## What is a Shock Waveform?

Knowing and understanding what is behind a shock waveform is crucial for the engineers and designers in the department of packaging development.

As you know the main objective we look for in packaging, related to transportation issues, are mainly product protection, easy handling and storage, transportation efficiency, easy identification, environmental responsibility and, of course, meeting customer needs, but the ultimate goal is to ensure that the product is received in good condition by the final consumer.

All of us know our product but not many know the associated hazards and their intensity in the distribution cycle of their products, therefore the optimization of protective packaging can only be achieved if the distribution hazards are accurately known and understood.

During transportation products and their packages are handled and therefore dropped, kicked, thrown or severely mishandled. Also, they may fall from forklifts or conveyors. In the vehicle, they may be subjected to impacts due to vehicle maneuvers, road bumps or potholes on the road and railroad crossings, or jolting.

Mechanical Shocks are the consequence of each impact that the package undergoes against another object like the floor, the pallet, truck bed-walls or another package.

### What kind of wave is a shock wave?

Those impacts produced during handling and transportation are characterized by a fast increase in acceleration followed by a fast decrease over a short period of time.

The acceleration versus time plot of real shocks is complex but because environmental shocks usually are close to a characteristic half-sine shape, it is easier to understand and make calculations.

### How to analyze a shock Waveform

To understand and have a good estimate of the potential damage a shock could cause, we must know the maximum peak acceleration and the duration of the shock.

The energy that shock waveforms transmit to the package or product is directly related to the change velocity during impact.

The maximum peak acceleration and time duration are easy to obtain directly from the acceleration plot versus time.

The maximum peak acceleration will be the maximum acceleration value shown in the graph and the duration time will be the time difference between the point where acceleration starts to increase fast and the point where acceleration becomes zero after starting to decrease fast.

The change in velocity, instead, is calculated by computing the area below the acceleration curve between those two points from which we have previously obtained the time duration of the shock.

Because a free fall packaging drop is easy to calculate and understand, all the mechanical theories of shocks around packaging are based on its analysis and understanding.

## Analyzing and understanding the free fall drop of a packaging

In a free fall drop, the velocity change during the shock duration is the sum of the absolute values of the impact and rebound velocities.

The impact velocity is easy to calculate by applying the equations of the principle of conservation of Energy between the instant the package starts to fall from a determined height and the moment where the package hits the floor.

All the potential energy will be transformed into kinetic energy, therefore impact velocity will be obtained by the formula:

Where g is the gravitational acceleration and h is the drop height.

The amount of bounce will depend on the nature of the package and the surface it hits. The coefficient of restitution allows us to easily describe the rebound velocity as a function of the impact velocity. This coefficient will range from 0 to 1. Typical values for packaging are between 0.2 to 0.5.

Then the velocity change as the sum of the absolute values of the impact and rebound velocities is derived in the formula:

From this formula, we can derive the formula to get the free fall drop height:

If we record a shock waveform in our transportation environment, we can define an equivalent effective drop height that will be equivalent to a free fall drop with the same velocity change for a determined coefficient of restitution:

## How to record proper shock data from the transportation environment

Depending on what we want to measure, we must follow a different strategy. It is not the same to measure impacts to a package coming from bumps between packages, free fall drops, bumps against the walls of the truck than to measure impacts to a vehicle or train loading platform, coming from road irregularities like bumps, or potholes through the vehicle suspension, or coming from railroad crossings, humps or shocks. For the second and third cases of the vehicle and train, the data recorder can be mounted directly attached to the loading platform, but for the first case of the packaging, a different mounting strategy must be used.

In order for the information registered by a data recorder on shockwaves from impacts and drops on packages during transportation to be useful, we must perform a very important task before installing the data recorder inside the packaging or closure we have designed for that purpose.

This task is called “Equivalent Height Drop Data Recorder Calibration”. The data recorder must be installed inside a padded box or packaging in order to protect the data recorder. The data recorder must be surrounded by a cushion in order to avoid empty spaces. This package is made mainly of wood or plastic, with foam inside around the data recorder, the data recorder placed in the center of gravity of the packaging, and around the wooden or plastic box a corrugated cardboard box simulating a real package to be shipped.

The calibration task consists of performing several free fall drops from different heights and different positions (flat, edge, corner). You can do this manually or, for higher calibration accuracy, by using a free fall drop machine.

A full description of this methodology can be found in the paper “Interpreting shock data to estimate drop height levels during handling” by Dr. Manuel Garcia-Romeu, 2007, Applied Mechanics and Materials, 7-8. pp. 243-250. ISSN 1660-9336 (print) 1662-7482 (online).

Then, the acceleration shock waveforms registered in the calibrations can be computed using the height drop formula that we have deducted before and obtain the value of the coefficient of restitution “e“ from our measurement package system:

In this formula, the velocity change will be obtained from the acceleration waveform of the three axes and the value of the height “h” is the free fall drop corresponding to that registered acceleration.

In summary, if we want to measure the statistical distribution about impacts intensity that a package will suffer during transportation, we must adopt the second strategy and compute the effective drop height equivalence and impact orientation from the shock waveforms registered by our data recorder, taking into account the previous calibration performed on the coefficient of restitution. On the other hand, if we want to measure what is the statistical distribution on the intensity that a certain vehicle or train platform will transmit during transportation to the load that it is placed on top, we must undertake the first strategy and compute the velocity change, maximum peak acceleration and shock time duration.

In the first strategy, the statistical values of velocity change, maximum peak acceleration and shock duration will allow us to define the testing parameters to simulate that environment using for example programable impact testing machines.

In the second strategy, the statistical values of EDH and impact orientation obtained will allow us to define the testing parameters to simulate that environment using for example free fall drop machines.

## How to use the shock waveform information to develop the right protective packaging to protect products?

When a package is subjected to a drop or impact, on the frame of the product that it is inside in contact with the cushion or the protective packaging, it is subjected to the shock waveform recorder.

As you know, there are elements within the products that are more sensitive to breakage than the frame. we call those elements “critical elements” because the product will not be useful if those products are damaged.

The shock wave form will be transmitted from the frame of the product to the critical elements. Those elements have their own natural frequency and the shock waveform of the drop or impact transmitted by the frame also has a specific frequency content associated with it. That frequency content associated with the shock waveform may be the inverse of the period of a theoretical full period sine-wave, in other words, the inverse of the shock duration time divided by two.

When the frequency content associated with the shock waveform match or is very close to the own natural frequency of the critical element the shock will have more potential damage to the product than a critical element whose own natural frequency is far from the frequency content associated with the shock waveform, independently of whether the shock duration in the first case is shorter than in the second case.

Obviously, if the critical element starts to resonate the displacement of the critical element will be greater than the displacement of the frame, and the same will happen for the peak acceleration that the critical element will be subjected to.

Then, in order to assess the maximum peak acceleration that the critical element will undergo due to the shock waveform transmitted through its frame, we have to solve the response of a single degree of freedom (SDOF) theoretical system (mass, spring, damper) by solving the differential equation of this system when the base (the frame) is subjected to a transient input (the shock waveform) for a discrete number of SDOFs with increasing natural frequencies from 0 to a number of Hertz greater than the critical element of the product.

This is solved numerically by software and plotted by obtaining the well-known computational tool SRS (shock response spectrum), which we prefer to call TRS (transient response spectrum). This tool, which defines the frequency response of a system to a determined transient excitation, is also extensively used to compare the severity of different transient excitations.

In other words, a Transient or Shock Response Spectrum is a graphical presentation of a transient acceleration waveform potential to damage a product or structure. It can be used to represent the maximum response of a series of equally damped Single Degree Of Freedom (SDOF) systems (or critical elements) to a given transient waveform.

Other parameters can also be calculated in the response spectrum, the Primary Negative Peak Response, the Primary Positive Peak Response, the MAXIMAX RS which corresponds to the Maximum Peak of the positive and negative response, the Residual positive RS and the Residual negative RS. Although the most common is the MAXIMAX because it is the maximum absolute peak response.

In addition, if you need help to protect your products against distribution hazards or you are looking for a solution to optimize your product + packaging system, we at Safe Load TT, put our two decades of experience in transportation simulation and packaging engineering at your service. Contact us and let’s talk about how we can help you.