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CN-121997449-A - Propulsion shafting vibration prediction method considering tooth side gap bidirectional coupling effect

CN121997449ACN 121997449 ACN121997449 ACN 121997449ACN-121997449-A

Abstract

The invention discloses a propulsion shafting vibration prediction method considering a tooth side gap bidirectional coupling effect, which comprises the following steps of S1, obtaining first time-varying meshing stiffness and effective transmission errors corrected by tooth side gap functions based on initial tooth side gaps at t time, S2, correcting related parameters of a gear meshing unit by utilizing the first time-varying meshing stiffness and the effective transmission errors to establish a propulsion shafting motion differential equation corrected by the tooth side gaps, solving the propulsion shafting motion differential equation to obtain vibration displacement of each node of a propulsion shafting at t time, S3, correcting the tooth side gaps by the vibration displacement of the propulsion shafting at t time to obtain initial tooth side gaps at t+1 time, and repeating the steps S1-S3 to obtain vibration characteristics of tooth side gap-shafting vibration bidirectional coupling of the propulsion shafting at any moment. The dynamic backlash is introduced into propulsion shafting calculation to provide support for shafting vibration prediction.

Inventors

  • JIANG CHENXING
  • WANG YUHANG
  • WANG XI
  • WANG ZHIZHENG

Assignees

  • 厦门大学

Dates

Publication Date
20260508
Application Date
20251219

Claims (9)

  1. 1. A propulsion shafting vibration prediction method considering a tooth side clearance bidirectional coupling effect is characterized by comprising the following steps of: s1, correcting time-varying meshing stiffness and transmission errors of a helical gear at a moment through a tooth side clearance function based on an initial tooth side clearance at the moment t, and obtaining first time-varying meshing stiffness and effective transmission errors corrected through the tooth side clearance; S2, correcting related parameters of the gear meshing unit by utilizing the first time-varying meshing stiffness and the effective transmission error to establish a propulsion shafting motion differential equation corrected by the tooth flank clearance, and solving the propulsion shafting motion differential equation to obtain vibration displacement of each node of the propulsion shafting at the moment t; S3, correcting the tooth side gap through vibration displacement of the propulsion shafting at the t moment to obtain an initial tooth side gap at the t+1 moment, and repeating the steps S1-S3 to obtain the vibration characteristic of bidirectional coupling of tooth side gap-shafting vibration of the propulsion shafting at any moment.
  2. 2. The method for predicting vibration of a propulsion shafting taking into account the backlash two-way coupling according to claim 1, wherein in step S2, the parameters related to the gear engagement unit include a stiffness matrix, a damping matrix and an excitation column vector of the gear engagement unit; correcting the rigidity matrix of the gear meshing unit and the damping matrix of the gear meshing unit by utilizing the first time-varying meshing rigidity; correcting the excitation column vector of the gear meshing unit by utilizing the first time-varying meshing stiffness and the effective transmission error; Stiffness matrix of modified gear engagement unit Damping matrix for gear engagement unit And gear engagement unit excitation column vector The method comprises the following steps: ; ; ; wherein V is the displacement projection column vector generated by each degree of freedom displacement component of the gear meshing unit along the meshing line of the bevel gears, ζ m is the meshing damping ratio, Is the mass of the driving wheel, For the mass of the driven gear wheel, The first time-varying engagement stiffness at time t, Is the effective transfer error at time t.
  3. 3. The propulsion shafting vibration prediction method considering the backlash two-way coupling according to claim 1, wherein: in step S1, the method for calculating the first time-varying engagement stiffness includes the steps of: s101, calculating time-varying meshing stiffness of the helical gear without considering influence of backlash at t time ; S102, calculating the transmission error of each thin-plate gear pair without considering the influence of the tooth side clearance at the time t based on the meshing force F under the given torque; ; Wherein, the The meshing component force applied to the ith thin-plate gear pair of the jth simultaneous meshing tooth pair at the moment t is obtained by dividing the meshing force F under the given torque by the number of pairs of thin-plate gear pairs in contact at the moment t, The transmission error of the ith thin-plate gear pair of the jth simultaneous meshing tooth pair is set at the t moment, The time-varying meshing stiffness of the ith thin-plate gear pair of the jth simultaneous meshing tooth pair is set at the t moment; taking the maximum value of the transmission errors of each thin-plate gear pair as the transmission error of the helical gear ; S103, introducing a tooth side clearance function, and transmitting error to the bevel gear Correcting to obtain a first transmission error ; S104, based on the step S103, re-judging the actual contact condition of each thin gear pair, when When the rigidity contribution coefficient of the corresponding gear pair is 0, the rigidity contribution coefficient under the other conditions is 1; s105, calculating the actual meshing force of the helical gear , ; Wherein, the The time-varying meshing stiffness corresponding to the ith thin gear pair of the jth simultaneous meshing gear pair at the t moment, The stiffness contribution coefficient corresponding to the ith thin-plate gear pair of the jth simultaneous meshing tooth pair at the t moment, A first transmission error of an ith thin plate gear pair of a jth simultaneous meshing tooth pair at a t-time point corrected for a tooth flank clearance; Will actually engage force Compared with the meshing force F under the given torque, when the relative error between the two is smaller than or equal to the error allowable threshold value, the first transmission error Namely, effectively transmitting errors When the relative error between the two is larger than the error allowable threshold value, the first transmission error is recovered Correcting until the corrected first transmission error Can enable The relative error with F is smaller than or equal to the error allowance threshold, and at the moment, the corrected first transmission error To effectively transfer errors Through the following steps of And efficiently transmitting errors To calculate a first time-varying engagement stiffness; ; Wherein, the To effectively transmit errors, F is the actual meshing force.
  4. 4. The method for predicting vibration of a propulsion shafting with consideration of backlash bi-directional coupling as set forth in claim 3, wherein in step S105, a first transmission error is determined The correction method of (2) is as follows: ; To correct the first transmission error Substituting into step S105, the actual engagement force is recalculated Up to The relative error with F is less than or equal to the error tolerance threshold.
  5. 5. The method for predicting vibration of a propulsion shafting with consideration of the backlash two-way coupling in accordance with claim 3, wherein in step S101, a time-varying meshing stiffness of the helical gear at time t is calculated: ; Wherein Ceil (epsilon) represents the minimum integer not less than the total degree of engagement epsilon, n is the total number of pairs of sheet gears of a single pair of gear teeth, The stiffness contribution coefficient corresponding to the ith thin-plate gear pair of the jth simultaneous meshing gear pair at the t moment is 0, and the rest is 1; Wherein, the Time-varying meshing stiffness corresponding to ith thin-plate gear pair of jth simultaneous meshing tooth pair at t moment Wherein, the meshing stiffness of the ith thin gear pair of the jth simultaneous meshing tooth pair The calculation method of (1) is as follows: under the premise of not considering the tooth side clearance, the bevel gear is divided into a plurality of slicing microelements by a slicing method, wherein each slicing microelement can be regarded as a straight gear, and the meshing stiffness of each slicing straight gear is calculated by a potential energy method, so that the meshing stiffness of the ith sheet gear pair of the jth simultaneous meshing tooth pair is as follows: ; where k h is the Hertz contact stiffness, 、 、 、 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.
  6. 6. The method for predicting vibration of a propulsion shafting taking into account the backlash two-way coupling as set forth in claim 3, wherein in step S103, a backlash function is introduced for the transmission error in step S102 Correcting to obtain a first transmission error ; ; Where b i,j represents half of the initial tooth flank clearance of the ith thin plate gear pair of the jth simultaneous meshing tooth pair at that time.
  7. 7. The method for predicting vibration of a propulsion shafting in consideration of a backlash two-way coupling according to claim 1, wherein in the step S3, the method for calculating the initial backlash at time t+1 comprises the steps of: S301, extracting vibration displacement of a gear engagement node of a propulsion shafting at the moment t, and calculating correction terms of gear clearances of different thin-plate gear pairs under translational degrees of freedom ; S302, calculating correction terms of tooth flank clearances of different thin-plate gear pairs at time t under the rotation freedom degree ; S303, correcting the tooth side gap at the time t, namely, the initial tooth side gap of each thin gear pair at the time t+1; ; Wherein, the The initial tooth flank clearance of the lower bevel gear pair at time t.
  8. 8. The method for predicting vibration of propulsion shafting with consideration of gear backlash bidirectional coupling effect as set forth in claim 7, wherein correction terms of gear backlash of different pinion pairs at time t under translational degrees of freedom are used The calculation method of (1) is as follows: Establishing a propulsion shaft system global coordinate system OXYZ, wherein the global coordinate system OXYZ takes the geometric center of a driving wheel as an origin O, the axial direction of a driving gear as a Z axis, a gear pair central line as an X axis, the direction of the driving wheel pointing to a driven wheel as the positive direction of the X axis, and the axis vertical to the XOZ plane as a Y axis to obtain the actual center distance of the gear pair in the XOY plane under the influence of the backlash and the shafting vibration ; ; Wherein, the For the initial center distance of the gear pair in the XOY plane, 、 Respectively vibrating displacement of the driving wheel and the driven wheel in the X direction, 、 Vibration displacement of the main driven wheel and the driven wheel in the Y direction respectively; calculating the actual end face pressure angle at this time: ; Wherein, the 、 The base radius of the main wheel and the driven wheel are respectively; And then the correction term of the tooth flank clearance at the moment under the translational degree of freedom can be obtained: ; Wherein, the Is the initial end face pressure angle of the gear pair, 。
  9. 9. The method for predicting vibration of a propulsion shafting taking account of two-way coupling of tooth flank clearance as set forth in claim 7, wherein said correction term for tooth flank clearance of different pinion pairs at time t is a rotational degree of freedom The calculation method of (1) is as follows: ; Wherein, the Is the Z-axis coordinate value of the geometric center of the driving wheel of the ith thin gear pair of the jth simultaneous meshing tooth pair, 、 The rotation angles of the driving wheel and the driven wheel are respectively when the driving wheel and the driven wheel rotate anticlockwise around the Y axis.

Description

Propulsion shafting vibration prediction method considering tooth side gap bidirectional coupling effect Technical Field The invention relates to the technical field of propulsion shafting, in particular to a propulsion shafting vibration prediction method considering a tooth side clearance bidirectional coupling effect. Background The propulsion shafting is a core component of the ship power equipment, and the vibration characteristic of the propulsion shafting can be directly related to the overall reliability, riding comfort and stealth capability of the ship. The vibrations are mainly due to excitation forces generated by the operation of the power plant, such as diesel engines or gas turbines, which are transmitted to the hull through shafting, bearings, supporting structures, etc., ultimately resulting in the body vibrating and radiating noise outwards. In a complex vibration transmission path, the gearbox is used as a key transmission node of the power transmission device, the dynamic characteristics of the gearbox have a decisive influence on system vibration, and particularly nonlinear factors such as a tooth side clearance, time-varying meshing stiffness and the like can cause strong dynamic excitation to generate shaft frequency and meshing frequency vibration components related to tooth number and rotating speed. More notably, a bidirectional coupling effect exists between the tooth side gap and the shafting vibration, namely, on one hand, the size of the tooth side gap can change the actual meshing position of the gear, so that the time-varying meshing rigidity is influenced, and the shafting transverse-longitudinal-torsional coupling vibration is influenced, and on the other hand, the shafting transverse-longitudinal-torsional coupling vibration can cause the relative displacement of the gear pair, so that the effective tooth side gap change is changed, and the nonlinear characteristic of the tooth side gap is aggravated. The gap-vibration bidirectional coupling effect is particularly prominent under variable speed and variable load working conditions, and can lead to nonlinear dynamic behaviors such as bifurcation, chaos and the like of the system, thereby remarkably aggravating vibration and noise level. At present, two types of active or passive control technology are mainly adopted for directly facing shafting vibration control technology, such as ultralow frequency vibration control realized by adjusting the pressure of an air chamber, or vibration transmission inhibition by adding a rubber vibration isolator or a floating raft vibration isolation system between power equipment and a machine body. However, the existing method focuses on the suppression of linear vibration components or the local intervention of transmission paths, or only compensates for the linear vibration components, and does not systematically establish a dynamic model capable of describing the bidirectional coupling relation between the nonlinear time-varying characteristic of the tooth flank clearance and the shafting vibration, so that the problems of insufficient precision and limited control effect of the vibration prediction of the propulsion shafting exist. The present case is thereby created. Disclosure of Invention The invention aims to provide a propulsion shafting vibration prediction method considering a tooth side gap bidirectional coupling effect, and solves the technical problem of providing the propulsion shafting vibration prediction method which introduces the tooth side gap into the propulsion shafting vibration calculation, corrects the tooth side gap at the next moment through the vibration calculation result at the current moment and realizes the bidirectional coupling of the tooth side gap and shafting vibration. In order to achieve the purpose, the invention provides a propulsion shafting vibration prediction method considering the bidirectional coupling effect of a tooth flank clearance, which comprises the following steps: s1, correcting time-varying meshing stiffness and transmission errors of a helical gear at a moment through a tooth side clearance function based on an initial tooth side clearance at the moment t, and obtaining first time-varying meshing stiffness and effective transmission errors corrected through the tooth side clearance; S2, correcting related parameters of the gear meshing unit by utilizing the first time-varying meshing stiffness and the effective transmission error to establish a propulsion shafting motion differential equation corrected by the tooth flank clearance, and solving the propulsion shafting motion differential equation to obtain vibration displacement of each node of the propulsion shafting at the moment t; S3, correcting the tooth side gap through vibration displacement of the propulsion shafting at the t moment to obtain an initial tooth side gap at the t+1 moment, and repeating the steps S1-S3 to obtain the vibration characteristic of bidirectional cou