Stern bearing lubrication characteristic analysis method coupled with three-dimensional vibration influence of stern shaft

Abstract

The invention relates to a stern bearing lubrication characteristic analysis method coupled with the influence of three-dimensional vibration of a stern shaft, and the analysis method comprises the steps: S1, inputting global parameters into a bearing lubrication performance and kinetic parameter calculation module and a propulsion shaft system vertical, horizontal and torsional three-dimensional vibration calculation module, and completing the corresponding calculation; s2, obtaining a bearing transfer matrix; s3, obtaining a system transfer matrix; s4, the forced vibration calculation module completes corresponding calculation; s5, a bearing relative position feedback module completes corresponding calculation; and S6, judging whether the calculation of one work cycle is completed or not, and storing and outputting the working characteristic result of the stern shaft-stern bearing in the cycle. By designing a bearing lubrication performance and kinetic parameter calculation module and a propulsion shafting vertical and horizontal torsion three-dimensional vibration calculation module, the vibration and lubrication coupling effect between a stern shaft and a stern bearing is fully considered, and a stern shaft vertical and horizontal torsion three-dimensional vibration and stern bearing lubrication characteristic bidirectional coupling model is established. And a vibration lubrication mutual feedback mechanism under a complex vibration condition is disclosed.

Description

TECHNICAL FIELD

[0001] The present application relates to the field of ship propulsion shafting simulation, in particular to a stern bearing lubrication characteristic analysis method coupled with stern shaft three-dimensional vibration influence. BACKGROUND

[0002] The ship propulsion system is the "artery" of the ship, the stern shaft-stern bearing is the key friction pair of the ship propulsion system, used to support the propeller shaft to transmit torque, reduce the wear of the stern shaft, and ensure the safe operation of the ship, which is the key support in the ship shafting, and its working characteristics directly determine the ship propulsion performance and service life.

[0003] The water-lubricated stern bearing has been widely used in the shipbuilding industry due to its advantages of no oil leakage, low cost, and wide source of lubricating medium. However, due to the low viscosity of the lubricating medium, the large length-diameter ratio of the bearing, and the large concentrated load of the propeller, the water-lubricated stern bearing is usually in a poor lubrication state such as mixed lubrication or dry friction. Due to the alternating torque excitation of the main engine and the propeller, the uneven flow field of the propeller, and other factors, the stern shaft is prone to longitudinal, lateral and torsional three-dimensional vibration, which further deteriorates the lubrication performance of the stern bearing.

[0004] The existing technology mainly focuses on the influence of single vibration form of the stern shaft on lubrication, but does not consider the influence of longitudinal, lateral and torsional three-dimensional coupled vibration of the stern shaft on the lubrication characteristics, and does not consider the influence of longitudinal, lateral and torsional three-dimensional vibration of the stern shaft and the tribology of the bearing on the lubrication characteristics.

[0005] Therefore, it is urgent to design a stern bearing lubrication characteristic analysis method coupled with stern shaft three-dimensional vibration influence to solve the above problems existing in the prior art. SUMMARY

[0006] Therefore, the present application provides a stern bearing lubrication characteristic analysis method coupled with stern shaft three-dimensional vibration influence, aiming to reveal the vibration and lubrication interaction mechanism of the stern bearing during operation, and further reflect the lubrication characteristics of the stern bearing under complex vibration working conditions.

[0007] To achieve the above purpose, the technical scheme adopted by the present application is as follows:

[0008] A stern bearing lubrication characteristic analysis method coupled with stern shaft three-dimensional vibration influence, the analysis method comprising:

[0009] S1. input the global parameters into the bearing lubrication performance and dynamics parameter calculation module and the propulsion shafting longitudinal, lateral and torsional three-dimensional vibration calculation module, and complete the corresponding calculation, specifically as follows:

[0010] S1-A. input the global parameters into the bearing lubrication performance and dynamics parameter calculation module to obtain the stern bearing lubrication characteristic parameters and the dynamics characteristic parameters; the stern bearing lubrication characteristic parameters include water film thickness and water film pressure; the dynamics characteristic parameters include bearing stiffness and bearing damping;

[0011] S1-B. input the global parameters into the propulsion shafting longitudinal-lateral-torsional three-dimensional vibration calculation module to obtain the stern shaft section transfer matrix;

[0012] S2. input the stern bearing dynamics characteristic parameters into the propulsion shafting longitudinal-lateral-torsional three-dimensional vibration calculation module to obtain the bearing transfer matrix;

[0013] S3. multiply the bearing transfer matrix and the stern shaft section transfer matrix in sequence to obtain the system transfer matrix, and calculate the system transfer matrix under each order natural frequency;

[0014] S4. solve the system matrix in the forced vibration calculation module, input the system transfer matrix under each order natural frequency into the forced vibration calculation module, and calculate the stern shaft vibration response by combining the system matrix and using the Newmark algorithm;

[0015] S5. input the result of the stern shaft vibration response at the moment into the bearing relative position feedback module, extract the lateral vibration response at the stern bearing, convert it into the journal position at the next moment, and modify the bearing relative position at the moment according to the result of the lateral vibration response at the stern bearing;

[0016] S6. judge whether the calculation of one working cycle is completed, if not, calculate the bearing working characteristics at the next moment based on the journal relative position at the moment;

[0017] if the calculation of one working cycle is completed, judge whether the working characteristics of the stern shaft-stern bearing system in the cycle converge, if yes, save and output the working characteristics result of the stern shaft-stern bearing in the cycle; if not, update the journal position and return to the bearing lubrication performance and dynamics parameter calculation module for recalculation.

[0018] Further, the step S1-A. input the global parameters into the bearing lubrication performance and dynamics parameter calculation module to obtain the stern bearing lubrication characteristic parameters and the dynamics characteristic parameters, specifically as follows:

[0019] Firstly, the initial position of the journal is assumed according to the input global parameters, and the water film thickness of the stern bearing is determined through the water film thickness equation;

[0020] Secondly, on the one hand, whether the friction pair is in the mixed lubrication state is judged through the film thickness ratio, and the micro asperity contact pressure is calculated based on the GT contact model;

[0021] On the other hand, the bearing pressure matrix is initialized first, then the Reynolds boundary condition is selected as the pressure boundary condition, the average Reynolds equation is solved by using the finite difference method combined with the water film thickness to obtain a water film pressure matrix; whether the water film pressure distribution converges is judged, if yes, the pressure iteration loop is exited; if not, the bearing pressure matrix is initialized again, and the average Reynolds equation is solved based on the over-relaxation iteration method;

[0022] Then, based on the water film pressure and the micro-convex body contact pressure obtained by the above calculation, the shaft deflection displacement of the stern shaft under the multiple actions of the water film pressure, the micro-convex body contact force and the load is calculated based on the displacement superposition method, and the water film thickness is updated, and then the new water film pressure and the micro-convex body contact pressure are obtained;

[0023] Finally, the water film carrying capacity is calculated according to the water film pressure and the micro-convex body contact pressure obtained by the above calculation; and the dynamic characteristic parameters of the stern bearing are calculated based on the perturbation method, the dynamic characteristic parameters including the bearing stiffness and the bearing damping.

[0024] Further, the water film thickness equation is as follows:

[0025]

[0026] In the formula, h is the water film thickness; c is the radius gap, the calculation formula is c=R-r, wherein R is the radius of the bearing, and r is the radius of the journal; e x is the eccentricity in the x direction when it is assumed that the stern shaft does not deform; e y is the eccentricity in the y direction when it is assumed that the stern shaft does not deform; x is the bearing circumferential direction; y is the bearing radial direction; and θ is the circumferential position coordinate of the journal; is the deflection angle of the journal; e i is the eccentricity of the i-th shaft section considering the deflection deformation, and the specific calculation formula is: Wherein v ix is the deflection deformation amount of the i-th shaft section in the x direction, v iy is the deflection deformation amount of the i-th shaft section in the y direction.

[0027] Further, the calculation formula of the micro-convex body contact pressure is as follows:

[0028] p c =K·E·F 2.5 (H);

[0029] In the formula, p c is the micro-convex body contact pressure; K is the elastic coefficient; E is the comprehensive elastic modulus of the journal and the bearing shell; F 2.5 (H) is the Gaussian distribution function.

[0030] Further, the average Reynolds equation is as follows:

[0031]

[0032] where p is the density of lubricating medium; h is the water film thickness; η is the viscosity of lubricating medium; p f is the water film pressure; U is the relative rotating speed of journal and bearing bush; x is the bearing circumferential direction; y is the bearing radial direction; t is time; σ is the comprehensive surface roughness; φ x is the pressure flow factor in the bearing circumferential direction; φ y is the pressure flow factor in the bearing radial direction; φ s is the shear flow factor; φ c is the contact flow factor.

[0033] Further, the stern shaft deflection displacement calculation formula is:

[0034]

[0035] where x is the bearing circumferential direction; y is the bearing radial direction; υ zx , υ zy are the components of stern shaft deflection displacement in x and y directions; P is the propeller gravity; F ix and F iy are the x and y direction components of the total load borne by the i-th shaft section; E is the elastic modulus of stern shaft material; I is the rotational inertia of stern shaft; z i is the axial distance of the i-th shaft section from the starting point; n is the number of divided axial nodes; l is the beam length.

[0036] Further, the water film carrying capacity calculation formula is:

[0037]

[0038] where P x is the water film carrying capacity in x direction, P y is the water film carrying capacity in y direction; p is the water film pressure distribution, the calculation formula of which is p = p f + p c , p f is the water film pressure, p c is the asperity contact pressure; R is the bearing radius, Rdθ = dx, θ direction is the x direction, and B is the bearing width.

[0039] Further, S1-B. The global parameters are input into the propulsion shafting longitudinal-lateral-torsional three-dimensional vibration calculation module to obtain the shaft section transfer matrix, which is specifically as follows:

[0040] The shaft section transfer matrix G is:

[0041]

[0042] In the formula, T x is a straight beam unit longitudinal transfer matrix; T our is a straight beam unit torsion transfer matrix; T x-z is a straight beam unit transverse vibration transfer matrix in the x-z plane; T x-y is a straight beam unit transverse vibration transfer matrix in the x-y plane.

[0043] Further, the S2. The stern bearing dynamic characteristic parameters are substituted into the propulsion shaft system longitudinal, transverse and torsional three-dimensional vibration calculation module to obtain a bearing transfer matrix, and the specific process is as follows:

[0044] The bearing transfer matrix [T k ] is as follows:

[0045]

[0046] In the formula, k x is the bearing stiffness in the x direction, k y is the bearing stiffness in the y direction, and k z is the bearing stiffness in the z direction; x is the bearing circumferential direction; y is the bearing radial direction; and z is the bearing axial direction.

[0047] Compared with the prior art, the beneficial effects of the present application are:

[0048] The stern bearing lubrication characteristic analysis method of the coupling stern shaft three-dimensional vibration effect of the present application sets a bearing lubrication performance and dynamics parameter calculation module, a propulsion shaft system longitudinal, transverse and torsional three-dimensional vibration calculation module, a forced vibration calculation module and a bearing relative position feedback module, and each time, the four modules are recalculated according to the calculation results of the previous time to simulate the dynamic characteristics of the propulsion system and form a propulsion shaft-bearing system coupling transient characteristic calculation method to solve the system matching characteristic calculation problem.

[0049] By designing the bearing lubrication performance and dynamics parameter calculation module and the propulsion shaft system longitudinal, transverse and torsional three-dimensional vibration calculation module, the vibration and lubrication coupling effect between the stern shaft and the stern bearing is fully considered, a stern shaft longitudinal, transverse and torsional three-dimensional vibration and stern bearing lubrication characteristic bidirectional coupling model is established, and the vibration lubrication mutual feedback mechanism under complex vibration conditions is revealed.

[0050] By taking into account the time-varying dynamic characteristics of the bearing, the bidirectional influence of lubrication and vibration at each moment is accurately simulated, and the real working conditions of the stern shaft-stern bearing are reflected; by considering the effect of the high length-diameter ratio and large concentrated load of the stern shaft, the influence of the stern shaft deflection phenomenon on the lubrication characteristics of the stern bearing is truly reflected, and the bearing working characteristic calculation is more accurate.

[0051] Additional features and advantages of the present application will be set forth in the description that follows, and in part will be apparent from the description, or can be learned by practice of the present application. The objectives and other advantages of the present application will be realized and attained by the structure particularly pointed out in the written description and claims thereof as well as the appended drawings. BRIEF DESCRIPTION OF DRAWINGS

[0052] In order to more clearly illustrate the technical solutions in the embodiments of the present application or the prior art, the following will briefly introduce the drawings needed to be used in the embodiments or the prior art description. Obviously, the drawings described below are some embodiments of the present application, and the ordinary skilled in the art can obtain other drawings according to these drawings without any creative effort.

[0053] Fig. 1 A flow chart of the stern bearing lubrication characteristic analysis method coupling the three-dimensional vibration influence of the stern shaft is shown;

[0054] Fig. 2 A specific coupling method flow chart in the stern bearing lubrication characteristic analysis method coupling the three-dimensional vibration influence of the stern shaft is shown. DETAILED DESCRIPTION

[0055] In order to make the objects, technical solutions and advantages of the embodiments of the present application clearer, the following will combine the drawings in the embodiments of the present application to clearly and completely explain the technical solutions in the embodiments of the present application. Obviously, the described embodiments are some of the embodiments of the present application, rather than all the embodiments. Based on the embodiments in the present application, all other embodiments obtained by the ordinary skilled in the art without any creative effort are within the protection scope of the present application.

[0056] The embodiments of the present application propose a stern bearing lubrication characteristic analysis method coupling the three-dimensional vibration influence of the stern shaft, as shown in the accompanying drawings Figs. 1-2 The analysis method includes:

[0057] S1. Input the global parameters to the bearing lubrication performance and dynamics parameter calculation module and the propulsion shaft system longitudinal-lateral-torsional three-dimensional vibration calculation module, and complete the corresponding calculation, as follows:

[0058] S1-A. Input the global parameters to the bearing lubrication performance and dynamics parameter calculation module to obtain the stern bearing lubrication characteristic parameters and the dynamics characteristic parameters; the stern bearing lubrication characteristic parameters include the water film thickness and the water film pressure; the dynamics characteristic parameters include the bearing stiffness and the bearing damping;

[0059] S1-B. Input the global parameters to the propulsion shaft system longitudinal-lateral-torsional three-dimensional vibration calculation module to obtain the stern shaft segment transfer matrix;

[0060] S2. Substitute the stern bearing dynamic characteristic parameters into the propulsion shafting longitudinal-lateral-torsional three-dimensional vibration calculation module to obtain a bearing transfer matrix;

[0061] S3. Multiply the bearing transfer matrix and the stern shaft section transfer matrix in sequence to obtain a system transfer matrix, and calculate the system transfer matrix under each order natural frequency;

[0062] S4. Substitute the system transfer matrix under each order natural frequency into the forced vibration calculation module, combine the system matrix, and calculate the stern shaft vibration response by using the Newmark algorithm;

[0063] S5. Input the stern shaft vibration response result at this moment into the bearing relative position feedback module, extract the lateral vibration response at the stern bearing, convert it into the journal position at the next moment, and modify the bearing relative position at this moment according to the result of the lateral vibration response at the stern bearing;

[0064] S6. Determine whether a working cycle calculation is completed, if not, calculate the bearing working characteristics at the next moment on the basis of the journal relative position at this moment;

[0065] If the working cycle calculation is completed, determine whether the stern shaft-stern bearing system working characteristics in the cycle converge, if yes, save and output the stern shaft-stern bearing working characteristics result in the cycle; if not, update the journal position, return to the bearing lubrication performance and dynamic parameter calculation module to recalculate.

[0066] The working characteristics result includes the water film thickness, the water film pressure, the stern shaft deflection displacement, the bearing stiffness, and the bearing damping.

[0067] The global parameters in the step S1 include: (1) stern shaft parameters: stern shaft length, relative rotating speed, stern shaft segmentation number, each shaft section density, each shaft section elastic modulus, each shaft section shear elastic modulus, stern shaft roughness, each shaft section cross section shape (rectangle or circle), cross section size (length and width or inner diameter and outer diameter), bearing position; (2) bearing parameters: bearing width, journal outer diameter (consistent with the corresponding shaft section), radius gap, initial eccentricity, initial offset angle, bearing roughness, lubricating medium density, and lubricating medium viscosity; (3) overall parameters: system natural frequency number, working rotating speed, load size, load action position, stern shaft rotating angle segmentation step number, and load; (4) calculation method parameters: bearing grid segmentation number, and bearing water film pressure convergence precision.

[0068] The step S1-A. inputs the global parameters into the bearing lubrication performance and dynamic parameter calculation module to obtain the stern bearing lubrication characteristic parameters and the dynamic characteristic parameters, and the specific steps are as follows:

[0069] First, the initial position of the journal is assumed based on the input global parameters, and the water film thickness of the stern bearing is determined using the water film thickness equation;

[0070] The water film thickness equation is as follows:

[0071]

[0072] Where h is the water film thickness; c is the radius clearance, and the calculation formula is c=Rr, where R is the radius of the bearing and r is the radius of the journal; e x is the eccentricity in the x direction when the stern shaft is assumed to be free of bending deformation; e y is the eccentricity in the y direction when the stern shaft is assumed to be free of bending deformation; x is the bearing circumferential direction; y is the bearing radial direction; θ is the circumferential position coordinate of the journal; is the offset angle of the journal; e i is the eccentricity of the i-th shaft segment after considering the flexural deformation. The specific calculation formula is: where v ix is the flexural deformation of the i-th axis segment in the x direction, v iy is the flexural deformation of the i-th axis segment in the y direction.

[0073] Secondly, the film thickness ratio is used to determine whether the friction pair is in a mixed lubrication state. Based on the GT contact model (Greenwood-Tripp model), the asperity contact pressure is calculated. The film thickness ratio is calculated as H = h / σ, where h is the water film thickness and σ is the comprehensive surface roughness.

[0074] On the other hand, the bearing pressure matrix is ​​first initialized, and then the Reynolds boundary condition is selected as the pressure boundary condition. The finite difference method is used to solve the average Reynolds equation in combination with the bearing water film thickness to obtain the water film pressure matrix.

[0075] Determine whether the water film pressure distribution converges. If so, exit the pressure iteration loop. If not, reinitialize the bearing pressure matrix and continue solving the average Reynolds equation based on the over-relaxation iteration method.

[0076] The calculation formula of the asperity contact pressure is:

[0077] p c =K·E·F 2.5 (H);

[0078] Where p c is the contact pressure of the micro-convex body; K is the elastic coefficient; E is the comprehensive elastic modulus of the journal and the bearing; F 2.5 (H) is the Gaussian distribution function;

[0079] The calculation formula of elastic coefficient K is:

[0080]

[0081] wherein ξβσ = 0.03 ~ 0.04, β is the radius of curvature of the roughness peak of the microconvex body; σ is the integrated surface roughness, and ξ is the density of the microconvex body;

[0082] Gaussian distribution function F 2.5 (H) is as follows:

[0083]

[0084] wherein H is the film thickness ratio, and the calculation formula is H = h / σ, wherein h is the water film thickness, and σ is the integrated surface roughness;

[0085] The average Reynolds equation is as follows:

[0086]

[0087] wherein ρ is the density of the lubricating medium; h is the water film thickness; η is the viscosity of the lubricating medium; p f is the water film pressure; U is the relative rotating speed of the journal and the bearing bush; x is the bearing circumferential direction; y is the bearing radial direction; t is time; σ is the integrated surface roughness; φ x is the pressure flow factor in the bearing circumferential direction; φ y is the pressure flow factor in the bearing radial direction; φ s is the shear flow factor; φ c is the contact flow factor.

[0088] Then, based on the water film pressure and the microconvex body contact pressure calculated above, the shaft deflection displacement of the stern shaft under the multiple actions of the water film pressure, the microconvex body contact force and the load is calculated based on the displacement superposition method, and the water film thickness is updated, and then the new water film pressure and the microconvex body contact pressure are obtained;

[0089] The formula for calculating the shaft deflection displacement of the stern shaft is as follows:

[0090]

[0091] wherein x is the bearing circumferential direction; y is the bearing radial direction; υ zx , υ zy are the components of the shaft deflection displacement in the x and y directions; P is the gravity of the propeller; F ix and F iy are the x and y direction components of the total load borne by the i-th shaft section; E is the elastic modulus of the stern shaft material; I is the rotational inertia of the stern shaft; z i is the axial distance of the i-th shaft section from the starting point; n is the number of axial nodes divided; and l is the beam length.

[0092] Finally, the water film bearing capacity is calculated based on the water film pressure and asperity contact pressure obtained above. The dynamic characteristic parameters of the stern bearing, including bearing stiffness and bearing damping, are calculated based on the micro-perturbation method.

[0093] The calculation formula of the water film bearing capacity is:

[0094]

[0095] Among them, P x is the water film bearing capacity in the x direction, P y is the water film bearing capacity in the y direction; p is the water film pressure distribution, and the calculation formula is p=p f +p c , p f is the water film pressure, p c is the contact pressure of the micro-convex body; R is the bearing radius, Rdθ=dx, the θ direction is the x direction, and B is the bearing width.

[0096] S1-B. Input the global parameters into the propulsion shaft system longitudinal, transverse and torsional three-dimensional vibration calculation module to obtain the stern shaft section transfer matrix, which is as follows:

[0097] The axis segment transfer matrix G is:

[0098]

[0099] Where, T x is the longitudinal transfer matrix of the straight beam element; T our is the torsional transfer matrix of the straight beam element; T x-z is the lateral vibration transfer matrix of the straight beam element in the xz plane; T x-y is the lateral vibration transfer matrix of the straight beam element in the xy plane.

[0100] Longitudinal transfer matrix T of straight beam element x for:

[0101]

[0102] Where, ω is the natural circular frequency, E is the elastic modulus of the stern shaft material, ρ is the density of the beam; l is the length of the beam; A is the cross-sectional area of ​​the beam;

[0103] Straight beam element torsional transfer matrix T our for:

[0104]

[0105] in, ω is the natural circular frequency, G is the shear elastic modulus, ρ is the density of the beam; l is the beam length; I pis the polar moment of inertia;

[0106] For a circular beam, the polar moment of inertia I P =π(D 4 -d 4 ) / 32, where D is the outer diameter of the beam; d is the inner diameter of the beam;

[0107] For rectangular cross-sections, torsion will produce warping. The polar moment of inertia at this time is known from the torsion theory of rectangular cross-section rods in material mechanics. Its polar moment of inertia I P =νhb 3 , where h represents the long side of the rectangular cross section; b represents the short side of the rectangular cross section; v represents the polar moment of inertia correction parameter;

[0108] Transverse vibration transfer matrix T of the straight beam element in the xz plane x-z for:

[0109]

[0110] Where, σ, τ, and c0-c5 are intermediate variables, l is the beam length, E is the elastic modulus of the beam, I y is the moment of inertia in the y direction, G is the Young's modulus of the material shear, A is the cross-sectional area, k is the correction coefficient, μ s is the linear density of the beam, and ω is the circular frequency of free vibration.

[0111] Transverse vibration transfer matrix T of the straight beam element in the xy plane x-y for:

[0112]

[0113] σ, τ, and c0-c5 are intermediate variables, l is the beam length, E is the elastic modulus of the beam, I z is the moment of inertia in the z direction, G is the Young's modulus of the material shear, A is the cross-sectional area, k is the correction coefficient, μ s is the linear density of the beam, and ω is the circular frequency of free vibration.

[0114] S2. Substitute the stern bearing dynamic characteristic parameters into the propulsion shaft system longitudinal, transverse and torsional three-dimensional vibration calculation module to obtain the bearing transfer matrix, which is as follows:

[0115] Bearing transfer matrix [T k ]for:

[0116]

[0117] Where k x is the bearing stiffness in the x-direction, k yKyy is the bearing stiffness in the y direction z Kzz is the bearing stiffness in the z direction; x is the bearing circumferential direction; y is the bearing radial direction; and z is the bearing axial direction.

[0118] The coupling stern shaft three-dimensional vibration influence stern bearing lubrication characteristic analysis method of the application, through setting bearing lubrication performance and dynamics parameter calculation module, propulsion shafting longitudinal-lateral-torsional three-dimensional vibration calculation module, forced vibration calculation module, bearing relative position feedback module, according to the last time calculation result, each time re-calculates the four modules to simulate the dynamic characteristics of the propulsion system, forms the propulsion shaft-bearing system coupling transient characteristic calculation method, to solve the system matching characteristic calculation problem.

[0119] By designing the bearing lubrication performance and dynamics parameter calculation module and the propulsion shafting longitudinal-lateral-torsional three-dimensional vibration calculation module, the vibration and lubrication coupling effect between the stern shaft and the stern bearing is fully considered, a two-way coupling model of the stern shaft longitudinal-lateral-torsional three-dimensional vibration and the stern bearing lubrication characteristics is established, and the vibration lubrication mutual feedback mechanism under complex vibration conditions is revealed.

[0120] By taking into account the time-varying dynamic characteristics of the bearing, the two-way influence of lubrication and vibration at each moment is accurately simulated, and the real working conditions of the stern shaft-stern bearing are reflected; by considering the effect of the high length-diameter ratio and large concentrated load of the stern shaft, the influence of the stern shaft deflection phenomenon on the lubrication characteristics of the stern bearing is truly reflected, and the bearing working characteristic calculation is more accurate.

[0121] Although the application is described in detail with reference to the foregoing embodiments, those skilled in the art should understand that the technical solutions recorded in the foregoing embodiments can be modified, or some technical features can be replaced by equivalent ones; and these modifications or replacements do not make the essence of the corresponding technical solutions deviate from the spirit and scope of the technical solutions of the embodiments of the application.

Claims

1. A method for analyzing lubrication characteristics of a stern bearing coupled with the influence of three-dimensional vibration of the stern shaft, characterized in that: The analysis method comprises: S1. Input the global parameters into the bearing lubrication performance and dynamic parameter calculation module and the propulsion shaft system longitudinal, transverse and torsional three-dimensional vibration calculation module, and complete the corresponding calculations, as follows: S1-A. Input the global parameters into the bearing lubrication performance and dynamic parameter calculation module to obtain the stern bearing lubrication characteristic parameters and dynamic characteristic parameters; the stern bearing lubrication characteristic parameters include water film thickness and water film pressure; the dynamic characteristic parameters include bearing stiffness and bearing damping; S1-B. Input the global parameters into the propulsion shaft system's three-dimensional longitudinal, transverse, and torsional vibration calculation module to obtain the stern shaft section transfer matrix. S2. Substitute the stern bearing dynamic characteristic parameters into the propulsion shafting three-dimensional vibration calculation module to obtain the bearing transfer matrix; S3. Multiply the bearing transfer matrix and the stern shaft transfer matrix in sequence to obtain the system transfer matrix, and calculate the system transfer matrix at each natural frequency. S4. The forced vibration calculation module solves the system force matrix and simultaneously inputs the system transfer matrix at each natural frequency into the forced vibration calculation module. The Newmark algorithm is used to calculate the stern shaft vibration response in combination with the system force matrix. S5. Input the result of the stern shaft vibration response at this moment into the bearing relative position feedback module, extract the lateral vibration response at the stern bearing, convert it into the journal position at the next moment, and modify the relative position of the bearing at this moment according to the result of the lateral vibration response at the stern bearing; S6. Determine whether a working cycle calculation is complete. If not, calculate the bearing operating characteristics at the next moment based on the relative position of the journal at that moment; If a working cycle calculation has been completed, determine whether the operating characteristics of the stern shaft-stern bearing system have converged within the cycle. If so, save and output the operating characteristics results of the stern shaft-stern bearing within the cycle. If not, update the journal position and return to the bearing lubrication performance and dynamic parameter calculation module for recalculation.

2. The method for analyzing lubrication characteristics of a stern bearing coupled with the influence of three-dimensional vibration of the stern shaft according to claim 1, characterized in that: The step S1-A inputs the global parameters into the bearing lubrication performance and dynamic parameter calculation module to obtain the stern bearing lubrication characteristic parameters and dynamic characteristic parameters, as follows: First, the initial position of the journal is assumed based on the input global parameters, and the water film thickness of the stern bearing is determined using the water film thickness equation; Secondly, on the one hand, the film thickness ratio is used to determine whether the friction pair is in a mixed lubrication state, and the asperity contact pressure is calculated based on the GT contact model; On the other hand, the bearing pressure matrix is ​​first initialized, and then the Reynolds boundary condition is selected as the pressure boundary condition. The average Reynolds equation is solved using the finite difference method combined with the bearing water film thickness to obtain the water film pressure matrix; it is determined whether the water film pressure distribution converges. If so, the pressure iteration loop is exited; If it does not converge, the bearing pressure matrix is ​​initialized again and the average Reynolds equation is solved based on the over-relaxation iteration method; Then, based on the water film pressure and asperity contact pressure calculated above, the stern shaft deflection displacement under the multiple effects of water film pressure, asperity contact force, and load is calculated using the displacement superposition method, and the water film thickness is updated to obtain the new water film pressure and asperity contact pressure. Finally, the water film bearing capacity is calculated based on the water film pressure and asperity contact pressure obtained above. The dynamic characteristic parameters of the stern bearing are calculated based on the micro-perturbation method, and the dynamic characteristic parameters include bearing stiffness and bearing damping.

3. The method for analyzing lubrication characteristics of a stern bearing coupled with the influence of three-dimensional vibration of the stern shaft according to claim 2, characterized in that: The water film thickness equation is as follows: Where h is the water film thickness; c is the radius clearance, and the calculation formula is c=Rr, where R is the radius of the bearing and r is the radius of the journal; e x is the eccentricity in the x direction when the stern shaft is assumed to be free of bending deformation; e y is the eccentricity in the y direction when the stern shaft is assumed to be free of bending deformation; x is the bearing circumferential direction; y is the bearing radial direction; θ is the circumferential position coordinate of the journal; is the offset angle of the journal; e i is the eccentricity of the i-th shaft segment after considering the flexural deformation. The specific calculation formula is: where v ix is the flexural deformation of the i-th axis segment in the x direction, v iy is the flexural deformation of the i-th axis segment in the y direction.

4. The method for analyzing lubrication characteristics of a stern bearing coupled with the three-dimensional vibration of the stern shaft according to claim 2, characterized in that: The calculation formula of the asperity contact pressure is: p c =K·E·F 2.5 (H); Where p c is the contact pressure of the micro-convex body; K is the elastic coefficient; E is the comprehensive elastic modulus of the journal and the bearing; F 2.5 (H) is the Gaussian distribution function.

5. The method for analyzing lubrication characteristics of a stern bearing coupled with the influence of three-dimensional vibration of the stern shaft according to claim 4, characterized in that: The average Reynolds equation is as follows: Where ρ is the density of the lubricating medium; h is the thickness of the water film; η is the viscosity of the lubricating medium; p f is the water film pressure; U is the relative speed between the journal and the bearing; x is the bearing circumference; y is the bearing radial direction; t is the time; σ is the comprehensive surface roughness; φ x is the pressure flow factor in the bearing circumference; φ y is the pressure flow factor in the radial direction of the bearing; φ s is the shear flow factor; φ c is the contact flow factor.

6. The method for analyzing lubrication characteristics of a stern bearing coupled with the three-dimensional vibration of the stern shaft according to claim 5, characterized in that: The calculation formula for the stern shaft bending displacement is: Where x is the bearing circumferential direction; y is the bearing radial direction; υ zx 、υ zy is the component of the stern shaft bending displacement in the x and y directions; P is the propeller gravity; F ix and F iy are the x and y components of the total load on the i-th shaft segment; E is the elastic modulus of the stern shaft material; I is the moment of inertia of the stern shaft; z i is the axial distance from the i-th axial segment to the starting point; n is the number of axial nodes; l is the beam length.

7. The method for analyzing lubrication characteristics of a stern bearing coupled with the influence of three-dimensional vibration of the stern shaft according to claim 6, characterized in that: The calculation formula of the water film bearing capacity is: Among them, P x is the water film bearing capacity in the x direction, P y is the water film bearing capacity in the y direction; p is the water film pressure distribution, and the calculation formula is p=p f +p c , p f is the water film pressure, p c is the contact pressure of the micro-convex body; R is the bearing radius, Rdθ=dx, the θ direction is the x direction, and B is the bearing width.

8. The method for analyzing lubrication characteristics of a stern bearing coupled with the influence of three-dimensional vibration of the stern shaft according to claim 1, characterized in that: S1-B. Input the global parameters into the propulsion shaft system longitudinal, transverse and torsional three-dimensional vibration calculation module to obtain the stern shaft section transfer matrix, which is as follows: The axis segment transfer matrix G is: Where, T x is the longitudinal transfer matrix of the straight beam element; T our is the torsional transfer matrix of the straight beam element; T x-z is the lateral vibration transfer matrix of the straight beam element in the xz plane; T x-y is the lateral vibration transfer matrix of the straight beam element in the xy plane.

9. The method for analyzing lubrication characteristics of a stern bearing coupled with the influence of three-dimensional vibration of the stern shaft according to claim 1, characterized in that: S2. Substitute the stern bearing dynamic characteristic parameters into the propulsion shaft system longitudinal, transverse and torsional three-dimensional vibration calculation module to obtain the bearing transfer matrix, which is as follows: Bearing transfer matrix [T k ]for: Where k x is the bearing stiffness in the x-direction, k y is the bearing stiffness in the y direction, k z is the bearing stiffness in the z direction; x is the bearing circumferential direction; y is the bearing radial direction; and z is the bearing axial direction.

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