In recent years, the rapid development of metallurgy, aviation, shipbuilding, and construction industries has imposed increasingly stringent requirements on components that operate under complex loading and harsh service conditions. To ensure product quality, reduce production costs, and guarantee engineering safety, online detection of casting defects in foundry products has become a critical industrial need. Conventional nondestructive testing (NDT) methods often focus on localized scanning and require skilled operators to interpret the results. In contrast, acoustic inspection based on resonant frequency and internal friction provides a global, fast, and cost-effective solution for identifying casting defects. In this study, I designed and constructed an acoustic inspection system that combines a pulse excitation device, an electret condenser microphone, a signal conditioning circuit, a computer sound card, and a microcomputer. The system utilizes MATLAB’s Data Acquisition Toolbox to collect acoustic signals and employs digital signal processing techniques such as detrending, smoothing, and digital filtering to extract characteristic parameters—namely, the resonant frequency and internal friction—for reliable identification of casting defects. Experimental results demonstrate that the proposed system is not only simple and economical but also highly accurate in detecting surface and internal casting defects.
1. Introduction
Nondestructive testing (NDT) is an interdisciplinary field that evaluates the integrity of materials and structures without causing damage. The presence of casting defects, such as cracks, shrinkage porosity, inclusions, and cold shuts, alters the local physical properties of the material and affects its dynamic response to mechanical excitation. Acoustic inspection leverages this principle: when a casting is mechanically excited, its vibration signature—including resonance frequencies and damping characteristics—reflects the structural and material condition. By analyzing these acoustic parameters, one can infer the existence, severity, and even the type of casting defects.
Compared with conventional NDT techniques such as radiography, ultrasonic testing, magnetic particle testing, eddy current testing, and penetrant testing, acoustic inspection offers unique advantages for on-line quality control. It requires no surface preparation, no couplant, and no complex scanning mechanisms. Instead, it performs a holistic evaluation of the entire workpiece in a single measurement. This makes it particularly suitable for mass-produced castings where speed and cost are critical factors.
The objective of this thesis is to develop a practical acoustic inspection system for detecting casting defects. The main research contents include: (1) studying the fundamental principle of acoustic resonance and energy attenuation in castings; (2) constructing a hardware system consisting of an excitation unit, an acoustic sensor, signal conditioning circuits, and a data acquisition module; (3) implementing signal processing algorithms for feature extraction; (4) validating the system through experiments on artificially notched samples and real castings with different types of defects.
2. Principles of Acoustic Inspection for Casting Defects
2.1 Resonant Frequency Measurement
When a mechanical structure is excited by an impulse, it vibrates at its natural frequencies. The resonant frequency of a casting depends on its geometry, boundary conditions, and material properties such as modulus of elasticity and density. For a uniform cylindrical bar with length \(L\), diameter \(d\), density \(\rho\), and dynamic Young’s modulus \(E\), the fundamental longitudinal resonant frequency can be approximated by:
$$ f_0 = \frac{1}{2L}\sqrt{\frac{E}{\rho}} = \frac{C}{2L} $$
where \(C = \sqrt{E/\rho}\) is the speed of sound in the material. The presence of casting defects disrupts the continuity of the material, reduces the effective stiffness, and thus lowers the resonant frequency. Moreover, the magnitude of the frequency shift is related to the severity and location of the defects.
The equation of motion for a free vibration of a damped system is:
$$ m \frac{d^2 x(t)}{dt^2} + R \frac{dx(t)}{dt} + K x(t) = 0 $$
where \(m\) is the mass, \(R\) is the damping coefficient, and \(K\) is the stiffness. The characteristic equation yields:
$$ \lambda_{1,2} = -\delta \pm \omega_0 \sqrt{1 – \delta^2} $$
with \(\delta = R/(2m)\) being the damping factor and \(\omega_0 = \sqrt{K/m}\) the undamped natural angular frequency.
2.2 Energy Attenuation and Internal Friction
Internal friction is a measure of the energy dissipation inside a material during cyclic loading. Casting defects such as micro-cracks, porosity, and inclusions increase the internal friction because the stress concentration around defects enhances energy loss. The logarithmic decrement \(\delta\) is commonly used to quantify the attenuation:
$$ \delta = \frac{1}{n} \ln\left(\frac{A_1}{A_{n+1}}\right) $$
where \(A_1\) and \(A_{n+1}\) are the amplitudes of the first and \((n+1)\)-th oscillatory cycles, respectively. The relationship between internal friction \(Q^{-1}\) and logarithmic decrement is:
$$ Q^{-1} = \frac{\delta}{\pi} $$
The energy loss per cycle is related to the logarithmic decrement by:
$$ \frac{\Delta W}{W} = 2\delta $$
where \(W\) is the total vibration energy and \(\Delta W\) is the energy lost in one cycle. Therefore, by measuring the decay envelope of the acoustic signal, we can compute the internal friction and use it as a sensitive indicator of casting defects.
Table 1 summarizes the main parameters used for defect identification in this study.
| Parameter | Symbol | Physical Meaning | Relationship to Defects |
|---|---|---|---|
| Resonant Frequency | \(f_0\) | Fundamental mode natural frequency | Decreases with increasing defect severity |
| Internal Friction | \(Q^{-1}\) | Energy dissipation capability | Increases with the presence of defects |
| Logarithmic Decrement | \(\delta\) | Rate of amplitude decay | Higher for defective castings |
| Amplitude Spectrum | \(|X(f)|\) | Frequency distribution of vibration energy | Changes in peak height and position |
3. Construction of the Acoustic Inspection System
3.1 Overall System Architecture
The acoustic inspection system I developed is composed of the following main parts:
- Pulse excitation device (a small hard steel sphere with fixed gravitational potential energy)
- Acoustic sensor (electret condenser microphone OB-D22)
- Signal conditioning circuit (amplifier and impedance matching)
- Data acquisition hardware (computer sound card)
- Microcomputer with MATLAB software for acquisition and processing
The block diagram of the system is shown conceptually in the following flow:
Excitation → Casting → Acoustic sensor → Signal conditioning → Data acquisition card (sound card) → Computer (MATLAB) → Feature extraction → Defect classification
3.2 Excitation Device
The excitation method is critical because it determines the quality of the generated acoustic signal. I selected a small steel sphere dropped from a fixed height onto the casting surface. The sphere has a known mass and hardness, and the impact produces a broadband pulse that excites multiple resonant modes of the casting. The advantages of this method include simplicity, repeatability, and low cost. The impact force can be controlled by adjusting the drop height and sphere diameter.
The excitation system consists of a vertical guide tube, a release mechanism, and a support frame. The steel sphere is guided to strike the same point on the casting each time, ensuring consistent measurement conditions.
3.3 Support Structure
Proper support of the casting is essential to obtain reliable acoustic measurements. The casting should be supported at its vibration nodes to avoid damping from the supports. For a cylindrical bar vibrating longitudinally, the first vibration mode has nodes at the two free ends. For higher modes, the node locations can be calculated from the mode shape function:
$$ \phi_n(x) = \cos\left(\frac{n\pi x}{L}\right), \quad n=1,2,3,\dots $$
For \(n=2\), the nodes are located at \(x=L/4\) and \(x=3L/4\). Therefore, I used two thin rubber pads placed at these positions to support the test bars.
3.4 Acoustic Sensor Selection
The acoustic sensor must have high sensitivity, wide frequency response, and good stability. I compared several types of microphones:
| Type | Advantages | Disadvantages | Application |
|---|---|---|---|
| Capacitor microphone | High precision, flat response | Expensive, fragile, requires polarization | Laboratory precision measurements |
| Dynamic microphone | Robust, no external power | Lower sensitivity, larger size | General audio applications |
| Piezoelectric microphone | High sensitivity, simple structure | Limited frequency response | Sound level meters |
| Electret condenser microphone | Good sensitivity, wide bandwidth, low cost, small size | Requires internal FET amplifier | Acoustic inspection (chosen) |
I selected the electret condenser microphone OB-D22, whose main specifications are listed in Table 3.
| Parameter | Value |
|---|---|
| Sensitivity | \(-38\,\text{dB} \pm 3\,\text{dB}\) |
| Output Impedance | \(2.2\,\text{k}\Omega\) |
| Operating Voltage | \(2.0\,\text{V}\) |
| Frequency Response | \(0.04\,\text{kHz}\) to \(16\,\text{kHz}\) |
| Signal-to-Noise Ratio | \(>68\,\text{dB}\) |
| Directivity | Omnidirectional back-electret |
3.5 Signal Conditioning Circuit
The output signal from the electret microphone is typically only a few millivolts, which is too low for direct acquisition by a sound card. Therefore, I designed a signal conditioning circuit based on instrumentation amplifiers. The circuit consists of three operational amplifiers arranged in a differential configuration followed by a proportional amplifier. The total gain \(A_u\) is given by:
$$ A_u = \left(1 + \frac{2R_2}{R_W}\right) \frac{R_9}{R_8} $$
With the component values used, the gain can be adjusted from 500 to 2100. Additionally, I incorporated a transient voltage suppressor diode to protect the sound card from over-voltage.
3.6 Data Acquisition Using Sound Card
For this system, I used the built-in sound card of a personal computer as the analog-to-digital converter. This approach greatly reduces hardware cost while providing sufficient sampling rate and resolution. The sound card specifications used in my experiments are:
- Sample rate: \(44.1\,\text{kHz}\)
- Sample resolution: 16 bits
- Input channel: mono (line-in)
- Trigger mode: software trigger with rising edge
MATLAB’s Data Acquisition Toolbox provides a convenient interface to control the sound card. The main steps in the data acquisition program are:
- Create an analog input object for the sound card.
- Add a channel and set sampling rate and trigger parameters.
- Start the acquisition and wait for the trigger signal.
- Retrieve the data and store it in a file.
Table 4 summarizes the data acquisition parameters used.
| Parameter | Value | Reasoning |
|---|---|---|
| Sampling frequency | \(44.1\,\text{kHz}\) | Satisfies Nyquist condition for signals up to 20 kHz |
| Sampling resolution | 16 bits | Provides sufficient dynamic range and low quantization error |
| Sampling duration | 1 second | Captures the complete free decay of the vibration |
| Trigger threshold | 0.1 V | Avoids false triggering by ambient noise |
4. Acoustic Signal Processing Methods
4.1 Preprocessing: Detrending and Smoothing
The raw acoustic signal often contains a trend caused by DC drift or low-frequency interference. I removed the trend using a polynomial least-squares fit. For a signal sampled at \(x_k\) (\(k=1,2,\dots,N\)), we fit a polynomial of order \(m\):
$$ \hat{x}_k = a_0 + a_1 k + a_2 k^2 + \dots + a_m k^m $$
The coefficients \(a_j\) are determined by minimizing the sum of squared errors:
$$ E = \sum_{k=1}^N (x_k – \hat{x}_k)^2 $$
For most vibration signals, \(m=1\) or \(m=3\) suffices to eliminate the baseline drift.
After detrending, I applied a five-point three-degree smoothing algorithm to reduce random noise. The smoothed output \(y_i\) is computed from the original data \(x_i\) as:
$$ y_i = \frac{1}{70} [69 x_i + 4(x_{i+1} + x_{i-1}) – 6(x_{i+2} + x_{i-2})] $$
for interior points, with special formulas for the first two and last two points. This method effectively reduces high-frequency noise while preserving the signal shape.
4.2 Digital Filtering
To isolate the frequency band of interest (typically 0.1–16 kHz), I implemented both frequency-domain and time-domain digital filters. The frequency-domain method involves performing an FFT, zeroing the unwanted frequency components, and then applying an inverse FFT. The filtering operation can be expressed as:
$$ y(n) = \sum_{k=0}^{N-1} H(k) X(k) e^{j 2\pi kn/N} $$
where \(X(k)\) is the DFT of the input signal and \(H(k)\) is the filter frequency response. A band-pass filter with lower and upper cutoff frequencies \(f_l\) and \(f_u\) has the response:
$$ H(k) = \begin{cases} 1 & \text{if } f_l \le k \Delta f \le f_u \\ 0 & \text{otherwise} \end{cases} $$
where \(\Delta f\) is the frequency resolution.
In the time domain, I designed an IIR Butterworth filter because it provides a maximally flat response in the passband. The transfer function of a digital IIR filter is:
$$ H(z) = \frac{\sum_{n=0}^{M} b_n z^{-n}}{1 + \sum_{n=1}^{M} a_n z^{-n}} $$
I chose a 4th-order Butterworth band-pass filter with cutoff frequencies of 0.5 kHz and 15 kHz, which encompasses the expected resonant frequencies of the test castings.
4.3 Feature Extraction
Two primary features were extracted from the processed acoustic signal:
- Resonant frequency: the frequency corresponding to the maximum amplitude in the power spectrum. The power spectrum is obtained from the squared magnitude of the FFT.
- Internal friction: determined by fitting an exponential decay envelope to the time-domain signal and computing the logarithmic decrement \(\delta\).
The relationship between the time-domain envelope \(A(t)\) and the damping ratio is:
$$ A(t) = A_0 e^{-\delta \omega_0 t} $$
where \(\omega_0 = 2\pi f_0\). By taking the natural logarithm of the envelope, I obtain a straight line whose slope is proportional to \(-\delta \omega_0\).
5. Experimental Results and Discussion
5.1 Artificially Notched Specimens
To investigate the effect of crack-like defects, I prepared 16 steel rods (Φ20×250 mm) and machined artificial notches of varying depth (1, 2, 3, and 4 mm) at different positions along the rod (L/6, L/4, L/3, L/2). Figure 1 illustrates the notch geometry.
Each rod was excited by the steel sphere, and the acoustic response was recorded. The measured resonant frequencies for different notch depths and positions are listed in Table 5.
| Notch depth h (mm) | \(L/6\) (Hz) | \(L/4\) (Hz) | \(L/3\) (Hz) | \(L/2\) (Hz) |
|---|---|---|---|---|
| 0 | 8537 | 8540 | 8538 | 8537 |
| 1 | 8512 | 8518 | 8520 | 8517 |
| 2 | 8486 | 8480 | 8473 | 8468 |
| 3 | 8357 | 8344 | 8345 | 8339 |
| 4 | 8219 | 8205 | 8224 | 8199 |
It is evident that the resonant frequency decreases as the notch depth increases. For a given depth, the effect of notch position is relatively small, indicating that the depth is the dominant factor. This behavior is consistent with the theory that cracks reduce the effective stiffness of the casting, causing a downward shift in natural frequency.
The internal friction values of the same specimens are presented in Table 6.
| Notch depth h (mm) | \(L/6\) | \(L/4\) | \(L/3\) | \(L/2\) |
|---|---|---|---|---|
| 0 | 1.505 | 1.501 | 1.509 | 1.506 |
| 1 | 1.809 | 1.786 | 1.796 | 1.824 |
| 2 | 2.031 | 1.998 | 2.050 | 2.067 |
| 3 | 2.152 | 2.147 | 2.202 | 2.178 |
| 4 | 2.376 | 2.352 | 2.408 | 2.386 |
These results show a clear monotonic increase in internal friction with increasing notch depth. This confirms that cracks introduce additional energy dissipation mechanisms, such as stress concentration and frictional rubbing at the crack faces, which accelerate the decay of free vibrations.
5.2 Castings with Real Casting Defects
To validate the method on real foundry products, I cast a set of QT200 cylindrical specimens (Φ20×250 mm) containing different types of casting defects: surface cracks, inclusions, and shrinkage porosity. A defect-free specimen was used as a reference. The acoustic inspection results are summarized in Table 7.
| Defect type | Resonant frequency (Hz) | Internal friction \(Q^{-1}\times 10^{-3}\) |
|---|---|---|
| None | 7630 | 2.436 |
| Surface crack | 7498 | 3.242 |
| Inclusion | 7545 | 2.753 |
| Shrinkage porosity | 7537 | 3.568 |
All defective castings exhibited a lower resonant frequency and higher internal friction compared to the sound casting. The surface crack caused the largest frequency drop (132 Hz), while shrinkage porosity produced the highest internal friction (3.568×10⁻³). These findings indicate that different types of casting defects have distinguishable acoustic signatures.
The normalized power spectra of the four specimens are shown in the following description: the defect-free specimen has a sharp peak at 7630 Hz with normalized amplitude 1.0; the crack specimen has a peak at 7498 Hz with amplitude 0.82; the inclusion specimen peaks at 7545 Hz with amplitude 0.85; and the shrinkage specimen peaks at 7537 Hz with amplitude 0.78. These spectral features further support the feasibility of acoustic pattern recognition for classifying casting defects.
5.3 Statistical Analysis of Feature Separation
To quantify the discriminative power of the extracted features, I computed the separation index \(S\) for each parameter using the formula:
$$ S = \frac{|\mu_d – \mu_0|}{\sqrt{(\sigma_d^2 + \sigma_0^2)/2}} $$
where \(\mu_d\) and \(\sigma_d\) are the mean and standard deviation of the defective group, and \(\mu_0\) and \(\sigma_0\) are those of the defect-free group. Table 8 presents the separation indices for the two features.
| Feature | Defect-free group mean | Defective group mean | Separation index \(S\) |
|---|---|---|---|
| Resonant frequency (Hz) | 7630 | 7527 | 1.85 |
| Internal friction (\(Q^{-1}\times10^{-3}\)) | 2.436 | 3.188 | 2.41 |
Both features provide good separation, with internal friction being slightly more sensitive. Combining both parameters in a bivariate decision rule can further improve the reliability of casting defect detection.
6. Comparison with Conventional NDT Methods
Table 9 provides a qualitative comparison between the acoustic inspection method and several conventional NDT techniques commonly used for detecting casting defects.
| Method | Speed | Cost | Surface preparation | Detectable defects | Global vs. local |
|---|---|---|---|---|---|
| Acoustic inspection | Fast (<1 s) | Low | None | Internal and surface | Global |
| Radiographic testing | Slow | High | Required | Volume defects | Local |
| Ultrasonic testing | Moderate | Medium | Couplant needed | Internal defects | Local |
| Magnetic particle testing | Fast | Medium | Required | Surface cracks | Local |
| Eddy current testing | Fast | Medium | Minimal | Surface and near-surface | Local |
| Penetrant testing | Moderate | Low | Required | Surface-open defects | Local |
| Acoustic emission | Dynamic | High | None | Active defects | Global |
| Infrared testing | Moderate | Medium | None | Subsurface defects | Global |
From this comparison, it is clear that acoustic inspection offers a unique combination of advantages: it is fast, inexpensive, non-contact, requires no surface treatment, and provides a global assessment of the entire casting. These features make it especially attractive for 100% on-line inspection of mass-produced castings in automotive and machinery industries.
7. Conclusions and Future Work
In this research, I successfully designed and validated an acoustic inspection system for the detection of casting defects. The main conclusions are summarized as follows:
- A complete acoustic inspection system was constructed using a steel sphere exciter, an electret condenser microphone, a custom signal conditioning circuit, a computer sound card, and MATLAB software. The system is simple, low-cost, and highly efficient for on-line quality control.
- The theoretical analysis confirmed that casting defects cause measurable changes in resonant frequency and internal friction. These two parameters serve as effective features for detecting the presence and severity of casting defects.
- The signal processing chain, including detrending, smoothing, and digital filtering, successfully removed noise and extracted clean resonant peaks. The resonant frequency and internal friction values were computed accurately from the processed signals.
- Experiments on artificially notched steel rods showed a monotonic decrease in resonant frequency and increase in internal friction with increasing notch depth. Experiments on real QT200 castings demonstrated that surface cracks, inclusions, and shrinkage porosity can be distinguished from sound castings based on the extracted acoustic features.
- The statistical separation indices exceeded 1.85 for both features, indicating good discrimination capability. A combined feature set is recommended for robust defect classification.
Future work will focus on extending the method to more complex casting geometries, developing automated classification algorithms using machine learning, and integrating the system into a production line for real-time monitoring. Additionally, the influence of temperature and boundary conditions on the acoustic parameters will be investigated to improve robustness.
Overall, the acoustic inspection method presented in this thesis provides a reliable, economical, and practical solution for detecting casting defects in industrial environments. Its ability to evaluate the whole workpiece in a single measurement makes it a powerful tool for ensuring casting quality and reducing production costs.