Advances in Acoustics and Vibration

Volume 2016 (2016), Article ID 9820768, 9 pages

http://dx.doi.org/10.1155/2016/9820768

## Vibration Sideband Modulations and Harmonics Separation of a Planetary Helicopter Gearbox with Two Different Configurations

Mechanical Engineering Department, Prince Mohammad Bin Fahd University, AL-Khobar, Saudi Arabia

Received 20 June 2016; Revised 19 September 2016; Accepted 11 October 2016

Academic Editor: Kim M. Liew

Copyright © 2016 Nader Sawalhi. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

#### Abstract

This paper examines the spectrum and cepstrum content of vibration signals taken from a helicopter gearbox with two different configurations (3 and 4 planets). It presents a signal processing algorithm to separate synchronous and nonsynchronous components for complete shafts’ harmonic extraction and removal. The spectrum and cepstrum of the vibration signal for two configurations are firstly analyzed and discussed. The effect of changing the number of planets on the fundamental gear mesh frequency (epicyclic mesh frequency) and its sidebands is discussed. The paper explains the differences between the two configurations and discusses, in particular, the asymmetry of the modulation sidebands about the epicyclic mesh frequency in the 4 planets arrangement. Finally a separation algorithm, which is based on resampling the order-tracked signal to have an integer number of samples per revolution for a specific shaft, is proposed for a complete removal of the shafts harmonics. The results obtained from the presented separation algorithms are compared to other separation schemes such as discrete random separation (DRS) and time synchronous averaging (TSA) with clear improvements and better results.

#### 1. Introduction

Vibration signals originating from a helicopter transmission gearbox represent a rich source for monitoring its health. Many failures that occur in rotating components such as gears and bearings often show their signature in the vibration signal and can be well detected at early stages. Monitoring these vibrations often requires an extensive interpretation by a trained diagnostician, due to the complexity of such systems [1]. A major part of this involves the correct understanding and identification of the frequency content of the vibration signal. Understanding the frequency content of the signal and the different families of harmonics and sidebands would enable a correct analysis of the health of the machine.

Signals are mixtures of different sources. For successful handling and interpretation of signals, analysts often need to separate these different sources and process them separately. One of the most successful ways of interpreting signals is the use of Fast Fourier Transformation (FFT), which transforms the signal from the time domain into the frequency domain by using sines and cosines as base functions for the signal decomposition. FFT requires the transformed signal to be stationary; that is, it has some statistical parameters which do not change with time. For nonstationary signals (have time dependent statistics), the use of time-frequency presentation such as the spectrogram (short time-frequency analysis), the wavelets, the winger vile transform, and so forth is commonly used. Stationary signals are mainly composed of deterministic (discrete) components and random components. Random components contain all nonstationary signals in addition to any nondeterministic part. Deterministic components are those which can be expressed as a series of discrete sinusoidal signals (thus they are predictable and periodic). Deterministic component can be interchangeably referred to as discrete signals. They generally fall into two main categories:(i)Periodic (cyclic): they are composed of sinusoids whose frequencies are all integer multiples of some fundamental frequency like the shaft speed in rotating machinery; The multiples of the fundamental frequencies are known as harmonics, with the fundamental being the first harmonic; periodic components can also manifest themselves as sidebands around a carrier frequency in the case of a modulated signal (e.g., a gearbox signal where the shaft speed (low frequency) modulates the gear mesh frequency (high frequency))(ii)Quasi-periodic: they have at least two frequency components that are not rationally related and thus never repeated themselves exactlySignal modulation or distortion occurs when the amplitude, frequency, or phase of a waveform is altered by the introduction of another physically related periodic signal or disturbance. The high frequency signal is known as the “carrier.” The spectrum of the combined signal exhibits a discrete and dominant frequency (carrier) bounded by “sidebands” or peaks (modulator) spaced on either side of the carrier at the modulation frequency. Figure 1 illustrates the amplitude modulation. Figure 1(a) is the carrier signal, a pure sine wave with 30 Hz frequency in the time domain. Figure 1(b) displays the modulating signal, a pure sine wave with 5 Hz frequency. Figure 1(c) shows the modulated signal in the time domain. Figure 1(d) is the modulated signal in the frequency domain. The two sidebands can be identified easily.