Gear Research Articles

Calculation of Time-Varying Mesh Stiffness of Internal Gears based on Precise Tooth Profile and Dynamic Analysis of Planetary Systems with Root Cracks

The internal meshing spur gear pair is the research object, and the potential energy method is applied to calculate the time-varying meshing stiffness of the internal gear. The internal gear tooth profile is divided into two parts: involute and transition curves, and the gear tooth stiffness is calculated by numerical integration based on accurate tooth profile, which improves the calculation accuracy. Analyzed the influence of different crack size parameters on the stiffness of internal meshing gears. A coupled dynamic model of a planetary system with internal gear crack faults was established, and the influence of cracks on the dynamic response of the planetary system was studied using Zoom-FFT spectrum and cepstrum analysis methods. The simulation results show that as the crack parameter size increases, the mesh stiffness of the internal gear pair gradually weakens, and the periodic vibration impact of the planetary-internal gear pair is also more severe. Cepstrum analysis can easily capture weak fault characteristic frequency information in the system and discover their variation patterns. The research results can provide a theoretical basis for the state monitoring and fault diagnosis of gear systems with crack defects.

A novel method for helical gear modeling with an experimental validation

Dynamic models are important for developing gear diagnostics methods since they allow physical phenomena occurring during operation to be studied in a relatively simple environment. The main challenge in gear modeling is the calculation of the time-variant gear mesh stiffness, and this challenge is even greater in helical gears. The mechanism of helical gears is more complex than in spur gears; the helix angle both adds an axial component to the contact force and also makes the contact line three-dimensional. This study suggests a novel dynamic model for helical gear vibrations that combines an existing validated dynamic model for spur gears with a unique extension for helical gears. The extension is based on a common method called “multi-slice”, according to which the helical tooth width is divided into infinitesimal slices, and each slice is treated as spur tooth. The suggested model introduces a novel implementation of the multi-slice method that overcomes the aforementioned challenges with only few parameters and calculations, depends on the tooth geometry. Furthermore, for the first time in helical gear modeling, the manufacturing profile errors are integrated to the model to generate scatter in the data that can better reflect the reality. The model is validated experimentally and for two different test-rigs by a qualitative comparison of the RMS of the vibration signal. The simulations and the measured data show similar behavior at different ranges of rotational speed and applied load, emphasizing the potential inherent in the model for future work on gear fault diagnosis.

A Generalized Algorithm and Simulation Verification of Non-circular Gear Tooth Surface Data Points

A Generalized Algorithm and Simulation Verification of Non-circular Gear Tooth Surface Data Points

Modelling approaches for surface densification process of sintered gear teeth

Modelling approaches for surface densification process of sintered gear teeth

A high-power-density design method for polymer gear systems via an adaptive non-dominated sorting genetic algorithm III and surrogate sub-models

There is a growing and prevalent trend in the power transmission field of high-performance polymers replacing metallic materials given the strict light-weight requirement. Polymer gears exhibit a low elasticity modulus, high-temperature sensitivity, and increased geometric design flexibility, presenting technical challenges to the straightforward application of metallic design methods to polymer gear systems. This study is centred on the development of a high-power-density polymer gear transmission system for the accessory unit of a gas turbine engine, utilising an adaptive NSGA-III algorithm and surrogate sub-models. A comprehensive assessment indicator for the operating performance of the transmission system is suggested, encompassing gear strength, bearing temperature, and shaft torsional stiffness. The model made it possible to simultaneously optimise forty-six structural parameters, including gear tooth module, web thickness, and bearing clearance. In contrast to the original steel design scheme, the optimised polymer gear transmission system indicated a 49% reduction in weight and a 1.96-fold increase in power density. This presents a method for substituting steel with polymers for effective power transmission.

Modeling and analysis of elastohydrodynamic lubrication of orthogonal face gear with installation errors

Installation error is one of the most prominent factors affecting the lubrication of face gear. To analyze the lubrication performance of the face gear with installation errors, the installation error model of the orthogonal face gear transmission system is established. Then, the contact path, equivalent curvature radius, load distribution and entrainment velocity are studied using the face gear loaded tooth contact analysis (LTCA). On this basis, the lubrication governing equations of the face gear are established according to the elastohydrodynamic lubrication (EHL) theory. In addition, the oil film thickness, oil film pressure and coefficient of friction in the process of face gear drives are calculated using the method of progressive mesh densification (PMD). Finally, the effects of axis intersection angle error, axis intersection error and axial displacement error on lubrication characteristics are analyzed. The results reveal that when the axial intersection angle error and axial displacement error are negative and the axial intersection error is positive, the minimum oil film thickness of the face gear tooth surface is less than that without error. When the error values are the same, the minimum oil film thickness and coefficient of friction have larger changes with the axial displacement error than with the axis intersection error, and the contact path has a bigger movement range.

Effect of Gear Tooth Cracks on the Dynamic Characteristics of Gear Transmission System of High-Speed Train

Abstract In order to study the dynamic characteristics of a high-speed train gear transmission system with cracks, time-varying meshing stiffness of gear teeth with different cracks was obtained using energy method. A torsional vibration model of the gear transmission system of a high-speed train was established. Based on the model, the ρ-value describing the change in stiffness was used to obtain the analytical solution of a system with crack faults. The influence of the degree of crack on the dynamic characteristics of a system under torque excitation of the driving end and load end was analyzed. In contrast with a normal gear system, a system containing a crack fault generated no harmonic response. Moreover, for a given set of working conditions, the degree of crack only affected the resonance amplitude and frequency of the system. These results form a robust guide for the detection of crack faults in the gear transmission system of a high-speed train.

Performance evaluation of 3D-printed ABS and carbon fiber-reinforced ABS polymeric spur gears

Acrylonitrile butadiene styrene (ABS) polymer and carbon fiber reinforced acrylonitrile butadiene styrene (CF/ABS) spur gears were 3D-printed using fusion deposition modeling (FDM) with different fillet radii of 0.25, 0.50, and 0.75 mm. The performance of the fabricated gears was studied with the effect of fillet radius on varying load and speed conditions. The thermal properties of the gears were also investigated. The results indicated that 3D-printed CF/ABS spur gear exhibited better performance than the pure ABS. The 3D-printed CF/ABS gear with fillet radius of 0.25 mm recorded the highest wear and thermal stresses. However, the optimum performance was exhibited by the gear sample with highest fillet radius of 0.75 mm. Repeated gear tooth loading during service caused an increase in gear temperature due to the hysteresis and friction. Using optical microscopy, the tooth structures of both 3D-printed ABS and CF/ABS spur gears were analyzed before and after loading conditions to establish their failure mechanism. Evidently, various applications of the FDM 3D-printed spur gears depend on their different performances under loads and operating speeds. The methods and findings of this work can be regarded as helpful for future related work related to cellulosic reinforcing particles in a polymer matrix.

Failure analysis of gear using continuous wavelet transform applied in the context of wind turbines

One of the main reasons for failure in the wind turbine is the wear between the gear teeth during the power conversion and changes in the rotation speed, which is also generally associated with changes in the lubrication regimes. In this sense, vibration and signal analysis are frequently used in predictive maintenance as they usually permit the identification of deviations in the proper functioning of the equipment. Thus, this work aims to apply the continuous wavelet transform (CWT) to correlate gear wear and vibration signals, using visual and straightforward analysis. An experimental setup of a gear system was used to analyze vibration signals from different tooth gear damages. Gears with different levels and modes of damage were used in order to evaluate the sensitivity of vibration signals to them. The features from vibration signals were extracted by Morlet wavelet analysis. Results demonstrate that the proposed method accurately detected the early failure by visualization in frequency–time maps.

Surface Durability of 3D-Printed Polymer Gears

This paper proposes a series of experimental determinations carried out with the aim of generating new conclusions regarding the ability of 3D-printed gears to be integrated into mechanisms without lubrication. The main factors that influence the appearance of wear in non-lubricated contact are sliding speed, material hardness, surface finish, surface geometry, and material microstructure. The tests considered the type of material from which they were made and the 3D printing technology type. For testing the gear wheels, a mechatronic experimental setup was made consisting of two shafts with adjustable axial distances, a wheel loading system gears, an electric motor, and a command-and-control system. In terms of materials, four types of materials were monitored: PA (polyamide), PLA (polylactic acid), ABS (acrylonitrile butadiene styrene) and PP (photopolymer). The evaluation of the gear wear was carried out by checking the gearing on two flanks (Frenco ZWP 06) and by scanning with the ATOS CORE 135 3D scanner. The PA and PP gears failed to meet the structural integrity standards after the tests. The PLA gears exhibited superior resistance to abrasive wear compared to the ABS gears, whereas the ABS gears generally demonstrated stronger structural integrity.

Manufacturing bamboo spur gears and assessing dynamic performance

Manufacturing bamboo spur gears and assessing dynamic performance

Improved mesh stiffness model of spur gear considering spalling defect influenced by surface roughness under EHL condition

Gear tooth spalling is a typical tooth surface defects in gear transmission. The accurate calculation of the time-varying mesh stiffness of the gear pair with spalling defect under mixed elastohydrodynamic lubrication (EHL) plays an important role in tooth damage prediction and fault feature analysis. In this work, an improved time-varying mesh stiffness (TVMS) model of spalling faulty gear in mixed EHL line contact considering the coupled effect of rough surface topography is established. The proposed model considers the combined effect of spalling defect, surface roughness topography, and lubrication on the contact characteristics of the meshing interface to obtain a revised contact stiffness, which is further used to determine the comprehensive TVMS. The cylindrical contact coefficient for curved meshing interface with spalling fault is derived and incorporated into the statistical micro-contact Greenwood and Williamson model (GW model) to obtain the asperity contact stiffness. The revised contact stiffness at the rough faulty gear interface is obtained from the parallel action of the asperity contact stiffness and oil film stiffness under load-sharing concept. The dynamic responses of the gear system are analyzed using the established mesh stiffness model through the six degrees of freedom translational-torsional dynamic model, in which the dynamic meshing force is calculated iteratively using the transit surface topography and geometrical parameters along the line of contact instead of a quasi-static meshing force. Effects of multi-parameters as surface roughness, spalling fault size, and lubricant on the mesh characteristics and dynamic responses of the gear system are further investigated and discussed.

Prediction of mechanical efficiency of spur gear pairs based on tribo-dynamics model of multi-tooth meshing

The prediction of load-dependent losses of gear pairs is a topic of constant concern, which depends largely on the modelling of friction coefficient in tooth meshing. Although the current load-sharing based models can handle the friction coefficient in mixed elastohydrodynamic lubrication regimes, dynamics behaviour of each tooth pair or the time variation of direction of normal contact load is not taken into consideration. This study proposes a new method for modelling efficiency of spur gear pairs in transient operating conditions by coupling the multi-tooth meshing model with the friction coefficient model. The friction coefficient is modelled through load-sharing function, and the gear dynamics model is established with regard to alternate meshing of single-double tooth pair and time variation of direction of normal load and mesh stiffness. The model is validated by comparing the calculated results of friction coefficients and load-dependent losses with experimental data in published literatures, showing good agreement. At the end, the efficiency model is applied to two types of gear pairs to investigate the influence of tooth shapes and operating parameters on the load-dependent losses of gear pairs.

Dimensional Deviations and Distortion Mechanism of Polymer Spur Gear Fabricated by Fused Deposition Modeling

Dimensional Deviations and Distortion Mechanism of Polymer Spur Gear Fabricated by Fused Deposition Modeling

Эластичные хоны для полирования профилей зубьев термообработанных цилиндрических колес специального назначения

Introduction. The most important component of the technological process of manufacturing of gear wheels of critical products is the operation of teeth honing. Special requirements are imposed on the surface quality of special-purpose gears, where imported abrasive tools were used, the supply of which in modern economic conditions is impossible. Purpose of work: development of formulation, technological equipment and technology of manufacturing of elastic diamond gear hones instead of imported ones for teeth honing of gear wheels of special purpose. Research methods. Subject of research are samples of imported elastic gear hones and created domestic analogs. The mechanical properties, morphology and chemical composition of the abrasive (diamond) layer of the working surface of the teeth and the annular gear were determined. The content of chemical elements was controlled in separate points of the surface and by scanning over the area on a scanning electron microscope. The formulation and technology of production of annular gears were determined. Results and Discussion. Designs of molds for forming the abrasive layer and the hub of the gear hone are developed. The peculiarities of morphology of the material of the working layer and the annular gear of the elastic diamond gear hone are revealed. On the basis of the conducted research, domestic analogs of materials of constituent elements of the gear hone are determined. Two manufacturing technologies were considered: pressing and injection molding. Two molds were made to test the technology: a simplified model consisting of two teeth and a round mold. Several methods of manufacturing hone teeth were analyzed: manufacturing of an abrasive layer with different degree of pre-vulcanization, subsequent introduction of gear material and final vulcanization of the whole product. The mechanical properties of the materials of the working abrasive layer and the annular gear were determined. The chemical composition of the components of the hone and the boundary zone are studied. As a result of the conducted research, recommendations on the formulation of the abrasive layer and the annular gear, technology of manufacturing of the gear hone intended for final treatment of teeth of heat-treated spur wheels of special purpose are given.

An improved dynamic model of spur gears considering delayed meshing out of the contact point due to root crack

Tooth root crack generally causes large deformation of meshing gear pairs, which results in delayed meshing out of the contact point. In this paper, an improved dynamic model of spur gears considering delayed meshing out of the contact point due to root crack is proposed, which takes several factors of mesh stiffness, mesh damping coefficient and delayed meshing out force into account. The effects of different crack depths and angles on the dynamic characteristics of the gear system are investigated through various simulation and experimental tests. Further, the improved gear dynamic model is validated by comparison with acceleration responses obtained from the experimental test rig under different working conditions. The findings indicate that the acceleration responses of the improved dynamic model are consistent with experimental results, in both time and frequency domains under different crack depths and angles.

Studying the Performance of Reinforced Polymer Gear Wheels: Development of an Advanced Test Bench for Wear Analysis

In recent years, polymeric materials have gained prominence as a competitive option for gear manufacturing. Nevertheless, the absence of comprehensive literature addressing the wear due to the coupling of these materials presents a real challenge in response to this innovative trend. Wear of plastic gearwheels represents, in fact, a key issue, traditionally assessed using standard formulations under optimal dry operating conditions. These calculations often rely on coefficients derived from specialized gear tests, but their applicability is constrained to specific polymer–metal combinations. This research was dedicated to the development of a test bench tailored to evaluate the wear of glass fiber-reinforced self-lubricating polymer gearwheels under different operating conditions. This study commenced with a comprehensive exploration of wear phenomena in thermoplastic gearwheels and the inherent challenges associated with utilizing existing standards and the scientific literature for wear analysis. This was followed by a careful evaluation of the operational needs of the test bench, which, starting from a basic solution already implemented, improved its use in various aspects. Finally, this study introduced an optical-based methodology for average linear wear control. This research strived to establish a testing approach that minimizes uncertainties when assessing the wear of thermoplastic gears.

Improving the Load Carrying Capacity through Asymmetric Spur Gear using WC-Fe Metal Matrix Composite for Automobile Applications

Gears are the components that have been used for a century to transmit power from one place to another place. Symmetric spur gears are commonly used in the gearbox to transmit power between two parallel shafts. In order to increase the load carrying capacity of the spur gear with reduced noise and vibration, its profile can be modified. This can be achieved by changing the gear tooth design into asymmetric form. Asymmetrically toothed gears are used in power transmission for transmitting the power in one direction. These teeth help to improve the load carrying and power transmitting capacity of the gear. The strength can be further increased by changing the material used in gears. This can be made possible by using Metal Matrix Composite as a gear material. The metal matrix composites have high stiffness and strength to weight ratio compared to the Alloy Steel. The main objective of this project is to increase the load carrying capacity of the spur gear by using WC-Fe metal matrix composite material. The symmetric and asymmetric gear modeling has been done for existing car gear (Maruthi 800) using Ansys parametric design language software. The contact stress, bending stress and von Mises stress of the composite, as well as conventional gear material, is analyzed and the results are compared to find the percentage increase in strength of the gear.

Integrated CFD-FEM approach for external gear pump vibroacoustic field prediction

In this work, a three-dimensional fluid-structural and vibro-acoustics coupled model of a gear pump is presented. Gear pumps represent the majority of the positive displacement machines used for flow generation in fluid power systems. Typically, the dynamics of gear pumps are dependent on the characteristics of the fluid dynamics inside the pump, which translates into vibrations to the housing. These vibrations then propagate to the surrounding medium and emit sound. The purpose of this study is to propose a three-dimensional fully integrated computational model to simulate the complete gear pump behaviour from the fluid dynamics to the structural vibrations, up to the vibroacoustic response. In this hybrid configuration, a transient CFD (Computational Fluid Dynamics) model is first developed to simulate the 3D flow field with a deforming and re-meshing approach to take into account the variation of the volume between the gears. Second, the internal pressure field calculated at each time step is then used as a loading into a structural FEM (Finite Element Method) model of the gear pump to compute the actual stresses and deformations of the housing. Third, the results of the structural response are used as excitation in a vibroacoustic sub-model to simulate the radiated noise using a high-order FEM technique. The comparison between the numerical and experimental flow curves validates the CFD model. The sound power calculations from the vibroacoustic model show good comparison with the sound intensity measurements around the pump casing, confirming the validity of the proposed coupled model. The described CFD-FEM approach proves to be a powerful gear pump design tool: it provides a reliable estimate of gear pump working parameters such as fluid power and vibroacoustic characteristics, starting from the CAD (Computer-Aided Design) geometry of the components. Furthermore, being one of the first multi-domain simulation models of a gear pump, this work can be useful to researchers as a starting point to correlate the noise emitted with the internal flow in full 3D conditions.

COMPUTER SUPPORT FOR THE DESIGN OF THE HOB CUTTER

The aim of the work is to create a computer program in the 3D CAD system T Flex CAD allowing the creation of parametric models for the design and construction of a modular hob cutter for the selected gearing. The thesis includes the analysis of the problem of hob cutters for the production of spur gearing with an involute profile, the analysis of the initial surface and the shape of the tool cutting edge for the involute surface, the determination of the basic profile of the cutting edge of the hob cutter (geometry of the basic worm, geometry of the cutting edge) and the calculation of the design parameters of the tool. The individual calculations will be programmed in the 3D CAD system T Flex CAD, which will allow to generate a specific 3D model of the hob cutter based on the change of input requirements for the production of a given spur gear (module, engagement angle, tooth inclination angle), with the possibility of displaying the required tool in a 2D view in its base, normal and side planes, which will be in the form of a standard technical drawing. This paper presents the preparation (unification calculations, introduction) before the final version of the computer program for the creation of the parametric tool models.