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Application NoteCM3023

SKF Reliability Systems

Synchronous Time Averaging/

Machine Balancing

AccelerometerTransducer

CurrentSource

Overload

Anti-Aliasing

Fmax A To DConverter

Filter

FFT

SampleTime

SampleClock

PulseCircuit

ExternalTrigger

Sample Rate = 2.56 Fmax

Number of Samples =

2.56 Number of Lines

T = Number of SamplesSample Rate

ProcessorSpectrum

Display

Block Diagram FFT Analyzer

A

Data Buffer

Abstract

Machine balancing is a maintenance

requirement that extends machinecomponent life and improves process

performance. Programs have been written

to calculate the required corrective balance

weights from amplitude and phase data

relative to a shaft reference. Precision

balancing depends on stable, accuratephase and amplitude measurements.

Synchronous time averaging insures phase

stability by discriminating against noise

and machine cross talk during trim balance

runs. This paper discusses the concept of

synchronous time averaging as applied to

order tracking balancing methods for

multiple cooling tower fans arranged side

by side in a weather protected housing.

Definition

A synchronous time average is an averageof only those synchronous rotational

components which are coherent with amachine shaft reference. Noise and non-

synchronous signals tend to average to

zero.

Block Diagram

Figure 1 is a simplified block diagram of a

generic FFT analyzer.

Transducer

Generally, the transducer used in making

synchronous time average measurements isan accelerometer incorporating an

integrated amplifier. The amplifier

provides a low impedance output that

allows its sensitivity to be independent of

cable length.

Analyzer

The FFT analyzer used in makingsynchronous time average measurements

incorporates a current source to energize

the transducers amplifier. The analyzers

input gain amplifier auto-ranges to insure

optimum dynamic range without circuit

saturation. In accordance with FFTconversion techniques, the collected raw

signal is filtered to attenuate all signal

components above the selected frequency

domain, thereby minimizing aliasing errors.

A/D Converter

After filtering, the analog-to-digital

converter periodically samples the filteredsignal at a sample rate of 2.56 x the

maximum frequency range. That is, if the

frequency range is 1 kHz then the sample

rate is 2.56 kHz.

Figure 1. A Simplified Block Diagram.

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Sampled Data Buffer

The samples are next stored in the sampled data buffer

whose memory length is 2.56 x number of FFT lines of

resolution. If 400 lines of resolution is selected, then the

length of sampled memory is 1024 sample points. The

memory length in terms of the data time interval is equal to

the number of data samples divided by the sample rate, that

is:

Once the buffer is full, the data is converted from the time

domain to a spectrum domain by the FFT processor.

Normal Averaging

In the normal averaging mode, each converted spectrum

ensemble is sequentially summed together, divided by the

number of spectrum ensembles and displayed as the

average. For example, if the number to be averaged is 10,

then each of 10 sequential spectrums are summed and the

sum divided by 10 to obtain the mean.

Synchronous Time Averaging

Synchronous time averaging is different from normal

averaging in that the time domain buffer is summed and

averaged prior to the FFT conversion process.

The averaging process is meaningful only if a trigger

synchronizes the sampling process so it is coherent with

T =2.56 x Number of Lines

2.56 x Fmax

if number of lines = 400 and Fmax= 1000

then, T = 400 millisec.

rotation. This is implemented by sensing the trigger signal

to initiate a count of the sampled data entering the buffer.

When the count equals the buffer sample length (1,024 in

this example), each time sample ensemble is summed until

the selected average number is reached.

Each sample point sum is divided by the average number to

obtain the mean. Since the high spot amplitudes are always

delayed the same amount of time from the trigger, the

sequential sums of these coherent signals will be enhanced

while noise and non-synchronous signals tend to a zero

average. The result is that synchronous time averaging

stabilizes and improves phase and amplitude measurement

accuracy.

Phase Measurement Accuracy

ABSOLUTEPHASE

The measurement of absolute phase of the 1-per-revolution

imbalance component requires special circuit considerations

to achieve repeatability and accuracy.

A normal single channel FFT analyzer operation, with fixed

range anti-aliasing filters and a sample rate independent of

rotation, contributes significant errors to phase measurement

calculations. The following is a discussion of these major

error sources.

TRACKINGALIASERRORS

It is necessary that measurements not be affected by large

speed variations which can introduce aliasing components.

These problems are avoided if the anti-aliasing filter is

converted to a tracking filter whose high frequency cutoff

tracks the rotational speed.

Since sample rate is related to the selected maximum

frequency range, the sample clock must proportionately

AccelerometerSignal

Tracking

Filter

N = Maximum Orders

Wide = 20% = 20 (1X)

Narrow = 5% = 5 (1X)

Normal = 10% = 10 (1X)

Order Tracking Block Diagram

Gain

NX (1X)

WideNarrowNormal

A/D FFT

NX (1X) 2.56NX (1X)Trigger

Figure 2. An Order Tracking Block Diagram.

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track the shaft trigger signal. This changes the spectrum

display from a fixed frequency plot to an order diagram

where the machine speed is the first order and maximum

range is the number of orders selected from a menu option.

PHASEMEASUREMENTACCURACYOPTIMIZED

Phase measurement accuracy is optimized when the ratio of

FFT lines per order is an integer. For example, if the FFT

line resolution is 400, a maximum order of 20, 10, or 5

would be desirable whereas 3, 7, or 9 would not.

Whenever an integer line-per-order relationship is used, the

FFT phase process is said to be bin centered and the FFT

phase error contribution is zeroed.

TRACKINGFILTERERROR

A phase error is introduced by the tracking filter. The filterphase is not constant but increases with higher orders.

These filter errors are eliminated by subtracting the known

filter phase shift from each integral order. Essentially, the

filter is modeled in firmware to provide a tabular listing of

order vs. phase.

Figure 2 shows a simplified order tracking block diagram.

VIBRATIONSIGNALGAIN

The vibration signal gain is again optimized by auto-ranging

the input amplifier. The signal is filtered by the tracking

filter whose cutoff is continuously adjusted by the 1Xtrigger. In this case the Fmaxcutoff is equal to N (maximum

orders) x (1X) rotation speed. The filter cutoff frequency

varies with rotation. The sample clock also tracks the

rotation speed where SR (sample rate) equals 2.56 x N x

(1X).

This maintains the zero bin relationship required for zero

FFT phase contribution. The final phase calculation is

corrected by subtracting the known filter phase shift by

means of a firmware modeling algorithm.

Comparison Of Phase Accuracy Methods

FREQUENCYAVERAGINGVS. SYNCHRONOUSTIMEAVERAGING

An experimental setup was arranged with a Signal

Generator that allows for simulated rotation signals

precisely phase shifted relative to a reference. A signal

from this setup was combined with a non-synchronous

nearby rotation signal.

SIMULATED MACHINEBALANCINGMEASUREMENTS

The first measurement was to establish the reference run

under the most stable conditions. A 61.4 Hz sine wave wasprogrammed with a phase lead and was measured in

Figure 3. A Stationary Sine Tone.

Figure 4. Sine Tone plus Swept Sine Frequency Domain Averaging.

Figure 5. Sine Tone plus Swept Sine Synchronous Time Averaging.

conjunction with a square wave reference. Both normal

averaging and synchronous time averaging measurements

were the same in both amplitude and phase.

Figure 3 shows the tabulated results of these measurements

under the reference run heading.

Next, a signal sweeping between 59 and 62 Hz at a slow rate

was summed with the original sine wave. Figure 4 showsthe results of normal averaging where the amplitude was

measured as 1/3 the first reading and the phase was more

then 20lag from the correct measurement.

The last tabulated measurement was performed with

synchronous time averaging (Figure 5) where both

amplitude and phase were within 0.2% of the correct value.

Since synchronous time averaging tends to zero out the non-

coherent signal, using a long enough averaging process

causes the resultant data to converge to the stable coherent

component.

The following plots graphically compare the time signal

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SKF Reliability Systems

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San Diego, California 92123

USA

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Web: www.skf.com/reliability

Although care has been taken toassure the accuracy of the datacompiled in this publication, SKF

does not assume any liability forerrors or omissions. SKFreserves the right to alter any part

of this publication without priornotice.

SKF is a registered trademarkof SKF.

All other trademarks are theproperty of their respectiveowners.

CM3023 (Revised 6-04)

Copyright 2004 by

SKF Reliability SystemsALL RIGHTS RESERVED

"SynchronousTime Averaging/

Machine

Balancing"

averaging results of

synchronous time

averaging and normal

frequency domain

averaging of signals with

nearby crosstalk

components. Figure 6

shows the effects of the

beat frequency.

Figure 7 displays the

results of time averaging

where the crosstalk signals

are incoherent with the

reference and averages

towards zero.

Figure 8 is signal without

crosstalk. The time

averaging process

amplitude compares

precisely with the signal

alone.

The regular averaging

method shows

considerable large

amplitude discrepancy

relative to the coherent

rotational component.

This approach can prove

to be advantageous during

a precision balancingoperation where the final

trim run amplitude is

either buried in noise or in

close proximity to a

crosstalk signal from a

nearby machine.

Conclusion

Accurate and repeatable

phase measurement is a

difficult problem at bestwith single channel FFT

analyzers. It requires a

tracking filter for speed

variations, adjustable

clock sampling

proportional to speed, and

filter phase compensation

for measurement

precision.

In the practical world,

both noise and nearbyrotational signals often

Figure 6. Frequency Ensemble: AveragingMachine and Crosstalk.

0 80.0 160.0 240.0 320.0 400.0MS

OVERALL

6.8124

2.0

Gs/Div

10.0

-10.0

Figure 7. Synchronous Time AveragingMachine and Crosstalk.

0 80.0 160.0 240.0 320.0 4MS

OVERALL

3.9454

2.0

Gs/Div

10.0

-10.0

Figure 8. Signal (No Crosstalk) Frequency Ensemblee Averaging.

0 80.0 160.0 240.0 320.0 400.0MS

OVERALL

3.9006

2.0

Gs/Div

10.0

-10.0

introduce variables that cause significant unstable results.

Synchronous time averaging minimizes these variable

components to levels that allow for accurate and stable on-

site phase readings. Precision machine balancing

measurements can be performed under circumstance which

introduce substantial noise and nearby rotational amplitudes

from the normal production operation. These measurements

can simply be accomplished with a battery operated hand-held analyzer incorporating resident balancing firmware.