With the development of the times, automobiles have become an indispensable household item. However, as the usage time increases, the gears of the car will experience varying degrees of wear, especially the wear of the spiral bevel gear of the rear axle. This is because during the driving of the car, there is coupled vertical vibration in the rear axle, which leads to the wear of the spiral bevel gear of the rear axle. If timely detection is not carried out, the safety of the car will be reduced. Therefore, it is of great significance to study an effective gear wear detection method to improve the detection accuracy of gear wear and ensure the safety of driving.
1. Introduction
The wear of automotive gears is a common problem that affects the performance and safety of the vehicle. In particular, the spiral bevel gear of the rear axle is prone to wear due to the coupled vertical vibration during driving. Traditional gear wear detection methods often have limitations, such as insufficient consideration of noise interference, inaccurate wear surface fitting, and large noise in sample data, which reduce the detection accuracy. To address these issues, this paper proposes a wear detection method for automotive spiral bevel gears based on Delaunay triangulation.
2. Tooth Surface Non-Feature Discrete Data Blocking
To accurately detect the wear of the spiral bevel gear, we first need to perform non-feature discrete data blocking on the tooth surface. This is achieved by constructing an automotive spiral bevel gear model using NURBS (Non-Uniform Rational B-Splines) surfaces and applying Delaunay triangulation to process the discrete data on the gear surface.
The Delaunay triangle network has the property that there will be no other points within the circumcircle of any triangle, and the triangles are formed by the closest points. This ensures consistent results regardless of where the processing starts on the tooth surface and helps improve the detection accuracy of gear wear.
The NURBS surface of the gear is constructed using the tensor product form, as shown in the following expression:
where i and b represent the surface directions, A(i, b) is the NURBS surface function, q is the number of center points in the direction i, m is the number of center points in the direction b, Bai is the center point of the surface, N. is the spline basis function in the direction i, N_{6, i} is the spline basis function in the direction b, and 5.1 is the weight factor.
After measuring the discrete data on the gear surface using the scanning method, the discrete data is processed using the Delaunay triangulation principle. Let αi represent the scan line, then we have: i = 1, 2, 3,…, n, αi, αi + 1 represent two adjacent scan lines, αi(k), k = 1, 2, 3,…, y; αi + 1(K), K = 1, 2, 3,…, y represent the test points, and y represents the number of test points.
The starting and ending points on two adjacent scan lines are connected, and then the nearest measurement points on the other line corresponding to each measurement point on one scan line are connected. The space area between the two scan lines is divided into several regions, as shown in Figure 1(a). The triangle and quadrilateral space regions are detected, and the quadrilateral space region is divided according to the maximum minimum interior angle criterion to complete the Delaunay triangulation。
By performing Delaunay triangulation on the non-feature discrete data of the tooth surface, the data is blocked into blocks. A random triangle on the NURBS tooth surface model is selected as the central triangle CenTri, and the values of all central triangles are calculated using the following formula:
where n = 1, 2, 3, ε is the angle between two triangles, and Y is the value of the central triangle region.
The central triangle with the smallest regional value is selected as the starting triangle, as shown in Figure 2(a). The adjacent triangle with the smallest angle to the starting triangle is selected as the central triangle. If Equation (2) is satisfied, the starting central triangle is excluded, and the angle between the surrounding triangles and the starting triangle is calculated. The triangle with the smallest angle is selected as the central triangle. Otherwise, the starting triangle is reselected. Following the above operations, all triangles are traversed to complete the non-feature discrete data blocking of the gear。
Through the triangular region interpolation algorithm, the tooth surface data is calculated to achieve a comprehensive description of the gear surface area.
| Figure | Description |
|---|---|
| Figure 1 | Delaunay Triangulation of Adjacent Scan Lines |
| Figure 2 | Non-Feature Discrete Data Blocking for Gear Models |
3. Gear Wear Detection Using Hermite Interpolation Algorithm
Based on the results of the tooth surface non-feature discrete data blocking, we use the local mean decomposition (LMD) algorithm in the Hermite interpolation algorithm to detect the wear of the tooth surface. The specific detection steps are as follows:
(1) Set the original discrete data as c(y) and convert the original strong noise discrete data c(y) into small parameter data.
(2) Perform denoising processing on the small parameter data obtained in step (1) in the cascaded bistable stochastic resonance (CBSR) system to obtain the denoised discrete data c*(y).
(3) Perform extension processing on the extreme points of the denoised discrete data to obtain a new sequence cp.
(4) Starting from one end of the new sequence, select the maximum or minimum point and generate two envelope lines using the Hermite interpolation algorithm.
(5) Calculate the local mean function using the following formula:
where q(y) is the local mean function, Rap(y) is the upper envelope line, and Rdum(y) is the lower envelope line.
(6) Calculate the envelope estimation function using the formula:
where s(y) is the envelope estimation function.
(7) Separate the envelope data from the original tooth surface data using the LMD analysis method and calculate the PF (product function) component amplitude of the envelope data using the formula:
where f0(y) is the PF component amplitude, and the value of f(y) ranges from [0, 1]. If the calculation result of Equation (5) is outside this range, it is determined that wear occurs in this region.
These steps are repeated infinitely until all the triangular meshes of the gear are traversed and detected.
4. Experimental Analysis
To verify the effectiveness of the proposed wear detection method for automotive spiral bevel gears, a comparative test experiment is conducted.
In this study, the spiral bevel gear of the Santana 2015 manual car is selected as the research object, and 20 gears of the same model are used for the study. This spiral bevel gear operates stably, has a large transmission ratio, transmits large power, and has a compact structure, which can meet the requirements of this experiment.
The material properties of the automotive spiral bevel gear are shown in Table 1, and the experimental equipment used is shown in Figure 3. The wear situation of the automotive spiral bevel gear is shown in Figure 4, and the Delaunay triangulation result of the worn gear is shown in Figure 5.
| Table | Description |
|---|---|
| Table 1 | Material Properties of Automotive Spiral Bevel Gears |
Based on the above experimental equipment and material property data, the experimental process is planned to obtain more accurate experimental results. The specific experimental process is as follows:
(1) Keep the gear wear experimental equipment running continuously for 200 hours, and collect the wear data of the gear within 200 hours. The data collection interval is 5 minutes, and 12 sets of wear data can be collected within one hour.
(2) Set the gear wear depth, gear wear rate, and detection accuracy of the wear area as the test indicators for this experiment.
(3) Select the detection method based on reverse engineering proposed in Reference and the detection method based on the improved Mask Scoring R – CNN proposed in Reference as the comparison methods for this experiment.
(4) Conduct experimental verification using the three different methods according to the set experimental indicators.
| Figure | Description |
|---|---|
| Figure 3 | Experimental Equipment |
| Figure 4 | Wear of Spiral Bevel Gears |
| Figure 5 | Delaunay Triangulation Results of Worn Gears |
4.1 Gear Wear Depth
The wear of the gear mainly occurs between the driving gear and the driven gear, and the wear depth of the gear will change with the increase of operating time. The wear depth results of the driving gear and the driven gear are 。
5. Future Research Directions
Although the proposed method based on Delaunay triangulation has shown promising results in the wear detection of automotive spiral bevel gears, there are still some areas that can be further explored and improved in future research.
One possible direction is to optimize the Delaunay triangulation algorithm to enhance the efficiency and accuracy of the data blocking process. This could involve developing more efficient algorithms for triangle construction and mesh generation, as well as improving the robustness of the algorithm in handling complex tooth surface geometries.
Another area of research could be the integration of multiple sensor data for more comprehensive gear wear assessment. For example, combining vibration, acoustic, and temperature sensors could provide more detailed information about the gear’s operating condition and wear status, leading to more accurate detection and diagnosis.
In addition, the development of real-time monitoring systems based on the proposed method would be highly valuable. Such systems could enable continuous monitoring of the gear wear in real-time, providing early warnings and allowing for timely maintenance actions to prevent potential failures.
Furthermore, exploring the application of machine learning and artificial intelligence techniques in gear wear detection could also be beneficial. These techniques could be used to analyze the large amounts of data collected during the detection process, identify patterns and trends, and make more intelligent predictions about the gear’s wear behavior.
6. Conclusion
In conclusion, the wear detection of automotive spiral bevel gears is a critical issue for ensuring the safety and reliability of vehicles. The proposed method based on Delaunay triangulation offers a novel and effective approach for detecting gear wear, with the potential to improve the detection accuracy and provide valuable information for maintenance and repair decisions.
However, there is still room for further research and development in this field to address the remaining challenges and to meet the increasing demands of the automotive industry. Continued efforts in this area will contribute to the advancement of gear wear detection technology and the overall performance and safety of automobiles.
It is hoped that this research will inspire further studies and innovations in the field of automotive gear wear detection, leading to more reliable and efficient solutions for the automotive industry.
| Table | Description |
|---|---|
| None | Future research directions and conclusions could be summarized in a table, but specific content would depend on the details of the research and future plans. |
| Figure | Description |
|---|---|
| None | Relevant figures could be added to illustrate future research directions or experimental setups, but this would depend on the specific research focus. |