CN-116384183-B - Multi-degree-of-freedom coupling dynamics model building method for plunger pump rotor system

CN116384183BCN 116384183 BCN116384183 BCN 116384183BCN-116384183-B

Abstract

A method for building a multi-degree-of-freedom coupling dynamics model of a plunger pump rotor system includes the following steps of obtaining a kinetic energy expression of a cylinder body through a movement degree of a cylinder body centroid along x, y and z and a rotation degree of freedom around x and y under a global coordinate system, obtaining potential energy and dissipation energy expressions through mutual movement relations among the cylinder body, a main shaft, the cylinder body, the plunger and a valve plate, carrying out kinetic analysis on the cylinder body to obtain acting force acting on the cylinder body by a part connected with the cylinder body, obtaining a motion differential equation of the cylinder body by using Hamiltonian theorem, carrying out kinetic analysis on the plunger, the main shaft and the sliding shoe to obtain kinetic energy expressions of the plunger, the main shaft and the sliding shoe, carrying out kinetic analysis on the plunger, the main shaft and the sliding shoe to obtain acting force acting on the plunger, the main shaft and the sliding shoe by parts connected with all the parts, and obtaining the motion differential equation of the plunger, the main shaft and the sliding shoe by using Hamiltonian theorem.

Inventors

YE SHAOGAN
CHEN LANG
ZHENG CHENLIANG
LIU WANSHAN
LI CHUNMEI

Assignees

厦门大学

Dates

Publication Date: 20260505
Application Date: 20230320

Claims (3)

1. The method for establishing the multi-degree-of-freedom coupling dynamics model of the plunger pump rotor system is characterized by comprising the following steps of: 1) Obtaining a kinetic energy expression of the cylinder body through the freedom degree of movement of the mass center of the cylinder body along x, y and z and the freedom degree of rotation around x and y under a global coordinate system; 2) The expression of potential energy and dissipation energy is obtained through the mutual motion relation between the cylinder body and the main shaft, between the cylinder body and the plunger and between the cylinder body and the valve plate; 3) Carrying out dynamic analysis on the cylinder body to obtain acting force acting on the cylinder body by a component connected with the cylinder body; 4) According to the kinetic energy expression, potential energy expression and dissipation energy expression of the cylinder body, using the Hamiltonian theorem to obtain a motion differential equation of the cylinder body; 5) Performing kinematic analysis on the plunger, the main shaft and the sliding shoe, and considering the movement degrees of freedom of the mass centers of all components along the x, y and z axes and the rotation degrees of freedom around the x and y axes under a global coordinate system, so as to obtain kinetic energy expressions of the plunger, the main shaft and the sliding shoe; 6) The dynamic analysis is carried out on the plunger, the main shaft and the sliding shoe, so that acting forces acting on the plunger, the main shaft and the sliding shoe by the components connected with the components are obtained; 7) According to the kinetic energy expression, potential energy expression and dissipation energy expression of the plunger, the main shaft and the sliding shoe, the Hamiltonian theorem is used to obtain a motion differential equation of the plunger, the main shaft and the sliding shoe; 8) According to the solved motion differential equation of each component, solving the vibration response of each component: 8.1 The differential equation of motion of each component coupling system is as follows: wherein M is a mass matrix, C is an initial damping matrix, K is an initial stiffness matrix, 、、 Respectively corresponding to displacement, speed and acceleration matrixes of the components, Forces generated on other components by microscopic vibration: 8.2 Giving an initial predicted value by taking acting force as system exciting force, dividing time into step sizes, predicting response by an explicit solving method, solving displacement and speed vectors at the next moment by initial displacement and speed, and calculating the following formula (1.2): Wherein X n 、V n 、A n represents t=n, respectively Displacement vector, velocity vector and acceleration vector at time Δt, Δt being the time step and X n+1 、V n+1 being t= (n+1) respectively Displacement vector and velocity vector at time delta t, A n-1 is t= (n-1) Acceleration vector at Δt; 、 The free parameters of the stability and the numerical dissipation of the control algorithm are respectively; 8.3 Correcting the solved predicted value and a preset check value, wherein the corrected equation is as follows: Wherein ε xp and ε vp are correction coefficients, m represents correction value, p represents predicted value, c represents check value, X m,n+1 and V m,n+1 are respectively t= (n+1) Correction values of displacement vector and velocity vector at time delta t, wherein X p,n+1 and V p,n+1 are respectively t= (n+1) Predicted values of displacement vector and velocity vector at time delta t, X p,n and V p,c are t=n respectively Predicted values of displacement vector and velocity vector at time delta t, X c,n and V c,n are t=n respectively The displacement vector at the time delta t and the check value of the velocity vector; 8.4 The displacement and speed correction vector is brought into a system motion differential equation to obtain a predicted force and a predicted acceleration at the next moment of the system, and the equation of the predicted force and the predicted acceleration is as follows: wherein a p,n+1 is t= (n+1) Acceleration vector predicted value at Δt, F p,n+1 is t= (n+1) Predicted values of resultant force matrixes born by the cylinder body at the moment delta t; 8.5 Checking the predicted acceleration by adopting an implicit algorithm, solving the predicted displacement and the speed of the mechanism according to a motion differential equation by the acceleration, wherein the implicit algorithm checking equation is as follows: Wherein, beta, Is a free parameter, X c,n+1 and V c,n+1 are respectively t= (n+1) The displacement vector at time Δt and the velocity vector are checked, and a p,n-1 is t= (n-1) Acceleration vector predicted value at time Δt, A n being t=n Acceleration vector at Δt; 8.6 Correcting the solved prediction speed and displacement and the prediction speed and displacement solved by an explicit algorithm, wherein the corrected equation is as follows: Wherein epsilon xc 、ε xc is the correction coefficient of the displacement and velocity vector respectively, X n+1 、V n+1 is the corrected displacement and velocity vector respectively, and X c,n+1 and V c,n+1 are t= (n+1) respectively The displacement vector at the time delta t and the check value of the velocity vector; 8.7 The corrected predicted displacement and acceleration are brought into the dynamic equation of the mechanism to obtain the corrected acceleration, as follows: Wherein M is a mass matrix, C is an initial damping matrix, K is an initial stiffness matrix, F n+1 is a resultant force matrix born by the cylinder body, The corrected acceleration is obtained.
2. An electronic device comprising a memory, a processor and a computer program stored on the memory and executable on the processor, characterized in that the processor implements the steps of the method of claim 1 when executing the computer program.
3. A computer readable medium having non-volatile program code executable by a processor, wherein said program code causes said processor to perform the method of claim 1.

Description

Multi-degree-of-freedom coupling dynamics model building method for plunger pump rotor system Technical Field The invention relates to the field of plunger pumps, in particular to a method for establishing a multi-degree-of-freedom coupling dynamics model of a plunger pump rotor system. Background The plunger pump is characterized by compact structure, high power-weight ratio, convenient variable control and the like, and is widely applied to matched hydraulic transmission systems of various heavy machinery and national defense equipment as a core power element, thus being a key component for determining the reliability and service life of the hydraulic system. The internal coupling interface of the plunger pump is a precondition for realizing the energy conversion function between mechanical energy and hydraulic energy, is also a source for generating singular, disturbance and faults, and is extremely easy to induce the overall function degradation and performance degradation of the system under extreme working conditions. The interaction of multiple parts in the plunger pump has obvious influence and complex dynamic characteristics. At present, the dynamic characteristic analysis of a rotor system of a plunger pump is not deep enough, the traditional modeling method lacks the capability of analyzing coupling characteristics, and the problem of microscopic vibration of each component is not considered. Therefore, on the basis of analyzing the structural relationship and the coupling condition among subsystems, the invention provides a novel method for establishing a multi-degree-of-freedom coupling dynamics model of a rotor system of a plunger pump. Disclosure of Invention The invention aims to solve the problems in the prior art, and provides a method for establishing a multi-degree-of-freedom coupling dynamics model of a plunger pump rotor system, which is used for analyzing interaction influence of a cylinder body, a plunger, a main shaft and a sliding shoe which form the plunger pump rotor system, the multi-degree-of-freedom coupling dynamics model of the plunger pump rotor system is built, the knowledge of the operation rule of the plunger pump rotor system is deepened, design defects are found in advance, parameters are optimized, development efficiency and quality are greatly improved, repeated experiments of objects are reduced, development risks are reduced, development process is accelerated, and great economic benefits are achieved. In order to achieve the above purpose, the invention adopts the following technical scheme: In a first aspect, the present invention provides a method for establishing a model, applied to dynamic characteristic solving of global coupling of a plunger pump, including: 1) Performing kinematic analysis on a cylinder assembly, establishing a local coordinate system on the cylinder, solving the motion displacement and the velocity of mass points on the cylinder, thereby solving a kinetic energy expression between the cylinder and other assemblies, performing coupling analysis, obtaining a potential energy expression and a dissipation energy expression of the cylinder, combining a Lagrange equation, obtaining a motion differential equation of the cylinder, and performing integral solution by adopting an implicit solution and another explicit solution, thereby solving the vibration response of the system; 2) Performing kinematic analysis on a main shaft component, establishing a local coordinate system on the main shaft, solving the motion displacement and the speed of mass points on the main shaft, thereby solving a kinetic energy expression between the main shaft and other components, performing coupling analysis, obtaining a potential energy expression and a dissipation energy expression of the main shaft, combining a Lagrange equation, obtaining a motion differential equation of the main shaft, and performing integral solution by adopting an implicit solution and another explicit solution, thereby solving a vibration response of the system; 3) Performing plunger kinematics analysis, establishing a local coordinate system on the plunger, solving the motion displacement and the velocity of mass points on the plunger, thereby obtaining a kinetic energy expression between the plunger and other components, performing coupling analysis, obtaining a potential energy expression and a dissipation energy expression of the plunger, combining a Lagrange equation, obtaining a motion differential equation of the plunger, and performing integral solution by adopting an implicit solution and another explicit solution, thereby obtaining a system vibration response; 4) And carrying out the kinematic analysis of the sliding shoe assembly, establishing a local coordinate system on the sliding shoe, solving the motion displacement and the velocity of mass points on the sliding shoe, thereby solving the kinetic energy expression between the sliding shoe and other assemblies, carrying out the