Knowledge of the accelerations and vibrations acting on an asset is essential for planning predictive, planned, preventive, and, in extreme cases, corrective maintenance actions on machines and structures. These actions can optimize the Structural Integrity equipment when performed assertively.

The finite element method can simulate the behavior of these machines and structures when subjected to such accelerations and vibrations. Even if a structure is approved from a static point of view, its dynamic behavior may cause structural collapse due to the vibration frequency of oscillatory equipment. To obtain these frequencies, it is possible to use equipment capable of measuring vibration data, such as camera/sensors and accelerometers.

The aim of this article is to present, in detail, the use of accelerometry to analyze vibrations and dynamics in structures.

What is the accelerometer?

In short, an accelerometer is an electronic sensor that can be attached to the surface of an object of study from which you want to collect acceleration and vibration data. This makes it possible to determine the body's position in space as a function of time [1]. One of these sensors can be seen in Figure 1. 

Figure 1: Accelerometer [2]

The accelerometry method consists of instrumenting the asset with accelerometers at strategic points, connected to a data acquisition system which is responsible for electronically recording the information collected. To identify the points where the sensors are to be installed, a preliminary study is carried out to map the points most susceptible to variations in acceleration and vibration values.

 An acquisition system commonly used in this type of test can be seen in Figure 2. Once the data has been collected, computer processing is carried out to refine the values found. These values can then be inserted into the computer model for structural verification.

Figure 2: Compact data acquisition system. [2]

Mass-spring system

The basic principles of an accelerometer come from the physical system of a mass coupled to a spring, known as a mass-spring system. This is a harmonic oscillator that restores its initial position from the force stored in the spring when it is removed from its original state by an applied force. Figure 3 shows a schematic of this system.

Figure 3: Schematic of a mass-spring system. [2]

The equation for this movement is obtained from Newton's second law and is illustrated in Equation 1, where damping forces have been applied. These forces can come from air resistance, friction or other dissipative effects.

Equation 1: Calculation of force as a function of time.

Where:

• f (t) = force as a function of time;
• m = mass of the system;
• x'' component of the acceleration;
• c = damping coefficient (varies mainly according to air resistance and friction);
• x' = velocity component;
• k = spring stiffness;
• x = displacement of the mass in relation to its equilibrium point. 

This model is highly relevant to the study of natural phenomena, as it generates acceptable results for studies of small movement amplitudes.

Similar to the mass-spring system, the mass present in the accelerometer causes deformations in the piezoelectric materials inside the sensor, which act as extensometers, generating an electrical charge proportional to the existing deformation. With the internal mass constant and the deformation generated proportional to the electrical charge, it is then possible to calculate the acceleration of the body. 

Accelerometry applications

In theory, natural frequencies depend only on the mass and stiffness of the system, which makes it possible to perform modal analyses using this information. These analyses consist of studies using the finite element method method to understand the structural responses to the natural vibration modes of the object. However, the available data is not always accurate, and in some cases, no information is available. Thus, an asset can be instrumented with accelerometers to calibrate the computational model.

Due to the characteristics of the equipment, it is common to use accelerometry in vibrating equipment such as screens and crushers, as well as in the buildings and structures that receive such equipment.

To establish the Structural Integrity assets, it is essential to perform the applicable dynamic analyses. If the operating frequency of a machine is equal to its natural frequency, resonance will occur, amplifying vibrations and potentially leading to premature failure.

Figure 4 shows an example of vibration measurement at the base of a sieve, in an area close to the spring, showing the locations where the accelerometers were attached.

 

Figure 4: Example of typical attachment points used in vibration measurement. [2]

The results of the accelerometry activity were used to feed the finite element model of the base of the building in which the screens are inserted and Figure 5 shows the modal analysis of the structure for a given natural frequency.

 

Figure 5: Result of the modal analysis of the sieve structure and support. The data collected by accelerometry is used to feed the computer model.

If you would like to learn more about Vibration Analysis and Structural Dynamics, check outKot's article on the subject by clicking here!

Conclusion

Although structures and equipment may not present problems in their static behavior, it is necessary to check the natural vibration frequencies to avoid the resonance phenomenon that can lead to wear and premature failure of system components. Kot has extensive experience in analyses of this nature and can evaluate different conditions and study scenarios in various oscillatory equipment. To learn more about the applications and what your company's assets need, contact the Kot team!

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References

[1] Jost. D. (2019/07/11). What is an accelerometer?. Disponível em: <https://www.fierceelectronics.com/sensors/what-accelerometer>

[2] Kot Engenharia Collection.