Spur Gearbox Research Articles

Design Optimization of Two Stage Spur Gear Box with Critical Mechanical and Tribological Constraints by Nature Inspired Algorithms

Design Optimization of Two Stage Spur Gear Box with Critical Mechanical and Tribological Constraints by Nature Inspired Algorithms

A comparative experimental research on the diagnosis of tooth root cracks in asymmetric spur gear pairs with a one-dimensional convolutional neural network

Gearboxes transfer rotational motion and handle precision functionalities in many fields, including aviation, wind turbines, and industrial services. Their health management is essential to minimize workforce risks, increase the level of safety, and avoid machine breakdowns. From this standpoint, the present experimental research work developed a convolutional neural network-based method for diagnosing different levels of tooth root cracks (25 %-50 %-75 %-100 %) for symmetric (20°/20°) and asymmetric (20°/30°) profiled gear pairs. A series of vibration experiments were performed on a one-stage spur gearbox to achieve this by using a tri-axial accelerometer under variable working loads. The main purpose of this experimental research study is to explore the influence of the tooth profile on spur gears’ vibration responses and whether utilizing an asymmetric tooth profile would positively impact a deep learning algorithm's classification accuracy to add to the enhancements it provides in terms of fatigue life, mesh stiffness, and impact strength. Experimental results revealed that the overall classification accuracy could be increased by 7.712 % by feeding the proposed deep learning model with vibration data measured using test samples with asymmetric teeth.

A simple yet realistic integrated dynamical modeling of an induction motor and one-stage spur gearbox system with broken tooth

The development of accurate, useful, dynamical models of electromechanical systems under fault conditions for industrial applications is crucial for further development of fault diagnosis systems. Models including complex physical phenomenology have been proposed, which could have low practical applicability. In this study, we develop the dynamical model of an electromechanical system composed by an induction motor coupled to a one-stage spur gearbox considering the effects of time-varying mesh stiffness, time-varying viscous damping, transmission error, and backlash. The time-varying mesh stiffness includes faulty conditions according to different loss sizes of broken tooth. Thus, this simple yet realistic model can explain the system dynamics under different fault severity scenarios. Experimental and simulated data are compared to validate the proposed model with different levels of pinion broken tooth under constant load conditions on the gearbox. Proper results were obtained, and we conclude that our model is useful for further analysis oriented to fault diagnosis. The simplicity of the proposed model represents a good approximation of the system behavior in steady state, with less complexity than other models with a higher number of DOF.

Tacho-less spur gear condition monitoring at variable speed operation using the adaptive application of variational mode extraction

Effective condition monitoring of machine components contributes to a safer working environment for operators and assists in averting critical machinery shutdowns. In real-world industrial scenarios, fault detection must remain simplified, user-friendly and robust despite speed variations. The operational demands of machinery frequently result in speed fluctuations, leading to spectral smearing, thereby compromising the efficiency of the analysis methodology. Furthermore, the intricacies of parameter initialisation often increase the complexity of the analysis methods. This study introduces a fault diagnosis algorithm that requires minimal initialisation and operates independently of tacho pulses. The algorithm proposed in the study incorporates variational mode extraction with the maxima tracking algorithm for instantaneous frequency estimation. Hankel matrix-based selective spectral fusion is proposed to mitigate the impact of frequency tracking errors caused by transient noise. The results of spectral side-band-based fault severity analysis, conducted on an in-house spur gearbox test-bed with seeded tooth chips, underscore the superior performance of the proposed algorithm when compared to contemporary non-stationary analysis methods.

Selection of the level of vibration signal decomposition and mother wavelets to determine the level of failure severity in spur gearboxes

AbstractSpur gearboxes are an integral component in the operation of rotary machines. Hence, the early determination of the severity level of a failure is crucial. This manuscript delineates a methodology for selecting essential mother wavelets and filters from the wavelet transform (WT) to process the vibration signal within the time‐frequency domain, aiming to ascertain the severity level of failures in spur gearboxes. Initially, information is garnered from the gearbox through vibration signals in the time domain, utilising six accelerometers. Subsequently, the signal is partitioned into various levels, and information from each level is extracted using diverse mother wavelets and their respective filters. The signal is segmented into sub‐bands, from which the condition state is ascertained using an energy operator. After that, the appropriate level of wave decomposition is determined through ANOVA tests and post‐hoc Tukey analyses, evaluating performance in failure classification via the Random Forest (RF) model. Upon establishing the decomposition level, the analysis proceeds to identify which mother wavelets and filters are most suitable for determining the severity level of different types of failure in spur gearboxes. Moreover, this study investigates the impact of sensor positioning and inclination on acquiring the vibration signal. This aspect is explored through factorial ANOVA tests and multiple comparisons of the data derived from the sensors. The RF classification model achieved exceedingly favourable results (accuracy 96% and AUC 98%), with minimal practical influence from the positioning and inclination of a sensor, thereby affirming the proposed methodology's suitability for this type of analysis.

Contribution of friction-induced vibration to the realistic failure analysis of spur gear cracked teeth

A cracked tooth is a common occurrence in gears. However, the dynamic behavior of gears with cracks and poor lubrication that leads to rubbing between the teeth is poorly understood, limiting the reliability and precision of gear transmission. This article proposes a comprehensive model for studying the dynamic behavior of a one-stage spur gearbox with cracked teeth under poor lubrication conditions. The inter-teeth rubbing generated by the sliding of one surface relative to another is caused by the variation in the curvature radii of both mating teeth when the contact point moves along the line of contact. In addition, under the load transmitted between the mating teeth, the common elastic deformed area, computed by Hertz's theory, also varies, generating noise with modulated and constant amplitudes. Adding this friction-induced noisy vibration to the impulsive periodic response was found to realistically mimic natural behavior experimentally measured on a test rig specially developed for this investigation. According to the time-domain statistical indicators, the study concluded that the combination of both components of friction-induced noise and the primary impacting response was found to accurately and realistically simulate the dynamic behavior of the gearbox.

Badanie wpływu wybranych kontrolowanych czynników na współczynnik tarcia ślizgowego za pomocą eksperymentalnych metod planowania

The article presents the use of mathematical statistics to determine controllable factors that influence the coefficient of friction in a dual-flow three-stage spur gear transmission of a newly designed sucker rod pumping unit. The load acting on the bearing units, the rotational speed of the main and auxiliary shafts, and the diametrical gap between the shaft and the bushing were assessed through tests. The tests were carried out in random order. The multivariate testing was used to determine the number of tests to be performed as well as the test conditions in order to achieve the required accuracy bushing. In the statistical analysis of the results, the Cochrane criterion was applied to verify the homogeneity of the variance values. Student's t-test was used to verify the significance of the coefficients included in the regression equation, Fisher’s F-test was used to determine the suitability of the adopted output function for describing the real object of study, i.e., the adequacy of the model, and sensitivity coefficients were used to assess the influence of the corresponding parameters on the optimization parameter. The analysis also considered the dispersion of optimization parameters, measurement repeatability, and errors in the model coefficients. Experimental values of the criteria, along with the dispersion of the adequacy and repeatability of the mathematical model, were evaluated to determine whether the model is fully suitable for the object of study. The impact of significant factors and their combinations, as well as their critical values, were assessed by comparing calculated values of the criteria. The significance or insignificance of the corresponding coefficients of the regression equation was determined. To investigate the impact of these controlled factors — load, rotational speed of the main and auxiliary shafts, and the diametrical gap between the auxiliary shaft and the bushing — on the sliding friction coefficient, a modernized device was developed. This device simulates the operating conditions of a double friction sliding bearing in a dual-flow, three-stage spur gearbox bushing. The experiments were conducted using I-40A industrial oil at room temperature. It has been determined that these factors significantly impact the coefficient of friction in a double friction bearing. Consequently, it is necessary to calculate their limit values to ensure the bearing assembly operates without failure during the required service life. Compared to other examined parameters, the optimization parameter, i.e., the coefficient of friction, is most significantly influenced by the diametrical gap between the auxiliary shaft and the bushing, and least affected by the magnitude of the load acting on the bearing assembly. The overall impact of controlled factors on the coefficient of friction is minimal. Employing the test planning method, a mathematical formula was derived, enabling the determination of the coefficient of friction in a double sliding friction bearing without additional tests within the range of limit bushing values of contact parameters.

Dynamic modeling of spur gear transmission system with evolutive coupling fault of fatigue crack and wear

Parallel shaft spur gear system is widely used in various machineries because of its simple structure, high transmission efficiency and strong adaptability. The health status of spur gear greatly affects the safety and reliability of equipment in service, so it is quite necessary to reveal the evolution law of gear fault and clarify the fault dynamic response. Fatigue crack is a typical gear fault, and it is often accompanied by wear which is generally unavoidable in the life cycle of gear transmission system. The two typical gear faults reduce the meshing stiffness of the gear pair, whereupon a calculation approach of time-varying meshing stiffness for the coupling fault of fatigue crack and wear is proposed. First, the prediction models of fatigue crack and wear are respectively investigated, then a coupling fault evolution model is built by combining them. Using this model, a new approach for calculating the time-varying meshing stiffness is put forward. Via embedding the obtained meshing stiffness into the eight-degree-of-freedom dynamics model of spur gear transmission system as the fault excitation, an evolutive coupling fault dynamics model is constructed. Finally, the effectiveness and accuracy of the proposed evolutive fault dynamics model is verified by the experiment on a faulty single-stage gearbox. The proposed model has important guiding significance for the fault diagnosis and prognosis of spur gearbox.

Experimental study and comparative analysis of pitting fault in spur gear system

This paper uses a dynamic six-degree-of-freedom model that considers torsional and lateral motions to predict the impact of pitting on vibration parameters in a spur gearbox for various operating speeds and torque loads. The study examines the dynamic characteristics of a gearbox with localized pitting damage on a single gear tooth using theoretical and experimental approaches. The research analyzes the forced vibrations of a single-stage spur gear system with pitting damage, which includes variations in mesh stiffness, damping, and gear error excitation, to identify symptoms of default. The equation of motion for the rotary gearbox system is established using the Lagrangian method in tandem with Short-Time Fourier Transform (STFT) and frequency-RPM map fault diagnosis. During real-time vibration monitoring, vibration signals are captured via accelerometers and processed in both the time and frequency domains using the LabVIEW data acquisition signal processing package to extract diagnostic information. The experimental findings demonstrate how vibration analysis combined with time-frequency processing can recognize machine conditions even in harsh operational conditions. Moreover, the experimental results indicate a significant similarity with the theoretical analysis and validate the effectiveness of the RPM frequency technique-based pitting detection method, which can be an asset in gear fault monitoring.

Experimental Investigations to Study the Effectiveness of Cepstral Features to Detect Surface Fatigue Wear Development in a FZG Spur Geared System Subjected to Accelerated Tests

Gears are essential machine elements used to transmit power and motion from one unit to another under desired angular velocity ratio. Various types of gears have been developed to fulfill power transmission requirements in industrial applications. Under normal or fluctuating operating conditions, increase in fatigue load cycles, transition in lubrication regimes, fluctuating loads and speeds, etc., result in various surface fatigue wear modes which affect the performance of geared system. The severity of wear anomalies developed on gear tooth surfaces can be assessed by using vibration signals acquired from the gear box. On the other hand, reliable wear assessment is very important to perform maintenance action which depends on the sensors, data acquisition procedure, vibration signal analysis and interpretation. This paper presents results of the experimental investigations carried out to assess initiation and propagation of surface fatigue failure wear modes developed on gear tooth contact surfaces. A FZG back to back power recirculation type spur gearbox was used to conduct fatigue test experiments on spur gears under accelerated test conditions. Accelerated test conditions resulted in a rapid transition of lubrication regimes, i.e., hydrodynamic lubrication regime to boundary lubrication regime which triggered surface fatigue faults on gear tooth surfaces. A cepstral analysis method was used to assess fault severity in the geared system. The results obtained from the cepstral features were correlated to various surface fatigue faults and reduction in gear tooth stiffness. Results obtained from the experimental investigations highlighted the suitability of cepstral features to assess incipient faults developed on spur gear tooth surfaces.

Transmission-error- and vibration-based condition monitoring of gear wear with contaminated lubricant

The presence of contaminant particles in lubricants could cause severe gear wear and damage. Conventional condition monitoring techniques, i.e., gear inspection and oil/wear debris analysis, are often utilised to assess the presence of wear due to contaminants and its severity such as wear depth. However, the traditional approaches require experience or off-line analysis. Although vibration is a non-invasive technique for fault detection and diagnostics, it is less well developed for wear analysis. Recently, an alternative sensor technology, i.e., transmission error (TE), combining angular measurements obtained from the input and output shafts has shown strong potential for wear monitoring. This work aims to investigate the usage of vibration and TE to identify the existence of contaminants and measure the gear wear severity caused by the oil contamination. This is achieved by conducting gear wear tests on a spur gearbox rig, using clean and contaminated lubricants with silica sand. The test in a normal lubrication condition provides a healthy reference of the spur gearbox under a nominal operating condition. In addition to the nominal operating condition, TE and vibration measurements are collected throughout the tests at different operating conditions, together with moulds of the gear tooth surfaces for wear analysis. The results show that the absolute TE can quantitively measure wear depth, and the RMS of vibration can qualitatively correlate with the trend of the average wear depths. The proposed technique extends the field of using TE to diagnose and predict gear wear in contaminated lubricant conditions.

Analysis of spur gearbox dynamics considering tooth lubrication and tooth crack severity progression

A novel tribo-dynamic model of a spur gearbox considering both tooth lubrication and tooth crack is proposed, which integrates an elastohydrodynamic lubrication (EHL) model of a spur gear pair into a gearbox lumped parameter model. The combined stiffness and combined damping of a spur gear pair with a tooth crack are obtained using the oil film stiffness and oil film damping provided by the EHL model and the tooth mesh stiffness and tooth mesh damping calculated by the potential energy method. Effects of tooth lubrication and tooth crack severity progression on combined stiffness, combined damping, and gearbox vibration responses are studied. It is found that considering the tooth lubrication in gearbox dynamic modeling leads to a backward shift of the frequency components induced by tooth crack. A comparison has been made between the proposed tribo-dynamic model and the conventional model of a spur gearbox, and the effectiveness of RMS and Kurtosis for tracking tooth crack severity progression is investigated in the presence of tooth lubrication. The comparison results reveal that the consideration of tooth lubrication overall reflects tooth crack signatures better.

Analysis of vibration signals and detection for multiple tooth cracks in spur gearboxes

Tooth crack diagnosis is important to ensure the reliability of gearboxes. However, most reported studies on tooth crack diagnosis only involved the scenario of one tooth crack in a gearbox, which is not always the case since gearboxes may also suffer from multiple tooth cracks in the industry. To overcome this problem, this study first brings some insights into the vibration characteristics of a spur gearbox with multiple tooth cracks using dynamic modelling. Three scenarios of multiple tooth cracks are considered, including two nonadjacent tooth cracks on the pinion and a healthy gear, two adjacent tooth cracks on the pinion and a healthy gear, and one tooth crack on the pinion and one tooth crack on the gear. Tooth mesh stiffness is analytically evaluated using the potential energy method and is further inserted into the spur gearbox dynamic model to generate vibration responses. Analyses of mesh stiffness and vibration responses are conducted in both time and frequency domains. Besides, a novel method focusing on the crack induced impulses (CII) is proposed to detect the number and locations of multiple tooth cracks. Firstly, the CII are extracted from gearbox vibration signals using a new strategy based on the singular value decomposition. Time synchronous average (TSA) is conducted on the CII to get the TSA signals for both the pinion and the gear. Afterwards, detection of the number and locations of multiple tooth cracks is achieved via analyzing the squared envelopes of the TSA signals for both the pinion and the gear. The obtained insights into vibration characteristics for multiple tooth cracks and the effectiveness of the proposed method for detecting the number and locations of multiple tooth cracks are demonstrated using both simulated gearbox vibration signals and experimental gearbox vibration datasets.

Removal of transfer function effects from gear vibration signals under constant and variable speed conditions

Gear faults generally cause changes to the forcing functions of the system, which are usually hard to measure. Vibration is a common tool for gear condition monitoring, it being generated by a forcing function exciting responses through a transmission path from the excitation to the measurement point. The diagnostic information in the vibration measurements is often distorted by transfer function effects, in particular for local faults, such as cracks, where the waveform is important. In such cases, more direct diagnostic information can be extracted by removing the transfer function effects. However, a very limited amount of research has been carried out to reconstruct the time-domain waveforms of the forcing functions, except some making the assumption that the forcing functions are impulsive. A method was previously developed to identify and remove the transfer function effects from transmission error (TE) measurements at constant speeds to reconstruct the excitations, utilising a cepstrum-based operational modal analysis (OMA) method. In the current paper, this method is extended to vibration signals under constant and variable speed conditions. Since vibration has more complex transfer functions than TE, this paper establishes an additional pre-processing procedure, which removes the deterministic components in order to facilitate the OMA process. After removing the transfer function effects from measured vibration signals, the proposed technique reconstructs forcing functions that are much more clearly indicative of the faults at all speeds and which approximate the meshing forces at the gear teeth. The fault features are effectively enhanced and localised in the forcing functions, and the importance of phase modification to the reconstruction of forcing function waveforms is demonstrated. The technique was validated using vibration measurements obtained from a single stage spur gear box with a tooth root crack.

Condition Monitoring of Spur Gear Box based on Acoustic Emission Signal Analysis

Abstract: Monitoring the condition of rotating machinery, such as gearbox is an important task in order to enhance its performance. Acoustic Emission (AE) and vibration analyses are some of the most accomplished techniques used for this purpose. Acoustic emission technique has the ability to detect the initial phase of component degradation. This paper presents the experimental investigation of gearbox condition using acoustic emission techniques. AE signals of gearbox under different conditions are acquired. AE signal parameters such as RMS, amplitude and rise time have provided information about the condition of the gearbox. Hence, AE technique can also be used for monitoring the gearbox.

Condition Monitoring of Two-Stage Spur Gearbox Using Vibration Signature Spectrum Analysis

Condition Monitoring of Two-Stage Spur Gearbox Using Vibration Signature Spectrum Analysis

Application of EMD based statistical parameters for the prediction of fault severity in a spur gear through vibration signals

ABSTRACT Health monitoring of Mechanical drives had been a challenging task for the researchers, to estimate the fault severity for necessary corrective actions. Signal processing techniques made the task of finding faults quickly in the easiest way, to predict machine condition. Steps of preventive maintenance would always help in reducing the machine down time. Vibrations in mechanical systems, found to be the most common source for degrading the performance, and uncontrollable vibrations usually lead to catastrophic situations. Hence regulating machine vibrations would solve majority of the problems and prevents the state of being abnormal. In this context an empirical mode decomposition technique is utilised to study the vibration severity of a spur gearbox. This method decomposes a complex raw signal into a finite number of Intrinsic mode function (IMFs), based on the local characteristic time scale. These IMFs divulge the intrinsic oscillation modes entrenched in the signal. This enables the fault diagnosis of gears and to take essential corrective action. The present study includes acquisition of vibration signals, decomposition into IMF’s, extraction of respective statistical parameters and analysis for the quantification of various faults. The work also demonstrates the effectiveness of the processed signal over the raw signals of vibration.

AutoML for Feature Selection and Model Tuning Applied to Fault Severity Diagnosis in Spur Gearboxes

Gearboxes are widely used in industrial processes as mechanical power transmission systems. Then, gearbox failures can affect other parts of the system and produce economic loss. The early detection of the possible failure modes and their severity assessment in such devices is an important field of research. Data-driven approaches usually require an exhaustive development of pipelines including models’ parameter optimization and feature selection. This paper takes advantage of the recent Auto Machine Learning (AutoML) tools to propose proper feature and model selection for three failure modes under different severity levels: broken tooth, pitting and crack. The performance of 64 statistical condition indicators (SCI) extracted from vibration signals under the three failure modes were analyzed by two AutoML systems, namely the H2O Driverless AI platform and TPOT, both of which include feature engineering and feature selection mechanisms. In both cases, the systems converged to different types of decision tree methods, with ensembles of XGBoost models preferred by H2O while TPOT generated different types of stacked models. The models produced by both systems achieved very high, and practically equivalent, performances on all problems. Both AutoML systems converged to pipelines that focus on very similar subsets of features across all problems, indicating that several problems in this domain can be solved by a rather small set of 10 common features, with accuracy up to 90%. This latter result is important in the research of useful feature selection for gearbox fault diagnosis.

Establishing Statistical Correlation Between Sensor Signature Features and Lubricant Solid Particle Contamination in a Spur Gearbox

This paper aims to predict the severity of solid particle contaminants present in the lubricant in a Spur Gearbox using Vibration, Acoustic Emission, and Sound Signature features. Sensor signatures are acquired at various contaminant conditions of lubricant with different speed and load conditions. Statistical Features are extracted in the time domain, and feature ranking is carried out using the analysis of variance approach. Statistical models are developed using the selected features of Sound, Acoustic Emission, and Vibration separately and fusing the features in the feature level. Decision Trees and Support Vector Machine algorithms are used in this study to build statistical models. AE features have a good correlation with lubricant conditions compared to sound and vibration features. The feature-level fusion approach predicts the lubricant conditions with an accuracy of more than 99%. The feature-level fusion models built using dominant features are computationally efficient without compromising the prediction ability.

Catia customization for Design and Modeling of Two stage spur Gearbox

In this paper, we describe how the customization of design task, in solid modeling with CATIA V5 for two stage spur gearbox can be approached, by means of macros (piece of code) and with GUI form. The user has to supply some basic requirements of the gearbox and rest of the different parameters for design of gearbox is calculated by formulas. And then with the help of these parameters, part model of gearbox is created.