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The power spectral density is a complex mathematical calculation related to vibrational forces. In the packaging industry, vibrations are one of the key factors that might negatively affect the goods during the distribution cycle, and it is essential to keep them in mind.

To this end, power spectral density calculation is a vital step when designing and optimizing packaging that is able to protect your products during transportation.

What is power spectral density PSD in packaging?

As per its technical definition, power spectral density (PSD) is the energy variation that takes place within a vibrational signal, measured as frequency per unit of mass. In other words, for each frequency, the spectral density function shows whether the energy that is present is higher or lower.

Therefore, a power spectral density analysis is used in the packaging industry to measure how vibrations may affect the goods.

  • On one hand, the word “power” indicates that the magnitude of the power spectral density function corresponds to the root mean square of the signal that has been analyzed.

In other words, in the PSD analysis, the “power” does not refer to a power measured in volts or horsepower; instead, the root mean square of any value is known as the power of that value.

  • On the other hand, the word “spectral” indicates that the power spectral density PSD is a frequency-based function. This means that the power spectral density represents the distribution of a signal on a frequency spectrum.
  • Lastly, the word “density” indicates that the magnitude of the spectral density function has been normalized to a bandwidth of 1hz. For example, for an acceleration signal measured in g’s, the units of the PSD function will be g²/hz.

Since the name of the power spectral density function does not include the value that has been measured, the word “power” is sometimes replaced by the measured value. For example, one could talk about an ASD (Acceleration Spectral Density) function.

Spectral density function in packaging

In the packaging industry, the spectral density function is used to determine how much energy is transferred to the packages and goods during their transportation by road, sea or air, and how it is transferred.

In the case of road transportation, for example, most of the energy transferred to the products being transported is linked to the truck’s suspension.

It generally ranges from 2 to 8hz, depending on whether the truck is full or empty.

In addition, these frequencies are followed by the energy that is transmitted from the wheels, which generally ranges from 15 to 20hz depending on whether the wheels have a high or low pressure.

Lastly, the energy that is transferred due to the truck bed is added to these frequencies, which can range from 50 to 100hz depending on whether the bed is full or empty.

If the frequencies transmitted by the transport vehicle match the natural frequencies of the packages and their products, the products may enter into resonance with the vibrations and get damaged or deteriorate.

This is to say that an adequate protection against vibrations in the transportation of a load will involve designing a package that prevents the goods from entering into resonance with the vibrations of the transport vehicle.

This is why, by performing a power spectral density calculation, we can carry out a psd analysis and determine whether the vibrations can be damaging to the packaging and the product being transported.

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Power spectral density calculation

The power spectral density calculation procedure is performed by estimating the spectrum of the signal frequency.

>The Fourier transform is applied for the power spectral density formula.

This formula is based on the principle that any signal can be reconstructed by a summation of sine and cosine wave series, each of which will be relative to an integer, determinate and different number of cycles.

It is a complex mathematical calculation that, when applied to the packaging industry, successfully protects the goods being transported thanks to foresight and the optimization of the packaging.

>The power spectral density is calculated based on a signal that has been previously measured. This measurement can be performed using equipment such as the Data Recorder which, when installed in the means of transportation that one wants to measure, monitors the existing vibrations and other hazards. To this end, the transportation simulation based on the power spectral density analysis must be as close to the real transportation conditions as possible.

>If an outdated spectral density function is used (obtained many years prior), you will be at risk of designing packages that cannot withstand the real transportation conditions.

This means that you may end up choosing a packaging that is far from the optimal design, over-packaging or under-packaging in relation to what the transportation conditions actually require.

>Why measuring the spectral density is important
Measuring the spectral density is an essential part of the studies to optimize a package.

Protecting the goods during their transportation by road, sea or air is vital to prevent losses, damaged products and a bad image before the end consumer.

In order to make sure that the vibrations do not affect the goods during transportation, we will need to calculate the spectral density, so as to know what types of vibrations the packaging will need to withstand.

Then, after having performed the power spectral density calculation, this information will be used at a packaging laboratory in a transport simulation.

Using a vibration table, it is possible to simulate the conditions that will exist during the transportation of goods – vibrations included.

In this way, we will be able to determine the vibrations that the packages and products will be subject to during transportation. Using this information, it is possible to optimize the packaging in a way that guarantees the safety of the goods.

Vibration simulation to optimize your packaging

When applied to packages, a power spectral density calculation can be used in a vibration table when performing transport simulations. By applying a psd vibration analysis to the transport simulation, it is possible to forecast the effect of vibrations on the goods within the controlled conditions of a packaging laboratory.

A vibration table can therefore be used to optimize the packaging based on the real transportation conditions that will be experienced by the goods. An optimized packaging implies cost savings and reduced losses caused by inadequate packaging.

This equipment can, in turn, be complemented with a Pitch & Roll module, which combines the power spectral density formula with the pitch and roll motions that usually take place during transportation. This module uses technology patented by Safe Load Testing Technologies to bring simulation equipment closer to real conditions. Therefore, by using a vertical vibration + Pitch & Roll machine you can obtain simulations –and a packaging optimization – that are closer to real transportation conditions.

Vibration simulations are some of the essential tests among the package testing methods on the market.If you need assistance performing the power spectral density analysis and applying it to your packaging, at Safe Load TT we can help. Our team has a track record of two decades in the packaging and transport simulation industry.

Furthermore, we work as per the ISTA, ASTM and ISO international standards in order to guarantee the safety of your loads during shipping & handling.

We make sure to offer solutions based on a constant innovation and personalization. Get in touch with us and we will work together to save costs, prevent losses and improve your customer service through your packaging.

Manuel Garcia-Romeu

Product Development Manager

Dr. Manuel García-Romeu serves as the Director of Product Development at Safe Load Testing Technologies, boasting extensive experience in packaging engineering, transportation simulation, and load stability. Manuel has been featured as an expert at key industry events and holds the presidency of the EUMOS 40509/20202 editorial committee.

He also plays roles as a member of UNE and is involved in key associations like IAPRI and ISTA. His focus is centered on research, development, and innovation.

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