This study proposes an innovative detection system for worm gear tooth pitch measurement using synchronous displacement sampling principles. The system addresses limitations in traditional contact/non-contact measurement methods by implementing real-time angular displacement monitoring during worm gear operation, achieving micron-level accuracy with 85% efficiency improvement compared to conventional pitch measuring instruments.
1. Theoretical Framework
The measurement principle combines synchronous displacement sampling with high-frequency clock interpolation. For worm gear pairs with transmission ratio i, the transmission error (TE) is defined as:
$$ TE = \varphi_0′ – \varphi_0 = \varphi_0′ – \frac{\varphi_i}{i} $$
where $\varphi_i$ and $\varphi_0’$ represent the input (worm) and output (worm gear) angular displacements respectively. The actual tooth pitch $P_i$ is calculated through pulse interpolation:
$$ P_i = \frac{\left[ n + \frac{T_{c(i)} – T_{c(i-1)}}{N_H} \right] \cdot \pi m}{P_0} $$
Key parameters for measurement system design are summarized in Table 1.
| Parameter | Value | Description |
|---|---|---|
| $\lambda_1$ | 2048 lines | Worm shaft encoder resolution |
| $\lambda_2$ | 32768 lines | Worm gear encoder resolution |
| $f_{clk}$ | 40 MHz | Interpolation clock frequency |
| Measurement range | φ50-500 mm | Worm gear diameter |
2. System Architecture
The hardware implementation consists of three main modules:
- Signal conditioning circuit with 1Vpp differential to 3.3V TTL conversion
- FPGA-based data processing core (Cyclone IV EP4CE15)
- USB 2.0 communication interface (CY7C68013A)
The signal processing flow follows:
$$ \text{Encoder Signal} \rightarrow \text{Quadrature Decoding} \rightarrow \text{Clock Interpolation} \rightarrow \text{Data Packaging} \rightarrow \text{USB Transmission} $$
3. Key Technologies
3.1 Pulse Subdivision
The 4× frequency multiplication logic improves angular resolution:
$$ N_{effective} = 4 \times \lambda = 8192\ \text{CPR} $$
Digital interpolation extends resolution to 0.02μm level through:
$$ \Delta P = \frac{\pi m}{Z_2} \cdot \frac{\Delta T}{T_H} $$
3.2 Error Compensation
System errors are minimized through:
$$ \Delta P_{max} = \frac{\Delta \varphi \cdot r}{1296Z_2} $$
where $\Delta \varphi$ represents encoder system error (≤1.54″) and r is pitch circle radius.
4. Experimental Verification
Testing results for a Z=144 worm gear show:
| Tooth Surface | Conventional Method | Proposed System | Deviation |
|---|---|---|---|
| Left Flank | 11.9346 | 11.9333 | 1.3 |
| Right Flank | 11.9352 | 11.9350 | 0.2 |
The measurement efficiency comparison reveals:
$$ \eta = \frac{t_{conventional}}{t_{proposed}} = \frac{300\text{s}}{120\text{s}} = 2.5\times $$
5. Conclusion
This worm gear detection system demonstrates:
- Measurement accuracy ≤3μm, meeting VDI/VDE Class 1 requirements
- 150% efficiency improvement over traditional methods
- Non-contact measurement capability during actual operation
Future work will focus on miniaturization and adaptive error compensation for different worm gear types. The proposed methodology provides a new paradigm for precision transmission component quality control in intelligent manufacturing systems.