CN110712731A - Ship shafting alignment and cyclotron vibration multidisciplinary optimization method - Google Patents
Ship shafting alignment and cyclotron vibration multidisciplinary optimization method Download PDFInfo
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Abstract
The invention belongs to the field of design of ship power devices, and particularly relates to a ship shafting alignment and cyclotron vibration multidisciplinary comprehensive design optimization method. The initial arrangement of a shaft system to be optimized, the material properties of a shaft section and a bearing, the stern profile of a ship body, the structural size of a propeller and the material properties are obtained. Based on the structural dimensions, various profile lines and material attributes of the shaft section, the bearing, the stern shell and the propeller, a geometric model is established, and then a shafting multidisciplinary finite element model comprising a centering calculation model, a vibration calculation model and a propeller model is established. And selecting an optimized evaluation index variable, wherein the index variable is obtained by numerical calculation of the multidisciplinary model and measurement or conversion of an actual rack. And establishing a fluid calculation model. According to the optimization target, selecting design variables and defining an optimization numerical range. The invention can improve the defects of the prior design method on the multidisciplinary coupling design of the shafting, and has engineering practice value on the actual shafting design and the shafting improvement of the actual ship.
Description
Technical Field
The invention belongs to the field of design of ship power devices, and particularly relates to a ship shafting alignment and cyclotron vibration multidisciplinary comprehensive design optimization method.
Background
The shafting is an important component of the power device and is used for transmitting the power of the main engine to the propeller to enable the ship to move. The shafting centering quality and the vibration characteristic are two important indexes related to the overall quality of the modern ship shafting. The shafting structure is complicated, the spare part is many, relates to numerous disciplines such as rotor dynamics, hydrodynamics, friction mechanics, structural mechanics, electromagnetic mechanics, and the close coupling of the discipline is complicated, and the analysis calculated volume is huge. Disturbance excitation borne by the shafting is from the coupled disciplines, the operating shafting generates cyclotron vibration due to non-centering disturbance excitation, shafting resonance is caused due to overlarge cyclotron vibration, and the sound stealth performance of the ship is reduced.
With the development of modern ship prime movers to high speed, the rotating speed of a shafting is increased due to factors such as an electric propulsion mode, the power of a main engine and the like, the transmitted torque and the thrust of the shafting are increased, the exciting force of a propeller is increased, the inherent frequency of the shafting is reduced, the influence of multidisciplinary coupling factors on the vibration of the shafting is more obvious, and the rotary vibration caused by misalignment of the shafting is most obvious. Correspondingly, vibration causes heating and wear of the bearings, which in turn changes the centering quality of the shafting. According to the general technical and tactical requirements of ships, the considered factors of the existing shafting optimization design method are single, the analysis of the coupling condition of multiple design factors is lacked, the shafting vibration reduction is realized by commonly used methods of changing the natural frequency of the shafting, reducing the disturbance excitation amplitude, using vibration isolators at key positions and the like, but the effect is limited. The numerical method of shafting cyclotron vibration and correction calculation is mature, but the design method of comprehensively considering both the shafting cyclotron vibration and the correction calculation and the coupling discipline is less, so the optimization result is lack of comprehensiveness. In order to comprehensively optimize the shafting centering quality and the vibration performance, improve the working state of a bearing, particularly a stern bearing, and improve the overall quality of a ship shafting, multidisciplinary factors and the coupling strength of the multidisciplinary factors need to be comprehensively considered in the design stage, an effective method is selected for decoupling, finally, the multidisciplinary design optimization of the shafting is completed, and the comprehensive performance of the shafting is improved.
Disclosure of Invention
The invention aims to provide a simple, convenient and effective multidisciplinary optimization design method for comprehensively improving the centering quality and the vibration characteristic of a ship shafting on the premise of considering multidisciplinary factors and coupling analysis and decoupling thereof.
On the basis of ship power device alignment design and long-term research and analysis of ship shafting vibration, the invention summarizes and subject division of multidisciplinary factors influencing shafting alignment and vibration, wherein the main factors influencing shafting alignment comprise: a) influence of shafting arrangement, especially the number and span of bearings; b) static rigidity of the bearing and dynamic rigidity of a supporting oil film; c) the angle of the inclined bore hole of the tail bearing. d) The shaft section and other parts of the shaft system have the self weight. The main factors affecting the vibration transmission and response characteristics include: a) arranging shafting, including the length of the shafting, the supporting mode of a bearing and the installation position of shafting components; b) the dynamic characteristics of the support bearing, including stiffness, damping, friction and wear; c) the shafting alignment state comprises a bearing axial position, a bearing vertical position, an alignment mode and the like; d) hydrodynamic effects of the propeller, particularly propeller excitation; e) the main machine excites the force. The division is performed from the subject, and the shafting design subject comprises dynamics, statics, structural mechanics, material mechanics, hydromechanics, mechanical transmission, hydraulics, friction mechanics, electromagnetic mechanics and the like.
The method is limited by the existing shafting optimization design method, shafting alignment and vibration optimization are independently carried out on a certain factor or a certain subject, and the method has an unobvious effect, and the strength of mutual influence among design variables and the influence on vibration transmission and response are different due to different alignment forms, different shafting structure parameters and different support modes.
Based on the current situation and the gist of the invention, on the basis of the existing principle and method of research and reasonableness correction, the method establishes a shafting multidisciplinary design optimization framework, and divides the shafting design into structural size, hydrodynamic calculation, fluid-solid coupling, correction calculation, vibration calculation and optimized quality evaluation; selecting an optimizable variable through sensitivity analysis according to an optimization design target; the load of each bearing is obtained through the initial structure size and the shafting arrangement, the load influence coefficient is further calculated, and the centering quality is optimized by taking the bearing load mean variance and the bearing reaction as indexes so as to accelerate the overall optimization efficiency; calculating propeller exciting force through hydrodynamic force, and giving out a propeller and shafting fluid-solid coupling boundary condition; calculating torsional vibration, longitudinal vibration and back vibration responses of the shafting under different working states through the obtained exciting force, and taking the response amplitude and the natural frequency of each order as vibration evaluation indexes; through the design of a variable scheme, calculating the index response of the overall model under a series of initial points, and analyzing the variable coupling strength and weakness degree; and finally, optimizing the overall model under a multidisciplinary design optimization algorithm, and comprehensively optimizing shafting alignment and vibration.
In order to achieve the purpose, the invention adopts the following technical scheme. A ship shafting alignment and cyclotron vibration multidisciplinary optimization method comprises the following steps:
the method comprises the steps of firstly, obtaining initial arrangement of a shafting to be optimized, material attributes of a shaft section and a bearing, a stern profile of a ship body, a propeller structure size and material attributes. The initial arrangement comprises the length, the outer diameter, the inner diameter, the bearing type, the radial rigidity and the vertical rigidity of each shaft section; the material properties include material density, Young's modulus, shear modulus of elasticity, Poisson's ratio; the propeller structure size and material properties comprise propeller outer diameter, blade number, blade surface profile of each blade, material density, elastic modulus and Poisson ratio.
And secondly, establishing a geometric model based on the structural sizes, the profile lines and the material attributes of the shaft section, the bearing, the stern part shell and the propeller, and then establishing a shafting multidisciplinary finite element model comprising a centering calculation model, a vibration calculation model and a propeller model. For the centering calculation model, a shaft system is simplified into a multi-support constant-section continuous beam, and a rigidity matrix of a beam unit can be expressed as
Wherein beta is a shear deformation influence coefficient, based on a uniform cross section assumption
G is the shear modulus of elasticity; [ K ]]Is a shafting stiffness matrix, can be represented by [ K ]]eiObtaining the stress and deformation relation { F } - [ K } of the whole shafting simultaneously][v]And in combination with the calculation of the actual geometric parameters and the supporting rigidity of the shafting, the shafting alignment calculation model can be expressed as follows:
[K+Koil]·(Y0+Y1+Y2)+{Fs-([Koil]·Y2)}+{F}+G0＝0
wherein [ K ]oil]The bearing support stiffness matrix can be obtained by connecting an oil film stiffness matrix and a bearing contact stiffness matrix in series. Y is0，Y1，Y2The initial distance vector of the shaft center line and the bearing center line, the distance vector of the shaft center and the support center, and the distance vector of the shafting center and the supporting point reference line are respectively.
The rotor dynamics equation based on the propeller propulsion shafting:
establishing a vibration calculation model, simplifying a non-thrust bearing into a spring unit with vertical stiffness and transverse stiffness, establishing a shaft section Beam unit by using Beam188, and completing spring unit modeling by using combination 14; the thrust bearing was simplified to a spring unit with vertical, lateral and axial stiffness, and modeling of the thrust bearing was accomplished using the combination 214.
And thirdly, selecting an optimized evaluation index variable, wherein the index variable is obtained through numerical calculation of the multidisciplinary model and measurement or conversion of an actual rack. The centering index variables comprise bearing support reaction force, a corner between shaft sections, shaft deflection and stress and a load difference value between bearings; the vibration index variables comprise maximum amplitude of each order, critical rotating speed of each order and stern noise at the vibration monitoring point, and the checking indexes comprise shaft section strength, safety factor and the like.
And step four, establishing a fluid calculation model. The method comprises propeller hydrodynamic calculation and bearing liquid film rigidity calculation.
According to the lifting line theory of the propeller, the propeller is divided into Nm sections along the radial direction, and when the blade angle is theta', the thrust, the torque and the tangential force of the main blade of the propeller can be expressed as follows:
the rotor runs in the bearing, the oil film is distributed in the gap between the rotor and the bearing bush, and the Reynolds equation of the liquid film between the shaft diameter and the bearing bush is as follows:
assuming that the oil film pressure at the bearing boundary is 0 and the shaft section has no inclination inside the bearing, the radial force Fbd and the tangential force Fbt of the bearing in steady operation can be expressed as:
wherein R isbIs the bearing radius, omega is the shaft speed, mu is the lubricating oil viscosity coefficient, LbAs to the length of the bearing,the average value of the radial clearance inside the bearing is shown, and epsilon is the eccentricity of the bearing. Resultant force F of oil film radial force and tangential forceoilActing on the bearing through the bearing bush, can be expressed as:
the load of the shafting can be obtained through the centering calculation model established above, and the magnitude and direction of the load are equal to F in numerical valueoilSimilarly, further derivation can obtain the bearing eccentricity epsilon and the force attitude angle
Expression (c): - (3+ pi)2Sf 2)ε2+(6-Sf 2(16-π2))ε4-4ε6+1＝0
Wherein SfIs a non-dimensionary mofield coefficient (Sommerfeld number),
by the above formula, the rest parameters can be approximately solved according to any two parameters of load, rotating speed and eccentricity. In order to simplify calculation and construct an oil film support stiffness model suitable for multidisciplinary optimization design, the bearing stiffness is simplified into linear springs in the transverse direction and the vertical direction, and then a stiffness matrix of an oil film can be approximately expressed as follows:
h represents the oil film thickness value and the transverse rigidity KzzAnd a vertical stiffness KyyCan be respectively expressed as:
Kzz＝4h(π2(2-ε2)+16ε2)
h＝(π2(1-ε2)+16ε2)-1.5
and step five, establishing a nonlinear coupling variable response surface. According to the optimization target, selecting design variables and defining an optimization numerical range. The design variables are mapped to the respective sub-disciplinary calculation models. And setting step length for each variable to carry out operation by taking the design variable as model input, the index variable as model output, the strength of the shafting and the bearing load as the model as limiting conditions, and obtaining the numerical calculation result of the design point in the design range. And analyzing the calculation result, and learning to obtain the multidisciplinary coupling variable approximate response surface for the nonlinear coupling relation through the RBF neural network.
Step six, establishing an optimized target dimensionless functionγjFor the optimized variable numbered j, αjThe optimization weight is numbered j for the variable. The optimization variables include: fiBearing support reaction force thetai-the angle of rotation between the shaft sections; li-shaft section deflection; sigmam-stress in section m; delta-difference in load between bearings; l isnj-the maximum amplitude of the j-th order at vibration monitoring point n; omeganj-critical speed of the jth order; s-danger interface safety factor. The vibration monitoring points are selected according to the point with the largest amplitude on the shaft section under the initial working condition, and the dangerous section is selected from the section with the smallest safety factor under the initial working condition. The optimization weight can be obtained by a fuzzy comprehensive evaluation method and normalization, gamma is the optimization rate of the index variable, and the optimization degree of a single index variable is reflected as follows:
in the above formula, c0To optimize the initial values of the parameters, c1For the optimized value of the parameter, the optimization degree of the parameter in the table is expressed by the optimization rate.
And seventhly, optimizing the multidisciplinary model. After the design variables are selected, a multi-dimensional design variable space is formed, and at present, genetic algorithms are usually used for optimizing the multi-dimensional design variables, but the multi-dimensional design variables are easy to fall into local optimization. The method applies the firework algorithm to the shafting multidisciplinary design optimization process. Firstly, generating an initial firework population in a feasible interval of design variables based on a uniform random principle, calculating individual fitness according to a shafting multidisciplinary model, and calculating the individual fitness according to the shafting multidisciplinary modelThe explosion operator calculates the explosion radius r of the kth fireworkkAnd the number of sparks N generated by the explosionkThe generated spark is based on the migration rule Deltax and the mutation operator
Migration and variation are realized, and the explosion radius formula is as follows:
wherein phi isminAnd phimaxRespectively is a minimum fitness value and a maximum fitness value in the current firework population; ε is avoidance ofkAnd NkA very small constant with a denominator of 0; phi (K) is the fitness value of the kth firework, and K is the total number of the fireworks; constants R and m are the explosion radius amplitude and the spark maximum, respectively, and the migration rule and mutation operator can be expressed as:
wherein g (0, r)k) Denotes that r is [0, rk]The random value of the (c) bit of the (c),
the function values are in Gaussian distribution, and the mean value and the variance are both 1; t represents the dimension number of an individual. Migration and variation are carried out through a mapping rule, a shafting design variable individual with the largest fitness value is reserved to complete screening of the next-generation fireworks, and the mapping rule and a distance-based selection strategy formula are as follows: x is the number ofk t＝xmin t+|xk t|％(xmax t-xmin t)
In the above formula, xmax tAnd xmin tThe upper and lower bounds of the individual in the dimension t,% is the modulus operator, d (x)k,xj) Is the Euclidean distance between individuals, D (x)k) Is the Euclidean distance, P (x) of the individualk) Indicating the probability that each individual other than the best individual is randomly retained for fitness,are the set of sparks generated by explosion and the variations.
The final optimized result is an optimizing result, the finally reserved design variables are input into the shafting multidisciplinary model, modal analysis, centering analysis and vibration analysis of the optimized shafting can be carried out, and the correctness of the result is determined through strength check and vibration check.
The invention has the beneficial effects that:
the invention can improve the comprehensive performance of the correction and vibration of the propeller shafting, establishes the approximate models of various sub-disciplines and the overall multidisciplinary model on the basis of fully considering multidisciplinary coupling factors in the shafting design and decoupling, realizes the comprehensive optimization of design variables related to the shafting material attribute, the shafting arrangement, the structure size and the vibration performance through numerical calculation simulation, and improves the safety performance and the vibration performance of ships. The invention can improve the defects of the prior design method on the multidisciplinary coupling design of the shafting, and has engineering practice value on the actual shafting design and the shafting improvement of the actual ship.
Drawings
FIG. 1 is a schematic view of a bearing thrust reaction force response surface
FIG. 2 is a schematic representation of the response surface of the stern bearing vertical stiffness Kyy for shaft speed;
FIG. 3 is a schematic diagram comparing the vertical vibration of the rear stern bearing Y;
FIG. 4 is a schematic diagram comparing the forward stern bearing gyroscopic vibrations;
FIG. 5 is a schematic diagram comparing the rotational vibration of a thrust bearing.
Detailed Description
The invention is described in detail below with reference to specific embodiments.
A ship shafting alignment and cyclotron vibration multidisciplinary optimization method comprises the following basic steps:
the method comprises the steps of firstly, obtaining initial arrangement of a shafting to be optimized, material attributes of a shaft section and a bearing, a stern profile of a ship body, a propeller structure size and material attributes. The initial arrangement comprises the length, the outer diameter, the inner diameter and the type of each shaft section, and the radial and vertical rigidity of the non-thrust bearing, the axial rigidity and the radial rigidity of the thrust bearing are estimated through an empirical formula; the material properties include material density, Young's modulus, shear modulus of elasticity, Poisson's ratio; the propeller structural dimensions and material properties include propeller outer diameter, number of blades, profile of each blade face, young's modulus, density and poisson's ratio of the propeller material.
And step two, selecting an optimized evaluation index variable, and obtaining the optimized evaluation index variable through numerical calculation of the multidisciplinary model and measurement or conversion of an actual rack. The centering index variables comprise bearing support reaction force, a corner between shaft sections, shaft deflection and stress and a load difference value between bearings; the vibration index variables comprise maximum amplitude of each order, critical rotating speed of each order and stern noise at the vibration monitoring point, and the checking indexes comprise shaft section strength, safety factor and the like.
And step three, establishing a geometric model based on the structural dimensions, the profile lines and the material properties of the shaft section, the bearing, the stern part shell and the propeller, and then establishing a shafting multidisciplinary finite element model comprising a centering calculation model, a vibration calculation model, a propeller model and a lubricating liquid film model. For the centering calculation model, a shaft system is simplified into a multi-support constant-section continuous beam, and a rigidity matrix of a beam unit can be expressed as
Wherein beta is a shear deformation influence coefficient, based on a uniform cross section assumption
G is the shear modulus of elasticity; [ K ]]Is a shafting stiffness matrix, can be represented by [ K ]]eiObtaining the stress and deformation relation { F } - [ K } of the whole shafting simultaneously][v]On the basis of ensuring the calculation precision, in order to accelerate the optimization result, the approximate model in shafting alignment can be expressed as follows:
[K+Koil]·(Y0+Y1+Y2)+{Fs-([Koil]·Y2)}+{F}+G0＝0
wherein [ K ]oil]The bearing support stiffness matrix can be obtained by connecting an oil film stiffness matrix and a bearing contact stiffness matrix in series. Y is0，Y1，Y2The initial distance between the axis of the shaft section and the central line of the bearing, the distance vector between the shaft center and the center of the support and the distance vector between the axis of the shaft section and the marked line of the supporting point are respectively.
Establishing a vibration calculation model based on a rotor dynamic equation of a propeller shafting:
simplifying a non-thrust bearing into a spring unit with vertical stiffness and transverse stiffness, establishing a shaft section Beam unit by using Beam188, and completing spring unit modeling by using combination 14; the thrust bearing was simplified to a spring unit with vertical, lateral and axial stiffness, and modeling of the thrust bearing was accomplished using the combination 214.
Selecting optimized evaluation index variables, wherein the correction index variables comprise bearing support reaction force, turning angles between shaft sections, shaft deflection and stress and load difference between bearings; the vibration index variables comprise maximum amplitude of each order, critical rotating speed of each order and stern noise at the vibration monitoring point, the checking indexes comprise shaft section strength, safety coefficient and the like, and the index variables can be obtained through numerical calculation of the multidisciplinary model.
And step four, establishing a fluid calculation model. The method comprises propeller hydrodynamic calculation and bearing liquid film rigidity calculation.
According to the theory of the propeller lift line, if the Z-blade propeller is divided into Nm sections in the radial direction, when the blade attack angle is θ ', the generated thrust Fx, torque Mx and tangential force F θ' of the propeller blades can be expressed as:
the rotor runs in the bearing, the oil film is distributed in the gap between the rotor and the bearing bush, and the Reynolds equation of the liquid film between the shaft diameter and the bearing bush is as follows:
assuming that the oil film has a pressure of 0 at the bearing boundary and the shaft section has no inclination in the bearing, the radial force F of the bearing in stable operationbdAnd tangential force FbtCan be respectively expressed as:
wherein R isbIs the bearing radius, omega is the shaft speed, mu is the lubricating oil viscosity coefficient, LbAnd r is the average value of the radial clearance inside the bearing, and epsilon is the eccentricity of the bearing. Resultant force F of oil film radial force and tangential forceoilActing on the bearing through the bearing bush, can be expressed as:
the load of the shafting can be obtained through the centering calculation model established above, and the load is uploaded in numerical valueThe magnitude and direction of the load are equal to FoilSimilarly, further derivation can obtain the bearing eccentricity epsilon and the force attitude angle
Expression (c):
-(3+π2Sf 2)ε2+(6-Sf 2(16-π2))ε4-4ε6+1＝0
wherein
Is a dimensionless number. According to any two parameters of load, rotating speed and eccentricity, the rest parameters can be solved approximately. In order to simplify calculation and construct an oil film support stiffness model suitable for multidisciplinary optimization design, the bearing stiffness is simplified into linear springs in the transverse direction and the vertical direction, and then a stiffness matrix of an oil film can be approximately expressed as follows:
h represents the oil film thickness value and the transverse rigidity KzzAnd a vertical stiffness KyyCan be respectively expressed as:
Kzz＝4h(π2(2-ε2)+16ε2)
h＝(π2(1-ε2)+16ε2)-1.5
according to the above formula, when the rotating speed is constant, the oil film stiffness can be approximately regarded as a function of the load and eccentricity for a specific bearing, so that the response surface of the oil film stiffness is the rotating speed-bearing load-eccentricity-stiffness response surface.
And step five, establishing a nonlinear coupling variable response surface. According to the optimization target, selecting design variables and defining an optimization numerical range. The design variables are mapped to the respective sub-disciplinary calculation models. And setting step length for each variable to carry out operation by taking the design variable as model input, the index variable as model output, the strength of the shafting and the bearing load as the model as limiting conditions, and obtaining the numerical calculation result of the design point in the design range. And analyzing the calculation result, and learning to obtain the multidisciplinary coupling variable approximate response surface for the nonlinear coupling relation through the RBF neural network.
Step six, establishing an optimized target dimensionless function
γjFor the optimized variable numbered j, αjThe optimization weight is numbered j for the variable. The optimization variables include: fiBearing support reaction force thetai-the angle of rotation between the shaft sections; li-shaft section deflection; sigmam-stress in section m; delta-difference in load between bearings; l isnj-the maximum amplitude of the j-th order at vibration monitoring point n; omeganj-critical speed of the jth order; s-danger interface safety factor. The vibration monitoring points are selected according to the point with the largest amplitude on the shaft section under the initial working condition, and the dangerous section is selected from the section with the smallest safety factor under the initial working condition. The optimization weight can be obtained by a fuzzy comprehensive evaluation method and normalization, gamma is the optimization rate of the index variable, and the optimization degree of a single index variable is reflected as follows:
in the above formula, c0To optimize the initial values of the parameters, c1For the optimized value of the parameter, the optimization degree of the parameter in the table is expressed by the optimization rate.
And seventhly, optimizing the multidisciplinary model. After the design variables are selected, a multi-dimensional design variable space is formed, and at present, genetic algorithms are usually used for optimizing the multi-dimensional design variables, but the multi-dimensional design variables are easy to fall into local optimization. The method applies the firework algorithm to shafting multidisciplinary design optimizationAnd (5) optimizing. Firstly, generating an initial firework population in a feasible interval of design variables based on a uniform random principle, calculating individual fitness according to a shafting multidisciplinary model, and calculating the explosion radius r of the kth firework according to an explosion operatorkAnd the number of sparks N generated by the explosionkThe generated spark is based on the migration rule Deltax and the mutation operator
Migration and variation are realized, and the explosion radius formula is as follows:
in the formula, phiminAnd phimaxRespectively is a minimum fitness value and a maximum fitness value in the current firework population; ε is avoidance ofkAnd NkA very small constant with a denominator of 0; phi (K) is the fitness value of the kth firework, and K is the total number of the fireworks; constants R and m are the explosion radius amplitude and the spark maximum, respectively, and the migration rule and mutation operator can be expressed as:
wherein g (0, r)k) Denotes that r is [0, rk]The random value of the (c) bit of the (c),the function values are in Gaussian distribution, and the mean value and the variance are both 1; t represents the dimension number of an individual. Migration and variation are carried out through a mapping rule, a shafting design variable individual with the largest fitness value is reserved to complete screening of the next-generation fireworks, and the mapping rule and a distance-based selection strategy formula are as follows:
xk t＝xmin t+|xk t|％(xmax t-xmin t)
in the above formula, xmax tAnd xmin tThe upper and lower bounds of the individual in the dimension t,% is the modulus operator, d (x)k,xj) Is the Euclidean distance between individuals, D (x)k) Is the Euclidean distance, P (x) of the individualk) Indicating the probability that each individual other than the best individual is randomly retained for fitness,
are the set of sparks generated by explosion and the variations.
Finally, the design variable obtained by optimization is input into a shafting multidisciplinary model, modal analysis, centering analysis and vibration analysis of the optimized shafting can be carried out, and the correctness of the result is determined through strength check and vibration check.
The ship shafting alignment and cyclotron vibration multidisciplinary comprehensive design optimization method is compared with the existing method by combining an example, the design variable set in the design scheme has N dimensionalities, and trial calculation points are obtained by uniformly sampling on each dimensionality. And taking the design parameters of the trial calculation points as input, and solving the multidisciplinary model to obtain a state parameter analysis value. On the basis of solving to obtain all sample point analytic values, learning to obtain a response surface of the sample point analytic values relative to the input design parameters by using a radial basis function neural network method. For example, a vertical position y2 of a middle bearing of a certain shafting and a vertical position y3 of a stern bearing are selected as design variables, the initial vertical positions are 800mm, sample points are uniformly taken at intervals of 1mm between [ -790,810] according to engineering practice, 400 initial sample points are obtained in total, and the response surfaces of the stern bearing support reaction force relative to y2 and y3 are obtained through radial basis neural network learning after calculation and are shown in fig. 1 and fig. 2.
When the coupling variables are more, the response surface cannot be expressed by the surface form, but the approximate coupling relation between the variables can be obtained by deep learning.
Optimizing and comparing: for a propeller shaft system supported by three bearings (a rear stern bearing, a front stern bearing and a thrust bearing), six variables of vertical deflection and axial deflection of the three bearings are taken as design variables, the longitudinal amplitude of an exciting force is 1000N, the radial amplitude is 400N, optimized calculation is carried out by the method, the vertical optimized deflection of the three bearings is [ -8.9,6.1 and 0.7] mm respectively, the axial optimized deflection is [ -83.3, -44.6 and-92.6 ] mm respectively, and compared with the reasonable centering optimization method, the vibration optimization calculation results of the three bearings are shown in figures 3, 4 and 5; the data are shown in Table 1. the vibration optimization calculation results at three bearings in Table 1
| Variable names | Unit of | Rational school optimization | MDO optimization |
| Rear stern bearing load | kN | 62.19 | 54.47 |
| Fore-aft bearing load | kN | 18.25 | 40.41 |
| Thrust bearing load | kN | 20.12 | 29.13 |
| Vertical maximum amplitude of rear stern bearing monitoring point | mm | 1.36 | 0.71 |
| Vertical maximum amplitude of front stern bearing monitoring point | mm | 0.71 | 0.32 |
| Thrust bearing monitoring point vertical maximum amplitude | mm | 0.5 | 0.33 |
Compared with a reasonable centering method, the lower vertical amplitude and the transverse amplitude of the first-order natural frequency of the rear stern bearing, the front stern bearing and the thrust bearing are optimized and have obvious effects, wherein the optimized value of the vertical amplitude of the rear stern bearing is 0.65mm, the optimized value of the vertical amplitude of the front stern bearing is 0.39mm, the optimized value of the vertical amplitude of the thrust bearing is 0.17mm, and the vibration of the rest orders is effectively inhibited; the load of a stern bearing is reduced by 7.72kN, the load of a middle bearing is increased by 22.16kN, the load of a thrust bearing is increased by 9.01kN, although the loads of a front stern bearing and the thrust bearing are increased, the front stern bearing and the thrust bearing are still in the safe working range of the bearing, the load distribution of a shafting is more uniform, the support characteristic of the stern bearing and the centering characteristic of the whole shafting are improved, the natural frequency of a low frequency band deviates to a high frequency direction, and the cyclotron vibration characteristic is improved.
Finally, it should be noted that the above embodiments are only used for illustrating the technical solutions of the present invention, and not for limiting the protection scope of the present invention, although the present invention has been described in detail with reference to the preferred embodiments, it should be understood by those skilled in the art that modifications or equivalent substitutions can be made on the technical solutions of the present invention without departing from the spirit and scope of the technical solutions of the present invention.
Claims (1)
1. A ship shafting alignment and cyclotron vibration multidisciplinary optimization method is characterized by comprising the following steps:
the method comprises the steps of firstly, obtaining initial arrangement of a shafting to be optimized, material attributes of a shaft section and a bearing, a stern profile of a ship body, a propeller structure size and material attributes. The initial arrangement comprises the length, the outer diameter, the inner diameter, the bearing type, the radial rigidity and the vertical rigidity of each shaft section; the material properties include material density, Young's modulus, shear modulus of elasticity, Poisson's ratio; the structural size and material properties of the propeller comprise the outer diameter of the propeller, the number of blades, the profile of each blade surface, the material density, the elastic modulus and the Poisson ratio;
secondly, establishing a geometric model based on the structural dimensions, the profile lines and the material properties of the shaft section, the bearing, the stern part shell and the propeller, and then establishing a shafting multidisciplinary finite element model comprising a centering calculation model, a vibration calculation model and a propeller model; for the centering calculation model, a shaft system is simplified into a multi-support constant-section continuous beam, and a rigidity matrix of a beam unit can be expressed as
Wherein beta is a shear deformation influence coefficient, based on a uniform cross section assumption
G is the shear modulus of elasticity; [ K ]]Is a shafting stiffness matrix, can be composed of
The simultaneous obtaining can further obtain the whole axial stressDeformation relation { F } - [ K ]][v]And in combination with the calculation of the actual geometric parameters and the supporting rigidity of the shafting, the shafting alignment calculation model can be expressed as follows:
[K+Koil]·(Y0+Y1+Y2)+{Fs-([Koil]·Y2)}+{F}+G0＝0
wherein [ K ]oil]The support stiffness matrix for the bearing can be obtained by connecting an oil film stiffness matrix and a bearing contact stiffness matrix in series; y is0，Y1，Y2Respectively an initial distance vector of a shaft center line and a bearing center line, a distance vector of the shaft center and a support center, and a distance vector of a shafting center and a supporting point reference line;
the rotor dynamics equation based on the propeller propulsion shafting:
establishing a vibration calculation model, simplifying a non-thrust bearing into a spring unit with vertical stiffness and transverse stiffness, establishing a shaft section Beam unit by using Beam188, and completing spring unit modeling by using combination 14; simplifying the thrust bearing into a spring unit with vertical stiffness, transverse stiffness and axial stiffness, and completing the modeling of the thrust bearing by using a combination 214;
selecting an optimized evaluation index variable, wherein the index variable is obtained by numerical calculation of a multidisciplinary model and measurement or conversion of an actual rack; the centering index variables comprise bearing support reaction force, a corner between shaft sections, shaft deflection and stress and a load difference value between bearings; the vibration index variables comprise maximum amplitude of each order, critical rotating speed of each order and stern noise at the vibration monitoring point, and the checking indexes comprise shaft section strength, safety factor and the like;
step four, establishing a fluid calculation model; the method comprises the steps of calculating the hydrodynamic force of a propeller and calculating the rigidity of a bearing liquid film;
according to the lifting line theory of the propeller, the propeller is divided into Nm sections along the radial direction, and when the blade angle is theta', the thrust, the torque and the tangential force of the main blade of the propeller can be expressed as follows:
the rotor runs in the bearing, the oil film is distributed in the gap between the rotor and the bearing bush, and the Reynolds equation of the liquid film between the shaft diameter and the bearing bush is as follows:
assuming that the oil film pressure at the bearing boundary is 0 and the shaft section has no inclination inside the bearing, the radial force Fbd and the tangential force Fbt of the bearing in steady operation can be expressed as:
wherein R isbIs the bearing radius, omega is the shaft speed, mu is the lubricating oil viscosity coefficient, LbAs to the length of the bearing,
the mean value of the radial clearance in the bearing is shown, and epsilon is the eccentricity of the bearing; resultant force F of oil film radial force and tangential forceoilActing on the bearing through the bearing bush, can be expressed as:
the load of the shafting canObtained by the calibration calculation model established above, and the magnitude and direction of the load are equal to F in numerical valueoilSimilarly, further derivation can obtain the bearing eccentricity epsilon and the force attitude angle
Expression (c):
-(3+π2Sf 2)ε2+(6-Sf 2(16-π2))ε4-4ε6+1＝0
wherein SfIs a non-dimensionary mofield coefficient (Sommerfeldnumber),according to the formula, other parameters can be approximately solved according to any two parameters of load, rotating speed and eccentricity; in order to simplify calculation and construct an oil film support stiffness model suitable for multidisciplinary optimization design, the bearing stiffness is simplified into linear springs in the transverse direction and the vertical direction, and then a stiffness matrix of an oil film can be approximately expressed as follows:
h represents the oil film thickness value and the transverse rigidity KzzAnd a vertical stiffness KyyCan be respectively expressed as:
Kzz＝4h(π2(2-ε2)+16ε2)
h＝(π2(1-ε2)+16ε2)-1.5
step five, establishing a nonlinear coupling variable response surface; selecting design variables and defining an optimized numerical range according to an optimization target; respectively mapping the design variables to each sub-discipline calculation model; taking a design variable as model input, an index variable as model output, strength of a shafting and bearing load as a model as limiting conditions, setting step length of each variable for operation, and obtaining a numerical calculation result of a design point in a design range; analyzing the calculation result, and learning to obtain a multidisciplinary coupling variable approximate response surface for the nonlinear coupling relation through an RBF neural network;
step six, establishing an optimized target dimensionless function
γjFor the optimized variable numbered j, αjThe optimization weight with variable number j; the optimization variables include: fiBearing support reaction force thetai-the angle of rotation between the shaft sections; li-shaft section deflection; sigmam-stress in section m; delta-difference in load between bearings; l isnj-the maximum amplitude of the j-th order at vibration monitoring point n; omeganj-critical speed of the jth order; s-dangerous interface safety coefficient; the selection of the vibration monitoring points is selected according to the point with the maximum amplitude on the shaft section under the initial working condition, and the dangerous section is selected from the section with the minimum safety factor under the initial working condition; the optimization weight can be obtained by a fuzzy comprehensive evaluation method and normalization, gamma is the optimization rate of the index variable, and the optimization degree of a single index variable is reflected as follows:
in the above formula, c0To optimize the initial values of the parameters, c1For the optimized value of the parameter, the optimization degree of the parameter in the table is expressed by the optimization rate;
seventhly, optimizing a multidisciplinary model; after the design variables are selected, a multi-dimensional design variable space is formed, and the prior multi-dimensional design variable optimization generally uses a genetic algorithm, but is easy to fall into local optimization; the method applies the firework algorithm to the shafting multidisciplinary design optimization process; based first on uniformityGenerating an initial firework population in a feasible interval of design variables according to a random principle, calculating individual fitness according to a shafting multidisciplinary model, and calculating the explosion radius r of the kth firework according to an explosion operatorkAnd the number of sparks N generated by the explosionkThe generated spark is based on the migration rule Deltax and the mutation operator
Migration and variation are realized, and the explosion radius formula is as follows:
wherein phi isminAnd phimaxRespectively is a minimum fitness value and a maximum fitness value in the current firework population; ε is avoidance ofkAnd NkA very small constant with a denominator of 0; phi (K) is the fitness value of the kth firework, and K is the total number of the fireworks; constants R and m are the explosion radius amplitude and the spark maximum, respectively, and the migration rule and mutation operator can be expressed as:
Δxk t＝xk t+g(0,rk)
wherein g (0, r)k) Denotes that r is [0, rk]The random value of the (c) bit of the (c),
the function values are in Gaussian distribution, and the mean value and the variance are both 1; t represents the dimension number of the individual; migration and variation are carried out through a mapping rule, a shafting design variable individual with the largest fitness value is reserved to complete screening of the next-generation fireworks, and the mapping rule and a distance-based selection strategy formula are as follows:
xk t＝xmin t+|xk t|％(xmax t-xmin t)
in the above formula, xmax tAnd xmin tThe upper and lower bounds of the individual in the dimension t,% is the modulus operator, d (x)k,xj) Is the Euclidean distance between individuals, D (x)k) Is the Euclidean distance, P (x) of the individualk) Indicating the probability that each individual other than the best individual is randomly retained for fitness,
is a set of sparks generated by explosion and variations;
finally, the reserved design variables are input into a shafting multidisciplinary model, modal analysis, centering analysis and vibration analysis of the optimized shafting can be carried out, and the correctness of the result is determined through strength check and vibration check.
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