Coupled modeling of multi-mass dynamics and oil film lubrication behavior for plunger pumps

Abstract

The coupling modeling method of plunger pump multi-mass dynamics and oil film lubrication behavior comprises: 1) using a prediction check algorithm to predict and check the initial dynamics behavior of the mass to solve the vibration response of the mass; 2) according to the vibration response of the mass, the oil film thickness field of the friction pair is solved, and the coupling relationship energy equation of the mass is established; 3) according to the obtained oil film thickness field, combined with the oil film boundary condition, the oil film pressure field is solved through the oil film fluid motion equation, and the oil film lubrication characteristics are output; 4) according to the obtained oil film pressure field, the oil film supporting force system and torque are solved, and then the force and torque acting on the mass are obtained; 5) combined with the obtained force and torque acting on the mass and the coupling relationship energy equation, the mass dynamics model is established, which is used to solve the vibration response and oil film lubrication characteristics at the next time. The modeling method can solve the dynamics of the plunger pump multi-mass and the key friction pair oil film lubrication characteristics at the same time.

Description

Technical Field

[0001] This invention relates to the field of plunger pumps, and more specifically to a coupled modeling method for plunger pump multibody dynamics and oil film lubrication behavior. Background Technology

[0002] Piston pumps, as core power components, are widely used in the hydraulic transmission systems of various heavy machinery and defense equipment, and are key components determining the reliability and lifespan of hydraulic systems. In physics and computer science, a multi-mass system refers to a system composed of multiple particles; in mechanics, it refers to a system composed of multiple masses with a certain mass. The piston pump contains multiple friction pairs within its multi-mass system, making its internal structure compact and complex. These friction pairs include the kinematic friction between the piston and cylinder, the kinematic friction between the slipper and swashplate, and the kinematic friction between the cylinder and distributor plate. The oil film formed by the lubricating oil between these friction pairs—piston and cylinder, slipper and swashplate, cylinder and distributor plate—is a thin film formed by lubricating oil. The coupling effect between the multi-mass system and the oil film within the piston pump affects oil film friction wear and mass damage, thus impacting the pump's lifespan and reliability.

[0003] Currently, there are many existing plunger pump models, including models that can be established separately for plunger pump dynamics and friction pair oil film lubrication. However, these models do not consider the coupling effect between the two, so they cannot simultaneously and accurately predict the multibody response of the plunger pump and obtain the oil film lubrication characteristics. This significantly reduces the accuracy of plunger pump reliability design, hindering practical engineering applications and causing economic losses. To solve this problem, a new model needs to be developed that takes into account the coupling effect between the multibody and oil film of the plunger pump. Summary of the Invention

[0004] The purpose of this invention is to solve the above-mentioned problems in existing plunger pump modeling methods and to propose a coupled modeling method for plunger pump multibody dynamics and oil film lubrication behavior. This modeling method can more accurately predict the multibody response of the plunger pump through a prediction-verification combined algorithm and obtain the lubrication characteristics of the oil film, which can provide important theoretical basis and technical support for pump design, manufacturing, use and maintenance.

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

[0006] A coupled modeling method for the dynamics of a plunger pump and the lubrication behavior of an oil film includes the following steps:

[0007] 1) The initial dynamic behavior of the mass is predicted and verified using a prediction and verification algorithm in order to solve the vibration response of the mass;

[0008] 2) Based on the vibration response of the mass, solve for the oil film thickness field of the friction pair and establish the coupling relationship energy equation of the mass;

[0009] 3) Based on the obtained oil film thickness field and combined with the oil film boundary conditions, solve the oil film pressure field through the oil film fluid motion equation and output the oil film lubrication characteristics;

[0010] 4) Based on the obtained oil film pressure field, solve for the oil film supporting force system and torque, and then obtain the force and torque acting on the mass;

[0011] 5) Combining the obtained forces, torques and coupling relationship energy equations acting on the mass, establish a mass dynamics model to solve the vibration response and oil film lubrication characteristics at the next moment;

[0012] In step 2), the coupling relationship energy equation is specifically as follows:

[0013]

[0014]

[0015]

[0016] Where T is the kinetic energy generated by the vibration of the mass, U is the potential energy generated by the vibration of the mass, D is the dissipated energy generated by the vibration of the mass, M is the mass of the mass, and X is the displacement generated by the vibration of a particle on the mass. K is the vibrational velocity of a particle on the mass. e This is a correction factor for potential energy and dissipated energy.

[0017] In step 3), the oil film boundary conditions are specifically as follows:

[0018]

[0019] Where p(r,2π) is the pressure value at (r,2π), p(r,0) is the pressure value at (r,0), p(R1,θ) is the pressure value at (R1,θ), and p(R2,θ) is the pressure value at (R2,θ). Let be the rate of change of pressure with respect to θ at (r,0). Let R1 be the outer diameter of the inner ring of the sealing strip, R2 be the inner diameter of the inner ring of the sealing strip, and p be the rate of change of pressure with respect to θ at (r, 2π). s p is the oil pressure in the central oil chamber. c Let θ be the oil pressure in the casing, θ be the angle subtended by any point in polar coordinates, and r be the polar coordinate radius of any point.

[0020] Step 3) The oil film lubrication characteristics include tilting angle, oil leakage power, and friction power;

[0021] Overturning angle:

[0022]

[0023] Where, α c For the overturning angle, h max h is the maximum oil film clearance height. min R3 is the minimum oil film gap height, and R3 is the outer diameter of the outer ring of the sealing band.

[0024] The frictional power generated by the oil film due to frictional resistance:

[0025]

[0026] Where E1 is the friction power, μ is the dynamic viscosity of the oil, ω is the angular velocity of the cylinder block, τ is the tangential stress of the oil film, and φ is the angular velocity of the cylinder block. c Let R be the contact factor, r be the polar radius of the point, h be the oil film thickness, and θ1 and θ2 be the angles subtended by any two points in polar coordinates. i R j These are the outer and inner diameters of the parallel clearance.

[0027] Oil film gap leakage:

[0028]

[0029] Among them, Q L Where h is the leakage rate between the oil film gaps and h is the oil film thickness. R1 is the outer diameter of the inner ring of the mass seal, R2 is the inner diameter of the inner ring of the mass seal, and v is the oil film thickness change rate. r Radial velocity;

[0030] The oil leakage power is: E2 = Q L Δp

[0031] Where E2 is the oil leakage power, Δp is the working pressure difference, and Q L This refers to the leakage rate in the oil film gap.

[0032] Compared with the prior art, the beneficial effects of the present invention are as follows:

[0033] 1. This invention considers the coupling effect of multibody dynamics and oil film lubrication behavior of plunger pumps, and takes into account the role of oil film in mass dynamics of key friction pairs. It can more accurately predict the multibody response of plunger pumps and obtain the lubrication characteristics of oil film, and provides important theoretical basis and technical support for the design, manufacture, use and maintenance of pumps.

[0034] 2. This invention can more accurately predict the wear of friction pairs, which helps to optimize the material selection and surface processing of friction pairs.

[0035] 3. In the existing technology, the traditional process of solving the oil film lubrication performance using the Newton iteration method is too complicated. The present invention uses a solution algorithm that combines prediction and verification to consider the influence of the vibration response of the coupled components on the oil film, thereby improving the calculation efficiency and accuracy. Attached Figure Description

[0036] Figure 1 This is a schematic diagram of the coupling model relationship between the multibody dynamics and oil film lubrication behavior of a plunger pump.

[0037] Figure 2 This is a schematic diagram of the vibration velocity response of each degree of freedom of the cylinder in this embodiment.

[0038] Figure 3 This is a schematic diagram of the vibration displacement response of each degree of freedom of the cylinder in this embodiment.

[0039] Figure 4 This is a schematic diagram of the oil film lubrication characteristics output in this embodiment. Detailed Implementation

[0040] The present invention provides a coupled modeling method for the multibody dynamics and oil film lubrication behavior of a plunger pump. This method couples the plunger pump dynamics model and the oil film lubrication model. The following example, considering the oil film of the spherical distribution sub-phase, is used to further illustrate the present invention with reference to the accompanying drawings.

[0041] Figure 1 This is a schematic diagram of the coupling model relationship between the multibody dynamics of a plunger pump and the oil film lubrication behavior. The specific steps include the following:

[0042] 1) The initial dynamic behavior of the mass is predicted and verified using a prediction and verification algorithm in order to solve the vibration response of the mass;

[0043] 2) Based on the vibration response of the mass, solve for the oil film thickness field of the friction pair and establish the coupling relationship energy equation of the mass;

[0044] 3) Based on the obtained oil film thickness field and combined with the oil film boundary conditions, solve the oil film pressure field through the oil film fluid motion equation and output the oil film lubrication characteristics;

[0045] 4) Based on the obtained oil film pressure field, solve for the oil film supporting force system and torque, and then obtain the force and torque acting on the mass;

[0046] 5) By combining the obtained forces, torques and coupling relationship energy equations acting on the mass, a dynamic model of the mass is established to solve the vibration response and oil film lubrication characteristics at the next moment.

[0047] This embodiment is based on the following conditions:

[0048] The maximum outlet pressure of the pump is set to 14 MPa, and the cylinder speed is set to 1000 r / min.

[0049] Establish a coordinate system O-XYZ, with the center of the distribution disk as the origin O, the Z-axis along the main axis, the Y-axis pointing from the inner dead point of the distribution disk to the outer dead point, and the X-axis perpendicular to the OYZ plane.

[0050] First, the cylinder block vibration response prediction solution is performed, and the initial cylinder block vibration displacement X is used. n Vibration velocity V n The vibration acceleration A at the previous moment n-1 Predict and correct, and obtain the corrected displacement A at the next time step. n+1 Acceleration X n+1 , will A n+1 X n+1 Substituting these values ​​into the system's differential equations of motion yields the predicted force and predicted acceleration. Then, a verification algorithm is used to evaluate A. n+1 and X n+1 After verification and correction, the corrected vibration displacement and velocity, as well as the corrected force and acceleration, are obtained. The specific formulas are as follows:

[0051] Prediction formula:

[0052]

[0053] V p,n+l =V n +(1+χ)A n Δt-χA n-1 Δt

[0054] Where ψ and χ are the free parameters controlling the stability and numerical dissipation of the control algorithm, respectively, and X n V represents the vibration displacement at that moment. n A represents the vibration velocity at that moment. n A represents the vibration acceleration at that moment. n-1 X represents the vibration acceleration at the previous moment, Δt represents the time interval between the two moments, and X represents the vibration acceleration at the previous moment. p,n+l V represents the predicted value of the vibration displacement at the next moment. p,n+l This represents the predicted value of the vibration velocity at the next moment.

[0055] Prediction correction formula:

[0056] X m,n+l =X p,n+1 +ε xp (X p,n -X q,n )

[0057] V m,n+l =V p,n+1 +ε vp(V p,n -V q,n )

[0058] Where, ε xp and ε vp As a correction factor, X m,n+l V represents the correction value for the vibration displacement at the next moment. m,n+l X represents the correction value for the vibration velocity at the next moment. p,n+l V represents the predicted value of the vibration displacement at the next moment. p,n+l X represents the predicted value of the vibration velocity at the next moment. p,n V represents the predicted value of the vibration displacement at that moment. p,n X represents the predicted value of the vibration velocity at that moment. q,n V represents the verification value of the vibration displacement at that moment. q,n This represents the verification value of the vibration velocity at that moment;

[0059] Verification formula:

[0060]

[0061] V q,n+l =V n +(1-γ)A n Δt+γA p,n+1 Δt

[0062] Where η and γ are free parameters, X n V represents the vibration displacement at that moment. n A represents the vibration velocity at that moment. n X represents the vibration acceleration at that moment, Δt represents the time interval between the two moments, and X represents the vibration acceleration at that moment. q,n+1 V represents the verification value of the vibration displacement at the next moment. q,n+1 A represents the check value of the vibration velocity at the next moment. p,n+1 This represents the predicted value of the vibration acceleration at the next moment;

[0063] Verification and correction formula:

[0064] X n+l =X q,n+1 +ε xc (X p,n+1 -X q,n+1 )

[0065] V n+l =V q,n+1 +ε vc (V p,n+1 -V q,n+1 )

[0066] Where, ε xc ε xcThese are the correction factors for the displacement and velocity vectors, respectively, X. n+1 V represents the vibration displacement at the next moment. n+1 X represents the vibration velocity at the next moment. q,n+1 V represents the verification value of the vibration displacement at the next moment. q,n+1 X represents the check value of the vibration velocity at the next moment. p,n+l V represents the predicted value of the vibration displacement at the next moment. p,n+l This represents the predicted value of the vibration velocity at the next moment.

[0067] Figure 2 , Figure 3 These are schematic diagrams of the vibration velocity response and vibration displacement response of the cylinder block for each degree of freedom, respectively. Figure 2 , Figure 3 It can be known that the microscopic vibration velocity and vibration displacement of the particles on the cylinder are the translational degrees of freedom along the x, y, and z directions and the two rotational degrees of freedom around the x and y axes.

[0068] Based on the displacement and velocity obtained after verification and correction, the following energy equation for cylinder coupling relationship is established:

[0069]

[0070]

[0071]

[0072] Among them, T c U is the kinetic energy generated by the vibration of the cylinder. c The potential energy generated by cylinder vibration, D c M is the dissipated energy generated by cylinder vibration. c For cylinder block mass, X c This refers to the displacement caused by the vibration of particles on the cylinder block. K is the vibration velocity of the particles on the cylinder. e This is a correction factor for potential energy and dissipated energy.

[0073] The center oil film thickness h0(t+Δt) and the center film thickness change rate for the next progress step are calculated based on the cylinder vibration displacement response and vibration velocity response. As shown in the formula:

[0074] h0(t+Δt)=h0(t)+z1

[0075]

[0076] Where h0(t+Δt) represents the center oil film thickness of the next progress step, and h0(t) represents the center oil film thickness of the current progress step. The z-axis represents the rate of change of the central film thickness, and z1 represents the vibration displacement of the cylinder in the z-direction. This represents the vibration velocity of the cylinder in the z-direction.

[0077] Let the position of any point on the cylinder block in polar coordinates be (r, θ), and let the oil film thickness h and the rate of change of oil film thickness be... As shown in the formula:

[0078] h(r,θ)=h0-rsinθα c -rcosθβ1

[0079]

[0080] Where h(r,θ) is the oil film thickness at position (r,θ) on polar coordinates. Let be the rate of change of oil film thickness at position (r, θ) on polar coordinates, and h0 be the center thickness. α is the rate of change of oil film thickness. c β1 is the overturning angle, and β2 is the tilt angle. The rate of change of overturning angle. Let r be the rate of change of the tilt angle, r be the polar coordinate radius of any point, and θ be the angle subtended by any point in polar coordinates.

[0081] Based on the oil film boundary conditions, the oil film pressure field is obtained according to the oil film fluid motion equation.

[0082] The oil film boundary conditions are:

[0083]

[0084] Where p(r,2π) is the pressure value at (r,2π), p(r,0) is the pressure value at (r,0), p(R1,θ) is the pressure value at (R1,θ), and p(R2,θ) is the pressure value at (R2,θ). Let be the rate of change of pressure with respect to θ at (r,0). Let R1 be the outer diameter of the inner ring of the distribution plate sealing band, R2 be the inner diameter of the inner ring of the distribution plate sealing band, and p be the rate of change of pressure with respect to θ at (r, 2π). s p is the oil pressure in the central oil chamber. c Let θ be the oil pressure in the casing, θ be the angle subtended by any point in polar coordinates, and r be the polar coordinate radius of any point.

[0085] A micro-element model of the oil film fluid in the distribution sub-distribution is established, and a spherical coordinate system is set up with the origin located at the center of the distribution disk. The positive direction of the Z-axis points from the origin to the main axis, with clockwise as the positive direction. The polar axis points to the center of the waist-shaped groove. Force balance analysis is performed in the coordinate system, and the motion equation of the oil film fluid in the spherical distribution sub-distribution is obtained as follows:

[0086]

[0087] Where p is the oil pressure, ρ is the oil density, τ is the tangential stress of the oil film, and θ is the angle subtended by any point on polar coordinates. Let R1 be the azimuth angle of any point on polar coordinates, and v be the outer diameter of the inner ring of the distribution plate sealing band. ω This refers to the circumferential velocity.

[0088] Figure 4 The output characteristic diagram of the oil film lubrication model obtained in this embodiment includes overturning angle, friction power, and leakage power, specifically:

[0089] Overturning angle:

[0090]

[0091] Where, α c For the overturning angle, h max h is the maximum oil film clearance height. min R3 is the minimum oil film gap height, and R3 is the outer diameter of the outer ring of the sealing band.

[0092] The frictional power generated by the oil film due to frictional resistance:

[0093]

[0094] Where E1 is the friction power, μ is the dynamic viscosity of the oil, τ is the tangential stress of the oil film, and φ is the dynamic viscosity of the oil. c ω is the contact factor, r is the angular velocity of the cylinder block, h is the polar coordinate radius of the point, R1 is the outer diameter of the inner ring of the distributor plate sealing strip, and R2 is the inner diameter of the inner ring of the distributor plate sealing strip.

[0095] Oil film gap leakage:

[0096]

[0097] Among them, Q L Where h is the leakage rate between the oil film gaps and h is the oil film thickness. R1 is the outer diameter of the inner ring of the distribution plate sealing band, R2 is the inner diameter of the inner ring of the distribution plate sealing band, and v is the oil film thickness variation rate. r Radial velocity;

[0098] The oil leakage power is: E2 = Q L Δp

[0099] Where E2 is the oil leakage power, Δp is the working pressure difference, and Q L This refers to the leakage rate in the oil film gap.

[0100] Furthermore, the oil film support force and torque are solved based on the obtained oil film pressure field. In this embodiment, the cylinder block is mainly subjected to two forces: one is the support force and torque of the distribution auxiliary oil film on the cylinder block, and the other is the clamping force and torque caused by the plunger-slipper assembly and the central spring.

[0101] clamping force

[0102] Where, m p plunger mass, m s Ski boot quality, R c β is the pitch circle radius of the plunger bore, and β is the swashplate tilt angle. Let be the azimuth angle of any point on the surface of the distribution plate in polar coordinates.

[0103] The cylinder block support force consists of oil film pressure, and the oil film support force can be obtained from the oil film pressure field:

[0104] In the formula: R1 is the outer diameter of the inner ring of the distribution plate sealing strip, and R2 is the inner diameter of the inner ring of the distribution plate sealing strip;

[0105] The force and torque balance equations acting on the cylinder block are represented by matrix E as follows:

[0106]

[0107] in

[0108]

[0109]

[0110]

[0111]

[0112] In the formula F o To distribute the auxiliary oil film's support force on the cylinder block, T ocx T is the torque acting on the X-axis. ocy F is the torque acting on the Y-axis. sp F is the force exerted by the central spring on the cylinder. Ny T represents the y-axis component of the swashplate's support force on the plunger slipper assembly. px T py T represents the components of the hydraulic pressure torque in the x and y directions. cx T cy Let T be the components of the viscous friction torque in the x and y directions. nx Z represents the supporting torque of the swashplate on the plunger slipper assembly. s F is the lever arm of the supporting torque on the plunger.c For viscous friction, z c F is the lever arm of the centrifugal torque acting on the plunger. p R is the oil pressure in the plunger chamber. c The radius of the plunger bore pitch circle is 1. Let N be the azimuth angle of any point on the surface of the distribution plate in polar coordinates. p N represents the number of plungers; in this embodiment, N is taken as the number of plungers. p =7.

[0113] Using the aforementioned energy equations for cylinder coupling and the forces and torques acting on the cylinder, the cylinder dynamics equations can be obtained: In the formula M c For cylinder block mass, C c K c q represents the damping coefficient and stiffness coefficient. c This refers to the cylinder block vibration displacement. The cylinder vibration speed, F is the acceleration due to cylinder vibration. c This refers to the excitation force experienced by the cylinder block.

[0114] Based on the obtained cylinder dynamics model, the vibration response and oil film lubrication characteristics at the next moment are calculated.

[0115] Table 1 provides a comparison of the plunger pump dynamics model, the oil film lubrication model, and the method of this invention.

[0116] Table 1

[0117] Modeling methods Plast response Lubrication characteristics Plunger pump dynamics model It can be solved Unable to solve Oil film lubrication model Unable to solve It can be solved Method of the present invention It can be solved It can be solved

[0118] As shown in Table 1, compared to the plunger pump dynamics model and the oil film lubrication model, the method of this invention can simultaneously solve for the plunger pump mass response and lubrication characteristics. This invention uses multi-mass dynamics to determine the dynamic behavior of the masses constituting the key friction pairs, substitutes this dynamic behavior into the oil film lubrication model, and thus solves for the forces and torques acting on the masses. A combined prediction and verification algorithm is then used to solve for both the mass dynamics and the oil film lubrication characteristics.

Claims

1. A coupled modeling method for multibody dynamics and oil film lubrication behavior of a plunger pump, characterized in that, Includes the following steps: 1) Use a prediction and verification algorithm to predict and verify the initial dynamic behavior of the mass in order to solve the vibration response of the mass; 2) Based on the vibration response of the mass, solve for the oil film thickness field of the friction pair and establish the coupling relationship energy equation of the mass; 3) Based on the obtained oil film thickness field and combined with the oil film boundary conditions, solve the oil film pressure field through the oil film fluid motion equation and output the oil film lubrication characteristics; 4) Based on the obtained oil film pressure field, solve for the oil film supporting force system and torque, and then obtain the force and torque acting on the mass; 5) Combining the obtained forces, torques, and coupling relationship energy equations acting on the mass, establish a mass dynamics model to solve for the vibration response and oil film lubrication characteristics at the next moment; In step 2), the coupling relationship energy equation is: Where T is the kinetic energy generated by the vibration of the mass, U is the potential energy generated by the vibration of the mass, D is the dissipated energy generated by the vibration of the mass, and M is the mass of the mass. The displacement is caused by the vibration of particles on the mass. The vibrational velocity of a particle on the mass. This is a correction factor for potential energy and dissipated energy; Step 3) The oil film lubrication characteristics include tilting angle, oil leakage power, and friction power; Overturning angle: in, For the overturning angle, The maximum oil film gap height, R3 is the minimum oil film gap height, and R3 is the outer diameter of the outer ring of the mass seal band. The frictional power generated by the oil film due to frictional resistance: Where E1 is the friction power, μ is the dynamic viscosity of the oil. The cylinder angular velocity, The tangential stress of the oil film. Let R be the contact factor, r be the polar radius of the point, and θ1 and θ2 be the angles subtended by any two points in polar coordinates. i R j These are the outer and inner diameters of the parallel gap, respectively. Oil film gap leakage: Among them, Q L Where h is the leakage rate between the oil film gaps and h is the oil film thickness. R1 is the outer diameter of the inner ring of the mass seal band, and R2 is the inner diameter of the inner ring of the mass seal band. Radial velocity; The oil leakage power is: in, For oil leakage power, The difference in working pressure. This represents the leakage rate in the oil film gap.

2. The coupled modeling method for multibody dynamics and oil film lubrication behavior of a plunger pump as described in claim 1, characterized in that: Step 3) The oil film boundary conditions are as follows: in, In order to be in The pressure value at that location, In order to be in The pressure value at that location, In order to be in The pressure value at that location, In order to be in The pressure value at that location, In order to be in The rate of change of pressure with respect to θ In order to be in The rate of change of pressure with respect to θ, where R1 is the outer diameter of the inner ring of the mass sealing strip, and R2 is the inner diameter of the inner ring of the mass sealing strip. For the oil pressure in the central oil chamber, Let θ be the oil pressure in the casing, θ be the angle subtended by any point in polar coordinates, and r be the polar coordinate radius of any point.

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