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MEASUREMENT AND ANALYSIS OF TORSIONAL VIBRATION
IN AUTOMOTIVE DEVELOPMENT
Dr. Seán Adamson
VISPIRON ROTEC GmbH
Originally published in German in VDI-Berichte No. 2077, 2009
Abstract
Torsional vibrations are mechanical vibrations caused by time-alternating torques which are
superimposed on the otherwise steady running speed of a rotating shaft. In automotive
engineering torsional vibration is primarily caused by the fluctuations in engine power output.
This results in crankshaft angular velocity fluctuations which cause twisting and untwisting
of the shaft. The effects of torsional vibration are amplified by torsional resonance which
occurs when a shaft‘s natural frequency coincides with its torsional frequency. Excessive
torsional vibrations can result in unwanted noise, powertrain component wear and, in severe
cases, broken shafts. To identify such effects in advance and adopt measures to avoid them
before ex-cessive damage has occurred, the development engineer requires dedicated,
state-of-the-art measuring equipment incorporating application-specific software to
simplify measurement setup and provide quick analysis. This paper begins by discussing
several subtleties of dynamic torsional vibration testing. Two applications in automotive
development – clutch/dual-mass flywheel measurements (conducted in-vehicle) and timing
belt optimisation (on a dedicated engine test rig) – are then described in detail.
1. INTRODUCTION
Accurate measurement and analysis of torsional vibration is often a requirement in vehicle
development, refinement and optimisation [1 - 7]. In recent years torsional excitation sources
have increased in power and complexity. In addition, the use of lighter materials in engines and
powertrains make them more prone to torsional excitation. In order to alleviate the resulting
comfort and durability problems which arise while developing new vehicles, continuous
optimisation of engine and powertrain components is required. Development engineers can
use driveline simulation models to e.g. predict and identify torsional resonance scenarios and
design-out the problems during the development phase. However, detailed and accurate
experimental data are essential for fine-tuning, control and confirmation of all vehicle
improvement measures. Without appropriate experimental data, accurate and meaningful
modelling is not possible since dynamic test data are a prerequisite for both parameterising
and verifying the modelling assumptions. The main cause of torsional vibrations is the internal
combustion engine. The conversion of reciprocating power to rotating power through the
crank mechanism generates a variable torque because of the geometry of the system. Each
cylinder accelerates at the time of combustion, generating a torque pulse which is followed
by deceleration through the exhaust and intake strokes. The resulting crankshaft torsional
vibrations deserve careful attention because they are transmitted via belt, chain and/or gear
drives to the camshaft(s) and accessory drive components. Furthermore, they may also
reach the gearbox, propeller shaft, differentials and side shafts. Crankshaft dampers, dual-
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mass flywheels and driveline vibration absorbers may be employed as a means of reducing
or eliminating unacceptable levels of torsional vibration.
2. MEASUREMENT AND ANALYSIS PRINCIPLES
Vispiron Rotec, based in Munich, Germany, provides specialist equipment for the
measurement and analysis of torsional vibration. The company‘s core product is the Rotation
Analysis System (ROTEC-RAS), a pc-based signal acquisition and analysis system [8].
Torsional vibration measurement re-quires detection of the times of occurrence of equally
spaced angular positions around a rotating shaft (e.g. measurement of gear tooth or encoder
pulse passage frequencies). Several types of transducers can be used to provide pulse signals
which are proportional to a shaft‘s rotational frequency. The RAS speed channels use digital
counters with a high-frequency clock (10 GHz, 40 bit) to record the time intervals between
pulses. This angular sampling provides a fixed number of data points per revolution which
is independent of the rotational speed. The momentary angular velocity of rotating shafts
is thus measured, i.e. the mean velocity from pulse to pulse. The vibration angle and the
angular acceleration are obtained by integration and differentiation of the measured angular
velocity respectively. These two calculations are important when investigating torsional
vibration problems. Another important calculation is the angle between two speed channels
(angle of twist of a shaft, transmission error between two coupled shafts). The RAS analysis
software, working primarily in the angle domain, provides comprehensive analyses in the
time and spectral domain (FFT order and frequency analysis). The RAS‘s near real-time
capability with display and analysis of all channels allows adjustment of test parameters
during the measurement. Apart from digital, 10GHz speed channels, RAS systems are also
fitted with additional measuring channels which facilitate conditioning and cap-ture of a
variety of analogue signals with sampling rates up to 400kHz. The distinctive feature of
ROTEC-RAS is the phase-matched acquisition of all signals: speed signal acquisition with
variable discretization of time (angle-equidistant sampling) and acquisition of analogue
signals – acceleration, force, pressure, torque, etc. – at constant time intervals (timeequidistant sampling).
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3. ROTATIONAL SPEED SENSORS
Measuring the rotational speed (angular velocity) of a rotating shaft is generally accomplished
by one of three methods (Figure 1):
• mounting a precision gear on the shaft and using a stationary, non-contacting magnetic pickup to generate a pulse each time a gear tooth passes the pickup
• reflecting a laser light source off lined tape attached to the shaft (analogous to the pulses obtained from the gear and particularly useful in hard to reach places)
• mounting a magnetic or optical incremental encoder onto the shaft [9].
The sensor electronics must output an angular velocity signal in the form of a TTL pulse
train. De-ciding to use a particular sensor depends on the application, physical constraints
in applying the sensor as well as the required accuracy and resolution. The accuracy of
different methods, sources of error such as gear tooth pitch etc. were discussed in detail
elsewhere [1].
Figure 1:
Ferromagnetic toothed wheel as target for magnetic pickup (left).
Striped tape as reflecting target for laser sensor (centre).
Incremental rotary encoder (right).
3.1 SCANNING A TOOTHED WHEEL
Figure 2 shows schematically the principle of non-contact speed measurement with a
differential magnetic sensor. The sensor head consists of two magnetoresistors and a
permanent magnet which form a measuring bridge circuit which is energised by a bridge
voltage. The sensor detects the movement of ferromagnetic materials such as gear teeth.
A tooth or a gap moving past the sensor changes the magnetic field. This causes changes
in the internal bridge resistance values. Signal Conditioning electronics convert the resulting
sinusoidal voltage to a digital square-wave signal whose leading and falling edges are then
output as a TTL pulse train with narrow pulses. The differential principle ensures that the
leading and falling edges correspond to the middle of the tips and roots of the gear teeth
respectively. The number of data points per revolution is thus doubled w.r.t. the number
of teeth. This is significant for analyzing higher orders since the accuracy of the calculated
amplitudes of rotational order harmonics depends on the number of data points per
revolution. The relationship between the number of teeth and the maximum order which can
be measured is given in [1].
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Figure 2: Rotational Speed Measurement with Differential Sensor, Angular velocity = Dq / DT
A: Rotating target gear.
B: Stationary, differential speed sensor.
C: Sinusoidal signal from sensor.
D: Intermediate square-wave from sensor electronics.
E: TTL output pulse train from sensor electronics.
3.2 ROTATIONAL DIRECTION REVERSAL
A reversal of the direction of rotation of a shaft may occur during startup and stopping of an
engine. The rotational direction may be sensed using a fourfold sensor. The magnetoresistors
are arranged in pairs as two differential sensors (Figure 3). Signal-conditioning electronics
generate two phase-shifted speed signals and a logic operation determines the direction of
rotation. Pulse train #1 (speed signal) and a direction bit are then output.
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Figure 3: Sensor with rotational direction recognition
A: Rotating target gear.
B: Stationary, fourfold sensor comprising two
differential sensors 1 & 2.
C: Two phase shifted pulse trains from sensor electronics .
3.3 ABSOLUTE ANGULAR DISPLACEMENT
Calculating the angular displacement between two speed channels is a frequent requirement.
In the standard analysis, this angle is set to zero at the beginning of the calculation process
(relative angle). In order to calculate the absolute angle, once per revolution reference marks
on both channels are required. The angle between these marks is then estimated and input
to the RAS software before the measurement is started. When using toothed wheels as
targets, a single tooth may be removed by machining to produce the once per revolution
mark. If one tooth is missing on the target wheel, a speed value approximately 50% lower
than the actual speed is measured once per revolution since the periodic time of the TTL
signal across the missing-tooth gap increases by a factor of two (Figure 4).
Figure 4: A: Target wheel with missing tooth. B: Differential speed sensor.
C: TTL signal with pulse period 2T once per revolution.
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Toothed wheels and gears have some degree of variation in tooth spacing. A toothed wheel
and magnetic sensor arrangement will generally provide less accurate angular velocity data
than an incremental rotary encoder. As shown in Figure 5, rotary encoders generally output
two wave forms which are 90 degrees out of phase with each other and a third output –
reference – which happens once every turn [9].
Analogous to the fourfold magnetic sensor (section 3.2), the order of arrival of the two
pulse trains, A and B, indicates the direction in which the encoder is turning. The reference
pulse, C, can be used to trigger measurements. Conditioning RAS electronics also allow
suppression of a pulse on pulse train A each time the reference mark is detected. Two rotary
encoders may thus be used for precise measurement of the absolute angular displacement.
The electronics also have LEDs for indicating the index pulse and facilitate setting the static
angular difference.
Figure 5: Output signals from an incremental rotary encoder.
Two phase-shifted square waves A & B. Reference mark C.
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4. APPLICATIONS
4.1 CLUTCH AND DUAL-MASS FLYWHEEL
A common application for ROTEC-RAS is in-vehicle testing of clutches and dual-mass
flywheels (DMF). To identify dynamic torsional vibration effects in torque transmission,
simultaneous measurement of speed on both sides of the clutch or DMF is required. On the
engine side, the starter ring gear may be scanned with a magnetic sensor. On the transmission
side a gear on the gearbox input stage must be accessed. Alternatively, a toothed rim can be
attached to the gearbox input shaft or bar code stripes wrapped around the shaft for speed
measurement with a laser.
4.1.1 CLUTCH MEASUREMENTS
Figure 6 shows test results from a speed run-up in fourth gear (4-cylinder engine, conventional
clutch). Magnetic speed sensors were used on the starter gear (132 teeth) and on a gearwheel
on the gearbox input shaft (27 teeth).
4500
4000
Speed [rpm]
3500
Engine
3000
Gearbox
2500
2000
1500
1000
500
0
5
10
15
20
Time [s]
Figure 6: Speed ramp. Time history data on both sides of the clutch
Figure 7 shows two revolutions of the speed curves in detail. The data points from the speed
measurements are also shown. The engine‘s firing order can be clearly seen (2nd order, twice
per revolution).
An FFT analysis shows additional orders since cyclical combustion is not a purely sinusoidal
process. The 3D waterfall plots (Figure 8) show order analyses of angular acceleration as
a function of speed. The gearbox acceleration peaks which occur at resonance-critical
speeds contribute to the unwelcome audible noise known as gearbox rattle. These 2nd
order resonance peaks can be reduced by modifying clutch friction and torsional stiffness.
Alternatively, a dual-mass flywheel (DMF) may be used. The main purpose of a DMF is to
counter gearbox rattle by damping the torsional vibrations at the input to the gearbox.
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Speed [rpm]
2450
2400
Gearbox
2350
Engine
2300
2250
2200
2150
200.0
200.5
201.0
201.5
Engine Revolutions
202.0
Figure 7: Speed data over two revolutions
1: 2.0000
Angular Acceleration [rad/(s*s)]
Engine
5000
4500
4000
3500
3000
2500
2000
1500
1000
500
0
0
4000
3500
1
3000
2
Order
2500
3
2000
4
1500
Engine Speed [rpm]
1000
2: 2.0000
Angular Acceleration [rad/(s*s)]
Gearbox
5000
4000
3000
2000
1000
0
4000
0
3500
1
3000
2
Order
2500
3
2000
4
1500
Engine Speed [rpm]
1000
Figure 8: Angular acceleration [rad/s2], engine and gearbox
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4.1.2 MEASUREMENT OF DMF DRIVELINE RESONANCES
Dual mass flywheels (DMF) are installed in many modern vehicles with manual transmissions.
The DMF is located between the engine and the gearbox replacing the conventional flywheel.
The DMF isolates the driveline from engine excitation thus increasing driving comfort.
The primary inertial mass is connected to the output shaft of the engine. The secondary
inertial mass is connected to the input shaft of the gearbox thus increasing the moment
of inertia of the transmission. These two decoupled masses are linked by an elastic spring
system which permits relative rotary motion between the primary and secondary masses
(Figure 9). The use of the secondary mass and appropriate spring constants have the effect
of shifting the resonance speeds which excite the natural rattling frequency below the
engine idling speed, i.e. outside the normal driving ranges. The secondary mass also forms
one of the two friction surfaces for the clutch disc. The main disadvantage of the DMF is
that every time the engine is started or stopped it has to run through this resonance point.
Problems can then arise if e.g. the vehicle gets stuck in resonance. A further disadvantage of
the DMF is an increase in engine-side torsional vibrations due to the DMF‘s lower effective
moment of inertia on the engine side compared to a conventional flywheel.
Primary
mass
Starter
gear
Secondary
mass
Clutch
Gearbox
Engine
Spring damping system
Figure 9: Dual-mass-flywheel, schematic assembly
Figure 10 shows speed data from a measurement where the vehicle is sharply braked in
4th gear until drive train vibrations arise below idle speed. Speed sensors with directional
recognition were used (starter gear with 132 teeth, toothed rim with 170 teeth attached to
the secondary side). The data show large speed fluctuations when resonance is reached and
the direction of rotation reverses for a short time.
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1200
1000
800
Speed [rpm]
600
400
200
Transmission side
0
Engine side
-200
-400
-600
5
11
10
9
8
7
6
16
15
14
13
12
Time [s]
Figure 10: DMF driveline resonance. Time histories
With decreasing engine speed, the excitation in the transmission increases until, at
resonance, the primary to secondary mass angle reaches 120 degrees and the maximum
permissible engine torque is exceeded (Figure 11). This can damage the DMF or other
driveline components. Torque overload protection is provided by a torque limiter in the DMF.
When the torque limit is exceeded the DMF slips between the primary and secondary masses.
The drivetrain remains in resonance unless the clutch is activated or the vehicle is brought
to rest.
Relative Angular Displacement [degrees]
200
150
100
50
0
-50
-100
-150
-200
5
6
7
8
9
10
11
12
13
14
15
16
Time [s]
Figure 11: Driveline resonance. DMS relative angular displacement
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4.1.3 STARTING THE VEHICLE
As stated above, the main disadvantage of shifting transmission resonance below idling
speed is that when the vehicle is started it has to run through resonance. Figure 12 shows
data from a normal engine start – the engine runs through the resonance point and reaches
idling speed. The DMF angular displacement (angle between the engine and transmission
sides) reaches a maximum of about 45 degrees.
120
1100
100
1000
80
Transmission side
900
60

40
(1) Speed [rpm]
800
Engine side
700



20
600
0
500
-20
400
-40
300
-60
200
-80
100
-100
0
1.5
2.0
2.5
3.0
Time [s]
3.5
4.0
4.5
(2) Relative Angular Displacement [degrees]
1200
-120
5.0
Figure 12: Good engine start behaviour. Time and angular displacement

1200
120
1100
100
1000
80
900
60
800
40
700
20

600
0
Transmission side
500
-20
Engine side
400
-40
300
-60
200
-80
100
-100
0
4.0
4.5
5.0
5.5
6.0
Time [s]
6.5
7.0
(2) Relative Angular Displacement [degrees]
(1) Speed [rpm]
Figure 13 shows data from a bad engine start. The magnitude of the DMF angular displacement
causes the spring components to lock-out. The maximum DMF angular displacement is 60
degrees in both directions. The resulting torque causes the friction clutch disc to slip through
and the angular displacement curve runs away. In this case, poor engine management
parameters (injection volume, duration and time) in combination with a high DMF spring
rate caused the bad engine starting behaviour. The aim of this type of measurement is to
optimise the starting conditions and keep the DMF angular displacement below a set value
(for this particular DMF below 45 degrees).
-120
7.5
Figure 13: Bad engine-start behaviour. Time and angular displacement curves
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4.2 SYNCHRONOUS BELT DRIVE SYSTEM
Detailed experimental work is essential when developing today‘s valvetrain and timing drive
systems since the constituent components interact with each other and combine to produce
system performance characteristics. The complexity of modern engines often demands
acquisition and analysis of 8 or more speed channels together with multiple acceleration,force,
displacement, pressure, temperature, etc. signals.
The development work described below involves the timing (synchronous) belt system of
a 4-cylinder, common rail diesel engine. The benefits of common rail fuel injection systems
include reduced exhaust emissions, improved fuel comsumption and lower engine noise.
In order to help comply with emission limits for the next generation of engines a new injection
pump was installed. The main purpose of timing belt systems is to drive the camshaft
synchronously w.r.t. the crankshaft. The belt system described here additionally incorporates
the water pump and the injection pump within a single layer drive as shown in Figure 14.
On this particular engine the water pump pulley also served as idler pulley.
Following replacement of the injection pump the belt drive properties had to be investigated
and optimised. Speed ramp tests were conducted at full load on a motored test rig.
The aim of the first stage of the work was to define the optimised injection pump position.
Since proper tensioning is vital for belt performance and longevity, the purpose of the second
stage of the work was to define the correct tension range at the optimised injection pump
position (production tolerances and maximum/minimum allowable belt tension).
Camshaft
Injection pump
Belt tensioner
TIGHT SIDE
SLACK SIDE
Water pump
Crankshaft
Figure 14: Timing belt system
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The instrumentation used in the measurements is summarised in Table 1. The RAS system
enables parallel, phase-matched acquisition of the speed and analogue signals. In addition
to the standard RAS online and offline analysis software, an animated wire-frame model of
the belt drive system highlights the dynamics of amplitude and phase relationships versus
engine speed between all measurement positions.
Position
Signal
Sensor
Front of
crankshaft
Speed [rpm]
Incremental encoder
Camshaft pulley /
toothed wheel
Speed [rpm]
Magnetic sensor /
toothed wheel
Injection pump /
toothed wheel
Speed [rpm]
Magnetic sensor /
toothed wheel
Water pump pulley
Speed [rpm]
Laser / striped
disc encoder
Tensioner arm
Tensioner arm
movement [mm]
Potentiometer
Belt surface
(slack side)
Belt span
vibrations [mm]
Laser triangulation
Crankshaft pulley /
toothed wheel
Force [N] (1)
Strain gauges
(1) Effective belt tension = Difference in belt tension between the
entering (tight) and leaving (slack) sides of the crankshaft (driver) pulley
Table 1: Belt drive system: Measurement positions, signals and sensors used
4.2.1 OPTIMAL INJECTION PUMP POSITION
An important parameter for assessing the dynamic behaviour of the belt drive is the so-called
effective belt force (belt tension fluctuation). This is the difference in belt tension between
the tight and slack side spans and may be measured by attaching a strain gauge system to
the crankshaft pulley which is subjected to a torque along its radius. The belt forces may
be derived from this torque. The resulting analogue signal is then input to a RAS analogue
channel (sampling rate adjustable up to 400 kHz). Figure 15 shows the effective belt tension
for different injection pump positions (7 measurements: ± 1, ± 2, ± 3 teeth). Seven adjacent
teeth were marked on the belt. Between measurements, the belt was removed and the pump
shifted to a new angular position (i.e. one tooth forward or back relative to its initial position).
The effective belt tension is the force on the engaging belt teeth around the circumference
of the crankshaft pulley. This force determines the shearing load on the belt teeth.
Lower effective belt tension means lower loads on the teeth. The lower the tooth load is,
the longer the life of the timing belt. It follows that the injection pump position at +2 teeth
(bright red curve) is the optimal position regarding timing belt lifetime since the effective
belt tension is lowest for this position averaged over the entire speed range.
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1500
0
+2
-2
+1
-3 Teeth
+3
-1
Effective Belt Tension, max. [N]
1300
1100
900
700
500
300
800
1300
1800
2300
2800
Engine Speed [rpm]
3300
3800
4300
Figure 15: Maximum effective belt tension for different injection pump positions
The camshaft vibration angle (Figure 16) shows the influence of the injection pump position
on camshaft pulley torsional vibration and, in particular, torsional resonances. For example,
the data show a torsional resonance peak at an engine speed of 4000 rpm (pump position
-2 teeth, blue curve). Excessive torsional vibration indicates improper meshing of the belt
and sprocket teeth. Specified upper limits of vibration angle may not be exceeded since
this could result in reduced belt drive lifetime. Low values of vibration angle over the entire
speed range reflect proper belt meshing with the pulleys. Figure 17 shows similar data for the
injection pump pulley.
Vibration Angle, Camshaft Order 2 [degrees]
1.2
0
-2
+2
+1
-1
-3
+3
Teeth
1.0
0.8
0.6
0.4
0.2
0
800
1300
1800
2300
2800
Engine speed [rpm]
3300
3800
4300
Figure 16: Camshaft vibration angle for different injection pump positions
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Vibration Angle, Camshaft Order 2, [degrees]
1.2
0
-2
+2
+4
+1
-1
+3
-3
Teeth
1.0
0.8
0.6
0.4
0.2
0
800
1300
1800
2300
2800
Engine speed [rpm]
3300
3800
4300
Figure 17: Injection pump vibration angle for different pump positions
4.2.2 DEFINING THE TENSION AND DAMPING RANGE OF THE TIMING BELT SYSTEM
Correct tensioning of the timing belt is of the utmost importance since under-tensioning
causes slippage and overtensioning causes shorter belt life and excessive loads.
Because of manufacturing tolerances there is a significant degree of variation in the pretension and damping properties of timing drives. Once the best position of the injection
pump had been found, the tension range for proper belt installation had to be defined
keeping manufacturing tolerances in mind.
The dynamic behaviour of the timing belt drive with different pre-tensioning and damping
parameters was investigated. The drive‘s tension and damping range is based on certain
acceptance criteria for various measured parameters such as tensioner arm movement.
Tensioner Arm Movement, peak-peak [degrees]
18
16
14
12
10
8
6
800
1300
1800
2300
2800
Engine speed [rpm]
3300
3800
4300
Figure 18: Tensioner arm movement
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Figure 18 shows the envelope curve of the tensioner arm movement. The tensioner
moves constantly back and forth between the upper (red) and lower (blue) curves.
The difference between the two curves is the tensioner arm amplitude in degrees.
Durability tests are run to determine the lifetime of the tensioning system for difference
amplitudes and arm movement frequencies. The data from the envelope curves are then
used to confirm that tolerance limits important for tensioner lifetime are adhered to.
Effective tension is another parameter used for assessing the dynamic behaviour of the belt
drive (Figure 19). As stated above (Figure 15), the effective tension is the difference in belt
tension between the tight and slack sides of the crankshaft pulley and reflects the positive
values of tooth load on the driven sides and the negative values of tooth load on the driving
sides of the teeth. Changing the tension and damping range affects the effective tension.
1500
Effective Belt Tension [N]
1200
900
Max. Force
600
300
Average Force
0
-300
-600
-900
800
Min. Force
1300
1800
2300
2800
3300
3800
4300
Engine speed [rpm]
Figure 19: Effective belt tension
Belt span vibrations must also adhere to acceptance criteria when assessing the dynamic
behaviour of the belt drive system for different tensioners (Figure 20). Excessive belt vibration
causes noise, increased tensioner movement and incorrect belt tooth meshing with the pulleys
all of which must be avoided by determining optimal damping and tensioning paremeters.
A laser displacement sensor is used for measuring belt span vibrations (triangulation
principle).
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10
8
Belt Span Vibration [mm]
6
Maximum
4
2
0
-2
-4
Minimum
-6
-8
-10
800
1300
1800
2300
2800
3300
3800
4300
Engine speed [rpm]
Figure 20: Belt span vibrations
1. CONCLUSION AND OUTLOOK
5.
The Rotation Analysis System (ROTEC-RAS) was presented and shown to be a useful tool for
automotive development, in particular where the emphasis is placed on torsional vibration
testing. Worked examples were presented of both in-vehicle and test-rig testing which
dealt with typical engine and transmission torsional vibration issues. The data show how
multichannel measurement and analysis of both torsional vibration and related signals can
provide insight into the interactions between powertrain components even in the early
stages of the design process. The use of dedicated measurement and analysis equipment
helps shorten development cycles even further with the aim of achieving faster and more
effective realisation of new powertrain concepts.
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ACKNOWLEDGEMENTS
The author wishes to thank Ralf Till of ZF Sachs AG, Schweinfurt and Thomas Kirch of Gates
GmbH, Aachen for providing the measurement data presented in section 4.
REFERENCES
1.
Seán Adamson. Improved Approaches to the Measurement and Analysis of Torsional Vibration. SAE Technical Paper 2004-01-1723 (ISBN 0-7680-1319-4)
2. Michael Lauer, Jörg Gindele and Roland Ries. Hochauflösende Drehschwingungsmessung
zur Analyse von Verzahnungsgeräuschen im Triebsstrang. Haus der Technik Fachbuch,
Band 79. expert verlag 2007 (ISBN 978-3-8169-2686-3)
3.
Carsten Weber, Dirk Beismann, Seán Adamson and Markus Prem. Drehschwingungsanalyse
an Verbrennungsmotoren. MTZ 62 (2001) 3 (ISSN 0024-8525)
4. Seán Adamson. Verbesserte Verfahren zur Messung und Analyse von Drehschwingungen.
Haus der Technik Fachbuch, Band 25. expert verlag 2003 (ISBN 3-8169-2260-0)
5. Seán Adamson. Messung und Analyse von Drehschwingungen in der Kfz-Entwicklung.
VDI-Berichte No. 2077, VDI Verlag Düsseldorf 2009, pages 237-248 (ISBN 978-3-18-
092077-1)
6. Jeff. G. Sczepanski. New Equipment and Methodology to Perform High Speed Valvetrain
Dynamics Testing and Analysis. SAE Technical Paper 2004-01-1720 (ISBN 0-7680-
1319-4)
7. J. Derek Smith. Gear Noise and Vibration, Marcel Dekker, 1999 (ISBN 0-8247-6005-0)
8. Steve Goldmann. Vibration Spectrum Analysis. Industrial Press Inc., New York, N.Y. 1999,
pages 223-232. (ISBN 0-8311-3088-1)
9. Vispiron Rotec GmbH, Munich, Germany. ROTEC-RAS 2009 User‘s Manual. www.vispironrotec.de
10. Heidenhain GmbH, Traunreut, Germany. Rotary Encoders Catalogue 2008.
www.heidenhain.de
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VISPIRON ROTEC GmbH
Frankfurter Ring 224 • 80807 Munich • Germany • ) +49 (89) 323 651 0 • 7 +49 (89) 323 651 56 • rotec@vispiron.de • vispiron.de