cylinder block, representing the stiffness damping in the x and y directions. cpz1 The distance in the z-direction from the cylinder block's center of mass to the piston ground surface is the distance along the x and y axes of stiffness damping. cpz2 The distance in the z-direction from the cylinder block's center of mass to the top surface of the piston-cylinder contact point, representing the x and y stiffness damping; l fcz The distance in the z-direction from the spindle's center of mass to the spindle cylinder block's x and y stiffness damping; l cfz x is the distance in the z-direction from the cylinder block's center of mass to the main shaft cylinder block's x and y stiffness damping; f y f z f The displacement of the principal axis in the x, y, and z directions, z c Let θ be the displacement of the cylinder block in the z-direction. fx θ fy The angle of deviation of the principal axis about the x and y directions, θ cx θ cy The angle of deviation of the cylinder block around the x and y directions.

[0040]

[0041]

[0042]

[0043] Where, x pi y pi z pi Let x be the displacement in the x, y, z directions of the piston coordinate system. c y c This represents the displacement of the cylinder body in the x and y directions of the coordinate system. R is the deflection angle of the plunger relative to the spindle. c θ is the diameter of the cylinder block cavity. pxi θ pyi Let x be the angle of rotation of the plunger around x and y in the coordinate system.

[0044] Analyzing the cylinder block assembly, considering the frictional losses between the cylinder block and the spindle, the frictional losses between the cylinder block and the plunger, and the energy dissipation of the cylinder block and other components as the spindle rotates, the energy dissipation expression for the cylinder block assembly can be obtained as follows:

[0045]

[0046] Where D c C represents the dissipated energy of a cylinder block mass.pc and C cf These are the dissipation stiffness coefficients for the cylinder block, main shaft, and plunger, respectively. Let be the vibration velocity of the cylinder mass in each coordinate system. The vibration velocity of the cylinder block's center of mass relative to the bottom and top surfaces of the piston is as follows:

[0047]

[0048]

[0049]

[0050]

[0051] Among them, C pcx C pcy C pcz Ccfx, Ccfy, and Ccfz are the dissipative stiffness coefficients of the cylinder block and piston in the x, y, and z directions of the coordinate system, respectively. Let be the vibration velocity of the principal axis in the x, y, and z directions of the coordinate system. The vibration velocity of the cylinder block in the x, y, and z directions. The vibration velocities of the plunger in the x, y, and z directions are... The vibration velocity of the plunger in the x and y directions in the relative coordinate system. The angular velocity of the cylinder block about the x and y directions. Let ω be the angular velocity of the piston around the x and y directions in the relative coordinate system. The angular velocities of the plunger around the x and y directions are given.

[0052] Based on the expressions for the kinetic energy, potential energy, and dissipated energy of the cylinder block mass, and combining them with the Lagrange equation, the differential equation of motion for the cylinder block mass can be obtained as follows:

[0053]

[0054] L c =T c -U c (2.14)

[0055] q c =[X c Y c Z c θ cx θ cy ] T (2.15)

[0056] Where Lc T represents the energy received by the cylinder from other components. c For the kinetic energy of the cylinder, U c Let q be the cylinder potential energy. c This represents the displacement matrices of the cylinder mass point in the global coordinate system, including its x, y, and z coordinates and its displacement around the X and Y axes.

[0057] Processing the above equations, we obtain the position of the cylinder block mass point in X. c Expression of the differential equation of motion in the direction:

[0058]

[0059] Processing the above equations, we obtain the cylinder block mass in the Y region. c Expression of the differential equation of motion in the direction:

[0060]

[0061] Processing the above equations, we obtain the cylinder block mass at Z... c Expression of the differential equation of motion in the direction:

[0062]

[0063] Processing the above equations, we obtain the cylinder block mass orbiting around X. c The expression for the differential equation of motion of the axis, where M pcxi For it to circle X c The rotational torque of the shaft.

[0064]

[0065]

[0066] Where F pci This is the pressure exerted by the cylinder block on the piston chamber.

[0067] Processing the above equations, we obtain the cylinder block mass orbiting around the Y-axis. c The expression for the differential equation of motion of the axis, where M pcyi For it to circle Y c The rotational torque of the shaft;

[0068]

[0069]

[0070] S3. Further, a dynamic analysis of the plunger is performed, and the dynamic derivation of the plunger is as follows:

[0071] By performing a kinematic analysis of the plunger, and considering the forces exerted on the plunger and slide shoe by the cylinder block and slide shoe as the spindle rotates, the positional change of the plunger's center of mass can be obtained, and X can be derived. pi M is the vibrational displacement of the piston's center of mass. p Given the mass matrix of the plunger, its vibration velocity can be obtained by differentiating the displacement of the plunger's center of mass. Its expression is as follows:

[0072]

[0073]

[0074] Among them l po The distance in m from the center of mass of the piston at top dead center in the global coordinate system along the Z direction is the distance from the center of mass of the piston at top dead center. p For the plunger mass, x pi y pi z pi Let be the position of the plunger pump's center of mass in the local coordinate system. Based on the analysis of the plunger's motion state, the kinetic energy expression for the plunger mass can be obtained as follows:

[0075]

[0076] Where T pi X represents the kinetic energy of the plunger. pi I represents the vibrational displacement of the piston's center of mass; px I py I pz M represents the moment of inertia of the piston's center of mass in the x, y, and z directions; p Let θ be the mass of the plunger, ω be the angular velocity of the plunger rotating about the main shaft, and θ be the angular velocity of the plunger. pxi θ pyi Let be the angular velocity of the plunger about the local coordinate axis.

[0077] Solving for the relevant potential energy and dissipated energy of the plunger, the forces between the plunger, cylinder, and slipper are equivalent to stiffness damping. As the spindle rotates, the plunger is subjected to forces from the cylinder and slipper. As the assembly operates, potential energy and dissipated energy are generated between them. The potential energy expression of the plunger is as follows:

[0078]

[0079] Among them U pi K represents the potential energy of the plunger. pc X is the equivalent stiffness damping coefficient between the plunger and the cylinder block. pcli X is the distance in the z-direction from the center of mass of the plunger to the bottom surface of the cylinder block. pc2i K is the distance in the z-direction from the center of mass of the plunger to the top surface of the cylinder block. psThe equivalent stiffness damping coefficient between the plunger and the slipper is given by the following expressions:

[0080]

[0081]

[0082]

[0083]

[0084] Among them l pcz1 l is the distance in the z-direction from the plunger's center of mass to the plunger's bottom surface in the x and y directions, representing the stiffness and damping. pcz2 The distance in the z-direction from the plunger's center of mass to the contact surface between the plunger and the cylinder block, representing the x and y stiffness damping; l cpz1 The distance in the z-direction from the cylinder block's center of mass to the piston's bottom surface (x, y) for stiffness damping; l cpz2 The distance in the z-direction from the cylinder block's center of mass to the top surface of the piston-cylinder contact point, representing the x and y stiffness damping; l psz l is the distance in the z-direction from the plunger's center of mass to the ball joint's x and y stiffness damping; spz K is the distance in the z-direction from the center of mass of the slipper to the x and y stiffness damping of the ball joint. psx K psy K psz This is a correction factor for the changes in potential energy between the slipper and the plunger in the x, y, and z axes.

[0085] Kinematic analysis of the plunger is performed, considering the frictional losses between the plunger and the cylinder block, the frictional losses between the plunger and the slipper, and the energy dissipation of the cylinder block and other components as the spindle rotates; the expression for the plunger's dissipated energy can be obtained as follows:

[0086]

[0087] Where D pi C is the energy dissipated by the plunger; pc C is the dissipation correction factor between the plunger and the cylinder block. ps This is the dissipation correction factor between the plunger and the slipper; The vibration velocity is obtained by differentiating the vibration displacement from the center of mass of the plunger to the ball joint. The vibration velocity of the plunger's center of mass relative to the top surface of the cylinder block; Let be the vibration velocity of the plunger's center of mass relative to the plunger's bottom surface; the expressions for each parameter are as follows:

[0088]

[0089]

[0090]

[0091]

[0092] Among them l pc1i l is the distance from the plunger's center of mass to the plunger's bottom surface in the x, y, and z directions of stiffness damping; pc2i Let l be the distance from the piston's center of mass to the z-direction of the contact surface between the piston and the cylinder block, representing the stiffness damping in the x and y directions. cpz1 The distance in the z-direction from the cylinder block's center of mass to the piston ground surface is the distance along the x and y axes, representing the stiffness and damping. cpz2 The distance from the cylinder block's center of mass to the top surface of the piston-cylinder contact point in the x and z directions represents the stiffness and damping; psz l is the distance in the z-direction from the plunger's center of mass to the plunger slipper's x and y stiffness damping; spz C is the distance in the z-direction from the center of mass of the slipper to the piston slipper's x and y stiffness damping. psx C psy C psz This is a correction factor for the dissipation variation between the slipper and the plunger in x, y, and z.

[0093] Based on the expressions for the kinetic energy, potential energy, and dissipated energy of the plunger particle, and combining them with the Lagrange equation, the differential equation of motion for the plunger particle can be obtained as follows:

[0094]

[0095] L p =T p -U p (2.37)

[0096] q p =[x p1 y p1 z p1 θ px1 θ py1 ;...;x pn y pn z pn θ pxn θ pyn ] T (2.38)

[0097] Where L p T represents the energy exerted on the plunger by other components. p For the kinetic energy of the plunger, U p For the plunger potential energy, q p Let x, y, z be the displacement transformation matrices of the plunger mass in the global coordinate system, as well as its displacement around the X and Y axes.

[0098] Processing the above equations, we obtain the piston mass in X. pExpression of the differential equation of motion in the direction;

[0099]

[0100] Processing the above equations, we obtain the piston mass in the Y direction. p Expression of the differential equation of motion in the direction;

[0101]

[0102] Processing the above equations, we obtain the piston mass in Z... p Expression of the differential equation of motion in the direction;

[0103]

[0104] Processing the above equations, we obtain the piston mass orbiting around X. p Expression of the differential equation of axis motion;

[0105]

[0106] By processing the above equations, the piston's rotation around Y is obtained. p Expression of the differential equation of axis motion;

[0107]

[0108] S4. Further, a dynamic analysis of the spindle is performed. The dynamic derivation of the spindle is as follows:

[0109] Considering the forces acting on the main shaft and the cylinder block, the relationship between the positional changes of the main shaft's center of mass can be obtained, and X can be derived. f M is the vibrational displacement of the piston's center of mass. f The vibration velocity can be obtained by differentiating the mass matrix of the main shaft with respect to the vibration displacement of the plunger's center of mass. The kinetic energy expression for the main shaft is as follows:

[0110]

[0111]

[0112] Where T f The kinetic energy of the main axis; m f The main spindle mass, ω is the main spindle rotational angular velocity, I fx I fy I fz The moment of inertia of the principal axis in the x, y, and z directions; I fo x is the z-direction distance from the centroid of the principal axis at the top endpoint in the global coordinate system; f , y f z fThe displacement of the main axis in various directions; The vibration velocity of the main axis in the x, y, and z directions of the coordinate system;

[0113] Solving for the relevant potential energy and dissipated energy of the spindle assembly, the force between the spindle and the cylinder is equivalent to stiffness damping. As the spindle rotates, it is subjected to the force of the cylinder. As the assembly operates, potential energy and dissipated energy are generated between them. The expression for the potential energy of the spindle is as follows:

[0114]

[0115] Among them U f Potential energy along the main axis; K cf Stiffness damping coefficient between the main shaft and the cylinder block; K bf Potential energy correction factor between spindle and bearing; X bf1 X bf2 X bf3 These represent the displacements between the spindle's center of mass and the three bearings; their parameter values ​​are shown below:

[0116]

[0117]

[0118]

[0119] Among them l zfb1 l zfb2 l zfb3 These are the lengths from the spindle's center of mass to the three bearings; l fcz The distance in the z-direction from the spindle's center of mass to the spindle cylinder block's x and y stiffness damping; l cfz K is the distance in the z-direction from the cylinder block's center of mass to the main shaft cylinder block's x and y stiffness damping; cfx K cfy K cfz K is the correction coefficient for the change in potential energy between the main shaft and the cylinder in the x, y, and z directions. bfx K bfy K bfz θ is the correction factor for the change in potential energy between the spindle and the bearing in the x, y, and z directions. fx θ fy It refers to the rotation angle of the main axis around the x and y directions.

[0120] A kinematic analysis of the spindle is performed, considering the frictional losses between the cylinder block and the spindle, the frictional losses between the spindle and the bearings, and the energy dissipation of the spindle and other components as the spindle rotates; the expression for the dissipated energy of the spindle can be obtained as follows:

[0121]

[0122] Where D f The energy dissipated by the main shaft; C bf The dissipative stiffness damping coefficient between the main shaft and the bearing; C cf The dissipation stiffness damping coefficient between the main shaft and the cylinder block; The vibration velocity of the main shaft's center of mass relative to the cylinder block; the expressions for each parameter are as follows:

[0123]

[0124]

[0125]

[0126]

[0127] Among them l zfb1 l zfb2 l zfb3 These are the lengths from the spindle's center of mass to the three bearings; l fcz The distance in the z-direction from the spindle's center of mass to the spindle cylinder block's x and y stiffness damping; l cfz C is the distance in the z-direction from the cylinder block's center of mass to the spindle cylinder block's x and y stiffness damping; bf The dissipation stiffness damping coefficient between the main shaft and the bearing; The vibration velocity of the main shaft's center of mass relative to the cylinder block; C bfx C bfy C bfz The dissipation stiffness damping coefficients between the main shaft and the bearings in the x, y, and z directions; It is the rotational angular velocity of the main axis about the x and y directions.

[0128] Based on the expressions for the kinetic energy, potential energy, and dissipated energy of the principal axis particle, and combining them with the Lagrange equation, the differential equation of motion of the principal axis particle can be obtained as follows:

[0129]

[0130] L f =T f -U f (2.56)

[0131] q f =[X f Y f Z f θ fx θ fy ] T (2.57)

[0132] Where Lf The energy T borne by the main shaft from other components f Main axis kinetic energy, U f Principal axis potential energy, q f It is the matrix of displacement changes of the principal axis mass in the global coordinate system, including x, y, z, and around the X and Y axes;

[0133] Processing the above equations, we obtain the position of the principal axis mass point in X. f Expression of the differential equation of motion in the direction;

[0134]

[0135] Processing the above equations, we obtain the principal axis mass point in the Y direction. f Expression of the differential equation of motion in the direction;

[0136]

[0137] Processing the above equations, we obtain the principal axis mass point in Z... f Expression of the differential equation of motion in the direction;

[0138]

[0139] Processing the above equations, for θ fx By taking the partial derivative, we can find the mass about the principal axis around the X-axis. f Expression of the differential equation of axis motion;

[0140]

[0141] Processing the above equations, we obtain the principal axis mass point about the Y-axis. f Expression of the differential equation of axis motion;

[0142]

[0143] S5. Further, a dynamic analysis of the skate shoe is performed, and the dynamic derivation of the skate shoe is as follows:

[0144] Considering the sliding shoe and the force exerted by the plunger, we can obtain the relationship between the position change of the sliding shoe's center of mass and X. si M is the vibrational displacement of the shoe's center of mass. s Given the mass matrix of the skate, its vibration velocity can be obtained by differentiating the vibrational displacement of the skate's center of mass. Given the vibration acceleration A1, the kinetic energy expression for the slipper is as follows:

[0145]

[0146]

[0147] Where Tsi The kinetic energy of the skate; ω si Let I be the angular velocity of the shoe rotation. sx I sy I sz Let I be the moment of inertia of the skate in the x, y, and z directions; so x is the z-direction distance from the global coordinate system to the centroid of the upper stop shoe; si , y si z si I represents the displacement of the skate in each direction; sg θ is the distance from the center of the ball joint to the center of mass of the slipper; sxi θ syi Let m be the rotation angle of the shoe about the local coordinate system. s For the quality of the skates.

[0148] Solving for the relevant potential energy and dissipated energy of the slipper assembly, the force between the slipper and the plunger is equivalent to stiffness damping. As the spindle rotates, the slipper assembly will be subjected to a blocking force. As the assembly moves, potential energy and dissipated energy will be generated between the two. The potential energy expression of the plunger is as follows:

[0149]

[0150] Among them U si K represents the potential energy of the skate; ps K is the stiffness damping coefficient between the slipper and the plunger. ws X is the potential energy correction factor between the ball joint and the slipper; wsi1 X wsi2 X wsi3 These represent the stiffness displacement differences between the shoe's center of mass and the three ball joints; their parameter values ​​are shown below:

[0151]

[0152]

[0153] Among them l psz l is the distance in the x and y directions from the center of mass of the plunger to the stiffness damping of the ball joint; spz R is the distance from the center of mass of the slipper to the z-direction of the ball joint's x and y stiffness damping; sy R is the inner diameter of the slipper sealing strip. sx For the outer diameter of the slipper sealing bag; K wsz This is the potential energy correction coefficient in the z-direction between the ball joint and the slipper;

[0154] Kinematic analysis of the slipper is performed, considering the frictional losses between the slipper and the plunger, as well as the energy dissipation of the slipper and other components, as the spindle rotates. The expression for the dissipated energy of the slipper is as follows:

[0155]

[0156] Where D si C is the energy dissipated by the skate shoe; ps C is the dissipative stiffness damping coefficient between the slipper and the plunger; ws is the dissipation stiffness damping coefficient between the slipper and the ball joint; The velocity difference is the damping force of the ball joint; the expressions for each parameter are shown below:

[0157]

[0158]

[0159]

[0160] Among them l psz l is the distance in the x and y directions from the center of mass of the plunger to the stiffness damping of the ball joint; spz R is the distance from the center of mass of the slipper to the z-direction of the ball joint's x and y stiffness damping; sy R is the inner diameter of the slipper sealing strip. sx C is the outer diameter of the slipper sealing bag. wsz C is the dissipative stiffness damping coefficient in the z-direction between the slipper and the ball joint; psx C psy C psz The dissipation stiffness damping coefficients between the slipper and the plunger in the x, y, and z directions;

[0161] Based on the expressions for the kinetic energy, potential energy, and dissipated energy of the shoe particle, and combining them with the Lagrange equation, the differential equation of motion for the shoe particle can be obtained as follows:

[0162]

[0163] L s =T s -U s (2.73)

[0164] q s =[x s1 y s1 z s1 θ sx1 θ sy1 ;…;x sn y sn z sn θ sxn θ syn ] T (2.74)

[0165] Where Ls For the energy of other components on the skate, T s For the kinetic energy of the skates, U s For the potential energy of the skate, q s Let x, y, z be the displacement transformation matrices of the shoe mass in the global coordinate system, as well as its displacement around the X and Y axes.

[0166] Processing the above equations, we obtain the value of the shoe particle in X. si Expression of the differential equation of motion in the direction;

[0167]

[0168] Processing the above equations, we obtain the value of the shoe mass in the Y direction. si Expression of the differential equation of motion in the direction;

[0169]

[0170] Processing the above equations, we obtain the value of the shoe particle in Z. si Expression of the differential equation of motion in the direction;

[0171]

[0172] Processing the above equations, we obtain the value of the shoe mass orbiting around X. si Expression of the differential equation of axis motion;

[0173]

[0174] Processing the above equations, we obtain the value of the shoe mass orbiting the Y-axis. si Expression of the differential equation of axis motion;

[0175]

[0176] S6. Based on the differential equations of each component obtained above, solve for the vibration response of each component. This invention uses a novel prediction-correction algorithm, employing a new explicit method (Zhai model) as the prediction factor and the Newmark implicit algorithm as the correction factor; and uses the vibration acceleration A at time t = n-1. n-1 and the vibration displacement X at time t=n n and vibration velocity V n Solve for the vibration displacement X at time t = n+1. n+1 and vibration velocity V n+1 The predicted value at time t = n + 1 is corrected by a prediction correction algorithm. The corrected value is then substituted into the component's motion differential equation to obtain the vibration acceleration A at time t = n + 1. n+1 An implicit algorithm is used to process A. n+1After correction, return to the first step and substitute the vibration acceleration from the previous moment into the formula, repeating the cycle to obtain the system's motion characteristics at any given moment.

[0177] This example illustrates the process of solving the vibration response of a cylinder block assembly:

[0178] A. The initial vibration displacement X of the cylinder assembly, calculated in the previous moment. n and vibration velocity V n And the vibration acceleration A at the previous two moments. n A n-1 Substitute into the following formula:

[0179]

[0180] Where the subscript p represents the predicted value, X p,n+1 V is the predicted vibration displacement of the cylinder block at the next moment. p,n+1 The predicted vibration velocity of the cylinder block at the next moment; ψ, Δt is a free parameter used to control the stability of the algorithm and the numerical dissipation.

[0181] B. To improve the accuracy of the algorithm, the basic prediction-correction algorithm can be modified by considering local truncation errors, as shown in the following equation:

[0182]

[0183] Where the subscript 'c' represents the check value, 'm' represents the correction value, and X represents the value of the checksum. m,n+1 V is the correction value for the vibration displacement of the cylinder at time t = (n+1)*Δt. m,n+1 X is the correction value for the vibration velocity of the cylinder at time t = (n+1)*Δt. c,n and V c,n For the given cylinder displacement velocity verification value, ε xp ε vp This represents the correction factor related to the truncation error;

[0184] C. Similarly, by solving for the predicted vibration responses of the spindle, piston, and slipper, and substituting the predicted displacement and velocity correction values ​​of the cylinder block, spindle, and piston obtained above into equations (2.16) to (2.20), the vibration acceleration of the cylinder block assembly at time step t = (n+1)*Δt can be obtained as follows:

[0185] A p,n+1 =M -1 (F n+l -CV m,n+l -KX m,n+l (2.82)

[0186] Equation (2.82) is a simplification of equations (2.16) to (2.20), A p,n+1 X is the predicted vibration acceleration of the cylinder block. m,n+1 V is the correction value for the vibration displacement of the cylinder at time t = (n+1)*Δt. m,n+1 Let M be the correction value for the vibration velocity of the cylinder at time t = (n+1)*Δt, C be the mass matrix, K be the initial damping matrix, and F be the initial stiffness matrix. n+1 The resultant force matrix of the cylinder block is expressed as equations (2.16) to (2.20), which are the external forces acting on the piston and spindle vibration response and the piston cavity pressure. These matrices are mentioned in equations (2.16) to (2.20) above.

[0187] D. Using the Newmark implicit algorithm as the correction factor, the vibration acceleration of the cylinder assembly at time t = (n+1)*Δt is substituted into the equation, and the resulting cylinder vibration displacement and vibration velocity verification matrix is ​​as follows:

[0188]

[0189] Where X n V n For cylinder vibration displacement and vibration velocity, A p,n+1 X is the vibration acceleration of the cylinder block. c,n+1 V c,n+1 This is the verification matrix for cylinder vibration displacement and vibration velocity. β and γ are free parameters.

[0190] E. To improve the accuracy of the algorithm, the basic prediction-correction algorithm can be modified by considering local truncation errors, as shown in the following equation:

[0191]

[0192] Where X c,n+1 V c,n+1 This is the verification matrix for cylinder vibration displacement and vibration velocity. X p,n+1 V is the vibration displacement matrix of the cylinder at time t = (n+1)*Δt. p,n+1 The vibration velocity matrix of the cylinder at time t = (n+1)*Δt; ε xc ε vc These are correction factors related to the truncation error; Figure 9 and Figure 10 This diagram illustrates the vibration velocity and displacement response of the cylinder block at each degree of freedom in this example. The diagram clearly shows the microscopic vibration velocity and displacement of the cylinder block particles in the x, y, and z directions, as well as around the x and y axes, at various moments.

[0193] F. Similarly, based on the above method, the actual vibration response of the spindle, piston, and slipper at the next moment can be calculated. Substituting the obtained vibration displacement and vibration velocity of the cylinder block, spindle, and piston into the process described in C above, the cylinder block vibration acceleration corrected by the implicit algorithm at time step t = n + 1 can be obtained as follows:

[0194] A n+1 =M -1 (F n+l -CV n+l -KX n+l (2.85)

[0195] The obtained cylinder vibration acceleration value is the final value at this time, which can be substituted back into the first step to solve for the cylinder vibration acceleration at the next moment. Figure 8 This diagram illustrates the vibration acceleration response of the cylinder block at each degree of freedom in this example. The diagram clearly shows the microscopic vibration acceleration of the cylinder block particles in the x, y, and z directions, as well as around the x and y axes, at various moments. Therefore, the vibration response of the cylinder block can be obtained.

[0196] Using a method similar to that used for the cylinder block, the vibration response accelerations of the spindle, piston, and slipper at the next instant can be solved. Comparing this to the theoretical dynamic model of the axial piston pump [S.Ye, J.Zhang, B.Xu, S.Zhu, J.Xiang, H.Tang. Theoretical investigation of the contributions of the excitation forces to the vibration of an axial piston pump. Mech.Syst.Signal Process., 129(2019), pp.201-217], the axial piston pump is modeled as a dynamic system with four masses and 19 degrees of freedom. The pump is divided into four lumped mass points. The assembly of the rotating swashplate and housing is represented as FLMP, the assembly of the slipper, piston, and return plate as PLMP, the assembly of the cylinder block and spindle as CLMP, and the assembly of the end cap and valve plate as ECLMP. The main analysis focuses on the vibration characteristics and the contribution of the excitation force to the housing vibration.

[0197] Table 1 compares the number of degrees of freedom between the theoretical dynamic model of the axial piston pump and the multi-degree-of-freedom coupled dynamic model of the piston pump rotor system according to the method of this invention.

[0198] Table 1 Comparison between the theoretical dynamic model of the axial piston pump and the method of this invention

[0199] Modeling methods degrees of freedom Cylinder response plunger response Spindle Response Slipper Response Theoretical dynamic model of axial piston pump 19 It can be solved Unable to solve It can be solved Unable to solve Method of the present invention 100 It can be solved It can be solved It can be solved It can be solved

[0200] As can be seen from Table 1, compared to the theoretical dynamic model of the axial piston pump, the piston-slipper model integrates nine pistons and slippers together, simplifying the interaction between the swashplate and the slipper to a Z-axis... pi The equivalent stiffness and damping coefficient of the shaft. Along X pi axis and Y pi The shaft stiffness and damping coefficients are set to zero to simplify calculations. The interaction between the piston and cylinder is simplified to a Z-axis. C The equivalent stiffness and damping coefficient of the shaft, and along X C axis and Y C The shaft stiffness and attenuation coefficient are set to zero. Therefore, this method only integrates the nine degrees of freedom of the plunger-slipper along the Z direction. Furthermore, compared to the method of this invention, which couples the plunger and slipper analysis, it cannot solve for the vibration response of the plunger and slipper. The method of this invention, when modeling the plunger-slipper system, analyzes each plunger and slipper independently, considering the independent motion degrees of freedom of each plunger and slipper. Moreover, the low-rank nature of the multiple separable computational matrices in this invention replaces the low-rank nature of the constraint large-scale structured matrix. Although the model reconstruction time is longer than that of the theoretical dynamic model of the axial plunger pump, the calculation results consider more system component degrees of freedom, are more accurate, have smaller calculation errors, deepen the understanding of the operating laws of the plunger pump rotor system, facilitate parameter optimization, and significantly improve development efficiency and quality.

[0201] Based on the kinematic and dynamic analysis of each component, a coupled force analysis is performed to obtain the forces acting on the cylinder block. Figures 3 to 7 This diagram illustrates the forces acting on the cylinder block and other adjacent components in the x, y, and z directions, and the moments acting about the x and y axes. Figure 3 It can be seen that the torque on the cylinder block in the x-direction mainly originates from the distribution pair and the plunger cavity; from Figure 6 It can be seen that the torque on the cylinder block around the y-axis comes from the plunger and the main shaft; the cylinder block is mainly subjected to the forces of the plunger, the main shaft and the distributor plate. Figure 8 The diagram shows the vibration acceleration response of the cylinder at each degree of freedom in this example. It is clear from the diagram that the microscopic vibration acceleration of the cylinder mass at each moment is in the x, y, and z directions and around the x and y axes. Figure 9 and Figure 10 The diagram shows the vibration velocity and displacement response of the cylinder at each degree of freedom in this example. It can be clearly seen from the diagram that the microscopic vibration velocity and displacement of the cylinder mass at each moment are in the x, y, z directions and around the x and y axes.

Claims

1. A method for establishing a multi-degree-of-freedom coupled dynamic model of a plunger pump rotor system, characterized in that... Includes the following steps: 1) Obtain the kinetic energy expression of the cylinder by measuring the degrees of freedom of movement of the cylinder's center of mass along x, y, and z in the global coordinate system, as well as the degrees of freedom of rotation about x and y. 2) By understanding the mutual motion relationships between the cylinder block and the main shaft, the cylinder block and the plunger, and the cylinder block and the distributor plate, we can obtain expressions for potential energy and dissipated energy. 3) Perform dynamic analysis on the cylinder block to obtain the forces exerted on the cylinder block by the components connected to it; 4) Based on the kinetic energy expression, potential energy expression, and dissipated energy expression of the cylinder, Hamilton's theorem is used to obtain the differential equation of motion of the cylinder; 5) Perform kinematic analysis on the plunger, spindle, and slide shoe, considering the degrees of freedom of movement of the center of mass of each component along the x, y, and z axes in the global coordinate system, as well as the degrees of freedom of rotation about the x and y axes, to obtain the kinetic energy expressions for the plunger, spindle, and slide shoe. 6) Perform dynamic analysis on the plunger, spindle, and slide shoe to obtain the forces acting on the plunger, spindle, and slide shoe by the components connected to each assembly; 7) Based on the kinetic energy, potential energy, and dissipated energy expressions of the plunger, main shaft, and slide shoe, Hamilton's theorem is used to obtain the differential equations of motion for the plunger, main shaft, and slide shoe. 8) Based on the differential equations of motion of each component obtained above, solve for the vibration response of each component: 8.1) The differential equations of motion for the coupled system of each component are in the form of: Where M is the mass matrix, C is the initial damping matrix, and K is the initial stiffness matrix. , , These are the displacement, velocity, and acceleration matrices for the corresponding components. The forces exerted on it by the microscopic vibrations of other components: 8.2) Taking the applied force as the excitation force of the system, the initial predicted value is given. The time is divided into steps, and the response is predicted by explicit solution method. The displacement and velocity vectors at the next moment are solved by the initial displacement and velocity, as shown in the following equation (1.2): Where X n V n A n They represent t=n The displacement vector, velocity vector, and acceleration vector at time Δt, where Δt is the time step, X n+1 V n+1 Let t = (n + 1) Displacement vector and velocity vector at time Δt; A n-1 Let t = (n - 1) The acceleration vector at time Δt; , These are the free parameters that control the stability of the algorithm and the numerical dissipation, respectively. 8.3) The solved predicted values ​​and the pre-given verification values ​​are corrected using the following equation: Where, ε xp and ε vp Here, m represents the correction factor, p represents the predicted value, and c represents the validation value; X m,n+1 With V m,n+1 Let t = (n + 1) Corrected values ​​for the displacement and velocity vectors at time Δt; X p,n+1 With V p,n+1 Let t = (n + 1) Predicted values ​​of displacement and velocity vectors at time Δt; X p，n With V p，c They are respectively t=n Predicted values ​​of displacement and velocity vectors at time Δt; X c，n With V c，n They are respectively t=n The verification values ​​of the displacement vector and velocity vector at time Δt; 8.4) Substituting the displacement and velocity correction vectors into the system's differential equations of motion, we obtain the predicted force and predicted acceleration of the system at the next moment. The equations for the predicted force and acceleration are as follows: Among them, A p，n+1 Let t = (n + 1) Predicted acceleration vector value F at time Δt p，n+1 Let t = (n + 1) Predicted value of the resultant force matrix acting on the cylinder at time Δt; 8.5) An implicit algorithm is used to verify the predicted acceleration. The predicted displacement and velocity of the mechanism are solved based on the acceleration and the differential equation of motion. The implicit algorithm verification equation is as follows: Among them, β, X is a free parameter; c，n+1 With V c，n+1 Let t = (n+1) The verification values ​​of the displacement vector and velocity vector at time Δt, A p，n-1 Let t = (n - 1) Predicted acceleration vector value at time Δt; A n For t=n The acceleration vector at time Δt; 8.6) The predicted velocities and displacements obtained by the solution are corrected from those obtained by the explicit algorithm. The corrected equations are as follows: Where, ε xc ε xc These are the correction factors for the displacement and velocity vectors, respectively; X n+1 V n+1 These are the corrected displacement and velocity vectors, respectively; X c，n+1 With V c，n+1 Let t = (n+1) The verification values ​​of the displacement vector and velocity vector at time Δt; 8.7) Substitute the corrected predicted displacement and acceleration into the dynamic equations of the mechanism to obtain the corrected acceleration, as shown below: Where M is the mass matrix, C is the initial damping matrix, K is the initial stiffness matrix, and F is the initial stiffness matrix. n+1 The matrix of the resultant forces acting on the cylinder block. This is the corrected acceleration.

2. An electronic device, comprising a memory, a processor, and a computer program stored in the memory and executable on the processor, characterized in that: When the processor executes the computer program, it implements the steps of the method of claim 1.

3. A computer-readable medium having processor-executable non-volatile program code, characterized in that: The program code causes the processor to execute the method of claim 1.

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