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New testing innovations increase the accuracy and efficiency of torsional vibration analysis

High Level of Integration Simplifies the Assessment of Torsional Vibration in
Conjunction with other Noise and Vibration Signals

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 behavior of systems and components to be assessed accurately in order to avoid comfort and durability related problems. The innovative LMS QTV (Quad Torsional Vibration) modules allow engineers to analyze the torsional vibrations of transmission-related systems and components in context of other synchronously processed noise and vibration performance characteristics. The QTV modules’ capacity to directly measure encoded pulse trains and convert them into data streams enables them to accurately quantify undesired speed fluctuations of rotating components. LMS Test.Lab software and LMS SCADAS hardware in combination with the new QTV module form an integrated testing solution capable of performing complete dynamic test surveys that also include torsional vibration measurements.

The source-transfer-receiver model 

A common way to describe dynamic problems is applying the source transferreceiver model (Figure 1). Responses observed at a certain "receiver" location can be described in function of a "source" signal on one hand, and the way this signal is transmitted to the structure on the other hand. The effects of resonance and anti-resonance make that source signals can be amplified or attenuated as they travel along specific transmission paths to the receiver locations. 

The vibrations at receiver locations are a combination of rigid-body modes and flexible modes. Typically, rigid-body modes do not generate excessive internal stresses, while flexible-body modes Figure 1: The source-transfer-receiver model for torsional vibration are able to generate stress levels that potentially cause durability problems. Transfer path analysis is performed to determine the relationships between noise signals at specific receiver and source locations, by taking into account the available transmission paths present and their respective dynamic transfer functions. 

Torsional vibrations can be treated in a similar way. At the source side, there is a specific excitation, for example an acyclic input moment that is applied to an engine. The transfer of this excitation is not just influenced by system dynamics like shaft resonances, but also by dynamics that relate to gear or belt transmissions, for example. At the receiver side, the speed variations of the rotating components are measured. If these rotational speed variations are uniform along a specific axis, they are not considered as "torsion" in the strict sense (e.g. "rigid body mode" of translational vibration analysis). However, if the rotational speed variations show phase and/or amplitude differences along such an axis, real "torsion" occurs. And in case the frequency of the excitation approximates the rotational resonance frequency, excessive internal stresses may occur and introduce durability problems. 

Figure 1: The source-transfer-receiver model for torsional vibration

In this application note, rotational speed variations are called "torsional vibration", regardless whether real torsion is involved or not. As with any other NVH source, rotational speed variations and the resulting variations in torque need to be assessed when testing and optimizing the dynamic performance of systems.

Engine-related torsional vibration sources

Figure 2: Example gas pressure vs. crank angle for different rpm values

In drivelines that are powered by reciprocating engines, the primary source of torsional vibrations is often the engine itself. The operation of reciprocating engines typically introduces varying gas forces, which have a specific component that creates varying mechanical moments around the crankshaft axis (Figure 2). This results in irregular rotational speed and torque variations of the crankshaft. 

Also the inertia effects of moving parts, such as piston and connecting rod, induce torque variations on the crankshaft. Today, an increasing number of engines are designed in such a way that these motion irregularities are smoothened to a large extent, for example by tuning the characteristics of flywheels and torsion dampers. Although certain levels of torque variations remain present under normal stationary conditions, other phenomena, such as cylinder misfiring, engine start/stop and load variations, may cause abnormal or transient torque variations. Manufacturers across a wide range of industries are confronted with torsional vibration issues, since this phenomenon influences the comfort and durability performance of practically any powerdriven mechanical system, including cars, trucks, boats, power units and propeller aircrafts. 

Electrical engines are another type of engines that create varying torques and generate torsional vibrations. AC synchronous engines inherently generate important torque fluctuations that are proportional to the slip of the engine, which represents the difference between the actual speed and its nominal speed (net frequency). This means that specific problems may occur during the start up of such engines, for example when torque fluctuations coincide with important structural resonances. Once these engines are at operational speed, these significant torque variations no longer exist. Torque and rotational speed variations may also result from varying loads, which may be caused by gas or fluid pressure pulsations in compressors, turbochargers or pumps.

Figure 3: Example of frequency map gear whine (left) and gear rattle (right) problems in a gearbox (rpm vs. frequency axis)

Transmission-induced torsional vibrations

Apart form the engine itself, torsional vibrations can also be generated or amplified at many other locations in the transmission. Hooke’s, Cardan or universal joints inherently create a variation of the rotational speed, which depends on the angle of the joint. If both the incoming and outgoing axes are parallel, the use of a double joint is an aid that significantly reduces torsional vibration. However, the slightest misalignment between both axes automatically leads to increased levels of torsional vibration. 

Clutches also have to be well designed to reduce the risk for torsional vibrations. Clutch chatter occurs when a periodic torque change is generated in a slipping clutch, whose natural frequency range is similar to that of the drivetrain dynamically separated from the clutch. While in most cases the chatter appears as a vibration in the longitudinal direction of the vehicle, passengers sometimes perceive it as interior noise. Another clutch-related discomfort is clutch whoop, which occurs during engaging and disengaging the clutch. This induces a low frequency vibration of the pedal that increases during the pedal travel and is accompanied by an unpleasant noise.

Shafts need to be carefully designed to make sure their torsional resonance frequencies will not interfere too explicitly with the operating range of the engine. It is a fact that torque variations result in torsional resonances as well as bending resonances. Resonances in belts can also create rotational speed variations of the pulleys they drive, or the other way around, rotational speed variations may cause changing belt tension, and hence slip between belts and pulleys.

Torsional vibration also plays an important role in gearbox design and manufacturing, as this phenomenon potentially creates different types of discomforts. Gear mesh irregularities can create high contact forces, which in turn may create variations in torque and rotational speed. Gear whine, for example, is a noise problem that is introduced by torque fluctuations at the contact points between powered gears. As can be seen on Figure 3, gear whine is very much order-related. The generated noise will be transmitted to the gearbox, and may be amplified further when the frequency coincides with a resonance frequency of the housing. 

Figure 4: Measuring multiple torsional vibration signals along with other noise and vibration signals,
using a LMS SCADAS III front-end containing a QTV module

Gear rattle is a random noise that is generated by the teeth of non-powered gears that impact one another, due to variations of the input torque. This explains why gear rattle noise is a rather broadband noise. Also during transient situations, for example when shifting gears, specific dynamic phenomena may occur, with disturbing noises as a result.

How to measure torsional vibration?

The most common way to measure torsional vibration is the approach of using equidistant pulses over one shaft revolution. Dedicated shaft encoders as well as gear tooth pickup transducers (induction, hall-effect, variable reluctance,
etc.) can generate these pulses. The resulting encoder pulse train is converted into either a digital rpm reading or a voltage proportional to the rpm. Typically, digital readings are difficult to integrate and synchronize with other measurement channels, while rpm-proportional voltages introduce significant inaccuracies resulting from high-frequency frequencyto- voltage conversions. 

The use of a dual-beam laser is another technique that is used to measure torsional vibrations. The operation of the dual-beam laser is based on the difference in reflection frequency of two perfectly aligned beams pointing at different points on a shaft. Despite its specific advantages, this method yields a limited frequency range and represents an expensive solution in case several measurement points need to be measured in parallel. 

A new alternative approach is the LMS QTV (Quad Torsional Vibration) module, which can be plugged into any frontend of the LMS SCADAS III family of multichannel acquisition systems. The QTV module features digital frequencyto- rpm conversions that are accurate and practical at the same time. These modules are able to directly convert encoder pulse trains into data streams consisting of time samples that represent the instantaneous rotational speed at different moments in time. Besides eliminating rather inaccurate external frequency-to-voltage conversions, the use of QTV modules allows torsional vibration measurements to be acquired simultaneously and synchronously with other measured sound and vibration signals. In addition, QTV modules offer higher measurement accuracy and increase the flexibility and efficiency of measurement setups. 

Figure 5: The LMS SCADAS III front-end family

The LMS SCADAS III front-end family

LMS SCADAS represents a modular hardware platform that covers a wide variety of noise and vibration measurement applications. Its front-end frames come in 3 different sizes, and each frame is set up either as a master or a slave unit. The AC or DC powered LMS SCADAS 305 frame is ideal for small portable solutions, as it offers up to 60 measurement channels. Larger LMS SCADAS frames can be configured to provide up to several hundreds of measurement channels that can be acquired simultaneously. 

All LMS SCADAS acquisition modules can be used in any frame size. They all operate on 24-bit ADC and provide sampling frequencies up to 204.8 kHz per channel. In throughput mode, raw time signals can be recorded at a sustained throughput rate of more than 6 Megasamples per second. This means that the system is capable of recording the pulse train signals of many channels simultaneously. 

The QTV module has 4 input channels per module, and generates samples equal to the instantaneous rotational speed. The channels of QTV modules that are not used for torsional vibration measurements can be switched into analog mode, which allows these channels to be used as acceleration or microphone channels. 

Besides the QTV module, there exists a wide variety of LMS signal conditioning modules: the PQA and PQFA for voltage or ICP input, the QMO for microphone input and the PQCA for charge input. The QDA module also includes digital signal audio input. All these signals are conditioned and processed internally to generate synchronous data, which are readily available for further processing such as FFT, synchronous order tracking or octave analysis. The possibility to record all raw time signals is also offered. This extensive offering of conditioning modules enables test teams to easily combine the acquisition of torsional vibration, translational vibration and sound measurements. 

Figure 6: Rotating Machinery testing solutions with LMS Test.Lab

Measuring torsional vibration with LMS Test.Lab

Next to enabling data-acquisition hardware, the availability of suitable and powerful software solutions is also critical, not just to drive the hardware but also to process the results in a well-organized and efficient manner. 
The LMS Test.Lab software family is designed for general sound and vibration measurements and tightly integrates with the LMS SCADAS III measurement platform. One member of the LMS Test. Lab product family is a dedicated solution for rotating machinery testing and shares a common platform and database with all other solutions integrated in LMS Test.Lab.

Figure 7: Example of the workflow that consecutively guides users through each individual process
step – each with its own specific screen layout (shown: pulse signal with detection level)

The software has been designed to streamline the complete process and to guide users through consecutive process steps, without eliminating the flexibility to go back to a previous process step or to customize the way the processing has to be performed. 

A typical workflow (Figure 7) covers the measurement setup, test definition, test execution, test validation and reporting. The execution of a test may include one or more processing types and the validation of the acquired data can be efficiently verified or compared with previous references. For torsional vibration, this workbook concept allows efficiently setting up the parameters that define the measurement and decoding of the pulse signals. The instantaneous rpm values can be viewed and evaluated on the screen. Also raw time signals can be visualized, which makes it easy to quickly set up parameters such as trigger level, trigger slope, hold-off and hysteresis. Such time signal displays also facilitate troubleshooting efforts in case poorquality signals are acquired, for example due to a defective probe. 

Figure 8: Time, frequency, order and spectral map of a torsional vibration signal

The processing of torsional vibration channels can be performed similarly to other types of vibration signals, which provides the additional benefit of being fully synchronized with them. 

Figure 9: Verification measurements of drivetrain torsional vibrations
Upper right: rotational measurement location
Lower left: spectral map showing torsional resonances
Lower right: calculated versus measured torsional vibrations

In LMS Test.Lab, it is possible to process signals to instantaneous values of the rpm, which can be expressed in rpm, rad/ sec or deg/s (Figure 8). In this practical case, rpm variations are measured on an engine flywheel. LMS Test.Lab performs the integration or differentiation of dominant cycles per revolution on-line, allowing angular displacement or angular acceleration to be calculated on the spot. The spectral content can be measured instantaneously, or in function of rpm (spectral map). The same data can also be resampled synchronously (order map). Individual frequencies, or individual harmonics or orders, can be extracted and expressed in function of any of the measured rpm signals, including the QTV signals. These powerful capabilities make that post-processing is rarely required.

In addition to processing each specific channel individually, the possibility is offered to derive calculated quantities on-line. By using this "derived channel" concept, it is very easy to calculate for example the frequency spectrum of the relative shaft torsion (by integrating and subtracting channels). Further processing on the incoming data can be defined using the "time signal calculator". This calculator enables engineers to perform mathematical operations on incoming time data, such as filtering and removing trend, or integrating and differentiating data. Such processing capabilities can be applied as part of pure interactive post-processing or instant automatic calculations that take place immediately after the measurements. In this way, relative torsion angles or the slip between pulleys can be efficiently measured, or rotational speed can be converted systematically to tangential acceleration or displacement. Since the phase information is kept together with other measurement data, it is possible to animate both rotational and translational vibrations on a geometry model. This provides a better understanding of the vibration shapes that may occur under specific operating conditions.

Figure 10: Example of time signals indicating rpm variations during a coastdown measurement (left)and  corresponding spectral maps (4 torsional vibration and 2 accelerometer signals) Shaft resonances appear as vertical lines in the upper 4 spectral maps.

Application examples

1. Analysis of engine and driveline torsional vibration

Driveline torsional vibrations that occur in vehicles that are equipped with an automatic gearbox may lead to increased fuel consumption. At low rpm, the torque converter of the automatic gearbox is active. The earlier the torque converter can be disengaged and bypassed by a lock-up clutch, the better the fuelefficiency. Torsional vibrations in the drivetrain may prevent this early locking of the torque, which results in increased fuel consumption and decreased driver comfort. Figure 9 illustrates a project that features a hybrid approach that has been developed to predict the torsional vibrations of a full vehicle during an engine runup performed on a chassis dyno. The foundation of this hybrid approach is a multibody model of the full car, which takes into account the flexibility of all major component.

As the project proceeded, the engineers were able to gradually assemble a reliable model, as more and more subcomponents were validated individually. To validate the complete model, the engineers performed full-vehicle verification measurements, including 4 microphone, 120 acceleration and 9 torsional vibration signals.

2. Torsional vibration on multiple shafts

This section describes the measurements that were performed to analyze the rotational vibration behavior of a machine with 2 shafts, which are fully synchronized by means of synchronization gears. The shafts are measured both at the drive side and the synchronization side. The controlled coastdown measurements (Figure 10) are performed using inductive transducers on the gears. The time signal of the drive engine serves as the reference (green line), and the rotational speed values of the first shaft are shown in red and blue. The spectral maps of the 4 rpm signals and two additional vibration signals are also shown. 

The vibration around an averagely decreasing rpm is clearly indicated. It is also visible that the rpm variation has a component that is proportional to the harmonics of the shaft rotation, and that there are a number of fixed frequency resonances. Also interesting is that the spectral maps of both synchronization gearwheels are very similar. Analysis of their respective phases reveals that the phases of these vibrations are opposite, as can be explained by the fact that both gearwheels are synchronized and rotate in opposite directions.

3. Torsional Vibration analysis of a forestry mower

Figure 11 shows the rpm signal that is measured during the startup of a forestry mower as well as during opening and closing operations of the clutch. 

The rpm of the engine is displayed in red, the rpm of the clutch in blue. During full-throttle acceleration, the engine rpm remains stable during a fraction of a second, while the clutch rpm starts oscillating at a fixed frequency. The torsional resonance is excited by the 0.5th harmonic of the engine, which in this case is a 1-cylinder 4 cycle engine. Detailed analyses of the rotational signals indicate  that there is a 6-degree oscillation around this frequency. The oscillation corresponds to the gear teeth clearance in the gear transmission that is close to the tool. This situation creates gear rattle, and generates a reaction force in the gear transmission under a skewed angle. In addition, the tool protector resonance coincides with the same frequency.

Figure 11: Illustration of rpm variation analysis of a forestry mower


Torsional vibrations potentially cause durability problems as well as noise vibration and comfort problems, due to the interaction of torsional and structural vibrations. The QTV module in combination with LMS Test.Lab software and LMS SCADAS III hardware greatly simplifies the way torsional vibration measurements are performed. Moreover, QTV modules provide highly accurate readouts of multiple torsional vibration measurements in real-time, which can be processed as part of larger assessments that also include other noise and vibration signals.

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