Abstract
To mitigate operational and maintenance costs associated with oil pumping units, the remanufacturing of pump reducers has gained significant attention. This study focuses on the repair of worn double circular arc gears found in these reducers. Building upon existing research, we propose a methodology that leverages reverse engineering to extract gear design parameters and assess the degree of wear. Utilizing 3D laser scanning technology, we acquire data from worn gear models, process them in Geomagic Design X software, and adopt a surface sketch fitting approach to measure the gear module and derive the helix angle of the reference circle. Through the application of the double circular arc tooth profile equation, we construct a precise solid model of the gear. Additionally, we conduct parameter extraction and deviation analysis on double circular arc gear shafts in practical engineering contexts, aligning the 3D gear model with the scanned model in Geomagic Control X for comprehensive deviation assessment. The results indicate that our proposed method not only ensures measurement accuracy but also mitigates measurement complexity, thereby enhancing gear measurement efficiency compared to manual techniques.
Introduction
The double circular arc gear, an innovative evolution of traditional gears, has found widespread application in decelerators for oil pumping units and hoists. In the Daqing Oilfield, for instance, approximately 55,000 oil pumping units are in operation, with approximately 2% experiencing downtime due to faults annually. Notably, over 40% of these faults are attributed to reducer issues, with gear tooth breakage and wear accounting for roughly 12% of these cases. Given the substantial cost associated with replacing worn double circular arc gears due to their high value within the reducer, the adoption of remanufacturing technologies in conjunction with reverse engineering emerges as a viable option to effectively reduce maintenance expenses.
Reverse engineering, also known as reverse technology, represents a process whereby product design is replicated. It involves converting physical models into digital CAD models, facilitating subsequent analysis, design refinement, and reproduction. Prior studies have demonstrated the potential of this approach in extracting gear parameters and analyzing errors. However, existing methods for measuring worn double circular arc gears often suffer from inefficiency and inaccuracies, prompting the need for a more effective solution. This study addresses this gap by proposing a precise measurement and deviation analysis method tailored specifically for double circular arc gears, leveraging reverse engineering techniques.
Measurement Principles
1. Laser Scanning Technology
Laser scanning technology operates by projecting a laser beam onto the surface of the part being measured. The camera captures the light strip reflected from the surface, and through image analysis, the geometric relationships of the light strip center are deciphered to generate point cloud data of the part. This process involves filtering, denoising, smoothing, and streamlining the acquired point cloud data to ensure a clean and accurate digital representation of the part.
Table 1: Key Performance Indicators of HandySCAN300 3D Laser Scanner
| Performance Indicator | Parameter |
|---|---|
| Sampling Rate | 205,000 samples/second |
| Scanning Accuracy | 0.04 mm |
| Volume Accuracy | 0.02 mm |
| Part Size Range | 0.1 to 4 meters |
| Laser Class | Class II (eye-safe) |
| Software | VXelements |
2. Reverse Measurement Principles for Double Circular Arc Gears
The tooth roots and tips of double circular arc gears typically exhibit minimal wear during operation. By leveraging reverse engineering software, we can directly measure parameters such as the tip circle diameter (R_a), root circle diameter (R_f), number of teeth (Z), and helix lines. These measurements facilitate the back-calculation of fundamental parameters, including full tooth height (h), module (m), pressure angle (α), helix angle (β), and pitch circle radius (R).
Gear Modeling
The fabrication of double circular arc gears involves the use of arc-shaped tooth profiles in the normal plane. Consequently, the creation of a gear model necessitates the integration of tooth profiles and helix lines. By employing the arc gear tooth surface equation, we can derive the end-face equation, enabling the precise construction of double circular arc gear tooth profiles.
Measurement and Parameter Extraction
1. Model Scanning
To commence the scanning process, circular fiducial markers are affixed to the workpiece to facilitate accurate alignment. Utilizing the HandySCAN300 3D laser scanner in conjunction with the VXelements software, a high-fidelity 3D model of the gear shaft is acquired. This model is subsequently imported into reverse engineering software for further processing.
2. Data Processing and Model Refinement
The imported point cloud data undergoes filtering, denoising, and smoothing to enhance its quality. Holes and redundant facets are repaired using dedicated tools within the reverse engineering software, resulting in a refined model suitable for subsequent measurements and analysis.
3. Gear Parameter Measurement
Table 2: Gear Radius Measurements
| Sketch No. | Tip Circle Radius (mm) | Root Circle Radius (mm) | Module (m) Calculated |
|---|---|---|---|
| 1 | 60.3336 | 51.5069 | 4.41335 |
| 2 | 60.3827 | 51.4943 | 4.44420 |
| 3 | 60.3528 | 51.5245 | 4.41415 |
| 4 | 60.3453 | 51.5357 | 4.40480 |
| 5 | 60.4027 | 51.5326 | 4.43505 |
| 6 | 60.3633 | 51.5643 | 4.39950 |
| 7 | 60.3830 | 51.5532 | 4.41490 |
To determine the gear module, effective meshing sections are identified, and parallel cross-sections are created at specific intervals to avoid the influence of chamfered tooth ends. The average tip and root circle radii are calculated from multiple measurements, and the module is approximated based on these values, subsequently rounded to the nearest standard value.
The helix angle is measured by fitting surfaces to selected tooth flank areas, constructing a cylinder intersecting these surfaces to extract helix lines, and calculating the helix angles on the respective cylinders. The final helix angle on the pitch circle is derived using geometric relationships.
3. Gear Model Construction
With the extracted gear parameters, a precise solid model of the double circular arc gear is constructed using MATLAB to compute tooth surface equations and CAD software for model assembly.
Deviation Analysis
Deviation analysis is conducted to identify sources of errors, including manufacturing, measurement, and wear-related deviations. Using Geomagic Control X, a comprehensive analysis of the scanned model against the CAD design is performed, revealing areas of deviation beyond acceptable tolerances.
Table 3: Deviation Analysis Results
| Tolerance | Deviation Observation |
|---|---|
| ±0.1 mm | Minor wear and chipping observed |
| 0.02 mm | Plastic deformation and wear evident |
At a tolerance of ±0.1 mm, the analysis indicates minor wear and chipping primarily concentrated at the tooth tips. When the tolerance is tightened to 0.02 mm, significant plastic deformation and wear become apparent, particularly on the convex and concave arc surfaces of the working flanks.
Conclusion
This study presents a comprehensive approach for measuring and analyzing deviations in worn double circular arc gears using reverse engineering techniques. By integrating 3D laser scanning with advanced software tools, we have successfully demonstrated the ability to accurately extract gear parameters and construct precise solid models. Our method not only ensures measurement accuracy but also enhances efficiency when compared to traditional manual and semi-automated techniques.