comparison of torsional vibration measurement...

Comparison of torsional vibration measurement techniques

K. Janssens, L. Britte

LMS International

Interleuvenlaan 68, Researchpark Z1 3001, Leuven, Belgium

e-mail: [email protected]

Abstract Noise and vibration performance plays an important role in the development of rotating components, such

as engines, drivelines, transmission systems, compressors and pumps. The presence of torsional vibrations

and other specific phenomena require the dynamic behaviour of systems and components to be designed

accurately in order to avoid comfort and durability related problems. This paper provides an overview of

the instrumentation and challenges related to torsional vibration testing. The accuracy and performance of

five measurement techniques (high-speed incremental encoder, dual beam laser interferometer, zebra tape,

zebra disc, direct pulse measurements with magnetic probe) are investigated by measurements on a Fiat

Punto 1.4 liter engine. The potential sources of error are discussed for each technique.

1 Introduction

With eco-engineering comes a new range of NVH issues to solve. New powertrain designs like start-stop

systems, downsized engines, advanced torque lock-up strategies and the generic trend for weight reduction

of the powertrain raise the importance of an in-depth understanding of torsional vibrations as they

negatively impact comfort and ultimately engine and driveline efficiency. Torsional vibrations are of

importance whenever power needs to be transmitted using rotating shafts or couplings, like is the case for

e.g. automotive, truck and bus drivelines, recreation vehicles, marine drivelines or power-generation

turbines.

Torsional vibrations are angular vibrations of an object, typically a shaft along its axis of rotation. As

mainly rotational speeds are measured, torsional vibrations are assessed as the variation of rotational speed

within a rotation cycle. These RPM variations are typically induced by a non-smooth driving torque or a

varying load. Structural sensitive frequencies along a driveline may then amplify and transfer these

phenomena leading to comfort, durability or efficiency problems. The level of torsional vibration is

influenced by a number of parameters, such as material properties, operating conditions like temperature,

load and RPM.

Despite tremendous progress in modeling accuracy, overall system complexity still necessitates accurate

qualification and quantification of these torsional vibrations, under controlled or real-life operating

conditions, in order to better understand and refine counter measures.

This paper provides an overview of the instrumentation and challenges related to torsional vibration

testing, reports on the advantages and drawbacks of various measurement techniques and compares their

accuracy and performance by measurements on a engine test bench.

1447

2 Torsional vibration measurement sensors

Various measurement techniques are available for torsional vibration testing. The best sensor can be

selected for each individual case based on the physical quantity to be measured, the type of analysis, the

accessibility of the shaft, the ease of instrumentation and the required accuracy or level of detail.

2.1 Direct measurements

Linear accelerometers

Two linear accelerometers are fixed in a face-to-face configuration on the rotating shaft. The two

accelerometers will measure the tangential acceleration. As they have opposite direction in the fixed

system of the rotation axis, any translational acceleration of the shaft is cancelled by taking the average of

both accelerometer signals.

Advantages:

High dynamic range directly determined by the dynamic range of the accelerometers

Low sensitivity to shaft translational vibrations when the two accelerometers are properly aligned

Disadvantages:

Expensive telemetry system or sensitive slip rings are needed to transfer the acceleration signals

from the rotating shaft to the measurement hardware

Mass loading for relatively small shafts influencing the structural behaviour of the shaft, e.g.

causing torsional resonances to shift in frequency or shaft unbalance

Bigger shafts at relatively high RPM cause centrifugal forces that may lead to dangerous loss of

accelerometers and measurement equipment when not sufficiently well glued

Since acceleration is measured, and angle and speed can only be derived by integration, no

absolute angular position is available. Angle domain processing for example will not be possible

Angular accelerometers

Sensor manufacturers propose fully integrated angular accelerometers to be fixed on the shaft extremities

including the sensors and the slip ring. Some are based on linear accelerometers applying the method

described above. Other techniques like torsional springs can also be used.

Dual-beam laser interferometers

Laser interferometers can be used as well to measure torsional vibrations. Laser manufacturers typically

propose specific systems for rotating measurement based on dual beam techniques to cancel the effect of

translational movement of the shaft. The angular velocity is computed from the velocity measured in the

direction of the laser beams on the two pointed areas through the Doppler shift.

Advantages:

Contactless measurement

Low sensitivity to shaft translational vibration

Low sensitivity to the shape of the shaft

Easy instrumentation

1448 PROCEEDINGS OF ISMA2012-USD2012

Disadvantages:

Expensive device. Since it is often required to measure torsional vibrations at different shaft

locations simultaneously, this is often a very large drawback

Exact angular speed and position are not known. Since velocity is measured, angle can only be

derived by integration, no absolute position is available. Angle domain processing for example

will not be possible

The size of the device does not allow using it in a confined environment. Its use in real-life mobile

conditions is very difficult or nearly impossible

2.2 Coder-based techniques

Coder-based techniques make use of equidistantly spaced markers on the shaft or rotating component. The

system measures every time a marker passes in front of a sensor and the time difference between two

markers is used to estimate the angular velocity.

The coder-based techniques have the advantage to deliver RPM and discrete angle position. The data

resolution is determined by the number of markers: the more markers, the more accurate information.

Different types of coders are used, for example stripes drawn or glued on the shaft or the teeth of gears.

Also different sensors are available to detect the markers, such as electro-magnetic pick-ups or optical

sensors. Incremental encoders are devices combining the coder and sensor in one single hardware.

Magnetic pick-ups

Magnetic pick-ups detect changes in the magnetic field or magnetic flux, typically resulting from metallic

teeth passing the sensor. They are often used in industrial applications because of their robustness and low

sensitivity to ambient dust. Set-ups for this are often very practical as well, since existing gear sets on the

machine can be used as coder, e.g. the gear teeth on flywheels of transmissions. Resulting from that,

magnetic pick-ups are very popular for measuring torsional vibrations, as they are easy to set up, as they

work very well with existing gear teeth and as they are very robust. Most combustion engines today are

equipped, by default, with these sensors to transfer the different shaft positions to the engine or gearbox

controllers.

Passive sensors like the magneto-resistive or magneto-inductive pick-ups are the most popular and most

cost effective. The measured voltage from the sensor is generated by the changing flux, given by

Faraday’s law. As the change of the magnetic flux comes from the rotation of the shaft, the sensor does

not need to be powered. The amplitude and shape of the delivered signal however vary with the speed of

the shaft and may affect the accuracy of the teeth detection, mostly at low rotational speeds.

Other magnetic sensors are based on the Hall-effect. Often those sensors are equipped with miniaturized

electronic circuit to condition the output to deliver a TTL type of output signal. They also need to be

powered.

Advantages:

Price. Mass production of magnetic pick-ups for automotive and industrial applications has a very

positive influence on their end-user price

Simplicity of instrumentation. The sensor is typically fixed on non-rotating components, which

avoids the need for e.g. telemetry. Coders are mostly generated by existing gear sets

Robust sensors with low sensitivity to ambient dust

DYNAMIC TESTING: METHODS AND INSTRUMENTATION 1449

Disadvantages:

The number of gear teeth sets limits to the number of pulses per revolution which could be

insufficient to capture all torsional content

The accuracy of the measurement is very much dependent on the machining accuracy and

deformation of the gear teeth

The sensor must be fixed very close to the rotating shaft (less than 0.5 cm) which is sometimes

difficult, e.g. when the shaft has an important translational movement

Relative displacements between the magnetic pick-up and the shaft, due to shaft bending or due to

displacement of the sensor attached on a too soft mounting, influence the quality of the measured

pulses and generate a fictive torsional vibration

Coder wheels sometimes come with one or two consecutive missing teeth to generate an absolute angular

reference position per rotation. Engine manufacturers use this reference to synchronize the equipment

linked to the coder with the cylinders’ top death center (TDC). However, when such set-up is used to

provide coder pulses for torsional vibration analysis, a missing pulse correction algorithm is needed. If

not, the missing coder pulse generates a spike into the RPM or angle estimation.

Optical sensors

Many types of optical sensors can be found on the market, however most of them are designed for object

detection. To measure torsional vibrations, the sensor not only needs to be able to detect a high rate of

events per second, also the timing accuracy of the detection is very important and this accuracy is often

insufficient.

Optical sensors generate an electric signal proportional to the received light intensity. Optical fibers are

used to conduct the light from the emitter to the sensor head and back from the sensor head to the receptor.

They can be configured in reflection or transmission configuration.

Optical sensors can be used with many different types of coders as long as the visible contrast between the

stripes is sufficient. Most optical sensors deliver a TTL output signal.

Advantages:

The instrumentation is very simple as the sensor is typically fixed on non-rotating components.

Only the coder needs to rotate

Optical sensors can be directly instrumented on gears as is the case with magnetic pick-ups, under

condition that the reflection of the material gear surface is sufficient

Coders can easily be implemented on shafts with contrasted paint or zebra tape

The fast response and good phase accuracy of high-quality optical sensors allow the measurement

of very high pulse rates

Disadvantages:

The sensitivity to ambient light and/or the quality of the material reflection complicate the direct

instrumentation of the gears in gearboxes

The sensor must be fixed very close to the rotating shaft (less than 0.5 cm) which is sometimes

difficult when the access is limited or when the shaft has some important translational movement

Relative displacements between the optical sensor and shaft influence the quality of the measured

time stamps and lead to torsional vibration measurement errors

Black and white tapes are more and more used to quickly implement a coder on a shaft. They can be used

to create a coder when no gear wheel is available or when a higher number of pulses per rotation is

required. There are two families of tape depending on whether it must be glued around the shaft (zebra


tape) or on the extremity (zebra disc). Zebra tapes and discs exist in multiple stripe width to adapt the

number of pulses per revolution in function of the shaft diameter.

Although zebra tape is very easy to instrument, an error will be introduced onto the measurement at the

location where the two zebra tape endings come together. When this point passes the optical sensor it will

introduce a discontinuity in the RPM signal. A butt joint correction should therefore be applied before

analysing the measurement signal [1].

Zebra discs do not suffer from this butt joint problem, however proper care needs to be taken to properly

center the disc. Since perfect centering is never possible, torsional order 1 is typically not reliable when

using this coder set-up.

Incremental encoders

Incremental encoders are devices typically used in automat or robotic applications for accurate detection

of shaft positions. Their high accuracy makes them very attractive for torsional vibration analysis

applications as well. Often based on optical technology, incremental encoders combine the coder and the

sensor in one single device. They consist of both a rotating (rotor) and static (stator) component and the

full sensor needs to be mounted on the set-up. Incremental encoders come in many different shapes and

sizes, to cover all required applications.

The incremental encoder makes use of three embedded coders: one detecting one single pulse per

revolution, called index, as absolute angle reference and two more high resolution encoders called A and

B. The A and B signals have exactly the same number of pulses but the B signal is phase shifted with a

quarter of a pulse cycle (90 degrees) compared to A. The combination of these two coder signals allows

detecting the sense of rotation of the coder.

Advantages:

The fully integrated approach allows developing accurate coders with potentially very high pulse

rate. Incremental encoders can be delivered with the appropriate number of pulses, depending on

the application and desired accuracy typically 50 to 500 The sense of rotation can be a great advantage, e.g. for the investigation of the start/stop behaviour

on engines

The integrated index signal allows duty cycle related analysis with accurate TDC identification

(e.g. engine combustion analysis)

Disadvantages:

The relative complex instrumentation limits their usage for in-vehicle or mobile measurements.

Incremental encoders are mainly used when working on test benches where the instrumentation

makes part of the test bench equipment.

3 Pulse signal conditioning

Magnetic pick-ups, optical sensors and incremental encoders all output periodic signals to be processed

into angular velocity and/or position by acquisition hardware. Some sensors have dedicated circuit to pre-

process or pre-condition the signal into a standardized type of output signal like TTL or RS422/485.

The torsional vibration measurement system must detect accurately the time stamps, named tacho

moments, at which a predefined level is crossed by the periodic sensor signal assuming a fixed angle

increment between pulses. The required hardware signal conditioning depends on the type of sensor being

used and its corresponding signal type.


Analog Tacho

The output signal is delivered as measured by the sensor, which means in practice that it can have any

shape. A user defined trigger level is used to identify the tacho moments. Up to 40.000 pulses per second.

Digital Tacho - TTL

Most optical sensors and some magnetic pick-ups are equipped with dedicated level detection circuit

delivering a standardized digital signal (TTL), which allows clear and accurate detection of the tacho

moments at higher pulse rates than the classical analog tacho. Up to 1 million pulses per second.

Digital Tacho - Differential TTL

Single ended signals are more sensitive to electrical noise than differential signals, especially when longer

cable lengths are needed. That is why the differential standards RS422/485 are recommended for

incremental encoders, where the distance between the emitter and sensor head cannot be changed. Up to 1

million pulses per second.

4 RPM reconstruction

When using coder based sensors, each pulse detection moment corresponds to a known increase in angular

position, i.e. at each tacho moment the angular position with respect to the first tacho moment is known.

To process the data in time or frequency domain, interpolation techniques must be used to estimate the

position or the speed between two detected tacho moments and to generate a time-equidistant RPM or

angle trace at the desired sampling frequency. The interpolation method used can have an important

impact on the quality of the analysis. Best techniques use digital reconstruction filters to avoid aliasing.

5 Angle domain aliasing

The quality of coder-based torsional measurements is heavily impacted by a correct selection of the

minimum number of pulses per rotation. In case too few markers per revolution are available, this will add

an error, known as angle domain aliasing, to the measured data. The minimum coder resolution can be

identified according to the principles summarized below:

Nyquist-Shannon sampling theorem

In principal, the number of pulses per revolution required is determined by the Nyquist theorem applied to

an angle domain acquisition. If a angular function x(α) contains no order higher than Omax, it is completely

determined by giving its ordinates at a series of points spaced π/Omax radians apart. In other words, the

number of pulses per rotation must be at least two times higher than the maximum order.

Response bandwidth

Mechanical system responses to a certain excitation are band limited in frequency. The relevant frequency

range for torsional vibrations is limited to a maximum and this maximum depends on the structural

dynamics of the mechanical system (shaft or component under analysis). It also means that once for a

specific RPM the order exceeds the bandwidth, this order is no longer of importance. The maximum order


observed is function of the bandwidth of the system and the rotational speed. For varying speeds (run-ups,

run downs…), the minimum RPM determines this maximum observed order.

Required number of pulses per rotation

Based on these principles, the required coder resolution can be estimated as follow:

As the bandwidth of the system cannot always easily be estimated, a safety factor between 2 and 4 is often

applied. In many cases, test engineers do not have the luxury of selecting the optimal coder for their test.

When using coders available as part of the structure, like for example teeth in gearboxes, it is always

important to estimate the error made with too few pulses. Equation (3) can be used in its reverse form to

estimate the bandwidth of the coder for specific RPM conditions:

Figure 1 illustrates the risk of angle domain aliasing. The same torsional vibration is measured with a 60-

ppr coder (left display) and a 20-ppr coder (right display). Orders 1 and 2 are perfectly measured with both

coders. Order 17, on the other hand, is not measured with the 20-ppr coder (Nyquist-Shannon theorem)

and, even more dramatically, aliased back into order 3.

Figure 1: Angle domain aliasing

500.000.00 Hz

Torsion_60ppr (CH1)

5900.00

700.00

rpm

Tacho (

T1)

20.00

-20.00

dB

rpm

1.00 2.00 3.00

10.00

17.00

500.000.00 Hz

Torsion_20ppr (CH2)

5900.00

700.00

rpm

Tacho (

T1)

20.00

-20.00

dB

rpm

1.00 2.00 3.00

10.00

17.00


6 Test campaign

6.1 Test set-up

An experimental test campaign was carried out on a 4-cylinder Fiat Punto 1.4 l engine (figure 2). The

engine was driven by an electric motor controlling the speed profile. The engine crankshaft and electric

motor were connected by a pulley.

Torsional vibration measurements were conducted on both the cam- and crankshaft. The shafts were

instrumented as follows:

Camshaft (figure 3 right):

o Dual beam laser (RLV 5500 Polytec system)

o High speed incremental encoder (Heidenhaim ROD 426, 1024 pulses per rotation)

o Zebra tape (142 stripe pairs, 1 mm stripe width, Optel Thevon optical sensor)

o Zebra disc (120 pulses per revolution, Optel Thevon optical sensor)

Crankshaft (figure 3 left):

o Dual beam laser (RLV 5500 Polytec system)

o High speed incremental encoder (Heidenhaim ROD 426, 1024 pulses per rotation)

o Zebra tape (188 stripe pairs, 2 mm stripe width, Optel Thevon optical sensor)

o Direct pulse measurements on flywheel (116 teeth, magnetic pick-up)

Various constant speed and run-up tests were carried out. The tests were conducted in two different

conditions:

4 cylinders open (spark plugs removed); limited torsional content related to the piston movements

(mass and friction)

1 cylinder closed; large torsional content due to the high pressure changes (compression and

expansion) in the closed cylinder, once per rotation of the camshaft

Figure 2: Fiat Punto engine set-up

Pulley

Crankshaft

Camshaft


Figure 3: Instrumentation of crank- (left) and cam- (right) shaft for torsional vibration testing

6.2 Camshaft measurement results

4 cylinders open

Figure 4 shows the RPM-frequency colormap of the torsional vibration measurements on the camshaft by

the dual beam laser, incremental encoder, zebra disc and zebra tape in a run-up test with 4 open cylinders.

There is obviously a good match between the results of the 4 measurement techniques within a 30 dB

dynamic range. The dominant orders 4, 12 and 16 are well captured by all methods. Only slight

differences are noticeable for the least significant order components. The zebra disc results are of lower

quality in the 70-90 Hz frequency range, possibly due to the vibrations of the optical probe which is not

idealy fixed. Also the 100 Hz frequency component from the electric motor is clearly more visible

compared to the other techniques. One can finally notice that the zebra disc is not perfectly centered on the

shaft, causing an order 1 misalignment error.

Interesting as well are the order cuts in figure 5, showing the amplitude and phase profile of orders 1, 4

and 16 as obtained with the 4 measurement techniques. There is clearly a good match in both amplitude

and phase, even for the less important torsional orders with small amplitudes of less than 0.01 degrees.

The zebra disc misalignment error is very clear from the order 1 profile. Remarkable as well are the

relatively large order 1 fluctuations in case of the laser measurements which might be related to the

surface irregularities of the shaft. More research is needed to further investigate on this.

The time-domain results in figure 6 are very convincing as well. The figure compares the RPM variations

obtained from the zebra tape measurements with those of the incremental encoder before (lower graph)

and after (upper graph) application of a zebra butt joint correction. The spikes in the RPM data are clearly

removed, illustrating the effectiveness of the correction method. The corrected zebra tape measurements

and incremental encoder RPM data match very well.

Incremental encoder

Magnetic pick-up

Zebra tape

Zebra tape

Incremental encoder

Zebra disc


Figure 4: RPM-frequency colormap of torsional vibration measurements on camshaft in run-up test with 4

open cylinders: dual beam laser, incremental encoder, zebra disc and zebra tape

200.000.00 Hz

DBL_delta_angular_velocity (CH3)

460.00

95.00

20.00

-10.00

dB

rpm

200.000.00 Hz

Incremental_Encoder1024ppr (CH13)

460.00

95.00

20.00

-10.00

dB

rpm

200.000.00 Hz

Zebra_tape142ppr_c2 (CH9)

460.00

95.00

20.00

-10.00

dB

rpm

200.000.00 Hz

Zebra_disc120ppr(g) (CH14)

460.00

95.00

20.00

-10.00

dB

rpm

460.0095.00 rpm

Incremental_Encoder1024ppr_Smooth (T4)

0.44

0.00

Am

plit

ude (

RM

S)

°

180.00

-180.00

°

Order 1.00 DBL_delta_angular_velocity

Order 1.00 Incremental_Encoder1024ppr

Order 1.00 Zebra_disc120ppr(g)

Order 1.00 Zebra_tape142ppr_c2

460.0095.00 rpm


0.15

0.00

°

180.00

-180.00

°





Zebra disc Zebra tape

Dual beam laser Incremental encoder

Order 1

Order 4


Figure 5: Measured torsional orders of camshaft in run-up test with 4 open cylinders

Figure 6: RPM time variations of camshaft in run-up test with 4 open cylinders; measurements with zebra

tape (with and without butt joint correction) and incremental encoder

1 cylinder closed

The torsional vibration measurement results for a run-up test with 1 cylinder closed are shown in figures

7-9. The large pressure changes (once per camshaft revolution) in the closed cylinder cause strong RPM

variations which are clearly visible in figure 9. The large RPM drop every rotation yields multiple

torsional orders as shown in the RPM-frequency colormap in figure 7. Here again, the torsional vibration

results of the 4 measurement methods are very similar within the 30 dB dynamic range. This is also clear

from the order sections in figure 8, showing very similar amplitude and phase profile, with the order 1

from the zebra disc as the only exception.

460.0095.00 rpm


0.02

0.00

°

180.00

-180.00

°





171.05170.71 s

435.00

300.00

Real

rpm

F 4001:Zebra_tape142ppr

F 4006:Zebra_tape142ppr_c2

F 4003:Incremental_Encoder1024ppr

171.05170.71 s

435.00

410.00

Real

rpm



Order 16


Figure 7: RPM-frequency colormap of torsional vibration measurements on camshaft in run-up test with 1

cylinder closed: dual beam laser, incremental encoder, zebra disc and zebra tape

70.000.00 Hz


265.00

80.00

20.00

-10.00

dB

rpm

70.000.00 Hz


265.00

80.00

20.00

-10.00

dB

rpm

70.000.00 Hz

Zebra_disc120ppr(g) (CH14)

265.00

80.00

20.00

-10.00

dB

rpm

70.000.00 Hz


265.00

80.00

20.00

-10.00

dB

rpm


Zebra disc Zebra tape

265.0080.00 rpm


4.21

0.00

°

180.00

-180.00

°





265.0080.00 rpm


1.20

0.00

°

180.00

-180.00

°





Order 3

Order 1


Figure 8: Measured torsional orders of camshaft in run-up test with 1 cylinder closed

Figure 9: RPM time variations of camshaft in run-up test with 1 cylinder closed; measurements with zebra

tape (with and without butt joint correction) and incremental encoder

6.3 Crankshaft measurement results

From the measurements on the crankshaft, similar observations can be made with regard to the dual beam

laser, incremental encoder and zebra tape. The interesting new element here are the results of the direct

pulse measurements on the flywheel with the magnetic pick-up. From the colormaps in figure 10 one can

clearly notice that the torsional vibration footprint obtained from the magnetic pick-up measurements is

similar to those of the other techniques. This is also confirmed by the order profiles in figure 11, showing

that even the very low torsional orders with amplitudes of less than 0.01 degrees are properly identified by

all methods. The high performance of all techniques is also clearly reflected in figure 12, showing the

RPM variations in a short time period of 3 seconds. The two butt joint spikes per cycle (crankshaft rotates

twice as fast as the camshaft) are well removed by the butt joint correction algorithm.

265.0080.00 rpm


0.34

0.00

°

180.00

-180.00

°





Order 5

111.05109.89 s

182.21

98.10

Real

rpm




111.05109.89 s

182.21

152.66

Real

rpm




Figure 10: RPM-frequency colormap of torsional vibration measurements on crankshaft in run-up with 1

cylinder closed: dual beam, incremental encoder, zebra tape and gear teeth measurements

Figure 11: Measured torsional orders of crankshaft in run-up test with 1 cylinder closed

100.000.00 Hz


525.00

160.00

30.00

-15.00

dB

rpm

100.000.00 Hz


525.00

160.00

30.00

-15.00

dB

rpm

100.000.00 Hz

Flyw heel_magnet116ppr (UNKNOWN16)

525.00

160.00

30.00

-15.00

dB

rpm

100.000.00 Hz


525.00

160.00

30.00

-15.00

dB

rpm


Zebra tape Magnetic pick-up

525.00160.00 rpm


7.30

0.00

°

180.00

-180.00

°




Order 0.50 Flyw heel_magnet116ppr

525.00160.00 rpm


0.03

0.00

°

180.00

-180.00

°




Order 5.00 Flyw heel_magnet116ppr

Order 0.5

Order 5


Figure 12: RPM time variations of crankshaft in run-up test with 1 cylinder closed; measurements with

zebra tape (with and without butt joint correction), incremental encoder and magnetic pick-up

7 Conclusion

It is known since a long time that the dual beam laser and incremental encoder are good and accurate

measurement techniques for torsional vibration testing. However, the set-up space of the laser system and

relative complex instrumentation of the incremental encoder limit their usage for in-vehicle and mobile

measurements. Zebra tape, zebra disc and direct gear teeth measurements do not suffer from these

limitations which is obviously a benefit. Next to this, they also perform well in terms of accuracy. With

various experimental tests on a Fiat Punto engine, we have demonstrated that the torsional vibration

results obtained with these measurement techniques correspond very well to those of the dual beam laser

and incremental encoder.

References

[1] K. Janssens, P. Van Vlierberghe, W. Claes, B. Peeters, T. Martens, Ph. D’Hondt, 2010. Zebra tape

butt joint correction algorithm for rotating shafts with torsional vibrations. ISMA Conf., Leuven,

Belgium, 20-22 Sept., 2010.

26.0623.70 s

191.00

98.00

Am

plit

ude

rpm

1.00

0.00

Am

plit

ude



F 3334:Flyw heel_magnet116ppr

26.0623.70 s

192.00

98.00

Am

plit

ude

rpm

1.00

0.00

Am

plit

ude




F 3334:Flyw heel_magnet116ppr


comparison of torsional vibration measurement...

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