Do you know how to analyze vibration data with LTspice?

The advancement of digital technology shows no signs of slowing down and has permeated every aspect of our lives. Giving machines intelligence is not an Orwellian dystopia; it can make factory automation more efficient, as automated feedback loops help reduce direct maintenance time.

Industry 4.0 describes the concept of bringing the benefits of big data to the factory floor. Machines equipped with sensors monitor their own performance and communicate with each other to share the overall workload while providing important diagnostic information to the backend, whether they are in the same building or on different continents.

A quick survey of ADI products shows that ADI is primarily focused on providing solutions for the Industrial Internet of Things (IIOT), i.e., a variety of robust and reliable high-performance signal chain components from sensor to cloud.

One application area in industrial automation is condition-based monitoring (CbM), which involves carefully calibrating a machine’s nominal operating characteristics and then closely monitoring the state of the machine itself using local sensors. Deviations from the nominal signal indicate that the machine needs maintenance. As a result, machines equipped with condition-based monitoring systems can be maintained based on actual need, rather than on a relatively arbitrary maintenance schedule.

A good way to determine the health of a motor is to examine its vibration signature. ADI’s MEMS technology can be used to continuously monitor the vibration signature of a motor and compare it to the signature of a known fault-free motor to determine the health of the motor. In fact, every motor fault has its own unique harmonic signature. By looking at the harmonic content of the vibration pattern, faults in bearings, inner and outer races, and even gearbox teeth can be detected.

To generate data for Fourier analysis in LTspice, three ADXL1002 accelerometers are connected to the motor, as shown in Figure 1, to measure lateral, vertical, and longitudinal (X, Y, and Z, respectively) vibrations.

Figure 1. Vibration in the X, Y, and Z channels is measured in the lateral, vertical, and longitudinal directions, respectively.

Download and save the vibration data to a Microsoft Excel spreadsheet. Sampling the data at 500 kSPS gives one second of vibration data with three columns of Microsoft Excel data, each 500,000 rows long. The X, Y, and Z data samples are shown in Figure 2.

Figure 2. Extracting X, Y, and Z data.

Now we can examine this data for harmonic content to determine the health of the motor. Fourier analysis is a mathematical process that extracts the spectrum of components from a waveform. A pure sine wave has only one frequency in its spectrum, called the fundamental frequency. If a sine wave is distorted, other frequencies besides the fundamental frequency will appear. By analyzing the spectrum of the motor's vibration patterns, we can accurately diagnose its health.

Since the hardware and software capable of performing Fourier analysis are typically very expensive, here we present a method that can perform Fourier analysis on MEMS data at essentially no cost.

LTspice is a powerful, freely available circuit simulator that can use vibration data acquired from MEMS sensors in condition monitoring systems to plot the spectrum of any waveform via Fourier analysis.

With the data format shown in Figure 3, LTspice is able to generate a Fourier analysis plot where each vibration data point is paired with its corresponding timestamp.

Figure 3. Format of the time and voltage example.

It is relatively easy to convert data into this format using Microsoft Excel. The process is as follows.

First, separate the data columns in Figure 2 into three worksheets in an Excel file, named X, Y, and Z, as shown in Figure 4.

Figure 4. After creating the three worksheets, copy the X, Y, and Z data into the corresponding worksheets.

Insert a column to the left of the data - this column will be the timestamp for each data value.

Since 500,000 data samples are taken in one second, each data point is 2 µs apart. Therefore, in the first cell of the new column, enter

2E-6

Represents the first timestamp at 2µs.

The easiest way to fill in the remaining timestamp columns with values ​​is to use the Series command. In the Microsoft Excel search box, type "Series" to display the menu options shown in Figure 5.

Select Fill Series or Pattern from the drop-down menu , then select Series… .

Figure 5. How to fill multiple cells in Microsoft Excel.

The dialog box shown in Figure 6 appears. Select the Columns and Linear radio buttons. Enter 2E-6 in the Step value and 1 in the Stop value .

Figure 6. Filling cells using a linearly expanding dataset.

Clicking OK populates the left column of data timestamps, incrementing from 2 µs to 1 second. You can accomplish the same goal by filling in the first few values ​​and then dragging the cursor all the way to the bottom cell at the end of the data range—but with 500,000 rows of data, that's a long way to go.

Now we have the data in a format that LTspice can process, as shown in Figure 7.

Figure 7. Columns showing timestamps and corresponding data samples.

If the data set is large and the sampling interval is short, Microsoft Excel may round the timestamps to an inappropriate number of decimal places. If this occurs, highlight the first column and select Format > Format Cells, as shown in Figure 8.

Figure 8. Reformat the cells to remove any rounding errors.

Select the appropriate number of decimal places, as shown in Figure 9.

Figure 9. Increasing timestamp resolution to 5 decimal places.

After populating the timestamp columns and extending the number of significant digits, copy the two columns from each worksheet into a Notepad or other text editor file as shown in Figure 10.

Figure 10. Text file containing time and vibration data.

There should be three text files total containing the vibration data for the X, Y, and Z axes of the condition monitoring system.

This data can now be read directly into LTspice.

Build the schematic in LTspice as shown in Figure 11. In this design, there are six voltage sources corresponding to the X, Y, and Z axis data for both the faulty and non-faulty motors. This allows a Fourier analysis to be performed on the vibration data of the new motor and compared to the Fourier analysis of the suspected faulty motor data. A major advantage of this approach is that the frequency plot of the new (non-faulty) motor can be overlaid on the frequency plot of the suspected faulty motor, so the performance difference is immediately apparent.

Figure 11. LTspice schematic showing the voltage output of vibration data for a faulty and non-faulty motor.

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Removing the default compression setting in LTspice can sometimes produce cleaner results. If this line is omitted, simulations will run faster but may produce less accurate results.

Once the schematic is complete, right-click each voltage source, select the Advanced button, select the PWL File radio button, and enter the file name of the corresponding text file containing the vibration data, as shown in Figure 12. This will create a piecewise linear voltage source containing a series of voltages and their corresponding time instances. This is much easier if these text files are stored in the same directory as the LTspice files.

Figure 12. Creating a piecewise linear voltage source from vibration data.

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The simulation results for the faulty and non-faulty motors are shown in Figure 13. The experiment was conducted on a motor running at 587.3 rpm with a faulty bearing, misaligned outer race, and a 12 lb load. The vibration pattern of the non-faulty motor at the same speed is also shown. Clearly, the vibration signature amplitude of the faulty motor is significantly higher compared to the non-faulty motor.

Figure 13. Time domain results for faulty and non-faulty motor vibration data.

Highlight the Waveform window and select View > FFTT from the menu bar . This will calculate the FFT based on the transient data.

From the data in Figure 2, we can see that at such a high offset voltage of 35,000 V, we can see only a small change in the numbers. When simulated in LTspice, these data are converted to a DC offset voltage of 35,000 V with an AC waveform superimposed on this offset voltage.

In the Fourier analysis plot, this offset voltage appears as a large spike at DC in the spectrum location, so when LTspice automatically scales the Y-axis, the associated harmonics are scaled very small. Right-click the X-axis and specify a frequency range above the DC voltage where the DC offset voltage is negligible—5 Hz to 1 kHz should be sufficient.

Right-click on the Y-axis and select the Linear radio button to view the harmonics, as shown in Figure 14.

Figure 14. Fourier plot with DC spur removed displayed in a linear coordinate system.

By right-clicking in the graphics area, you can add additional drawing panes to present the vibration spectrum components as X, Y, and Z graphs, as shown in Figure 15.

Figure 15. X, Y, and Z vibration graph separation.

The motor’s rotation frequency of 10 Hz can be clearly seen, as well as significant harmonics at 60 Hz, 142 Hz, and 172 Hz. While this article will not analyze which components within the motor are causing these harmonics, there is no doubt that the vibration pattern has changed due to motor wear.

ADI’s family of MEMS accelerometers can provide critical data for early detection of motor failures, but this is only half the solution. This data must be carefully studied through Fourier analysis. Unfortunately, the equipment or software that can perform Fourier analysis is usually expensive. LTspice can accurately analyze CbM data at no charge, enabling early detection and diagnosis of machine failures.