Abstract
The design theory and experimental research of the cylindrical geometric elements constructed tooth gear shaving cutter. As a new type of gear, the geometric elements constructed gear exhibits unique characteristics such as point contact between convex and concave tooth surfaces, resulting in strong load-bearing capacity and excellent lubrication performance. After years of research and development, various processing methods for this type of gear have been established, but there has been no relevant research on gear shaving, one of the efficient and economical finishing processes. Therefore, this thesis takes the cylindrical geometric elements constructed gear as the object to study the basic design theory of its shaving cutter and verifies the correctness of the theoretical research through experimental studies.
1. Introduction
The cylindrical geometric elements constructed gear, with its characteristics of constant power transmission, largely determines the performance of equipment and thus occupies a strategically important position in national economic construction and national defense. Over the past two decades, research and development in this field have led to the formation of technical foundations in basic meshing theory, tooth surface construction methods, meshing performance analysis, processing methods and equipment, inspection theory and equipment, as well as experimental research. Various types of geometric elements constructed gears have been developed, and related research results have obtained domestic and international patents and software copyrights.
Despite these advancements, there has been no research on gear shaving for geometric elements constructed gears. Therefore, this thesis aims to study the design theory of the shaving cutter for cylindrical geometric elements constructed gears and verify its correctness through experimental research.
2. Literature Review
Table 1 summarizes some of the key research in the field of gear shaving and geometric elements constructed gears.
| Reference | Topic | Year |
|---|---|---|
| [67] | Modification gear shaving cutter | 2011 |
| [68] | Theoretical and Practical Investigations on the Design of Plunge Shaving Cutter | 2013 |
| [69] | Serration Design for a Gear Plunge Shaving Cutter | 2011 |
| … | … | … |
3. Basic Meshing Principle of Cylindrical Geometric Elements Constructed Gear
The cylindrical geometric elements constructed gear features a unique meshing mechanism between convex and concave tooth surfaces. To derive the tooth surface equations, such as the working section, tooth root transition section, and tooth top transition section, analytical solutions are obtained based on the conjugate curve theory.
4. Design Theory of Gear Shaving Cutter for Cylindrical Geometric Elements Constructed Gear
4.1 Conjugate Curve Theory
The basic definitions of conjugate curves are given, and the relationships between relative motion velocity and normal vector are solved. The meshing equation and conjugate curve equation for parallel-axis cylindrical geometric elements constructed gear pairs are derived.
4.2 Tooth Surface Equation of Gear
Using the gear-rack method, combined with the basic tooth profile of the rack’s normal plane, the solution method for the tooth surface equation of the corresponding gear pair is presented.
4.3 Software Design for Gear Shaving Cutter
Based on Python, a software for designing cylindrical geometric elements constructed gear shaving cutters was developed. The software realizes functions such as basic tooth profile design, strength verification, and data point and geometric parameter design for the shaving cutter.
Table 2 outlines the functional requirements of the software.
| Function | Feature Points | Description |
|---|---|---|
| Gear Verification | Set Default Reference Values | Obtain default reference values and modify gear parameters based on them |
| Gear Parameter Input | Basic Parameters | Modulus, normal pressure angle, gear width, backlash, tooth number, helix angle, etc. |
| Recommended Design Parameters | Parameter Range | Calculate parameter ranges such as start offset, end offset, and envelope surface radius |
| Shaving Cutter Calculation | Similar to gear verification but specific to shaving cutter design |
4.4 Software Interface Design and Interaction
The software interface design focuses on user-friendliness and efficiency. The interface for drawing basic tooth profiles and the shaving cutter design section.
5. Experimental Research on Gear Shaving Processing
5.1 Introduction
Experimental research was conducted to verify the correctness and feasibility of the designed shaving cutter.
5.2 Shaving Processing Scheme Design
Table 5.1 lists the parameters for the gear shaving process.
| Parameter | Symbol | Convex Gear | Concave Gear |
|---|---|---|---|
| Modulus (mm) | n_m | 6 | 6 |
| Gear Tooth Number | 2Z | 30 | 30 |
| Shaving Cutter Tooth Number | 1Z | 41 | 30 |
| Helix Angle (°) | 33.8217 | 33.8217 | |
| Pressure Angle (°) | 25 | 25 | |
| Gear Width (mm) | 2b | 80 | 80 |
| Shaving Cutter Width (mm) | 1b | 50 | 50 |
| … | … | … | … |
5.3 Processing Procedure and Results
The processing involved hobbing and shaving steps. The Y4232CNC2 gear shaving machine was used for the shaving process.
5.4 Measurement of Tooth Surface Roughness
The surface roughness of the gears before and after shaving was measured using an Alicona InfiniteFocus G5 optical 3D measuring instrument.
5.5 Experimental Results
The surface roughness of both convex and concave cylindrical geometric elements constructed gears decreased significantly after shaving, proving the feasibility of the proposed shaving cutter design method.
6. Conclusion and Future Work
6.1 Main Conclusions and Innovations
The main conclusions of this thesis include:
- Established a mathematical model for the basic meshing principle of cylindrical geometric elements constructed gears.
- Developed software for designing shaving cutters, improving design efficiency.
- Conducted experimental research, verifying the correctness of the shaving cutter design.
6.2 Future Work
To further improve the research, the following areas need to be addressed:
- Incorporate the gear shaving TCA (Tooth Contact Analysis) calculation program into the software.
- Conduct more extensive experimental research to validate the design under various conditions.