A method for calculating combined lubrication and dynamics characteristic parameters of flanged bearings.
Patent Information
- Application Number
- JP2024501818
- Authority / Receiving Office
- JP · JP
- Patent Type
- Patents
- Current Assignee / Owner
- Priority Date
- 2022-12-27
- Filing Date
- 2023-02-28
- Publication Date
- 2025-03-04
- Estimated Expiration
- 2043-02-28
AI Technical Summary
【0030】 上記技術的解決手段から分かるように、従来技術に比べて、本発明の開示はフランジ付き軸受の結合潤滑と動力学特性パラメータを計算する方法を提供し、従来技術に比べて以下の有益な効果を有する。
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Figure 0007638581000033
Abstract
Description
[Technical field]
[0001] The present invention relates to the technical field of diesel engine simulation, and belongs to a method for calculating the combined lubrication and dynamic characteristic parameters of flanged bearings. [Background technology]
[0002] The crankshaft-bearing system is an important part of the diesel engine, and its lubrication performance directly affects the reliability and service life of the diesel engine. The flanged bearing is generally located at the end of the crankshaft and is an important component that supports the crankshaft radially and prevents it from jumping up in the axial direction. However, it is easy to have a very small oil film gap, which makes the lubrication working conditions relatively poor and always accompanies the high temperature abrasion phenomenon, which further shortens the service life of the diesel engine.
[0003] At present, research on flanged bearings in China has a certain foundation, but most of the research is done by simplifying flanged bearings to thrust bearings, and the actual location of abrasion is not only the thrust surface of the flanged bush, but also the bush surface close to the thrust side of the radial part, so this phenomenon cannot be explained by the simplified analysis of individual radial or thrust bearings. And with the operation of the crankshaft, the dynamic characteristics of the bearing also change, which further affects the stability of the flanged bearing.
[0004] Therefore, it is a problem that those skilled in the art must solve to propose a method for calculating the coupled lubrication and dynamic characteristic parameters of flanged bearings, establish a simulation model that comprehensively takes into account the radial thrust thermal elastohydrodynamic lubrication and dynamic characteristics of flanged bearings, and establish the relationship between the pressure coupling and thermal coupling of the radial thrust part of the flanged bearing, thereby more accurately explaining the lubrication mechanism by which abrasion occurs, clarifying the lubrication and dynamic laws of flanged bearings in the transient process, providing theoretical support for the abrasion failure and instability analysis of flanged bearings, and solving the difficulties existing in the prior art. Summary of the Invention [Problem to be solved by the invention]
[0005] In view of this, the present invention provides a method for calculating the coupled lubrication and dynamics characteristic parameters of flanged bearings, and establishes a simulation model that comprehensively considers the radial thrust thermal elastohydrodynamic lubrication and dynamics characteristics of flanged bearings, and the relationship between the pressure coupling and thermal coupling of the radial thrust part of the flanged bearing, thereby more accurately explaining the lubrication mechanism in which abrasion occurs, clarifying the lubrication and dynamics laws of flanged bearings in the transient process, and providing theoretical support for the abrasion failure and instability analysis of flanged bearings. [Means for solving the problem]
[0006] To achieve the above objectives, the present invention uses the following technical solutions:
[0007] 1. A method for calculating combined lubrication and dynamics characteristic parameters of a flanged bearing, comprising the steps of: Step S1 of obtaining structural parameters and operating mode of a flanged bearing; Step S2 of setting a time t; Step S3: calculating and obtaining the oil film bearing force by using the radial thrust thermal elastohydrodynamic combined lubrication module of the flanged bearing; After completing S3, a step S4 of calculating stiffness damping using a dynamic characteristic parameter calculation module of the flanged bearing; Step S5, after completing S4, utilizes the flanged bearing relative position feedback module to judge whether the calculation cycle of the internal combustion engine is completed, if completed, output and store the working characteristic parameter result of the flanged bearing, if not completed, proceed to S6; and step S6 of calculating the radial and axial displacements of the flanged bearing based on the load at the corresponding time, updating the calculation area and network of the thrust part, and continuing the calculation with the relative positions of each bearing at the next time as input parameters of the radial thrust thermal elastic-hydrodynamic coupled lubrication module of the flanged bearing and the calculation module of the dynamic characteristic parameters of the flanged bearing.
[0008] In the above method, the specific content of S3 is optionally as follows: Calculate the oil film thickness in the radial and thrust parts based on the input structural parameters and operating mode of the flanged bearing; After obtaining the oil film thickness, the average Reynolds equation considering the axial velocity is introduced, the average Reynolds equation is solved, and the finite difference method is used to calculate and obtain the oil film pressure distribution in the radial part and the thrust part, respectively. The loop is repeated until the pressure convergence judgment is satisfied, and the Reynolds boundary condition is used for the pressure boundary. The finite difference method is used to solve the three-dimensional energy equation of the radial section and the thrust section, and the heat conduction equation of the bush respectively. The boundary conditions include that the oil supply side temperature of the radial section and the thrust section is a predetermined oil supply temperature, the outside of the bush is in a convection heat exchange condition with the environment, the heat quantity of the oil discharge side of the radial section and the inner diameter region of the thrust section is calculated according to the heat flow continuity condition, and the loop is updated every time the loop is repeated, and the temperature is looped until it satisfies the convergence condition; Using the deformation matrix method, calculate the thermal deformation of each node of the radial part and the thrust part based on the calculated oil film pressure, substitute the thermal deformation amount into the oil film thickness, and repeat the previous calculation of the oil film pressure until the thermal deformation meets the convergence; Based on the current pressure, the elastic deformation matrix is used to calculate the elastic deformation of each node of the radial part and the thrust part, and then substituted into the oil film thickness equation. The previous calculation of the oil film pressure is repeated, and at this time, the boundary condition that the pressure near the thrust side end face of the radial part and the oil film pressure at the inner diameter part of the thrust part satisfy the flow rate and pressure continuity conditions is increased, and the loop calculation is performed until the elastic deformation meets the convergence, and the oil film pressure is integrated to obtain the oil film supporting force.
[0009] In the above method, optionally, the equation for the oil film thickness in the radial portion is:
[0010]
number
[0011] The equation for the oil film thickness in the thrust section is:
[0012]
number
[0013] The Reynolds equation for the radial part is:
[0014]
number
[0015] The Reynolds equation for the thrust section is:
[0016]
number
[0017] In the above method, optionally, the heat flow continuity condition is:
[0018]
number
[0019] The calculation of thermal deformation and elastic deformation using the deformation matrix method is expressed as follows:
[0020]
number
[0021] The flow and pressure continuity conditions are as follows:
[0022]
number
[0023] In the above method, optionally, in S4, after calculating the oil film bearing force, the disturbance Reynolds equation under the action of coupling effect is derived and solved to calculate the disturbance radial force and axial force, and the stiffness damping of each part is calculated according to the coupling stiffness damping matrix.
[0024] In the above method, optionally, the disturbance Reynolds equation used to calculate the combined disturbance force is:
[0025]
number
[0026] After the disturbance pressure is calculated according to the disturbance equation, the disturbance pressure is integrated, and the coupling oil film stiffness and damping value of each part are determined. The specific formula is as follows:
[0027]
number
[0028] In the above method, optionally, in S6, using a three-dimensional equation of motion to calculate the relative position between the journal / thrust shoulder of the crankshaft and the bush at the next time, analyzing the dynamic pressure lubrication characteristics of the thermoelastic fluid of the composite bush at the next time, and further updating the lubrication characteristic parameters in real time; The three-dimensional equations of motion that solve for the radial and axial displacements and then calculate the radial and axial positions at the next time instant are as follows:
[0029]
number
[0030] As can be seen from the above technical solutions, compared with the prior art, the disclosure of the present invention provides a method for calculating the combined lubrication and dynamic characteristic parameters of flanged bearings, and has the following beneficial effects compared with the prior art:
[0031] 1. The lubrication coupling effect of the radial part and thrust part of the flanged bush is fully taken into consideration, and the lubrication conditions of the radial part and thrust part are combined to make the pressure and temperature distribution more consistent with the actual situation.
[0032] 2. Taking into account the time-varying calculation area of the axial speed and thrust part, the state of the flanged bearing at each time under the radial thrust integral motion can be more accurately reflected, thereby more accurately simulating the lubrication performance of the flanged bearing under actual time-varying load.
[0033] 3. By considering the influence of the coupling effect of flanged bearings on dynamic performance, the stiffness damping results are more suitable for the actual driving conditions, and the stability analysis of flanged bearings is more accurate. [Brief description of the drawings]
[0034] In order to more clearly describe the embodiments of the present invention or the technical solutions of the prior art, the drawings that need to be used in the description of the embodiments or the prior art are briefly described below, and it is obvious that the drawings described below are only embodiments of the present invention, and those skilled in the art can also obtain other drawings based on the drawings provided without requiring creative labor.
[0035] [Figure 1] FIG. 1 is a flow chart of a method for calculating combined lubrication and dynamic characteristic parameters of a flanged bearing according to the present invention. [Diagram 2] FIG. 2 is a flow chart of calculations based on the radial thrust thermal elastohydrodynamic coupled lubrication and dynamics model of the flanged bearing according to the present invention. [Diagram 3] FIG. 3 is a flow chart of a specific calculation method for radial thrust thermal elastohydrodynamic coupled lubrication and dynamics of a flanged bearing according to the present invention. DETAILED DESCRIPTION OF THE PREFERRED EMBODIMENTS
[0036] Hereinafter, the technical solutions of the embodiments of the present invention will be described clearly and completely with reference to the drawings of the embodiments of the present invention, and it is obvious that 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 labors are all within the protection scope of the present invention.
[0037] In this application, the terms "comprise", "including" or any other variations thereof are intended to cover a non-exclusive inclusion, whereby a process, method, article or device comprising a set of elements not only includes those elements, but also includes other elements not expressly listed or further elements inherent to such process, method, article or device. In the absence of further limitations, an element qualified by the phrase "comprises a..." does not exclude the presence of other identical further elements in the process, method, article or device that comprises said element.
[0038] As shown in FIG. 1, the present invention discloses a method for calculating the combined lubrication and dynamic characteristic parameters of flanged bearings, Step S1 of obtaining structural parameters and operating mode of a flanged bearing; Step S2 of setting a time t; Step S3: calculating and obtaining the oil film bearing force by using the radial thrust thermal elastohydrodynamic combined lubrication module of the flanged bearing; After completing S3, a step S4 of calculating stiffness damping using a dynamic characteristic parameter calculation module of the flanged bearing; Step S5, after completing S4, utilizes the flanged bearing relative position feedback module to judge whether the calculation cycle of the internal combustion engine is completed, if completed, output and store the working characteristic parameter result of the flanged bearing, if not completed, proceed to S6; and step S6 of calculating the radial and axial displacements of the flanged bearing based on the load at the corresponding time, updating the calculation area and network of the thrust part, and continuing the calculation with the relative positions of each bearing at the next time as input parameters of the radial thrust thermal elastic-hydrodynamic coupled lubrication module of the flanged bearing and the calculation module of the dynamic characteristic parameters of the flanged bearing.
[0039] As shown in FIG. 2, further input the global parameters into the radial thrust thermal elastic fluid coupled lubrication module of the flanged bearing, calculate the oil film thickness of the radial bearing according to the input eccentricity and eccentric angle of the radial part, and calculate the oil film thickness of the thrust part according to the average oil film gap assumed at the beginning of the thrust part and the inclination angle of the thrust bush; Based on the oil film thickness, the Reynolds boundary condition is used to solve the Reynolds equations of the radial part and thrust part respectively by the finite difference method, and the calculation speed is improved by using the super-relaxation iteration in the loop calculation, and the oil film pressure is output until it meets the convergence condition; Then solve the temperature field of each part, and use the finite difference method to solve the three-dimensional energy equation of the oil film region of the radial part and the thrust part, and the heat conduction equation of the bushing region respectively, and the boundary conditions include that the oil supply side temperature of the radial part and the thrust part is a predetermined oil supply temperature, the outside of the bushing is regarded as a convection heat exchange condition with the environment, and the inside is regarded as a convection heat exchange condition with the oil film, and the heat quantity of the oil discharge side of the radial part and the inner diameter region of the thrust part is calculated according to the heat flow continuity condition. In the loop calculation, the super-relaxation iteration is used to improve the calculation speed, and the temperature is output until it meets the convergence condition.
[0040] Then, using the obtained temperature field, calculate the thermal deformation amount of each node by the deformation matrix method, and substitute it into the oil film thickness equation. Repeat the above pressure and temperature calculations until the thermal deformation amount meets the convergence condition. Based on the current temperature, perform the elastic deformation calculation. Based on the current pressure field, calculate the elastic deformation amount of each node by the deformation matrix method, and substitute it into the oil film thickness equation. Repeat the above pressure field calculation. In the pressure field calculation, increase the boundary condition that the oil film pressure of the thrust side end face of the radial part and the oil film pressure at the inner diameter part of the thrust part meet the flow rate and pressure continuity conditions. Loop calculation until the elastic deformation amount meets the convergence condition. At this time, obtain the pressure distribution of each part of the bearing searched here and there at the initial predetermined position. The oil film supporting force is integrated based on the oil film pressure distribution, and the stiffness damping of the equilibrium position is calculated using the small disturbance method.
[0041] Furthermore, the equation for the oil film thickness in the radial portion is:
[0042]
number
[0043] The equation for the oil film thickness in the thrust section is:
[0044]
number
[0045] The Reynolds equation for the radial part is:
[0046]
number
[0047] The Reynolds equation for the thrust section is:
[0048]
number
[0049] Furthermore, the heat flow continuity condition is:
[0050]
number
[0051] The calculation of thermal deformation and elastic deformation using the deformation matrix method is expressed as follows:
[0052]
number
[0053] The flow and pressure continuity conditions are as follows:
[0054]
number
[0055] The global parameters also include bearing parameters (1) such as bearing width, journal outer diameter (which matches the corresponding shaft part), radial clearance, initial eccentricity, initial eccentricity angle, bush roughness, bush elastic modulus, bush Poisson's ratio, and bush thermal conductivity coefficient, other parameters (3) such as lubricant density, lubricant viscosity, oil supply temperature, environmental temperature, rotational speed, and load, and calculation method parameters (4) such as the number of divisions of the bearing mesh and the convergence accuracy of the bearing oil film pressure.
[0056] In addition, in S4, after calculating and obtaining the oil film bearing force, the disturbance Reynolds equation under the action of the coupling effect is derived and solved to calculate and obtain the disturbance radial force and the disturbance axial force, and the stiffness damping of each part is calculated based on the coupling stiffness damping matrix. Specifically, the disturbance Reynolds equation is established, and the disturbance pressure in the stable state, including the disturbance forces in three directions, axial, horizontal and vertical, is solved to obtain. The disturbance pressure is integrated to obtain the main stiffness damping and cross stiffness damping in each direction.
[0057] Furthermore, the disturbance Reynolds equation used to calculate the coupled disturbance force is:
[0058]
number
[0059] After the disturbance pressure is calculated according to the disturbance equation, the disturbance pressure is integrated, and the coupling oil film stiffness and damping value of each part are determined. The specific formula is as follows:
[0060]
number
[0061] In addition, it is determined whether the working cycle of the internal combustion engine is completed, and if the calculation is not completed, the radial and axial displacements of the flanged bearing are calculated according to the load at the corresponding time, the calculation domain is updated, and the lubrication domain between the thrust part and the thrust shoulder changes, and the number of meshes and the boundary mesh number need to be changed according to the transient relative displacement, and the interval of the calculation domain is further changed. When the displacement length and the number of unit meshes are not divisible, the number of meshes of the updated calculation domain needs to be rounded up to change the size of the unit mesh. The relative position of each bearing at the next time is used as an input parameter of the bearing lubrication performance and dynamics parameter calculation module to continue the calculation, and if the working cycle of the internal combustion engine is completed, the working characteristic results of the flanged bearing in the cycle are saved.
[0062] In addition, in S6, the three-dimensional equation of motion is used to calculate the relative position between the journal / thrust shoulder of the crankshaft and the bush at the next time, and the dynamic pressure lubrication characteristics of the thermoelastic fluid of the composite bush at the next time are analyzed, and the lubrication characteristic parameters are updated in real time; In the process of performing the lubrication calculation at the next time, for the radial part, the change in the radial position of the journal directly affects the lubrication eccentricity, and further changes the geometric clearance between the journal and the radial part, which affects the oil film thickness, and at the same time changes the axial velocity in the Reynolds equation. For the thrust part, the change in the axial position directly affects the geometric clearance between it and the thrust shoulder, which further affects the film thickness equation, and at the same time changes the lubrication area between the thrust part and the thrust shoulder, and it is necessary to change the mesh number and boundary mesh number according to the transient relative displacement, and further change the section of the calculation area. When the displacement length and the unit mesh number are not divisible, it is necessary to round up the mesh number of the updated calculation area to change the size of the unit mesh.
[0063] The three-dimensional equations of motion that solve for the radial and axial displacements and then calculate the radial and axial positions at the next time instant are as follows:
[0064]
number
[0065] Further, in the radial thrust thermal elastohydrodynamic coupling lubrication module and the flanged bearing coupling dynamics calculation module, input the global parameters into the radial thrust thermal elastohydrodynamic coupling lubrication module, and calculate the geometric oil film thicknesses at the initial positions of the radial section and the thrust section respectively according to the initial position of the bearing, and then calculate the oil film pressures at the corresponding positions of the corresponding sections respectively using the corresponding Reynolds equations; According to the obtained pressure, the surface temperature of the flanged bushing is solved by using the energy equation of each part, and when convergence is met, the bushing surface temperatures of the individual radial parts and the individual thrust parts are obtained, and the bushing surface temperatures of the radial parts and the thrust parts are corrected according to the thermal continuity condition, and the bushing surface temperatures of each part considering the thermal coupling effect are obtained, that is, the temperatures of the two parts are corrected according to the heat flow continuity condition, and the bushing surface temperatures of each part of the flanged bearing are obtained by comprehensively considering the coupling effect; According to the stable bushing surface temperature, update the thermal deformation of the node, update the oil film pressure of each part according to the flow continuity condition and the pressure continuity condition, and when the convergence condition is met, output the oil film pressure distribution of each part of the flanged bearing considering the flow coupling effect at a given position, that is, update the thermal deformation of the bushing according to the bushing surface temperature considering the heat flow coupling effect, and then correct the pressure distribution according to the flow continuity condition to obtain the oil film pressure of each part considering the flow and pressure coupling effects; Calculate the axial and radial bearing forces of the flanged bearing based on the pressure of each part, change the position of the bearing based on the load, and repeat the above operations until the bearing force meets the load requirement, and obtain a stable lubrication state of the bearing at that time; After obtaining the oil film pressure by comprehensively considering the flow rate, heat and pressure coupling effects, the disturbance pressure in the stable state is solved and obtained by using the disturbance Reynolds equation, and the stiffness damping is integrated, that is, the disturbance Reynolds equation is used to solve the coupled axial disturbance force and the coupled radial disturbance force, and the disturbance pressure is integrated according to the stiffness damping definition formula to calculate the coupled stiffness damping of each part, thereby indicating the stability of the flanged bearing.
[0066] After the calculation of the lubrication and dynamic characteristics at that time is completed, the three-dimensional equation of motion is used to calculate the relative position of the flanged bearing at the next time, and the lubrication calculation area at each time is updated based on the amount of displacement. Furthermore, the number of calculation meshes is changed, and the above calculation is repeated. It is determined whether the operating cycle of the internal combustion engine is completed, and if the calculation is not completed, the calculation is continued using the relative position of the flanged bearing at the next time as an input parameter, and if the operating cycle of the internal combustion engine is completed, the operating characteristic results of the flanged bearing within said cycle are output and stored.
[0067] Each embodiment in this specification is described in an inventive manner, and the same or similar parts between each embodiment may be referred to each other, and the focus of the description of each embodiment is the difference between each embodiment and other embodiments. In order to clearly describe the compatibility of hardware and software, the above description generally describes the configurations and steps of each embodiment according to functions. Whether these functions are performed in hardware or software depends on the specific application and design constraints of the technical solution. Those skilled in the art may realize the described functions in different ways for each specific application, but such realization should not be considered as going beyond the scope of the present invention.
[0068] The above description of the disclosed embodiments enables one skilled in the art to realize or use the present invention. Various modifications to these embodiments will be apparent to those skilled in the art, and the general principles defined herein may be implemented in other embodiments without departing from the spirit or scope of the present invention. Thus, the present invention is not intended to be limited to the embodiments shown herein, but is to be accorded the widest scope consistent with the principles and novel features disclosed herein.
Claims
1. 1. A method for calculating combined lubrication and dynamics characteristic parameters of a flanged bearing, comprising the steps of: Step S1 of obtaining global parameters and an operating mode of a flanged bearing; Step S2 of setting a time t; Calculate the oil film thickness in the radial portion and the thrust portion based on the input structural parameters and operating mode of the flanged bearing; After obtaining the oil film thickness, the average Reynolds equation considering the axial velocity is introduced, and the Reynolds boundary condition is used for the pressure boundary. The finite difference method is used to solve the average Reynolds equation by loop calculation until the pressure convergence condition is satisfied, and the oil film pressure at each position of the radial portion and the thrust portion is obtained. Using the finite difference method, the temperature at each position of the radial portion and thrust portion is calculated by looping the three-dimensional energy equation of the radial portion and thrust portion and the heat conduction equation of the bush until the temperature convergence condition is satisfied, using the boundary conditions that the oil supply side temperature of the radial portion and thrust portion is a predetermined oil supply temperature, the outside of the bush is in a convective heat exchange condition with the environment, the inside of the bush is considered to be in a convective heat exchange condition with an oil film, and the heat quantity of the oil discharge side of the radial portion and the inner diameter region of the thrust portion is in a heat flow continuity condition. Using a deformation matrix method, calculate the amount of thermal deformation at each position of the radial portion and the thrust portion based on the calculated temperature at each position, substitute the amount of thermal deformation into an equation for the oil film thickness, and repeat the calculation of the oil film pressure until the thermal deformation satisfies a convergence condition; Step S3: based on the oil film pressure obtained from the thermal deformation amount, calculate the elastic deformation at each position of the radial part and the thrust part using an elastic deformation matrix, and substitute the elastic deformation amount into the equation for the oil film thickness. At this time, a boundary condition is added that the oil film pressure near the thrust side end face of the radial part and the oil film pressure at the inner diameter part of the thrust part satisfy the flow rate and pressure continuity conditions. The calculation of the oil film pressure is repeated until the elastic deformation satisfies the convergence condition to obtain the oil film pressure, and the obtained oil film pressure is integrated to obtain the oil film support force in the axial and radial directions. After completing step S3, a disturbance Reynolds equation is derived and solved based on the oil film thickness corresponding to the oil film supporting force to calculate the disturbance radial force and axial force, and the stiffness and damping value of each part is calculated based on the coupling stiffness damping matrix in step S4; After completion of S4, a step S5 is performed to determine whether the operation cycle of the internal combustion engine is completed based on the time t. If the operation cycle is completed, the calculation is terminated. If the operation cycle is not completed, the calculation is terminated. If the operation cycle is not completed, the calculation is terminated. and a step S6 of calculating radial and axial displacements of the flanged bearings based on the load at the time t, and calculating the relative positions of each bearing at the next time. A method for calculating combined lubrication and dynamics characteristic parameters of a flanged bearing, comprising:
2. The equation for the radial oil film thickness is: [0010] The equation for the oil film thickness in the thrust section is: [0025] The Reynolds equation for the radial part is: [0030] The Reynolds equation for the thrust section is: [0045] The method for calculating the combined lubrication and dynamics characteristic parameters of flanged bearings according to claim 1 .
3. The heat flow continuity condition is as follows: [0050] The calculation of thermal and elastic deformation using the deformation matrix method is expressed as follows: [006] The flow rate and pressure continuity conditions are as follows: [0070] The method for calculating the combined lubrication and dynamics characteristic parameters of flanged bearings according to claim 1 .
4. The disturbance Reynolds equation is as follows: [0080] After calculating and obtaining the disturbance pressure according to the disturbance Reynolds equation, the disturbance pressure is integrated, and the coupling oil film stiffness and damping value of each part are determined. The specific formula is as follows: [0090] The method for calculating the combined lubrication and dynamics characteristic parameters of flanged bearings according to claim 1 .
5. In S6, the three-dimensional equation of motion is used to calculate the relative positions of the journal / thrust shoulder of the crankshaft and the bush at the next time, the dynamic pressure lubrication characteristics of the thermoelastic fluid of the composite bush at the next time are analyzed, and the lubrication characteristic parameters are updated in real time. The three-dimensional equation of motion for solving the radial and axial displacements and calculating the radial and axial positions at the next time is as follows: [0010] The method for calculating the combined lubrication and dynamics characteristic parameters of flanged bearings according to claim 1 .