We present a comprehensive automatic ultrasonic detection method for internal flaws in straight spur gears, based on an XY motion platform. The proposed system integrates ultrasonic longitudinal wave testing, a zigzag scanning path tailored to gear tooth profiles, signal modeling and feature extraction, and visualization via C-scan imaging. Experimental results on a manufactured gear specimen with artificial defects validate the effectiveness of the approach.
1. Introduction
Internal flaws such as pores, inclusions, and cracks frequently occur during the manufacturing and service of straight spur gears. These defects significantly compromise the safety and performance of mechanical systems if not detected in a timely manner. Ultrasonic nondestructive testing offers high sensitivity, deep penetration, accurate defect localization, and harmlessness to operators, making it an ideal choice for inspecting internal defects in straight spur gears. However, the complex geometry of gear teeth makes manual ultrasonic testing difficult and inefficient. Therefore, we aim to develop an automated ultrasonic testing system that can scan straight spur gears precisely, acquire signals, and visualize internal flaws. This paper describes our design, path planning, signal analysis, software implementation, and experimental validation.
In contrast to conventional “gear rotation + probe radial feed” methods, which suffer from boundary effects and idle scanning over tooth gaps, our method uses a planar XY motion platform and a specifically designed zigzag path that stays entirely within the tooth profile region. This approach improves detection accuracy and efficiency for straight spur gears.
2. System Architecture
The overall system for automatic ultrasonic detection of internal flaws in straight spur gears is shown schematically in the following figure. It consists of an ultrasonic probe, a probe holder, an XY motion platform, servo drives, and an industrial PC equipped with a motion controller and an ultrasonic card.
The ultrasonic probe is immersed in water (couplant) together with the gear. The probe is oriented vertically, and the gear end face is perpendicular to the probe. The probe moves in the horizontal plane along a predetermined path within the tooth profile range. Synchronized with the motion, the ultrasonic card acquires A-scan signals, which are processed to extract defect information and generate C-scan images.
3. Scanning Path Planning for Straight Spur Gears
3.1 Path Design
Based on the tooth profile characteristics of straight spur gears, we adopt a single-tooth zigzag scanning path as illustrated in the conceptual diagram (not reproduced here). The path consists of concentric circular arcs centered at the gear rotation center, connected by straight line segments. The scanning width is set to the probe beam width \(b\), and the distance between adjacent arcs is also \(b\). This ensures that the ultrasonic beam remains within the gear material without crossing the tooth boundaries. The path starts at point A and ends at point B, covering the entire tooth and rim region efficiently, with minimal idle scanning. Adjustments are made near transitions (e.g., from tooth to rim) to maintain full coverage.
3.2 Path Coordinate Calculation
To generate the scanning path, we compute coordinates of all intersection points between the arcs and the connecting lines. A Cartesian coordinate system is established with origin \(O\) at the gear center. The gear parameters are known: module \(m\), number of teeth \(z\), profile shift coefficient \(x\), pressure angle \(\alpha\), scanning width \(b\), and rim boundary radius \(R\). Derived parameters include pitch circle radius \(r\), addendum radius \(r_a\), dedendum radius \(r_f\), base circle radius \(r_b\), tooth height \(h\), tooth thickness \(s\), and pressure angle \(\alpha_k\) at a generic radius \(r_k\).
For a point \(P\) on the involute part of the first tooth, the tooth thickness at radius \(r_k\) is given by:
$$ s_k = s \frac{r_k}{r} – 2 r_k (\text{inv}\,\alpha_k – \text{inv}\,\alpha) $$
where
$$ s = \left( \frac{\pi}{2} + 2x \tan\alpha \right) m $$
$$ \alpha_k = \arccos\left( \frac{r_b}{r_k} \right) $$
The arc length \(l\) for the scanning path at radius \(r_k\) is:
$$ l = s_k – b $$
The angle \(\theta_k\) between \(OP\) and the \(x\)-axis is:
$$ \theta_k = \frac{l}{2r_k} $$
Thus the coordinates of \(P\) are:
$$ x_{1,j} = r_k \cos \theta_k, \quad y_{1,j} = r_k \sin \theta_k $$
For points on the trochoid (transition curve), we use the appropriate transition curve equation. Similarly, for points on the rim (circular arcs), coordinates are straightforward. The coordinates for any tooth \(i\) (where \(i\) is the tooth index) are obtained by rotation:
$$ x_{i,j} = x_{1,j} \cos \phi_i – y_{1,j} \sin \phi_i $$
$$ y_{i,j} = x_{1,j} \sin \phi_i + y_{1,j} \cos \phi_i $$
$$ \phi_i = \frac{2\pi (i-1)}{z} $$
The radii \(r_k\) of successive arcs are determined by starting from the outermost arc and decreasing by \(b\) until the innermost arc is reached. Table 1 summarizes the key parameters used in the path computation.
| Symbol | Description | Typical value/range |
|---|---|---|
| \(m\) | Module | 10 mm |
| \(z\) | Number of teeth | 8 |
| \(x\) | Profile shift coefficient | 0 (or specified) |
| \(\alpha\) | Pressure angle | 20° |
| \(b\) | Scanning width (probe beam) | 3 mm |
| \(R\) | Rim boundary radius | 60 mm |
| \(r_a\) | Addendum radius | 60 mm |
| \(r_f\) | Dedendum radius | 45 mm |
| \(v\) | Scanning speed | 2.5 mm/s (adjustable up to 100 mm/s) |
4. Ultrasonic Signal Analysis and Defect Visualization for Straight Spur Gears
4.1 Signal Feature Extraction
We use the ultrasonic longitudinal wave pulse-echo method. The probe emits a pulse that propagates through the gear material; reflections occur at the gear surface, internal defects, and the back wall. The acquired A-scan signal is a sequence of sampled amplitudes:
$$ w(n) = \{ f(i) \mid i = 1, 2, \dots, n \} $$
where \(n\) is the total number of samples and \(f(i)\) is the amplitude at sample \(i\). The distance between two successive wave peaks (e.g., surface echo and defect echo) is given by:
$$ d = \frac{c (p – e)}{2 f_s} $$
where \(c\) is the sound velocity in the gear material, \(f_s\) is the sampling frequency, and \(e\), \(p\) are the indices of the first samples of the two wave groups. This distance yields the depth of the defect.
Each wave group consists of rising and falling edges. For a rising edge from sample \(p\) to \(q\), the amplitude is modeled linearly:
$$ y[f(p), f(q)] = \frac{f(q)-f(p)}{q-p} (i-p) + f(p), \quad i = p, p+1, \dots, q $$
The energy of this edge segment is:
$$ \sum_{i=p}^{q} f(i)^2 = (q-p+1) \left\{ f(p)^2 + f(p)[f(q)-f(p)] + \frac{(2q-2p+1)[f(q)-f(p)]^2}{6(q-p)} \right\} $$
The total energy of a wave group (e.g., defect echo) is the sum of energies of its constituent edges. This energy serves as the feature for C-scan imaging.
4.2 C-Scan Imaging
We map the defect wave energy at each scanning position to a grayscale or color value. Let \(\{E_1 \le \dots \le E_n\}\) be the sorted energy values with differences \(\Delta E_i = E_i – E_{i-1}\). A color table \(\{C_1, \dots, C_n\}\) with RGB components is defined. The mapping is:
$$ \{E_1, \dots, E_n\} \rightarrow \{C_1, \dots, C_n\} \in \mathbb{R}^3 $$
Typically, we divide the energy into 4–8 levels, each assigned a distinct color. The resulting C-scan image clearly reveals internal defects in straight spur gears.
Table 2 lists the typical mapping from defect wave energy to color.
| Energy level | Color (R, G, B) | Interpretation |
|---|---|---|
| 0 – low | (0, 0, 255) blue | No defect |
| Low–medium | (0, 255, 0) green | Small indication |
| Medium–high | (255, 255, 0) yellow | Likely defect |
| High | (255, 0, 0) red | Large defect |
5. Software Implementation
We developed the automatic detection software using Visual C++ 6.0 MFC. The software consists of two main modules: motion control and ultrasonic signal acquisition/processing. The motion control module accepts gear parameters (module, teeth, profile shift, etc.) and scanning parameters (speed, scanning width). It implements homing, start, pause, and resume functions. The ultrasonic module sets probe parameters, displays real-time A-scan waveforms, and performs signal feature extraction and C-scan imaging using OpenGL.
Motion control is realized with a GT-400-SV-PCI programmable motion controller and GXY-series XY platform from Googol Technology. In the VC environment, we include #include "GT400.h" and link the library. Coordinated XY motion is achieved by switching to the coordinate mode and queuing multiple trajectory segments (arcs and lines) into the motion buffer. The ultrasonic card functions are provided by a commercial library.
6. Experimental Validation on Straight Spur Gears
To verify the proposed method, we manufactured a gear-shaped specimen with a module of 10 mm and 8 teeth (with profile shift). Four artificial defects with diameters of 1 mm, 2 mm, 3 mm, and 5 mm were embedded. The scanning step was set to 3 mm and scanning speed to 2.5 mm/s. We compared our zigzag method with the traditional “gear rotation + radial feed” method. The traditional method took 1178 seconds to scan the entire gear, while our method took only 706 seconds, a saving of approximately 40% in scanning time.
Figure 6 in the original paper (not repeated here) showed the C-scan image of the gear specimen, where all four artificial defects were clearly detected. The 1 mm defect was the smallest resolvable in the projection plane. This demonstrates that our method can effectively detect internal flaws in straight spur gears with diameters as small as 1 mm.
7. Conclusion
We have presented an automatic ultrasonic detection method for internal flaws in straight spur gears based on an XY motion platform. The key contributions are:
- A zigzag scanning path that minimizes scanning area and eliminates boundary effects, improving detection efficiency for straight spur gears.
- Signal feature extraction using defect wave energy, enabling effective C-scan imaging.
- Software that integrates motion control and signal acquisition, achieving automated inspection.
- Experimental results confirming the ability to detect defects down to 1 mm in size.
Our method is currently optimized for defects with significant axial extent. Future work will focus on enhancing sensitivity to axially oriented flaws and extending the approach to other gear types.