Natural frequencies

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Each machine part can vibrate at one or more characteristic frequencies, the natural frequencies, after mechanical excitation due to its geometric and mechanical properties. In mechanical engineering, vibrating components or machines can become sources of interference. Vibrations, e. g. from rotating elements of a machine, can excite housing parts, the machine installation or the environment of the machine.

In order to prevent corresponding vibration and noise emissions, it is necessary to examine machine parts and the entire machine for natural frequencies. Standards such as ISO 10816 or DIN 4150 define allowable vibration values for machines and their surroundings.

Natural frequencies can be determined by two measurement methods:

Measuring method 1: Excitation by impact

Ideally, all excitation frequencies are generated at the same time and natural frequencies are visible over a wide frequency range. In addition, qualitative parameters such as dynamic stiffness can be obtained from the transfer function.

For this purpose, the InnoScope and InnoAnalyzer instruments are required in VibroMatrix.

Measuring method 2: Excitation by variable excitation frequency.

The excitation can take place from the outside, for example with a tunable shaker exciter. However, the machine itself can also act as exciter, e. g. due to unbalance-conditioned vibrations, which always occur at the current speed. This is the principle of run-up analysis. The machine is operated in run-up or run-down mode and the vibrations are displayed at rotational speed. For example, the optimum operating point can be found. This technology is naturally limited to the speed range of the machine. Such analyses can be performed with the InnoAnalyzer Speed for tracking analysis or the InnoAnalyzer 3D for waterfall representation.

Practical example

Let's start with the impact test on a component. The principle is to measure both the force impact induced by a pulse hammer into the component and the response of the system. The ratio of the response signal to the applied force is called the transfer function or frequency response function.

A force shock theoretically contains all frequencies. The frequency range is practically influenced by the choice of the hammer tip. As shown, a hard tip produces the largest frequency range up to several kHz. The softer tips reduce the range to a few hundred Hz and are therefore particularly suitable for excitation of low frequencies, as the energy content of the impact is distributed over a smaller range. For this example we use a medium hard tip.

The best way to measure the transfer function is to use the coupling between InnoScope and InnoAnalyzer. In this way, the time signals of the impact and the response as well as the resulting transfer function can be displayed and triggered together.

In the InnoAnalyzer, the mode "Frequency response function" is already preselected. Different ratios can be formed from both signals depending on whether the acceleration, velocity or displacement signal is used. . We measure the accelerance. This is the ratio of vibration acceleration to force.

Selecting H0 to H4 allows you to change the estimate function, which results in a better signal-to-noise ratio at low signal levels. We use H4 because it is the most accurate method.

The time window depends on the trigger times, it is recommended to use a rectangular window for impact tests. Furthermore, we perform an averaging over 3 impacts and use the logarithmic representation of the y-axis.

Machines must have a suitable placement. We want to investigate this using a model machine. A distinction is made between rigid installation, where the excitation frequency is below the natural frequency of the installation and flexible installation, where the excitation frequency is above the natural frequency of the installation. These two operating states are also referred to as subcritical and supercritical.

If a natural frequency is crossed, this is shown by characteristic features: The amplitude is maximized in the eigenfrequency and the phase has a 180° change.

The force impact and the subsequent oscillation of the component are clearly visible during the impact. The averaging smoothes out the transfer function. At 800 Hz and 2500 Hz strong oscillations can be seen in the curve, these are the component's natural frequencies. In addition, qualitative statements can be made about the transfer behaviour.

Practically, we demonstrate this with the InnoAnalyzer Speed on the model machine, which was initially set up in a soft position. The displayed run-up has a maximum at 12 Hz, this is the strongest natural frequency in measuring direction. The distinct phase change is clearly visible. Other natural frequencies of the setup can also be easily identified by the phase change.

The InnoAnalyzer 3D instrument allows waterfall representations, i. e. the sequential representation of frequency analyses. In the run-up shown here, the increasing rotational frequency and its higher orders are seen as diagonal lines. In addition, the natural frequencies of the setup are shown as straight lines above the frequency. When the rotational frequency enters the range of the natural frequency, the first order is increased because of resonance.

The placement is usually tuned in such a way that the operating frequency is at least three times the natural frequency. With this installation, the model machine can be operated at a minimum of 60 Hz.

What is the effect of a rigid placement? To do this, we remove the springs underneath the model machine. The run-up and the waterfall display show a smooth course. The vibrations emitted by the machine are transmitted into the foundation. In this way, amplitudes due to component eigenfrequencies can propagate into the surroundings. This can lead to increased vibration loads in the surrounding area. Here, the limit values of the applicable standards must be observed.

The excitation of eigenfrequency can also be reduced by balancing. Since a smaller excitation amplitude already leads to reduced resonance amplitudes.

In order to determine all natural frequencies at once, it is also possible to carry out a impact test on the flexibly positioned machine. For this we use the same measuring environment as shown above.

You can clearly see the natural frequencies below 50 Hz that are identified from the tracking analysis. However, various natural frequencies also occur at higher frequency values. These come from various parts of the machine.

In addition, the attenuation can be determined from the decay behaviour of the response signal. We use a soft hammer tip to stimulate small frequencies, filter the signal in the 3-30 Hz range and activate the evaluation of the decay time in the InnoScope. The logarithmic decrement is determined from the decrease in amplitude. This is proportional to the damping factor D.

This means that the functionality of the damped installation can be checked accordingly.

VibroMatrix offers various possibilities to determine the eigenfrequency of components and machines. The natural frequencies excited by a variable speed can be well visualized in the InnoAnalyzer Speed and InnoAnalyzer 3D. In this way, the suitability of the machine placement can be checked or a safe range for the operating speed can be found.

An impact test with InnoScope and InnoAnalyzer shows all natural frequencies in a wide frequency range at a one sight.

In addition, qualitative parameters of the transfer function can be used for comparison with corresponding computer simulations and the damping coefficient of the installation can be determined from the decay behaviour.

With VibroMatrix you can reliably determine natural frequencies and analyze the vibration emissions of your machines. If sources of disturbance are identified, constructive measures or changes to the placement can help.

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