CN115758930A - Bidirectional fluid-solid coupling numerical simulation method for paddle-shaft coupling system - Google Patents
Bidirectional fluid-solid coupling numerical simulation method for paddle-shaft coupling system Download PDFInfo
- Publication number
- CN115758930A CN115758930A CN202211399807.8A CN202211399807A CN115758930A CN 115758930 A CN115758930 A CN 115758930A CN 202211399807 A CN202211399807 A CN 202211399807A CN 115758930 A CN115758930 A CN 115758930A
- Authority
- CN
- China
- Prior art keywords
- flow field
- propeller
- shafting
- excitation
- model
- Prior art date
- Legal status (The legal status is an assumption and is not a legal conclusion. Google has not performed a legal analysis and makes no representation as to the accuracy of the status listed.)
- Pending
Links
Images
Classifications
-
- Y—GENERAL TAGGING OF NEW TECHNOLOGICAL DEVELOPMENTS; GENERAL TAGGING OF CROSS-SECTIONAL TECHNOLOGIES SPANNING OVER SEVERAL SECTIONS OF THE IPC; TECHNICAL SUBJECTS COVERED BY FORMER USPC CROSS-REFERENCE ART COLLECTIONS [XRACs] AND DIGESTS
- Y02—TECHNOLOGIES OR APPLICATIONS FOR MITIGATION OR ADAPTATION AGAINST CLIMATE CHANGE
- Y02T—CLIMATE CHANGE MITIGATION TECHNOLOGIES RELATED TO TRANSPORTATION
- Y02T90/00—Enabling technologies or technologies with a potential or indirect contribution to GHG emissions mitigation
Landscapes
- Management, Administration, Business Operations System, And Electronic Commerce (AREA)
Abstract
The invention aims to provide a bidirectional fluid-solid coupling numerical simulation method for a paddle-shaft coupling system, which comprises the following steps of: carrying out numerical modeling on the propeller flow field part; carrying out shafting dynamics partial numerical modeling; introducing the established model into a flow field solver, wherein a shaft system dynamics part is introduced into the solver through a secondary development program, and after compiling, realizing bidirectional coupling calculation of a flow field and a structural field in the same solver; and performing bidirectional fluid-solid coupling numerical simulation on the propeller-shaft coupling system, and acquiring results of propeller flow field excitation force and shafting vibration displacement, speed and acceleration in real time in the solving process. The method comprehensively considers the conditions of non-uniform inflow, propeller flow field excitation, shafting mass unbalance excitation and the like, carries out high-efficiency and accurate numerical simulation on the dynamics of the coupling system, and serves for researching the transient dynamics response characteristics of the coupling system under various complex excitation conditions.
Description
Technical Field
The invention relates to a numerical simulation method, in particular to a numerical simulation method of a ship propeller flow field.
Background
The propeller-propulsion shafting coupling system is an important component in a ship power device, and the safety and the reliability of the system during operation have important influence on whether a ship can stably sail. When a ship sails, due to the action of uneven incoming flow of ocean and wake flow of a ship body, a propeller inevitably works in the uneven incoming flow and generates periodic excitation, the excitation action can cause shafting vibration on a propulsion shafting, and severe shafting vibration can be transmitted to the ship body through a bearing, so that the quietness and the comfort of the ship are seriously influenced. The multi-degree-of-freedom vibration of the elastic shafting can generate a feedback effect on the propeller and induce the mass center of the propeller to do complex spatial motion, and taking the shafting rotary vibration as an example, the propeller can generate the coupling of rotation and revolution at the moment and influence the flow and excitation characteristics of the propeller. Therefore, the paddle-shaft system has a complicated fluid-solid coupling problem, and a numerical simulation method capable of considering the bidirectional fluid-solid coupling effect needs to be established for carrying out deep research on the paddle-shaft system.
Research on propeller hydrodynamics and excitation has been in progress for decades, from the initial lines of lift, lifting surfaces and low-order surface element method (BEM), which made strong assumptions about fluid flow, to the current Computational Fluid Dynamics (CFD) method that can take into account three-dimensional viscous fluid flow. For the research of shafting dynamics, a Finite Element Method (FEM) is the most mainstream simulation method at present, is widely applied to the analysis of structural mechanics and rotor dynamics, and can accurately simulate the whirling, torsion, longitudinal and coupled vibration of a propulsion shafting. The current research methods mainly include a one-way coupling method and a two-way coupling method, the one-way coupling method is mainly used for researching the shafting dynamic response problem under the excitation of propeller fluid, and the two-way coupling method can be used for predicting the complex dynamic behavior generated in the running process of the propeller-shaft coupling system and deeply researching the interaction between excitation and response.
The two-way fluid-solid coupling simulation method of the paddle-shaft system is mainly divided into a method based on FEM/BEM and a method based on a commercial software built-in fluid-solid coupling algorithm at present. The first method can accurately simulate the dynamic characteristics of a shafting, but the binning method is a simulation method based on the potential flow theory, and makes the assumption of no viscosity or no rotation on the fluid flow, so that the characteristics of the viscous flow of the propeller cannot be accurately predicted. The second method overcomes the defects of the former method, can accurately simulate the flow field and the structural field, but because the CFD and the FEM solver in the commercial software are in different architectures, real-time bidirectional data transmission is required during bidirectional coupling analysis, the process is generally realized by calling two solvers through an intermediate program, and because the intermediate program is adopted to call the solver to realize the real-time data transmission, more extra computing resources are occupied, so the method has the advantages of low solving speed and low computing efficiency during the bidirectional coupling analysis.
Disclosure of Invention
The invention aims to provide a bidirectional fluid-solid coupling numerical simulation method of a propeller-shaft coupling system, which can be applied to performance prediction and design optimization of a propulsion shafting and a ship propeller and can also be applied to bidirectional fluid-solid coupling dynamics research of other fluid machinery-rotor structures except the propeller-shaft system.
The purpose of the invention is realized as follows:
the invention discloses a bidirectional fluid-solid coupling numerical simulation method of a paddle-shaft coupling system, which is characterized by comprising the following steps of:
(1) Carrying out numerical modeling on a propeller flow field part, determining a flow field area range according to an input propeller geometric model, carrying out space dispersion on the flow field area, defining boundary conditions in the flow field, and preparing pretreatment for propeller CFD simulation;
(2) Carrying out shafting dynamics part numerical modeling, establishing a shafting dynamics numerical model according to input shafting geometry and material parameters, and loading equivalent rigidity and damping of bearing support into the model;
(3) Introducing the models established in the step (1) and the step (2) into a flow field solver, wherein the shaft system dynamics part is introduced into the solver through a secondary development program, and after compiling, bidirectional coupling calculation of a flow field and a structural field in the same solver is realized;
(4) Performing bidirectional fluid-solid coupling numerical simulation on the propeller-shaft coupling system, extracting propeller excitation after the flow field calculation of each time step is finished, loading the propeller excitation into a shafting dynamic model for response calculation, feeding back the obtained response result to the propeller flow field in a propeller centroid motion mode, and continuing the flow field calculation of the next time step; and in the solving process, the results of the flow field excitation force of the propeller and the vibration displacement, speed and acceleration of the shafting are obtained in real time.
The present invention may further comprise:
1. the step (1) is specifically as follows:
firstly, determining a flow field area range according to an input propeller geometric model, dividing the flow field area range into an inner flow field area and an outer flow field area for processing, wherein the inner flow field area simulates propeller rotation, and the outer flow field area simulates incoming flow and shafting vibration induced motion; then, carrying out space dispersion of a flow field domain, dividing a flow field calculation grid, selecting parameters of grid division according to the size of the propeller in the process, and selecting the height of a first layer of grid according to the working condition of propeller operation and a turbulence model selected by numerical simulation; and finally, defining boundary conditions in the flow field, finishing the pretreatment work of the propeller CFD simulation, and outputting a flow field model for use in the subsequent steps.
2. The step (3) is specifically as follows:
a. establishing a propeller and shafting dynamic coupling numerical model:
after the modeling process is completed, outputting the mass, the rigidity and the damping matrix in the model to the next step;
b. extracting propeller fluid excitation force in flow field simulation:
extracting the pressure borne by each unit surface on the blade after the flow field simulation of each time step is finished, integrating according to 6 degrees of freedom under a Cartesian coordinate to obtain fluid excitation force and moment under the time step, transmitting the obtained excitation to a dynamic response solving module, and repeating the process after the flow field solving of the next time step is finished;
c. performing shafting forced vibration response solving based on a Newmark-beta method:
combining the obtained shafting dynamic model and propeller fluid excitation, simultaneously calculating shafting mass unbalance excitation, inputting the mass, rigidity and damping matrix of the system and excitation data into a shafting forced vibration response solving module, and obtaining shafting dynamic response in the time step through calculation;
d. the flow field is fed back by the motion of the center of mass of the propeller:
after shafting dynamic response is obtained, on one hand, a response result and an excitation result are output to a document together, on the other hand, the feedback effect of the dynamic response on the propeller flow field is realized, and the flow field simulation of the next time step is started; and extracting a vibration speed result at the position of the propeller in the dynamic response result, endowing the vibration speed result to a corresponding fluid domain in a propeller flow field model, and realizing the feedback effect of shafting dynamics on the propeller flow field by rotating the propeller and simultaneously accompanying the translational motion with the vibration speed obtained in the previous time step as the speed in the flow field simulation of the next time step.
The invention has the advantages that: when the method is adopted to carry out bidirectional fluid-solid coupling numerical simulation on the propeller-shaft coupling system, on one hand, the coupling effect of viscous flow of the propeller and multiple degrees of freedom of the elastic shaft system is considered, and meanwhile, the influence of factors such as non-uniform incoming flow, propeller flow field excitation, shaft system mass unbalance excitation and the like is also considered, so that the dynamic characteristics of the coupling system under various complex excitations can be accurately simulated; on the other hand, as the shafting dynamics model is compiled into the flow field solver in a secondary development mode, the bidirectional coupling simulation has no additional computing resource requirement, the solving speed of the bidirectional coupling is very close to that of the conventional flow field, and the method provided by the invention has higher computing efficiency than a commercial software built-in fluid-solid coupling algorithm. In addition, when the method is adopted for simulation, researchers can also obtain results such as flow field excitation force of the propeller, vibration displacement, speed, acceleration and the like of a shaft system in real time, and the method is very favorable for researching the dynamic characteristics of a coupling system.
The method provided by the invention is used for carrying out bidirectional fluid-solid coupling numerical simulation analysis on the propeller-shaft coupling system, can be combined with a propeller flow field and a shafting dynamics numerical model, compiles the shafting dynamics model into a flow field solver through a secondary development program, and carries out bidirectional fluid-solid coupling simulation in the same solver, thereby obtaining abundant fluid excitation and dynamics response results for researchers to carry out analysis on the premise of saving a large amount of computing resources. In the shafting dynamics modeling process, the modeling can be directly carried out through input parameters without GUI operation in commercial software, so that the establishment and modification process of the dynamics model is very convenient. In the setting process of bidirectional coupling calculation, the bidirectional coupling setting can be completed in the flow field solver only by adding the step of compiling a secondary development program on the basis of the conventional CFD solving setting, and compared with the traditional method, the method is more convenient and faster, and the working efficiency of researchers is improved.
Drawings
FIG. 1 is a schematic view of a paddle-shaft coupling system of the present invention;
FIG. 2 is a flow chart of the present invention;
FIG. 3 is a propeller excitation force result for an embodiment of the present invention;
FIG. 4 shows the shafting dynamic response result in the embodiment of the present invention.
Detailed Description
The invention will now be described in more detail by way of example with reference to the accompanying drawings in which:
with reference to fig. 1-4, the specific steps of the embodiment of the present invention are as follows:
the method comprises the steps of firstly, carrying out numerical modeling on a part of a propeller flow field, determining a flow field area range according to an input propeller geometric model, carrying out space dispersion on the flow field area, defining boundary conditions in the flow field, and preparing pretreatment for propeller CFD simulation.
The implementation mode of the part is not greatly different from the pretreatment mode of the conventional propeller flow field simulation, and the flow field area range is determined according to the input propeller geometric model, wherein the flow field area range needs to be divided into an inner flow field and an outer flow field for processing, the inner flow field is used for simulating the rotation of the propeller, and the outer flow field is used for simulating the incoming flow and the movement induced by the vibration of the shafting. And then, carrying out space dispersion of a flow field area, dividing flow field calculation grids, reasonably selecting parameters of grid division according to the size of the propeller in the process, and reasonably selecting the height of the first layer of grids according to the operating condition of the propeller and a turbulence model selected by numerical simulation. And finally, defining boundary conditions in the flow field, finishing the pretreatment work of the propeller CFD simulation, and outputting a flow field model for use in the subsequent steps.
And step two, performing shafting dynamics partial numerical modeling, establishing a shafting dynamics numerical model according to input parameters such as shafting geometry and materials, and loading the bearings and other supports into the model equivalently as rigidity and damping.
With reference to the introduction of the unfolded paddle-shaft coupling system shown in fig. 1, the coupling system mainly comprises a propeller, a rotating shaft, a front stern bearing, a rear stern bearing, a middle bearing, a thrust bearing and other support structures, shafting dynamics modeling performed in the invention is based on a finite element method, the propeller is simulated by adopting a rigid disc unit, a shaft section of an elastic beam unit model is simulated by adopting an additional rigidity and damping mode, and the bearing support is simulated. In the shafting dynamic modeling, the water attaching effect of the propeller is considered, and the water attaching mass and the damping of the propeller are corrected in the mass and damping matrix. According to the dynamic numerical modeling method, the dynamic numerical modeling can be completed only by importing the geometric and material parameters of the shafting into the program through the dynamic modeling part in the written program, and can be completed only by importing new parameters again when the model needs to be modified.
And step three, introducing the models established in the first two steps into a flow field solver, wherein the shaft system dynamics part is introduced into the solver through a secondarily developed program, and the bidirectional coupling calculation of the flow field and the structural field in the same solver is realized after compiling.
The realization of the bidirectional coupling calculation of the flow field and the structural field in the same solver through a secondary development program is the core content of the invention, and the calculation method of the bidirectional coupling and the programming realization of the secondary development are explained by combining with the graph 2.
(1) And establishing a propeller and shafting dynamic coupling numerical model.
The embodiments of this section have been described in detail above, wherein the modeling of the shafting dynamics is performed by means of a secondary development program, and after the modeling process of the first step is completed in the program, the mass, stiffness and damping matrix in the model are output to the next step.
(2) The propeller fluid excitation force is extracted in the flow field simulation.
After the flow field simulation of each time step is finished, the pressure borne on each unit surface of the paddle is extracted through a secondary development program, the fluid excitation force and the torque under the time step are obtained through integration according to 6 degrees of freedom (3 translation degrees of freedom and 3 rotation degrees of freedom) under the Cartesian coordinate, the obtained excitation is transmitted to a dynamic response solving module, the dynamic response solving and the propeller flow field feedback can be continuously carried out in the subsequent steps, and the process is repeated after the flow field solving of the next time step is finished.
(3) And performing shafting forced vibration response solving based on a Newmark-beta method.
And (3) combining the shafting dynamic model obtained in the above (1) and (2) with propeller fluid excitation, simultaneously calculating shafting mass unbalance excitation, inputting data such as mass, rigidity, damping matrix, excitation and the like of the system into a shafting forced vibration response solving module, and obtaining shafting dynamic response in the time step through calculation. The reason for adopting the Newmark-beta method is that the Newmark-beta method has good convergence, and the numerical solution is forced to converge under the condition that the convergence coefficient value is reasonable, so that the method is widely applied to the response characteristic solution of various dynamic systems. The dynamic response obtained in the step is used for feedback of the propeller flow field in the subsequent step and the result is output.
(4) The flow field is fed back by the motion of the center of mass of the propeller.
After the shafting dynamic response is obtained in the step (3), on one hand, the response result and the excitation result are output to a document together, on the other hand, the feedback effect of the dynamic response on the propeller flow field is realized, and the flow field simulation of the next time step is started. And extracting a vibration speed result at the position of the propeller in the dynamic response result, and endowing the vibration speed result to a corresponding fluid domain in a propeller flow field model, so that in the flow field simulation of the next time step, the propeller rotates and simultaneously the vibration speed obtained in the previous time step is the translational motion of the speed, and the feedback effect of shafting dynamics on the propeller flow field is realized.
The above-described processes all take place in the calculation of a time step, on the basis of which the secondary development program of the invention will loop until the end of the simulation time period to the target.
Step four, carrying out bidirectional fluid-solid coupling numerical simulation on the propeller-shaft coupling system, extracting propeller excitation after the flow field calculation of each time step is finished, loading the propeller excitation into a shafting dynamic model for response calculation, feeding back the obtained response result to the propeller flow field in a propeller mass center movement mode, and continuing the flow field calculation of the next time step; in the solving process, the results of propeller flow field excitation force, shafting vibration displacement, speed, acceleration and the like can be obtained in real time.
By combining the propeller fluid excitation and shafting dynamics response results in fig. 3 and 4, it can be seen that the method provided by the invention realizes the functions described above, and by using the method, a convergence and accurate simulation result can be obtained under limited computing resources, so as to perform research on bidirectional fluid-solid coupling dynamics of a propeller-shaft coupling system. The numerical method provided by the invention can be applied to performance prediction and design optimization of a propulsion shafting and a ship propeller, and can also be applied to research on bidirectional fluid-solid coupling dynamics of other fluid machinery-rotor structures except a propeller-shaft system.
Claims (3)
1. A bidirectional fluid-solid coupling numerical simulation method for a paddle-shaft coupling system is characterized by comprising the following steps:
(1) Carrying out partial numerical modeling of a propeller flow field, determining a flow field area range according to an input propeller geometric model, carrying out space dispersion of the flow field area, defining boundary conditions in the flow field, and preparing pretreatment for propeller CFD simulation;
(2) Carrying out shafting dynamics part numerical modeling, establishing a shafting dynamics numerical model according to input shafting geometry and material parameters, and loading equivalent rigidity and damping of bearing support into the model;
(3) Introducing the models established in the step (1) and the step (2) into a flow field solver, wherein the shaft system dynamics part is introduced into the solver through a secondary development program, and after compiling, bidirectional coupling calculation of a flow field and a structural field in the same solver is realized;
(4) Performing bidirectional fluid-solid coupling numerical simulation on the propeller-shaft coupling system, extracting propeller excitation after the flow field calculation of each time step is finished, loading the propeller excitation into a shafting dynamic model for response calculation, feeding back the obtained response result to the propeller flow field in a propeller centroid motion mode, and continuing the flow field calculation of the next time step; and acquiring results of the propeller flow field excitation force and the shafting vibration displacement, speed and acceleration in real time in the solving process.
2. The bidirectional fluid-solid coupling numerical simulation method of the paddle-shaft coupling system as claimed in claim 1, wherein the method comprises the following steps: the step (1) is specifically as follows:
firstly, determining a flow field area range according to an input propeller geometric model, dividing the flow field area range into an inner flow field area and an outer flow field area for processing, wherein the inner flow field area simulates propeller rotation, and the outer flow field area simulates incoming flow and shafting vibration induced motion; then, carrying out space dispersion of a flow field domain, dividing a flow field calculation grid, selecting parameters of grid division according to the size of the propeller in the process, and selecting the height of a first layer of grid according to the working condition of propeller operation and a turbulence model selected by numerical simulation; and finally, defining boundary conditions in the flow field, finishing the pretreatment work of the propeller CFD simulation, and outputting a flow field model for use in the subsequent steps.
3. The bidirectional fluid-solid coupling numerical simulation method of the paddle-shaft coupling system as claimed in claim 1, wherein the method comprises the following steps: the step (3) is specifically as follows:
a. establishing a propeller and shafting dynamic coupling numerical model:
after the modeling process is completed, outputting the mass, rigidity and damping matrix in the model to the next step;
b. extracting propeller fluid excitation force in flow field simulation:
extracting the pressure borne by each unit surface on the blade after the flow field simulation of each time step is finished, integrating according to 6 degrees of freedom under a Cartesian coordinate to obtain fluid excitation force and moment under the time step, transmitting the obtained excitation to a dynamic response solving module, and repeating the process after the flow field solving of the next time step is finished;
c. solving shafting forced vibration response based on a Newmark-beta method:
combining the obtained shafting dynamic model and propeller fluid excitation, simultaneously calculating shafting mass unbalance excitation, inputting the mass, rigidity and damping matrix of the system and excitation data into a shafting forced vibration response solving module, and obtaining shafting dynamic response in the time step through calculation;
d. the flow field is fed back by the motion of the center of mass of the propeller:
after shafting dynamic response is obtained, on one hand, a response result and an excitation result are output to a document together, on the other hand, the feedback effect of the dynamic response on a propeller flow field is realized, and the flow field simulation of the next time step is started; and extracting a vibration speed result at the position of the propeller in the dynamic response result, endowing the vibration speed result to a corresponding fluid domain in a propeller flow field model, and realizing the feedback effect of shafting dynamics on the propeller flow field by rotating the propeller and simultaneously accompanying the translational motion with the vibration speed obtained in the previous time step as the speed in the flow field simulation of the next time step.
Priority Applications (1)
Application Number | Priority Date | Filing Date | Title |
---|---|---|---|
CN202211399807.8A CN115758930A (en) | 2022-11-09 | 2022-11-09 | Bidirectional fluid-solid coupling numerical simulation method for paddle-shaft coupling system |
Applications Claiming Priority (1)
Application Number | Priority Date | Filing Date | Title |
---|---|---|---|
CN202211399807.8A CN115758930A (en) | 2022-11-09 | 2022-11-09 | Bidirectional fluid-solid coupling numerical simulation method for paddle-shaft coupling system |
Publications (1)
Publication Number | Publication Date |
---|---|
CN115758930A true CN115758930A (en) | 2023-03-07 |
Family
ID=85368685
Family Applications (1)
Application Number | Title | Priority Date | Filing Date |
---|---|---|---|
CN202211399807.8A Pending CN115758930A (en) | 2022-11-09 | 2022-11-09 | Bidirectional fluid-solid coupling numerical simulation method for paddle-shaft coupling system |
Country Status (1)
Country | Link |
---|---|
CN (1) | CN115758930A (en) |
Cited By (1)
Publication number | Priority date | Publication date | Assignee | Title |
---|---|---|---|---|
CN116579217A (en) * | 2023-05-30 | 2023-08-11 | 兰州理工大学 | Digital twinning-based control valve flow-induced vibration fatigue life prediction method |
-
2022
- 2022-11-09 CN CN202211399807.8A patent/CN115758930A/en active Pending
Cited By (1)
Publication number | Priority date | Publication date | Assignee | Title |
---|---|---|---|---|
CN116579217A (en) * | 2023-05-30 | 2023-08-11 | 兰州理工大学 | Digital twinning-based control valve flow-induced vibration fatigue life prediction method |
Similar Documents
Publication | Publication Date | Title |
---|---|---|
CN109543243B (en) | ADAMS-based carrier-borne aircraft arresting ship dynamics simulation analysis method | |
CN105653781A (en) | Composite material propeller cavitation performance calculation method | |
Fabiano et al. | Adjoint-based aeroacoustic design-optimization of flexible rotors in forward flight | |
CN104077428A (en) | Remote finite element analysis method serving for industry alliance | |
CN115758930A (en) | Bidirectional fluid-solid coupling numerical simulation method for paddle-shaft coupling system | |
CN108663948A (en) | A kind of design method of aeroengine control system Numerical Simulation Analysis platform | |
CN115906718B (en) | CFD system of rotary machine | |
Zou et al. | Study on characteristics of propeller exciting force induced by axial vibration of propulsion shafting: Theoretical analysis | |
Poli et al. | Exploiting GPU-based HPC architectures to accelerate an unsteady CFD solver for turbomachinery applications | |
CN106886666B (en) | Boundary layer grid solving method for lift-drag ratio of underwater glider under different attack angles | |
CN104615807B (en) | A kind of emulation mode of multi-machine parallel connection liquid-propellant rocket engine structure low frequency | |
CN116738589B (en) | Vibration energy transfer analysis method suitable for discontinuous load-carrying structure system | |
Johnson | Requirements for next generation comprehensive analysis of rotorcraft | |
Wu et al. | Analytical study on vibration behaviors of pump-jet–shaft–submarine hull system in wavenumber–frequency domain | |
Chen et al. | The application of transfer matrix method for multibody systems in the dynamics of sail mounted hydroplanes system | |
Yang et al. | Overlapping grid technique for numerical simulation of a fast-cruising catamaran fitted with active T-foils | |
Abras | Enhancement of aeroelastic rotor airload prediction methods | |
CN104992012A (en) | Automobile rear door rigidity analysis method | |
Tanabe et al. | A new hybrid method of overlapping structured grids combined with unstructured fuselage grids for rotorcraft analysis | |
Kumar et al. | Rapid reconfiguration of engines for dynamics simulation | |
CN112883499B (en) | Method and device for acquiring coupling vibration of box body and gear shaft system | |
Choi et al. | Investigation of the effect of adaptive characteristics on non-cavitating noise for flexible propeller in non-uniform flow via the fluid-structure interaction model | |
CN101567022A (en) | Method for optimizing bracket of crankshaft used for large boat | |
CN109684698B (en) | Aircraft hydraulic system power modeling optimization method based on engineering simulator | |
CN117852429A (en) | Pitch axis system dynamics analysis method and device, computer equipment and storage medium |
Legal Events
Date | Code | Title | Description |
---|---|---|---|
PB01 | Publication | ||
PB01 | Publication | ||
SE01 | Entry into force of request for substantive examination | ||
SE01 | Entry into force of request for substantive examination |