Abstract
Herringbone gear, characterized by high bearing capacity and low axial load, are widely utilized in large power equipment such as ship propulsion and aerospace systems. The neutrality of the tooth surfaces on both sides of a herringbone gear directly influences the uniformity of contact load distribution, vibration, and noise during transmission, thereby affecting its service life. Due to asymmetry issues in the contact lines of the same-side tooth surfaces of gear teeth on both sides after processing, it inevitably leads to eccentric loading, axial vibration, and uneven meshing transmission, reducing the stability and reliability of herringbone gear transmission. Therefore, this paper has important theoretical and engineering significance for the design and manufacture of herringbone gear by investigating the measurement and evaluation of symmetry errors of gear teeth on both sides from a performance-oriented perspective.
1. Introduction
1.1 Research Background and Significance
Table 1: Research Background and Significance
| Aspect | Details |
|---|---|
| Source of the Project | Aerospace Engine Double Helical Gear Symmetry Measurement, Evaluation System Construction, and Engineering Technology |
| Research Background | High precision required in transmission for herringbone gear; current measurement and evaluation methods do not fully reflect manufacturing accuracy |
| Significance | Supports high-precision design and verifies processing accuracy of herringbone gear |
The herringbone gear is often used in fields requiring high transmission accuracy. Therefore, verifying the processing accuracy of herringbone gear and providing support for their high-precision design are crucial. Currently, the measurement and evaluation methods for herringbone gear still adopt the standard system for helical cylindrical gear, which means the two oppositely helical gears of a herringbone gear are measured and evaluated independently, failing to accurately and comprehensively reflect the manufacturing accuracy of herringbone gear.
1.2 Research Status at Home and Abroad
Table 2: Research Status on Herringbone Gear Transmission Systems and Measurement
| Research Area | Domestic Status | International Status |
|---|---|---|
| Transmission Systems | Focus on dynamic performance, vibration, and noise reduction | Emphasis on optimization of gear geometry and materials |
| Measurement | Utilizing standard helical gear measurement methods | Developing specialized measurement techniques for herringbone gear |
1.3 Main Content of This Paper
Table 3: Main Research Content and Basic Ideas
| Research Aspect | Details |
|---|---|
| Basic Idea | Starting from the performance of herringbone gear, studying the mathematical model and error evaluation method of contact lines on tooth surfaces; designing measurement methods and software; conducting experiments on measuring machines |
| Main Research Content | Definitions of contact lines and symmetry errors; evaluation methods; measurement principles; measurement software design; experimental verification and analysis |
2. Definitions of Contact Lines and Their Symmetry Errors
2.1 Definition of Contact Lines of Herringbone Gear
Illustration: Diagram of Contact Line on Herringbone Gear Tooth Surface
The contact line on the same-side tooth surface of the gear teeth on both sides of the herringbone gear reflects its meshing state.
2.2 Definition of Symmetry Errors
Table 4: Types of Symmetry Errors
| Type of Error | Description |
|---|---|
| Individual Tooth Symmetry Error | Deviation of the contact line from the ideal symmetrical position on a single tooth |
| Difference in Symmetry Error Between Adjacent Teeth | Variation in symmetry errors between consecutive teeth |
| Total Symmetry Error | Cumulative symmetry error across all teeth |
| Average Symmetry Error | Mean of symmetry errors across all teeth |
3. Theoretical Research on Evaluation Method Based on Contact Line Symmetry
3.1 Mathematical Model of Contact Lines
The mathematical model of the herringbone gear contact line is established by simulating the theoretical contact line and discrete data of the actual contact line with superposition errors in the coordinate system.
Illustration: Mathematical Model of Contact Line
3.2 Extraction of Discrete Measurement Points on Contact Lines
Table 5: Methods for Solving Theoretical and Actual Measurement Points
| Method | Description |
|---|---|
| Theoretical Measurement Points | Based on gear geometry and tooth profile |
| Actual Measurement Points | Considering manufacturing errors, added random errors to theoretical points |
3.3 Least Squares Fitting and Error Calculation
Using the least squares method, the theoretical and actual measurement points are fitted to obtain the contact line, and the symmetry error is calculated.
3.4 Verification Example
A herringbone gear was measured, and the symmetry errors of two teeth with a circumferential angle of 120° were calculated as -0.0275 mm and -0.0256 mm, respectively.
Table 6: Symmetry Error Verification Results
| Tooth Number | Calculated Symmetry Error (mm) | Measured Symmetry Error by Sectional Method (mm) |
|---|---|---|
| 1 | -0.0275 | -0.0278 |
| 10 | -0.0256 | -0.0258 |
4. Measurement Principle of Contact Lines
The evaluation coordinate system of the herringbone gear contact line is applied to the measuring machine to form the measurement coordinate system and determine the axial measurement reference.
Illustration: Measurement Coordinate System
5. Design of Measurement Software
The software is designed using C++ for the measuring machine, establishing an axial measurement reference, controlling the movement of the measuring probe and turntable, acquiring measurement data, and processing it to obtain the symmetry error of the herringbone gear contact line.
6. Experimental Verification and Analysis
6.1 Measurement Results
Table 7: Measurement Results of Small and Large Module Gears
| Gear Type | Evaluation Interval (mm) | Individual Tooth Symmetry Error Range (mm) | Total Symmetry Error (mm) | Difference in Symmetry Error Between Adjacent Teeth (mm) | Average Symmetry Error (mm) |
|---|---|---|---|---|---|
| Small | [16, 34] | -0.0201 ~ -0.0002 | 0.0199 | 0.0101 | -0.0113 |
| Large | [19, 48] | -0.0322 ~ -0.0245 | 0.0077 | 0.0056 | -0.0281 |
6.2 Comparison of Measurement Methods
The contact line method, although slower, offers higher measurement accuracy compared to the sectional method.
Table 8: Comparison of Measurement Methods
| Method | Measurement Time | Measurement Accuracy |
|---|---|---|
| Contact Line | Longer | Higher |
| Sectional | Shorter | Lower |
6.3 Measurement Uncertainty Analysis
Standard uncertainty is calculated using statistical methods to assess the measurement variability.
Conclusion
This paper presents a method for measuring and evaluating the symmetry of herringbone gear based on contact lines, filling a gap in gear measurement centers. The main conclusions are:
- Definition and Significance: The definition of contact line symmetry error for herringbone gear is proposed, revealing the root causes of uneven load distribution and axial movement.
- Evaluation Method: A method based on the least squares principle is proposed to evaluate the symmetry error.
- Experimental Verification: The contact line method is verified through experiments, showing higher accuracy than the sectional method.
Innovations
- Definition and Mathematical Model: First research on the definition and mathematical model of contact line symmetry error for herringbone gear.
- Measurement Method: First proposal of a measurement method for contact lines of herringbone gear, enhancing measurement precision.
This research provides new insights and directions for future studies on the measurement and evaluation of herringbone gear symmetry.