Torsional and rotational 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.


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-mass flywheels and driveline vibration absorbers may be employed as a means of reducing or eliminating unacceptable levels of torsional vibration.


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 (time-equidistant sampling).


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).


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].

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.


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.

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.


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 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.

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.

Author: Séan Adamson


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. REFERENCES1. 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 Drehschwingungsmessungzur 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. 10. Heidenhain GmbH, Traunreut, Germany. Rotary Encoders Catalogue 2008.