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Interpretation of RMS values in time domain - MPB10
Article No: KA-09572
Version: 1.0
Subject to change without notice
This article is about the calculation method of the MPB10s key values in time domain and things to consider.
Related Products
MPB10-VS00VSIQ00 MULTIPHYSICSBOX
Table of Contents
General
One essential outcome from the MPB10 sensor are the v-RMS (velocity-root mean square) or a-RMS (acceleration-root mean square) values. As is well known, the sensor records data blocks and then calculates all available key values and information from the raw data in a processing block.
Most of the values are described as RMS values, which is the abbreviation for "root mean square". Why these RMS values are used and what the benefits are, are described in the following sections of this article.
Theory of RMS Calculation
The formula for an RMS (root mean square) value is calculated like follows:
Notation 1:
Notation 2:
Like the name implies, each data value (x_{n }or x_{i}) is squared, then summarized with all other values, divided by the total number of available data values and finally the root is extracted. The RMS value is directly related to the energy content of the vibration profile and thus, for example, the destructive capability of the vibration.
RMS values in relation to the block length of the MPB10
For the MPB10, the total number of available data values is defined by the block length. See page 14 of operating instruction.
As longer the block length and thus the recording time (same sampling frequency), as more representative and accurate the RMS is worth. A change of vibration or a change of amplitude or frequency during record will have less impact on a longer block length than a shorter one.
Example, whereas the array and its length represent the block length of a recording:
Array1 = [2,2,2,2,10,2,2,2,2] RMS-Value = 3.830 (i.e. a short block length with one disturbance)
Array2 = [2,2,2,2,2,2,2,2,2,2,10,2,2,2,2,2,2,2,2,2,2] RMS-Value = 2.928 (i.e. a long block length with one disturbance)
Array3 = [2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2] RMS-Value = 2.000 (i.e. a long block length without any disturbance)
This behavior is also mentioned in the MPB10s operating instruction (chapter 4.3.2): “The block length represents a compromise between the update rate of the characteristic values and the noise of these values. A shorter block length means more frequent updating, a longer block length means higher averaging and thus lower noise of the indication values. The block length can be set between 20 and 1,280 ms, whereby the maximum duration can only be used in single-axis mode.”
In the real world, the end-user has to decide which block length fits the most for his specific application. For example, using a longer block length allows to filter out disturbing vibrations coming from other parts which not belong to the observed motor. Whereas a shorter block length allows a more frequent/ faster update of the needed vibration values.
In real-world applications, however, the focus is on observing the change in the assigned values over time and not on the absolute values of the outcome.
In frequency domain, the block length also affects the smallest measurable frequency, as mentioned in the operating instruction as well.
Keywords: root mean square, RMS, MPB10, vibration, RMS value, time domain