Gear Misalignment Research Articles

Research on Calculation and Optimization Methods for Tooth Flash Temperature and Meshing Power Loss of the Gear System in Drum Shearer

The operating conditions of the drum shearer are very complex, and its ranging arm gear system often suffers from gear scuffing and wear. Gear scuffing is caused by the adhesive wear, which is due to the instantaneous friction and flash temperature of the tooth surface, and the gear meshing power loss is also caused by tooth surface friction. In order to resist tooth scuffing and improve meshing efficiency of the transmission system, an improved semi-analytical tooth surface flash temperature calculation method was used. The tooth flash temperature status under various working conditions were analyzed in detail. Based on the mechanical model of the shearer drum picks, the load condition of the drum was analyzed. Under these load and boundary conditions, the misalignments of each gear pair in the ranging arm were calculated. The tooth surface load distribution was calculated under the gear misalignments, and then the theoretical tooth surface flash temperature and meshing power loss were determined. Next, the tooth micro-geometry was modified to reduce flash temperature and meshing power loss. The flash temperature distribution pattern of the optimized tooth surface was studied under various working conditions, and the meshing power loss was also obtained. Finally, experiments were conducted to verify the effects of the optimized tooth surface on the friction temperature rise and the effectiveness of the modification method. Tooth surface optimization aimed at reducing tooth surface flash temperature can also effectively reduce meshing power loss, which has a significant effect on gear anti-scuffing and energy saving.

Vibration characteristic investigation of an eccentric rotor system with rubbing

Assembly errors can lead to the eccentricity of rotors, further resulting in angular misalignment of rotors and inducing some secondary misalignments, such as the angular misalignment of gears and tilt misalignment of the inner ring of bearings (TMIRB). Ultimately, these misalignments can lead to rubbing faults. However, these misalignments have not raised significant concern, this article investigates their influence on the vibration responses of a dual-rotor-gear-bearing system with rubbing. First, a finite element model (FEM) of the system is built by using an in-house beam element code, and the nonlinear force model of the bearing is established based on the Hertz contact theory. Then, a new model to simulate angular misalignment of gears is proposed by changing the time-varying meshing stiffness (TVMS). Furthermore, the nonlinear dynamic characteristics of the system are investigated in detail under different misalignment angles and rotating speeds, and some interesting conclusions are summarized as follows. Specifically, analyses of the spectrum cascade of radial and axial responses reveal the presence of rich multi-time frequencies and combined frequencies. Moreover, as the misalignment angle increases, the system experiences partial rubbing, the rotating speed threshold (RST) corresponding to initial rubbing decreases, and the mesh stiffness of gears decreases. In summary, the proposed model and the results of the analysis offer valuable insights into the vibration characteristics of such systems and these findings can be instrumental in optimizing their design and operation.

Effect of combined (radial-axial-angular direction) misalignment on sliding wear of spur gears: A comprehensive study

This study explores accelerated gear failures due to misalignment-induced geometric stress concentration. A mathematical model is derived to assess misalignment effects on sliding wear of driver gears using MATLAB. The model's accuracy is validated against literature and experiments. A parametric study investigates the impact of design parameters on wear in combined misaligned gear pairs. Findings show that increasing radial misalignment raises pressure and sliding wear in the single-tooth contact zone, while axial misalignment decreases the contact zone, resulting in increased wear throughout the mesh cycle. Angular misalignment reduces the contact zone, leading to non-linear wear distribution along the tooth flank. Combined misalignment has the most severe effects, causing higher contact pressure, non-linear wear distribution, and increased wear in transition zones.

A dynamic gear load distribution model for epicyclic gear sets with a structurally compliant planet carrier

Structural deformations in a planet carrier under operating conditions results in misalignment of planet gears, which can significantly effect the gear mesh load distribution and load sharing of a planetary gear set. Therefore, to capture the influence of structural compliance associated with planet carrier, planet pin, and input/output shaft, a hybrid planetary dynamic load distribution model is developed in this paper. Finite element sub-structuring techniques are employed to ensure that the model is computational efficiency. The proposed model employs a simplex algorithm to iteratively solve for the elastic gear mesh contacts in conjunction with a numerical integration scheme, which enables it to inherently capture the influence of several component and system level design variations without the need for an empirical mesh stiffness formulation or transmission error excitation of the system. The developed formulation is used to study the effects of planet carrier flexibility on both the quasi-static and dynamic response of planetary gearsets. The discussed results not only illustrate the influence of carrier flexibility on the system response but also highlight the need for such computationally efficient models which could be used as design tools.

An elastic model for tooth contact analysis of spur gears using FEM simulation

Gears are a class of machine parts very often used in the most diverse industries due to their many advantages. In addition to the many benefits they provide, gears also have some disadvantages related to the noise and vibrations they can introduce into the system they are part of. The operating drawback which may occur is closely related to the geometry of contact and manufacturing and assembling errors. Investigation of the contact error effect on the operating condition should be first carried out through simulation approach. Gear efficiency can be investigated through the tooth contact analysis (TCA) method and stress analysis. The main target of TCA is to set up the contact path and to determine the transmission error function caused by clearance, gear misalignments or backlash. Generally, TCA is performed considering the elastic behaviour, which frequently implies to get data for different contact positions for full meshing analysis. Nevertheless, TCA outcome delivers noteworthy data about kinematic errors, contact ellipses and the estimation of the instantaneous contact point of the meshing gears. A numerical tool was developed in this work to obtain the contact path in spur gears, which allowed to compute the displacements, stress and strain fields in the contact regions. Furthermore, an analysis of the influence of manufacturing and assembling errors on the contact path and mesh quality was performed. Such an approach may provide an optimal design solution for spur gears.

Modelado por elemento finito de la fatiga en engranes de reductores de velocidad con desalineamiento radial y axial

Este artículo presenta un análisis de fatiga en engranes de reductores de velocidad sometidos a desalineamiento radial y axial. Se empleó el método del elemento finito para el cálculo de los ciclos de vida y del estado de esfuerzos alternantes en los engranes. El desalineamiento se consideró en función del módulo del engrane, M. El desalineamiento radial fue M0.2 y M0.5 y el desalineamiento axial fue M0.2 y M0.3. El mecanismo analizado corresponde a los engranes piñón y rueda de la primera etapa del reductor de velocidad de un vehículo todo terreno. En ambas condiciones de desalineamiento la máxima reducción en los ciclos de vida ocurre en el engrane piñón causados por elevados esfuerzos alternantes a medida que se incrementa el torque. Las variaciones en la zona de contacto entre los dientes debido a los desalineamientos en los engranes provocó concentraciones de esfuerzos en la cara y la raíz del diente

Fault detection for planetary gearbox based on an enhanced average filter and modulation signal bispectrum analysis

Transient impulses are important information for machinery fault diagnosis. However, the transient features contained in the vibration signals generated by planetary gearboxes are usually immersed by a large amount of background noise and harmonic components. Even mathematical morphology (MM) is an excellent anti-noise signal processing method that can directly extract the geometry of impulse features in the time domain, but the four basic operators of MM can only extract one-way impulses while cannot extract the bidirectional impulses effectively at the same time. To accurately extract the impulse feature information, a novel method for fault detection of planetary gearbox based on an enhanced average (EAVG) filter and modulated signal bispectrum (MSB) is proposed. Firstly, the properties of the extracted impulses based on the four basic operators of MM will be divided into two categories of enhanced average operators. The four EAVG filters consist of the average weighted combination of enhanced average operators, and then the best EAVG filter is selected based on correlation coefficient to implement on the original vibration signal. It allows EAVG filter to extract positive and negative impulses of vibration signal, thereby improving the accuracy of planetary gearbox fault detection. Subsequently, the performance of the EAVG filter is influenced by the length of its structural element (SE), which is adaptively determined using an indicator based kurtosis. Then, the EAVG filter selects the optimal SE length to eliminate the interference of background noise and harmonic components to enhance the impulse components of the vibration signal. However, the nonlinear modulation components that are related to the fault types and severities are not extracted exactly and still remained in the filtered signal by EAVG. Finally, the MSB is utilized to the EAVG filtered signal to decompose the modulated components and extract the fault features. The advantages of EAVG over average (AVG) filter are clarified in the simulation study. In addition, the EAVG-MSB is validated by analyzing the vibration signals of planetary gearboxes with sun gear chipped tooth, sun gear misalignment and bearing inner race fault. The results indicate that the EAVG-MSB is effective and accurate in feature extraction compared with the combination morphological filter-hat transform (CMFH) and average combination difference morphological filter (ACDIF), and the feasibility of the EAVG-MSB are proved for planetary gearbox condition monitoring and fault diagnosis.

Classification of pitting fault levels in a worm gearbox using vibration visualization and ANN

Mechanical power transmission systems are an indispensable part of the industrial process. The most complex equipment of these processes is the gear systems. Among the gear systems the worm gearboxes are used in various applications, especially those that need high transmission ratios in one reduction stage. However, worm wheel manifests defects easily because it is made of soft material, in comparison with the worm. The stress on each tooth surface may increase because of overload, shock load, cyclic load change, gear misalignment, etc. This often causes pitting faults in worm gearboxes. This paper focuses on the detection of localized pitting damages in a worm gearbox by a vibration visualization method and artificial neural networks (ANNs). For this purpose, the vibration signals are converted into an image to display and detect pitting defects on the worm wheel tooth surface. In addition, statistical parameters of vibration signals in the time and frequency domains are used as an input to ANN for multi-class recognition. Later, the results obtained from ANN are compared for both axial and radial vibration. It is found that the ANN can classify with high accuracy for any sample of the vibration data obtained from the radial direction according to fault severity levels.

A new method for testing polymer gear wear rate and performance

This paper provides details of a new test rig design and methodology intended for, and successfully applied to, measuring the gear wear rate and performance of polymer composite gears under both dry and lubricated conditions. One of its unique contributions is that it continuously measures the gear wear rate, a feature essential for understanding polymer gear behaviour. While sharing some concepts with the traditional back-to-back test configuration used for steel gears, the new method introduces a rotary freedom to the block supporting the polymer gears under test. This block rotates if the gear tooth thickness is reduced, which aids control of the test load. The gear surface wear rate is recorded continuously by using a capacitance transducer to measure the pivot block motion. A second unique contribution of the new test method involves splitting the support block so that controlled misaligned gear engagements (not reported in other designs) can be introduced and subsequent changes to wear behaviour studied. The paper first outlines the test rig concepts and design before discussing in more detail the gear wear rate measuring principles, the methods of centre distance adjustment and the achievement of virtually constant gear loading. Finally, a selection test results are presented in summary to further validate the new test method and illustrate potential applications.

Influence of Housing Stiffness of the Slewing Reducer of a Tower Crane on the Load Distribution Pattern over the Gear Tooth Flank

To increase the life of slewing reducers, the reliability of their gearboxes is essential. They should be designed, simulated, and tested considering the installation environment and actual load conditions. Many studies have been conducted on the reliability improvement of gearboxes for reducers; however, a few studies have considered actual input load conditions. Furthermore, there is insufficient research on the effects of housing stiffness on gear misalignment, gear life, and load distribution and maximum contact load of the gear tooth flank. In this study, the effects of housing stiffness were analyzed using input torque measurements to investigate the causes of ring gear damage during durability tests on a slewing reducer. The contact pattern of the gear tooth flank was analyzed by applying dyes to all gears inside the reducer, and the results were compared with simulation results. A large edge contact in the first-stage ring gear of conventional slewing reducers was suggested as the cause of the ring gear damage. A new simulation model using a gearbox housing with an increased stiffness showed that edge contact was improved by the decreased gear misalignment. No abnormal wear and/or partial fracture of the ring gear occurred during the durability test on the improved model under the same conditions as those of the initial model. These results indicate that an increase in the stiffness of the housing reduced the gear misalignment, improved the load distribution, decreased the maximum load of the tooth flank, and increased the gear life.

Design and application of a hybrid alignment platform for a double-sided hot embossing process

Hot embossing is a novel technique for the cost-effective production of micro-parts. Misalignment between the top and bottom surfaces of a product that has double-sided microstructures reduces its functions. Most solutions involve repairing or reproducing the embossing mold, which increases the cost for the molding process. This study proposes a hybrid alignment platform that allows accurate positioning and angular alignment for the embossing processes. The hybrid alignment platform includes two units. The upper unit allows angular adjustment using a precision rotary table. The lower unit allows positional adjustment using two orthogonal micrometers. Calibration tests are conducted for a series of adjustment steps along the X, Y and C axis. Only one alignment step is necessary for each axis. The alignment platform allows rapid positioning and increases replicability. The hybrid mold adjustment platform is used to resolve a problem with gear misalignment and the problem of eccentricity in the production of micro-gears is effectively resolved.

Experimental study of the effect of assembly error on the lightly loaded transmission error of spur gear with crown modification

Experimental measurement of transmission error and vibration of a gear pair with crown modification are developed. With the help of high-precision optical encoder, effects of gear misalignment on unloaded and lightly loaded dynamic transmission error, which are relative to gear rattle, are investigated. The gear mesh misalignment is introduced by eccentric sleeve assembled on the output shaft. Effects of modification and misalignment on the dynamic transmission error, are studied at different load and driving velocity conditions. The experimental results show that, with the increase of the crown amplitude, the peak-to-peak values of dynamic transmission error are decreasing dramatically. Impact deformation or elastic deformation is a very important part of the dynamic transmission error although they are unloaded or lightly loaded. The components in harmonics of meshing frequency will change distinctly comparing cases at low input shaft velocity without and with misalignment, but different phenomena are detected while increasing the input shaft velocity. Finally, the relation between transmission error and gear box vibration is illustrated, and spectrum kurtosis is introduced to reveal gear rattle.

Gear misalignment diagnosis using statistical features of vibration and airborne sound spectrums

Failure in gears, transmission shafts and drivetrains is very critical in machineries such as aircrafts and helicopters. Real time condition monitoring of these components, using predictive maintenance techniques is hence a proactive task. For effective power transmission and maximum service life, gears are required to remain in prefect alignment but this task is just beyond the bounds of possibility. These components are flexible, thus even if perfect alignment is achieved, random dynamic forces can cause shafts to bend causing gear misalignments. This paper investigates the change in energy levels and statistical parameters including Kurtosis and Skewness of gear mesh vibration and airborne sound signals when subjected to lateral and angular shaft misalignments. Novel regression models are proposed after validation that can be used to predict the degree and type of shaft misalignment, provided the relative change in signal RMS from an aligned condition to any misaligned condition is known.

A survey on gear meshing quality based on tooth contact analysis

Gears are common mechanical elements in power transmission systems. In order to avoid failure of transmission systems, it is necessary to inspect the gear meshing condition with respect to kinematic and dynamic parameters. Tooth contact analysis (TCA) method represents a useful tool for designing and analysing gear performance. It represents an important method to examine gear tooth contact points, contact ratios and kinematic errors. The primary objective of TCA is to establish the contact trail on gear tooth surfaces, and also to determine the transmission error functions generated by gear misalignments. TCA has several branches such as the loaded tooth contact analysis, unloaded tooth contact analysis and tooth contact analysis with errors. The determination of the initial contact point is necessary in order to achieve an accurate solution. The present survey allows a new insight into the improvement of the gear meshing quality, based on tooth contact analysis and transmission error.

Sensitivity Analysis of Helical Gears with Tooth Surface Modification to Applied Torque and Gear Misalignment

The numerical calculation model of time-varying mesh stiffness, static transmission error and composite mesh error of modified helical gears is developed based on loaded tooth contact analysis (LTCA) model. To minimize the fluctuation of vibration excitation force, the optimal modification parameters of three modification methods under designed applied torque and ideal tooth contact condition are determined, and the effects of three modification methods on time-varying mesh stiffness, static transmission error and composite mesh error are analyzed. In order to analyze the sensitivity of the three modification methods to applied torque and gear misalignment, the effects of applied torque in wide range and gear misalignment on vibration excitation force and dynamic transmission error are investigated. The results show that the difference of time-varying mesh stiffness, static transmission error, composite mesh error of helical gears with different modifications methods are obvious. However, the fluctuation of vibration excitation force of helical gears is reduced significantly. When the applied torque is higher than the designed applied torque, the three modification methods show a great reduction of system vibration. When the applied torque is too low, the vibration of modified helical gears is larger than unmodified ones. Meanwhile, the resonance speed of the helical gears is slightly lower. With the increase of gear misalignment, the resonance speed becomes lower correspondingly and the effect of the three modification methods on the reduction of vibration excitation force is not obvious any more. The results can provide effective reference for establishing robust optimization method for tooth surface modification.

A numerical method for calculating the misalignments of planetary gears

Because misalignments derived from the deflections of transmission systems have significant effects on the load capacity of planetary gears, these misalignments should be accurately considered in the analysis of planetary gears. Here, we develop a new approach for misalignment calculations of cylindrical planetary gears. A nonlinear model of a planetary gear transmission system is built based on the finite element method and nonlinear bearing theory for misalignment calculations that can precisely simulate the structural characteristics and mechanical properties of a planetary gear system. The nonlinear static equation of a planetary system is solved efficiently using the Newton–Raphson method. Gear misalignments of all the planet branches are determined by the results of the system static analysis. The reliability and advantages of the proposed method are discussed via case studies. The effects of including the variation of the planet positions and the nonlinearity of the bearing stiffness on the planetary gear misalignments under different load conditions are studied. The misalignments can be reliably determined using the proposed method for calculating the load capacity of planetary gears.

Effect of gear misalignment on contact area: Theoretical and experimental studies

Parallel and angular gear misalignments reduce effective contact area and increase contact stresses, which in turn accelerate gear surface fatigue failure. In the present study, experiments on gear tooth contact area by varying degree and extent of misalignment have been performed. Theoretical model to estimate contact area as a function of misalignment is proposed. A methodology to measure contact area using coordinate measuring machine (CMM) is also discussed.The results of effective contact area obtained from theoretical and experimental studies show good agreement. It is observed that in the case of axial and radial misalignments, the contact patch area reduces linearly in proportion to amount of misalignment while in case of angular misalignment it follows a non-linear behaviour. As far as the angular misalignment is concerned, the contact patch changes from rectangular to quadrilateral and finally to triangular shape depending upon angle of misalignment. At an angular misalignment of 9°, contact patch shifts from quadrilateral to triangular shape. Combined parallel and angular misalignments result in larger reduction in contact area as compared with individual axial, radial and angular misalignment.

A calculation method of tooth profile modification for tooth contact analysis technology

Tooth contact analysis (TCA) technology is an approach for computerized simulation of meshing of aligned and misaligned gear, which has been widely used in the design of gears. In TCA technology, the gear modification is completed by first modifying the cutter and then using the cutter to cut the gear blank. The obtained results are the modification parameters of cutter rather than those of gear. With the rapid development of numerical control technology, directly modifying tooth profile becomes more convenient than modifying cutter to the complete tooth profile modification. However, at present, there is no bridge between TCA technology and tooth profile direct modification. Therefore, a calculation method of tooth profile modification for TCA technology is proposed in this paper. Firstly, the simulation process of machining gear by standard rack cutter is introduced. The profile equation and coordinates for standard gear tooth profile are given. Secondly, the simulation process of machining gear by modified rack cutter is introduced. The profile equation and coordinates for modified gear tooth profile are derived. Finally, by comparing the standard tooth profile with the modified tooth profile, the modification of tooth profile is calculated. Thus, the modification parameters of rack cutter obtained by TCA technology can be converted into the modification of tooth profile. An experiment which verified the accuracy of method is provided by the comparison between measuring curve of tooth profile of actual modification and theoretical curve of modified tooth profile.

Dynamic Stiffness Effect of Mechanical Components on Gear Mesh Misalignment

In this work, we propose a method that considers the dynamic elastic stiffness of mechanical components in a quasi-static condition, and we investigate this parameter’s effect on gear mesh misalignment. Unlike conventional approaches, which consider static stiffness only, the proposed method allows compensation of the dynamic response of the gearbox components under the quasi-static assumption, enabling more precise and practical gear design. A two-stage parallel gearbox is presented, designed, and numerically analyzed. The results demonstrate that the dynamic stiffness has a significant effect on gear misalignment and should, therefore, be carefully considered in the gear design process.

Online condition monitoring of misaligned meshing gears using wear debris and oil quality sensors

PurposeThis paper aims to investigate the effect of misalignment on wear of spur gears and on oil degradation using online sensors.Design/methodology/approachThe misalignment effect on gears is created through a self-alignment bearing, and is measured using laser alignment system. Several online sensors such as Fe-concentration sensor, moisture sensor, oil condition sensor, oil temperature sensor and metallic particle sensor are installed in the gear test rig to monitor lubricant quality and wear debris in real time to assess gearbox failure.FindingsOffset and angular misalignments are detected in both vertical and horizontal planes. The failure of misaligned gear is observed at both the ends and on both the surfaces of the gear teeth. Larger-size ferrous and non-ferrous particles are traced by metallic particle sensor due to gear and seal wear caused by misalignment. Scanning electron microscope (SEM) images examine chuck, spherical and flat platelet particles, and confirm the presence of fatigue (pitting) and adhesion (scuffing) wear mechanism. Energy-dispersive X-ray spectroscopy analysis of SEM particles traces carbon (C) and iron (Fe) elements due to gear failure.Originality/valueGear misalignment is one of the major causes of gearbox failure and the lubricant analysis is as important as wear debris analysis. A reliable online gearbox condition monitoring system is developed by integrating wear and oil analyses for misaligned spur gear pair in contact.