Abstract
The bed is one of the crucial components of a CNC internal gear power honing machine. To achieve comprehensive optimization in terms of bed mass, first-order natural frequency, and maximum deformation, this paper proposes an optimization design method that combines a response surface model with a genetic algorithm. Central composite experimental design is conducted on the primary design parameters. Based on the experimental design, sensitivity analysis is performed on the design parameters, followed by the establishment of a response surface model. Genetic algorithm is then utilized to optimize the response surface model, and the optimal solution is determined in conjunction with production processes. Taking the Y4830CNC as an example, after optimizing the bed using the aforementioned method, the first-order natural frequency of the bed increased by 14%, the mass decreased by 6.5%, and the maximum deformation reduced by 13.26%. This method provides a new approach for the optimal design of gear honing machine beds.
1. Introduction
The bed serves as a vital structural component of a machine tool, supporting the workbench and connecting key parts such as columns. It also bears the static loads of the machine tool and the cutting loads generated during machining. The static and dynamic performance of the bed directly influences the machining performance of the entire machine. Therefore, it is necessary to optimize the bed structure [1]. In the structural design and optimization of critical machine tool components, scholars domestic and international commonly adopt size optimization methods.
Table 1 summarizes some previous research efforts on the optimization of machine tool beds.
| Reference | Research Focus | Optimization Objective | Optimization Method |
|---|---|---|---|
| [2] | NC gear milling machine bed | Reducing bed mass | Varying rib thickness and arrangement |
| [3] | Worktable of high-speed vertical machining center | Improving stiffness | Static analysis using ANSYS |
| [4] | Bed of a certain machine tool | Reducing mass and improving stiffness | Combining topology and size optimization |
The current research on the beds of CNC machine tools is abundant, but most studies use finite element analysis for modal analysis of the beds, with limited adoption of parametric modeling and multi-objective optimization methods for optimizing bed structural dimensions.
In this paper, the bed of a gear honing machine is taken as the research object. With bed mass as a constraint, and the first-order natural frequency and maximum deformation as objectives, based on sensitivity and response surface analysis, a multi-objective genetic algorithm is used to optimize its structural dimensions to improve seismic resistance and meet lightweight design requirements.
2. Finite Element Modeling of the Bed
The three-dimensional model of the Y4830CNC CNC internal gear power honing machine. The columns, traverse slides, and longitudinal slides are connected to the bed via guide rails. The workpiece table slide, workbench pad, workpiece housing, and machine are connected through guide rails. The tailstock is connected to the bed via bolts.
The force diagram of the bed is depicted. The bed experiences a gravity force of 2,190 N at point A from the tailstock, 3,650 N at point B from the workbench pad, workbench slide, and workpiece housing, and 12,140 N at point C from the column, longitudinal slide, and traverse slide. The honing forces on the honing tool and workpiece at points D and E are 4,518.9 N and 5,518.2 N, respectively.
The three-dimensional solid structural model of the Y4830CNC bed is imported into the ANSYS platform for pre-processing before finite element analysis to create a finite element calculation model.
3. Modal Analysis Results
The modal analysis results of the bed’s first four orders are summarized in Table 2.
| Order | Natural Frequency (Hz) | Mode Shape Description |
|---|---|---|
| 1 | 206.9 | Vibration mainly along the Y-axis direction |
| 2 | 265.3 | Torsion and bending vibration |
| 3 | 302.1 | Vibration mainly along the Z-axis direction |
| 4 | 348.7 | Complex bending and torsional vibration |
Table 2: Modal analysis results of the bed’s first four orders
4. Multi-objective Optimization of the Bed
Structural optimization design involves establishing a mathematical model for the component to be optimized, determining the corresponding parameters to be optimized, solving the mathematical model to obtain the optimal solution for the objective function, verifying the optimization results based on practical requirements and constraints, and finally determining the optimal design scheme.
4.1 Mathematical Model for Multi-objective Optimization Design of the Bed
During the multi-objective optimization design of the bed, the primary parameters are optimized without changing its structural shape, based on experimental design, sensitivity analysis, and response surface analysis. The multi-objective optimization of the machine tool structure can be represented by the following mathematical model:
find x=(x1,x2,…,xn)
minimize fi(xj)=F(xj)
subject to a≤x≤b
Where x are the design variables; f(x) is the objective function of the design variables; and the constraints are determined based on actual conditions. The design variable lower bound a=(25,15,165,190,85,140,165) and upper bound b=(35,25,210,240,115,180,210).
4.2 Multi-objective Optimization Based on Genetic Algorithm
After fitting the response surface model, the efficient and easy-to-implement MOGA (Multi-Objective Genetic Algorithm) is used to solve the objective function. MOGA, based on the genetic algorithm, rapidly seeks optimal solutions within a large design variable space, is suitable for calculating global maxima and minima, avoids local optimum traps, uses quicksort to find non-dominated solutions, preserves elite populations, and maintains population diversity. MOGA is employed to perform multi-objective optimization on the bed’s design variables, with the objectives of maximizing the first-order natural frequency and minimizing deformation. To ensure that the optimized mass is not higher than the initial value, the bed’s mass in its initial state is set as a constraint.
5. Optimization Results and Analysis
After optimization, the comparison of key performance indicators is shown in Table 3.
| Sequence | Mass (10^3 kg) | First-Order Natural Frequency (Hz) | Maximum Deformation (μm) |
|---|---|---|---|
| 1 | 3.610 | 70 | 240.99 |
| Optimal | 3.609 | 241.21 | 5.82 |
| Initial | 3.987 | 206.9 | 6.71 |
Table 3: Comparison of optimization results
To select the optimal solution, three sets of non-dominated solutions in Table 3 are evaluated. The third set is chosen to increase the first-order natural frequency while reducing the bed’s mass. The design variables in the optimal solution are then revised, considering the sensitivity histogram of the bed’s design variables to avoid blindness in dimension correction. Sensitivity analysis reflects the influence of each design variable on the objective function and guides the adjustment of variable values.