The 2D graph can display values of the currently selected point with the crosshair cursor. When clicking on such a point with the left mouse button, the marker line will be added showing the x-axis value on the x-axis and showing the y-axis value of a certain point above the marked point. All points can be removed by pressing the right mouse button and select the Delete selected marker.
Let's make a square wave with a frequency of 200 Hz in Dewesoft math and put the signal into the FFT analyzer.
When we go to measure and FFT graph, we can see that the square wave is composed of a sum of sine waves with different frequencies. We can see those frequencies as peaks in the FFT graph, but now we would like to know the exact position of those peaks.
Image 60: FFT of a square wave
Select an icon for Free marker and click on the FFT graph to add it.
Image 61: Adding a new Free marker
Free markers can be freely added. The marker shows us the frequency of the peak at which it stands and its amplitude.
Image 62: Free marker displayed on the 2D graph
With Show marker table selected you can see the table of markers - its ID, type, channel, color, its frequency (X-axis), and its amplitude (Y-axis). You can select if you want markers to be visible or not, you can also edit and remove it.
Image 63: Option show marker values in a table
Max marker finds the highest amplitude in the spectrum. Move the mouse to the FFT graph and select icon for Max marker.
Image 64: Adding a new Max marker
When we select Max marker and click on the FFT graph with the left mouse button the following setup opens.
Image 65: Max marker options
First, we select the FFT curve to which the marker is related. The position is calculated by the program.
Interpolation - estimating frequency and amplitude
Depending on the selected window type, the frequency component (actual peak) can fall in between two adjacent lines.
In the example below, we have a signal with a frequency of 256.5 Hz and an amplitude of 1. The frequency resolution in our case is 2 Hz. When we add a free marker on the peak (non-interpolated), we see that the marker is at 256 Hz and has an amplitude of 0,97 (because the amplitude is split between two peaks).
Image 66: Non-interpolated position of the marker
If we want to get the exact value, we have to interpolate the peak. To get the right interpolation, at least three lines on each side (left and right) have to have a smaller value than the peak. Now, the frequency of the peak is in the exact position. Also, the amplitude has the right value.
Image 67: The interpolated position of the marker
It is possible to estimate the actual frequency and amplitude to a greater resolution than given by delta frequency (df). Dewesoft uses a weighted average of the values around a detected peak to calculate exact frequency and amplitude values.
Also, if two or more frequency peaks are within six lines of each other, they contribute to inflating the estimated powers and skewing the actual frequencies. But anyway, if two peaks are that close, they are probably already interfering with one another because of the spectral leakage.
Number of peaks
Then we select a number of peaks we want to find. If that number is 1 program will only find the peak with maximum amplitude. If that number is 3 it will find also the peak with the third-highest amplitude. The picture below shows the max marker with 3 number of peaks selected.
Image 68: Number of max marker peaks
RMS marker will sum up all the FFT lines in the selected band and calculates the RMS value. Move the mouse to the FFT graph and select the icon for the RMS marker.
Image 69: Adding a new RMS marker
RMS marker calculates RMS value of the channel between cursors or between defined areas.
Image 70: RMS marker options
The RMS value of the channel between cursors can also be adjusted by dragging cursor with a mouse. RMS will be calculated automatically if the area changes.
Image 71: RMS is calculated automatically for the selected area
The sideband marker monitors the modulated frequencies to the left and right from the selected centerline.
Let's generate an amplitude modulated signal with a carrier frequency of 1000 Hz and the baseband signal with a frequency of 100 Hz.
Sideband markers have a center marker and several equally spaced sideband markers. By selecting the center marker, you can drag the sideband markers to different positions while still maintaining the individual sideband space.
Each sideband cursor can be selected and moved to a different frequency hence changing the individual ratio of the sidebands with respect to that of the center cursor.
On the FFT, the graph select the icon for the Sideband marker.
Image 72: Adding a new Sideband marker
The sideband marker draws markers around the selected peak. We have to define the number of bands (for how many bands in each direction we want to see drawn lines) and Delta (distance between bands in Hz). For example, the selected position is 1000 Hz, a number of bands are 1, and Delta frequency is 100.
Image 73: Sideband marker options
We can see that the central position is at 1000 Hz and we have one band in each direction. So the line on the left side is at 900 Hz and the line on the right side is at 1100 Hz. Distance between the lines can be defined by the user, in our example, it was 100 Hz.
Image 74: Sideband marker on the 2D graph
The harmonic marker is a great help when identifying the fundamentals of the frequency.
The harmonic marker can be enabled at any frequency. The harmonic marker will mark the harmonics of the selected frequency. The base marker of the harmonic marker can be selected and moved to any other frequency with the harmonics updated live.
Monitoring harmonics is very important in the order tracking analysis. An example was made with a blue toy in the picture below (accelerometer was attached to the machine). We run the machine to 3000 RPMs and measure vibrations in the process.
Image 75: Demo equipment for rotational vibration measurements
Move the mouse to the FFT graph and select the icon for a Harmonic marker. Then select the base frequency with the mouse and add a harmonic marker with the click on the left button.
Image 76: Adding a new Harmonic marker
We select the first peak at 21.97 Hz.
Image 77: Harmonic marker options
If we select the Number of harmonics as 3, we will see lines at 21.77 Hz, 43.54 Hz (2 x 21.77 Hz), and at 65.31 Hz (3 x 21.77 Hz). And the theoretical harmonics also nicely match our measurement results - the first three harmonics are nicely seen.
Image 78: Harmonic marker displayed on the 2D graph
You can also pick and drag the fundamental frequency through the FFT spectrum. Harmonics will automatically follow.
Damping markers are best to use in modal testing when we want to find out how our transfer curve is damped. We select it when we are interested in the quality factor, damping ration, or attenuation rate of a selected peak.
Image 79: Modal test demonstration with a modal hammer as excitation and accelerometer as a response
Move the mouse to the FFT graph and select the icon for the Damping marker. Then click on the mouse button to the position, where you want to add a damping marker.
Image 80: Adding a new damping marker
When selecting the damping marker the following setup appears:
Image 81: Damping marker options
Damping factor type can be selected from the following options:
Image 82: Different damping factor types
Image 83: Definition of the Q factorThe Q (quality) factor of the damped system is defined as: The higher the Q, the narrower, and 'sharper' the peak is.
Damping ratioDamping ratio and quality factor Q are related through the equation:
Attenuation rateAttenuation is the gradual loss in intensity of any kind of flux through a medium. It is usually measured in units of decibels per unit length of the medium.
In the picture below we can see a transfer curve of a beam. On each of the peak, we attach a damping factor and in the marker table we can see the quality factor (Q), which tells us, how much the transfer curve is damped.
Image 84:Transfer function and damping factor of peaks
If the Damping factor type is chosen as a Damping ratio, the result is Zeta for each peak.
Image 85: Results for damping displayed in Zeta coefficients
If the Damping factor type is chosen as Attenuation, the result is the attenuation ratio for each peak.
Image 86: Results for damping displayed as Attenuation ratio
Bearing cursors are used to identify the bearing frequencies and bearing faults.
To use Bearing cursor we have to add Envelope detection math channel.
Image 87: Adding a new Envelope detection math
Image 88: Envelope detection setup
Each bearing database includes bearing data (what is the base of component (cage, rolling element, outer race, and inner race) at 1 Hz and at which frequency has the component a peak in the frequency domain).
To add a new bearing go to Kinematic cursor editor.
Image 89: Entering editor for Kinematic cursors
In the Kinematic cursor editor, add a new bearing or select from the existing database, selecting the Append bearing option.
Image 90: Kinematic cursor setup
Channel calculated with Envelope detection math must be now set as the input channel to the FFT analyzer.
At the measurement screen of the FFT analyzer, select the icon for the Kinematic cursor.
Image 91: Adding a new Kinematic cursor
Now we can see bearing cursors at frequencies that are defined is bearing database. The table shows to which mechanical part the frequency is related.
Image 92: Kinematic cursor displayed on the 2D graph
The FFT lines are responsible for the frequency resolution. The higher the FFT lines value, the better the resolution. This line resolution depends on the sampling rate and the number of lines chosen for the FFT. So if we want to have fast response on the FFT, we choose fewer lines, but we will have a lower frequency resolution. If we want to see the exact frequency, we set a higher line resolution.
If our peak falls between frequency lines, the frequency will not be exact. Because harmonics are multipliers of the fundamental frequency, the error will increase at every higher harmonic.
Image 93: Non interpolated peak and the error, that increases with harmonics
If we mark the interpolate peak options, our markers will be interpolated in frequency and in amplitude!
Image 94: Interpolated peaks