Structure reconstruction of anchor winch drum based on parameterized surrogate model with lightweight design

2.1. The design of the channel model

To ensure the safety and flexibility of the windlass, the structure of the designed winch drum is shown in Fig. 1, which is composed of a cylinder body, side plates, rib plates, and a braking zone. Flanges are arranged at both ends of the winch drum to fix the ends of the anchor chain, preventing axial movement of the anchor chain during winding and unwinding. The braking zone can be connected to a brake and is equipped with an overload protection function. To adapt to the winch drum that bears heavy anchor chains and operates at high winding and unwinding speeds, reinforcing ribs are adopted to enhance structural strength and stiffness. Additionally, the design of the long shaft of the winch drum is intended to prevent the anchor chain from deviating during transmission. Considering the effects of each component on mass and mechanical properties, and on the premise of no structural interference or impact on assembly, the initial design values and value limits of five parametric dimensions are defined and presented in Table 1.

Fig. 1Overall structure and parameter definition of anchor winch drum

a) Windlass transmission structure

b) Parametric dimensions

To ensure strength and toughness, the winch drum is made of Q235 steel, which can withstand large tensile forces. When parametric modeling is performed in SolidWorks, a prefix “DS” needs to be added before the names of dimensional parameters to ensure these parameters can be recognized by ANSYS, enabling synchronous data update.

Fig. 2Parameterized model coupling flowchart

In ANSYS, the coupling between modality and strength is usually achieved by setting multi-field coupling relationships [9, 10]. Relevant modules in ANSYS Workbench (such as System Coupling) can be utilized to define this coupling relationship, as shown in Fig. 2. Specifically, it is necessary to correlate the structural vibration characteristics obtained from modal analysis (e.g., natural frequencies and mode shapes of each order) with the structural stress and deformation characteristics derived from strength analysis (e.g., deformation and stress values). This correlation is intended to clarify how deformation caused by vibration affects stress distribution and how stress distribution, in turn, influences vibration characteristics during structural vibration.

2.2. Loads and boundary conditions

The external loads acting on the anchor winch drum during operation mainly include the gravitational load, which is composed of the weight of the drum's own structure and the stored chain, the tension force exerted by the chain tensioning device, and the starting inertial load generated during the starting and braking phases of the winch. At a specific winding angle of the chain on the drum, the chain tension can be orthogonally decomposed into the tangential direction and the radial direction relative to the drum. The tangential force is mainly used to drive the drum rotation, while the radial force directly acts on the surface of the drum barrel, forming the radial load on the drum. As the chain is continuously wound on the drum, due to the differences in contact arc length and friction coefficient between each layer of the chain and the drum, the tension load distribution of different layers exhibits significant nonlinear characteristics. To accurately analyze the stress state of the drum, it is necessary to comprehensively consider factors such as the chain conveying angle and friction characteristics, and establish a force analysis model for the chain winding around the anchor winch drum, as shown in Fig. 3. Let the chain pulling force be $F$, at the contact point $Q$, the moment acting on the anchor winch drum is:

The tangential force can be calculated as:

Fig. 3Mechanical analysis model

When the anchor winch drum is started, the chain needs to be accelerated from a static state to a certain operating speed, and inertial forces are thereby generated. Based on the extreme working conditions of the anchor winch, the inertial load can be applied by defining the maximum starting acceleration. The anchor winch drum is mounted using a dual-support configuration, meaning both ends are mounted on the support via bearings. The bearings at both ends restrict the radial displacement of the anchor winch drum, and displacements in the direction perpendicular to its axis are limited, thus can be regarded as radial fixed constraints. For axial constraints, one end restricts axial displacement, while the other allows a certain degree of axial movement.

2.3. Mesh generation and quality verification

For finite element analysis, the quality of mesh generation exerts a crucial influence on computational accuracy, convergence rate, and result reliability [11]. Given the complex structural characteristics of the anchor winch drum assembly, an adaptive mesh generation technique combining global mesh sizing with local mesh refinement is employed in this study to significantly improve the analytical accuracy of critical stress concentration regions while ensuring computational efficiency. Through this approach, the final model is found to consist of 332,520 elements and 401,895 nodes, with the overall mesh configuration shown in Fig. 4(a). To ensure that the mesh quality meets the requirements of subsequent mechanical analysis, key indicators such as the element quality and aspect ratio are systematically calculated and verified, with the specific results presented in Fig. 4(c-d), respectively. According to Eq. (1-2), taking into account the gravity factor, the cylindrical surface of the bearing connection inside the drum is defined as a fixed constraint, and the torque on the outer cylindrical surface is set to 1.44×10⁵ N·m, as shown in Fig. 4(b).

The element quality coefficient is a core quantitative indicator for evaluating whether the mesh element size settings and shapes in a finite element model are reasonable and appropriate. The value range of this coefficient is typically from 0 to 1. The closer the value is to 1, the more regular the shape of the mesh element (such as approaching a square or a regular tetrahedron), and the better the mesh quality. The closer the value is to 0, the more deformed the element shape (such as elongated, flat, or severely distorted), and the worse the mesh quality. In engineering practice, to ensure the accuracy and stability of numerical calculations, it is generally required that the average value of the element quality coefficient is not less than 0.7. When the overall coefficient meets this standard, it can be determined that the current mesh size setting is feasible.

Fig. 4Mesh verification and boundary condition setting

a) Boundary condition setting

d) Boundary condition setting

b) The division of the finite element mesh

c) Distribution of element quality coefficients

The aspect ratio is another key mesh quality indicator, which is defined as the ratio of the length of the longest side to the shortest side of an element. This ratio directly reflects the geometric shape characteristics of the element. For triangular elements, the ideal aspect ratio is 0.577. For quadrilateral elements, the ideal aspect ratio is 1. Typically, the more the element shape deviates from an equilateral triangle or a square, the larger its aspect ratio becomes. In the default settings of finite element analysis software, when the aspect ratio of an element reaches 20, a warning message will be issued, prompting the user that there may be problems with the mesh quality in this area and that it needs to be checked or adjusted. When the aspect ratio exceeds 106, an error message will be directly popped up, forcing the calculation to be interrupted, as the element shape will have been severely distorted at this point, which can lead to the divergence of the numerical solution or the unreliability of the results.

2.4. Convergence verification of finite element model

Convergence verification is a core step for ensuring that the constructed finite element model can accurately and stably simulate actual physical phenomena. This process involves systematically varying key computational parameters such as mesh density and time step size, and tracking and analyzing core response indicators output by the model (such as maximum residual force, maximum degree of freedom increment, and stress/displacement distribution), to determine whether they tend to a stable and accurate value with the optimization and adjustment of parameters. This verification can not only evaluate the numerical stability of the model itself and the effectiveness of the solution algorithm, but also fundamentally ensure the reliability and physical meaning of the final calculation results, making it an indispensable quality control link in engineering simulation and scientific computing.

The variation laws of maximum residual force and maximum degree of freedom increment with the number of iterations are shown in Fig. 5. From the curves in the figure, it can be clearly observed that with the increase of the number of iterations, both of these two indicators show an obvious downward trend and eventually tend to be flat without significant changes. At the same time, by calculating the relative error between the results of two adjacent iterations and comparing it with the preset convergence criterion, it is found that the relative error also meets the convergence requirements. The above phenomena collectively indicate that under the current calculation settings, the selection of the time step is appropriate, the calculation process has reached a convergent state, and the calculation results of the model have sufficient accuracy and reliability to be used for subsequent engineering analysis and decision-making.

Fig. 5Convergence verification curves

a) Verification results of maximum residual force

b) Verification results of maximum degree of freedom increment

2.5. Strength and modal analysis

Under the condition where the anchor chain reaches its maximum design tension, the final strength analysis results are obtained through iterative calculations, as shown in Fig. 6. From the obtained stress cloud and displacement cloud diagrams, it can be clearly observed that: the anchor winch drum maintains a relatively high safety factor under this extreme load, with its maximum stress value being much lower than the yield strength of the selected material, indicating sufficient load-bearing margin of the material; meanwhile, no obvious stress concentration problem occurs in the key parts of the structural design scheme, further verifying the rationality and reliability of the design. In terms of displacement response, the maximum displacement of the anchor winch drum model is only 0.33 mm, indicating that the structure has good stiffness when subjected to extreme loads and can effectively meet the safety requirements of ship mooring operations.

Fig. 6Static structural analysis results

a) Stress results

b) Displacement results

To verify the consistency between the established finite element model and the actual working conditions and ensure the reliability of numerical simulation results, the DH5902 data acquisition and analysis system was adopted in this study, and high-precision strain gauges were used to conduct synchronous and long-term dynamic stress tests on the critical stress areas of the anchor winch drum side plate. The test data were systematically compared with the finite element simulation results, and the specific test and comparison process and results are shown in Fig. 7. The photographs used for experimental verification were taken by Guangqian Zhou on December 20, 2025, in Chengdu city. The DH5902 dynamic signal test and analysis system is a professional test equipment with a wide range of applications. Its core advantage lies in the powerful ability of multi-channel parallel synchronous high-speed long-term continuous sampling, which can collect high-precision data with extremely high reliability and stability in complex dynamic loading environments. Under the same loading conditions as the simulation, the test points were arranged 200mm inward from the anchor winch drum side plate to capture the real stress response of this area under extreme working conditions.

Fig. 7Experimental verification of the finite element model

a) Data acquisition system

b) The installation position of strain gauges

c) Tested and simulated stress values

From the comparative analysis results in Fig. 7(c), it can be clearly observed that when the load is maintained at 14.5 s, the stress response value rises rapidly and finally tends to a stable state, with an average stress value of 27.9 MPa after stabilization. A quantitative comparison was made between the measured value of this steady-state stress and the finite element simulation results (26.6 MPa) as shown in Fig. 6(a), and it was found that the deviation between the two is only 4.7 %, which is within the engineering acceptable range. The above results collectively prove that the finite element model established in this study has good computational accuracy and predictive ability, and fully meets the accuracy requirements for subsequent engineering analysis and applications.

Through the simulation calculation of the coupled strength and modal model, the first two-order natural frequencies and mode shape contour plots of the anchor winch drum under the influence of structural loads are obtained, as shown in Fig. 8. It can be seen that the first-order and second-order natural frequencies are in the range of about 80-85 Hz, and the main vibration is located on the side flange plate. According to the extreme speed range of the driving and transmission components of the anchor windlass, such as the excitation components, the external maximum excitation frequency (about 27-60 Hz) is lower than the low-order natural frequencies of the anchor winch drum. Therefore, there will be no significant resonance problem in this structural design.

Fig. 8Results of the first four order modal analysis

a) The first order mode shape contour plot

b) The second order mode shape contour plot

c) The third order mode shape contour plot

d) The fourth order mode shape contour plot

3.1. Combination of discrete design variables

The combination of discrete design variables serves as the foundation for establishing an optimization mathematical model, requiring an appropriate sample size [12, 13]. If the sample size is too small, the relationship between parameter variations and objectives may not be accurately reflected, leading to significant deviations in results. Conversely, an excessively large sample size will increase experimental costs and time consumption. According to the parametric dimension limits shown in Table 1, the value ranges of the vast majority of design variables exhibit a symmetric distribution. Therefore, the adoption of the Central Composite Design (CCD) method for parameter sample design can not only fully account for the interaction effects between different parameters but also achieve high surrogate model fitting accuracy with fewer sample data points.

Assuming that the objective function of the optimization calculation is $G$ and the optimization variables are $x_j$ ($j=$1, 2, 3, 4, 5), the local sensitivity can be expressed as:

The first-order natural frequency is defined as P6, the mass is defined as P7, the stress peak value is defined as P8, the maximum deformation is defined as P9, and the relative stiffness coefficient is defined as P10, where P10 = P6·P6·P7. The local sensitivity can express the magnitude of the rate of change of different design variables with respect to the optimization objective. The analysis results of the local sensitivity are shown in Fig. 9. It can be seen that the selected design variables are all parameters that have a critical impact on the mechanical properties, and the sensitivity trends of strength and natural frequency are opposite. Therefore, in lightweight design, design variables that simultaneously satisfy the optimization objective can be sought. The parametric combination results of the five design variables are presented in Fig. 10. It can be observed that the interactive influence between different parameters is significant, and no obvious duplicate or invalid sample data is generated. Consequently, the proposed sample design scheme is deemed feasible.

Fig. 9Results of sensitivity analysis

Fig. 10Interaction results of design variables

a) P1, P2 and P3

b) P4 and P5

3.2. Construction and error verification of surrogate models

Response surface functions are capable of accurately interpreting and predicting the performance and structure of the anchor winch drum by establishing mathematical relationships between input variables and output responses [14]. Therefore, this method is adopted in this study for the construction of surrogate models. To ensure the reliability of the surrogate models, the response surface functions are constructed using the Genetic Algorithm (GA), Neural Network (NN), and Kriging (K) methods, respectively.

In the construction of the response surface function using the Genetic Algorithm, a set of initial parameter combinations is determined as population individuals. By calculating the corresponding objective function values of the individuals and undergoing multiple iterations, the optimal form and parameters of the response surface function are gradually approached. In the construction of the response surface function using the Neural Network method, the mapping relationship between input and output is learned by adjusting the weights of connections between neurons, thereby constructing a response surface function that can better fit the actual data. In the construction of the response surface function using the Kriging method, the values of unknown points are predicted mainly based on the spatial distribution characteristics and correlations of known data points. A model that can reflect this spatial correlation is constructed, and then the model is used to predict unknown points, thereby forming the response surface function [15].

Fig. 11Construction of the surrogate model

a) The response surface of P1 and P2 for P6

b) The response surface of P3 and P4 for P6

c) The response surface of P1 and P2 for P7

d) The response surface of P3 and P4 for P7

e) The response surface of P1 and P2 for P8

f) The response surface of P3 and P4 for P8

The fitting accuracies of the three response surface functions are compared. The error determination results are presented in Table 2, with the coefficient of determination $R^2$ (the optimal value is 1), the root mean square error RMS (the optimal value is 0), the relative maximum absolute error RMAE (the optimal value is 0), and the relative average absolute error RAAE (the optimal value is 0) as the evaluation criteria. It can be seen that both the Kriging model and the GA model can achieve high fitting accuracy. Due to the relatively small sample data of the design variables, the GA model is prioritized as the construction scheme for the surrogate model. The response surface fitting results of the first-order natural frequency, mass, and peak stress are presented in Fig. 11. It can be observed that the surrogate model belongs to a typical nonlinear function, and no singular values appear within the domain.

3.3. Solution of optimization mathematical model

To ensure that the strength and stiffness of the winch drum are not reduced after lightweight design, the target parameters P6 and P8 are converted into boundary conditions. With the minimum mass of the winch drum as the objective function, the constraints include the strength not being lower than the design value, the stiffness meeting the vibration frequency requirement, and the stability limit [12, 16-18]. The response surface method is adopted to achieve the balance between structural lightweight and performance. According to the performance requirements of the winch drum, an optimization mathematical model is established as:

where $X$ is the design variable matrix of the winch drum, $Y_6$ is the initial value of the first order natural frequency, $Y_8$ is the initial value of the stress peak, $x_{imin}$ and $x_{imax}$ are the minimum and maximum values of each design variable, respectively.

Due to the presence of nonlinear expressions in the objective function or constraints, the nonlinear programming method is adopted to solve the model. Nonlinear programming is relatively complex and requires continuous iteration to find the optimal value of the objective function. There are certain differences in the extreme value search obtained by different algorithms. To ensure the convergence, accuracy, and efficiency of nonlinear calculations, the sequential quadratic programming algorithm is adopted. This algorithm can reconstruct the model to search for the extreme value of a single objective function when dealing with multi-objective optimization functions. According to the results of strength analysis, the stress peak of the winch drum under the ultimate load is much smaller than the yield limit. To adjust the redundancy, two schemes are adopted for lightweight design. Scheme A sets the initial value of P8 as the boundary value, i.e., P8 ≤ 102.35 MPa. Scheme B sets the boundary value as 1.5 times the initial value of P8, i.e., P8 ≤ 153.53 MPa. The optimization objective remains unchanged. Based on the sequential quadratic programming algorithm, the parameter variables and objective extreme values of the two optimization schemes can be obtained, which are shown in Tables 3 and 4, respectively. It can be seen that Scheme A can reduce the weight of the winch drum by 17.4 % while keeping the maximum stress unchanged and slightly increasing the natural frequency. Scheme B can reduce the weight of the winch drum by 27.6 % with a maximum stress of 150.37 MPa and keep the natural frequency unchanged. Taking the two lightweight schemes as the selection basis for parts of winch drums with different power can significantly improve the cost performance of products and achieve good energy saving and consumption reduction effects.