Squeaks, rattles, shaking, noise, it’s easy to point the finger at sound and vibration as a sign of poor quality. Afterall, these and similar problems directly correlate to product recalls, dissatisfied customers, lost contracts, and scrapped parts. It’s no wonder that manufacturers have been trying to minimize or eliminate their presence for more than a century.

And while vibration can have a negative impact on quality, it’s important to understand that this natural forces also plays a role toward ensuring quality. Let’s examine the love/hate relationship between vibration, sound, and quality.

Quality Testing

Once largely subjective and open to a wide range of interpretation, quality testing has come a long way. For the most part guesswork and individual interpretation have been replaced by sophisticated test systems rooted in objective physics. These systems employ a non-destructive testing (NDT) approach to inspect parts on the manufacturing floor. In this way production defects or parts that do not conform to customer specifications can be identified before the parts leave the manufacturer.

While raw or machined metal cast, fabricated, sintered, forged, die cast, and ceramic parts are generally reliable, the processes under which they are manufactured create opportunities for cracks and other defects. And finding hidden or microscopic defects or discrepancies visually/manually is difficult if not impossible. For this reason, sophisticated inspection systems are needed to test the parts and identify flaws and anomalies.

Frequency Response Function

Frequency Response Function (FRF) is the science behind a non-destructive test method used to flag defective parts. It helps to identify cracks, material property differences, and dimensional changes. As a fundamental concept in the field of signal processing, control systems, and structural dynamics, FRF is a mathematical representation that describes the behavior of a part in the frequency domain.

In the case of quality control, FRF predicts the response to an input signal, and measures corresponding resonant frequencies and modes of vibration. Variations from the predicted response pattern will signal the presence of a flaw.

The Frequency Response Function is typically denoted as H(ω), where ω represents the angular frequency in radians per second. The FRF is often used in conjunction with the Fourier transform to convert time-domain signals into the frequency domain, allowing engineers to analyze and manipulate signals more effectively.

One of the key properties of the FRF is that it provides information about the amplitude and phase shift of the system’s response at different frequencies. The magnitude of H(ω) indicates how much the system amplifies or attenuates input signals at a specific frequency, while the phase angle of H(ω) shows the time delay or phase shift between the input and output signals. These two aspects are crucial for understanding how a system responds to different frequency components within an input signal.

FRF in Structural Dynamics

In structural dynamics, the FRF plays a vital role in assessing the dynamic behavior of parts and structures. Engineers use the FRF to identify the natural frequencies of a structure, which are the frequencies at which the structure is most likely to resonate. Understanding these natural frequencies is essential for preventing structural failures and ensuring the quality, safety, and reliability of a part, structure, or product. It is also important to calibrate manufactured parts to be tested for quality.

To obtain the FRF, engineers typically perform experimental tests or use simulation techniques. In experimental testing, a known input signal is applied to the system, and the resulting output signal is measured and analyzed using specialized equipment such as accelerometers and strain gauges. The FRF is then determined by comparing the input and output signals in the frequency domain.

In simulation, mathematical models are used to predict the behavior of a system or structure. These models can be based on physical principles or empirical data. By applying the Fourier transform to the input and output signals of the model, engineers can calculate the FRF and gain insights into the system’s behavior without conducting physical experiments.

Putting FRF to Work

Signalysis employs sound and vibration for its Dinger quality inspection system. The Dinger applies a calibrated input (i.e., hammer) and calibrated response measurement (i.e., noise). Vibration is measured with either an accelerometer or laser vibrometer.

Because cracks, changes in material density, and similar inconsistencies increase damping, the resonate response can be measured to determine their presence. This method is infinitely more reliable than relying on the human ear or visual inspection to determine quality.

The Frequency Response Function is a powerful tool for understanding the behavior of systems and structures in the frequency domain. It provides undisputed insights into how parts respond to different frequency components, making it essential quality control.

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