Angle domain analysis is a technique for viewing data acquired from rotating machinery. Data is referenced to the angle of rotation rather than the time domain. Referencing data to angle is useful in identifying the root causes of noise and vibration issues in rotating machinery.
Consider the example of a combustion engine shown in Figure 1. The exact degree position in the angular rotation of the crankshaft when mechanical interference occurs can be clearly determined by viewing the data in the angle domain. This is not obvious by viewing the data in the time domain.
Figure 1: Engine vibration (blue trace) peaks with cylinder pressure (green) at 180 degrees into the rotation of a crankshaft. This is caused by mechanical interference between the cylinder wall and piston (right).
Using the angle domain information, the geometries of the cylinder and piston can be adjusted to avoid the contact.
Other application examples where angle domain analysis can be used include the following: engine combustion analysis, electric motor performance, wheel rotation, and gear noise.
This article explains how to use the “Angle Domain Processing” add-in of Simcenter Testlab to perform angle-based analysis of noise and vibration data:
1. Angle Domain Background 2. Rotational Speed Data Required for Angle Domain Analysis 2.1 Angular Resolution 2.2 Missing Pulse as Reference 2.3 Incremental Encoder 2.4 Electric Motor Resolver 3. Getting Started with Simcenter Testlab Angle Domain Processing 3.1 Time Data Selection 3.2 Viewing Time versus Angle 3.3 Overview versus Detailed Display 4. Degrees, Revolutions, Cycles 4.1 Revolutions per cycle 4.2 Displays 5. Angle Strip Chart Display Analysis 5.1 Selecting the Resampling Tachometer 5.2 Angle Viewing: Buttons and Cursors 5.3 Defining the Zero Position 6. Angle Frame Statistics Analysis 6.1 Angle Frame Statistics in Time Data Processing 6.2 Angle Statistics over Multiple Cycles 6.3 Variation in Timing 6.4 Combustion
1. Angle Domain Background
To do angle domain analysis, data must be converted from the time domain (which is normally acquired by an acquisition system) into the angle domain.
Because the speed of rotating system often varies, the rotations are not guaranteed to be evenly spaced over time.
Figure 2 illustrates how a one pulse per revolution tachometer measurement (attached to a running piece of rotating machinery) get closer together when speed increases over time.
Figure 2: The pulses generated by a tachometer (green trace) get closer together as rotational speed increases.
As the speed increases, the time between pulses decreases.
A fixed time window would not be useful to average these revolutions or cycles together in this case. A time increment that corresponds to a single revolution at one speed would not correspond to a single revolution at a different speed.
By transforming the same data from the time domain to the angle domain, the data is evenly spaced in the angle domain regardless of speed (Figure 3).
Figure 3: Example of pulses evenly spaced when resampled based on angle and revolution.
A fixed amount of revolutions can be used to analyze the noise or vibration data.
In order to analyze data in the angle domain, specific rotational speed data must be acquired. This is outlined in the next section. This rotational speed data would be in addition to any sound or vibration data of interest.
2. Rotational Speed Data Required for Angle Domain Analysis
When acquiring data for angle analysis, it is helpful to measure the rotational speed in two different ways: • One Pulse per Revolution: A tachometer or encoder with a single pulse per revolution is useful as a zero-degree reference for each rotation. By marking zero degrees, the exact angle in which a problem occurs within a rotation can be determined. • Multiple Pulse per Revolution: A tachometer or encoder with a high number of pulses is used to accurately transform the time domain data to the correct angular position. Both rpm signals need to be recorded to perform an angular analysis.
2.1 Angular Resolution
The higher the number of pulses used to measure the rotational speed, the finer the angular resolution that can be achieved. This allows more detailed speed fluctuations to be measured. For example: • 360 Pulse per Revolution: One Degree Increment • 720 Pulse per Revolution: 0.5 Degree Increment • 3600 Pulse per Revolution: 0.1 Degree Increment
Speed fluctuations can be caused by overcoming inertias, mechanical interference, stick-slip conditions, torsional vibration, pistons firing, etc.
Some practical methods for measuring these speeds are covered next.
2.2 Missing Pulse as Reference
Gears, which have many teeth, can be used for multiple pulse per revolution speed measurements. A magnetic pickup is aligned with the gear teeth to measure the rotational speed. Some gears even have missing teeth which can be used for the zero-degree reference. An example is shown in Figure 4.
Figure 4. Gear with missing tooth (left) creates a tachometer signal (right) with a gap.
When defining a tachometer in Simcenter Testlab Signature, missing teeth can be defined used as a reference pulse as shown in Figure 5.
Figure 5: Missing pulses can be used to define a zero-reference pulse in the tachometer settings of the “Tracking Setup” worksheet of Simcenter Testlab Signature.
Turning on both the missing pulse algorithm and the reference pulse setting will automatically create two rpm signals from the tachometer: one for zero-reference and a multiple pulse per revolution.
If a gear with a missing tooth is not available, other possibilities include: • Two Tachometers: Install two separate physical tachometer measurement devices to measure the zero-reference and the multiple pulse per revolution. • Other Sensor Data: Use other measured information to determine the zero degree location.
Another device, called an incremental encoder, can also measure both the zero and multiple pulse signals simultaneously.
2.3 Incremental Encoder
An incremental encoder is often used when acquiring data for angle domain analysis. Unlike traditional tachometers, an encoder has both a single pulse per revolution output and a multiple pulse per revolution output in one device (Figure 6).
Figure 6: Incremental Encoder devices contain both a one pulse per revolution (INDEX), and two high pulse per revolution signals (A and B).
An incremental encoder outputs two high pulse per revolution signals (A and B in Figure 7). This gives incremental encoders another unique capability over traditional tachometers. An incremental encoder can detect forward and backward rotation (in other words, clockwise and counter clockwise) of a spinning system. A traditional tachometer device, which outputs only one set of pulses, cannot be used to detect forward and backward rotation.
2.4 Electric Motor Resolver
Most electric motors come with a resolver built into them. The resolver tracks the degree position of the rotor within the electric motor.
Resolver signals can be used to calculate the angular position with Simcenter Testlab as shown in Figure 7.
Figure 7: RESOLVER_TO_ANGLE function in Simcenter Testlab.
The resolver to angle function is part of the Simcenter Testlab Time Signal Calculator. For more information see the article: Time Signal Calculator Tips.
With the appropriate rotational speed data, angle domain analysis of noise and vibration signals can be performed.
3. Getting Started with Simcenter Testlab Angle Domain Processing
In Simcenter Testlab, to access the Angle Domain Processing workbook, go to “Tools -> Add-ins” and turn on “Angle Domain Processing” as shown in Figure 8.
Figure 8: Select “Angle Domain Processing” under “Tools -> Add-ins” in Simcenter Testlab.
Once this feature is turned on, the Angle Domain Validation Worksheet appears at the bottom of Simcenter Testlab as shown in Figure 9.
Figure 9: Angle Domain Validation Worksheet
Now the time data to be transformed into the angle domain must be selected in the Time Data Selection worksheet.
3.1 Time Data Selection
With the time data selected and already in the Input Basket, press the “Add” button at the upper left corner of the Time Data Selection worksheet (Figure 10).
Figure 10: In Time Data Selection, a time data set containing a one pulse per revolution signal, a 152 pulse per revolution, and vibration data is selected.
Once the dataset is selected, move to the Angle Domain Validation worksheet.
3.2 Viewing Time versus Angle
In the Angle Domain Validation worksheet, the data can be viewed referenced to time domain or angle domain as shown in Figure 11.
Figure 11: In Angle Domain Validation worksheet, clicking on a checkbox in the “View” column (far left) displays the data in the time domain. Clicking on a checkbox in the “View [alpha symbol]” column (second to left) displays data in the angle domain.
On the left side of the workbook, there are two columns that allow the user to select channels to be viewed referenced either to time or angle:
Clicking on a checkbox in the “View” column (far left) displays the data in the time domain.
Clicking on a checkbox in the “View [alpha symbol]” column (Second from left) displays data in the angle domain.
Settings in the lower left corner of Angle Domain Validation are used to convert from time to angle domain, which are described further on in the article.
3.3 Overview versus Detailed Displays
Once the checkbox is turned on in either of these two columns, the data is displayed in both an overview display (shows the entire data acquisition) and a detailed display (a zoomed in partial data display) as shown in Figure 12.
Figure 12: The overview display (top) shows the entire time history, while the detailed display (bottom) shows a zoomed in portion of the top. The icons (upper right) are used to view time or angle data and auto-size the displays.
The buttons in the upper right do the following:
The lower “script t” and “alpha” icons allow time, angle, or either types of data to be viewed in the displays.
The far-right button expands the display to the maximum size.
Either the overview display or the detail display can be turned on/off by clicking the check box located in the upper left corner of the respective display.
4. Degrees, Revolutions, Cycles
There are three different conventions for viewing data in the angle domain displays:
Degrees are used to indicate how far the rotating system has traveled. Every 360 degrees corresponds to one revolution of the rotating system. In Figure 13, both degrees and revolutions are marked on a shaft cross section.
Figure 13: Degrees and revolutions marked around a shaft cross section from a piece of rotating machinery.
Every multiple of 360 degrees matches up to another revolution. If the shaft rotates once, it has traveled 360 degrees. If the shaft rotates two times, it has traveled 720 degrees.
A cycle corresponds to a specific number of revolutions. For example, a complete four-stroke engine combustion cycle consists of two revolutions (or 720 degrees) as shown in Figure 14.
Figure 14: One complete combustion cycle of a four-stroke engine requires two revolutions.
In a four-stroke engine, the first revolution (or 360 degrees) contains the intake and compression events. The fuel is injected while the piston travels downward in the cylinder and then compressed as the piston travels back up. The next revolution contains the power and exhaust events. In the power event, the fuel mixture is ignited which causes the piston to be thrown downward. The burned fuel remnants are then exhausted out by the piston traveling back upward.
For many other rotating systems, a complete cycle corresponds to just one revolution. Examples include two stroke combustion engines, hydraulic pumps, and electric motors.
4.1 Defining Revolutions per Cycle
The number of revolutions that corresponds to a cycle is defined in the lower left corner of the Angle Domain Validation worksheet as shown in Figure 15.
Figure 15: In the lower left of the Angle Domain Validation worksheet, the revolutions per cycle can be set.
After entering the “Revolutions per Cycle”, the displays will change accordingly.
In the overview and detailed display, right clicking on the X-axis of angle display allows data to be viewed in either degrees, revolutions, or cycles as shown in Figure 16:
Figure 16: Right click on the X-axis of angle domain data to switch the view between degrees, revolutions, and cycles.
With the angle data displayed as desired, now the strip chart can be used to investigate the data further.
5. Angle Domain Strip Chart Analysis
After displaying data in the strip chart area, a resampling tachometer can be selected for interactive viewing.
5.1 Selecting the Resampling Tachometer
In the tab labelled “Angle Domain Definition” (in the lower left of the Angle Domain Validation worksheet), the high pulse per revolution tachometer can be selected for resampling to the angle domain as shown in Figure 17.
Figure 17: The tachometer signal to be used for conversion of time data to angle domain is selected in the Angle Domain Definition tab in the lower left of the Angle Domain Validation worksheet.
Now the data is ready for interactive viewing in the display area.
5.2 Angle Viewing: Buttons and Cursors
In the Angle Domain Validation workbook, the strip chart display located on the right side can be used to interactively investigate the angle domain data.
In the detailed view, the user can scroll through the data using the icons at the bottom of the detailed display as shown in Figure 18.
Figure 18. The icons and buttons underneath the detailed strip chart view can be used to interactively view the angle domain data.
Some useful display options shown in Figure 18 are:
Enter Limits: In the lower left and right corners of the detailed display, limits can be entered manually. The 51st cycle in the angle history is shown. The term “51:0” (left side) means cycle 51 starting at zero degrees. The term 52:0 (right side) means cycle 52 at zero degrees.
Arrow Buttons: Clicking on the right and left arrow buttons will move one cycle to the left or right. See below.
Zoom: The + and - buttons are used to zoom in and out in the display.
Using these features, it is possible to view the data one cycle at a time as shown in Figure 19.
Figure 19. Data analysis by cycling through multiple revolution cycles.
In this case, moving through the cycles shows that high levels of vibration consistently occur when cylinder pressure five is high. This is the case in all the cycles viewed. It is possible that cylinder five is misfiring, or has a dimensioning issues creating mechanical interference.
The high vibration, which occurs about half way through the cycle, can be marked by a cursor as shown in Figure 20.
Figure 20. The cursor displays the cycle number and degree position with a cycle:degree nomenclature.
When a cursor is placed in the display, it shows the cycle and angular position. For example, “51:307” means cycle 51 and 307 degrees.
To know where 307 degrees occurs during the rotation of the shaft, the zero-degree mark must be set appropriately as described in the next section.
5.3 Defining the Zero Position
The zero position, if not set during data acquisition (see previous sections about acquisition), can be set after the fact using the “Manual Zero Angle Defintion” tab (Figure 21) in the lower left of the Angle Domain Validation worksheet.
Figure 21. In the “Manual Zero Angle Definition” (lower left of Angle Domain workbook), a cursor is positioned at a known angle in the data and used to define the zero-degree location.
To define the manual zero angle manually:
Click on the “Show cursor” check box. A cursor with the label “Reference Angle” will appear.
A cursor appears in the strip chart display. Position the cursor at the desired zero angle location.
Press Apply to accept the defined location.
Using the “Expected angle value”, the cursor could also be positioned with an event that is known to occur at a specific angle. For example, suppose a valve always closes at 15 degrees. After positioning the cursor at the valve closing and entering 15 degrees in the “Expected angle value”, pressing apply will reset the zero accordingly.
With these parameters set, more analysis can be performed as described in the next sections.
6. Angle Frame Statistics Analysis
Consider the vibration due to changes in cylinder pressure shown over one cycle in the rotating machinery data shown in Figure 22.
Figure 22: Cylinder pressures (top graph) versus resulting vibration (bottom graph) are shown. Two cursors are used to define the angle range of vibration (red trace) due the pressure change (cyan curve) of a specific cylinder.
The vibration is clearly due to just one of the six pressure changes. In this case, it would be desirable to know the maximum vibration over the part of the cycle that corresponds to the pressure change of the specific cylinder (cyan curve in Figure 22).
When analyzing a cycle, the maximum of the entire cycle may not be the same as maximum in the range of interest defined by the two cursors.
6.1 Angle Gates in Time Data Processing
To analyze just a portion of the cycle, an angle domain “frame statistic” analysis can be performed. This is performed in Time Data Processing Worksheet within Simcenter Testlab.
With the Angle Domain add-in turned on, new options appear in Time Data Processing. For example, in the "Acquisition Parameters" menu as shown in Figure 23.
Figure 23: The "Acquisition Parameters" menu of Time Data Processing includes tracking on angle (left menu) and a "AD Acquisition" tab (right menu) for defining angle domain processing parameters.
The new options include being able to use angle as a tracking parameter. For example, in Figure 23, the left menu will process the first 100 cycles of the angle domain time history.
Under the “Frame Statistics AD” tab within "Section Settings" menu, various statistics over a specified range (called “gates”) can be defined (Figure 24). This will be done for the cycles identified within the "Acquisition Parameters" menu.
Figure 24. The “Frame Statistics AD” tab in the "Section Settings" menu of the Time Data Processing worksheet. On the left, statistics to be calculated are selected. On the right, “gates” for the statistics are defined with a name and angle range.
The selected statistics are calculated for each cycle over the specified gate. The gate is defined in degrees (to and from).
6.2 Angle Statistics over Multiple Cycles
These statistics, when calculated over several cycles, are useful understanding the variation in amplitudes and timing between cycles. Events are not exactly repeatable cycle to cycle. Using the combustion engine example, a piston does not hit the cylinder wall identically from cycle to cycle. As a result, the maximum vibration could be different in each cycle.
Because of this cycle to cycle variation, it is useful to look at the frame statistics over many cycles (for example: 100 cycles) and plot the maximums individually (as shown in Figure 25 below). Consider a case where the baseline condition of a piece of rotating machinery is compared to a modified condition (for example, if the timing of combustion was adjusted).
Figure 25: Comparison of maximum vibration over specific gate between baseline condition (red) and modified condition (blue). Plotted for 100 cycles.
In this example, the maximum vibration has been reduced, since the red curve (baseline) is higher than the blue curve (with modification). However, there are a few samples, out of a hundred, where the opposite is true.
If only these few samples were used in the analysis, the opposite conclusion would have been drawn. This underscores the importance of using many cycles in the analysis.
Often, it is not just the amplitude that is of interest, but the angular position of the maximum value. The angular position could indicate a problem with the timing of the rotating machinery. For example, perhaps a valve does not fully close properly from cycle to cycle.
6.3 Variation in Timing
The angle domain frame statistic functions of Simcenter Testlab also support calculating the angular position with the Maximum (X), Minimum (X), and Extremum (X) calculations as shown in Figure 26.
Figure 26: In the Frame Statistics menu, the Maximum function finds the highest amplitude over the gate, while Maximum(X) finds the angle at which the highest amplitude occurs.
Using this functions help determine if timing of events between cycles are consistent. An example of plotting the Maximum against the Maximum (X) in a XY graph is shown in Figure 27.
Figure 27: Plot of Maximum versus Maximum (X) in a XY plot to evaluate the timing of an event from cycle to cycle for two different conditions.
The plot in Figure 27 is the same data as shown in Figure 25. Figure 27 includes one additional piece of information (angular position) that is not in Figure 25.
In Figure 25, the maximum value is displayed against each individual cycle.
In Figure 27, the maximum value is displayed against each individual cycle and at the angle that the maximum occurs.
This plot can be used to determine if there are timing issues.
An extension to the angle domain is combustion analysis (Figure 28). Additional metrics include Indicated Mean Effective Pressure (IMEP), Pumping Mean Effective Pressure (PMEP), and Net Mean Effective Pressure (NMEP) among others.
Figure 28: Combustion Analysis add-on for Simcenter Testlab,
The combustion analysis is not part of Simcenter Testlab Angle Domain analysis. Contact your Siemens sales representative for more details if interested.