Aliasing, Orders and Wagon Wheels

These days most people collecting engineering and scientific data digitally have heard of and know of the implications of the sample rate and the highest observable frequency in order to avoid aliasing. For those people who are perhaps unfamiliar with the phenomenon of aliasing then an Appendix is included below which illustrates the phenomenon.

In saying that most people are aware of the relationship concerning sample rate and aliasing this generally means they are aware of it when dealing with constant time step sampling where digital values are measured at equal increments of time. There is far less familiarity with the relevant relationship when dealing with orders, where an order is a multiple of the rotational rate of the shaft. For example second order is a rate that is exactly twice the current rotational speed of the shaft. What we are considering here then is the relationship between the rate at which we collect data from a rotating shaft and the highest order to avoid aliasing.

The relationship depends on how we do our sampling as we could sample at constant time steps (equi-time step sampling), or at equal angles spaced around the shaft (equi-angular or synchronous sampling). We will consider both of these but first let us recall the relationship for regular equi-time step sampling and the highest frequency permissible to avoid aliasing. This is often known as Shannons Theorem [Learn more about Claude E Shannon].

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Vibration Condition Monitoring Using Your Android Smartphone

Ever been lying on the beach and begun to wonder about the state of your LP turbines? Or out on business and anxious to know if that troublesome exciter bearing has settled down? Well with a Prosig PROTOR system and a smartphone anything’s possible. Many of you will be familiar with using your phone as a camera, music player, web browser, email client, calculator or even a navigation device, but not many will have anticipated using it for vibration condition monitoring!

Here we will explain how to use one of the new Android based phones to connect to a PROTOR system. For the purposes of this example we used an Android-based phone and a WiFi connection. It is equally acceptable to use the network providers 2G/3G data connection. And although we chose an Android based phone, similar VNC-viewer apps exist for the iPhone and other smartphones.

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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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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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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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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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Updated Protor System For Ringhals, Sweden

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RinghalsProsig installed a PROTOR system at the Ringhals1 reactor in Sweden in 1992. This system was based on the PROTOR2 level of hardware and software and consisted of a Sun workstation and PC based acquisition system. The system has been successfully monitoring the two main turbine generators ever since. Last month Prosig upgraded this system to their latest PROTOR4 hardware and software.
The system now consists of a high-end rack-mount server PC containing RAID, hot-swap disks, dual high-speed Ethernet LANs and redundant power supplies together with two 32-channel 4700 data acquisition units.
The system is connected into the station alarm system so that control room staff are automatically alerted on vibration alarms. The system is fully integrated within the Ringhals network for data archiving, remote access and data transfer with the plant computer.

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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.

Regards.
etc.

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Measuring Torsional Twist & Vibration Along a Shaft or Through a Geartrain

The measurement of torsional twist, or the twist angle, between two points along a shaft or through a gear train may be derived from a pair of tacho signals, one at each end of the shaft. Typically the tacho signals would be derived from gear teeth giving a known number of pulses/revolution. For example one end of a shaft could have a gear wheel with say 60 teeth giving 60 pulses/revolutions when measured with say an inductive or eddy current probe. (more…)

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Order Tracking, Frequency and Hertz

In this article, we look at the relationships between frequency, the unit Hertz and order tracking. The most common form of digitising data is to use a regular time-based method. Data is sampled at a constant rate specified as a number of samples/second. The Nyquist frequency, fN, is defined such that fN = SampleRate/2. As discussed elsewhere, Shannon’s Sampling Theorem tells us that if the signal we are sampling is band limited so that all the information is at frequencies less than fN then we are alias free and have a valid digitised signal. Furthermore, the theorem assures us that we have all the available information on the signal.

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High Pass Filtering And Tacho Signals

It is sometimes necessary to perform high pass filtering to eliminate low frequency signals. These may arise for instance from whole body vibrations when perhaps our interest is in higher frequency components from a substructure such as an engine or gearbox mounting. The vibration levels are speed sensitive and the usual scheme is to record a once per revolution ‘tacho’ signal with the vibration data. The tacho signal, which ideally is a nice regular pulse train, is processed to find rotational speed and hence to select which part of the vibration signal is to be frequency analyzed. The most common form of analysis is a waterfall type such as shown below.

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Importance of tachometer/keyphasor signal conditioning and its relationship to phase measurements

This note describes the importance and setup of a keyphasor or tachometer signal for PROTOR Remote Monitoring Data Acquisition System (RMDAS) units. RMDAS units are provided with manual tachometer conditioning…

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