Vibration measurement and its use in simulations are vital processes to guarantee the protective capacity of the packaging during transport. Therefore, it is important to know how they work and the advantages and disadvantages of SDoF and MDoF systems. 


How to perform vibration measurement 

Vibration is defined as the oscillation of a physical property. For instance: imagine you have an object and you take a look at one of its properties, such as its length. As the body vibrates, its length will be constantly changing (increasing and decreasing), and thus, the shape of the body will be changing at every instant. 

If you measure that change for long enough, the average of these changes would be zero, by passing the value of the instantaneous length by a maximum and a minimum value. These changes in one of the properties of the body involve temporary energy changes. 

In the case of periodic oscillations, vibration measurement can be performed to accurately know the value of the property at any given time. However, in the case of transport, since you will be dealing with random oscillations, it is not possible to predict the intensity value of the property at the next moment. 

When observing any means of transport, linear oscillating movements can be seen along the three axes of the Cartesian system, as well as angular oscillating rotation movements along those same axes. 

Therefore, the linear oscillating movements of a moving vehicle are commonly measured with accelerometers. When it comes to angular oscillating movements, sensors are used that measure velocity or angular acceleration. 

In the case of vibration measurement in transport, performing a single measurement is not enough, as this value changes randomly over time. Thus, performing an accurate analysis requires recording the different values that are produced. 

Thus, in order to obtain the correct vibration measurement, it is necessary to apply the Nyquist Sampling theorem, using a capture frequency twice as large as the frequency that is to be measured. Therefore, in the case of the linear oscillations of the transport, between 500 and 1000 samples per second are used, while angular oscillations use between 20 and 50 samples per second. 

Regarding the simplest way of obtaining these samples, devices can be used to simultaneously record linear and angular vibrations as a result of pitch. 

However, the raw register of random vibrations is impractical to use, and therefore, it is necessary to process the entries to obtain the power spectral density (PSD) curves of the vibrations and their root mean square (RMS) value. This way, these curves will graphically represent the energy density values as a function of frequency per unit mass. 


From vibration measurement to simulation: the equipment 

There is a wide variety of vibration simulation techniques, the technology of which has been improved over time through research: 

– Initially, simple crank/rod machines were used. This equipment repeated the same movement and oscillation, which does not correspond to what happens in conventional transport. 

– Later, servo-actuators were used to reproduce the previously recorded oscillations in detail. In this case, the same trip was always reproduced, as if the transport always passed by the same places, with the road in the same conditions, the same level of traffic… 

– The rise of random vibration simulation brought the tests closer to the reality of transport. Thus, this simulation is carried out with a controller that can perform random vibrations, so that the next position cannot be predicted but can be adjusted to a response defined by the PSD (either from a regulation or from the register obtained by performing vibration measurement). 

In this sense, the current vibration simulation equipment emerged, allowing tests to be carried out according to what really happens in transportation. 


Single-axis or multi-axis vibration: main differences Regarding the vibration tests, there are two types: single shaft (SDoF), and multi-axis (MDoF)

The main difference between MDoF and SDoF systems is the amount of movements that each system can simulate: the former allows movements along several axes, while the latter only along one axis. 

According to literature on the subject, single-axis vibration machines must increase the intensity by a certain factor in order to add the contributions of the rest of the axes. This is, however, not a real solution, as there is no guarantee that this added signal will be produced on the same frequencies that are generated along the other directions. Thus, this is nothing more than a compromise solution for instances in which multi-axis vibration equipment is not available. 

On the other hand, MDoF multi-axis machines have shafts that are designed independently and treated separately. Likewise, two simulation techniques are implemented: a recorded path is replicated, or a random test is reproduced in relation to a PSD. Thereby, each axis has its own PSD that it must follow and comply with. 

Further research on vibration measurement has shown that “pitch and roll” movements must be incorporated into the simulation so that it better represents the reality of the transportation. 

For instance: imagine a half-filled water tank, which moves only in response to vertical vibrations. This tank could be damaged if the test exceeds 1g and the container bounces and crashes against the 

vibration platform. If you add lateral displacement to said movement, which produces waves on the surface of the liquid, that could also damage the tank even if the container does not bounce. 

Therefore, when choosing vibration simulation equipment, it is necessary to determine what you want to test and how you want to test it. 

If the intention is to perform tests according to the regulations, you need to choose equipment that complies with them. 

However, if you want to simulate real-world effects on something, you must observe the movements suffered by said element, which will generally include simultaneous movements along several axes. In this scenario, an MDoF system would be the appropriate solution. 

For instance, to simulate transportation by land or sea, the solution is the Vertical Vibration Pitch & Roll System, which includes 3 DoF systems (a linear one, and two rotational ones). 

In this way, the linear vertical axis simulates the linear vertical vibrations produced by the interaction between the truck’s suspension, wheels, transmission shaft and chassis due to road irregularities. At the same time, the rotational roll and pitch axes simulate the most important rotational vibrations that are commonly produced during transport, and that can destabilize the load of the truck. 

In any case, Safe Load’s Pitch & Roll module can transform any SDoF vertical vibration system into a multi-axial table (1+2). This module can be installed on any vibration table, regardless of its brand or manufacturer, as the module is compatible with any of them. 


Are you looking for the best vibration equipment that meets your needs? 

Contact us and feel free to rely on our two decades of experience in the world of transport simulation and packaging design so we can help you make a choice.

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