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ROTEC Publications - 102 -

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MEASUREMENT AND ANALYSIS OF TORSIONAL VIBRATIONIN AUTOMOTIVE DEVELOPMENT

Dr. Seán Adamson

VISPIRON ROTEC GmbH

Originally published in German in VDI-Berichte No. 2077, 2009

AbstractTorsional 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 (time-equidistant 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 / DTA: 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).

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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Figure 7: Speed data over two revolutions

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.

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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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.

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.

Figure 12: Good engine start behaviour. Time and angular displacement

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).

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).

Figure 14: Timing belt system

Crankshaft

Water pump

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Belt tensionerInjection pump

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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.

Table 1: Belt drive system: Measurement positions, signals and sensors used

4.2.1 OPTIMAL INJECTION PUMP POSITIONAn 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.

(1) Effective belt tension = Difference in belt tension between the entering (tight) and leaving (slack) sides of the crankshaft (driver) pulley

Strain gaugesForce [N] (1)Crankshaft pulley / toothed wheel

Laser triangulation Belt span vibrations [mm]

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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.

Figure 16: Camshaft vibration angle for different injection pump positions

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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 pre-tension 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.

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.

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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Figure 20: Belt span vibrations

1. CONCLUSION AND OUTLOOK

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 • [email protected] • vispiron.de

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