## Noise & Vibration Analysis: Back To Basics

Sometimes it doesn't hurt to revisit some of the basic building blocks that form the foundation of what we do. And so we have gathered together a few of our…

## “The History and Future of Fourier Analysis” Workshop at SAE 2015, Grand Rapids

Are you attending the SAE 2015 Noise and Vibration Conference and Exhibition in Grand Rapids, Michigan, USA from 22nd to 25th June 2015? Why not go and see Dr Colin Mercer,…

## Wide Band Integrators – What Are They?

For some time now it has been conventional ‘wisdom’ that using time based digital integration may cause amplitude errors in the result and that these get worse as the frequency increases. As a result of this, integration using Omega arithmetic has been prevalent by using Fourier Transforms of the signal. This, of course, remains a valid approach and is particularly useful if the data is already in the frequency domain, which was its prime purpose.

## Negative Frequencies – What Are They?

Normally when we are analysing a signal it is a purely real signal, that is it has no imaginary part. A classic example is of course a sine wave. When…

## What is Synchronous (Angular) Sampling?

The term synchronous data is usually applied to vibration or acoustic data that is captured from an item of rotating equipment at regularly spaced angle intervals as distinct from regularly spaced time intervals. The rotating part could be an engine, a gear wheel, a drive shaft, a turbine rotor, a propeller, a turbocharger or any other type of rotary mechanical device. Typically these items are subjected to out-of-balance forces that cause them to vibrate at frequencies that are multiples of the fundamental (once per revolution) rotation speed frequency. (more…)

## 10 Educational Mechanical Engineering Videos

We’ve had a good look around YouTube and dug up a great collection of educational mechanical engineering videos. There’s a wide range of information here from simple maths tutorial to explanations of the inner workings of the internal combustion engine. We hope you enjoy watching and if you have any favorites of your own please drop a comment in the box at the bottom of the page.

### 1. Gas Turbine Animation

Nice animation and explanation of the workings of a gas turbine [Edit: video link changed after first became unavailble]

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Figure 4: Energy corrected spectrum

## Amplitude And Energy Correction – A Brief Summary

Amplitude and energy correction has been and is a continuing point of confusion for many people calculating spectra from time domain signals using Fourier transform methods. The first thing to say, the information contained in data presented as amplitude and energy corrected spectra is equivalent. The only difference is the scaling of the numbers calculated.

## Data Windows : What, why and when?

Before we discuss the use of data windows, we should first remind ourselves of three basic properties of the FFT (Fast Fourier Transform) process.

• First, energy information in signal must be preserved during transformation. That is, the energy measured on time signal must equal the energy measured on the frequency representation of that signal.
• Second, an FFT converts the signal representation between time and frequency domains. The time domain representation shows when something happens and the frequency domain representation shows how often something happens.
• And finally, an FFT assumes that the signal is repetitive and continuous.

## Interpolation Versus Resampling To Increase The Sample Rate

These are two different techniques aimed at different objectives. First consider a simple sinewave that has been sampled close to the Nyquist frequency (sample rate/2).

Visually this looks very pointy. We will examine it using a filter based interpolation and a classical curve fitting procedure to obtain a better representation.

## Vibration Monitoring Phase Measurement And The Tacho Signal

Any vibration signal may be analyzed into amplitude and phase as a function of frequency. The phase represents fifty percent of the information so it is most important to measure phase for vibration monitoring. Most vibrations on a rotating machine are related to the rotational speed so it is clearly important to have a measure of the speed, either directly or as a once per revolution tacho pulse. A question sometimes arises as to whether a once per revolution tacho reference signal is needed to measure phase. Is it possible to get phase if we only have a speed signal? This note gives some insight into those questions.

Actually the question that should be asked is – “Can we measure a meaningful phase, for use in vibration monitoring, if we only have a speed signal as well as the vibration signals?”

## Average Waterfalls Or Average Orders?

[latexpage]One would expect that averaging waterfalls and then extracting orders would give the same result as extracting orders from individual waterfalls and then averaging them. This is not the case.

## What Is A Fourier Transform?

A Fourier Transform takes a signal and represents it either as a series of cosines (real part) and sines (imaginary part) or as a cosine with phase (modulus and phase form). As an illustration, we will look at Fourier analysing the sum of the two sine waves shown below. The resultant summed signal is shown in the third graph.

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