Dynamic lubrication characteristic analysis method for sliding shoe pair of aviation fuel plunger pump

Abstract

The invention discloses a dynamic lubrication characteristic analysis method for a sliding shoe pair of an aviation fuel plunger pump. The method comprises the following steps: 1, constructing a piston shoe pair kinematics and dynamics model; 2, establishing a piston shoe pair oil film pressure negative feedback regulation model, and constructing a piston shoe pair lubrication model according to the piston shoe pair kinematics and dynamics model established in the step 1; 3, solving the kinematics and dynamics model, established in the step 1, of the sliding shoe pair and the lubrication model, established in the step 2, of the sliding shoe pair; 4, based on the sliding shoe pair oil film lubrication model established in the above step and a solving method, conducting model simulation on the sliding shoe pair oil film lubrication characteristics under different plunger pump working conditions, analyzing the influences of working condition parameters of the rotating speed and the outlet pressure on the sliding shoe pair oil film thickness, the pressure distribution oil film and other lubrication characteristics, friction loss and leakage flow, and calculating the sliding shoe pair oil film lubrication characteristics. And obtaining the dynamic lubrication characteristics of the piston shoe pair of the aviation fuel plunger pump. The method has the characteristics of high prediction accuracy and high stability.

Description

TECHNICAL FIELD

[0001] The present application relates to the technical field of aviation fuel plunger pump, and particularly relates to a method for analyzing dynamic lubrication characteristics of a sliding shoe pair of an aviation fuel plunger pump. BACKGROUND

[0002] An aviation fuel pump is the core of an aero-engine, ensures that fuel with a certain flow rate and pressure reaches the combustion chamber smoothly, and provides the engine with work, which is a key element for ensuring that the aero-engine works stably and reliably under any environmental conditions and any working state. A plunger pump has the advantages of high volumetric efficiency, large and adjustable oil supply, good economy, and high working pressure, and is widely used in the aviation field. The friction pair of the plunger pump has the functions of lubrication and sealing, and is an important structure for determining the working performance and service life of the plunger pump. Due to the trend of continuous development of the aviation fuel plunger pump towards high pressure and high speed and the urgent demand of the country for high-performance plunger pumps, the lubrication characteristics of the sliding shoe pair, as one of the three friction pairs of the plunger pump, are key factors for determining the service life, working performance and reliability of the plunger pump.

[0003] At present, the analysis of the dynamic lubrication characteristics of the sliding shoe pair of the domestic aviation fuel plunger pump still has problems such as unreasonable setting of boundary conditions in the model establishment process, large difference from the actual situation, and over-simplified theoretical model leading to inability to accurately reflect the complex dynamic lubrication under real working conditions. The work done by Han Hao in “Dynamic Characteristics of Sliding Shoe Pair of Swash Plate Type Axial Plunger Pump” (document number: 10.27721 / d.cnki.gyzjc.2021.000554) ignores the contact force that may exist in the working of the sliding shoe pair, and the difference between the calculated value and the real value is large due to the use of node pressure to represent the real pressure when calculating the pressure field, so the research on the dynamic lubrication characteristics of the sliding shoe pair is of great significance for improving the performance and service life of the plunger pump. SUMMARY

[0004] In order to overcome the above technical problems, the purpose of the present application is to provide a method for analyzing the dynamic lubrication characteristics of the sliding shoe pair of an aviation fuel plunger pump, a lubrication model of the sliding shoe pair is constructed, the Reynolds equation is discretized by the finite difference method, and the lubrication model of the sliding shoe pair is solved by combining the Newton iteration method, and the lubrication characteristics of the sliding shoe pair of the plunger pump under different working conditions are simulated by MATLAB. This method is closely related to the actual situation, has the characteristics of high prediction accuracy and strong stability, and can truly reflect the real situation of the oil film lubrication of the sliding shoe pair during the working process of the plunger pump.

[0005] The technical scheme adopted by the present application is as follows: A method for analyzing the dynamic lubrication characteristics of the sliding shoe pair of an aviation fuel plunger pump, comprising the following steps: Step 1: Constructing a kinematics and dynamics model of the sliding shoe pair; Step 2: Establish a negative feedback adjustment model for the oil film pressure of the slipper pair, and construct a lubrication model for the slipper pair based on the kinematic and dynamic model of the slipper pair established in Step 1; Step 3: Solve the kinematic and dynamic model of the skid pair established in Step 1 and the lubrication model of the skid pair established in Step 2; Step 4: Based on the slipper pair oil film lubrication model and solution method established in the above steps, a simulation model of the slipper pair oil film lubrication characteristics under different plunger pump operating conditions is used to analyze the influence of operating parameters such as speed and outlet pressure on lubrication characteristics such as slipper pair oil film thickness, pressure distribution oil film, friction loss, and leakage flow.

[0006] The first step is as follows: 11) Establish a kinematic model of the ski boot Set the angular velocity of the skate's spin to be equal to the angular velocity of the skate's circular motion along the swashplate; set the above dead points. Let be the starting point of the motion of a set of plungers and slippers, and let the circular trajectory plane be the plunger distribution circle plane with radius . The swashplate inclination angle is When the plunger is Point rotation Arrive at any point At that time, the skates moved from the top dead center. Exercise The rotation angle is ; The skate shoe generates axial displacement during the motion, which can be obtained from geometric relationships: (1) The contact length between the plunger and the cylinder block is: (2) In the formula, This is the contact length between the plunger and the cylinder block when the plunger is at top dead center; The radius of the plunger distribution circle; Swashplate tilt angle; This is the angle of rotation of the plunger relative to the top dead center; plunger relative The axial velocity of the point is the first derivative of the axial displacement of the slipper with respect to time: (3) In the formula, The angular velocity of the cylinder block rotation; plunger relative The axial acceleration of the point is: (4) There is an angle between the swashplate and the piston distribution plane. The trajectory of the skate on the swashplate is an elliptical trajectory, and the parametric equation of the trajectory is: (5) The radius vector of motion of the center of the bottom surface of the skate is: (6) The rotation angle of the sliding shoe in the circumferential motion on the swash plate surface is: (7) The angular velocity of the sliding shoe in the circumferential motion on the swash plate surface is: (8) The velocity of the bottom center of the sliding shoe in the circumferential motion on the swash plate surface is: (9) In the formula, is the angle between the radius of any point on the sliding shoe bottom and the movement vector of the center; When the sliding shoe has self-rotation, the circumferential motion of the sliding shoe along the swash plate is not only the translation motion of a rigid body, but also the combined motion of translation and rotation, and the velocity of a point on the sealing belt of the sliding shoe bottom is: (10) The radial velocity and circumferential velocity of the point are respectively: (11) (12) The angle between the radial velocity and the resultant velocity is : (13) 12) Establish the dynamics model of the sliding shoe All the forces acting on the sliding shoe are divided into external forces, fluid forces and contact forces for modeling.

[0007] The specific steps are as follows: 121) External force Establish the local coordinate system of the sliding shoe The specific analysis of the force acting on the sliding shoe is as follows: Hydraulic pressure in the plunger cavity: (14) In the formula, is the fuel hydraulic pressure in the plunger cavity; is the diameter of the damping hole; is the diameter of the plunger; Inertial force of the axial motion of the plunger and the sliding shoe: (15) In the formula, is the mass of a single sliding shoe; is the mass of a single plunger; Center spring pressure: (16) In the formula, is the center spring stiffness; is the number of plungers; is the pre-compression amount of the center spring; Where the sliding shoe has rotation around the shaft, generating centrifugal force, the sliding shoe centrifugal force acts on the center of mass of the sliding shoe, and its size is: (17) wherein, By geometric relationship: (18) wherein, is the length from the bottom of the shoe to the center of the shoe ball; is the length from the center of gravity of the shoe to the center of the shoe ball; The centrifugal force will generate overturning moment around the local coordinate system of the shoe axis: (19) The total compressive force on the shoe is: (20) 122) Fluid force The fluid force analysis includes the support force, moment and viscous friction of the shoe by the lubricating oil film of the shoe pair; after the oil film pressure field of the shoe pair is solved, the support force and moment of the shoe pair on the shoe by the oil film are obtained by integrating the oil film pressure field, and the viscous friction and leakage of the oil film are obtained by further analyzing the oil film velocity and integrating.

[0008] Further, the following is a specific analysis: The oil film support force includes the support force of the sealing band oil film on the shoe and the support force of the central oil chamber oil, which is directly integrated from the pressure field: (21) wherein, is the inner diameter of the sealing band of the shoe; is the integral region, the sealing band region; p is the sealing band oil film pressure distribution of the shoe pair. Since the oil film pressure field is unevenly distributed, it will generate a moment on the shoe, and the oil film moment is also obtained by integration: (22) (23) Under the condition that the oil film pressure field of the shoe pair is known, based on the assumption that aviation fuel is a Newtonian fluid, the velocity distribution of the oil film is obtained, which is the result of the joint action of the velocity of the shoe pair and the pressure difference, and the variation law of the radial velocity and the circumferential velocity of the oil flowing at any point on the bottom surface of the shoe along the thickness is: (24) (25) wherein, is the maximum value of the oil film thickness at the point of the shoe oil film; , is the radial and circumferential velocity of the shoe at the point ; is the maximum value of the oil film thickness at the point Any point thickness value of the swash plate surface as the reference point; For fuel viscosity; For the oil film of the shoe pair The pressure value at the point; Integrate the radial velocity at any radius along the circumference and thickness to get the oil film leakage flow: (26) When the shoe moves on the swash plate surface, an oil film will be formed between the shoe and the swash plate. Since fuel is a viscous fluid, the shoe will be subjected to viscous friction from the oil film. According to Newton's internal friction law, the circumferential and radial shear stresses of the shoe oil film are respectively (27) (28) The viscous friction torque of the oil film on the shoe is obtained by integration: (29) The friction loss power of the oil film on the shoe is obtained by further calculation: (30) The viscous friction torque and the centrifugal torque combine to form the overturning torque, which is the reason for the overturning phenomenon of the shoe during movement and the formation of the wedge-shaped oil film; 123)Contact force When the oil film thickness at a certain point is less than the minimum value determined by the surface roughness of the shoe and the swash plate, the shoe and the swash plate come into contact and elastic deformation occurs, resulting in a contact force. The elastic deformation is represented by the following formula: (31) In the formula, h The thickness of the oil film of the shoe pair sealing belt; The sum of the roughness of the swash plate and the shoe; The stress along the normal direction of the contact point is: (32) In the formula, E The Young's modulus of the shoe, When the shoe and the swash plate come into direct contact, the force and torque received by the shoe are respectively: (33) (34) (35) In the formula, The stress of the shoe sealing belt at any point in polar coordinates; x And y The distance from the shoe sealing belt at any point to the y axis and x axis, i.e. the force arm; The second step is specifically: 21) The shoe pair oil film thickness equation The control equation describing the attitude of the sliding shoe and the thickness field of the oil film is obtained by using the method of three points determining a plane, which is expressed in polar coordinates as: (36) wherein, , , respectively represent the oil film thicknesses of three points separated by 120° on the outer circle of the sealing band of the sliding shoe pair; The rate of change of the thickness of an arbitrary point on the bottom surface of the sliding shoe is: wherein, , , respectively represent the rates of change of the oil film thicknesses of three points separated by 120° on the outer circle of the sealing band of the sliding shoe pair; 22) Reynolds equation of the sliding shoe pair Since the sealing band on the bottom surface of the sliding shoe is annular, the Reynolds equation is converted into the expression in polar coordinates as: (37) wherein, , respectively represent the radial velocity and the circumferential velocity of the oil film of the sliding shoe pair; The pressure boundary condition of the oil film of the sliding shoe pair is: (38) wherein, is the oil chamber pressure at the center of the sliding shoe; is the pressure of the pump housing; 23) Dynamic force balance equation of the sliding shoe pair According to the principle of force balance, the extrusion movement of the sliding shoe along z s is controlled by the normal support force of the oil film and the axial compression force borne by the sliding shoe; the deflection movement of the sliding shoe around x s , y s is respectively controlled by the overturning moment; the forces in the three directions are balanced respectively, and thus the coupling relationship between the force borne by the sliding shoe and the oil film of the sliding shoe pair is: (39) wherein, h is the thickness field of the oil film of the sealing band of the sliding shoe pair; is the rate of change of the thickness of the oil film of the sealing band of the sliding shoe pair; is the running time of the pump.

[0009] The step three is specifically: 31) Discretization of the Reynolds equation of the sliding shoe pair The control equation for the oil film pressure of the slipper pair is a partial differential equation, which is solved using a numerical method. First, the Reynolds equation is discretized using the finite difference method, and the partial differential equation is transformed into a system of linear equations. Solving the system of equations yields the pressure distribution in the solution domain. Following the approach of the finite difference method, we use a difference scheme to replace the differential operator. First, we discretize the Reynolds equation and simplify it to obtain: (40) in, Indicates node pressure; subscript i , j These represent the circumferential and radial node numbers after the discretization of the sealing strip, respectively.

[0010] Formula (40) reflects the linear relationship between the nodes of the sealing strip on the bottom surface of the slipper after the transformation by discretization and finite difference method. The meanings of each parameter are as follows: (41) 32) Numerical solution process for the oil film pressure field of the slipper pair The discrete equation system is solved using the over-relaxation iterative method, and the relaxation factor is selected. For values ​​of 1 to 2, the iterative scheme for the pressure field is: (42) Set convergence conditions based on the relative convergence criterion: (43) Select for ; After obtaining the pressure distribution through an iterative algorithm, the average pressure of the four nodes of the unit is taken as the unit pressure using the idea of ​​interpolation. 33) Dynamic solution method for slipper pair oil film The solution is obtained using Newton's iteration method, which has the following format: (44) Among them: (45) Among them, This indicates the rate of change of the oil film at three points.

[0011] Given an initial time and the initial thickness of the slipper pair oil film The unknown quantity can then be calculated. ,go through The oil film thickness at the next moment can be calculated by iterating continuously, and the oil film thickness field at all moments can be obtained. Using the difference scheme: (46) of which ; .

[0012] Step four specifically involves: 41) Influence of operating parameters on the lubrication characteristics of the slipper pair oil film Based on the established slipper pair oil film lubrication model and solution method, while keeping other parameters constant, the working condition parameters to be studied are changed, and simulations are performed according to steps one to three. The influence of the working condition parameters on the slipper pair oil film lubrication characteristics is compared and analyzed. For example, while keeping other parameters constant, the rotational speed is changed, and the slipper pair oil film lubrication characteristics at 1000 r / min, 2000 r / min, and 3000 r / min are simulated. By comparing the simulation results, the influence of rotational speed on the slipper pair oil film lubrication characteristics can be obtained.

[0013] The beneficial effects of this invention are: This invention first performs kinematic and dynamic modeling of the plunger pump slipper assembly, realizing the kinematic and dynamic analysis of the slipper pair during plunger pump operation, and providing kinematic and dynamic input information for its lubrication characteristic flow field modeling and analysis. Next, based on the slipper pair's damping characteristics, a pressure-flow negative feedback regulation model is established; the slipper pair oil film control equation is derived, and an oil film thickness model is established. The oil film control equation is discretized and solved using the finite difference method and the over-relaxation iteration method, obtaining the slipper pair oil film pressure distribution under a certain thickness. Subsequently, based on the kinematic and dynamic models and the lubrication model, a dynamic coupling equation between the slipper force and the slipper pair oil film is established, and the dynamic equilibrium equation is numerically solved using the Newton-Raphson iteration method, realizing the prediction of the slipper pair lubricating oil film thickness and pressure distribution within one operating cycle. Finally, using the controlled variable method, the correspondence between different operating conditions and oil film states was established. Reasonable inferences were made regarding the causes of abnormal wear in the slipper and swashplate from the perspective of slipper pair oil film lubrication. This provides theoretical guidance for a deeper understanding of the slipper pair oil film lubrication characteristics, improving slipper and swashplate structures, and enhancing related performance. It also provides guidance for the design and performance optimization of aviation fuel plunger pumps. Attached Figure Description

[0014] Figure 1 This is a kinematic analysis diagram of the plunger and slipper.

[0015] Figure 2 This is a graph analyzing the velocity of various points on the skate.

[0016] Figure 3 This is a diagram of the dynamics analysis of the skis.

[0017] Figure 4 This is a schematic diagram of the oil film thickness field determined by the method of defining a plane using three points.

[0018] Figure 5 This is a schematic diagram showing the division of the oil film area on the slipper.

[0019] Figure 6 This is a schematic diagram illustrating the interpolation method for calculating unit pressure.

[0020] Figure 7 This is a flowchart of the solution process for the lubrication model of the slipper pair.

[0021] Figure 8 This is a curve showing the thickness variation of the oil film at three points on the slipper pair within a cycle.

[0022] Figure 9 This is a full-cycle variation diagram of the oil film thickness field of the slipper pair.

[0023] Figure 10 It is a graph showing the change in the tilt angle of the skis.

[0024] Figure 11 This is a diagram showing the full-cycle variation of the oil film pressure distribution in the slipper pair.

[0025] Figure 12 This is a graph showing the change in leakage flow rate of an individual slipper pair's oil film.

[0026] Figure 13 This is a graph showing the change in frictional torque of a single slipper.

[0027] Figure 14 This is a graph showing the change in power loss due to friction of a single slipper. Detailed Implementation

[0028] The technical solutions of the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only some embodiments of the present invention, and not all embodiments. Based on the embodiments of the present invention, all other embodiments obtained by those skilled in the art without creative effort are within the scope of protection of the present invention.

[0029] like Figures 1-14 As shown, a method for analyzing the dynamic lubrication characteristics of an aviation fuel plunger pump slipper pair includes the following steps; Step 1: Constructing the kinematic and dynamic model of the ski boot pair The first step is as follows: 11) Establish a kinematic model of the ski boot When a swashplate axial piston pump is working, the slipper, as a key component connecting the piston and the swashplate, must not only follow the piston in reciprocating linear motion relative to the cylinder block, but also move circumferentially along the swashplate surface, and simultaneously rotate. To simplify calculations, the angular velocity of the slipper's rotation is set to be equal to the angular velocity of the slipper's circular motion along the swashplate. For example... Figure 1 The diagram shown is a simplified representation of the motion of the plunger and slipper during the operation of a plunger pump, with the above dead points set. Let be the starting point of the motion of a set of plungers and slippers, and let the circular trajectory plane be the plunger distribution circle plane with radius . The swashplate inclination angle is When the plunger is Point rotation Arrive at any point At that time, the skates moved from the top dead center. Exercise The rotation angle is ; The skate shoe generates axial displacement during the motion, which can be obtained from geometric relationships: (1) The contact length between the plunger and the cylinder block is: (2) This is the contact length between the plunger and the cylinder block when the plunger is at top dead center.

[0030] plunger relative The axial velocity of the point is: (3) In the formula, ω is the angular velocity of the cylinder.

[0031] plunger relative The axial acceleration of the point is: (4) Because there is an angle between the swashplate and the piston distribution plane. Therefore, the trajectory of the skate on the swashplate is an elliptical trajectory, and the parametric equation of the trajectory is: (5) The radius vector of motion of the center of the bottom surface of the skate is: (6) The rotation angle of the shoe as it moves circumferentially on the swashplate surface is: (7) The angular velocity of the skate as it moves circumferentially on the swashplate surface is: (8) Then, the velocity of the center of the base of the skate when it makes circumferential motion on the inclined plane is: (9) In the formula, Let be the angle between the radius of any point on the bottom of the skate and the radius vector of the center of the circle.

[0032] When the skate rotates, its circular motion along the swashplate is not only a translational motion of a rigid body, but a combination of translation and rotation. Therefore, the velocity vectors at different points on the skate's bottom surface are not equal, their directions are not equal, and their magnitudes are related to the distance from that point to the center of the skate's bottom surface. Figure 2 The speed of the sealing strip on the bottom of the skate can be obtained as follows: (11) (12) The angle between the radial velocity and the resultant velocity for: (13) 12) Establish a dynamic model of the ski boot The forces acting on the skate are modeled as external forces, fluid forces, and contact forces. The specific steps are as follows: 121) External force The external force analysis of the slipper is mainly based on the kinematic analysis of the slipper. The external forces acting on the slipper include the clamping force in the axial direction, the centrifugal force generated by the slipper rotating on the swashplate, and the viscous friction force of the oil film on the bottom surface. The clamping force includes the oil pressure in the piston chamber, the pressure of the central spring, the inertial force of the piston reciprocating linear motion relative to the cylinder block, and the frictional force. Figure 3 Establish the local coordinate system of the ski boot The specific analysis of the forces acting on the skate is as follows.

[0033] plunger chamber hydraulic pressure: (14) In the formula, The fuel pressure inside the plunger chamber; The diameter of the damping orifice; The diameter is the plunger diameter.

[0034] Axial inertial forces of the plunger and slipper: (15) In the formula, For the mass of a single skate shoe; For the mass of a single plunger.

[0035] Center spring pressure: (16) In the formula, For the central spring stiffness; Number of plungers; The pre-compression of the central spring.

[0036] The skate has a motion around its axis, generating centrifugal force. This centrifugal force acts at the skate's center of mass, and its magnitude is: (17) In the formula, Obtained through geometric relationships: (18) In the formula, The length from the bottom of the skate shoe to the center of the skate ball's socket; The length from the center of gravity of the skate to the center of the ball in the skate's nest; Centrifugal force will generate a local coordinate system around the slipper. Overturning moment of the shaft: (19) The slipper is also subject to frictional resistance generated by the piston's movement relative to the cylinder. Because this force is too small, it is usually not calculated in detail, but only considered in force analysis. Therefore, the resultant clamping force on the slipper is: (20) 122) Fluid Force Fluid dynamics analysis mainly includes the supporting force, torque, and viscous friction of the lubricating oil film on the slipper. After solving for the oil film pressure field of the slipper pair, the supporting force and torque of the oil film on the slipper pair are obtained by integrating the oil film pressure field. By further analyzing the oil film velocity of the slipper pair and integrating it, the viscous friction and leakage of the oil film can be obtained. The specific analysis is as follows.

[0037] The oil film support force includes the support force of the sealing strip oil film on the slipper and the support force of the oil in the central oil chamber, which can be obtained by directly integrating over the pressure field: (twenty one) In the formula, The inner diameter of the slipper sealing strip; This is the integration region, the sealed area.

[0038] Because the oil film pressure field is not uniformly distributed, it will generate a torque on the slipper. The oil film torque can also be obtained by integration: (twenty two) (twenty three) Given the known pressure field of the oil film in the skid pair, and based on the assumption that aviation fuel is a Newtonian fluid, the velocity distribution of the oil film, the combined effect of the skid pair's oil film velocity, the skid's velocity, and the pressure difference, can be obtained. This allows us to determine the oil level at any point on the skid's bottom surface. The radial and circumferential velocities of the flow along the thickness are as follows: (twenty four) (25) In the formula, For slipper oil film points Maximum oil film thickness at the location; , Add a touch to the skates Radial and circumferential velocities; For slipper oil film points The thickness value at any point with the swashplate surface as the reference point; Fuel viscosity; For the ski boot side oil film Pressure value at the point.

[0039] Integrating the radial velocity at any radius along the circumference and thickness yields the oil film leakage flow rate: (26) When the skate moves on the swashplate surface, an oil film forms between the skate and the swashplate. Since fuel is a viscous fluid, the skate experiences viscous friction from the oil film. According to Newton's law of internal friction, the circumferential and radial shear stresses of the skate's oil film are respectively... (27) (28) The viscous frictional torque of the oil film on the slipper is obtained by integration: (29) Further calculations yielded the following frictional power loss of the oil film on the slipper: (30) The combined overturning torque, resulting from the viscous friction torque and centrifugal torque, is the reason why the skis overturn and form a wedge-shaped oil film during movement.

[0040] 123) Contact force During motion, the skate shoe tilts due to the overturning moment, forming an angle with the swashplate and simultaneously creating a wedge-shaped oil film. If the tilt angle is too large, and the oil film thickness is too small at a certain point, the oil film will not remain intact and will break, causing the skate shoe to directly contact the swashplate. The force generated in this contact area is the contact force. To simplify the calculation, we define a minimum oil film thickness determined by the surface roughness of the skate shoe and swashplate as the point where the skate shoe contacts the swashplate and undergoes elastic deformation, generating a contact force. The elastic deformation is expressed by the following formula: (31) Then the stress along the normal direction at the contact point is: (32) Therefore, when direct contact occurs between the skate and the ramp, the forces and torques acting on the skate are as follows: (33) (34) (35) Step 2: Constructing a lubrication model for the slipper pair 21) Equation for oil film thickness of slipper pair By using the method of defining a plane by three points, the governing equations describing the skid attitude and oil film thickness field are obtained, which can be expressed in polar coordinates as follows: (36) The rate of change of thickness at any point on the sole of the skate is:

[0041] 22) Reynolds equation for the slipper pair Since the sealing strip on the bottom of the slipper is annular, the Reynolds equation can be converted to a polar coordinate form as follows: (37) In the formula, , These are the radial and circumferential velocities of the oil film on the slipper pair, respectively. The boundary condition for the slipper pair oil film pressure is: (38) 23) Dynamic force balance equations for the slipper pair According to the principle of force balance, the slipper edge z s The squeezing motion is controlled by the normal support force of the oil film and the axial clamping force on the slipper; the slipper rotates around... x s , y s The deflection motion is controlled by the overturning moment. The forces in these three directions are in equilibrium, thus the coupling relationship between the forces on the skid and the skid's auxiliary oil film can be obtained as follows: (39) Step 3: Solve the lubrication model of the slipper pair 31) Discretized shoe pair Reynolds equations The control equation for the oil film pressure of the slipper pair is a partial differential equation, which cannot be solved directly to obtain an analytical solution. Therefore, a numerical method is used to solve it. First, the Reynolds equation is discretized using the finite difference method, which transforms the partial differential equation into a system of linear equations. Solving the system of equations will yield the pressure distribution in the solution domain.

[0042] Following the approach of the finite difference method, we use a difference scheme to replace the differential operator. First, we discretize the Reynolds equation and simplify it to obtain: (40) This formula reflects the linear relationship between the nodes of the sealing strip on the bottom surface of the slipper pair after the transformation by discretization and finite difference method. The meanings of each parameter are as follows: (41) 32) Numerical solution process for the oil film pressure field of the slipper pair The discrete equation system is solved using the over-relaxation iterative method, and the relaxation factor is selected. For values ​​of 1 to 2, the iterative scheme for the pressure field is: (42) To ensure the accuracy of the iteration results, convergence conditions need to be set, which are given here based on the relative convergence criterion: (43) Select for .

[0043] After obtaining the pressure distribution through an iterative algorithm, since the calculated pressure is the pressure at each element node, the calculation of oil film support force and moment will be problematic. If the pressure at the inner node is used to represent the element pressure, the calculated oil film support force and moment will be too large; if the pressure at the outer node is used, the calculated result will be too small. Therefore, an interpolation approach is adopted, taking the average pressure of the four nodes of the element as the element pressure to reduce the error.

[0044] 33) Dynamic solution method for slipper pair oil film The solution is obtained using Newton's iteration method, which has the following format: (44) in: (45) Given an initial time and the initial thickness of the slipper pair oil film The unknown quantity can then be calculated. ,go through The oil film thickness at the next moment can be calculated by iterating continuously, and the oil film thickness field at all moments can be obtained.

[0045] Because the Jacobi matrix contains fluid forces, an analytical solution cannot be obtained directly. It is also impossible to express this in detail, as the Jacobi matrix cannot be obtained. Therefore, the difference scheme is used to solve this problem.

[0046] (46) of which ; .

[0047] Step 4: Based on the slipper pair oil film lubrication model and solution method established in the above steps, a simulation model of the slipper pair oil film lubrication characteristics under different plunger pump operating conditions is used to analyze the influence of operating parameters such as speed and outlet pressure on the slipper pair oil film thickness, pressure distribution oil film and other lubrication characteristics, friction loss and leakage flow.

[0048] Figure 4 middle Indicates any point on the bottom of the skate shoe and The included angle of the axis, where A, B, and C are three points 120° apart on the outer diameter of the shoe's bottom surface. Figure 5 and Figure 6 middle Indicates the pressure at discrete grid nodes, subscript i , j Indicates the circumferential and radial numbering of the nodes.

[0049] Part 5: Examples The advantages of this invention can be further illustrated by the following simulation experiments: 1) Simulation parameters During the operation of a plunger pump, the equilibrium position of the slipper varies depending on the position of the cylinder block. Because the position of the cylinder block changes continuously during one rotation, the motion state of the slipper changes continuously, and the forces acting on the slipper also change continuously. This results in the slipper's posture at equilibrium, as well as the pressure field and thickness field of the slipper pair, being constantly changing, i.e., the oil film thickness at three points on the slipper's bottom surface. The pump is constantly changing. Therefore, this invention will provide relevant pump parameters and simulation results of lubrication of the corresponding slipper assembly, along with related analysis. Specific parameters are shown in Table 1: Table 1. Simulation parameters of plunger pair lubrication characteristics Parameter Name Parameter Value Plunger Distribution Circle Radius (mm) 18.6 Sliding Shoe Bottom Seal Band Inner Diameter (mm) 3.5 Sliding Shoe Bottom Seal Band Outer Diameter (mm) 6.6 Plunger Quantity (pcs) 9 Sliding Shoe Mass (g) 6.2 Plunger Mass (g) 15.2 Plunger Diameter (mm) 8.62 Damper Hole Diameter (mm) 0.5 Damper Hole Length (mm) 2.2 Center Spring Stiffness (N / mm) 50 Center Spring Pre-Compression (mm) 10 Swash Plate Inclination Angle (°) 17 Housing Pressure (bar) 0.2 Fuel viscosity (mm 2 / s) 0.0466 Radial Node Quantity 31 Circumferential Node Quantity 21 Length from Sliding Shoe Center of Gravity to Sliding Shoe Spherical Socket Center (mm) 3 Length from Sliding Shoe Bottom to Sliding Shoe Spherical Socket Center (mm) 10 The program was written using MATLAB, inputting the various parameters of the studied slipper pair into MATLAB and setting the initial three-point oil film thickness. All are 5μm, the cylinder speed is 2000r / min, and the oil pressure change curve of the plunger cavity is combined with the solution of the coupling relationship model between the force on the slipper and the slipper pair oil film. The change of the thickness of the slipper pair oil film at three points during the iteration process can be obtained. The rotation angle is set as the solution domain and the step size is 1°. The dynamic lubrication characteristics of the slipper pair oil film are solved. The calculation process converges and the motion state of the slipper is basically stable.

[0050] 2) Simulation Results 21) Analysis of simulation results of oil film thickness of slipper pair Oil film thickness after stable operation, such as Figure 8 It can be seen that the thickness changes at the three points follow the same trend. When the skate moves in a circular motion along the swashplate within one cycle, the external force acting on the skate changes, and the skate will reach a state of force equilibrium at each point, exhibiting different equilibrium postures and forming wedge-shaped oil films of different shapes. Simultaneously, based on the three-point oil film thickness in the later stable phase, combined with the principle of three-point plane determination and the skate secondary oil film thickness model, the skate secondary oil film can be obtained. The development diagram of the skate secondary oil film thickness field at every 45° interval within one cycle of rotation from the relative top dead center (0°~360°) is shown below. Figure 9 It can be seen that between 0° and 180°, due to the higher oil pressure in the plunger cavity, the slipper is squeezed and moves towards the swashplate, the overall thickness of the slipper oil film gradually decreases, and the difference between the maximum and minimum values ​​of the slipper oil film thickness gradually decreases. At this time, the stability of the slipper oil film is worse. Between 180° and 360°, due to the lower oil pressure in the plunger cavity, the slipper is subjected to a clamping force less than the oil film supporting force, and moves away from the swashplate. The overall thickness of the slipper oil film gradually increases, and the difference between the maximum and minimum values ​​of the slipper oil film thickness gradually increases. At this time, the stability of the slipper oil film is higher. Compared with the oil film thickness in the two regions, the oil film stability is worse in the 0° to 180° region. The oil film is thinner and more prone to rupture, resulting in direct friction between the slipper and the swashplate, causing wear, and reducing the service life and reliability of the plunger pump.

[0051] The angle of the ski boot is as follows Figure 10 As shown, in the high-pressure region, the angle continuously decreases from 0.0035° to about 0.0021°, and then continuously rises to about 0.0032° in the low-pressure region. The rate of change in both regions is fast at first and then slows down, with the rate of change gradually decreasing. The tilt angle of the slipper in the high-pressure region is generally greater than that in the low-pressure region, and it shows a positive correlation with the rate of change of the slipper oil film thickness.

[0052] 22) Analysis of Simulation Results of Oil Film Pressure Distribution in Slipper Corresponding to the slipper pair oil film thickness distribution, a full-cycle variation diagram of the slipper pair oil film pressure distribution can be obtained. For example... Figure 11 This is a diagram showing the pressure field of the slipper pair oil film at 45° intervals within a cycle of rotation from the relative top dead center to 360°. Between 0° and 180°, due to the higher oil pressure in the plunger cavity, the maximum pressure distribution of the slipper pair oil film is larger, and these maximum values ​​all appear within the inner ring of the sealing band. Between 180° and 360°, due to the lower oil pressure in the plunger cavity, the maximum pressure distribution of the slipper pair oil film is smaller, but the maximum value still occurs within the sealing band. Compared to the oil film pressure distribution in the two regions, the oil film pressure is greater between 0° and 180°, resulting in stronger oil film support force, which aligns with the thickness field. At this point, the thickness is smaller, and the support force is less than the clamping force. The slipper moves towards the swashplate, generating a strong dynamic pressure effect, further increasing the oil film pressure to balance the clamping force.

[0053] 23) Analysis of simulation results of oil film leakage in slipper pair After obtaining the pressure distribution of the slipper pair, the oil film leakage flow rate of a single slipper pair can be calculated, and its variation curve over one cycle is shown in the figure. Figure 12 As shown, the leakage flow rate continuously decreases between 0° and 180° in the high-pressure zone, reaching its lowest value around 180°, and then continuously increases in the low-pressure zone between 180° and 360°. The variation pattern of leakage flow rate of a single slipper pair is consistent with the variation pattern of oil film thickness, indicating that the greater the oil film thickness, the worse the sealing performance of the slipper pair; the smaller the thickness, the better the sealing performance. Relatively speaking, the dead point of around 180° is the position where the leakage flow rate of this slipper is the minimum, at which point the sealing performance reaches the optimal value of the entire cycle.

[0054] 24) Analysis of simulation results of friction loss of slipper pair Simulation analysis can yield curves showing the variation of slipper friction torque and friction loss over a single cycle, such as... Figure 13 and Figure 14 .pass Figure 13 As can be seen, the frictional torque is at its minimum at the top dead center and at its maximum at the bottom dead center, generally increasing gradually in the high-pressure region and decreasing gradually in the low-pressure region. Figure 14It can be seen that the minimum friction loss occurs at the top dead center (GDC), while the maximum value does not occur at the bottom dead center (BDC), but rather has two peaks. Between 0° and 180°, the friction loss first increases and then decreases, before slightly increasing again at the bottom dead center (left of 180°), reaching its first peak around 108°. Between 180° and 360°, the friction loss first slightly decreases at the bottom dead center (right of 180°), then continuously increases and then decreases again, reaching its second peak around 255°. The friction loss curve and the friction torque curve share similar points. However, since friction loss depends not only on the friction torque but also on the angular velocity of the skate's circumferential motion on the swashplate, although the friction torque is larger at the GDC, the angular velocity of the skate around 108° is greater than that at the GDC. This results in an anomaly between the peak values ​​of friction loss and friction torque. The peak value of friction loss around 255° is similarly observed.

[0055] The simulation results above present the thickness field, pressure field, leakage flow rate, and friction loss of the oil film in the plunger pair. It can be seen that the slipper experiences significant stress in the discharge zone, and the oil film needs to withstand substantial pressure. The load-bearing capacity of the slipper pair oil film directly affects the operational stability of the plunger pump. Therefore, the design of the slipper should be carefully considered when designing a plunger pump. All simulation results were obtained under the same operating conditions. To analyze the impact of different operating conditions on lubrication characteristics, this method can be repeated multiple times.

[0056] This invention addresses the lubrication characteristics of the slipper pair in aviation fuel plunger pumps. By combining kinematic and force analyses of components such as the plunger, slipper, and cylinder, along with a hydrodynamic lubrication model of the slipper pair, the dynamic force balance equation of the slipper is numerically solved, establishing a hydrodynamic lubrication model for the slipper pair. MATLAB simulation is then used to model the lubrication characteristics of the slipper pair oil film during plunger pump operation. The correlation between the oil film state and slipper wear and leakage flow is constructed. This method closely reflects reality, exhibiting high predictive accuracy and strong stability. It accurately reflects the actual lubrication of the slipper pair by the oil film during plunger pump operation, providing guidance for the design and performance optimization of aviation fuel plunger pumps.

Claims

1. A method for analyzing the dynamic lubrication characteristics of a sliding shoe pair in an aviation fuel plunger pump, characterized in that, Includes the following steps; Step 1: Construct the kinematic and dynamic model of the ski boot pair; Step 2: Establish a negative feedback adjustment model for the oil film pressure of the slipper pair, and construct a lubrication model for the slipper pair based on the kinematic and dynamic model of the slipper pair established in Step 1; Step 3: Solve the kinematic and dynamic model of the skid pair established in Step 1 and the lubrication model of the skid pair established in Step 2; Step 4: Based on the slipper pair oil film lubrication model and solution method established in the above steps, a simulation model is used to analyze the slipper pair oil film lubrication characteristics under different plunger pump operating conditions. The influence of operating parameters such as speed and outlet pressure on the slipper pair oil film thickness, pressure distribution oil film and other lubrication characteristics, friction loss and leakage flow is analyzed, and the dynamic lubrication characteristics of the aviation fuel plunger pump slipper pair are obtained.

2. The method for analyzing the dynamic lubrication characteristics of an aviation fuel plunger pump slipper pair according to claim 1, characterized in that, The first step is as follows: 11) Establish a kinematic model of the ski boot Set the angular velocity of the skate's spin to be equal to the angular velocity of the skate's circular motion along the swashplate; set the above dead points. Let be the starting point of the motion of a set of plungers and slippers, and let the circular trajectory plane be the plunger distribution circle plane with radius . The swashplate inclination angle is When the plunger is Point rotation Arrive at any point At that time, the skates moved from the top dead center. Exercise The rotation angle is ; The skate shoe generates axial displacement during the motion, which can be obtained from geometric relationships: (1) The contact length between the plunger and the cylinder block is: (2) In the formula, This is the contact length between the plunger and the cylinder block when the plunger is at top dead center; The radius of the plunger distribution circle; Swashplate tilt angle; This is the angle of rotation of the plunger relative to the top dead center; plunger relative The axial velocity of the point is the first derivative of the axial displacement of the slipper with respect to time: (3) In the formula, The angular velocity of the cylinder block rotation; plunger relative The axial acceleration of the point is: (4) There is an angle between the swashplate and the piston distribution plane. The trajectory of the skate on the swashplate is an elliptical trajectory, and the parametric equation of the trajectory is: (5) The radius vector of motion of the center of the bottom surface of the skate is: (6) The rotation angle of the shoe as it moves circumferentially on the swashplate surface is: (7) The angular velocity of the skate as it moves circumferentially on the swashplate surface is: (8) Then, the velocity of the center of the base of the skate when it makes circumferential motion on the inclined plane surface is: (9) In the formula, Let be the angle between the radius of any point on the bottom of the skate and the radius vector of the center of the circle; When the slipper rotates, its circular motion along the inclined plane is not only a translational motion of a rigid body, but a combination of translation and rotation. The magnitude of the velocity at a point on the sealing strip of the slipper's bottom surface is: (10) The magnitudes of the radial and circumferential velocities at this point are obtained as follows: (11) （12） The angle between the radial velocity and the resultant velocity for: (13) 12) Establish a dynamic model of the ski boot The forces acting on the skate are modeled as external forces, fluid forces, and contact forces.

3. The method for analyzing the dynamic lubrication characteristics of an aviation fuel plunger pump slipper pair according to claim 2, characterized in that, The specific steps are as follows: 121) External force Establish the local coordinate system of the skid. The specific analysis of the forces acting on the skate is as follows; plunger chamber hydraulic pressure: (14) In the formula, The fuel pressure inside the plunger chamber; The diameter of the damping orifice; The diameter of the plunger; Axial inertial forces of the plunger and slipper: (15) In the formula, For the mass of a single skate shoe; For the mass of a single plunger; Center spring pressure: (16) In the formula, For the central spring stiffness; Number of plungers; The pre-compression amount of the central spring; The skate has a motion around its axis, generating centrifugal force. This centrifugal force acts at the skate's center of mass, and its magnitude is: (17) In the formula, Obtained through geometric relationships: (18) In the formula, The length from the bottom of the skate shoe to the center of the skate ball's socket; The length from the center of gravity of the skate to the center of the skate ball's socket; Centrifugal force will generate a local coordinate system around the slipper. Overturning moment of the shaft: (19) The combined clamping force on the skate is: (20) 122) Fluid Force Fluid dynamics analysis includes the supporting force, torque, and viscous friction of the lubricating oil film on the slipper. After solving for the pressure field of the slipper oil film, the supporting force and torque of the slipper oil film on the slipper are obtained by integrating the oil film pressure field. By further analyzing the slipper oil film velocity and integrating it, the viscous friction and leakage of the oil film can be obtained. The oil film support force includes the support force of the sealing strip oil film on the slipper and the support force of the oil in the central oil chamber, which can be obtained by directly integrating over the pressure field: (twenty one) In the formula, The inner diameter of the slipper sealing strip; This is the integration region, the sealed area; p The oil film pressure distribution in the slipper pair seal is shown. Due to the uneven distribution of the oil film pressure field, a torque is generated on the slipper. This oil film torque is also obtained by integration: (twenty two) （23） Given the known pressure field of the slipper's oil film, and based on the assumption that aviation fuel is a Newtonian fluid, the velocity distribution of the oil film is obtained. The combined effect of the slipper's oil film velocity, slipper velocity, and pressure difference yields the oil velocity at any point on the slipper's bottom surface. The radial and circumferential velocities of the flow along the thickness are as follows: (twenty four) （25） In the formula, For slipper oil film points Maximum oil film thickness at the location; , Add a touch to the skates Radial and circumferential velocities; For slipper oil film points The thickness value at any point with the swashplate surface as the reference point; Fuel viscosity; For the ski boot side oil film Pressure value at the point; Integrating the radial velocity at any radius along the circumference and thickness yields the oil film leakage flow rate: (26) When the skate moves on the swashplate surface, an oil film forms between the skate and the swashplate. Since fuel is a viscous fluid, the skate experiences viscous friction from the oil film. According to Newton's law of internal friction, the circumferential and radial shear stresses of the skate's oil film are respectively... (27) （28） The viscous frictional torque of the oil film on the slipper is obtained by integration: (29) Further calculations yielded the following frictional power loss of the oil film on the slipper: (30) The combined overturning torque, resulting from the viscous friction torque and centrifugal torque, is the reason why the skis overturn and form a wedge-shaped oil film during movement. 123) Contact force When the oil film thickness at a certain point is less than the minimum value determined by the surface roughness of the shoe and the swashplate, the shoe comes into contact with the swashplate and undergoes elastic deformation, generating a contact force. The elastic deformation is expressed by the following formula: (31) In the formula, h The thickness of the oil film on the slipper pair seal; This is the sum of the roughness of the swashplate and the shoe. The stress along the normal direction at the contact point is: (32) In the formula, E For the Young's modulus of the slipper, When direct contact occurs between the skate and the swashplate, the forces and torques acting on the skate are as follows: (33) （34） （35） In the formula, Let be the stress at any point on the slipper sealing strip in polar coordinates; x and y These represent any point on the slipper sealing strip to... y shaft and x The distance between axes, i.e., the lever arm.

4. The method for analyzing the dynamic lubrication characteristics of an aviation fuel plunger pump slipper pair according to claim 1, characterized in that, Step two specifically involves: 21) Equation for oil film thickness of slipper pair By using the method of defining a plane by three points, the governing equations describing the skid attitude and oil film thickness field are obtained, which are expressed in polar coordinates as follows: (36) In the formula, , , These represent the oil film thicknesses at three points spaced 120° apart on the outer circumference of the slipper pair sealing strip; The rate of change of thickness at any point on the sole of the skate is: In the formula, , , These represent the rate of change of oil film thickness at three points 120° apart on the outer circumference of the slipper pair sealing strip; 22) Reynolds equation for the slipper pair Since the sealing strip on the bottom of the slipper is annular, the Reynolds equation can be converted to a polar coordinate form as follows: (37) In the formula, , These are the radial and circumferential velocities of the oil film on the slipper pair, respectively. The boundary condition for the slipper pair oil film pressure is: (38) In the formula, The pressure in the center oil chamber of the slipper; This refers to the pressure inside the plunger pump housing. 23) Dynamic force balance equations for the slipper pair According to the principle of force balance, the slipper edge z s The squeezing motion is controlled by the normal support force of the oil film and the axial clamping force on the slipper; the slipper rotates around... x s , y s The deflection motion is controlled by the overturning moment; the forces in these three directions are in equilibrium, thus the coupling relationship between the forces on the slipper and the slipper's auxiliary oil film is obtained as follows: (39) In the formula, h For the oil film thickness field of the slipper pair sealing band; The change rate of oil film thickness in the sealing band of the slipper pair; This refers to the running time of the plunger pump.

5. The method for analyzing the dynamic lubrication characteristics of an aviation fuel plunger pump slipper pair according to claim 1, characterized in that, Step three specifically involves: 31) Discretized shoe pair Reynolds equations The control equation for the oil film pressure of the slipper pair is a partial differential equation, which is solved using a numerical method. First, the Reynolds equation is discretized using the finite difference method, and the partial differential equation is transformed into a system of linear equations. Solving the system of equations yields the pressure distribution in the solution domain. Following the approach of the finite difference method, we use a difference scheme to replace the differential operator. First, we discretize the Reynolds equation and simplify it to obtain: (40) in, Indicates node pressure; subscript i , j These represent the circumferential and radial node numbers of the discretized sealing strip, respectively. The linear relationship between each node of the sealing strip on the bottom surface of the slipper is shown below, with the meanings of each parameter as follows: (41) Among them, the subscript i , j These represent the circumferential and radial node numbers of the discretized sealing strip, respectively. Indicates the circumferential direction i The first, radial j Oil film thickness at each node; Indicates the Zhou Xiangdi i The first, radial j The radius of each node; Indicates the dynamic viscosity of fuel; and This represents the difference between the central angle of the discretized unit and the outer and inner radii. and These represent the radial and circumferential velocities of the bottom surface of the skid, respectively. 32) Numerical solution process for the oil film pressure field of the slipper pair The discrete equation system is solved using the over-relaxation iterative method, and the relaxation factor is selected. For values ​​of 1 to 2, the iterative scheme for the pressure field is: (42) Set convergence conditions based on the relative convergence criterion: (43) Select for ; After obtaining the pressure distribution through an iterative algorithm, the average pressure of the four nodes of the unit is taken as the unit pressure using the idea of ​​interpolation. 33) Dynamic solution method for slipper pair oil film The solution is obtained using Newton's iteration method, which has the following format: (44) Among them: (45) Among them, This indicates the rate of change of the oil film at three points; Given an initial time and the initial thickness of the slipper pair oil film The unknown quantity can then be calculated. ,go through The oil film thickness at the next moment can be calculated by iterating continuously, and the oil film thickness field at all moments can be obtained. Using the difference scheme: (46) of which ; .

6. The method for analyzing the dynamic lubrication characteristics of an aviation fuel plunger pump slipper pair according to claim 1, characterized in that, Step four specifically involves: 41) Influence of operating parameters on the lubrication characteristics of the slipper pair oil film Based on the established slipper pair oil film lubrication model and solution method, while keeping other parameters constant, the working condition parameters to be studied are changed, and simulations are performed according to steps one to three. The influence of the working condition parameters on the slipper pair oil film lubrication characteristics is compared and analyzed. While keeping other parameters constant, the rotational speed is changed, and the slipper pair oil film lubrication characteristics at 1000 r / min, 2000 r / min, and 3000 r / min are simulated. The simulation results are compared to obtain the influence of rotational speed on the slipper pair oil film lubrication characteristics.

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