Abstract:
Helical gear hobbing relies on two sets of electronic gearboxes for multi-axis synchronous control. Synchronization errors arise from the linear superposition of linkage errors between the rotational motion of the hob B-axis and the workpiece C-axis, as well as the axial motion of the hob along the Z-axis and the C-axis. Complex motion relationships and unstable processing conditions make traditional error compensation difficult in helical gear machining. This paper utilizes the wavelet packet algorithm for decomposition, studies the amplitude distribution patterns of sub-band signals within different frequency scales, performs error feature identification, and reconstructs synchronization errors in helical gear machining. Based on the error superposition principle, the reconstructed synchronization errors are decoupled into the respective servo axes involved in the linkage, and NC codes are modified to inversely compensate the error quantities to the servo axes. Finally, the effectiveness of the compensation method is verified through an example of helical gear machining error compensation on a Qinchuan YK3126 CNC hobbing machine, improving the processing accuracy of helical gear.
Keywords: gear hobbing; multi-axis synchronous motion; wavelet packet decomposition and reconstruction; error compensation
1. Introduction
High-speed dry gear hobbing is a new process for gear manufacturing and an efficient manufacturing technology for machining spur gears and helical gear. However, with a high spindle speed of 1200 r/min, the hobbing cutting speed fluctuates significantly, especially for helical gear processing, which requires two sets of electronic gearboxes for multi-axis synchronous control, making it difficult to ensure accuracy. Therefore, error compensation in helical gear machining is of great significance for improving processing accuracy. The processing accuracy of gear hobbing is affected by various factors, including tool errors, installation errors, thermal errors, servo errors, and synchronization errors in multi-axis linkage, among which synchronization errors are the primary influencing factor. There are mainly two methods to reduce gear processing errors: error prevention and error compensation. Error prevention aims to reduce processing errors by improving the accuracy of assembled parts, but as processing accuracy requirements increase, the cost of error prevention grows exponentially.
2. Structure of the Hobbing Machine and Axis Motion Relationships
The structural diagram of the YK3126 vertical CNC hobbing machine . When processing spur gears on a hobbing machine, only B-C axis linkage is required. For helical gear processing, besides B-C axis linkage, Z-C axis linkage is also needed. Therefore, the linkage relationship of the driven C-axis during helical gear processing is expressed as:
Parameters for Helical Gear and Hob Processing
| Parameter | Value | Parameter | Value |
|---|---|---|---|
| Normal Module (mm) | 3 | Number of Gear Teeth | 59 |
| Hob Number of Flutes | 3 | Feed Rate (mm/r) | 1.5 |
| Pressure Angle (°) | 20 | Feed Depth (mm) | 6.45 |
| Hob Hand | Right-hand | Hob Speed (r/min) | 680 |
| Gear Hand | Right-hand | Hobbing Method | Inverse Hobbing |
3. Analysis of Synchronization Errors
Due to the inherently complex structure of high-speed dry hobbing machines and the helical gear processing technology, the motion of key components involved in helical gear formation, such as the tool holder, hob, and direct-drive motors, are complex, non-stationary, and nonlinear processes. During high-speed dry helical gear processing, the unstable operating state of machine components and variable processing environmental factors result in composite signals influencing the collected synchronization errors. Synchronization error is defined as the difference between the coupled theoretical angular displacement of the additional rotation of the C-axis caused by the rotational motion of the B-axis and the axial movement of the Z-axis, and the actual angular displacement of the C-axis. During data sampling, the register number for collecting synchronization errors is D50. An absolute encoder, referred to as Encoder-C, installed on the C-axis measures the angular displacement of the C-axis.
4. Wavelet Packet Algorithm for Error Compensation
The wavelet packet decomposition and reconstruction algorithm is employed to perform multi-resolution analysis of the collected synchronization error signals. Based on the synchronization error composition principle in helical gear hobbing, error features are identified, and interfering noise is discarded to reconstruct the synchronization errors. According to the error superposition principle, the reconstructed errors are decoupled and compensated separately to the software axes, achieving precise error compensation.
Wavelet Packet Algorithm for Synchronization Error Compensation Model
The synchronization error on-machine compensation model using the wavelet packet decomposition and reconstruction algorithm.
The NC code is used for software compensation, with the decoupled linkage errors inversely compensated to the electronic gearboxes, achieving control compensation for the motion axes.
5. Experimental Results and Analysis
The electronic gearbox code is programmed as follows:
plaintext G146 Q={4, #101, #102, #103, #104, #105, #106, #107, #108} % HNC-SSTT electronic gearbox parameter settingsTable 2. Electronic Gearbox Parameter Settings
| Parameter | Value |
|---|---|
| … | … |
Table 3. Comparison of Gear Profile and Gear Direction Errors Before and After Compensation
| Error Type | Before Compensation (μm) | After Compensation (μm) |
|---|---|---|
| Gear Profile Error (Left Flank) | 17.8 | 8.9 |
| Gear Profile Error (Right Flank) | 23.0 | 9.3 |
| Gear Direction Error (Left Flank) | 12.1 | 11.5 |
| Gear Direction Error (Right Flank) | 18.0 | 15.3 |
| … | … | … |
As can be seen from Table 3, both gear profile errors and gear direction errors are generally reduced compared to before compensation. The overall gear processing accuracy is improved after adopting the wavelet packet algorithm for decomposition, reconstruction, and compensation of synchronization errors. The gear profile and gear direction processing accuracy have been enhanced by one grade. The use of signal processing methods for collected synchronization error data can improve the accuracy of error compensation, providing important guidance for gear manufacturing.
6. Conclusions
(1) The wavelet packet decomposition and reconstruction algorithm is proposed to perform multi-resolution analysis of synchronization errors collected by HNC-SSTT during helical gear machining.
(2) The reconstructed synchronization errors are decoupled into servo axes based on the linear superposition principle, and NC codes are modified for processing verification on a Qinchuan YK3126 CNC hobbing machine, demonstrating significant error compensation effects.
(3) The wavelet packet method is used to address error compensation issues in high-speed dry gear processing, providing a new approach for error compensation in high-speed dry helical gear machining.
The application of the wavelet packet algorithm in error compensation for helical gear hobbing not only enhances processing accuracy but also contributes to advancements in gear manufacturing technology.