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Order Tracking: Fixed Sampling versus Synchronous Sampling

Siemens Experimenter

11-12-2018
11:58 PM

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.

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:

- How the two techniques work
- The differences in results of both techniques
- 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.

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

*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.

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.

*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*.

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 1^{st} 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, 4^{th} order would create a 4 Hz smear during the 2 seconds.

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

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.

*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.

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

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:

*Fixed Sampling Global View*

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

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

*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).

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).

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.

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*.

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.

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*.

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”.

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

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*.

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*.

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

**More Rotating Machinery Links:**

- What is an order?
- Torsional Vibration: What is it?
- Zebra Tape Butt Joint Correction for Torsional Vibrations
- Balancing: Static, Coupled, and Dynamic
- Removing Spikes from RPM Signals
- Using the Smoothing function to remove rpm spikes
- RPM Calculation problems and Laser Tachometers
- Simcenter Testlab Signature
- Tips and tricks for acquiring torsional orders
- Harmonic Removal
- Interpreting Colormaps
- Cycle to Cycle Averaging in Simcenter Testlab

**More Digital Signal Processing Links:**

- Digital Signal Processing: Sampling Rates, Bandwidth, Spectral Lines, and more...
- Gain, Range, Quantization
- Aliasing
- Overloads
- Averaging Types: What's the difference?
- What is Fourier Transform?
- Time-Frequency Analysis: Wavelets
- Spectrum versus Autopower
- Autopower Function...Demystified!
- Power Spectral Density
- Shock Response Spectrum (SRS)
- Windows and Leakage
- Window Types
- Window correction factors
- RMS Calculations
- The Gibbs Phenomenon
- Introduction to Filters: FIR and IIR

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