*RMS Displacement Meter*

from KEUWLSOFT

## RMS Displacement Meter

Measures displacement by double integrating the acceleration from your device's linear acceleration sensor.

Any drift or error in the accelerometer is quickly magnified in the double integral, such that even a stationary device will quickly show displacement readings going wild. Therefore this App is for measuring alternating displacements. i.e we apply a drift reduction algorithm to remove any DC component and then measure the AC displacement by means of a Root Mean Square (RMS) value, or perform a Fast Fourier Transform (FFT) to obtain the frequency spectrum.

• Gauge to show the RMS displacement in the X,Y or Z directions, or its magnitude.

• RMS graph to show the gauge readings over time.

• Lower display shows time series data or a FFT from it.

• Peak indicators for the frequency spectrum.

• Save graph data to file.

• Units of cm, mm, m, inches or feet.

Linear acceleration sensors will vary in sampling speed, resolution and accuracy from one device to the next. For indication only.

## User Guide

Integrating acceleration gives velocity and a constant.

Integrating velocity gives displacement and a constant.

Any drift or error in the accelerometer is quickly magnified in the double integral, such that we apply a drift reduction algorithm to remove any DC component and then measure the AC displacement by means of a Root Mean Square (RMS) value, or perform a Fast Fourier Transform (FFT) to obtain the frequency spectrum.

The displacement, s, can be measured in either cm, mm, m, inches or feet as selected in the settings. Whilst initially set-up to give RMS readings. If the signal is known to be sinusoidal, then you can also select to view either the Peak to Peak or Amplitude values. The Peak to Peak Value is calculated by multiplying the RMS by 2 times the square root of two. The amplitude is just half the peak to peak value. For example, if you are moving your device in a circle, the peak to peak would give the diameter of the circle, whilst the amplitude the radius of the circle. For signals which are not sinusoidal, RMS should be used.

The displacement is measured in each of the device's X, Y and Z directions. The x-Axis is along the width of the meter in the direction from left to right. The y-Axis is along the height of the meter in the direction from bottom to top. The z-Axis is out of the plane of the device towards the viewer. The origin will be where the linear acceleration sensor is located inside your device.

The meter is split into two displays. The upper display shows either a gauge or a graph of the gauge values over time. The lower display shows either sampled displacement values or the Fast Fourier Transform (FFT) of them.

The

**zero**button resets averaging and clears the graphs.

The

**pause**button pauses measurement until it is pressed again.

To see the rms displacement meter in action, move the device in a circle whilst keeping the device orientation the same. You should see sinusoidal motion in two or three of the X, Y, Z traces in the lower time series graph. The peak to peak value value will be an estimate of the diameter of motion. The FFT spectrum will show a peak forming at the rotation frequency.

RMS Gauge and Time Series |
RMS Graph and FFT |

### Gauge

The gauge can be set to show the rms displacement in the X,Y or Z directions, or the rms of the magnitude of the displacement. Alternatively peak to peak or amplitude can be shown, by selecting the relevant mode in the settings.

There are 5 resolutions for the gauge which can be selected below the dial. The selected range is shown in a lighter colour.

By long pressing on the results, the current reading, max, min and average values can be saved to the clipboard ready for pasting into another application.

### RMS Graph

Above the RMS graph are 4 buttons (

**rms sx**,

**rms sy**,

**rms sz**and

**rms |s|**) which will turn each of the 4 avaliable traces on or off.

The y-Axis of the graph can be set to be logarithmic or linear in the settings.

The graph y axis is auto scaling by default. When paused or not in autoscale mode, double touching and stretching or pinching will scale the graph. Single touch panning will move the y-Axis scale up or down, or allow scrolling back to see earlier data on the x-axis.

Again, peak to peak or amplitude can be shown instead or rms by selecting the relevant mode in the settings

### Speed

The speed arrows control the sample speed for the data for the time series and FFT graphs in the lower display. The measurement frequency can be changed between 12 preset values (0.5 Hz, 1 Hz, 2 Hz, 5 Hz, 10 Hz, 20 Hz, 50 Hz, 100 Hz, 200 Hz, 500 Hz, 1 kHz and 2 kHz). The data is re-sampled for these frequencies, so going above the speed capability of your device will just result in multiple samples with the same reading. Sampling above the sensor's max measurement speed will also result in FFT traces becoming grey at above half the sensor's max sampling speed indicating that the data should be ignored. Tap the

**info**button in the app to see the measured sensor sampling speed along with other sensor details.

### Time Series Graph

This graph shows the displacement values versus time. It is auto scaling by default and scrolls once filled. Auto scale can be turned on or off in the settings.

When auto scale is off, or the detection is paused, the graph can be manually scaled. A single touch allows the graph y axis scale to be moved up or down, or in the case of the x-axis, pan back to see more recent data. A double touch, i.e. pinching on the graph can change the scales of either axis. Since the graph is small, using fingers on opposite hands can make this task much easier.

There are up to 4 traces shown on the graph corresponding to sx, sy, sz and |s|. They can be turned on of off at the top of the graph by tapping on the corresponding character.

### FFT Graph

The Frequency Spectrum is selected with the

**FFT graph**button at the bottom right. The FFT of the X, Y, Z and magnitude channels can be turned on or off with the corresponding buttons above the graph.

If the average button is selected, then in addition to the most recent FFT, an average of all the FFTs done since the FFT settings were changed or zero was pressed is also shown. The number of averaged traces is shown in the top right of the graph.

The FFT is not shown until at least sufficient data to fill the time series is obtained. This will depend on the sampling speed and FFT size. The time required to obtain this data is equal to the FFT size divided by the sample rate. Whilst the initial data is being gathered, a progress screen will be displayed instead of the FFT.

Both the axes can be either on logarithmic or linear scales as selected in the settings. The graph is by default auto scaling, but when this is off or the sampling is paused, then the graph can be scaled or panned as with the other graphs.

### Settings

Clicking the cogs button at the top left of the screen brings up a settings menu:

**Distance units**– The distance will can shown in either in units of cm, mm, m, inches or feet.

**Drift Reduction**- How harsh the algorithm removing drift should be. If it is set high, the distance values will stay closer to zero when the device is at rest but the measurement of lower frequencies will be damped more. Experiment to see what works best for your device.

**Stay awake**– Check this option to stop the device from sleeping.

**Sound On**– Button presses will make a click sound if this is enabled.

**Reset to defaults**– Resets all preferences back to their default values and clears the graph data.

**Measure**- Select between

**Root Mean Square (RMS)**,

**Peak to Peak**or

**amplitude**. Peak to peak or amplitude should only be used when you are measuring sinusoidal motion.

**RMS Graph Y-Axis Scaling**- The Y-Axis of the graph can be logarithmic or linear.

**Auto scale RMS graph Y-Axis**- The Y-Axis of the graph will be auto scaled when not paused. Otherwise panning or pinching on the graph can change the axis scales.

**RMS Graph Update Speed**- The update speed of the RMS graph and gauge can be changed to one of three preset values (slow, med or fast).

**Save RMS Graph Data**- Saves a comma separated text file containing the data from the RMS/Peak to Peak/Amplitude graph. Data file will include all 4 traces regardless of whether they are currently displayed on the graph. Files are saved in a 'keuwlsoft' directory on your device. In version 1.12 and above of the app, files are saved in the documents folder in a \keuwlsoft\rms_displacement_meter sub directory.

**FFT Graph X-Axis Scaling**- The Frequency Axis of the FFT graph can be set to be a logarithmic or linear scale.

**FFT Graph Y-Axis Scaling**- The Y-Axis of the FFT graph can be set to be a logarithmic or linear scale.

**Auto scale FFT graph Y-Axis**- Both axes of the FFT graph will be auto scaled when not paused. Otherwise panning or pinching on the graph can change the axis scales.

**Auto scale Time graph Y-Axis**- The Y-Axis of the time series graph will be auto scaled when not paused. Otherwise panning or pinching on the graph can change the axis scales.

**FFT Update Speed**- Once sufficient data has been received for the initial FFT, the FFT will be redone at intervals determined by this setting.

**FFT Size**- Select how many data points to use in the fast Fourier transform. The smaller the size, the faster the FFT becomes, but with lower frequency resolution. The number of data points in the frequency spectrum will be half the FFT size.

**Save Time Graph Data**- Saves the raw sampled data from the lower display time series graph. The data file will include all 4 traces regardless of whether they are currently displayed on the graph. Files are saved in a 'keuwlsoft' directory on your device. In version 1.12 and above of the app, files are saved in the documents folder in a \keuwlsoft\rms_displacement_meter sub directory.

**Save FFT Graph Data**- Saves the frequency spectrum data from the lower display FFT graph. The data file will include all 4 traces and their averages regardless of whether they are currently displayed on the graph. Files are saved in a 'keuwlsoft' directory on your device. In version 1.12 and above of the app, files are saved in the documents folder in a \keuwlsoft\rms_displacement_meter sub directory.