Abstract:
The prediction of honing forces in power gear honing with internal gear, aiming to obtain accurate numerical values for honing forces during the process. To achieve this, a Back Propagation (BP) neural network is introduced for prediction. Honing experiments are conducted with spindle speed, radial feed of honing wheel, and axial feed speed of honing wheel as design factors. The honing forces are measured using a Kistler force measuring instrument inside the machine tool. After collecting the experimental samples, a BP neural network is utilized for training to obtain a BP neural network model for honing force prediction. This model is then compared with an exponential model based on the same experimental samples. The results demonstrate that the BP neural network model can predict the honing forces in power gear honing with internal gear more accurately, with a general error not exceeding 5%, while the maximum error of the exponential prediction model reaches 18.94%. However, the exponential model has the advantage of simplicity in predicting honing forces. Therefore, both models have certain reference value for the research on honing forces in power gear honing with internal gear.
1. Introduction
Power gear honing with internal gear, compared to worm wheel grinding, has advantages such as large contact ratio and no tooth surface burning, making it widely used in gear finishing processes. The magnitude of the honing force directly affects the processing quality and cost of the honed workpiece. Therefore, in engineering practice, it is often desirable to obtain the value of the honing force to improve the surface quality of the honed workpiece and reduce processing costs.
Previous studies have laid a theoretical foundation for the research on honing forces. For example, the gear meshing principle has been used to derive the tooth surface equation of the internal honing wheel. A systematic study on the processing technology of power gear honing with internal gear has been conducted, proposing a method for predicting processing errors based on the response surface methodology. Additionally, the expression for the honing speed at the contact point during honing has been derived, and the relationship between honing speed and workpiece tooth surface quality has been obtained through experiments.
However, there have been few reports on the use of numerical models (such as exponential models and neural networks) for predicting honing forces in power gear honing with internal gear. As one of the classic methods for predicting cutting forces, numerical models play an irreplaceable role in traditional cutting processes. Therefore, this paper introduces numerical models into power gear honing with internal gear to explore prediction methods for honing forces.
2. Experimental Design
In this paper, honing experiments are conducted for the processing technology of power gear honing with internal gear, with spindle speed, radial feed of honing wheel, and axial feed speed of honing wheel as design factors. Then, a BP neural network is used to establish a prediction method for honing forces, and the prediction results are compared with those of a traditional exponential model to study the prediction accuracy and ease of use of different methods, thereby providing theoretical guidance for predicting honing forces in power gear honing with internal gear.
The main factor affecting the magnitude of the honing force is the radial force Fr during honing. Since honing is essentially low-speed grinding, the design factors for the experiment are selected as the three elements of grinding: back engagement, feed rate, and cutting speed. Therefore, the design factors for this experiment are spindle speed C2, radial feed of honing wheel fx, and axial feed speed of honing wheel fz.
To ensure the accuracy of the experimental data, an orthogonal experimental design combined with a single-factor experimental design is adopted. This scheme ensures that the experimental sample points are evenly distributed inside and on the surface of the design space, avoiding the defect of the experimental data being non-representative. Based on the existing orthogonal experiment, additional single-factor experiments are conducted to increase the internal sample points of the design space.
Table 1: Design Factors and Levels for Orthogonal Experiment
| Factor | Symbol | Levels |
|---|---|---|
| Spindle Speed (r/min) | C2 | 800, 1000, 1200, 1300, 1500 |
| Radial Feed of Honing Wheel (μm/stroke) | fx | 2.0, 3.0, 4.0, 5.0, 6.0 |
| Axial Feed Speed of Honing Wheel (mm/min) | fz | 60, 80, 100, 120, 130 |
3. BP Neural Network Prediction Model
After collecting the experimental data, a BP neural network is used for training to establish a prediction model for honing forces. The BP neural network is a multi-layer feedforward neural network trained using the backpropagation algorithm. It consists of an input layer, multiple hidden layers, and an output layer. The input layer receives the design factors (spindle speed, radial feed of honing wheel, and axial feed speed of honing wheel), and the output layer outputs the predicted honing force.
During the training process, the weights and biases of the neural network are adjusted to minimize the error between the predicted and actual honing forces. The performance of the BP neural network is evaluated using metrics such as mean squared error (MSE) and coefficient of determination (R²).
Table 2: Comparison of Prediction Errors Between BP Neural Network and Exponential Model
| Model | Mean Absolute Error | Maximum Error |
|---|---|---|
| BP Neural Network | <5% | – |
| Exponential Model | – | 18.94% |
4. Results and Discussion
The comparison between the prediction values of the BP neural network model and the experimental values is shown in Figure 8. It can be seen that the BP neural network model can predict the honing forces in power gear honing with internal gear accurately, with the prediction errors generally within 5%. In contrast, the prediction errors of the exponential model are larger, with a maximum error reaching 18.94%.
Despite the higher prediction accuracy of the BP neural network model, the exponential model has the advantage of simplicity in predicting honing forces. Therefore, both models have certain reference value for the research on honing forces in power gear honing with internal gear, and can be flexibly selected according to practical needs.
Figure 8: Comparison Between Model Prediction Values and Experimental Values
(Insert Figure 8 here, showing a comparison chart between the prediction values of the BP neural network model and the experimental values.)
5. Conclusion
In this paper, a BP neural network is introduced for predicting honing forces in power gear honing with internal gear. Experimental design, data collection, model training, and result analysis are conducted in a systematic manner. The results demonstrate that the BP neural network model can predict the honing forces more accurately than the traditional exponential model. Although the exponential model has the advantage of simplicity, the BP neural network model provides higher prediction accuracy. Therefore, both models have certain reference value for the research on honing forces in power gear honing with internal gear, and can be selected flexibly according to practical needs.
In future research, more design factors can be considered to further improve the prediction accuracy of the model. Additionally, the application of other advanced machine learning algorithms can be explored to establish more accurate and efficient prediction models for honing forces in power gear honing with internal gear.