Spiral bevel gears are widely used in high-speed and heavy-duty gear transmission systems in various fields such as aviation, automobiles, and machine tools due to their excellent transmission performance, such as long meshing line, large overlap coefficient, stable transmission, low noise, and high load-carrying capacity. However, the processing and assembly of spiral bevel gears are quite different from those of straight cylindrical gears due to their special characteristics. The axial, circumferential, and radial forces generated during the operation of spiral bevel gears can change the original assembly position of the gear pair and the meshing contact area, thus affecting the load-carrying capacity and working quality of the gear pair. Therefore, in the processing and assembly of spiral bevel gears, the tooth profile and tooth direction of the tooth surface need to be designed and corrected according to the principle of local conjugation, and the meshing contact area needs to be checked by applying coloring agents in various working positions to avoid edge contact caused by the change of the contact area due to assembly errors and the change of the force of the transmission system.
Introduction
In the design of spiral bevel gears, after the selection of transmission parameters, precision design, and load-carrying capacity check, the working meshing positions of the gear pair under various working conditions (such as starting working state, long-term working state, etc.) need to be analyzed according to the local conjugate contact method, and the meshing contact area specification for the processing and assembly of the gear pair is prepared for the detection during gear processing and assembly.
Generally, due to the complex working conditions and calculations of spiral bevel gears, the meshing specification is often determined by inferring and iterating from the metal wear marks after the gear pair works. The meshing specification has requirements for the installation position, coloring contact area imprint status, size, position layout, and backlash of the gear pair during grinding and assembly meshing inspection. The requirements for the shape and size of the imprint in the meshing contact area of the specification are shown in Figure 1a.
Coloring Detection of Meshing Contact Area
During the processing and assembly of spiral bevel gears, the traditional method for checking the meshing contact area is coloring meshing inspection. That is, the gear pair is installed on a special meshing equipment or special meshing tooling, one of the gear tooth surfaces is coated with color, the gear pair is operated, and the contact imprint on the other gear tooth surface is observed. The final processing method of the gear tooth surface is usually grinding, and the meshing contact area inspection in the grinding process is carried out on a special bevel gear rolling inspection machine (such as the Gleason No. 523 universal rolling inspection machine) (see Figure 2a), and the inspection standard is the meshing specification designed and compiled. The rough processing of the tooth surface is usually milling, which is arranged before the heat treatment of the gear part. The detection of the tooth surface in the milling process is not required in the specification, and most processing processes use a “standard gear” with a thinned tooth surface to observe and judge in an unloaded system on a special meshing rolling machine (see Figure 2b) or special tooling (such as a meshing disk, see Figure 2c) for meshing coloring inspection. The difference in the assembly process is that the gear pair is rotated manually, and it is difficult to achieve the limited loading requirements specified in the meshing specification.
| Inspection Method | Equipment or Tooling | Inspection Process |
|---|---|---|
| Grinding Process | Gleason No. 523 Universal Rolling Inspection Machine | The gear pair is installed on the machine, and the meshing contact area is checked according to the meshing specification. |
| Milling Process | Special Meshing Rolling Machine or Special Tooling (e.g., Meshing Disk) | A “standard gear” is used to observe and judge the tooth surface in an unloaded system. |
Three-Coordinate Detection of Meshing Contact Area
Mathematically, points can form lines, and lines can form surfaces. The meshing area surface of the gear pair can be detected and controlled by points. As long as there are enough measured points and the surface is fitted by points, the characteristics of the surface (such as flatness, profile, etc.) can be completely replaced. Especially with the emergence of digital three-coordinate measuring machines, it is feasible to replace the coloring inspection of the surface by the coordinates of the measured points.
Necessity Analysis
- Difficulties in measuring the size of the coloring contact area: Modern gear design requires deburring and chamfering the tooth profile and tooth direction. After chamfering and rounding, it brings difficulties to the measurement of the size of the gear meshing contact area and the judgment or color shape stamping of the size boundary, and the measurement error is relatively large. The actual coloring imprint of the gear meshing in the production site is shown in Figure 1b.
- Uncertainties in the judgment and size measurement standards of the coloring contact area: Spiral bevel gears are highly specialized, and most of them are processed and manufactured by external specialized gear manufacturers, and assembled by the engine manufacturer. The acceptance of the gear meshing contact area is traditionally done by stamping, which has many defects and uncertainties, such as the confirmation of the color shape of the coloring imprint, the confirmation of the size boundary, etc. Especially during assembly, the color shape and size of the meshing contact imprint under the unloaded state are different from those during grinding with loading, which has always been a difficult link to coordinate in the processing and assembly of spiral bevel gears.
- The coloring contact area inspection method is difficult to meet the requirements of modern gear design: With the improvement of user requirements, the design also puts forward higher requirements for the processing and assembly of gears. For example, the uniformity of the depth of the tooth surface penetration layer and the integrity of the tooth surface hardness, etc. The traditional practice of reserving sufficient processing allowance to ensure that the tooth surface can be ground out cannot meet the requirements of modern gear design. Therefore, in the milling process before heat treatment, the grinding allowance of the tooth surface needs to be controlled according to the requirement of the uniformity of the penetration layer, and an effective control means is to take the same tooth surface three-coordinate sampling inspection as in the grinding process.
Feasibility Analysis
- It is mathematically feasible to replace the surface measurement by fitting the surface with the measured points. As long as there are enough measured points, the characteristics of the surface can be fully expressed.
- After the gear tooth surface is divided into grids and points are measured and the surface is fitted, it can be used as a comprehensive measurement and evaluation index for the profile of the tooth surface (the difference between the actual fitted surface and the standard fitted surface), and also as a control requirement for the single point of the tooth surface. See Figure 3 for the grid division and three-coordinate measurement results of the tooth surface of a certain type of aero-engine spiral bevel gear.
- Currently, most commercially available gear digital three-coordinate measuring machines have the functions of automatic numerical control programming, automatic calculation, automatic evaluation, and printing of tooth surface grid division, tooth surface point measurement, and gear-related parameters.
It is recommended to use three-coordinate measurement to inspect the tooth profile and tooth direction of the bevel gear to replace the traditional coloring inspection method of meshing with the sample gear. As long as the measurement data in the grid diagram is qualified, the part is qualified and can be interchangeable without the need for pairing. The numerical values and directions of the tooth profile error and tooth direction error can be directly read out, just like in the Gleason company. The three-coordinate detection of the meshing contact area of the spiral bevel gear can be carried out in the same way as the inspection of the cylindrical gear.
Control of the Processing Meshing Contact Area
The processing process of spiral bevel gears can be divided into two stages before and after heat treatment based on the heat treatment, and into rough processing (milling) and fine processing (grinding) based on the tooth surface processing. The traditional process for detecting the meshing area in the grinding process is to perform meshing coloring and mutual meshing coloring detection between the processed gear and the inspection “standard gear,” and finally deliver them in pairs. According to the three-coordinate detection analysis of the meshing contact area, it is feasible to replace the meshing coloring detection with the three-coordinate detection. However, in actual operation, in order to provide data for gear processing and equipment adjustment (such as the adjustment displacement of the contact area V – H and the adjustment of equipment processing parameters), and for the comprehensive evaluation of the shape, trend, running stability, and noise of the meshing contact area, the “tooth surface three-coordinate detection as the main method, and meshing coloring inspection as a supplementary method” can be adopted to detect and control the meshing contact area in the grinding process.
Although the meshing specification does not require the detection of the meshing contact area in the milling process, in order to ensure the depth and uniformity of the penetration layer on the tooth surface, it is recommended to completely adopt the “three-coordinate detection to replace the meshing coloring detection” method for the rough processing of the tooth surface in the milling process.
| Processing Stage | Detection Method | Purpose |
|---|---|---|
| Grinding | Tooth surface three-coordinate detection as the main method, meshing coloring inspection as a supplementary method | Provide data for gear processing and equipment adjustment, and evaluate the meshing contact area. |
| Milling | Three-coordinate detection to replace the meshing coloring detection | Ensure the depth and uniformity of the penetration layer on the tooth surface. |
Control of the Assembly Meshing Contact Area
For spiral bevel gear transmissions, the control of the meshing contact area can be achieved by replacing the traditional meshing coloring inspection with the measurement of points on the tooth surface by a three-coordinate measuring machine during grinding. However, during assembly, how to confirm and control the meshing contact area under various working conditions can be achieved by adopting the method of “fixed-distance assembly supplemented by meshing coloring inspection.”
Fixed-Distance Assembly
The meshing specification of the spiral bevel gear is formed through continuous revision and repeated iteration based on the actual metal wear marks on the tooth surface after the gear works. It is used as the standard for grinding and assembling the gear pair to adjust the meshing contact area. This standard reflects the contact area requirements of the gear pair under various working conditions (i.e., the ideal meshing contact area). If the size of the transmission housing, bearings, and other components is adjusted during the assembly of the gear pair to ensure the assembly at the installation distance required in the meshing specification, the meshing contact area of the gear pair will be the most ideal. This operation is called “fixed-distance assembly.”
The position size of the gear pair is usually adjusted by the adjustment pads on the driving and driven shafts. When calculating the size of the adjustment pad, the measured values should be used for the dimensions of the transmission housing, the width of the bearings, etc. (the theoretical installation distance value is used for the gear pair). For the treatment of the axial clearance of the bearings, the large clearance and small clearance checks required in the meshing specification are designed and checked indicators considering the bearing clearance and the rigidity of the transmission system (such as elastic deformation, processing and assembly errors, etc.) under various working conditions. Under fixed-distance assembly, if the normal clearance, large clearance, small clearance, and radial runout of the gear ring meet the relevant technical conditions as specified in the meshing specification, it indicates that the assembly of the gear pair is in an ideal position.
The gear pair under fixed-distance assembly is in the theoretical position state during grinding, which is also the state required by the meshing specification. By calculating the thickness size of the adjustment pad according to the formula, as shown in Figure 4 for the calculation dimension chain diagram of the adjustment pad for a certain type of engine.
| Assembly Method | Process | Purpose |
|---|---|---|
| Fixed-Distance Assembly | Adjust the size of the transmission housing, bearings, and other components to ensure assembly at the installation distance required in the meshing specification. | Achieve the ideal meshing contact area of the gear pair. |
Supplemented by Meshing Coloring Inspection
Although the traditional meshing coloring inspection has shortcomings such as unclear size boundaries, inaccurate imprint judgment, and low measurement accuracy, it is necessary as an auxiliary means to cooperate with the three-coordinate detection and fixed-distance assembly to detect coarse errors and comprehensive errors. Especially for checking and verifying the calculation of the adjustment pad size, the measurement of the transmission housing, the width and clearance of the bearings, and the judgment of the status and position trend of the meshing contact imprint caused by the comprehensive errors are effective.
After adopting the measures of “fixed-distance assembly supplemented by coloring inspection,” the requirements for the processing and assembly of gears in the grinding and assembly sites are clear, the operation is simple and easy, the communication with external suppliers is fast and effective, the metal wear marks after the gear works are good, and nearly 4,000 sets have been produced and delivered without any quality faults caused by problems in the meshing contact area during grinding and assembly.
| Inspection Method | Role | Effect |
|---|---|---|
| Meshing Coloring Inspection | As an auxiliary means to detect coarse errors and comprehensive errors, and to verify the adjustment pad size, transmission housing measurement, bearing width, and clearance. | Help judge the status and position trend of the meshing contact imprint. |
Conclusion
In conclusion, the following conclusions can be drawn:
- The process method of “replacing the meshing coloring inspection with three-coordinate detection” for the control of the meshing contact area on the tooth surface of spiral bevel gears is feasible.
- For the detection of the meshing contact area in the processing and assembly of spiral bevel gears, the grinding process can adopt the “tooth surface three-coordinate detection as the main method, and meshing coloring inspection as a supplementary method,” and the milling process can adopt the “three-coordinate detection to replace the meshing coloring detection.”
- The same process method can also be adopted for the detection of the meshing area of the tooth surface of straight bevel gears.
In future research, we can further explore the application of more advanced detection technologies and methods in the processing and assembly of spiral bevel gears to improve the accuracy and reliability of the detection. Additionally, the optimization of the processing and assembly processes based on the detection results can also be studied to improve the performance and quality of the gear transmission system.