Vibration analysis for early pitting detection during operation

As a part of the industrial digitalisation initiative, there is a growing availability of operating data from machinery and industrial plants. This wealth of operational data provides the opportunity to detect damages and failures in machine components. Based on the early damage detection strategies such as condition-based maintenance and predictive maintenance improve the economic efficiency of machine operations [1]. Consequently, damage detection presents several financial advantages for machine operators [1]. Additionally, the field of prognostics and health management offers the possibility to adapt the operating strategy when damage is detected, thereby extending the remaining useful life [2].

The focus of the present study is on pitting damages, one of the two main damage mechanisms that can lead to gear failure [3]. Pitting damage progression (degradation) is described as either linear or progressive over time [4]. This characteristic enables the detection of pitting damages at an early stage of their occurrence, before they cause a machine downtime. The implementation of a condition monitoring system for pitting damage detection holds significant potential, especially for machines and plants with stringent operational reliability requirements, as well as high downtime and maintenance costs.

The objective of this study is to establish a method for the reliable detection of pitting damage. In pursuit of this goal, experiments using artificial pitting damages are conducted on a test bench, where the data of various sensors is acquired. This recorded measurement data is further analysed to detect the pitting damages. In addition, the study seeks to identify and quantify parameters that affect the detectability of pitting damage through a statistical analysis of the experiments.

The criteria for failure due to pitting damages are standardised. For non-hardened gears, the criterion for failure is defined as a percentage of the pitting area in relation to the entire area of the active tooth flanks, which is set at 2% [5]. For hardened gears, two standardised criteria for failure are specified. The first criterion considers the pitting area as a percentage of the entire area of the active tooth flanks, and it is set at 0.5% [5]. The second criterion for failure considers a percentage of the pitting area in relation to the area of a single active tooth flank, and is set at 4% [5]. This second criterion for failure for hardened gears is of particular relevance to the scope of this study, as damages initially occur on a single tooth [6]. In analogy to the standard, the percentage of the pitting area in relation to a single tooth flank area is used to characterise the pitting damages in this work. In the subsequent sections prior research by different authors on pitting detection using accelerometers is reviewed.

Sonawane et al. successfully detected pitting damages in the time domain, which were as small as 6.3% of the area of one active tooth flank [7]. The pitting damages were intentionally induced using an electrical discharge machine on a single gear within a single stage gearbox [7]. In their methodology for pitting detection, they computed the root mean square (RMS) value of the structure-borne noise data in the time domain [7]. For pitting detection, a comparison of the RMS value from measurement data obtained from a gear with pitting damage to the RMS value of an undamaged gear was employed [7].

In the publication of Fromberger et al. an approach of a time domain analysis for pitting detection without the need of reference data from an undamaged gear is presented [8]. Therefore, the time signal of an accelerometer, sampled at 51.2 kHz, is divided into sections for each tooth mesh [8]. For pitting detection, the maximum signal power is extracted from each section [8]. The analysis of an image of the naturally occurred pitting damage investigated by Fromberger et al. reveals, that it is greater in size than the standardised failure criterion.

In the approach by Korka et al. pitting damages on a single-stage helical gearbox were detected in the frequency domain [9]. Artificial pitting damages with a diameter of 3 mm and a depth of 0.5 mm each, were created on three adjacent teeth of the pinion [9]. The severity of these pitting damages was varied by increasing the number of pitting damages on the tooth flanks [9]. In the frequency domain analysis of the structure-born noise data, Korka et al. observed that pitting damages can best be detected at the second and third harmonic of the gear mesh frequency (GMF) [9]. In addition, their investigation revealed that the method used for pitting damage detection was more reliable at higher rotational speeds [9].

Hou et al. conducted investigations involving the creation of elliptical-shaped pitting damages on a single tooth flank [10]. These pitting damages are characterized by main axes, measuring 8 and 3 mm in length [10]. To achieve different levels of damage severity three, six and twelve of these artificial pitting damages were created around the pitch diameter of the gears [10]. In the frequency domain the acceleration amplitudes at the harmonics of the GMF and at sidebands of these harmonics are compared from measurements taken with pitting damages on the gear to reference data obtained without pitting damages [10]. The sidebands around the harmonics of the GMF indicating pitting damage were observed at distances corresponding to the rotational frequency of the damaged gear [10].

The investigations of Sarvestani et al. were carried out on the actual gearbox of a ball mill, rather than on a test bench [11]. In their experiments, naturally occurring pitting damages were observed, covering areas of 30%, 60% and 90% of a single tooth flank area [11]. The evaluation of structure-borne noise data was performed in the frequency domain [11]. In this analysis, the area below the computed signal in the frequency domain was calculated [11]. This approach allowed for the detection and classification of the observed pitting damages [11].

Grzeszkowski et al. utilized a support vector machine (SVM) for the classification of pitting damages [12]. The experiments were conducted on a back-to-back test rig, and structure-borne noise data was collected using two accelerometers, sampled at a rate of 200 kHz [12]. In this study, the pitting damages on the gears occurred naturally [12]. The SVM was able detect the examined pitting damages, yielding no false-negative results [12]. In 78.4% of the cases, the SVM results were consistent with the actual test condition, accurately identifying whether pitting damage was present on the gear or not [12]. This approach enabled the detection and classification of the smallest pitting damage, as small as 0.23% of the area of an active tooth flank [12].

For the detection of pitting damages in early stages of their development, experiments are carried out. The test bench and the experimental design are detailed in the subsequent sections.

The measurement data is imported into Matlab for data analysis. Within Matlab, the structure-borne noise data from the ultrasonic accelerometer is transferred from the time domain into the frequency domain using the fast Fourier transform (FFT). As outlined in the brief literature review, pitting damages can be detected in the frequency domain at the harmonics of the GMF and at sidebands around these harmonics [1, 10, 11]. The Sidebands are positioned at distances of multiples of the rotational frequency of the damaged gear around the harmonics of the GMF [1, 10, 15]. When analysing the frequency data, it is found that examining multiple frequencies contributes to more robust results. Consequently, 12 sidebands in each direction around the harmonics of the GMF are analysed. The harmonics of the GMF and their associated sidebands are collectively referred to as frequency bands. Within the Matlab script for data analysis, the acceleration amplitudes at all the frequency bands are determined for each experiment. In Fig. 3 a segment of the frequency spectrum from the ultrasonic accelerometer is displayed. The experimental settings for which the data for this figure was collected are a rotational input speed of 918 rpm, an output torque of 24 Nm, a viscosity of the lubricating oil of 81 mPa∙s and a size of the pitting damage of 1.65%. The amplitudes at the marked frequency bands around the 44th harmonic of the GMF at 24,232 Hz tend to be higher when pitting damages are present on the gear.

In a one-on-one comparison, the percentage change in amplitude at the harmonics of the GMF and the sidebands is calculated from the structure-borne noise data of the gear with pitting damage to the data of the undamaged gear. In the segment of the frequency spectrum shown in Fig. 3 the calculated percentage changes of the frequency bands exceed the value 1 for all but one frequency band. For each experiment of the CCD, the percentage changes of the frequency bands across the entire frequency spectrum are compared. It is observed that for the harmonics of the GMF and the sidebands between 24,000 and 40,300 Hz the percentage changes are predominantly of greater values than 1. Hence, this frequency range proves most effective for pitting damage detection. This effectiveness remains consistent across various rotational speeds, as different harmonics of the GMF are present in this frequency range for different speeds.

For the evaluation of the CCD with statistical DoE methods, additional data processing is required. The mean values of the adjusted parameters rotational input speed, output torque, and the temperature of the lubricating oil are extracted from the measurement data of each experiment. Then the viscosity is calculated based on the mean temperature of the lubricating oil. The therefore required temperature-viscosity correlation is based on data recorded at the Institute of Machine Components for this specific FVA reference oil No. 3. To evaluate the CCD, percentage changes of the frequency bands in the range between 24,000 and 40,300 Hz are consolidated to one target value. This is achieved by calculating the RMS value of the percentage changes in the specified frequency range. The RMS value is chosen due to its ability to assign greater weight to larger proportions, which, in this context, signify the presence of pitting damage. To enhance the quality of the analysis, the data is further processed by applying a filter to the target value. The CCD is statistically evaluated using this target value, along with the measured values of the rotational input speed, output torque, viscosity of the lubricant, and the pitting size. In this evaluation a model is created to explain the target value by considering the varied experimental parameters.

The calculated target value serves as an indicator for pitting detection. For all experiments conducted, except for one, the target value, respectively the RMS of the percentage change in amplitude at the frequency bands between 24,000 and 40,300 Hz exceeds the value of 1. This indicates that, on average, the amplitudes at the examined frequency bands are higher, when pitting damage is present on the gear compared to when it is undamaged. The detection rate of pitting damage is determined utilizing the confidence interval of the target value. The lower limit of the confidence interval is calculated for the binomially distributed target value at a confidence level of 95% using the procedure according to Wilson [17]. With only one false-negative result out of the 93 conducted experiments the calculated lower limit of the confidence interval illustrates that at least 95.92% of the pitting damages can be detected in 95% of the cases.

In the statistical evaluation of the CCD using the analysis of variance (ANOVA), parameters affecting the target value for pitting detection are identified [18]. The Pareto chart in Fig. 4 delineates the standardised effects of parameters and single interactions on the target value. These standardised effects are derived from the student’s t‑test conducted for each parameter and single interaction [19]. The t‑value, or standardised effect, indicates the deviation from the null hypothesis, suggesting no influence of the examined parameter or single interaction on the target value. The influences of the examined parameters on the detectability of pitting damage are interpreted below.

The linear effect of the rotational speed has the greatest standardised effect on the target value for pitting detection. In the time domain rising acceleration amplitudes are observed with an increase of the rotational speed. This rise is noted for overall accelerations, suggesting that the structure-borne noise signals of the pitting damage also experience an amplitude increase due to the higher rotational speed. As a result, the percentage changes in amplitudes at the examined frequency bands rise, leading to an increase in the target value. The physical cause of this observation is attributed to the transmitted power. Higher rotational speeds lead to increased vibrations caused by the disturbance of the ideal power flow. The observed effect aligns with findings from Korka et al. [9].

The size of the pitting damages has the second-greatest effect on the target value, with almost equal importance in both quadratic and linear terms. This suggests a superposition of the positive quadratic influence and the negative linear influence. Mathematically, this superposition of a linear and a quadratic term results in a displacement of the low point of the parabola towards larger pitting sizes. In essence, larger pitting damages result in an increased target value. Based on the method for calculating the target value this means that the acceleration amplitudes at the examined frequency bands increase for bigger pitting damages. The physical explanation lies in the stiffness of the meshing teeth, as investigated by Hou et al. [10]. Their simulation results show a modulation of mesh stiffness depending on the size of the pitting damage [10]. The different mesh stiffnesses cause accelerations in the tooth mesh and therefore changes in the acceleration amplitudes at the harmonics of the GMF and the rotational frequency.

In the Pareto chart, the viscosity appears next with a notably lower standardised effect. The viscosity exhibits a negative linear influence on the target value, indicating that the target value increases for lower viscosity values. Although no reliable physical cause supports this observation, it is assumed that lower viscosity causes less damping in the contact zone of the meshing gears. Consequently, the structure-borne noise signal stimulated by the pitting damage is less damped, allowing for a better recording of the signal with the accelerometer and thereby leading to an increase in the target value.

The interaction of torque and viscosity shows a similar standardised effect as viscosity. In the model, it is described as a positive effect, indicating that an increase in the interaction causes a rise in the target value. This interaction is assumed not to be related directly to the pitting damage. At higher viscosity of the lubricating oil, more torque is required to displace the excess oil from the gear mesh. This effect, similar to drag losses, is due to the higher shear strength of the oil at higher viscosity. Variations in the required torque are repeated periodically for every tooth mesh. Torque variations, respectively force variations acting on the mass of the gears cause an acceleration signal. Consequently, this resulting acceleration signal can be detected at the harmonics of the GMF, thereby affecting the target value.

The interaction of rotational speed and torque has a slightly lower standardised effect on the target value. For higher values of rotational speed and torque the target value increases. This interaction is linked to the linear influence of rotational speed. The rotational speed and torque are linked by the transmitted power. This correlation has already been described for the influence of the rotational speed. The comparatively low standardised effect is due to the small influence of torque, as interpreted in the next section.

The linear and quadratic influence of torque contribute the lowest standardised effect of any single parameter on the target value. Torque causes a force between the meshing teeth, and in the context of the modulated mesh stiffness due to pitting damage, this force induces tooth deformation [10]. However, for the examined torques the tooth deformation results in relatively small structure-borne noise signals. Consequently, the effect of torque on the target value and, thereby, on the method used in this work for pitting detection is low.

It is important to highlight that the variance inflation factor (VIF) of all the terms illustrated in the Pareto chart in Fig. 4 is greater than 15. This indicates a significant amount of multicollinearity in the model to describe the target value. The parameter levels of pitting size and viscosity vary due to production tolerances in creating the artificial pitting damages and tolerances in setting the temperature of the lubricating oil. These deviations in the parameter levels lead to a deviation from orthogonality of the experimental design manifesting as multicollinearities. The resulting elevated VIFs widen the confidence interval, thereby reducing the precision of the model in predicting the target variable under given operational conditions [20].

The model achieves an R²-value of 67.33%, signifying that over two thirds of the influences on the target value for pitting detection can be explained with the investigated parameters. The sources of the remaining uncertainty of the model cannot be identified. It is estimated that the altered conduction paths of the structure-borne noise, due to the rebuilding of the gearbox for each experiment may contribute to these unaccounted influences.