1. Introduction
Worm gear transmission systems are widely used in industrial applications such as CNC machine tools, automotive systems, and precision instruments due to their ability to achieve high transmission ratios, smooth operation, and self-locking capabilities. However, wear, manufacturing inaccuracies, and installation errors can lead to deviations in tooth pitch, directly affecting transmission accuracy and reliability. Traditional methods for measuring worm gear tooth pitch, including contact-based coordinate measuring machines (CMMs) and non-contact laser systems, often suffer from inefficiency, high costs, and limited adaptability to real-world operating conditions. This study proposes a high-efficiency detection system for worm gear tooth pitch based on the synchronous displacement sampling principle, integrating FPGA-based signal processing, USB2.0 data transmission, and real-time software analysis.
2. Theoretical Foundations
2.1 Synchronous Displacement Sampling Principle
The core idea involves sampling the angular displacement of the worm gear synchronously with the rotation of a reference worm. Let the theoretical angular displacement of the worm gear be φ0, and the actual displacement be φ0′. The **transmission error (TE)** is defined as:TE=φ0−φ0′=iφi′−φ0′
where i is the transmission ratio, and φi′ is the input angular displacement of the worm.
2.2 Worm Gear Tooth Pitch Measurement
The nominal tooth pitch P of a worm gear is calculated as:P=π⋅m
where m is the module. However, deviations caused by manufacturing or wear necessitate absolute measurement methods. The actual tooth pitch Pi′ for the i-th tooth is derived from the angular displacement αi and the pitch radius r:Pi′=αi⋅r
3. System Design
3.1 Hardware Architecture
The detection system comprises three modules:
- Signal Conditioning Circuit: Converts incremental encoder signals (1Vpp sinusoidal) into TTL-compatible square waves.
- FPGA-Based Data Acquisition: Implements pulse counting, interpolation, and synchronization logic.
- USB2.0 Communication: Transfers data to a PC for real-time analysis.
Key components include:
- Incremental Encoders: Heidenhain ERN180 (2,048 lines) and RCN8581 (32,768 lines).
- FPGA: Altera Cyclone IV (EP4CE15F23I7) for high-speed signal processing.
- USB Controller: Cypress CY7C68013A configured in SlaveFIFO mode.
3.2 Algorithm Design
The FPGA executes a four-step logic for tooth pitch calculation:
- Quadrature Decoding: 4× frequency multiplication of encoder signals.
- Sampling Interval Generation: Divides the worm shaft signal to create synchronization pulses.
- Integer and Fractional Pulse Counting:Δϕ=(ni+NHTc(i)−Tc(i−1))⋅N1where ni is the integer pulse count, Tc is the fractional count from a 50 MHz interpolation clock, and N1 is the angular resolution per pulse.
- Data Framing: Packages results into 16-bit words for USB transmission.
3.3 Software Platform
A C#-based application performs:
- USB Communication: Utilizes Cypress CyUSB.NET library for bulk data transfer.
- Real-Time Display: Plots tooth pitch deviations dynamically.
- Data Logging: Saves results in .txt format for post-analysis.
4. Experimental Validation
4.1 Simulation Testing
A simulated encoder signal generator validated the FPGA logic. Key parameters:
| Parameter | Value |
|---|---|
| Encoder Frequency | 1–5 kHz |
| Interpolation Clock | 50 MHz |
| Sampling Interval | 1 ms |
Results confirmed a counting resolution of ±0.1′′ and a maximum data throughput of 2 MB/s.
4.2 Practical Testing
A worm gear with 40 teeth (module m=2) was measured using both the proposed system and a semi-automatic pitch measuring instrument (Mitutoyo Model 178-561).
| Tooth Index | Proposed System (µm) | Mitutoyo (µm) | Deviation (µm) |
|---|---|---|---|
| 1 | 6.28 | 6.30 | -0.02 |
| 5 | 6.31 | 6.29 | +0.02 |
| 10 | 6.27 | 6.32 | -0.05 |
| 15 | 6.33 | 6.30 | +0.03 |
The maximum deviation of ±0.05μm fell within the Mitutoyo instrument’s ±0.1μm tolerance. Measurement time per tooth was reduced by 62% compared to traditional methods.
5. Advantages and Limitations
5.1 Advantages
- Efficiency: Continuous measurement at 200 teeth/min.
- Accuracy: ±0.1′′ angular resolution.
- Portability: Compact design (FPGA + USB module).
5.2 Limitations
- Requires precise alignment of the reference worm.
- Limited to axial measurements; helical worm gears need additional calibration.
6. Conclusion
This study demonstrates a robust solution for worm gear tooth pitch detection, combining synchronous displacement sampling with modern FPGA and USB technologies. The system achieves sub-micron accuracy while operating 2.6× faster than conventional methods. Future work will focus on multi-axis measurement capabilities and AI-driven error compensation for industrial-grade worm gear inspection.
Key Formulas and Tables
- Transmission Error:TE=iφi′−φ0′
- Tooth Pitch Calculation:Pi′=(ni+NHTc(i)−Tc(i−1))⋅P0πm
- System Performance:MetricValueAngular Resolution±0.1′′Data Throughput2 MB/sMeasurement Speed200 teeth/min
By addressing the limitations of traditional methods, this system provides a scalable and cost-effective tool for quality control in worm gear manufacturing and maintenance.