Abstract:
This paper focuses on the optimization of gear hobbing process parameters under high-speed conditions. A new non-dominated genetic algorithm, NSGA-Ⅱ, is employed to design a corresponding optimization mathematical model that aims to minimize energy consumption and maximize tool life. Furthermore, a genetic back-propagation (GABP) neural network is utilized to establish a prediction model and a fitness function, leading to the acquisition of Pareto optimal conditions matching the gear hobbing process after iterative optimization.
1. Introduction
With the continuous development of automotive transmission systems, gear products have increasingly stringent requirements for dimensional accuracy during processing, prompting the development of numerous new processing technologies . Among them, high-speed gear hobbing has gained widespread application due to its ability to achieve efficient and large-scale production requirements. However, during the processing, rapid and uniform heat release cannot be achieved, leading to localized temperature increases, significant stress in the gear structure, and ultimately decreased accuracy, which affects the performance of gear products . Therefore, further optimization and adjustment of high-speed gear hobbing technology are required to ensure effective heat dissipation from cutting, ultimately achieving effective control of energy consumption, extending tool life, improving overall product quality, and ensuring ideal processing performance for high-speed gear hobbing .
Current optimization research on the gear hobbing process mostly analyzes the changes in cutting energy based on processing parameters, focusing on the independent target parameter control state of gear hobbing machines and processing procedures. Corresponding validation schemes are designed to obtain optimal parameter ranges, and energy consumption calculation models under different processing parameters are established on this basis. This paper focuses on the setting and optimization of gear hobbing process parameters under high-speed conditions, employing a new non-dominated genetic algorithm, NSGA-Ⅱ, to design a corresponding optimization mathematical model.
2. Literature Review
Many researchers have investigated gear hobbing process parameter optimization. For instance, some studies have constructed simulation models for gear hobbing processing parameters and processing costs, tested the relationship between hob rotational speed and feed rate, and designed experimental schemes to assess tool surface wear . Others have established optimization analysis models for the impact frequency of hobs under different processing parameters and determined the cutting vibration performance of gear hobbing under various processing parameters through experimental testing . Furthermore, studies have tested dimensional accuracy under different gear hobbing conditions and constructed mathematical models among these parameters using optimized particle swarm algorithms to obtain higher gear processing accuracy by controlling tooth profile geometric deviations .
3. Methodology
3.1 BP Neural Network and GABP Algorithm
The back-propagation (BP) neural network is a type of multilayer feedforward artificial neural network capable of efficient data processing . However, the number of hidden layer neurons in this algorithm does not have a unified selection criterion. During neural network model training, the initial network is generated randomly, which can easily lead to local optimal solutions, ultimately resulting in reduced accuracy. The GABP algorithm is a neural network designed through optimized genetic algorithms. After neural network parameter encoding and iteration, it effectively overcomes the defects of traditional BP neural networks, thereby obtaining more accurate prediction results.
3.2 NSGA-Ⅱ Algorithm
NSGA-Ⅱ is an algorithm that can achieve multi-objective optimization, featuring low time complexity, population diversity, and efficient global search capabilities . It uses the first front-end principle to ensure the best individuals are obtained within the screening interval, significantly improving algorithm stability and adaptability. In this study, an improved NSGA-Ⅱ algorithm is employed for optimization decision-making on gear hobbing processing parameters. Compared with the NSGA-Ⅱ algorithm, the improved version adds optimal front-end individual parameters and sets dynamic coefficients.
3.3 Objective Model Solving
The gear hobbing process parameters include hob head number (pi1), cutting speed (pi2), axial feed speed (pi3), and hob rotational speed (pi4). The GABP algorithm is used to establish the NSGA-Ⅱ fitness function, and the iterative process parameters set PF is input to optimize OP. The following model expression for predicting processing energy consumption and tool life is obtained:
Where F represents the input-output mapping, pij represents the parameter set, si represents the product quality, MAX_T and ELI_Q represent the minimum processing time and quality qualification indicators, respectively.
4. Case Study
4.1 Establishment of the GABP Prediction Model
A CNC high-speed gear hobbing machine is selected as the test object, and the MATLAB software is used to establish the GABP prediction model. The neural network in this study includes four output parameters: tool life, processing energy consumption, product quality, and processing time. A total of 50 samples constitute the training set, and 12 samples are used for testing and analysis.
4.2 Optimization Results
After 5 cycles of calculation, the mean square error of the network is 10^-5, with an optimal value of 0.000425, indicating good stability of the network. Subsequently, the deviation between the GABP algorithm and the BP neural network prediction results is compared using test group parameters. The results show that the GABP algorithm achieves an error mean of 3.24 and 0.00319 for tool life and energy consumption predictions, respectively, while the BP neural network achieves error means of 2.6 and 0.00481. Compared with the BP neural network, the GABP algorithm reduces tool life errors by 16% and energy losses by 36%, demonstrating higher prediction accuracy and better convergence capabilities.
4.3 Pareto Optimal Solutions
The parameters of the improved NSGA-Ⅱ algorithm are set as follows: population size N=100, iteration number=200, front-end individual coefficient pf=0.14, gr=0.2, and co=0.7. Multi-objective optimization iterations are performed to obtain Pareto optimal solutions. As tool life increases, processing energy consumption first decreases and then stabilizes at 66.5×10^-3 kW·h, indicating the good stability of the method in calculating processing energy consumption.
5. Conclusion
This paper optimizes the gear hobbing process parameters using a new non-dominated genetic algorithm, NSGA-Ⅱ, designing a corresponding optimization mathematical model. After iterative optimization using the GABP neural network as the target, Pareto optimal conditions matching the gear hobbing process are obtained. The following beneficial results are obtained:
- The prediction model has a mean square error of 10^-5 after 5 cycles of calculation, with an optimal value of 0.000425, indicating good stability of the network. The tool life error is reduced by 16% compared to the BP neural network, and energy losses are reduced by 36%. The GABP algorithm demonstrates better convergence capabilities.
- The Pareto solution set exhibits better performance than similar processing sample sets, indicating that the multi-objective optimization model can ensure that both processing energy consumption and tool life reach optimal states simultaneously.
Table 1: Process Sample Set
| No. | pi1 | pi2 | pi3 | pi4 | Ti | Wi |
|---|---|---|---|---|---|---|
| U3 | 25 | 1.5 | 15.0 | 42.5 | 335.85 | 0.0879 |
| U17 | 45 | 3.0 | 17.5 | 47.2 | 309.18 | 0.0914 |
| U21 | 42 | 2.0 | 20.0 | 27.5 | 331.45 | 0.0952 |
| U49 | 32 | 2.5 | 14.5 | 35.5 | 321.50 | 0.0845 |
| U57 | 38 | 3.5 | 18.0 | 45.3 | 318.75 | 0.0933 |