## ROTATIONAL AND TORSIONAL VIBRATION ANALYSIS

## WHAT ARE ROTATIONAL AND TORSIONAL VIBRATIONS?

Torsional vibrations are mechanical vibrations that occur due to periodic torque fluctuations on a rotating shaft. The torque fluctuation leads to a speed fluctuation which is superimposed on the average rotational speed. A characteristic feature of torsional vibrations is that the frequencies of the speed and torque fluctuations are usually synchronous with the revolutions of the shaft. Instead of frequencies, one then speaks of rotational harmonics – also called orders.

## WHAT CAUSES TORSIONAL VIBRATIONS ?

Torsional vibrations are caused by non-uniformities:

• **Non-uniform drive torque**

fluctuations on the drive side e.g. in the case of the internal combustion engine due to the non-continuous combustion and the crankshaft geometry.

• **Non-uniform braking torque**

fluctuations on the driven side e.g. in reciprocating compressors due to non-uniform forces during compression.

• **Transmission error**

A non-uniform transmission occurs, among other things, in the universal joint due to the geometry when the shafts are not parallel. Or due to backlash in the drive train when the direction of rotation changes or the power flow changes when the input and output sides change. In gears (gear and belt), geometrical deviations (such as eccentricity and tooth profiles) as well as deformations under load cause torque and speed fluctuations. In addition, the stick-slip effect (frictional vibration), for example, can cause non-uniform transmission.

## HOW CAN SPEED FLUCTUATIONS AND THE CORRESPONDING VIBRATION ANGLES BE VISUALIZED?

###### NO SPEED FLUCTUATION

With periodic, sinusoidal speed fluctuation, the gear does not run at a constant speed during one revolution. On one half of the revolution it is slower than the average speed and on the other half it is faster.

###### SPEED FLUCTUATION

The speed fluctuation itself is not visible in the trick shot, but its effect is. Mathematically, this effect is the integral over the speed variation and is called the vibration angle. The vibration angle (red line in img. 4) is the periodic advance and delay of the non-uniformly rotating shaft in relation to a uniform motion. This vibration angle is clearly visible in the trick shot as the swinging motion of the gear. Here it is a vibration angle of 6 degrees, which corresponds exactly to one tooth pitch.

## WHAT SHOULD BE CONSIDERED IN THE CASE OF TORSIONAL VIBRATIONS?

**Elasticity of the involved elements**The elasticity of components always leads to torsional vibrations when torque and speed fluctuate.

In this process, the shafts twist or warp in themselves. When the natural frequencies are excited,

there is a risk of resonance overshoot.

**Vibration ****propagation**

The vibrations are transmitted to other structures via the bearings of the shafts.

**Torsional** **vibrations** **depend**** on **:

– Temperature (oil, damping, thermal expansion)

– Aging and degree of wear

– Load condition and rotational speed

## WHAT ARE THE EFFECTS OF TORSIONAL VIBRATIONS?

Torsional vibrations cause problems in terms of:

**Comfort ****issues**All types of noise and vibration (NVH) problems

**Safety**

Wear and component failure due to aging (fatigue) or overstressing

**Accuracy**

Transmission errors of rotary motion; shafts do not run perfectly synchronized

**Efficiency **

Additional energy input that does not contribute to the drive

## WHY DO TORSIONAL VIBRATIONS HAVE TO BE MEASURED?

Accurate measurement and analysis of torsional vibrations is a requirement in engineering and vehicle development departments. In recent years, torsional excitation sources have increased in power and complexity. In addition, the use of lighter materials in engines and drivelines makes them more susceptible to torsional excitations. Continuous optimization of the engine, drivetrain, and rotating components is required to mitigate the resulting comfort and durability issues in new vehicle and rotating component development. Drivetrain simulation models can help development engineers predict and identify torsional resonance scenarios, for example, and design out the problems during the development phase. Detailed and accurate data is essential for fine-tuning, checking and confirming all vehicle improvement measures. Without appropriate data, accurate and meaningful modeling is not possible, as dynamic test data is a prerequisite for parameterization and verification of modeling assumptions.

## WHERE DO TORSIONAL VIBRATIONS OCCUR?

Torsional vibrations occur in rotating components, motors and powertrains.

## WHICH SENSORS ARE USED TO MEASURE SPEED?

The measurement of the rotational speed or angular velocity is usually carried out by means of

**magnetic scanning**of an existing gear or an easily mounted toothed disk- Using an optical or magnetic incremental encoder on the shaft
- Scanning of black and white markings by means of
**laser optics**.

The use of the respective sensor depends on the particular application, the environmental conditions as well as the required resolution.

## ROTATIONAL AND TORSIONAL VIBRATIONS ANALYSIS PRINCIPLES AND MEASUREMENT

We provide 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 (12 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).