ISGA-III-based matching optimization method for ship shock absorbers in ice region

Abstract

The invention discloses an ice region ship shock absorber matching optimization method based on NSGA-III, which comprises the following steps: establishing a motor-silicone oil shock absorber-shafting-propeller coupling system kinetic model, calculating transient torsional vibration response under ice load impact by adopting a Newmark-beta method, and constructing a multi-target optimization model by taking the outer diameter, thickness, side clearance and top clearance of a shock absorber as design variables; an initial population is generated in combination with Latin hypercube sampling, and an optimal parameter combination is obtained after iterative optimization is conducted through an NSGA-III algorithm; experimental data show that the torsional vibration stresses of the motor shaft, the 1 # intermediate shaft, the 2 # intermediate shaft and the propeller shaft of the optimized shock absorber at the rated rotating speed are respectively reduced by 18.0%, 11.1%, 11.8% and 17.7%, and the effectiveness of the method is verified.

Description

Technical Field

[0001] The present invention relates to the technical field of vibration control of ship power plants, and in particular to a matching optimization method for ship shock absorbers in ice areas based on an NSGA-III algorithm. Background Art

[0002] In the design of ship propulsion systems operating in ice-covered areas, controlling shafting torsional vibrations is a core technical challenge for ensuring navigation safety. Dynamic contact between the propeller and the ice induces random impact loads. These loads are transient and broadband, easily inducing multimodal vibration coupling in the shafting system. This can lead to serious safety hazards such as excessive shafting torsional stress, bearing damage, and even shafting fracture.

[0003] The traditional parameter optimization method of silicone oil shock absorbers for ships in ice areas faces inherent limitations in two dimensions when dealing with such complex working conditions.

[0004] First, existing optimization strategies often focus on a single objective. In engineering practice, reducing the torsional stress of the motor shaft is generally the sole optimization goal. Local performance improvements are achieved by adjusting parameters such as the outer diameter and side clearance of the vibration damper, but the chain reaction effects of such adjustments on the dynamic response of the intermediate shaft and propeller shaft are ignored. This single-dimensional optimization logic leads the parameter matching process into a dilemma of "giving priority to one thing and losing another." For example, reducing motor shaft stress by increasing the outer diameter of the vibration damper may lead to increased stress on the intermediate shaft or propeller shaft, and even induce resonance, making it difficult to achieve coordinated stability of the overall dynamics of the shaft system.

[0005] Second, the dynamic modeling of ice loads is oversimplified. The mainstream approach equates random propeller-ice collisions with periodic excitations of constant amplitude. However, in real ice conditions, the amplitude and frequency of impact loads exhibit strong non-steady-state characteristics. These idealized assumptions lead to a deviation between the simulation model and the physical mechanisms of actual ship conditions. This makes it difficult for the optimized parameters to effectively suppress broadband vibration energy transfer in practical applications, limiting the engineering value of the design solution. Summary of the Invention

[0006] The purpose of the present invention is to provide an optimization method for matching vibration dampers for ships in ice regions based on the NSGA-III algorithm, so as to solve the engineering problems of excessive torsional vibration stress of the shafting under ice load impact and insufficient parameter optimization of traditional single-objective vibration dampers.

[0007] The technical solution adopted by the present invention to solve the technical problem is: a method for optimizing the matching of shock absorbers of ships in ice areas based on NSGA-III, comprising the following steps:

[0008] Step 1: Establish a dynamic model of the motor-silicone oil vibration absorber-shafting-propeller coupling system including a lumped parameter model, an ice load excitation model, a propeller torque excitation model, a motor torque excitation model, and a vibration absorber model; the steps of constructing the lumped parameter model are as follows: based on the shafting drawings and structural parameters of the ship to be analyzed, the shafting of the propulsion system is divided into M shaft segments and N mass blocks according to the cross-sectional characteristics, and the dynamic characteristics of components such as propellers, silicone oil vibration absorbers, and connectors are integrated, and the mass block moment of inertia parameter J is used. i (i=1,2,…,N) represents the moment of inertia of the shaft segment between the i-th and i+1-th segments, and the shaft segment stiffness parameter k is calculated based on the shaft segment geometric parameters and material properties. i (i=1,2,…,M) and internal and external damping parameters C ii 、C ei (i=1,2,…,M), and obtain the system dynamics equation of the coupled system Where J, C, and K are the inertia, damping, and stiffness matrices of the shaft segment, respectively. θ t are torsional angular acceleration, angular velocity, and angular displacement, respectively. T(t) is the vector synthesis of ice load excitation, propeller torque excitation, and motor torque excitation acting on the corresponding mass point, and t is time. At the same time, the total excitation vector is synthesized according to the ice load excitation model, propeller torque excitation model, and motor torque excitation model. At the same time, the structural parameter constraints of the vibration absorber model are applied.

[0009] Step 2: Solve the transient torsional vibration response: Import the above-mentioned coupled system dynamic model parameters into ANSYS APDL software to establish a finite element model, and solve the system dynamic equations using the Newmark-β method to obtain the transient torsional vibration response under ice load impact;

[0010] Step 3: Construct a multi-objective optimization model for the shock absorber and define the design variables and objective function: select the outer diameter R0, total thickness B1, and side clearance h of the silicone oil shock absorber inertia ring. R 、Top gap h g As the optimization design variables, the variable range of the optimization parameters of the silicone oil shock absorber is defined as follows: the outer diameter of the inertia ring of the silicone oil shock absorber R0∈(225.26, 425.68) mm; the total thickness B1∈(15.63, 30.53) mm; the side clearance h R ∈(0.4, 1.0) mm; top clearance h g ∈(0.5, 1.2) mm; the objective function is constructed as the weighted shaft stress of the shock absorber Where T m 、T p 、T s Respectively represent the motor shaft, propeller shaft, and 2# intermediate shaft iteration j times, r m 、r p 、r sRespectively represent the radius of the motor shaft, propeller shaft, and 2# intermediate shaft, J m 、J p 、J s Respectively represent the polar inertia moment of the motor shaft, propeller shaft, and 2# intermediate shaft, ω m 、ω p 、ω s Represents the weight factor, the value range is [0, 1], and satisfies ω m +ω p +ω s =1;

[0011] Step 4: Generate an initial population based on Latin hypercube sampling, use the NSGA-III algorithm to perform multi-objective iterative optimization on the shock absorber model parameters, and output the optimal parameter combination;

[0012] Step 5: Verify the performance of the optimized shock absorber.

[0013] Furthermore, the propulsion system shafting in step 1 sequentially includes a motor, a vibration damper, a first connector, a second connector, a third connector, a first connector, a fourth connector, and a propeller. The sections between the first connector and the second connector, and between the second connector and the second connector, serve as the front and rear halves of the second connector, respectively. The sections between the third connector and the first connector, and between the first connector and the fourth connector, serve as the front and rear halves of the first connector, respectively. The connectors include a highly elastic coupling and a hydraulic coupling. When constructing the lumped parameter model, shaft segment parameters are first extracted: the inner and outer diameters, length, material density, and elastic modulus of each shaft segment are measured, and the shear stiffness and moment of inertia are calculated. Then, the auxiliary structure parameters are integrated to obtain key parameters such as the dynamic torsional stiffness of the highly elastic coupling and the polar moment of inertia of the hydraulic coupling. The torsional stiffness of each shaft segment is determined by measuring the geometric dimensions (inner and outer diameters, length), material properties (density, elastic modulus) of the shaft segment, and calculating the shear stiffness and polar moment of inertia. The dynamic torsional stiffness and polar moment of inertia of the connector are then obtained.

[0014] Furthermore, the following simplification principles are followed when constructing the lumped parameter model:

[0015] Components with significant rotational inertia, such as the motor, shock absorber, propeller, and various connecting parts, are simplified as concentrated mass points at their centers of gravity. Intermediate shafts 1 and 2 were originally segments with continuously distributed inertia. In the model, a concentrated mass point is set in the middle of each segment to represent the torsional inertia of the entire segment. The torsional stiffness of the segments is simplified as elastic connections concentrated between the mass points, that is, every two adjacent mass points are connected by equivalent torsional stiffness. Among them, the first connecting part provides the first half of the torsional stiffness of the first half of the intermediate shaft 2 from the torsional inertia portion of the intermediate shaft 2; the second connecting part provides the second half of the torsional stiffness of the second half of the intermediate shaft 2 from the torsional inertia portion of the intermediate shaft 2 to the second connecting part; the third connecting part provides the first half of the torsional stiffness of the first half of the intermediate shaft 1 from the torsional inertia portion of the intermediate shaft 1; and the second connecting part provides the second half of the torsional stiffness of the second half of the intermediate shaft 1 from the torsional inertia portion of the intermediate shaft 1 to the fourth connecting part.

[0016] Furthermore, in step 1, a piecewise function is used to characterize the blade-ice contact, and the ice load excitation model established is: In the formula is the rotation angle (°) when the ice block first impacts, α i is the continuous rotation angle of the blade-ice interaction (°), C q is the shock amplification factor, Q max is the design load torque (kN·m), and the calculation formula for the design load torque of a polar ship using an open propeller is: Where k open is the open propeller coefficient, d is the hub outer diameter (m), P 0.7 is the pitch of the propeller at 0.7R (m), n is the bollard speed (r / min), D limit =1.8H ice , is the critical value of propeller diameter (m), D is the propeller diameter (m), H ice The maximum ice thickness (m) is determined by the ice class notation of each classification society.

[0017] Furthermore, the propeller torque excitation model in step 1 is obtained by expanding the propeller torque excitation torque into a Fourier series form with the propeller blade frequency as the base frequency through the formula: Where T p is the propeller excitation torque (N·m), T p0 is the average torque of the propeller (N·m), Z p is the number of propeller blades, v is the harmonic order, For vZ p The propeller torque excitation torque amplitude of the harmonic, ω is the angular frequency, For vZ p The phase angle between the harmonic excitation torque and the blade centerline, the propeller average torque Tp0 , the calculation formula for propeller torque corresponding to different speeds is: Where P pe is the propeller power (kW), n pe is the rated speed of the propeller (r / min), n pc is the propeller speed (r / min).

[0018] Furthermore, the motor torque excitation model established in step 1 is: when the motor speed drops to a specific threshold due to ice load impact, the motor switches from constant power mode to constant torque mode, and the motor torque excitation formula is Where Δn is the velocity change within the time step Δt (r / s), Δt is the solution time step (s); T engine is the motor torque excitation (N·m), which is obtained according to the motor torque characteristics under ice load impact; T prop is the propeller average torque (N·m), which is obtained according to the propeller open water torque characteristics; T ice is the propeller ice load torque excitation (N·m), I is the total system inertia including the propeller water inertia (kg·m 2 ).

[0019] Furthermore, the shock absorber model in step 1 is based on the initial parameters of the silicone oil shock absorber, and the outer diameter R2, inner diameter R3, and total thickness B1 (mm) of the inertia ring are simplified to outer diameter R0 (mm), inner diameter R1 (mm), and top clearance h g (mm), side clearance h R Function of (mm): R2=R0-h g , R3=R1+B2+C, B1=B+2h R +2B2.

[0020] Furthermore, the transient torsional vibration calculation in step 2 ignores the harmonic excitation of the motor and only takes its average torque; the rigid shaft model is used to calculate the motor torque excitation, propeller torque excitation and ice load excitation under the impact of ice load, and the formula is used. The speed drop of the propulsion system shafting under ice load impact is calculated, and the motor torque excitation for Newmark-β method loading is obtained.

[0021] Furthermore, the step 4 is specifically as follows:

[0022] a) Initialize the population: Generate 80 sets of initial parameter combinations through optimal Latin hypercube sampling as optimal Latin hypercube samples;

[0023] b) Reference point generation guidance: The Das-Dennis method is used to generate 12 reference points to guide the non-dominated sorting, and the solution set is screened hierarchically according to the objective function value to ensure that the Pareto solution set is evenly distributed;

[0024] c) Selection, crossover, and mutation: Calculate the crowding distance to maintain population diversity and retain diverse individuals;

[0025] d) Non-dominated sorting: Generate a progeny population by simulating binary crossover and polynomial mutation operations; after 50 iterations, converge to the Pareto frontier, output a set of non-inferior solutions, and obtain a Pareto optimal solution set.

[0026] e) Considering the weighted average of the stress reduction amplitudes of the three-axis segments, the optimal comprehensive matching solution is selected from the Pareto solution set based on the weighted comprehensive score.

[0027] The beneficial effects of the present invention are:

[0028] This paper applies the NSGA-III multi-objective optimization algorithm for the first time to the parameter matching of silicone oil vibration dampers on ships in ice areas, establishes a complete dynamic model of the motor-silicone oil vibration damper-shafting-propeller coupling system, and realizes accurate simulation of complex ice load conditions.

[0029] The proposed matching optimization method uses a multi-objective optimization algorithm to systematically optimize the problem of excessive shafting torsional stress and damper parameter matching under ice load impact. After optimization, the torsional stress of the motor shaft, No. 1 intermediate shaft, No. 2 intermediate shaft, and propeller shaft decreased by 18.0%, 11.1%, 11.8%, and 17.7%, respectively. This method breaks through the local optimum of single-objective optimization and better meets the needs of practical engineering applications. BRIEF DESCRIPTION OF THE DRAWINGS

[0030] Figure 1 This is the overall flow chart of the matching optimization method of the present invention;

[0031] Figure 2 Provides a model structure for the time-domain dynamic response calculation of electric propulsion systems;

[0032] Figure 3 This is the algorithm flow chart of NSGA-III of the present invention;

[0033] Figure 4 The comparison diagram of the torsional stress of the motor shaft before and after the shock absorber is added is shown;

[0034] Figure 5 The comparison diagram of torsional stress of 1# intermediate shaft before and after adding shock absorber is shown in Figure 2.

[0035] Figure 6 The comparison diagram of torsional stress of 2# intermediate shaft before and after adding shock absorber is shown;

[0036] Figure 7 This is a comparison diagram of propeller shaft torsional stress before and after adding vibration damper;

[0037] Figure 8 Comparison diagram of motor shaft torsional stress before and after parameter optimization;

[0038] Figure 9 This is a comparison chart of the torsional stress of the 1# intermediate shaft before and after parameter optimization;

[0039] Figure 10 Comparison diagram of torsional stress of 2# intermediate shaft before and after parameter optimization;

[0040] Figure 11 Comparison diagram of propeller shaft torsional stress before and after parameter optimization.

[0041] The figures are marked as follows: 1—motor, 2—shock absorber, 3—first connecting member, 4—2# intermediate shaft torsional inertia portion, 5—second connecting member, 6—third connecting member, 7—1# intermediate shaft torsional inertia portion, 8—fourth connecting member, 9—propeller. DETAILED DESCRIPTION

[0042] The following is combined with Figures 1 to 11 The specific embodiments of the present invention are described with examples so that those skilled in the art can better understand the present invention.

[0043] Reference Figure 1 As shown, the present invention discloses a method for optimizing the matching of shock absorbers of ships in ice areas based on the NSGA-III algorithm, which includes the following steps.

[0044] Step 1: Establish a dynamic model of the motor-silicone oil vibration absorber-shafting-propeller coupling system and calculate the shafting torsional stress.

[0045] The dynamic model of the motor-silicone oil vibration damper-shafting-propeller coupling system established in the above steps includes a lumped parameter model, an ice load excitation model, a propeller torque excitation model, a motor torque excitation model, and a vibration damper model. The lumped parameter model construction steps are as follows: based on the shafting drawings and structural parameters of the ship to be analyzed, the shafting of the propulsion system is divided into M shaft segments and N mass blocks according to the cross-sectional characteristics, and the dynamic characteristics of components such as the propeller, silicone oil vibration damper, and coupling are integrated.

[0046] Reference Figure 2As shown, the propulsion system's shafting, in this order, includes a motor 1, a vibration damper 2, a first connector 3, a second intermediate shaft torsional inertia unit 4, a second connector 5, a third connector 6, a first intermediate shaft torsional inertia unit 7, a fourth connector 8, and a propeller 9. The section between the first connector 3 and the second intermediate shaft torsional inertia unit 4 forms the front half of the second intermediate shaft, providing torsional stiffness for the front half. The section between the second intermediate shaft torsional inertia unit 4 and the second connector 5 forms the rear half of the second intermediate shaft, providing torsional stiffness for the rear half. The section between the third connector 6 and the first intermediate shaft torsional inertia unit 7 forms the front half of the first intermediate shaft, providing torsional stiffness for the front half. The section between the first intermediate shaft torsional inertia unit 7 and the fourth connector 8 forms the rear half of the first intermediate shaft, providing torsional stiffness for the rear half. The connectors include a highly elastic coupling and a hydraulic coupling. The vibration damper 2 consists of an inertia ring, a housing, bearings, and silicone oil.

[0047] The simplification principle followed when constructing the lumped parameter model is as follows: components with significant rotational inertia, such as the motor 1, vibration absorber 2, propeller 9, and various connecting parts, are simplified to concentrated mass points at their center of gravity; the 1# and 2# intermediate shafts were originally shaft segments with continuously distributed inertia. In the model, a concentrated mass point is set in the middle of each shaft segment to represent the torsional inertia of the entire shaft segment; the torsional stiffness of the shaft segment is simplified to an elastic connection concentrated between the mass points, that is, every two adjacent mass points are connected by equivalent torsional stiffness.

[0048] The specific steps for constructing the lumped parameter model are as follows.

[0049] a) Shaft segment parameter extraction: Measure the inner and outer diameters, length, material density, and elastic modulus of each shaft segment, and calculate the shear stiffness and moment of inertia.

[0050] b) Integration of auxiliary structure parameters: Obtain key parameters such as the dynamic torsional stiffness of the high-elasticity coupling and the polar moment of inertia of the hydraulic coupling.

[0051] The torsional stiffness of each shaft segment is determined by measuring the geometric dimensions (inner and outer diameters, length), material properties (density, elastic modulus) of the shaft segment, and calculating the shear stiffness and polar moment of inertia. The dynamic torsional stiffness and polar moment of inertia of the connector are then obtained.

[0052] In this embodiment, M is 8, N is 20, and the shaft system is divided into 20 mass blocks (J1~J 20 ) and 8 shaft segment stiffness (k1~k8), the moment of inertia of each shaft segment J i , stiffness k i , internal and external damping C ii and C ei It can be calculated by the inner and outer diameters, length and material density of the shaft segment. The mass block moment of inertia parameter J is used. i(i=1,2,…,20) represents the moment of inertia of the shaft segment between the i-th and i+1-th segments, and the shaft segment stiffness parameter k is calculated based on the shaft segment geometric parameters and material properties. i (i=1,2,…,8) and internal and external damping parameters C ii 、C ei (i=1,2,…,8), and the system dynamics equation containing 20 mass blocks is obtained Where J, C, and K are the inertia, damping, and stiffness matrices of the shaft segment, respectively. θ t are torsional angular acceleration, angular velocity, and angular displacement, respectively. T(t) is the vector synthesis of ice load excitation, propeller excitation, and motor torque excitation acting on the corresponding mass point. t is time.

[0053] This step synthesizes the total excitation vector based on the ice load excitation model, the propeller torque excitation model and the motor torque excitation model.

[0054] In this embodiment, a piecewise function is used to characterize the blade-ice contact, and the established ice load excitation model is expressed as In the formula is the rotation angle (°) when the ice block first impacts, α i is the continuous rotation angle of the blade-ice interaction (°), C q is the shock amplification factor, Q max is the design load torque (kN·m). The design load torque of a polar ship using an open propeller is calculated according to the formula: Where k open is the open propeller coefficient, which is 14.7 when the ice class is PC1 to PC5, and 10.9 when the ice class is PC6 to PC7; d is the propeller hub outer diameter (m); P 0.7 is the propeller pitch at 0.7R (m); n is the bollard speed (r / min); D limit =1.8H ice , is the critical value of propeller diameter (m); D is the propeller diameter (m); H ice The maximum ice thickness (m) is designed for and is determined by the ice class notation of each classification society.

[0055] The propulsion system of this embodiment adopts a 5-blade fixed pitch propeller, superimposes the 5 blade torques (considering the phase change of 360° / Z, where Z is the number of propeller blades), and uses a linear ramp function at the beginning and end of the impact process to make C q The value increases to the maximum within one revolution after the propeller starts calculating and decreases to zero within one revolution before the end of the calculation, so that the total ice load torque excitation under each working condition can be obtained.

[0056] In this embodiment, the propeller torque excitation torque is expanded into a Fourier series form with the propeller blade frequency as the base frequency, and the formula is expressed as follows: Where T p is the propeller excitation torque (N·m), T p0 is the average torque of the propeller (N·m), the number of propeller blades Z p =5, v is the harmonic order, For vZ p The propeller torque excitation torque amplitude of the harmonic, ω is the angular frequency, For vZ p The phase angle between the harmonic excitation torque and the blade centerline. The average propeller torque is T p0 , the calculation formula for propeller torque corresponding to different speeds is: Where the propeller receives power P pe =2500kW, rated speed of propeller n pe =120r / min, n pc is the propeller speed (r / min).

[0057] The motor torque excitation model established in this embodiment is: when the motor speed drops to a specific threshold due to ice load impact, the motor switches from constant power mode to constant torque mode. The motor torque excitation formula is: Where Δn is the velocity change within the time step Δt (r / s); Δt is the solution time step (s); T engine is the motor torque excitation (N·m), which is obtained according to the motor torque characteristics under ice load impact; T prop is the propeller average torque (N·m), which is obtained according to the propeller open water torque characteristics; T ice is the propeller ice load torque excitation (N·m); I is the total inertia of the system (kg·m 2 ), including propeller water inertia (kg·m 2 ).

[0058] This step also constrains the structural parameters of the shock absorber model.

[0059] The shock absorber model established in this embodiment is based on the initial parameters of the silicone oil shock absorber. The outer diameter R2, inner diameter R3, and total thickness B1 (mm) of the inertia ring are simplified to outer diameter R0 (mm), inner diameter R1 (mm), and top clearance h g (mm), side clearance h R Function of (mm): R2=R0-h g , R3=R1+B2+C, B1=B+2h R +2B2.

[0060] Step 2: Use the Newmark-β method to solve the system dynamic equations and obtain the transient torsional vibration response under ice load impact.

[0061] In this embodiment, the transient torsional vibration calculation of the electric propulsion shaft system under ice load is performed, ignoring the harmonic excitation of the motor and only taking its average torque. e When operating under ice loads, the motor will experience a significant speed drop if subjected to ice load impact. Within a specific speed range during the speed drop process, the motor operates at constant power. If the speed continues to drop, the motor will operate at constant torque. To accurately calculate the motor torque excitation, propeller torque excitation, and ice load excitation under ice load impact, a rigid shaft model (i.e., a single mass point model) is used. The speed drop Δn of the propulsion shafting under ice load impact is calculated using the formula: The motor torque excitation can be obtained and can be directly used for Newmark-β method loading.

[0062] The transient torsional vibration response solution steps in the above steps are: import the above coupling system dynamic model parameters into ANSYS APDL software to establish a finite element model, and use the Newmark-β method to solve the system dynamic equations. A numerical solution is performed to obtain the transient torsional vibration response under ice load impact. The time step Δt = 0.0014 s corresponds to the time interval for each 1° rotation of the propeller.

[0063] Step 3: Build a multi-objective optimization model for the shock absorber and define the design variables and objective functions.

[0064] The specific method for establishing the multi-objective optimization model of this embodiment is as follows: according to the structural characteristics of the silicone oil shock absorber, the outer diameter R0, the width (total thickness B1), the radial clearance (side clearance h R , axial clearance or top clearance h g As the optimization design variables, the variable ranges of the optimization parameters of the silicone oil vibration absorber are defined as follows.

[0065] The outer diameter of the inertia ring of the silicone oil shock absorber is R0∈(225.26, 425.68) mm.

[0066] Total thickness B1∈(15.63, 30.53) mm.

[0067] Side clearance h R ∈(0.4, 1.0)mm.

[0068] Top gap h g ∈(0.5, 1.2)mm.

[0069] The objective function is constructed as the shock absorber weighted shaft stress Where T m 、Tp 、T s Respectively represent the torque (N·m) of the motor shaft, propeller shaft, and 2# intermediate shaft at the jth iteration (jth step), r m 、r p 、r s Respectively represent the radius of the motor shaft, propeller shaft, and 2# intermediate shaft (m), J m 、J p 、J s Represents the polar inertia moment of the motor shaft, propeller shaft, and 2# intermediate shaft (kg·m 2 ),ω m 、ω p 、ω s Represents the weight factor, the value range is [0,1], and satisfies ω m +ω p +ω s =1. In this embodiment, the weight distribution is ω m =0.5,ω p =0.3,ω s =0.2.

[0070] Step 4: Combine Latin hypercube sampling to generate the initial population, apply the NSGA-III algorithm to perform multi-objective iterative optimization on the shock absorber model parameters, and output the optimal parameter combination.

[0071] The process of the NSGA-III algorithm in the above steps is as follows.

[0072] a) Initial population generation: 80 sets of initial parameter combinations are generated through optimal Latin hypercube sampling as optimal Latin hypercube samples. In this embodiment, the crossover rate is set to 0.9 and the mutation rate is set to 0.1.

[0073] b) Reference point generation guidance: The Das-Dennis method is used to generate 12 reference points to guide the non-dominated sorting, and the solution set is screened hierarchically according to the objective function value to ensure that the Pareto solution set is evenly distributed.

[0074] c) Diversity maintenance: Calculate the crowding distance to maintain population diversity and retain diverse individuals.

[0075] d) Genetic Iteration: Generate a progeny population by simulating binary crossover and polynomial mutation operations. After 50 generations, converge to the Pareto frontier, output a set of non-inferior solutions, and obtain the Pareto optimal solution set. In this example, the crossover rate is set to 0.9 and the mutation rate is set to 0.1.

[0076] e) Select the optimal solution from the Pareto solution set based on the weighted comprehensive score (considering the weighted average of the stress reduction amplitude of the three-axis section): outer diameter R0 = 329.072 mm, side clearance h R=0.648mm, top clearance h g =0.6mm, total thickness B1=25.3mm.

[0077] Reference Figure 3 As shown in the figure, the NSGA-III algorithm starts by initializing the population, then generating the offspring population, setting the number of evolutionary generations to 2, and then merging the parent and offspring populations to determine whether to generate a new parent population:

[0078] Otherwise, non-dominated sorting is selected, and the vertical distance to the reference line is calculated according to the pre-specified reference line. Then a new generation population is selected and it is repeatedly determined whether a new parent population is generated.

[0079] If yes, select, crossover, and mutate. If the number of generations is less than the maximum number of generations, end; otherwise, set the number of generations = the number of generations + 1, and repeat the steps of merging the parent and child populations.

[0080] Step 5: Verify the performance of the optimized shock absorber through simulation. The specific method of simulation verification in the above steps is as follows.

[0081] To eliminate the impact of step load response caused by motor loading, the ice load was set to begin after the propeller rotated 1000°. The solution time step was set to the time required for the propeller to rotate 1° at rated speed. Using MATLAB, the transient stress response curves of the 1# and 2# intermediate shafts, propeller shaft, and motor shaft under ice load condition 2 at rated speed were calculated with and without silicone oil dampers installed.

[0082] Through simulation data, it was found that the silicone oil vibration damper has a significant inhibitory effect on the torsional vibration stress of the shaft system, reducing the stress of the motor shaft by 27.0%, the 1# intermediate shaft by 15.5%, the 2# intermediate shaft by 18.5%, and the propeller shaft by 12.3%.

[0083] After selecting the comprehensive optimal parameters from the Pareto solution set, the silicone oil vibration damper was redesigned according to the design parameters. The dynamic model of the motor-silicone oil vibration damper-shafting-propeller coupling system was established, and the dynamic response analysis was performed to obtain the torsional response ratio of the target optimized shaft segment before and after optimization.

[0084] like Figures 4 to 11 As shown in the figure, by comparison, it can be seen that after optimization, the torsional stress of the motor shaft at rated speed is reduced by about 18.0%, the stress of the 1# intermediate shaft is reduced by 11.1%, the stress of the 2# intermediate shaft is reduced by 11.8%, and the stress of the propeller shaft is reduced by 17.7%.

[0085] like Figures 4 to 11As shown in the figure, by comparison, it can be seen that after optimization, the torsional stress of the motor shaft at rated speed is reduced by about 18.1%, the 1# intermediate shaft is reduced by 14.1%, the 2# intermediate shaft is reduced by 11.8%, and the propeller shaft stress is reduced by 12.3%.

[0086] By establishing a dynamic model and multi-objective optimization framework for the motor-silicone oil damper-shafting-propeller coupling, this paper achieves global coordinated optimization of damper parameters such as outer diameter, thickness, and clearance, while simultaneously reducing torsional stress in multiple shaft segments. This matching optimization method addresses the issues of excessive torsional stress in the shafting of ships in icy conditions caused by ice loads and the lack of systematic optimization of damper parameter matching.

[0087] The above description is merely a specific embodiment of the present invention, but the scope of protection of the present invention is not limited thereto. Any changes or substitutions that can be easily conceived by a person skilled in the art within the scope of the present invention should be included within the scope of protection of the present invention. Therefore, the scope of protection of the present invention should be based on the scope of protection of the claims.

Claims

1. A method for optimizing the matching of shock absorbers for ships in ice regions based on NSGA-III, characterized by: Includes the following steps Step 1: Establish a dynamic model of the motor-silicone oil vibration absorber-shafting-propeller coupling system including a lumped parameter model, an ice load excitation model, a propeller torque excitation model, a motor torque excitation model, and a vibration absorber model; The steps of constructing the lumped parameter model are as follows: based on the shafting drawings and structural parameters of the ship, the shafting of the propulsion system is divided into M shaft segments and N mass blocks, and the dynamic characteristics of the propeller, silicone oil vibration damper, and connector are integrated. The mass block moment of inertia parameter J is used. i (i=1,2,…,N) represents the moment of inertia of the shaft segment between the i-th and i+1-th segments, and the shaft segment stiffness parameter k is calculated based on the shaft segment geometric parameters and material properties. i (i=1,2,…,M) and internal and external damping parameters C ii 、C ei (i=1,2,…,M), and obtain the system dynamics equation Where J, C, and K are the inertia, damping, and stiffness matrices of the shaft segment, respectively. θ t are torsional angular acceleration, angular velocity, and angular displacement, respectively; T(t) is the vector synthesis of ice load excitation, propeller excitation, and motor torque excitation acting on the corresponding mass point; t is time; The total excitation vector is synthesized according to the ice load excitation model, the propeller torque excitation model and the motor torque excitation model; Apply structural parameter constraints to the shock absorber model; Step 2: Import the coupled system dynamics model into ANSYS APDL software to establish a finite element model, and solve it using the Newmark-β method to obtain the transient torsional vibration response under ice load impact; Step 3, constructing a multi-objective optimization model for the shock absorber; Select the outer diameter R0, total thickness B1, and side clearance h of the silicone oil shock absorber inertia ring R 、Top gap h g As the optimization design variables, the variable range of the optimization parameters of the silicone oil shock absorber is defined as follows: the outer diameter of the inertia ring of the silicone oil shock absorber R0∈(225.26, 425.68) mm; the total thickness B1∈(15.63, 30.53) mm; the side clearance h R ∈(0.4, 1.0) mm; top clearance h g ∈(0.5, 1.2) mm; The objective function is constructed as the shock absorber weighted shaft stress Where T m 、T p 、T s Respectively represent the motor shaft, propeller shaft, and 2# intermediate shaft iteration j times, r m 、r p 、r s Respectively represent the radius of the motor shaft, propeller shaft, and 2# intermediate shaft, J m 、J p 、J s Respectively represent the polar inertia moment of the motor shaft, propeller shaft, and 2# intermediate shaft, ω m 、ω p 、ω s Represents the weight factor, the value range is [0, 1], and satisfies ω m +ω p +ω s =1; Step 4: Generate an initial population based on Latin hypercube sampling, use the NSGA-III algorithm to perform multi-objective iterative optimization on the shock absorber model parameters, and select the optimal comprehensive matching solution; Step 5: Verify the performance of the optimized shock absorber.

2. The NSGA-III-based ice region ship shock absorber matching optimization method according to claim 1, characterized in that: The shaft system of the propulsion system in step 1 includes, in sequence, a motor (1), a vibration absorber (2), a first connecting member (3), a 2# intermediate shaft torsional inertia portion (4), a second connecting member (5), a third connecting member (6), a 1# intermediate shaft torsional inertia portion (7), a fourth connecting member (8) and a propeller (9); the first connecting member (3) and the 2# intermediate shaft torsional inertia portion (4) and the 2# intermediate shaft torsional inertia portion (4) and the second connecting member (5) are respectively used as the front half and the rear half of the 2# intermediate shaft; the third connecting member (6) and the 1# intermediate shaft torsional inertia portion (7) and the 1# intermediate shaft torsional inertia portion (7) and the fourth connecting member (8) are respectively used as the front half and the rear half of the 1# intermediate shaft; when constructing a lumped parameter model, the inner and outer diameters, lengths, material densities and elastic moduli of each shaft segment are first measured, the shear stiffness and moment of inertia are calculated, and then the dynamic torsional stiffness and polar moment of inertia of the connecting member are obtained.

3. The NSGA-III-based ice region ship shock absorber matching optimization method according to claim 2, characterized in that: The following simplification principles are followed when constructing the lumped parameter model: Components with significant rotational inertia, such as the motor (1), the vibration absorber (2), the propeller (9) and various connecting parts, are simplified as concentrated mass points at their centers of gravity; a concentrated mass point is set between the 1# intermediate shaft and the 2# intermediate shaft to represent the torsional inertia of the entire shaft section, and the torsional stiffness of the shaft section is simplified as an elastic connection concentrated between the mass points, and every two adjacent mass points are connected by equivalent torsional stiffness; the first connecting part (3) provides the torsional stiffness of the front half of the 2# intermediate shaft between the first connecting part (3) and the torsional inertia part (4) of the 2# intermediate shaft; the torsional stiffness of the rear half of the 2# intermediate shaft between the 2# intermediate shaft torsional inertia part (4) and the second connecting part (5); the torsional stiffness of the front half of the 1# intermediate shaft between the third connecting part (6) and the torsional inertia part (7) of the 1# intermediate shaft; and the torsional stiffness of the rear half of the 1# intermediate shaft between the 1# intermediate shaft torsional inertia part (7) and the fourth connecting part (8).

4. The NSGA-III-based ice region ship shock absorber matching optimization method according to claim 1, 2 or 3, characterized in that: In step 1, a piecewise function is used to characterize the blade-ice contact and establish an ice load excitation model. In the formula is the rotation angle of the blade when the ice block first hits it, α i is the continuous rotation angle of the blade interacting with the ice layer, C q is the impact amplification factor, design load torque Where k open is the open propeller coefficient, d is the hub outer diameter, P 0.7 is the pitch of the propeller at 0.7R, n is the bollard speed, and the critical value of the propeller diameter D limit =1.8H ice , D is the propeller diameter, H ice is the maximum design ice thickness.

5. The NSGA-III-based ice region ship shock absorber matching optimization method according to claim 4, characterized in that: The propeller torque excitation model in step 1 is to expand the propeller torque excitation torque into a Fourier series form with the propeller blade frequency as the base frequency: Where T p is the propeller excitation torque, T p0 is the average torque of the propeller, Z p is the number of propeller blades, v is the harmonic order, For vZ p The propeller torque excitation torque amplitude of the harmonic, ω is the angular frequency, For vZ p The phase angle between the harmonic excitation torque and the blade centerline, propeller torque Where P pe is the power received by the propeller, n pe is the rated speed of the propeller, n pc is the propeller's operating speed.

6. The NSGA-III-based ice region ship shock absorber matching optimization method according to claim 5, characterized in that: In the motor torque excitation model in step 1, when the motor speed drops to a specific threshold due to the impact of ice load, the motor switches from constant power mode to constant torque mode. The motor torque excitation formula is: Where Δn is the velocity change within the time step Δt, Δt is the solution time step, and the motor torque excitation T is obtained according to the motor torque characteristics under the impact of ice load. engine According to the propeller open water torque characteristics, the propeller average torque T is obtained. prop , T ice is the propeller ice load torque excitation, and I is the total system inertia including the propeller water inertia.

7. The NSGA-III-based ice region ship shock absorber matching optimization method according to claim 6, characterized in that: The shock absorber model in step 1 is based on the initial parameters of the shock absorber. The outer diameter R2, inner diameter R3, and total thickness B1 of the inertia ring are simplified to outer diameter R0, inner diameter R1, and top clearance h g , side clearance h R Function: R2=R0-h g , R3=R1+B2+C, B1=B+2h R +2B2.

8. The NSGA-III-based ice region ship shock absorber matching optimization method according to claim 7, characterized in that: The transient torsional vibration calculation in step 2 ignores the harmonic excitation of the motor and only takes its average torque; the rigid shaft model is used to calculate the motor torque excitation, propeller torque excitation and ice load excitation under the impact of ice load, and the formula is used. The speed drop of the propulsion system shafting under ice load impact is calculated, and the motor torque excitation for Newmark-β method loading is obtained.

9. The NSGA-III-based ice region ship shock absorber matching optimization method according to claim 8, characterized in that: The step 4 is specifically as follows: a) Initialize the population: Generate 80 sets of initial parameter combinations through optimal Latin hypercube sampling as optimal Latin hypercube samples; b) Reference point generation: The Das-Dennis method is used to generate 12 reference points to guide the non-dominated sorting and ensure that the Pareto solution set is evenly distributed; c) Selection, crossover, and mutation: Calculate crowding distance to maintain population diversity; d) Non-dominated sorting: Generate a progeny population by simulating binary crossover and polynomial mutation operations; after iteration, converge to the Pareto frontier, output a set of non-inferior solutions, and obtain a Pareto optimal solution set; e) Considering the weighted average of the stress reduction amplitudes of the three-axis segments, the optimal comprehensive matching solution is selected from the Pareto solution set based on the weighted comprehensive score.

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