Order Tracking: Fixed Sampling versus Synchronous Sampling

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Fixed sampling and synchronous sampling are two different digital signal processing methods that can be used to calculate spectral maps and orders during a rotating machinery measurement.

 

Fixed sampling acquires data at a fixed data rate, while synchronous sampling acquires data at a rate proportional to the speed of the rotating machinery.

 

The results of each technique are shown in the colormaps in Figure 1 below.  Fixed sampling gives a global overview of the speed sweep dynamics, while synchronous sampling has narrower and well defined orders.

 

Fixed_vs_Sync_Summary.pngFigure 1: Fixed sampling colormap (top) shows global view of speed sweep, including resonance. Order tracking colormap (bottom) based on synchronous sampling has narrower, better defined orders, but in this example, some resonance information is truncated.

Both techniques result in a colormap with three difference axes: frequency, rpm, and amplitude. However, the calculations involved in each technique are performed differently. 

 

This article covers:

  1. How the two techniques work
  2. The differences in results of both techniques
  3. How to perform fixed and synchronous sampling in Simcenter Testlab

 

Note: Sometimes synchronous sampling is also called order tracking.  The Simcenter Testlab software module that performs synchronous sampling is called ‘Order Tracking’.

 

How do fixed and synchronous sampling techniques work?

 

Both fixed sampling and synchronous sampling techniques calculate a series of spectrums at a defined tracking increment over a speed sweep.

 

Time versus Revolution Data Blocks

 

The difference in the two techniques is how the spectrums at each increment are calculated.

  • Fixed sampling is time based: At each increment, a Fourier Transform is performed on a fixed amount of time data (T).  The Fourier Transform of a time block is a frequency spectrum, which consists of amplitude versus frequency. The same amount of time data is used for each Fourier transform regardless of system speed.
  • Synchronous sampling is revolution based: At each increment, a Fourier Transform is performed on a fixed number of revolutions (R), regardless of speed. The result is an order spectrum, which consists of amplitude versus order. As system speed changes, so too does the amount of time data used to calculate the order spectrum.  As the rotational speed increases, the amount of time data required decreases as shown in Figure 2. The method is synchronized with the revolutions of the rotating system.

 

See Figure 2 for a comparison of the time data used for spectral calculations at four different speeds of the rotating system.  

 

Time_versus_Revolutions.pngFigure 2: In fixed sampling (left), the time data block (T) used for the Fourier Transform remains the same throughout the speed sweep. In synchronous sampling (right), the time block varies, keeping the number of revolutions (R) the same, throughout the speed sweep.

Once the block of data is captured, either an order or frequency spectrum is calculated.

 

key1_time_rev.png

 

Frequency Spectrum versus Order Spectrum

 

Figure 3 shows the difference between the results of a Fourier transform for fixed sampled data versus the synchronously sampled data. The fixed sampling data produces a frequency spectrum, while synchronous sampling produces an order spectrum.

 

frequency_spec_versus_order_spec.pngFigure 3: Fixed sampling uses a time block (top left) that produces a frequency spectrum (top right) while synchronous sampling uses a revolution basis (bottom left) that produces an order spectrum (bottom right).

 

A key difference between the order spectrum and frequency spectrum is how data is spaced along the x-axis (see Figure 5):

  • Frequency spectrum – Spectral lines are a fixed frequency distance apart (delta f = 1/T)
  • Order spectrum – Spectral lines are a fixed order distance apart (delta o = 1/R)

 

A result of this is that order content can appear “smeared” when fixed sampled, but not when order tracked.

 

key2_spec_ord.png

 

Smearing in Fixed and Synchronous Sampling

 

In fixed sampling, the Fourier Transform requires a fixed time frame of data.  During the fixed time frame, the speed of the rotating system changes. As the speed changes, the frequency of the order content also changes.

 

As the order content changes within the same data frame, there is a leakage, sometimes referred to as smearing, of the order content as shown in Figure 4.

 

smearing.pngFigure 4: Left – Frequency spectrum has a fixed frequency resolution, which creates smearing when frequency content changes, Right – Order spectrum adapts based on RPM, preventing smearing.

For example, if the fixed time frame is two seconds, and the rpm changes from 1000 rpm to 1060 rpm over this time period, the frequency of 1st order would change 1 Hertz (60 rpm = 1 rev per second = 1 Hz).  This would create a 1 Hz smear. For other orders, the change would be even greater.  For example, 4th order would create a 4 Hz smear during the 2 seconds.

 

This smearing effect is worse at higher orders (example: 54th, 72nd order) than lower orders (1st, 2nd, 3rd).

 

The order spectrum does not have this smearing.  The constant order resolution keeps spectral lines aligned with order frequencies, which prevents them from being smeared.

 

key3_smeearing.png

 

Preventing Smearing

 

To reduce the smearing due when the fixed sampling approach, three things can be done:         

  • Decrease speed sweep rate: If the speed sweep is slowed down, then the frequency content does not change as rapidly during the time block. For example, instead of taking 10 seconds to sweep from 1000 rpm to 6000 rpm, a longer time of 100 seconds could be used.
  • Change spectral resolution: The time frame can be shortened by increasing the spectral resolution. The spectral resolution is the inverse of the time frame.  A 0.5 Hz resolution corresponds to a 2 second frame. A 0.25 Hz resolution corresponds to 4 seconds. Unfortunately, by shortening the time frame, leakage/smearing can be created by the courser frequency resolution instead.
  • Use a synchronous sampling technique instead of fixed sampling.

 

There are several key settings that can affect the processed results.

 

Processing Parameters

 

Table 1 below lists the equations and parameters used in the two techniques.

 

Comparison_table_OT_FS.pngTable 1: Parameters and settings used in fixed sampling and synchronous sampling.

These same settings are illustrated in the diagrams in Figure 5.

 

deltaf_vs_deltao.pngFigure 5: Left –In fixed sampling, the spectral lines are fixed delta frequency apart, which are not aligned with the order content. In synchronous sampling, the spectral/order lines are a fixed delta order apart, which stays aligned with the order content even as rpm changes.

The next section illustrates the differences in the calculated results between fixed sampling and synchronous sampling results.

 

Results and Differences of Fixed Sampling and Synchronous Sampling

 

This section shows how the results differ between fixed sampling and synchronous sampling. See Table 2 below for a summary of the key differences between each of the techniques:

 

table2.pngTable 2: Summary of differences between fixed sampling versus synchronous sampling results.

Fixed Sampling Global View

 

A key benefit of fixed sampling is the “global view” that it provides as shown in Figure 6.

 

fixed_sampling_global.pngFigure 6: Fixed sampling provides a good global view of the system by demonstrating clear lines of resonance alongside order content.

Fixed sampling highlights both resonance information alongside with the order information. In a fixed sampled map, resonances appear as vertical lines at fixed frequencies.

 

key4_global.png

 

Synchronous Sampling: Narrow Orders

 

The benefit of using synchronous sampling is that a much finer order resolution can be achieved.

 

Look at Figure 7 below for an example of this. The orders are narrower and better defined on the synchronous sampling colormap plot (right) compared to the fixed sampling plot (left). 

 

smeared_orders.pngFigure 7: Left – Fixed sampled colormap (left graph) has wider orders (red) than the synchronously sampled colormap (right graph).

Because orders tend to be smeared more on fixed sampled data, caution must be used when performing order cuts. The width of the order cut is very important: when cutting an order from fixed sampled data, care must be taken to ensure that the width of the order is selected to properly contain the order content.

 

Example:

 

Order 10.5 is cut from both the fixed sampled and synchronous sampled plots from above (see Figure 8, below).

 

vary_order_width.pngFigure 8: Order cut comparison: Using the same order cut width of 0.2, the orders do not match (left graph). A wider order cut must be used on the fixed sampled data to ensure the proper match (right graph).

The same order width (0.2) is used for both cuts (Figure 8, left graph). Notice that the fixed sampled order (red) appears to be lower level than the order tracked order (green). This is because the order content for the fixed sample order has smeared beyond the 0.2 order width bandwidth. Therefore, the order cut is not capturing all of the energy content of the order.

 

However, if the order width of the fixed sampled data is increased to 0.4 order width, the results between fixed and synchronous sampling compare much more closely (Figure 8, right graph).

 

This is especially important when a rotating system has closely spaced orders.  If significant smearing is present in a fixed sampling technique, it can be impossible to separate the orders and get the correct results, because the adjacent orders smear together. 

 

key5_close_orders.png

 

For example, if a piece of rotating machinery made two orders: 10.1 and 10.3, a smearing of 0.4 order would not produce correct results for these orders.

 

Synchronous Sampling: Fast Speed Sweeps

 

Another area in which synchronous sampling has an advantage is fast speed sweeps.  The faster the rpm changes, the more the frequency content changes over time.

 

The synchronous sampling techniques reduces the smearing of the orders that are caused by a fast speed sweep as shown in Figure 9.

 

slow_versus_fast_runups.pngFigure 9: Upper Left – Fast sweep and fixed sampling have order smearing, Upper Right – Fast sweep with sync sampling does not have order smearing, Lower Left – Slow sweep with fixed sampling has no smearing, Lower Right – Slow sweep with sync sampling has no smearing.

In Figure 9, the difference between fixed sampling and synchronous sampling on a 4 second “fast” sweep and a 20 second “slow” runup is shown.  For the same data orders, the fixed sampling data for the four second runup shows order smearing.  The higher number orders also have more smear.

 

key6_runup_speeds.png

 

Either by slowing down the speed sweep, or by switching from fixed sampling to synchronous sampling, the order smearing can be reduced.

 

The next section explains how to perform fixed and synchronous sampling on speed sweep data in Simcenter Testlab.

 

Simcenter Testlab Settings

 

Both fixed sampling and synchronous sampling can be done in Simcenter Testlab. Both methods can be used simultaneously while processing the same data.

 

When using Signature Acquisition or Signature Throughput processing, the fixed sampling approach is used by default. However, synchronous sampling can also be turned on via the ‘Order Tracking’ add-in and used in parallel with the default fixed sampling.

 

Getting Started

 

Enable synchronous sampling by selecting “Tools -> Add-ins -> Order Tracking” from the main Simcenter Testlab menu as shown in Figure 10.

 

order_track_addin.pngFigure 10: To perform synchronous sampling in parallel with fixed sampling, select “Order Tracking” under “Tools -> Add-ins”.

The Order Tracking add-in requires 20 tokens.

 

Fixed Sampling versus Order Tracking Settings

 

In Figure 11, the Fixed Sampling and Order Tracking settings in Signature Throughput Processing are shown.  The Fixed Sampling settings are under the tab called “FS Acquisition” while the Order Tracking settings are under the tab called “OT Acquisition”.

 

fixed_vs_order_settings.pngFigure 11: Left – Fixed Sampling settings for 0.125 second frame size, Right – Order Tracking settings for 0.125 order resolution.

There is a fixed relationship between frequency, rpm, and maximum order, as shown in Equation 1:

 

equation.pngEquation 1: Relationship between frequency, rpm, and order.

When the maximum frequency of the acquisition, or bandwidth, is used in Equation 1, the maximum order and corresponding rpm can also be determined. These settings and relationships are also described in Table 1 above. 

 

For example, the software menus shown in Figure 11 indicate that 16th order can be measured up to 24000 rpm with a given frequency bandwidth of 6400 Hz.  This uses the equation: [6400 Hz = (16 * rpm)/60].  This maximum rpm is automatically calculated (Figure 11, right graph). To go to a higher rpm, and still measure 16th order, the frequency bandwidth would need to be increased. 

 

Engineers will often calculate both fixed sampled and order tracked results to get the benefits of both types of data processing.

 

Displays: Switching Axes between Order and Frequency

 

In Simcenter Testlab, it is possible to switch between frequency and order on the plot axis.

For a fixed sampled map, simply right click on the X Axis, and select “X axis ->  Frequency or Derived Order” as shown in Figure 12.

 

switch_axes_1.pngFigure 12: On a frequency spectrum map, right click on the X axis to switch between frequency and derived order.

For an order tracked map, simply right click on the X-axis and make the selection for either “Order” or “Derived Frequency” as shown in Figure 13.

 

switch_axes_2.pngFigure 13: On an order spectrum map, right click on the X axis and choose between order and derived frequency.

Questions?  Email scott.beebe@siemens.com or Siemens PLM GTAC Support.

 

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