Optimization of reduction gear in anchor winch based on modal analysis

2.1. Simplification and parameterization of the model

The structure and composition of the anchor winch transmission system are shown in Fig. 1, which is arranged axially and mainly responsible for anchoring, unanchoring, and hauling operations. The load on the reduction gear is mainly torque, which is crucial for ensuring the stability of the vessel during docking, so the structural integrity and safety of the system are one of the most important indicators of the performance of the anchor winch. The reduction gear bears a larger load, so it is selected from the modified 40Cr material, which can effectively meet the requirements of wear resistance, fatigue resistance, static strength, and impact toughness. To save materials, the overall structure of the reduction gear is designed as a hub plate, reinforced by reinforcing ribs, and the internal structure is set to be symmetrical hollow to avoid stress concentration caused by uneven loading. Since the gear tooth shape, module, and number of teeth all meet the national standard requirements, they are no longer considered as optimization design parameters. To improve the calculation efficiency, the pitch circle diameter is kept constant, and the tooth shape structure is omitted in the gear model, as shown in Fig. 2. The design variables mainly include five types of parameters, whose code and value ranges are shown in Table 1. In the parameterized model of the reduction gear, the rib is set to be a symmetrical structure, so the hole spacing between the two sides is set to change synchronously, i.e., P2 = P3.

Fig. 1Assembly model of transmission mechanism

Fig. 2Simplified model of the reduction gear

The reduction gear is the most important load-bearing component in the transmission system, and the main shaft that rotates synchronously with it is the torque output axis for the entire transmission device. According to actual engineering applications, the tooth profile of this gear has not shown any significant wear, cracking, or fracture faults in long-term heavy-duty conditions, and the tooth strength and safety factor are relatively high. Since adjusting the tooth shape would change the production process and significantly increase the equipment manufacturing cost, the structural parameters of the tooth are not considered as design variables in the lightweight design study. With the maximum load of 523 kN as the analysis condition, the limit load state of the anchor winch, the torque is converted from the equilibrium condition in mechanics and applied to the outer surface of the gear. The gear model in Creo is imported into ANSYS through the interface and defined in the modeling module. Then, the static structural analysis module is established in the ANSYS Workbench, and the modal analysis module is coupled with the structural analysis module, with the equivalent stiffness serving as a reference.

2.2. Modal analysis of prestress

In the material library, the material properties of the model are defined as 40Cr, and the quality parameter is set as the optimization target, with the code P7. For the mesh division, the adaptive type is used, and the mesh resolution level is set to 7, with the transition between different planes selected as a slow mode, the center of the span angle selected as a medium mode. Finally, the number of elements is 88168, the number of nodes is 141582, and the mesh division results are shown in Fig. 3. Through the mesh optimization and local refinement verification, it is shown that this mesh division method can achieve high accuracy and computational efficiency. The inner hole of the reduction gear is defined as a fixed constraint, and the gravity factor is considered. The torque of the outer cylindrical surface is set to 2.12e8 N·mm, and the final results of the equivalent stress, total deformation, and first-order vibration analysis are shown in Fig. 4, Fig. 5, and Fig. 6, respectively. It can be seen that the maximum stress (set code as P8) of the reduction gear is 278.46 MPa, far less than its yield limit of 785 MPa. The maximum deformation of the model is 1.2 mm, set code as P9. The first-order natural frequency in the prestressed condition (set code as P10) is 135.87 Hz. After returning to the parameter definition module, the equivalent stiffness parameter is increased and defined as P11.

Fig. 3Meshing results

Fig. 4Stress analysis results

Fig. 5Displacement analysis results

Fig. 6The first mode shape

3.1. Computation of discrete data samples

According to the range of values of the design variables, it can be seen that in the condition of allowable assembly dimensions, most of the design variables have a symmetrical distribution of values, but P1 and P5 have asymmetrical value results. Therefore, the Latin hypercube design (LHD) method is used to obtain sample data. In the continuous data interaction and iterative calculation between ANSYS and Creo, the parameter variables are shared in real time, and finally, the optimized objectives corresponding to different design variables are shown in Table 2. The target samples include P7 (mass), P8 (maximum stress), P9 (maximum deformation), P10 (first-order natural frequency), and P11 (equivalent stiffness). These discrete sample data are the key to completing the response surface function fitting. If the accuracy of the fitting function is insufficient, the sampling range and sampling scheme need to be adjusted. The parallel computing forms of the optimization objectives P7 and P8 are shown in Fig. 7, respectively, under the center group and design method conditions. The changes in the combination structure and sample values of the design variables and optimization objectives under the conditions of all boundary values and target extreme values are shown in Figs. 5 and 6, respectively. It can be seen that the maximum deformation and equivalent stiffness changes are typical inverse relationships, so parameter P9 can be represented to some extent by parameter P11.

To study the effects of design variables on the target and the lightweighting range, a model of the quality response surface, stress response surface, and equivalent stiffness response surface was built based on the experimental design data. The relationship between the design variables and the quality is linear, and the quality increases as the design variables increase. The relationship between the design variables and the maximum equivalent stress is nonlinear, and it decreases as the design variables increase.

3.2. Fitting of response surface functions

Based on the sample calculation results, a response surface model was established and the accuracy of the approximate model was verified. Response surface methodology (RSM) is an approximate model whose core idea is to create an approximate mathematical model to replace the finite element analysis model and use the approximate model for optimization design. In the engineering field, the response surface method is widely used in product design, process optimization, and quality control. By statistically analyzing and regression processing of experimental data, a mathematical expression describing the relationship between dependent and independent variables can be obtained, providing important reference in actual production.

In addition, the response surface method has strong robustness and universality, and can play a role in different industries and fields. It can help engineers better understand the complex interactions within the system and provide reliable basis for improving product design, improving production efficiency and reducing costs. At the same time, with the development of big data technology and artificial intelligence technology in modern manufacturing industry, the response surface method is gradually integrated into intelligent manufacturing systems, providing scientific support for enterprise decision-making. In summary, response surface methodology, as an effective experimental design and optimization tool, has played a positive role in advancing scientific research and engineering practice, and will continue to be valued and further improved and expanded in the future. Separately, the genetic clustering method (GA), neural network method (Neural Network, NN), and Kriging method (K) were used to construct the response surface function. Since P11 is determined by P7 and P10, the fitting effects of P7, P8, and P10 were validated. The fitting accuracy of various response surface functions was compared, and the evaluation criteria were the fitting coefficient of determination R2, root mean square error (RMS), relative maximum absolute error (RMAE), and relative average absolute error (RAAE). The error determination results are shown in Table 3. It can be seen that the Kriging model (shown in Fig. 7) is more suitable for the response surface function fitting under the conditions of the limit strength analysis of the large gear model.

Fig. 7The response of the design variables to the target

3.3. Fitting of response surface functions

In order to ensure that the gear reducer with lightweight design still has good strength and stiffness, we converted the target parameters P8 and P11 into boundary conditions, requiring P8 not to exceed 278.46 MPa and P11 not to be less than 1.69e7 N/m. The optimization goal is to make the mass parameter P7 reach the minimum value. After fitting and verifying the response surface function, we need to choose an appropriate optimization algorithm to find the extreme points of the function. For the bearing characteristics and lightweight design requirements of the gear parts, we conducted a comparative analysis of the multi-objective genetic algorithm MOGA and the sequential quadratic programming NLPQL, and obtained the parameter variables and target extreme value results shown in Table 4.

It can be seen that under the condition of the NLPQL algorithm, the mass of the large gear can be reduced by 39.9 %, while the maximum stress remains unchanged and the equivalent stiffness is not reduced, which is a very significant optimization effect.