*Advanced Structures India Pvt Ltd is an independent automotive product development company based out of Bangalore, India with operations in India, China and US. Below is blog entry from our engineers about Torsional Vibration – Measurement, Analysis and Failures. We can be contacted on business@advancedstructures.in for business enquiries and careers@advancedstructures.in for open positions.*

In recent years, the vibration behaviour of the rotating components has gained significant importance. Advancement in engineering technology, light weight designs, downsized engines and advanced torque lockup strategies , emphasize the importance of developing an in depth understanding of rotating component vibrations.

There are three methods for Analysing Vibration in Rotating Components:

i) **Angular Vibration:** How rotational speed is changing over individual rotations, it is also called as **Torsional Vibration**.

ii) **Twist:** Difference in rotation between the two points of the shaft.

iii) **General Noise and Vibration of Rotating Components: **This uses tachometer and other noise, vibration signal of the system to study the general characteristics of the rotating component.

In this blog our focus of discussion is on the Torsional Vibration (TV) parameters of rotary machine, its impact on them, measuring techniques, hardware requirement for data capture, processing, interpretation of result from the analysis and its reduction.

Torsional Vibration can diminish comfort as well as the efficiency of the machine and may even cause catastrophic failures. It has become a concern in the case of mechanical power transmission systems using rotating shafts and couplings, and is therefore important for automotive, turbo-machinery and marine drivelines to ensure robust design and to improve overall life of system.

# Understanding Torsional Vibration

Picture:-1. Torsional Vibration Graph

In the above graph blue line indicate the combined result of torsional vibration and mean RPM change, where as green line is the mean RPM. Torsional Vibration is the angular vibration in the rotating component of the machine. It represents the fluctuating component of the angular motion, which exists over the specific angular motion of the rotating machinery. Torsional vibrations are assessed as the variation of rotational speed within a rotation cycle.

Torsional vibration can be represented in three quantities i.e angular displacement, velocity and acceleration. All these are related to each other and can be obtained by integration or differentiation method.

## Torsional Vibration: Parameters and Affected Areas.

Picture:-2.TV parameters and affected areas

## Torsional Vibration in Internal Combustion Engine and Electric Drive

Picture:-3. Comparison ICE and ED

# Measurement of TV

## Measurement sensors for torsional vibration

For torsional vibration measurements the first step is to evaluate the rotational speed trace of the rotating object. Other parameters can be easily derived from this basic measurement. There are large numbers of sensors available for measurement of rotational speeds. Some of the commonly used sensors are:

Picture:-4. TV Measurement Sensors

## Data Capture (Hardware) Requirements for Measurement

Data acquisition parameters are associated with the actual acquisition of the physical quantity by a sensor/transducer. There are two main parameters that play a significant role in the quality of data acquired:

### 1. Number of Pulses Per Rotation (PPR)

Selection of number of pulses per rotation plays a vital role on the quality of data acquired. Less number of PPR will add error in data called aliasing effect in angle domain. The minimum-sensor resolution can be identified by using the three principles summarized below.** **

**i. Maximum order selection: **Maximum order that can be recorded is calculated based on bandwidth and the rotational speed. Thus for any fixed bandwidth, minimum RPM decides the maximum order that can be observed.** **

**MO = Bandwidth. 60 / RPM _{min}**

**ii. Frequency Bandwidth: **It is selected based on the system under analysis and should cover the highest order of interest. It is often difficult to estimate bandwidth of system, so to be on safer side 2 or 4 factor of safety can be applied.

**iii. Minimum pulses required per revolution- Nyquist-Shannon criteria: **If maximum order of interest is MO and system does not have any angular function above it, the ordinate points (i.e. pulse) should be spaced at 360/(2* MO) Deg[°] apart. In simple words number of pulse per rotation (PPR) must be greater than twice of MO.** **

**PPR > 2. MO**** **

### 2. Sampling Rate

Sampling rate is the number of equally spaced samples that we take for one second of signal. Sampling rate is of prime importance for accurate detection of tooth edges. It refers to the number of times the data acquisition system captures the sensor output. Hence if the sampling rate is too low the tooth edge would not be captured accurately. The capturing of the tooth edge plays a significant role in the accuracy of the detailed RPM curve derived using it. Therefore it should be kept as high as possible. The required sample rate depends on the size of the rotating element, number of teeth and maximum rotational speed.

Conventional data acquisition systems are limited in their precision by their maximum sampling rate, in some situations they simply cannot sample fast enough to quantify an entity that is moving very quickly. The measurement of torsional vibration has two factors to take into consideration: the underlying circular motion and the rotary fluctuation superimposed on the circular motion. Hence a data acquisition system should be quick enough to measure these fluctuations with accuracy and high sampling rate.

Picture:-5. Sampling Rate

Along with the sampling rate there is another quantity of interest called bit depth which represents the number of bits used for encoding each sample in memory (resolution of sampled point). Higher the bit depth will ensure better capture of the changes in the amplitude of the signal. The bit depth does not affect the performance of CPU as its operations are made on 32-/64- bit integer system, so there won’t be any issues in using 16-/24- bit data files during acquisition. Whereas, increasing the sampling rate (frequency) will take more amount of CPU memory for processing, as it would be capturing more points of data during acquisition.

# Processing and Analysis

Once the measurements are done, specific-processing techniques are used to quantify the torsional-vibration phenomena and to correlate them with other acoustic or vibration responses of the structure.

## Processing Domain

The pulsed data obtained by the tachometer is used for processing in the time domain as well as the angle domain. The details of analysis for both the domains using the basic pulse signal are as follows.

Picture:-6. Tacho Pulses

### 1. Processing in Time domain (Asynchronous sampling)

In time domain signal is sampled at equal intervals of time, without considering rpm of rotation throughout the measurement. The scheme has the advantage of being simple, and provides constant frequency bandwidth across measurement. Hence fixed sampling is an effective option when processing in time-frequency domain. Data acquired asynchronously may be converted to synchronously sampled data for further processing or can also be processed in time domain.

Picture:-7. Time Domain

### 2. Processing in Angle domain (Synchronous sampling)

Synchronous sampling refers to the sampling where the sensor input is processed at regular intervals of angle as opposed to time. For rotational measurements angle domain processing offers more advantages. Firstly, when processed in angle domain peak angular acceleration levels for individual crankshaft rotation can be evaluated, which can be correlated with the engine firing, pulses, etc. Secondly, angle domain processing allows for application of order based filters as opposed to single frequency filters. The advantage of working in the angle domain is that spectral analysis of the pulse periods produces order waterfalls and order spectra directly without recourse to interpolated resampling.

Picture:-8. Angle Domain

## Analysis after processing

Torsional vibration data is analysed to correlate with other parameters of sound and vibration and can be related to the components and their frequencies. Order and resonance based analysis are effective tool to identify torsional vibration levels in a rotating machinery.

– Torsional orders relates to a component with respect to the cyclic excitation of the rotating source. These orders are assessed at various critical moments to identify their behaviour and are correlated with the critical events and components. Colour map of torsional vibration data for a combustion engine provides relation between – speed, orders and amplitude, which helps in identifying frequency and order of interest.

**–**Resonance based analysis is useful to find the role of component natural frequency in amplifying the torsional vibrations. This analysis combined with modal analysis is effectively used to understand the natural frequencies of a structure, which are getting amplified based on torsional excitation from the source.

# Failures due to Torsional Vibration** **

Recognizing torsional vibration before excessive damage is difficult. Torsional oscillations occur as a twisting in the shaft, and can be measured only by the relative motion of rigid masses attached to the shaft. Some of the early warning indicators are excessive gear noise, gear hammer, gear wear, gear tooth failure, coupling failures, slippage of coupling hub, or high gearbox structural vibrations. It also causes loosening of coupling bolts or fretting corrosion under coupling hubs. Gear wear on unloaded side of the gear teeth should be monitored since excessive torsional vibration cause impacting of the gear teeth. If TV is suspected, shaft needs to be checked for fatigue cracks at any changes of geometry where high stress concentration occurs.

**The key areas at the risk of failures are:**

Picture:-9. Failures

# Reducing Torsional Vibrations** **

**Isolate excitation between components:**The coupling can protect the driven components by absorbing the dynamic torque generated by the engine.

Picture:-10. Damper** **

**Detune a torsional natural frequency:**With the use of a soft coupling, the first natural frequency can be tuned below minimum operating speed.

**Add damping to the system:**Some soft couplings can attenuate high torsional amplitudes which are the result of a resonant condition. Rubber elements provide hysteretic damping, shrink fit hubs, keyed, splined or bolted connections and sliding surface provide columbic damping and leaf springs provide viscous damping.

–

Harsh Gogri