Method for establishing reference limit values for vibration measurements in machines

When measuring, the accuracy of the measurement is as important as the reference level used. There is little point in taking very accurate measurements if the reference levels used to evaluate them are inappropriate. Therefore, when measuring vibrations in rotating equipment, the general rule is to use reference standards, such as ISO 20816, or set alarm levels according to the manufacturer's recommendations. However, although setting specific vibration reference levels for each machine is recommended by international standards, there is no proposed method, or mathematical support, for doing so in either the standards or the related literature. This situation leads, in practice, to the use of general and, therefore, non-specific boundaries to assess the functional status of each particular machine (good, alert, alarm, etc.) and, consequently, to many false positives or, even worse, false negatives when detecting machine failures. The purpose of this study, and a novelty in this field, is precisely to present a method that allows statistically determining the most appropriate vibration reference levels for each rotating machine. Using a vibration database with measurements taken over twelve years for hundreds of machines, this study demonstrates that the vibration measurements of a rotating machine can be statistically modelled, with an accuracy close to 100 %, using the Rayleigh Distribution Function, which allows successive vibration reference levels to be formulated between functional categories from the mode and standard deviation of said statistical distribution function. The final section presents an example of the implementation of this methodology in an industrial plant. © 2025 The Author(s)