Project topics and materials
Get Complete Project Material File(s) Now! »
Gearbox vibration signals under constant operating conditions
Gearbox vibration signals are dominated by the vibrations resulting from the periodic meshing of the gear teeth. This is attributed to the variation of the gear mesh stiness due to non-integer contact ratios, deviations from the involute gear prole and the deformation of the gear teeth under load which ultimately manifest as strong excitations at the gear mesh frequency [7, 16]. Gear damage results in changes in the gear mesh stiness of the gear [17, 18] which manifest as changes in the amplitude of the vibration signal [16] and changes in the instantaneous angular speed of the gears [19]. Localised gear damage results in localised amplitude modulation i.e. amplitude modulation with a short duration relative to the gear rotation period, while distributed gear damage results in amplitude modulation with a longer period [16].
In rolling element bearings, damage on the inner or outer race of the bearing results in impacts as the load-carrying rolling elements move through the damaged portion, whereas a damaged rolling element results in impacts as the damaged region makes contact with the inner and outer races of the bearing [20]. The magnitude of the bearing impulses is dependent on the load zone. For example, inner race and rolling element damage signals are amplitude modulated as the fault moves through a constant load zone, while the outer race damage signal remains constant with respect to a constant load zone [20]. The magnitude of the bearing impulses is also non-linearly related to the condition of the bearing. El-Thalji and Jantunen [21] and Cerrada et al. [22] illustrated how changes in the condition of the bearing in uence the magnitude of the impacts due to the damage and the measured vibrations.
The vibrations resulting from interacting machine components such as the impacts due to bearing damage in a gearbox are transmitted through the machine components (e.g. shafts and bearings) and casing of the machine to reach sensors such as accelerometers. The frequency response function of the transmission path acts as a lter on the vibration signal and therefore the measured vibration signal is dependent on the frequency response function of the machine, the location of the sensors and the rotational speed of the system [19, 23{25]. The interaction between the rotating components e.g. gear mesh interactions or bearing damage, also results in changes in the statistics of the vibration signal of the machine over time i.e. the vibration signals are inherently non-stationary. However, due to the periodic nature of the interactions, the statistics of the vibration signals are periodic as well and therefore the signals are a special class of non-stationary, namely, cyclostationary [23, 26, 27]. To be more precise, the signals are angle-cyclostationary under stationary operating conditions due to the angle-locked periodic mechanisms of rotating machine components [23]. Dierent types of cyclostationary signals are formally dened and related to machine vibration by Antoni et al. [23]. Pure rst-order cyclostationary signals, generated by misalignments and gear meshing for example have periodic means, while pure second-order cyclostationary signals generated by wear for example have periodic autocovariance functions. Hence, this distinction necessitates using appropriate techniques for rst-order and second-order cyclostationary component detection [23].
1 Introduction
1.1 Background
1.2 Literature survey
1.2.1 Gearbox vibrations for fault diagnosis
1.2.2 Signal analysis for fault diagnosis
1.2.3 Data-driven fault diagnosis .
1.3 Scope of work .
1.4 Layout of thesis .
2 Localised gear anomaly detection methodology
2.1 Introduction .
2.2 Methodology
2.2.1 Feature extraction and processing
2.2.2 Kullback-Leibler divergence
2.2.3 Data analysis for automatic condition inference
2.3 Validation
2.3.1 Experimental setup
2.3.2 Investigation
2.3.3 Investigation
2.3.4 Diagnosis of the pinion
2.4 Conclusion and recommendations
3 Discrepancy analysis methodology for bearings
3.1 Introduction .
3.2 Methodology .
3.2.1 Overview
3.2.2 Feature extraction
3.2.3 Feature modelling
3.2.4 Discrepancy signal generation .
3.2.5 Processing the discrepancy signal .
3.3 Numerical validation .
3.3.1 Phenomenological gearbox model .
3.3.2 Vibration data
3.3.3 Results
3.4 Experimental validation
3.4.1 Investigation 1 .
3.4.2 Investigation 2 .
3.5 Additional investigations .
3.6 Conclusion and recommendations .
4 Spectral coherence novelty detection methodology
4.1 Introduction
4.2 Methodology
4.2.1 Estimating the residual signal .
4.2.2 Order-Frequency Spectral Coherence (OFSCoh) .
4.2.3 Feature extraction
4.2.4 Healthy data model evaluation
4.2.5 Novelty detection .
4.3 Numerical validation
4.3.1 Phenomenological gearbox model
4.3.2 Results
4.4 Experimental validation
4.4.1 Procedure
4.4.2 Results
4.5 Conclusion and recommendations
5 Novel information enhancement methodology
5.1 Introduction
5.2 Methodology .
5.2.1 Signal decomposition and feature extraction
5.2.2 Feature modelling
5.2.3 Filter design to enhance novel information
5.2.4 Novel signal estimation
5.3 Phenomenological gearbox model
5.3.1 Model
5.3.2 Results with raw data .
5.3.3 Results with proposed methodology .
5.4 Experimental gearbox dataset
5.4.1 Overview of dataset
5.4.2 Results .
5.5 Conclusion and recommendations .
6 Open set recognition methodology
7 Conclusion and recommendations
Bibliography
