Read more about the article Amplitude And Energy Correction – A Brief Summary
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.


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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.


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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.


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How To Analyze & Measure Torsional Vibration

Torsional Vibration MeasurementKnowing how to measure torsional vibration is of key importance in the area of vehicle development and refinement. The main contributory source is the engine where periodically occurring combustion cycles cause variation in the crankshaft rotary vibration. This vibration is transmitted to and modified further by other components in the powertrain such as the gearbox and by other equipment driven off the drive belt or chain. Additional torsional vibrations are also likely to appear downstream at the drive shafts and wheels.


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Shaft Displacement Measurement Using A PROTOR System

Shaft displacement is an important vibration measurement for rotating machines. Shaft displacement is usually monitored by non-contact shaft displacement probes such as eddy-current probes. These probes produce a voltage proportional to the distance of the shaft surface relative to the tip of the probe. For maximum benefit, ideally two shaft displacement probes will be fitted to measure the displacement in both the horizontal and vertical directions. Actually the probes do not have to be exactly horizontal and vertical as Prosig’s PROTOR system is able to resolve into the horizontal and vertical directions.


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What Are dB, Noise Floor & Dynamic Range?

Most engineers are probably familiar with or have come across the decibel or dB as a unit of measurement. Its most common use is in the field of acoustics where it is used to quantify sound levels. However, as will be explained in this article, it is also useful for a wide variety of measurements in other fields such as electronics and communications.

One particular use of dB is to quantify the dynamic range and accuracy of an analogue to digital conversion system. This applies to Prosig’s P8000 range of data acquisition hardware where the noise floor, dynamic range and resolution are all specified in terms of dB.


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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?”


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Human Exposure To Vibration In Buildings (DIN 4150-2:1999-06 & DIN 45669-1:1995-06)

Standards DIN 4150-2:1999-06 and DIN 45669-1:1995-06 provide a means of assessing the effect on human beings of vibration caused by vehicle traffic, trains both above and below ground, construction work and occasional impulsive type vibration caused by, say, blasting and the like.

DIN 45669-1 describes the signal processing actions and DIN 4150-2 details how these are used. Provisions are included for day or night levels and for five categories of building:

  • Industrial
  • Predominantly Commercial
  • Mixed Commercial and Residential
  • Residential
  • Special Areas such as Hospitals


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Orders v Time – Comparing Overall Levels

By combining a speed signal with a data signal and using the Short Time FFT algorithm (Hopping FFT), it is possible to extract order data directly as a function of time (Orders from Hopping FFT) rather than as a function of speed (Waterfall). This is very useful when analyzing a complete operational cycle which includes run ups, rundowns and periods at operational speeds.


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Calculating Velocity Or Displacement From Acceleration Time Histories

It is quite straightforward to apply “classical” integration techniques to calculate either a velocity time history from an acceleration time history or the corresponding displacement time history from a velocity time history. The standard method is to calculate the area under the curve of the appropriate trace. If the curve follows a known deterministic function then a numerically exact solution can be found; if it follows a non-deterministic function then an approximate solution can be found by using numerical integration techniques such as rectangular or trapezoidal integration. Measured or digitized data falls in to the latter category. However, if the data contains even a small amount of low frequency or DC offset components then these can often lead to misleading (although numerically correct) results. The problem is not caused by loss of information inherent in the digitisation process; neither is it due to the effects of amplitude or time quantisation; it is in fact a characteristic of integrated trigonometric functions that their amplitudes increase with decreasing frequency.

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Sound Steering

The requirement was to develop a ‘standard’ test for assessing power steering pump noise (and sound quality) in vehicles. Measurements needed to be objective so that the method would be suitable for evaluating dissimilar vehicles and different types of pump.

Noise is an important consideration when a consumer is selecting a new vehicle. It is therefore imperative that every aspect of the vehicle’s acoustic profile is thoroughly understood and refined.

From an end user point of view the assessment criterion is simply how much will the driver or passengers hear the pump noise in relation to the vehicle background noise. That is, will the pump produce, what may be called, audible tones with the vehicle in different operating conditions.


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Measuring Torsional Crank Shaft Jitter

Using Prosig’s P8000 series data acquisition system with DATS signal analysis software, torsional analysis (crank shaft jitter) was performed on an automotive engine attached to an engine dynamometer. The significance of this is that only one tachometer channel was required to identify crank jitter.


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What Is Resonance?

We hear the word used a lot, but what is resonance? First, in order to explain we have to explain the terms we will use.

  • A period is the amount of time it takes to complete one cycle
  • The number of cycles in one second is the frequency of an oscillation.
  • Frequency is measured in Hertz, named after the 19th-century German physicist Heinrich Rudolf Hertz
  • One Hertz is equal to one cycle per second.


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Evaluating A Closed Loop Control System For High Pressure Pumps

Prosig were recently involved in the validation of a closed loop control system for an automotive pump supplier. The customer has a large number of test cells, each test cell has 8 pumps continually on test. Each pump is instrumented with a revolution or tachometer sensor, giving a once per revolution tachometer pulse. Additionally, there are various analogue transducers on each pump which measure parameters, such as pressure at the pump inlet and outlet.


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Order Cuts And Overall Level

Order cuts are taken from a set of FFTs, each one at a different rpm. The rms level is then found as the Square root of the Sum of the squares of each of the FFT values. Mathematically, if $latex x_{ks}$ is the modulus (magnitude) of the $latex k^{th}$ value of the FFT at speed s for $latex k = 1,\dots,N-1$ then the rms value at that speed is given by

$latex rms_s = \sqrt{\sum_{k=0}^{N-1}{x_{ks} ^2}}$

This takes into account the entire energy at that speed both the order and the non order components, including any noise.


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Acceleration, Velocity & Displacement Spectra – Omega Arithmetic

Accelerometers are robust, simple to use and readily available transducers. Measuring velocity and displacement directly is not simple. In a laboratory test rig we could use one of the modern potentiometer or LVDT transducers to measure absolute displacement directly as static reference points are available. But on a moving vehicle this is not possible.

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Examples Of Event Extraction And Removal

Event ExtractionIn many cases only significant events, such as bumps or other transients in a signal are of relevance. The objective is to be able to isolate these events in a meaningful manner so that they may be automatically recognised and either removed or extracted for analysis in a structured way.

There are two principle objectives initially: one is to be able to recognise an event and the other is to be able to mark it in some way so that subsequent software is able to operate on the actual event. We must also note that an event has a start and an end; the criterion we use to recognise the start may not necessarily be the same criterion we use to recognise the end. Searches for the start and end points are carried out on a Reference Signal. How the reference signal is formed is discussed in detail later, it includes the original signal, various running statistical measures such as the dynamic RMS, differentiation for slope detection, integration and so on. In many cases the start criterion will be some check on the level achieved by the reference signal. By the time any check level has been detected then it is almost certain that the event started earlier! That is, a pre trigger capability is essential.


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Measuring For Success With A Hammer Impact Test

The following application note shows the steps taken to perform structural analysis using a hammer impact test on an automotive exhaust pipe structure to improve the structural damping properties of the exhaust pipe mount. This application note follows up to a previous article – “Preventing Component Failure In The Fast Lane”.

A recent signal processing application note described how the Prosig sponsored Dalmeny Racing Formula Ford Team, whilst contesting the UK Formula Ford 1600cc championship, suffered several minor structural failures on a particular part of an exhaust pipe mount. Prosig dispatched a team of engineers, and after a brief survey of the damage, the engineers made an outline assessment. They concluded that “the exhaust itself is resonating at particular engine speeds. This is causing some shear forces in the mount. This in turn is causing stresses in the material leading to cracking and eventually failure.”


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Fatigue & Durability Testing

The following application note describes the test and measurement process for the fatigue & durability testing and development cycle of an automotive suspension component, specifically a tie rod. The component had been known to fail at various intervals. An estimate of the predicted fatigue life of the component was required in order to assess the feasibility of its continued use and to see if a design change was required. The component under test is shown in Figure 1. The testing was carried out by a major automotive manufacturer. Strain gauges were used to monitor the strain levels.


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Measuring Exhaust Noise Using A P8000 System

The following note describes measuring exhaust noise using a Prosig P8000/DATS system for the refinement of an automotive muffler design for a major after-market exhaust manufacturer in Europe. The particular vehicle under test was required by local legislation to have an overall radiated noise level of less than 70 dB. When tested, the vehicle was found to be producing 71.8 dB of radiated noise. The design of the exhaust system clearly needed to be reviewed and modified. (more…)

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Standard Octave Bands

The “standard” centre frequencies for 1/3 octave bands are based upon the Preferred Numbers. These date from the 19th century when Col. Charles Renard (1849–1905) was given the job of improving captive balloons used by the military to observe enemy positions. This work resulted in what are now known as Renard numbers. Preferred Numbers were standardised in 1965 in British Standard BS2045:1965 Preferred Numbers and in ISO and ANSI versions in 1973. Preferred numbers are not specific to third octave bands. They have been used in wide range of applications including capacitors & resistors, construction industry and retail packaging.


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Torsional Vibration, Tacho Pulses And Aliasing

With shafts, gears and the like, the general method of determining the rotational speed is to use some form of tachometer or shaft encoder. These give out a pulse at regular angular intervals. It we have N pulses per rev then obviously we have a pulse every (360/N) degrees. Determining the speed is nominally very simple: just measure the time between successive pulses. If this period is Tk seconds and the angle travelled is (360/ N) degrees then the rotational speed is simply estimated by 360/(N*Tk) degrees/second or 60/(N*Tk) rpm.


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Analyzing Shaft Twist And Repairing Damaged Tachos

This post discusses analyzing shaft twist and at the same time handling the less than perfect data that we have all come across.

A shaft has been instrumented with two shaft encoders, one at each end. Each shaft encoder gives out a once/rev pulse and a 720 pulses/rev signal. Each signal was digitised at 500,000 samples/second. The objective is to measure the twist in the shaft and analyze into orders. The test stand was already equipped with a data acquisition system so a Prosig acquisition system was not required. Instead it was decided that the data captured by the resident system would be imported into the DATS software. The only format available from the customer system was ‘comma separated variables’ or CSV. This is not ideal as it is an ASCII based format and therefore creates very large files.


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Phase Angle Between Signals

The following article was written in response to a question from a visitor to the website. The gentleman in question had been reading some of the Prosig signal processing articles and had the following question.

Dear Sir,

It was interesting reading the articles in your mail.I would like
to know the options available in hardware and/or software for measurement/calculation
of phase angle of first harmonic of a vibration signal which is
sinosoidal. The phase angle is the relative phase angle difference
between the signal and the tacho - one into rpm signal.



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