CN-121997448-A - Ship propulsion shafting low-vibration design method considering tooth surface roughness

CN121997448ACN 121997448 ACN121997448 ACN 121997448ACN-121997448-A

Abstract

The invention discloses a ship propulsion shafting low-vibration design method considering tooth surface roughness, which comprises the following steps of S1, carrying out structural analysis on a ship propulsion shafting, establishing a first ship propulsion shafting motion differential equation without considering engagement relation, S2, introducing tooth surface roughness to calculate relevant parameters of a gear engagement unit, S3, introducing the relevant parameters of the gear engagement unit in the step S2 into the first ship propulsion shafting motion differential equation in the step S1 to obtain a second ship propulsion shafting motion differential equation corrected by the tooth surface roughness, solving to obtain a change curve of vibration characteristics of each node of the ship propulsion shafting along with time in a steady state, S4, giving different preset tooth surface roughness values, calculating to obtain a roughness-vibration characteristic comprehensive change curve through the steps S1-S3, and analyzing to obtain a roughness range meeting a preset vibration characteristic target value. The method can accurately calculate the influence of the tooth surface roughness.

Inventors

JIANG CHENXING
WANG YUHANG
WANG XI
LIANG HUIQING
LI JIAZE
WANG ZHIZHENG
Ding Daoping

Assignees

厦门大学

Dates

Publication Date: 20260508
Application Date: 20251219

Claims (10)

1. A low vibration design method of a ship propulsion shafting considering tooth surface roughness is characterized by comprising the following steps: S1, performing structural analysis on a ship propulsion shafting, dividing the ship propulsion shafting into a connecting unit, a bearing unit, a shaft section unit and a gear engagement unit, wherein the ship propulsion shafting comprises a rotating shaft, a first ship propulsion shafting differential equation for eliminating the gear engagement unit is established by taking the rotating shaft as a unit, and the first ship propulsion shafting differential equation only comprises the connecting unit, the bearing unit and the shaft section unit; s2, introducing tooth surface roughness to calculate related parameters of the gear meshing unit, wherein the related parameters comprise tooth surface meshing force, tooth surface friction force, a rigidity matrix and a damping matrix, and calculating a quality matrix of the gear meshing unit; S3, introducing the related parameters and the mass matrix of the gear meshing unit in the step S2 into the motion differential equation of the first ship propulsion shafting in the step S1 to establish a dynamic coupling relation of each rotating shaft under the action of tooth surface roughness, obtaining a second ship propulsion shafting motion differential equation corrected by the tooth surface roughness, and solving to obtain a time change curve of vibration characteristics of each node of the ship propulsion shafting in a steady state; And S4, giving different preset tooth surface roughness values, calculating through the steps S1-S3 to obtain a roughness-vibration characteristic comprehensive change curve, and analyzing to obtain a roughness range meeting a preset vibration characteristic target value.
2. The method for designing the low vibration of the marine propulsion shafting considering the tooth surface roughness of claim 1, wherein in step S1, a finite node method is adopted to perform structural analysis on the marine propulsion shafting, and a mass matrix, a rigidity matrix and a damping matrix of each unit except for the gear engagement unit are established, and a first marine propulsion shafting differential equation excluding the gear engagement unit comprises the following steps: S101, establishing a shafting motion differential equation of each rotating shaft, wherein each rotating shaft comprises a connecting unit, a bearing unit and a shaft section unit, and the shafting motion differential equation of each rotating shaft is as follows: ; ; ; in the formula, A mass matrix for each rotating shaft, A damping matrix for each rotating shaft, For the stiffness matrix of each rotating shaft, ( ) For the excitation column vector of each rotation axis, Acceleration of each rotating shaft, The speed of each rotating shaft, A displacement column vector for each rotating shaft; S102, sequentially arranging the shafting motion differential equations of the rotating shafts in the step S101, and sequentially arranging the shafting motion differential equations along a main diagonal in a matrix form to obtain a first ship propulsion shafting motion differential equation: 。
3. The method for designing a marine propulsion shafting with low vibration taking into account tooth surface roughness as claimed in claim 2, wherein in step S1 the bearing unit and the connection unit do not take into account a mass matrix, wherein the shaft section unit comprises a mass matrix Stiffness matrix Damping matrix Comprising a stiffness matrix of the bearing unit Damping matrix The connection unit comprises a stiffness matrix Damping matrix 。
4. The method for designing a marine propulsion shafting with low vibration taking into account tooth surface roughness as claimed in claim 1, wherein in step S2, the gear engagement unit includes two nodes of a driving wheel and a driven wheel, and the node displacement column vector of the gear engagement unit The method comprises the following steps: ; mass matrix of a gear engagement unit The method comprises the following steps: ; in the formula, For the mass of the main gear, the gear, For the quality of the driven gear wheel, The rotating masses of the driving wheel and the driven gear around x, y and z axes are respectively.
5. The method for designing a marine propulsion shafting with low vibration taking into account the surface roughness of a tooth as claimed in claim 1, wherein in step S3, establishing the dynamic coupling relationship comprises the steps of: S301, mass matrix of gear meshing unit Rigidity matrix under action of tooth surface roughness And damping matrix The decomposition is carried out into four submatrices with the same size, and the decomposition process is as follows: ; ; ; s302, the quality matrix in the step S301 Stiffness matrix And damping matrix Respectively embedding the ship propulsion shafting integral mass matrix, the rigidity matrix and the damping matrix which do not consider the engagement relation into the engagement relation according to the engagement relation to obtain a mass matrix corrected by the tooth surface roughness Stiffness matrix Damping matrix ; On the basis of the excitation of the ship power system, the tooth surface meshing force is introduced As meshing excitation and introducing tooth surface friction As a friction stimulus and will And According to the arrangement and synthesis of the corresponding action nodes and the degrees of freedom, the total excitation column vector of the ship propulsion shafting is obtained And further obtaining a second ship propulsion shafting motion differential equation corrected by the tooth surface roughness: ; in the formula, Is the vibration acceleration column vector of the ship propulsion shaft system, Is the vibration velocity array vector of the ship propulsion shaft system, Is the vibration displacement array vector of the ship propulsion shaft system.
6. The method of designing a marine propulsion shafting with low vibration taking into account the tooth surface roughness as set forth in claim 1, wherein in step S2, the tooth surface roughness is first introduced to calculate the time-varying engagement stiffness and the tooth surface time-varying friction coefficient of the gear engagement unit, further, the tooth surface engagement force and the tooth surface friction force are calculated by the time-varying engagement stiffness and the tooth surface time-varying friction coefficient, and the system damping matrix correction term and the system stiffness matrix correction term of the engagement effect and the friction effect are respectively considered, and finally, the stiffness matrix and the damping matrix after the tooth surface roughness correction are obtained by the system damping matrix correction term and the system stiffness matrix correction term.
7. The method of designing a marine propulsion shafting with low vibration taking into account surface roughness of a tooth as claimed in claim 6, wherein in step S2, a time-varying friction coefficient is obtained by oil film shear stress τ (t) at time t and normal contact load P (t) of individual microprotrusions : ; Assume that the displacement projection column vector generated by the displacement component of each degree of freedom along the contact line at the moment t is The projected column vectors of friction forces generated along the contact line by the respective degrees are Obtaining tooth surface meshing force under the action of tooth surface roughness Friction force of tooth surface System damping matrix correction term considering meshing effect Sum matrix correction term And system damping matrix correction term considering friction effect And stiffness matrix correction term ; ; ; ; ; ; ; In the formula, Is a displacement column vector of the gear engagement unit, Is the velocity train vector of the gear engagement unit, Is the engagement stiffness coefficient per unit length of the contact line, Is the engagement damping coefficient on the contact line of unit length, dl is the contact unit length, W is the contact line length of the bevel gear at the moment t for the judgment coefficient of the direction of the driving wheel, Is the time-varying engagement stiffness per unit length of contact line, Time-varying meshing damping over a unit length of contact wire; further, the rigidity matrix of the gear meshing unit which is subjected to the gear surface roughness correction is obtained And damping matrix ; ; 。
8. The method for designing a marine propulsion shafting with low vibration taking into account tooth surface roughness as claimed in claim 6, wherein in step S2, the time-varying engagement stiffness is changed The calculation steps of (a) are as follows: Introducing the roughness of tooth surface Calculating the fractal dimension D and the fractal roughness G of the sample: ; ; then, based on the M-B fractal contact model, the contact stiffness after the tooth surface roughness correction is obtained : ; In the formula, Is a curved surface contact coefficient, psi is an expansion factor, Is the actual contact area of the microprotrusions, Is a dimensionless number of the actual contact area of the microprotrusions, A dimensionless number that is the critical contact area of the microprotrusions; Finally, the contact stiffness after the tooth surface roughness correction is carried out The time-varying meshing stiffness of the gear meshing pair can be obtained by replacing the Hertz contact stiffness before correction : ; In the formula, 、、、 The bending rigidity, the shearing rigidity, the radial compression rigidity and the matrix deformation rigidity of the driving wheel are respectively adopted in sequence, 、、、 The bending rigidity, the shearing rigidity, the radial compression rigidity and the matrix deformation rigidity of the driven wheel are respectively adopted in sequence.
9. The method for designing the low vibration of the marine propulsion shafting with the consideration of the tooth surface roughness as claimed in claim 1, wherein in the step S3, the motion differential equation of the marine propulsion shafting with the consideration of the tooth surface roughness is iteratively solved by using a Newmark time domain method.
10. The method of designing a low vibration of a marine propulsion shafting with consideration of the roughness of a tooth surface according to claim 1, wherein in step S4, a time change curve of vibration characteristics of all marine propulsion shafting nodes under the roughness in a steady state can be obtained through a preset roughness, a plurality of concerned nodes are selected, a time change curve of vibration characteristics of each node under a plurality of groups of roughness in a steady state is calculated, vibration characteristics of each node under different roughness are synthesized according to set weights of each node, and finally a roughness-vibration characteristic comprehensive change curve considering all concerned nodes is obtained, the minimum of the maximum value, average value, peak value and the like of comprehensive vibration displacement, vibration speed or vibration acceleration of each node is taken as a target, and a roughness range meeting the low vibration design of the marine propulsion shafting is obtained through the roughness-vibration characteristic comprehensive change curve, so that the required roughness of the tooth surface can be obtained.

Description

Ship propulsion shafting low-vibration design method considering tooth surface roughness Technical Field The invention relates to the technical field of propulsion shafting, in particular to a low-vibration design method of a ship propulsion shafting considering tooth surface roughness. Background The ship propulsion shafting is a core component of a ship power device and mainly comprises a main machine, a motor, a gear transmission system, a thrust bearing, an intermediate shaft and a propeller, wherein torque output by the main machine is transmitted to the intermediate shaft through a coupler after being decelerated by a gear box, and finally the propeller is driven to rotate so as to generate propulsion, wherein the gear transmission system realizes power transmission and direction conversion by means of a tooth surface which is meshed precisely, and is called an 'aorta' for power transmission and distribution of the ship propulsion shafting, and with the development of the ship propulsion shafting, people put forward requirements on the gear transmission system, such as high reliability, high efficiency, low vibration, low noise and the like. However, the current ship operation environment is complex, the ship propulsion shafting is easy to deform under severe sea conditions, so that the gear transmission system generates abrupt load impact in the operation process, the stability of the propulsion system is reduced, and when the gears are in an unstable state for a long time to operate, faults such as pitting corrosion, abrasion, gluing, tooth breakage and the like are easy to occur, and the reliability and the stability of the ship propulsion shafting are affected. At present, in the prior art, devices such as a hydraulic clutch, a magnetorheological damper, a periodic structure vibrator and the like are arranged in a shafting to control vibration, a scholars often adopt a lumped parameter method to carry out dynamic modeling on a ship propulsion shafting, and the tooth surface roughness which is a key influencing factor of gear engagement vibration is often simplified into ideal smooth tooth surface treatment. Meanwhile, vibration reduction devices such as magnetorheological vibration absorbers and periodic structure vibrators have very limited effects of suppressing medium-high frequency vibration of a shafting in a gear meshing frequency band. The existing multi-objective optimization method (such as a response surface-genetic algorithm) only takes shafting power consumption and total vibration level as indexes, and lacks of transmission path modeling of tooth surface excitation and system response. The process constraint limits the application of high-cost tooth surface polishing, and particularly under the heavy-load abrasion working condition, the economy and the reliability of the high-cost tooth surface polishing are difficult to balance, so that how to further reduce the medium-high frequency vibration of the ship propulsion shaft system in the gear meshing frequency band and improve the running reliability and stability of the ship propulsion shaft system becomes a problem to be solved. Disclosure of Invention The invention aims to provide a low-vibration design method of a ship propulsion shafting taking the tooth surface roughness into consideration, and solves the technical problem of providing a design method for introducing the tooth surface roughness into the ship propulsion shafting for correction so as to enable the influence of the tooth surface roughness to be considered in the vibration design of the ship shafting. In order to achieve the purpose, the invention provides a low vibration design method of a ship propulsion shafting taking the tooth surface roughness into consideration, which comprises the following steps: S1, performing structural analysis on a ship propulsion shafting, dividing the ship propulsion shafting into a connecting unit, a bearing unit, a shaft section unit and a gear engagement unit, wherein the ship propulsion shafting comprises a rotating shaft, a first ship propulsion shafting differential equation for eliminating the gear engagement unit is established by taking the rotating shaft as a unit, and the first ship propulsion shafting differential equation only comprises the connecting unit, the bearing unit and the shaft section unit; s2, introducing tooth surface roughness to calculate related parameters of the gear meshing unit, wherein the related parameters comprise tooth surface meshing force, tooth surface friction force, a rigidity matrix and a damping matrix, and calculating a quality matrix of the gear meshing unit; S3, introducing the related parameters and the mass matrix of the gear meshing unit in the step S2 into the motion differential equation of the first ship propulsion shafting in the step S1 to establish a dynamic coupling relation of each rotating shaft under the action of tooth surface roughness, obtaining a second ship propulsion sha