Vítejte!

If you are faced with the task of implementing and performing vibration diagnostics in your company, then do not panic. This area offers both simple and complex procedures and methods. You will start with the simplest ones and gradually work your way up to more complex ones. At the beginning, you will perform measurements very similar to those made with a voltmeter. Only you will not measure voltage, current or resistance, but vibration values.

The basic task of diagnostics is to prevent unexpected failures, because eliminating their consequences entails high costs. If a rolling bearing breaks down unexpectedly, then other machine components around it will also be damaged. That is why the repair is very expensive. Diagnostics will warn you in advance of the worsening condition of the bearing, you can plan a replacement during a regular shutdown and the costs will be much lower. The task of diagnostics is therefore to reduce maintenance costs.

In the past, machines ran until they broke down. Then they were repaired. This approach had two basic disadvantages. Let's imagine a relatively small problem, for example bearing wear down. Replacing of the bearing would be easy and quick. However, if the wear is great, then the bearing breaks down and the entire rotor stops rotating. The rotor weight is several hundred kilograms. It does not stop easily. There is enormous inertia present, which can destroy the entire machine in a few seconds. Then the repair is long and expensive.

Another disadvantage is the sudden stop of the production line, again due to the wear of one bearing. For example, the line produces products worth a million in 1 hour. If the repair takes several hours, then there will be a loss of several million.

The subsequent development of the maintenance system then reached the stage of preventive replacements. Every component that wears out over time was replaced at defined time intervals. Let us list the basic disadvantages.

• Maintenance costs are high because something is replaced all the time.
• Secondly, in most cases, it is replaced unnecessarily because the component is still in good condition.
• And thirdly every maintenance intervention is not completely perfect. For example, the installation of a new bearing can be performed poorly and the condition of the new bearing will deteriorate quickly, so that eventually an unexpected failure will occur anyway.

Subsequently, another maintenance system appeared, which is the predictive maintenance. The condition and wear out of the machine are measured regularly, and if it is getting worse, then maintenance intervention comes. That means, only when it is really needed.

What will we need? First of all, a measuring device, let's call it a vibration analyzer, a vibration sensor and a cable to connect the sensor to the device. Equipped like this, we go to the machines, we call this a route. We will perform measurements on each machine, which will be saved in the device's memory. After returning from the route, we will transfer the measured data to a computer and evaluate them.

To perform vibration diagnostics, we use a program supplied by the manufacturer of the vibration analyzer. We will create a list of machines and the measured data will be saved to them.

We will go to the route at regular intervals, the more often the better. Of course, we cannot go every day. The optimal interval is about 2 weeks. If we have machines whose operation is essential for the entire factory, then it is better to use online systems that measure continuously.

Now we have the data in the computer and it needs to be evaluated. This means determining the current machines condition and, if necessary, planning repairs or adjustments. How do we do this? There are several ways to look at the measured values.

If any standard exists, then it can be used. The standard will tell us the values of vibration limits. Usually, the warning and danger limits. If the warning limit is exceeded, the machine can still be operated, but we should plan a maintenance intervention as soon as possible. Exceeding the danger limit means the machine must be shut down immediately and repaired. The basic standard is ISO 20816.

Then other procedures are needed.

If we have several identical or similar machines, then we can compare the values between them. If the vibrations on five of six identical machines have a value of 2 and on the sixth the value is 8, then there is clearly something wrong with the sixth machine.

Another option is to analyze the trend of the development of vibration values. If the trend is stable over the long time, then the operating condition is also stable. If the vibration values increase, then some damage is increasing and the machine needs to be repaired or adjusted.

The trend or comparison with values from the past is the best way how to evaluate the machine condition. When we can see even a small increase; this means that the deterioration of the condition is only small and we have enough time to plan a maintenance intervention.

It is the same with vibration diagnostics. It will never be 100% successful. Sometimes the fault is too hidden inside the machine and may not be easy to find it in the vibrations. Or its development was very quick and during the last route everything was still fine.

Suddenly an unexpected break occurs. Then the warning and danger limits need to be reduced. So even an unexpected break can have a positive meaning for the future.

Vibration diagnostics is absolutely essential in taking care of the condition of machines. There is no other type of diagnostics that can find such a wide range of faults and wear.

Vibrations are the oscillating, repeated movement of mass between two extreme positions. The important is whether the amplitude of the vibrations (it means the distance between the extreme positions) is acceptable for the machine operation. The velocity of the oscillating movement is also important.

The curve shape of the vibrations is a basic shape and mathematically corresponds to the sine function. We will call the recording on the paper as a time signal of vibrations and we can evaluate other useful vibration parameters from it.

The amplitude of the vibration can be easily measured using the 0-P amplitude. We call it the peak value and it is the distance from the mean value of the signal (which corresponds to the rest position of the weight) to the maximum value.

For completeness, we should mention the P-P (Peak-Peak) value, which is the distance between the maximum and minimum values. For a symmetrical signal shape, the P-P value is twice the 0-P value.

The task of digitization is to convert an analog signal into numbers. We select a time and read the value. We will call it as the sample at defined time.

We need to read values at regular (equal) time intervals. If the signal length is, for example, 1 sec, then we will get 1000 samples, it is a series of 1000 numbers. In the future, we will always call individual readings in a time signal as samples. If we have enough samples, then we can apply various mathematical formulas to them and we can calculate other diverse results.

The amplitude of time signal can also be measured as the average value of all measured samples. The average value is calculated as the sum of the values of all samples and divided by their number.

The solution is to convert the signal waveform only into the positive half. We will achieve this by working with the absolute values of the samples. For the sine function, the average AVG value is always equal to 0.64 multiplied by the 0-P value.

Let‘s fill in and measure the area under the sine function. Now we will draw a signal whose samples all have the same value. The area under the signal is calculated as the length multiplied by this sample value. It is the area of the rectangle. Our task is to find such a value that the areas of both signals are identical. This desired value will be equal to 3.2 ($0.64 * 5$). This is the same approach as replacing the sinusoidal (irregular) waveform with just a signal where all amplitudes are equal to the average value. So, it is a straight line.

We have already described the case of a sinusoidal waveform. The average value is equal to the value 0-P multiplied by 0.64.

When we calculate the average value from a rectangular waveform, then after converting to an absolute value we see almost the same as after converting to a rectangle. It follows that the average value AVG is almost the same (only slightly smaller) as the value of 0-P.

If the signal contains only shocks, the situation is the opposite. The area inside the pulses is small, and thus the height of the rectangle for deriving the average AVG value is small. We have shown that there is no fixed relationship between the average and peak values.

A similar value is used, which we call RMS (Root Mean Square). Its advantage is that it corresponds to the energy contained in the signal. For example, in case of unbalance, it is the centrifugal force that brings us problems because it shakes the entire machine. If we reduce vibrations, we have reduced the force acting on the machine.

How is RMS calculated? It is similar to the average value, only all signal samples are squared first. This simultaneously achieves their transformation into positive values. Then the square root of the average value is calculated.

If the waveform of the signal corresponds to the sine function, then the RMS value is equal to the peak value 0-P multiplied by 0.71. I would like to remind you again that the conversion constant 0.71 can be applied only to a sinusoidal waveform.

Both the AVG and RMS values do not depend on the duration of the signal. The reason is clear. These are average values (we divide by the number of samples N). If the signal has more samples, then their sum will be larger, but after dividing by the number of samples we will get the same value as for a shorter signal.

For machines with speeds above 10 Hz (600 RPM), it is enough to measure a signal with a length of 1 second. For low-speed machines, we measure longer. The signal should contain at least 10 revolutions.

Frequency is how many periods of up and down movement the mass makes in a given time, usually 1 second.

The basic movement of up and down is called a period. The frequency is calculated in Hz and tells us how many times in one second the periodic motion repeats. If we denote the length of the period by T, then the frequency: (if T is in seconds), or alternatively: (if T is in miliseconds).

Even the speed (rotation) is a repetitive motion, where the basic period is one rotation of the shaft. The rotational frequency can also be expressed in Hz, which is the number of rotations per 1sec. We will call the rotational frequency a speed frequency or just speed. It is more common to measure in RPM (Revolutions Per Minute).

To record the time signal from the machine, a vibration sensor is needed, which converts mechanical movement (vibration) into an electrical voltage. This signal then goes to the input of the vibration analyzer.

What is the importance of frequency for machine diagnostics? It is essential. For example, unbalance is manifested by vibrations with the speed frequency (1x speed). Misalignment can be manifested by vibrations with 2x speed. Looseness is manifested by vibrations with 0.5x speed. This means that a different machine fault is manifested by a different vibration frequency. If we know the basic frequencies for individual machine faults, we can successfully diagnose the machine.

The second way is to calculate the frequency spectrum. The X-axis of the spectrum is not time but it is frequency. The spectrum itself shows us at which frequencies the vibrations are emitting energy i.e. at which frequencies the vibrations are and how strong they are, and at which frequencies they are negligible.

However, if we convert the time signal into a spectrum, we can distinguish the individual components. The different faults on the machines differ from each other specifically in the frequency image. The spectrum thus becomes a powerful tool in vibration analysis.

If there are also lines at multiples of speed (these are called harmonics), then there is a significant misalignment. The spectrum always responds to signal distortion by showing harmonic components.

The basic SI unit for length is the meter. In vibration diagnostics, however, the amplitudes are very small, and therefore we will use the unit of micrometer ($\mu m$). $1 \mu m$ = $0.000001 m$. The basic SI unit for velocity is $m/s$. The basic SI unit for acceleration is $m/s^2$.

Displacement is the measured distance between the extreme positions of the vibrating object. The measured value is usually expressed in $\mu m$ (micrometers). We can use displacement measurement to measure the overall vibration value. We can use displacement to find unbalance or misalignment of the machine.

Velocity of the vibrating motion is expressed in $mm/s$. The velocity is the most commonly used measurement quantity because its relationship to the severity of the machine fault is not very dependent on the frequency (or speed).

The unit for acceleration is $m/s^2$, but the unit $g$ (gravitational acceleration) is also often used. Acceleration je mainly used to measure high frequency vibrations.

The length of one period can also be thought of as 360 degrees. The advantage of this approach is that it don‘t depend on frequency. If we then want to say that the velocity waveform is shifted by a quarter of a period to the left (i.e., against time), then we say that it is shifted by minus 90 degrees. The phase shift is in degrees.

Vibration diagnostics has two basic tasks in practice. The first is to determine the machine condition has been changed. This is called problem detection. The second is to analyze the vibration in more depth and find out what fault or wear has occurred on the machine.

Overall measurements are used the most. The meaning of the word overall is that the measurement covers a wide band of frequencies. The measured value can then be RMS (which is the most used), 0-P, P-P and others. If we want to tell someone what overall value we have measured, we always have to tell them four parameters. (Value, Method - e.g. RMS, Band - e.g. 10-1000 Hz, Unit - e.g. mm/s).

The most common are piezoelectric accelerometers. This type of sensor measures acceleration. The advantage of these sensors is that they are very accurate, small and measure a wide range of frequencies, including high ones.

The sensor is most often attached to the machine with a magnet or a screw connection. The type of coupling strongly influences the transmission of high frequency vibrations. Screw connection is the best coupling. If we use a magnet, we should ensure the measuring surface is flat.

We measure at the bearings, where the highest vibration is often concentrated. If we want to determine the condition of the coupling, we measure on the motor and pump near the coupling. We must measure the vibration in two directions at the bearings. Radial direction (horizontal or vertical, perpendicular to the shaft) and axial direction (in the direction of the shaft).

The rotational speed of the shaft must be measured or entered manually. If the machine speed changes, then the vibration value will also change, even if the machine condition remains the same. Either we can measure them with a tacho probe and the analyzer will store the speed with measurement value, or we can enter the speed manually.

We always start with overall RMS values. We can do vibration diagnostics with them with excellent results. We can add more sophisticated methods later.

The basic measurement is a velocity measurement in the 10-1000 Hz band. The second measurement is the acceleration measurement in the 500-16000 Hz band. We start by the acceleration measurement. The most common use is to measure the bearing condition.

The basic faults we can detect using vibration diagnostics are: Unbalance, Misalignment, Looseness, and Bearing wear. Other faults are, e.g., electrical problems of electric motor (e.g. broken rotor bars) and gear faults.

We can use the following simple criteria for evaluating overall RMS values:

• Misalignment detection: If the vibrations in the axial direction are higher than in the radial directions, then misalignment is the most likely fault.
• Looseness detection: If there is a higher vibration value on one bolt than on the others, then there is a looseness.

Resonance is the effect when the excitation frequency of the machine is the same as its natural frequency. The amplitude of the vibration increases dramatically, and the machine can be destroyed in a short time. A natural frequency is the frequency at which the machine vibrates after an impulse. Every machine has a natural frequency. It is very important that the machine's operating speed is not close to the natural frequency.

The fault in the rolling bearing is most often manifested by a shock when the rolling element passes through the damaged spot. The shocks themselves have a very low amplitude and very high frequency. It is virtually impossible to directly detect a very small defect on a rolling bearing.

The solution is demodulation (also called envelope analysis). We take the time signal and extract the envelope from it. The time interval between shocks is converted into a frequency. This frequency is called the fault frequency (e.g., BPFO for outer ring fault).

The advantage of demodulation is that we can detect a bearing fault at a very early stage. Nothing is measured at the fault frequencies! The defect lines in the spectrum are created by calculation, not by measurement.

This is an old method of vibration evaluation. A screwdriver was pressed face down on the machine and the back surface pressed against the ear. Even today, our Adash instruments allow us to listen to vibrations. The signal from the sensor is fed into the headphones. The bearings (their noise or whistling) are most often listened to.

We can easily convert the measured acceleration value to velocity and displacement, and vice versa. This conversion is called integration (acceleration -> velocity -> displacement) or differentiation (displacement -> velocity -> acceleration). The calculation involves mathematical formulas. The problem is that the integration process greatly enhances low frequencies. Therefore, the conversion is not always accurate in practice.

The relationship between the three quantities (displacement, velocity, acceleration) is frequency-dependent. Displacement is more sensitive to low frequencies and less sensitive to high frequencies. Acceleration is less sensitive to low frequencies and very sensitive to high frequencies. Velocity is independent of frequency. This is why displacement is used for low frequencies (e.g., misalignment, unbalance) and acceleration for high frequencies (e.g., bearing condition).

Online systems measure continuously, 24/7. They are suitable for machines whose operation is critical for the production process or for inaccessible machines. They allow real-time monitoring of machine condition.

If the rotor has an uneven weight distribution, it is called unbalance. The resulting centrifugal force causes vibration at the rotational frequency (1x speed). Balancing is the process of adjusting the weight distribution of a rotor to minimize the unbalance and resulting vibrations.