Products are likely to fail when subject to consistent vibration. When the failure will occur, however, depends on several factors. To ensure the safety and longevity of a product, engineers must determine how long the product can withstand a specified vibration environment.

As a product may experience hundreds to thousands of hours of use, they require a vibration testing method to assess a product over many hours without expending significant time to do so.

### Random Vibration Test Acceleration

Using vibration test acceleration, engineers can test a product for years of service in a fraction of the time. Depending on the vibration environment, they can perform test acceleration in one of several ways.

#### What is a Random Vibration Test?

A random vibration test is a realistic method of bringing a product to failure, as real-world vibration is inherently random. A random test excites all frequencies in a defined spectrum at any given time. By exciting all the product’s resonances simultaneously, engineers can determine the interaction between multiple resonances.

### Random Test Acceleration with FDS

The fatigue damage spectrum (FDS) is a standard method of accelerating a random vibration test. It is based on Miner’s rule of cumulative damage, which states that a product will experience failure when it reaches its maximum amount of fatigue damage.

A product is likely to experience a range of vibration environments in its lifetime. In many cases, a vibration environment will be more complex than a simple sinusoid or Gaussian random waveform. The FDS can incorporate all the vibration environments a product will encounter throughout its use.

The FDS is calculated using a time-domain analysis that incorporates rain flow cycle counting. Using this time-domain analysis and defined material property (m), the relative damage can be calculated and an FDS can be created. For test purposes, an engineer can convert the FDS into a power spectral density (PSD) using Henderson-Piersol’s fatigue calculation method.

The FDS-generated PSD is the damage equivalent to the product’s lifetime based on the imported files, m and Q values, target life, test duration, and kurtosis. The engineer can use the resulting PSD in many stages of vibration testing, from initial product development to recreating field failures in a lab environment.

Unlike the fast Fourier transform (FFT), the FDS is based on the response of single-degree-of-freedom (SDOF) systems. Altogether, the FDS is a reliable method for generating a random test reflective of the real world, which is often non-Gaussian and non-stationary.

### FDS Parameters to Consider

#### Quality Factor (Q)

The quality factor determines the damping value of an oscillation. A higher Q value will result in a lower rate of energy loss and, therefore, a slower end to the oscillation. Conversely, a lower Q value will result in a higher rate of energy loss and a faster end to the oscillation. The resonance quality factor is 0.5 divided by the critical damping ratio (ζ).

In FDS analysis, the quality factor is related to the Q of the filters used to generate the single/narrowband time waveforms. This value should be greater than or equal to the sharpest resonance of the product within the test frequency range.

#### Slope of S-N Curve (m)

The S-N curve displays an inverse relationship between the maximum applied stress (S) and the number of cycles to failure (N) on a logarithmic scale. Cyclical stress above the yield stress can result in low cycle fatigue and cyclical stress below the yield stress can result in high cycle fatigue.

The value of m is obtained from the S-N curve. MIL-STD-810H (2019) recommends using an m value of 7.5 for random vibration excitations, “but values between 5 and 8 are commonly used.” However, engineers can come up with a value by testing several units with several different vibration levels until failure, then finding the value of m that is most suitable for the data.

#### Kurtosis

Shakers running periodic random excitations can display non-Gaussian vibration responses in structural resonances. Kurtosis describes a non-Gaussian random process. If the kurtosis of a random signal exceeds the Gaussian value of 3, the damage-inducing potential of the profile increases.

The FDS import assumes a Gaussian distribution of data because the Piersol method of computing fatigue converts the FDS back into a PSD using a Gaussian distribution. The PSD is based on the relative damage calculation computed for each frequency and, by default, will be a Gaussian distribution. Therefore, the generated test will not have the same peak distribution as the real-world environment. Kurtosis control, such as Kurtosion®, can be added to modify the distribution of peaks so it is similar to the real-world environment while still maintaining the damage based on the computed FDS, life duration, and desired test duration.

When kurtosis is added to the FDS software, the overall GRMS level of the test decreases. The duration of the test is a set value, and the lifetime fatigue value is not impacted. However, the distribution of peaks is different, so the overall GRMS of the test is lower. In the end, the damage is still equivalent to the imported waveforms.

### Test Acceleration and Dominant Sinusoidal Components

While the FDS is the standard tool for vibration test acceleration, there is an environment where the FDS falls short. If a product is subject to an environment with dominant sinusoidal components, the technician should use a sine-on-random (SoR) test—not a random test.

For sine-on-random test generation, the sine tones are accelerated separately from the random energy, which is accelerated with the FDS. Only after can the accelerated sine and random components be combined.

Vibration Research developed the Sine Tracking, Analysis and Generation (STAG) tool to create a Sine-on-Random test reflective of environments with rotational components, such as in engines. If the engineer selects the FDS for this type of environment, then the test profile may not accurately represent the dominant sine tones.

The STAG tool is an accurate and convenient method for developing an SoR test. Vibration Research developed the software to reduce the standard processing time and bypass manual entry for the highest level of accuracy.

### Conclusion

Vibration test acceleration saves time and costs compared to testing under normal conditions. Being attentive to the characteristics of the vibration environment(s) will lend to a more accurate accelerated test.

For a more detailed description of accelerated vibration testing, read the paper How Do I Measure the Life of My Product? Download a free demo of the VibrationVIEW software and try out the FDS software today.