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

Abstract

The invention discloses a ship propulsion shafting low-vibration design method considering tooth surface roughness, which comprises the following steps: S1, carrying out structural analysis on a ship propulsion shafting, and establishing a first ship propulsion shafting motion differential equation without considering a meshing relationship; s2, introducing tooth surface roughness to calculate relevant parameters of a gear meshing unit; s3, relevant parameters of the gear meshing unit in the step S2 are introduced into the first ship propulsion shafting motion differential equation in the step S1, a second ship propulsion shafting motion differential equation subjected to tooth surface roughness correction is obtained, and a change curve of vibration characteristics of each node of the ship propulsion shafting along with time in a steady state is solved; different preset tooth surface roughness values are given, a roughness-vibration characteristic comprehensive change curve is obtained through calculation in the steps S1-S3, and a roughness range meeting a preset vibration characteristic target value is obtained through analysis. The influence of the tooth surface roughness can be accurately calculated.

Description

Technical Field

[0001] This invention relates to the technical field of propulsion shafting, and in particular to a low-vibration design method for ship propulsion shafting that takes into account tooth surface roughness. Background Technology

[0002] The propulsion shafting system is a core component of a ship's power plant, primarily consisting of the main engine, motor, gear transmission system, thrust bearing, intermediate shaft, and propeller. The torque output from the main engine is reduced in speed by the gearbox and then transmitted to the intermediate shaft via a coupling, ultimately driving the propeller to generate propulsion. The gear transmission system, relying on precisely meshed tooth surfaces to achieve power transmission and direction conversion, is considered the "main artery" of power transmission and distribution in the propulsion shafting system. With the development of ship propulsion shafting systems, requirements for high reliability, high efficiency, low vibration, and low noise have been placed on gear transmission systems. However, the complex operating environment of ships today makes propulsion shafting systems highly susceptible to deformation under harsh sea conditions. This causes sudden load shocks in the gear transmission system during operation, reducing the stability of the propulsion system. Furthermore, when gears operate in an unstable state for extended periods, they are prone to pitting, wear, galling, and tooth breakage, affecting the reliability and stability of the ship's propulsion shafting system.

[0003] Currently, existing technologies often control vibration by installing devices such as hydraulic clutches, magnetorheological dampers, and periodic structural oscillators in the shafting system. Researchers frequently employ the lumped parameter method for dynamic modeling of ship propulsion shafting systems, but the key influencing factor of gear meshing vibration—tooth surface roughness—is often simplified to an ideal smooth tooth surface. Furthermore, damping devices such as magnetorheological dampers and periodic structural oscillators have limited effectiveness in suppressing mid-to-high frequency vibrations of the shafting system in the gear meshing frequency band. Existing multi-objective optimization methods (such as response surface-genetic algorithms) only use shafting power consumption and total vibration level as indicators, lacking modeling of the transmission path between tooth surface excitation and system response. Manufacturing constraints limit the application of high-cost tooth surface polishing, especially under heavy-load wear conditions, where its economy and reliability are difficult to balance. Therefore, how to further reduce mid-to-high frequency vibrations of ship propulsion shafting systems in the gear meshing frequency band and improve the reliability and stability of ship propulsion shafting operation has become an urgent problem to be solved. Summary of the Invention

[0004] The purpose of this invention is to provide a low-vibration design method for ship propulsion shafting that takes into account tooth surface roughness. The technical problem to be solved is to provide a design method that incorporates tooth surface roughness into the ship propulsion shafting for correction, so that the vibration design of the ship shafting can take into account the influence of tooth surface roughness.

[0005] To achieve the above objectives, the solution of the present invention is: a low-vibration design method for ship propulsion shafting considering tooth surface roughness, comprising the following steps: S1. Perform structural analysis on the ship propulsion shafting system. Divide the ship propulsion shafting system into connection units, bearing units, shaft segment units and gear meshing units. The ship propulsion shafting system includes a rotating shaft. Using the rotating shaft as the unit, establish the first ship propulsion shafting motion differential equation excluding the gear meshing unit. The first ship propulsion shafting motion differential equation only includes connection units, bearing units and shaft segment units. S2, introduce tooth surface roughness to calculate the relevant parameters of the gear meshing unit, including tooth surface meshing force, tooth surface friction force, stiffness matrix and damping matrix, and calculate the mass matrix of the gear meshing unit; S3. Introduce the relevant parameters and mass matrix of the gear meshing unit in step S2 into the first ship propulsion shaft system motion differential equation in step S1 to establish the dynamic coupling relationship of each shaft under the action of tooth surface roughness, obtain the second ship propulsion shaft system motion differential equation after tooth surface roughness correction, and solve to obtain the time variation curve of the vibration characteristics of each node of the ship propulsion shaft system under steady state. S4. Given different preset tooth surface roughness values, the roughness-vibration characteristic comprehensive change curve is obtained through steps S1 to S3, and analyzed to obtain the roughness range that meets the predetermined vibration characteristic target value.

[0006] Furthermore, in step S1, the finite node method is used to perform structural analysis on the ship's propulsion shafting, and the mass matrix, stiffness matrix, and damping matrix of each unit excluding the gear meshing unit are established. The first ship propulsion shafting motion differential equation excluding the gear meshing unit includes the following steps: S101, Establish the differential equations of motion for each shaft system. Each shaft includes connecting elements, bearing elements, and shaft segment elements. The differential equations of motion for each shaft system are as follows: ; ; ; In the formula, For the mass matrix of each axis, The damping matrix of each rotating shaft, Here are the stiffness matrices for each axis of rotation. ( () represents the excitation column vectors for each axis of rotation. For the acceleration of each rotating shaft, For the speed of each rotating shaft, These are the displacement column vectors for each axis of rotation; S102, then arrange the differential equations of motion of each shaft system in step S101 in sequence, and arrange them in matrix form along the main diagonal to obtain the first differential equation of motion of the ship propulsion shaft system: .

[0007] Furthermore, in step S1, the bearing unit and the connecting unit do not consider the mass matrix, while the shaft segment unit includes the mass matrix. Stiffness matrix and damping matrix The bearing unit includes the stiffness matrix. and damping matrix The connection element includes a stiffness matrix. and damping matrix .

[0008] Furthermore, in step S2, the gear meshing unit includes two nodes: a driving gear and a driven gear. The nodal displacement column vector of the gear meshing unit... for: ; Mass matrix of gear meshing unit for: ; In the formula, Mass of the main gear For the mass of the driven gear, The driving gear and the driven gear are respectively wound around x , y , z Rotational mass of the shaft.

[0009] Furthermore, in step S3, establishing the dynamic coupling relationship includes the following steps: S301, the mass matrix of the gear meshing unit Stiffness matrix under the action of tooth surface roughness With damping matrix It is decomposed into four submatrices of the same size. The decomposition process is as follows: ; ; ; S302, the mass matrix in step S301 Stiffness matrix With damping matrix Based on the meshing relationship, the mass matrix is ​​embedded into the overall mass matrix, stiffness matrix, and damping matrix of the ship's propulsion shafting system (excluding the meshing relationship) to obtain the mass matrix corrected for tooth surface roughness. Stiffness matrix Damping matrix ; Based on the excitation of the ship's power system, tooth surface meshing force is introduced. As a meshing excitation, and to introduce tooth surface friction. As a frictional excitation, and and According to the arrangement and synthesis of the corresponding action nodes and degrees of freedom, the total excitation column vector of the ship propulsion shaft system is obtained. This leads to the second ship propulsion shaft system motion differential equation after correction for tooth surface roughness: ; In the formula, Let this be the column vector of vibration accelerations of the ship's propulsion shafting. This represents the vibration velocity column vector of the ship's propulsion shaft system. This is the column vector of vibration displacements of the ship's propulsion shaft system.

[0010] Furthermore, in step S2, the tooth surface roughness is first introduced to calculate the time-varying meshing stiffness and the time-varying friction coefficient of the gear meshing unit. Then, the tooth surface meshing force and tooth surface friction force are calculated using the time-varying meshing stiffness and the time-varying friction coefficient of the tooth surface, as well as the system damping matrix correction term and system stiffness matrix correction term considering the meshing effect and friction effect respectively. Finally, the stiffness matrix and damping matrix after tooth surface roughness correction are obtained using the system damping matrix correction term and system stiffness matrix correction term.

[0011] Furthermore, in step S2, the time-varying friction coefficient can be obtained using the oil film shear stress τ(t) at time t and the normal contact load P(t) of a single micro-protrusion. : ; Assume that at time t, the displacement projection column vector generated by each degree of freedom displacement component along the contact line is... The projected column vector of the frictional forces generated along the contact line for each degree of freedom is: The meshing force of the tooth surface under the action of tooth surface roughness is obtained. Tooth surface friction The system damping matrix correction term considering meshing effect Sum degree matrix correction term And the system damping matrix correction term considering friction. With stiffness matrix correction term ; ; ; ; ; ; ; In the formula, This is the displacement column vector of the gear meshing unit. This is the velocity column vector of the gear meshing unit. This is the meshing stiffness coefficient per unit length of the contact line. dl is the meshing damping coefficient per unit length of the contact line, and dl is the length of the contact element. The driving gear direction determination coefficient is denoted by W, where W is the contact line length of the helical gear at time t. The time-varying meshing stiffness per unit length of contact line. The time-varying meshing damping is the unit length of the contact wire; This leads to the stiffness matrix of the gear meshing element after considering tooth surface roughness correction. With damping matrix ; ; .

[0012] Furthermore, in step S2, the time-varying meshing stiffness The calculation steps are as follows: First, introduce the tooth surface roughness. Calculate its fractal dimension D and fractal roughness G: ; ; Then, based on the MB fractal contact model, the contact stiffness after tooth surface roughness correction is obtained. : ; In the formula, Let ψ be the surface contact coefficient, and ψ be the spread factor. This represents the actual contact area of ​​the micro-protrusion. This is a dimensionless number representing the actual contact area of ​​the micro-protrusion. is the dimensionless number of the critical contact area of ​​the micro-protrusion; Finally, the contact stiffness after tooth surface roughness correction By replacing the original Hertzian contact stiffness, the time-varying meshing stiffness of the gear pair can be obtained. : ; In the formula, , , , The following are, in order: bending stiffness, shear stiffness, radial compressive stiffness, and matrix deformation stiffness of the driving wheel. , , , The following are, in order: bending stiffness, shear stiffness, radial compressive stiffness, and matrix deformation stiffness of the driven wheel.

[0013] Furthermore, in step S3, the differential equations of motion of the ship propulsion shaft system considering tooth surface roughness are solved iteratively using the Newmark time-domain method.

[0014] Furthermore, in step S4, by using a preset roughness, the vibration characteristics of all ship propulsion shaft system nodes under this roughness can be obtained under steady-state time variation curves. Several nodes of interest are selected, and by calculating the vibration characteristics of each node under several sets of roughness under steady-state time variation curves, and according to the set weight of each node, the vibration characteristics of each node under different roughness are synthesized, and finally the roughness-vibration characteristic comprehensive variation curve considering all nodes of interest is obtained. With the goal of minimizing the maximum, minimum, mean, and peak values ​​of the comprehensive vibration displacement, vibration velocity, and vibration acceleration of these nodes, the roughness range that meets the low vibration design of the ship propulsion shaft system can be obtained through the roughness-vibration characteristic comprehensive variation curve, and thus the required tooth surface roughness can be obtained.

[0015] After adopting the above solution, the beneficial effects of the present invention are as follows: First, this invention establishes a first differential equation of motion for the ship propulsion shafting without considering the gear meshing unit. Simultaneously, it calculates relevant parameters of the gear meshing unit by introducing tooth surface roughness. Then, it incorporates these parameters into the first differential equation of motion for the ship propulsion shafting, establishing the dynamic coupling relationship of the shafting system and refining the differential equation of motion. A second differential equation of motion for the ship propulsion shafting is then established under tooth surface roughness correction, allowing tooth surface roughness to be incorporated into the vibration calculation of the ship propulsion shafting. This enables the calculation of the time-varying vibration characteristics of each node in the ship propulsion shafting, including the influence of tooth surface roughness, under steady-state conditions. Furthermore, guided by low vibration of the ship propulsion shafting, it matches vibration characteristics to obtain tooth surface roughness values ​​that meet vibration conditions. This allows for the computational transmission of tooth surface excitation and the system response of the shafting, adapting to different application scenarios by calculating corresponding tooth surface roughness value ranges, reducing gear tooth surface machining costs. This approach reduces the cost of gear tooth surface machining while lowering the mid-to-high frequency vibration of the ship propulsion shafting in the gear meshing section and improving the reliability and stability of the ship propulsion shafting operation.

[0016] Secondly, this invention can accurately calculate the relationship between tooth surface roughness and stable operation of the propulsion shaft system, thereby obtaining the influence of tooth surface roughness on the entire ship propulsion shaft system. It can simultaneously take into account calculation accuracy and solution efficiency, and accurately reflect the vibration of the ship propulsion shaft system. Attached Figure Description

[0017] Figure 1 This is a schematic diagram of the surface morphology of the gear meshing contact surface according to the present invention.

[0018] Figure 2 This is a finite node model diagram of the ship propulsion shafting system of the present invention.

[0019] Figure 3 This is a graph showing the roughness-vibration characteristics at the node of interest in the ship propulsion shafting of this invention. Detailed Implementation

[0020] The present invention will be described in detail below with reference to the accompanying drawings and specific embodiments.

[0021] like Figures 1-3 As shown, this invention provides a low-vibration design method for ship propulsion shafting that considers tooth surface roughness, comprising the following steps: S1. The finite node method is used to perform structural analysis on the ship propulsion shaft system. The ship propulsion shaft system is divided into connection units, bearing units, shaft segment units and gear meshing units. The ship propulsion shaft system includes a rotating shaft. Taking the rotating shaft as the unit, the first ship propulsion shaft system motion differential equation excluding the gear meshing unit is established. The first ship propulsion shaft system motion differential equation only includes connection units, bearing units and shaft segment units. S2, introduce tooth surface roughness to calculate the relevant parameters of the gear meshing unit, including tooth surface meshing force, tooth surface friction force, stiffness matrix and damping matrix, and calculate the mass matrix of the gear meshing unit; S3. The relevant parameters and mass matrix of the gear meshing unit in step S2 are introduced into the first ship propulsion shaft system motion differential equation in step S1 to establish the dynamic coupling relationship of each shaft under the action of tooth surface roughness, obtain the second ship propulsion shaft system motion differential equation after tooth surface roughness correction, and solve the vibration characteristics of each node of the ship propulsion shaft system under steady state time variation curve. S4. Given different preset tooth surface roughness values, the roughness-vibration characteristic comprehensive change curve is obtained through steps S1 to S3, and analyzed to obtain the roughness range that meets the predetermined vibration characteristic target value.

[0022] Key points combined Figure 2As shown in the finite node model diagram, the middle part is a simplified diagram of the shaft system. A represents a gear meshing unit, consisting of a driving gear and a driven gear meshing together. B represents the motor, and C represents the load. There are two sets of gear meshing units, located on the left and right sides of the shaft system, respectively. Each gear meshing unit includes two nodes: a driving gear and a driven gear. The two sets of gear meshing units connect three different shaft assemblies. Each shaft assembly has multiple nodes and contains multiple shafts, divided into connecting units, bearing units, and shaft segment units. A shaft segment unit represents the shaft between two nodes. The connecting unit corresponds to the driving and driven ends of the coupling, used to connect the shafts. The bearing unit specifically represents bearings used to support the shafts. Figure 2 The upper and lower parts are schematic diagrams of the corresponding areas of the rotating shaft assembly decomposed using the finite node method. Each unit is represented by a corresponding legend, such as red dots representing nodes, yellow double columns representing connection units, blue triangles representing bearing units, green lines representing shaft segment units, and black I representing gear meshing units.

[0023] In step S1, the mass matrix, stiffness matrix, and damping matrix of each unit except the gear meshing unit are first established. These matrices are used to establish the differential equations of motion for each shaft system. The differential equations of motion for the first ship propulsion shaft system only include connecting units, bearing units, and shaft segment units, and do not include gear meshing units. Establishing the differential equations of motion for the first ship propulsion shaft system excluding gear meshing units includes the following steps: S101, first establish the differential equations of motion for the shaft system of each rotating shaft, including connecting units, bearing units, and shaft segment units. The differential equations of motion for the shaft system of each rotating shaft are as follows: ; ; ; In the formula, For the mass matrix of each axis, The damping matrix of each rotating shaft, Here are the stiffness matrices for each axis of rotation. ( () represents the excitation column vectors for each axis of rotation. For the acceleration of each rotating shaft, For the speed of each rotating shaft, These are the displacement column vectors for each axis of rotation; S102, then arrange the differential equations of motion of each shaft system in step S101 in sequence, and arrange them in matrix form along the main diagonal to obtain the first differential equation of motion of the ship propulsion shaft system: .

[0024] In this specific embodiment, the bearing unit and the connecting unit do not consider the mass matrix, while the shaft segment unit includes the mass matrix. Stiffness matrix and damping matrix The bearing unit includes the stiffness matrix. and damping matrix The connection element includes a stiffness matrix. and damping matrix .

[0025] In step S2, tooth surface roughness is first introduced to calculate the time-varying meshing stiffness of the gear meshing unit. Time-varying friction coefficient of tooth surface Furthermore, through time-varying meshing stiffness Time-varying friction coefficient of tooth surface To calculate the meshing force on the tooth surface Tooth surface friction The system damping matrix correction term and system stiffness matrix correction term are respectively considered for meshing and friction. Finally, the stiffness matrix and damping matrix after tooth surface roughness correction are obtained through the system damping matrix correction term and system stiffness matrix correction term.

[0026] In step S2, the method for calculating the relevant parameters of the gear meshing unit is as follows: The time-varying friction coefficient is obtained by using the oil film shear stress τ(t) at time t and the normal contact load P(t) of a single micro-protrusion. : ; Figure 1 D represents the peak average line of the micro-convexity; Assume that at time t, the displacement projection column vector generated by each degree of freedom displacement component along the contact line is... The projected column vector of the frictional forces generated along the contact line for each degree of freedom is: The meshing force of the tooth surface under the action of tooth surface roughness is obtained. Tooth surface friction The system damping matrix correction term considering meshing effect and system stiffness matrix correction terms And the system damping matrix correction term considering friction. With system stiffness matrix correction terms ; ; ; ; ; ; ; In the formula, This is the displacement column vector of the gear meshing unit. This is the velocity column vector of the gear meshing unit. This is the meshing stiffness coefficient per unit length of the contact line. dl is the meshing damping coefficient per unit length of the contact line, and dl is the length of the contact element. The driving gear direction determination coefficient is denoted by W, where W is the contact line length of the helical gear at time t. The time-varying meshing stiffness per unit length of contact line. The time-varying meshing damping is the unit length of the contact wire; This leads to the stiffness matrix of the gear meshing element after considering tooth surface roughness correction. With damping matrix ; ; .

[0027] In step S2, time-varying meshing stiffness The calculation steps are as follows: First, introduce the tooth surface roughness. Calculate its fractal dimension D and fractal roughness G: ; ; Then, based on the MB (Majumdar-Bhushan) fractal contact model, the contact stiffness after tooth surface roughness correction is obtained. : ; In the formula, Let ψ be the surface contact coefficient, and ψ be the spread factor. This represents the actual contact area of ​​the micro-protrusion. This is a dimensionless number representing the actual contact area of ​​the micro-protrusion. is the dimensionless number of the critical contact area of ​​the micro-protrusion; Finally, the contact stiffness corrected for tooth surface roughness is... By replacing the original Hertzian contact stiffness, the time-varying meshing stiffness of the gear pair can be obtained. : ; In the formula, , , , The following are, in order: bending stiffness, shear stiffness, radial compressive stiffness, and matrix deformation stiffness of the driving wheel. , , , The following are, in order: bending stiffness, shear stiffness, radial compressive stiffness, and matrix deformation stiffness of the driven wheel.

[0028] In step S2, the nodal displacement column vector of the gear meshing unit for: ; The mass matrix of the gear meshing unit is: ; In the formula, Mass of the main gear For the mass of the driven gear, The driving gear and the driven gear are respectively wound around x , y , z Rotational mass of the shaft.

[0029] In step S3, establishing the dynamic coupling relationship includes the following steps: S301, the mass matrix of the gear meshing unit Stiffness matrix under the influence of tooth surface roughness With damping matrix It is decomposed into four submatrices of the same size. The decomposition process is as follows: ; ; ; S302, the mass matrix in step S301 Stiffness matrix With damping matrix Based on the meshing relationship, the mass matrix is ​​embedded into the overall mass matrix, stiffness matrix, and damping matrix of the ship's propulsion shafting system (excluding the meshing relationship) to obtain the mass matrix corrected for tooth surface roughness. Stiffness matrix Damping matrix ; Key points combined Figure 2 As shown, taking the stiffness matrix of the gear meshing unit on the left as an example, its driving and driven gear meshing nodes are node 11 and node 19, respectively. This gear meshing unit connects shaft 1 and shaft 2. Since each node in this model has six degrees of freedom, the stiffness matrix is... submatrix in The submatrix is ​​synthesized to the positions of rows 61-66 and columns 61-66 in the overall stiffness matrix of the ship's propulsion shaft system. The submatrix is ​​synthesized to the positions of rows 61-66 to columns 109-114 in the overall stiffness matrix of the ship's propulsion shaft system. The submatrix is ​​synthesized to positions 109-114 and 61-66 in the overall stiffness matrix of the ship's propulsion shaft system. The components are synthesized into rows 109-114 and columns 109-114 of the overall stiffness matrix of the ship's propulsion shaft system to establish the dynamic coupling relationship between shaft 1 and shaft 2 under the action of tooth surface roughness. Similarly, the mass matrix is ​​synthesized into the matrix. With damping matrix The system stiffness matrix of the propulsion shafting is synthesized into the system stiffness matrix, thereby realizing the system stiffness and damping correction considering tooth surface roughness. This establishes the dynamic coupling relationship of each shaft under the action of tooth surface roughness. Furthermore, based on the excitation of the ship's power system, tooth surface meshing force is introduced. As a meshing excitation, tooth surface friction is introduced. As a frictional excitation and and According to the arrangement and synthesis of the corresponding action nodes and degrees of freedom, the total excitation column vector of the ship propulsion shaft system is obtained. Therefore, the differential equation of motion for the second ship propulsion shafting after correction for tooth surface roughness is: ; Among them, the ship's power system excitation includes diesel engine excitation and propeller excitation. The diesel engine is used to provide energy for the continuous rotation of the propeller. After the propeller receives the mechanical energy provided by the diesel engine, it converts the rotational mechanical energy into thrust to propel the ship forward by stirring the water flow. This will not be elaborated in detail.

[0030] In the formula, Let be the inertia matrix of the i-th node. , Let be the inertial quantum matrix of the i-th gear pair. Let be the damping matrix of the i-th node. Let be the relative damping matrix between the i-th and j-th nodes. , , , Let be the damping submatrix of the i-th gear pair. Let be the stiffness matrix between the i-th and j-th nodes. , , , Let be the stiffness submatrix of the i-th gear pair. Let the excitation force be at the i-th node. , These are the meshing excitation and friction excitation of the i-th gear pair, respectively. , , These are the vibration acceleration, vibration velocity, and vibration displacement column vectors of the i-th node, respectively.

[0031] Simplifying the above formula yields: ; In the formula, Let this be the column vector of vibration accelerations of the ship's propulsion shafting. Let V be the vibration velocity column vector of the ship's propulsion shafting. This is the column vector of vibration displacements of the ship's propulsion shaft system.

[0032] The Newmark time-domain method is used to iteratively solve the differential equations of motion for the second ship propulsion shaft system until the system reaches a steady state. This yields the vibration characteristics of the ship propulsion shaft system considering tooth surface roughness, including vibration displacement, velocity, and acceleration. The Newmark time-domain method involves initial calculations followed by calculations of displacement, velocity, and acceleration at each time step. The specific steps are as follows: Step 1, Initial Calculation, includes the following steps; S311, forming the mass matrix M Damping matrix C and stiffness matrix K ; S312, given initial displacement Initial velocity and initial acceleration ; S313, Select Time Step t Newmark coefficients α and β And calculate the integration constant: ; S314, forming an effective stiffness matrix: ; S315, Perform triangular decomposition on the effective stiffness matrix: ; Step 2: Calculate the displacement, velocity, and acceleration at each time step, including the following steps; S321, Calculation Time Effective payload: ; S322, Solution Time Displacement: ; S323, Calculation Time acceleration and velocity: ; ; In step S4, given a roughness, the vibration characteristics of all ship propulsion shaft system nodes under steady-state time variation curves can be obtained. Several nodes of interest are selected, and the vibration characteristics of each node under steady-state time variation curves under several sets of roughness are calculated. Based on the set weights of each node, the vibration characteristics of each node under different roughness are synthesized, and finally, a roughness-vibration characteristic comprehensive variation curve considering all nodes of interest is obtained. The weight coefficients are set according to the vibration magnitude of each node in the system or the attention to different vibration positions. The total weight coefficients are 1. Generally, the larger the vibration and the higher the attention, the larger the weight coefficient of the node position. With the goal of minimizing the maximum, minimum, mean, and peak values ​​of the comprehensive vibration displacement, vibration velocity, and vibration acceleration of the selected nodes of interest, the roughness range that meets the low vibration design of the ship propulsion shaft system can be obtained through the roughness-vibration characteristic comprehensive variation curve, and thus the required tooth surface roughness can be obtained.

[0033] In this specific embodiment, roughness is set to 0.4µm, 0.8µm, 1.6µm, and 3.2µm. The vibration characteristics of each node under steady state change over time are calculated for each roughness. Finally, the roughness-vibration characteristic change curves of each node are obtained. Node 7 at the input end bearing of the reduction gearbox input shaft of the ship's propulsion shaft system and node 17 at the end cover bearing of the reduction gearbox output shaft are selected as nodes of interest. A weighting coefficient for node 7 is set. The weight coefficient of node 17 is 0.6. The value is 0.4. The torsional vibration amplitude at the meshing frequency is synthesized according to the following formula with weights: ; In the formula, This represents the combined amplitude of torsional vibration at the meshing frequency. The torsional amplitude at the meshing frequency of node 7. The torsional amplitude value at the meshing frequency of node 17.

[0034] Key points combined Figure 3As shown, with the goal of minimizing the comprehensive amplitude of torsional vibration at the meshing frequency of the focus node, the roughness-vibration characteristic curve shows that in this ship propulsion shafting, as the tooth surface roughness increases, the torsion angle at the meshing frequency first increases and then decreases. Therefore, in order to reduce the impact of torsional vibration and reduce the vibration at the target position of the ship propulsion shafting, while also considering economy, the tooth surface roughness Ra of the ship propulsion shafting in this example should be controlled to be approximately 1.6 to 3.2 μm to allow for gear manufacturing accuracy adjustments during the manufacturing stage.

[0035] The above description is only a preferred embodiment of the present invention and is not intended to limit the design of this case. All equivalent changes made based on the key design features of this case shall fall within the protection scope of this case.

Claims

1. A low-vibration design method for ship propulsion shafting considering tooth surface roughness, characterized in that: Includes the following steps: S1. Perform structural analysis on the ship propulsion shafting system. Divide the ship propulsion shafting system into connection units, bearing units, shaft segment units and gear meshing units. The ship propulsion shafting system includes a rotating shaft. Using the rotating shaft as the unit, establish the first ship propulsion shafting motion differential equation excluding the gear meshing unit. The first ship propulsion shafting motion differential equation only includes connection units, bearing units and shaft segment units. S2, introduce tooth surface roughness to calculate the relevant parameters of the gear meshing unit, including tooth surface meshing force, tooth surface friction force, stiffness matrix and damping matrix, and calculate the mass matrix of the gear meshing unit; S3. Introduce the relevant parameters and mass matrix of the gear meshing unit in step S2 into the first ship propulsion shaft system motion differential equation in step S1 to establish the dynamic coupling relationship of each shaft under the action of tooth surface roughness, obtain the second ship propulsion shaft system motion differential equation after tooth surface roughness correction, and solve to obtain the time variation curve of the vibration characteristics of each node of the ship propulsion shaft system under steady state. S4. Given different preset tooth surface roughness values, the roughness-vibration characteristic comprehensive change curve is obtained through steps S1 to S3, and analyzed to obtain the roughness range that meets the predetermined vibration characteristic target value.

2. The low-vibration design method for ship propulsion shafting considering tooth surface roughness as described in claim 1, characterized in that: In step S1, the finite node method is used to perform structural analysis on the ship's propulsion shafting, and the mass matrix, stiffness matrix, and damping matrix of each unit excluding gear meshing units are established. The first ship propulsion shafting motion differential equation excluding gear meshing units includes the following steps: S101, Establish the differential equations of motion for each shaft system. Each shaft includes connecting elements, bearing elements, and shaft segment elements. The differential equations of motion for each shaft system are as follows: ； ； ； In the formula, For the mass matrix of each axis, The damping matrix of each rotating shaft, Here are the stiffness matrices for each axis of rotation. ( () represents the excitation column vectors for each axis of rotation. For the acceleration of each rotating shaft, For the speed of each rotating shaft, These are the displacement column vectors for each axis of rotation; S102, then arrange the differential equations of motion of each shaft system in step S101 in sequence, and arrange them in matrix form along the main diagonal to obtain the first differential equation of motion of the ship propulsion shaft system: 。 3. The low-vibration design method for ship propulsion shafting considering tooth surface roughness as described in claim 2, characterized in that: In step S1, the bearing unit and the connecting unit do not consider the mass matrix, while the shaft segment unit includes the mass matrix. Stiffness matrix and damping matrix The bearing unit includes the stiffness matrix. and damping matrix The connection element includes a stiffness matrix. and damping matrix .

4. The low-vibration design method for ship propulsion shafting considering tooth surface roughness as described in claim 1, characterized in that: In step S2, the gear meshing unit includes two nodes: the driving gear and the driven gear. The nodal displacement column vector of the gear meshing unit... for: ； Mass matrix of gear meshing unit for: ； In the formula, Mass of the main gear For the mass of the driven gear, The driving gear and the driven gear are respectively wound around x , y , z Rotational mass of the shaft.

5. The low-vibration design method for ship propulsion shafting considering tooth surface roughness as described in claim 1, characterized in that: In step S3, establishing the dynamic coupling relationship includes the following steps: S301, the mass matrix of the gear meshing unit Stiffness matrix under the influence of tooth surface roughness With damping matrix It is decomposed into four submatrices of the same size. The decomposition process is as follows: ； ； ； S302, the mass matrix in step S301 Stiffness matrix With damping matrix Based on the meshing relationship, the mass matrix is ​​embedded into the overall mass matrix, stiffness matrix, and damping matrix of the ship's propulsion shafting system (excluding the meshing relationship) to obtain the mass matrix corrected for tooth surface roughness. Stiffness matrix Damping matrix ; Based on the excitation of the ship's power system, tooth surface meshing force is introduced. As a meshing excitation, and to introduce tooth surface friction. As a frictional excitation, and and According to the arrangement and synthesis of the corresponding action nodes and degrees of freedom, the total excitation column vector of the ship propulsion shaft system is obtained. This leads to the second ship propulsion shaft system motion differential equation after correction for tooth surface roughness: ； In the formula, Let this be the column vector of vibration accelerations of the ship's propulsion shafting. Let V be the vibration velocity column vector of the ship's propulsion shafting. This is the column vector of vibration displacements of the ship's propulsion shaft system.

6. The low-vibration design method for ship propulsion shafting considering tooth surface roughness as described in claim 1, characterized in that: In step S2, the tooth surface roughness is first introduced to calculate the time-varying meshing stiffness and the time-varying friction coefficient of the gear meshing unit. Then, the tooth surface meshing force and tooth surface friction force are calculated using the time-varying meshing stiffness and the time-varying friction coefficient, as well as the system damping matrix correction term and system stiffness matrix correction term considering the meshing effect and friction effect respectively. Finally, the stiffness matrix and damping matrix after tooth surface roughness correction are obtained using the system damping matrix correction term and system stiffness matrix correction term.

7. The low-vibration design method for ship propulsion shafting considering tooth surface roughness as described in claim 6, characterized in that: In step S2, the time-varying friction coefficient can be obtained by using the oil film shear stress τ(t) at time t and the normal contact load P(t) of a single micro-protrusion. : ； Assume that at time t, the displacement projection column vector generated by each degree of freedom displacement component along the contact line is... The projected column vector of the frictional forces generated along the contact line for each degree of freedom is: The meshing force of the tooth surface under the action of tooth surface roughness is obtained. Tooth surface friction The system damping matrix correction term considering meshing effect Sum degree matrix correction term And the system damping matrix correction term considering friction. With stiffness matrix correction terms ; ； ； ； ； ； ； In the formula, This is the displacement column vector of the gear meshing unit. This is the velocity column vector of the gear meshing unit. This is the meshing stiffness coefficient per unit length of the contact line. dl is the meshing damping coefficient per unit length of the contact line, and dl is the length of the contact element. The driving gear direction determination coefficient is denoted by W, where W is the contact line length of the helical gear at time t. The time-varying meshing stiffness per unit length of contact line. The time-varying meshing damping is the unit length of the contact wire; This leads to the stiffness matrix of the gear meshing element after considering tooth surface roughness correction. With damping matrix ; ； 。 8. The low-vibration design method for ship propulsion shafting considering tooth surface roughness as described in claim 6, characterized in that: In step S2, time-varying meshing stiffness The calculation steps are as follows: First, introduce the tooth surface roughness. Calculate its fractal dimension D and fractal roughness G: ； ； Then, based on the MB fractal contact model, the contact stiffness after tooth surface roughness correction is obtained. : ； In the formula, Let ψ be the surface contact coefficient, and ψ be the spread factor. This represents the actual contact area of ​​the micro-protrusion. This is a dimensionless number representing the actual contact area of ​​the micro-protrusion. is the dimensionless number of the critical contact area of ​​the micro-protrusion; Finally, the contact stiffness after tooth surface roughness correction By replacing the original Hertzian contact stiffness, the time-varying meshing stiffness of the gear pair can be obtained. : ； In the formula, , , , The following are, in order: bending stiffness, shear stiffness, radial compressive stiffness, and matrix deformation stiffness of the driving wheel. , , , The following are, in order: bending stiffness, shear stiffness, radial compressive stiffness, and matrix deformation stiffness of the driven wheel.

9. The low-vibration design method for ship propulsion shafting considering tooth surface roughness as described in claim 1, characterized in that: In step S3, the differential equations of motion of the ship propulsion shaft system considering tooth surface roughness are solved iteratively using the Newmark time-domain method.

10. The low-vibration design method for ship propulsion shafting considering tooth surface roughness as described in claim 1, characterized in that: In step S4, by using a preset roughness, the vibration characteristics of all ship propulsion shaft system nodes under steady state time variation curves can be obtained. Several nodes of interest are selected, and by calculating the vibration characteristics of each node under steady state time variation curves under several sets of roughness, and according to the set weight of each node, the vibration characteristics of each node under different roughness are synthesized, and finally the roughness-vibration characteristic comprehensive variation curve considering all nodes of interest is obtained. With the goal of minimizing the maximum, minimum, mean, and peak values ​​of the comprehensive vibration displacement, vibration velocity, or vibration acceleration of these nodes, the roughness range that meets the low vibration design of the ship propulsion shaft system can be obtained through the roughness-vibration characteristic comprehensive variation curve, and thus the required tooth surface roughness can be obtained.

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