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1
Glodež, Srečko, and Marko Šori. "Bending Fatigue Analysis of PM Gears." Key Engineering Materials 754 (September 2017): 299–302. http://dx.doi.org/10.4028/www.scientific.net/kem.754.299.
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The paper discusses the computational and experimental approach for determination of the PM gears service life concerning bending fatigue in a gear tooth root. A proposed computational model is based on the stress-life approach where the stress field in a gear tooth root is determined numerically using FEM. The experimental procedure was done on a custom made back-to-back gear testing rig. The comparison between computational and experimental results has shown that the proposed computational approach is appropriate calculation method for service life estimation of sintered gears regarding tooth root strength. Namely, it was shown that in the case of proper heat treatment of tested gears, the tooth breakage occurred inside the interval with 95 % probability of failure, which has been determined using proposed computational model.
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Portron, Stéphane, Philippe Velex, and Vincent Abousleiman. "A hybrid model to study the effect of tooth lead modifications on the dynamic behavior of double helical planetary gears." Proceedings of the Institution of Mechanical Engineers, Part C: Journal of Mechanical Engineering Science 233, no. 21-22 (May 1, 2019): 7224–35. http://dx.doi.org/10.1177/0954406219846156.
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In this paper, a hybrid model is used to investigate the dynamic behavior of planetary gears. Sun-gear, planets, and ring-gear are modeled using lumped parameters elements, while planet carrier is integrated via a condensed finite element model. This approach intends to be more precise than the traditional lumped parameter models while keeping acceptable computational times. In some aeronautical applications, tooth lead modifications can be necessary to counterbalance the effect of planet carrier deflections on tooth load distribution. This study focuses on the influence of various lead modifications on the dynamic behavior of double helical planetary gears over a broad range of loads.
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Liu, Yanping, Yongqiang Zhao, Ming Liu, and Xiaoyu Sun. "Parameterized High-Precision Finite Element Modelling Method of 3D Helical Gears with Contact Zone Refinement." Shock and Vibration 2019 (July 7, 2019): 1–17. http://dx.doi.org/10.1155/2019/5809164.
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In order to perform a tooth contact analysis of helical gears with satisfactory accuracy and computational time consuming, a parameterized approach to establish a high-precision three-dimension (3D) finite element model (FEM) of involute helical gears is proposed. The enveloping theory and dentiform normal method are applied to deduce the mathematical representations of the root transit curve as well as the tooth profile of the external gear in the transverse plane based on the manufacturing process. A bottom-up modelling method is applied to build the FEM of the helical gear directly without the intervention of CAD software or creating the geometry model in advance. Local refinement methodology of the hexahedral element has been developed to improve the mesh quality and accuracy. A computer program is developed to establish 3D helical gear FEM with contact region well refined with any parameters and mesh density automatically. The comparison of tooth contact analysis between the coarse-mesh model and local refinement model demonstrates that the present method can efficiently improve the simulation accuracy while greatly reduce the computing cost. Using the proposed model, the tooth load sharing ratio, static transmission error, meshing stiffness, root bending stress, and contact stress of the helical gear are obtained based on the quasistatic load tooth contact analysis. This methodology can also be used to create other types of involute gears, such as high contact ratio gear, involute helical gears with crossed axes, or spiral bevel gears.
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Zorko, Damijan, Jože Duhovnik, and Jože Tavčar. "Tooth bending strength of gears with a progressive curved path of contact." Journal of Computational Design and Engineering 8, no. 4 (June 18, 2021): 1037–58. http://dx.doi.org/10.1093/jcde/qwab031.
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Abstract The article presents a comprehensive study on the tooth bending strength of spur gears with a progressive curved path of contact, or so-called S-gears. Systematic gear meshing simulations were conducted to study the effects of S-gear geometry parameters on tooth bending strength. Different S-gear geometries were analysed in a systematically organized manner, and a comparison was made against a standard 20° pressure angle involute shape. Furthermore, different material combinations, e.g. polymer/polymer, steel/polymer, and steel/steel, of both drive and driven gear were analysed within a meaningful range of loads. The gear profile shape, material combination of the drive and the driven gear, and the transmitted load were found as the main parameters affecting gear tooth bending stress. Complex, non-linear relations between the recognized effects and the corresponding root stress were observed. Based on the numerical results, a shape factor, which considers the above-mentioned effects, was introduced, and a model for root strength control of S-gears was proposed and verified employing the finite element method (FEM).
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Kahraman, A., P. Bajpai, and N. E. Anderson. "Influence of Tooth Profile Deviations on Helical Gear Wear." Journal of Mechanical Design 127, no. 4 (October 5, 2004): 656–63. http://dx.doi.org/10.1115/1.1899688.
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In this study, a surface wear prediction model for helical gears pairs is employed to investigate the influence of tooth profile deviations in the form of intentional tooth profile modifications or manufacturing errors on gear tooth surface wear. The wear model combines a finite-element-based gear contact mechanics model that predicts contact pressures, a sliding distance computation algorithm, and Archard’s wear formulation to predict wear of the contacting tooth surfaces. Typical helical gear tooth modifications are parameterized by an involute crown, a lead crown, and an involute slope. The influence of these parameters on surface wear are studied within typical tolerance ranges achievable using hob/shave process. The results indicate that wear is related to the combined modification parameters of a gear pair rather than individual gear parameters. At the end, a design formula is proposed that relates the mismatch of contacting surface slopes to the maximum initial wear rate.
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Lu, Fengxia, Meng Wang, Wenbin Pan, Heyun Bao, and Wenchang Ge. "CFD-Based Investigation of Lubrication and Temperature Characteristics of an Intermediate Gearbox with Splash Lubrication." Applied Sciences 11, no. 1 (December 31, 2020): 352. http://dx.doi.org/10.3390/app11010352.
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In this study, we propose a computational fluid dynamics (CFD)-based method to study the lubrication and temperature characteristics of an intermediate gearbox with splash lubrication. A volume of fluid (VOF) multiphase model was used to track the interface between oil and air. A multiple reference frame (MRF) model was adopted to accurately simulate the movement characteristics of the gears, bearings, and the surrounding flow field. The thermal-fluid coupling computational model of an intermediate gearbox with splash lubrication was then established. Combined with experimental results, we verified that the lubricating oil temperature was below the limit requirement (<110 °C). The numerical results revealed that large amounts of lubricating oil were splashed onto the tooth surfaces near the gear meshing area. A large convective heat transfer coefficient corresponds to a low gear tooth surface temperature. The tooth surface temperature of the driving gear is higher than that of the driven gear. The distribution law of oil volume fraction of the bearing roller was jointly affected by the roller rotation direction and gravity. The convective heat transfer coefficient of the roller wall was largely related to the lubrication environment of the roller, including the oil distribution inside the bearing cavity and the flow rate.
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Ji, Hongchao, Jianwei Dong, Weichi Pei, Haiyang Long, and Jing Chu. "Solution of Spur Gear Meshing Stiffness and Analysis of Degradation Characteristics." Mechanics 26, no. 2 (April 20, 2020): 153–60. http://dx.doi.org/10.5755/j01.mech.26.2.23270.
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The computational model of spur gear meshing stiffness is established by using the hypothesis of cantilever beam of the gear. The meshing stiffness of spur gear is calculated by analytical method, and the distributional curve of meshing stiffness is obtained by comparison with FEM. Experimental verification of simulated results is performed by mechanical test-bed of closed flow. The experimental results show that the simulation results are in good agreement with the experimental results. Based on the FEM models of gear tooth with cracks of different lengths, the comparison between degradation trends in different meshing regions that shows that the degree of degradation in a single tooth meshing area is much higher than in a double teeth meshing region. In the FEM models of gear tooth with cracks of different lengths, the stiffness degradation rate of the double tooth indentation area increases first and then decreases, and the crack length is most obvious between 4 and 8 mm.
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Bo, Shen Yun, Xuan Liu, and Li Jun Wang. "Design of double-crowned tooth geometry for spiroid gear produced by precision casting process." Proceedings of the Institution of Mechanical Engineers, Part B: Journal of Engineering Manufacture 232, no. 6 (September 8, 2016): 1021–30. http://dx.doi.org/10.1177/0954405416661003.
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A novel double-crowned tooth geometry is proposed by the application of ease-off topography for spiroid gear manufactured by precision casting process, with the goals of localizing the bearing contact and obtaining a perfect function of transmission errors. The modified tooth surface is applied as the reference geometry to machine the die cavity geometry that will produce such geometry of the gears. The tooth geometry of crowned gear was achieved first from a pre-designed controllable function of transmission errors along the desired contact path. Then, the desired ease-off topography along the contact line is designed and calculated computationally from the given mathematic model of surface modification. The geometry of double-crowned spiroid gear could be reconstructed by superimposing the ease off of contact line direction on the profile-crowned tooth surface. The article provides numerical examples to validate the feasibility of ease-off modification methodology that was used to produce the double-crowned tooth geometry for the gears, while tooth contact analysis is performed computationally to investigate the stability of bearing contact and function of transmission errors to alignment.
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Zhao, Ning, and Qing Jian Jia. "Research on Windage Power Loss of Spur Gear Base on CFD." Applied Mechanics and Materials 184-185 (June 2012): 450–55. http://dx.doi.org/10.4028/www.scientific.net/amm.184-185.450.
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The paper established three-dimensional Computational fluid dynamic (CFD) model of the oil-air mixture in the gearbox after meshing by ICEM CFD simulated the turbulence model by the CFD. The method of calculate the windage power loss (WPL) of the spur gear were put forward. In order to reduced the WPL, compared the results between the CFD model with different modulus、clearance of the shroud and radius of the modification of gear top. The modulus is major parameter to WPL; the gear with shroud have lower WPL , WPL of the tooth flank and clearance of the tooth flank shroud do not show the proportional relationship, the gear with smallest clearance of gear side have lowest WPL，the modification of gear top can reduce the eddy scale which can reduce the WPL.
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Liu, Xinrong, and Zhonghou Wang. "Analysis of Contact Part of Error Tooth Surface and Dynamic Performance Prediction for Involute Gear." Mathematical Problems in Engineering 2017 (2017): 1–11. http://dx.doi.org/10.1155/2017/6143054.
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Aiming at the problem of constructing digital model of involute gear with error, the method of linear interpolation combined with area weight interpolation is proposed. Based on the non-feature discrete data block technique, the true tooth surface discrete data obtained by the coordinate measuring instrument is divided into blocks, and then the interpolation method is used to interpolate the nonmeasurement area to construct the real tooth surface with errors. The contact part and dynamic performance of the gear are predicted by using the constructed error tooth surface. The contact error of the tooth surface and the transmission error of the gear are verified by the test, and the reliability of the judgment result is judged by measuring the vibration in the direction of the gear meshing line. Compared with the example, this method not only reduces the computational complexity of the interpolation algorithm, but also improves the accuracy of the tooth interpolation data points and the smoothness of the error tooth surface.
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Song, Chao Sheng, Cai Chao Zhu, Teik Chin Lim, and Rong Fan. "Computational Tooth Root Stress Analysis of Crossed Beveloid Gears with Small Shaft Angle." Applied Mechanics and Materials 86 (August 2011): 188–91. http://dx.doi.org/10.4028/www.scientific.net/amm.86.188.
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It is known that tooth bending failures are directly caused by the stress state at the tooth root or fillet regions of the gear teeth. In this study, the geometric and manufacturing of the fillet and root of crossed beveloid are investigated and a computational tooth stress prediction model is setup applying exact geometry-based mesh theory. The dominate fillet and root design parameter and load were examined in the loaded tooth contact analysis to analyze root stresses.
12
Spitas, C., and V. Spitas. "Coupled multi-DOF dynamic contact analysis model for the simulation of intermittent gear tooth contacts, impacts and rattling considering backlash and variable torque." Proceedings of the Institution of Mechanical Engineers, Part C: Journal of Mechanical Engineering Science 230, no. 7-8 (July 23, 2015): 1022–47. http://dx.doi.org/10.1177/0954406215596696.
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Variable torque conditions in geared powertrain applications are known to lead to tooth contact loss, contact reversal, tooth impacts, rattling vibration and noise. Displacements/ deflections dominate the low-torque high-vibration responses and, besides backlash, the real-time dynamic lateral deflections of the gear bodies and the occurrence of simultaneous double-sided tooth contact influence the instantaneous mesh excitation strongly. The faster deterministic and stochastic analytical models do not consider this coupling, whereas the numerical models that do so implicitly by simulating the contact of discretised tooth surfaces/ volumes are significantly limited by the accuracy and computational overhead of their discrete meshes. To provide a both fast and accurate solution of the contact problem, especially in displacement-dominated operating conditions, this work analyses the dynamic contact of gears starting from basic principles and derives an accurate analytical model for the coupling between the compliance, contact geometry, the backlash, and the torsional and lateral displacements and deflections in the general three-dimensional multi-DOF system. This serves as a foundation for a series of dynamical simulations of a single-stage spur gear transmission under different variable-torque excitations to predict tooth contact loss and contact reversal and the basic interactions that lead to impacts and rattling vibration. This approach can be used to predict critical torque fluctuation levels, beyond which these phenomena emerge.
13
Kačalová, Mária, and Slavko Pavlenko. "STRENGHT AND DYNAMIC ANALYSIS OF A STRUCTURAL NODE LIMITING THE MULTI-OUTPUT GEAR MECHANISM." Acta Polytechnica 57, no. 5 (October 31, 2017): 316. http://dx.doi.org/10.14311/ap.2017.57.0316.
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The rapidly advancing technological development leads to designing and researching a new multi- output gear mechanism. The investigated new double-output gear mechanism has two output coaxial shafts located against the input shaft on the other side of the gearbox. The gear mechanism achieves high gear ratios. Its limiting structural node is the output stage, to which the gears belong. The problem is addressed through the analysis of the stress resistance of tooth flanks in contact and bending. The content of the paper is a comparison of analytical computations with the modal analysis on the model. We expect that new findings will be beneficial for further optimization of the gear mechanism.
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Wang, Yanzhong, Yang Liu, Wen Tang, and Peng Liu. "Parametric finite element modeling and tooth contact analysis of spur and helical gears including profile and lead modifications." Engineering Computations 34, no. 8 (November 6, 2017): 2877–98. http://dx.doi.org/10.1108/ec-06-2016-0203.
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Purpose The finite element method has been increasingly applied in stress, thermal and dynamic analysis of gear transmissions. Preparing the models with different design and modification parameters for the finite element analysis is a time-consuming and highly skilled burden. Design/methodology/approach To simplify the preprocessing work of the analysis, a parametric finite element modeling method for spur and helical gears including profile and lead modification is developed. The information about the nodes and elements is obtained and exported into the finite element software to generate the finite element model of the gear automatically. Findings By using the three-dimensional finite element tooth contact analysis method, the effects of tooth modifications on the transmission error and contact stress of spur and helical gears are presented. Originality/value The results demonstrate that the proposed method is useful for verifying the modification parameters of spur and helical gears in the case of deformations and misalignments.
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de Vaujany, Jean-Pierre, Michèle Guingand, Didier Remond, and Yvan Icard. "Numerical and Experimental Study of the Loaded Transmission Error of a Spiral Bevel Gear." Journal of Mechanical Design 129, no. 2 (February 8, 2006): 195–200. http://dx.doi.org/10.1115/1.2406089.
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The design of spiral bevel gears in aeronautical gear boxes requires very precise and realistic numerical simulations. One important criteria is the loaded transmission error (LTE) that gear designers attempt to reduce at the nominal torque. This paper presents a numerical tool that simulates the loaded meshing of spiral bevel gears and experimental tests carried out on a real helicopter gear box. Tooth profile is defined by the Gleason cutting process and tooth bending effects and contact deformations are both taken into account. The bending effect computation uses a three-dimensional finite element model, while the contact deformations are obtained by using Boussinesq’s theory. Experimental measurements of the LTE were performed using magnetic and optical encoders rigidly connected with the pinion and gear shafts, giving access to the records of the instantaneous angular positions. The numerical simulations fit quite well the experimental results.
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Du, S., R. B. Randall, and D. W. Kelly. "Modelling of spur gear mesh stiffness and static transmission error." Proceedings of the Institution of Mechanical Engineers, Part C: Journal of Mechanical Engineering Science 212, no. 4 (April 1, 1998): 287–97. http://dx.doi.org/10.1243/0954406981521222.
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A modified transmission error (TE) model is introduced for analysing the effects on the transmission error of variation of tooth body stiffness with load application point, and a simulation program for transmission error computation with varying stiffness has been developed. In order to obtain the case where the tooth deflection component is the dominant source of the TE, nylon gears were used in this study. All the simulation results have been compared with the measured transmission errors from a single-stage gearbox. Even though carried out on low precision gears, the validity of the model for the more flexible nylon gears indicates that the model can be used for analysing the transmission error of high-precision gear sets.
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Lin, Chao, and Zhiqin Cai. "Modeling of dynamic efficiency of curve–face gear pairs." Proceedings of the Institution of Mechanical Engineers, Part C: Journal of Mechanical Engineering Science 230, no. 7-8 (December 17, 2015): 1209–21. http://dx.doi.org/10.1177/0954406215623308.
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The characteristics and the tooth distribution regularity of curve–face gear were analyzed based on the elastohydrodynamic lubrication. Then a model for the prediction of mechanical dynamic efficiency of curve–face gear was presented by the concentrated parameters, including dynamic-loading tooth force, coefficient, the oil film thickness, the space relative velocity and load distribution. The discretization method was introduced to solve the computational formulas of key factors above. A meshing period defined from trough (enter meshing point) to peak (outer meshing point) of the pitch curve and the tooth profile was discreted into some parts for calculation of the sliding and the rolling power losses. The dynamic and static efficiency of curve–face gear were analyzed, and the results of simulation and test were similar during the corresponding time, which verified the correctness of theoretical model.
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Rai, Paridhi, and Asim Gopal Barman. "Optimizing the design of straight bevel gear with reduced scoring effect." Engineering Computations 37, no. 7 (March 11, 2020): 2391–409. http://dx.doi.org/10.1108/ec-06-2019-0250.
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Purpose The purpose of this paper is to minimize the volume of straight bevel gear and to develop resistance towards scoring failure in the straight bevel gear. Two evolutionary and more advance optimization techniques were used for performing optimization of straight bevel gears, which will also save computational time and will be less computationally expensive compared to a previously used optimization for design optimization of straight bevel gear. Design/methodology/approach The following two different cases are considered for the study: the first mathematical model similar to that used earlier and without any modification to show efficiency of the optimization algorithm for straight bevel gear design optimization and the second mathematical model consist of constraints on scoring and contact ratio along with other generally used design constraints. Real coded genetic algorithm (RCGA) and accelerated particle swarm optimization (APSO) are used to optimize the straight bevel gear design. The effectiveness of the algorithms used has been validated by comparing the obtained results with previously published results. Findings It has been found that APSO and RCGA outperform other algorithms for straight bevel gear design. Optimized design values have reduced the scoring effect significantly. The values of the contact ratio obtained further enhances the meshing operation of the bevel gear drive by making it smoother and quieter. Originality/value Low volume is one of the essential requirements of gearing applications. Scoring is a critical gear failure aspect that leads to the broken tooth in both high speed and low-speed applications of gears. The occurrence of scoring is hard to detect early and analyse. Scoring failure and contact ratio have been introduced as design constraints in the mathematical model. So, the mathematical model demonstrated in this paper minimizes the volume of the straight bevel gear drive, which has been very less attempted in previous studies, with scoring and contact ratio as some of the important design constraints, which the objective function has been subjected to. Also, two advanced and evolutionary optimization algorithms have been used to implement the mathematical model to reduce the computational time required to attain the optimal solution.
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Silich, A. A., and Eh M. Yusupova. "Mathematical model of shaping toothed products using volumetric tool with one motion parameter." Advanced Engineering Research 20, no. 3 (October 5, 2020): 295–301. http://dx.doi.org/10.23947/2687-1653-2020-20-3-295-301.
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Introduction. The development of a mathematical model of one-parameter shaping of a toothed product is considered. As an example, shaping of the side surface of the teeth of the Novikov gearing is studied; the mode and magnitude of the change in the shaping error heightwise the wheel tooth are shown. The work objective was to develop a mathematical model of the surface of the product teeth as a generating surface envelope of the tool. A computational and experimental study is carried out. The mathematical models obtained can be used in devices with copiers when shaping the side surface of the teeth of the Novikov gear. As an example, we consider the deviation behavior of the teeth profile of the Novikov gear with the original profile of DLZ 0.7-0.15 Materials and Methods. When building the model and studying its characteristics, the mathematical tools of the gearing theory, calculation procedure for cylindrical gears (A.A. Silich’s author development) were used. The paper proposes new mathematical models of the equations of the lateral surface of the gear teeth formed with a tool whose axial profile coincides with the original one. In the model under consideration, the tool moves along the axis of the product while the latter rotates on its axis. In the course of the study, numerical modeling was carried out to determine the error value in shaping the product profile using the tool. Results. New mathematical models and software have been developed for numerical simulation of the shaping of a toothed product using a tool with one independent motion parameter. An algorithm has also been developed to determine the deviation error of the real profile from the nominal one for the tooth of the Novikov gear. Solutions to accurately reproduce the tooth profile are provided. Discussion and Conclusions. The parametric method of analytical description of the surface used in the work simplifies the calculation of the cutting tool displacements in the problems of numerical control. Solving the problem of synthesizing the technology of workpiece surface treatment on metal-cutting machines provides the development of a description of the entire shaping process and requires the representation of the workpiece surface in the form of a mathematical model. The results obtained can be used under creating finishing methods for processing teeth when improving the quality of gear wheels and gear drives, as well as production efficiency.
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Spitas, Vasilios A., Theodore N. Costopoulos, and Christos A. Spitas. "Optimum Gear Tooth Geometry for Minimum Fillet Stress Using BEM and Experimental Verification With Photoelasticity." Journal of Mechanical Design 128, no. 5 (November 27, 2005): 1159–64. http://dx.doi.org/10.1115/1.2216731.
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This paper introduces the concept of nondimensional gear teeth to be used in gear stress minimization problems. The proposed method of modeling reduces the computational time significantly when compared to other existing methods by essentially reducing the total number of design variables. Instead of modeling the loaded gear tooth and running BEA to calculate the maximum root stress at every iterative step of the optimization procedure, the stress is calculated by interpolation of tabulated values, which were calculated previously by applying the BEM on nondimensional models corresponding to different combinations of the design parameters. The complex algorithm is used for the optimization and the root stresses of the optimum gears are compared with the stresses of the standard gears for the same transmitted torque. Reduction in stress up to 36.5% can be achieved in this way. This reduction in stress has been confirmed experimentally with two-dimensional photoelasticity.
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Guo, Han, Jianwu Zhang, and Haisheng Yu. "Dynamic modelling and parametric optimization of a full hybrid transmission." Proceedings of the Institution of Mechanical Engineers, Part K: Journal of Multi-body Dynamics 233, no. 1 (July 17, 2018): 17–29. http://dx.doi.org/10.1177/1464419318784271.
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In this paper, vibro-impact-induced gear whine radiated by full hybrid transmission equipped with a compound type power-split planetary gear train is investigated. For accurate simulations of the planetary gear set vibrations, an integrated dynamic model of the transmission is established using professional software MASTA, on which compliance effects of gear pairs, bearings, shafts, housing and planetary carrier are counted for. Numerical analyses are carried out for dynamic responses of the hybrid transmission. Bench tests are also conducted for the present model validation. Computational effort is made to recognize parametrically resonate patterns that cause gear whine in experiment. An optimal tooth modification design is presented for the real planetary gear set. It is shown by test results using the optimized planetary gear sets that gear whine responses of the gearboxes are considerably improved.
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Abadjiev, Valentin, and Emilia Abadjieva. "One Approach to the Synthesis, Design and Manufacture of Hyperboloid Gear Sets With Face Mating Gears. Part 1: Basic Theoretical and Cad Experience." Journal of Theoretical and Applied Mechanics 46, no. 2 (June 1, 2016): 3–26. http://dx.doi.org/10.1515/jtam-2016-0007.
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Abstract Hyperboloid gear drives with face mating gears are used to transform rotations between shafts with non-parallel and non-intersecting axes. A special case of these transmissions are Spiroid and Helicon gear drives. The classical gear drives of this type are the Archimedean ones. The objective of this study are hyperboloid gear drives with face meshing, when the pinion possesses threads of conic convolute, Archimedean and involute types, or the pinion has threads of cylindrical convolute, Archimedean and involute types. For simplicity, all three types transmis- sions with face mating gears and a conic pinion are titled Spiroid and all three types transmissions with face mating gears and a cylindrical pinion are titled Helicon. Principles of the mathematical modelling of tooth contact synthesis are discussed in this study. The presented research shows that the synthesis is realized by application of two mathematical models: pitch contact point and mesh region models. Two approaches for synthesis of the gear drives in accordance with Olivier’s principles are illustrated. The algorithms and computer programs for optimization synthesis and design of the studied hyperboloid gear drives are presented.
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Dai, Yu, Feiyue Ma, Xiang Zhu, Qiao Su, and Xiaozhou Hu. "Evaluation and Optimization of the Oil Jet Lubrication Performance for Orthogonal Face Gear Drive: Modelling, Simulation and Experimental Validation." Energies 12, no. 10 (May 20, 2019): 1935. http://dx.doi.org/10.3390/en12101935.
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The oil jet lubrication performance of a high-speed and heavy-load gear drive is significantly influenced and determined by the oil jet nozzle layout, as there is extremely limited meshing clearance for the impinging oil stream and an inevitable blocking effect by the rotating gears. A novel mathematical model for calculating the impingement depth of lubrication oil jetting on an orthogonal face gear surface has been developed based on meshing face gear theory and the oil jet lubrication process, and this model contains comprehensive design parameters for the jet nozzle layout and face gear pair. Computational fluid dynamic (CFD) numerical simulations for the oil jet lubrication of an orthogonal face gear pair under different nozzle layout parameters show that a greater mathematically calculated jet impingement depth results in a greater oil volume fraction and oil pressure distribution. The influences of the jet nozzle layout parameters on the lubrication performance have been analyzed and optimized. The relationship between the measured tooth surface temperature from the experiments and the corresponding calculated impingement depth shows that a lower temperature appears in a situation with a greater impingement depth. Good agreement between the mathematical model with the numerical simulation and the experiment validates the effectiveness and accuracy of the method for evaluating the face gear oil jet lubrication performance when using the impingement depth mathematical model.
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Dai, Yu, Jifu Jia, Bin Ouyang, and Jianeng Bian. "Determination of an Optimal Oil Jet Nozzle Layout for Helical Gear Lubrication: Mathematical Modeling, Numerical Simulation, and Experimental Validation." Complexity 2020 (May 12, 2020): 1–18. http://dx.doi.org/10.1155/2020/2187027.
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To provide a basic guidance for the selection of nozzle layout, a mathematical model of the impingement depth for helical gears under oil jet lubrication is established. Furthermore, computational fluid dynamics (CFD) methods are adopted to validate the effectiveness and accuracy of the derived impingement model. Firstly, the distribution characteristics of the oil volume fraction and oil-gas pressure in meshing area were obtained in flow field simulation. Meanwhile, the influence of spray angle, jet velocity, and gear ratio on lubrication effect was obtained. Then, the transient temperature field of the tooth surface was simulated by the method of thermal-fluid coupling analysis, and the lowest temperature distribution and the corresponding oil jet velocity were determined. Finally, experiments on the temperature characteristics measured by an infrared thermal imager of helical gears with different nozzle parameters were carried out in a gear test rig. The simulation results of transient temperature field are in good agreement with those obtained by experiments, and it indicates that the thermal-fluid coupling analysis method is correct and feasible to predict the temperature field of the helical gear pair under oil injection jet lubrication.
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Corvaglia, Alessandro, Massimo Rundo, Paolo Casoli, and Antonio Lettini. "Evaluation of Tooth Space Pressure and Incomplete Filling in External Gear Pumps by Means of Three-Dimensional CFD Simulations." Energies 14, no. 2 (January 9, 2021): 342. http://dx.doi.org/10.3390/en14020342.
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The paper presents the computational fluid dynamics simulation of an external gear pump for fluid power applications. The aim of the study is to test the capability of the model to evaluate the pressure in a tooth space for the entire shaft revolution and the minimum inlet pressure for the complete filling. The model takes into account the internal fluid leakages and two different configurations of the thrust plates have been considered. The simulations in different operating conditions have been validated with proper high dynamics transducers measuring the internal pressure in a tooth space for the entire shaft revolution. Steady-state simulations have been also performed in order to detect the fall of the flow rate due to the incomplete filling of the tooth spaces when the inlet pressure is reduced. It has been demonstrated that, despite the need of a compromise for overcoming the limitation of considering fixed positions of the gears’ axes and of the thrust plates, significant results can be obtained, making the CFD approach very suitable for such analyses.
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Corvaglia, Alessandro, Massimo Rundo, Paolo Casoli, and Antonio Lettini. "Evaluation of Tooth Space Pressure and Incomplete Filling in External Gear Pumps by Means of Three-Dimensional CFD Simulations." Energies 14, no. 2 (January 9, 2021): 342. http://dx.doi.org/10.3390/en14020342.
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The paper presents the computational fluid dynamics simulation of an external gear pump for fluid power applications. The aim of the study is to test the capability of the model to evaluate the pressure in a tooth space for the entire shaft revolution and the minimum inlet pressure for the complete filling. The model takes into account the internal fluid leakages and two different configurations of the thrust plates have been considered. The simulations in different operating conditions have been validated with proper high dynamics transducers measuring the internal pressure in a tooth space for the entire shaft revolution. Steady-state simulations have been also performed in order to detect the fall of the flow rate due to the incomplete filling of the tooth spaces when the inlet pressure is reduced. It has been demonstrated that, despite the need of a compromise for overcoming the limitation of considering fixed positions of the gears’ axes and of the thrust plates, significant results can be obtained, making the CFD approach very suitable for such analyses.
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Abadjiev, Valentin, and Emilia Abadjieva. "One Approach to the Synthesis, Design and Manufacture of Hyperboloid Gear Sets with Face Mating Gears. Part 2: Review of Practical Realization." Journal of Theoretical and Applied Mechanics 46, no. 3 (September 1, 2016): 3–16. http://dx.doi.org/10.1515/jtam-2016-0013.
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Abstract Hyperboloid gear drives with face mating gears are used to transform rotations between shafts with non-parallel and non-intersecting axes. A special case of these transmissions are Spiroid1 and Helicon gear drives. The classical gear drives of this type are Archimedean ones. The objective of this study are hyperboloid gear drives with face meshing, when the pinion has threads of conic convolute, Archimedean and involute types, or the pinion has threads of cylindrical convolute, Archimedean and involute types. For simplicity, all three type transmissions with face mating gears and a conic pinion are titled Spiroid and all three type trans- missions with face mating gears and a cylindrical pinion are titled Helicon. Principles of the mathematical modelling of tooth contact synthesis are discussed in Part 1: Basic theoretical and CAD experience of this study. The second part of this article is a brief overview of the innovations and inventions created in this field at the Institute of Mechanics – Bulgarian Academy of Sciences in the last three decades. This study is also dedicated on elaboration of the specialized face gear sets for implementation into bio-robot hand. It is based on the application of 3D software technology, using 3D print for the realization of the physical models of the gear drives.
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Wang, Jian D., and Ian M. Howard. "Error Analysis on Finite Element Modeling of Involute Spur Gears." Journal of Mechanical Design 128, no. 1 (May 2, 2005): 90–97. http://dx.doi.org/10.1115/1.2114891.
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Finite element analysis can incorporate two-dimensional (2D) modeling if the geometry, load, and boundary conditions meet the requirements. For many applications, a wide range of problems are solved in 2D, due to the efficiency and costs of computation. However, care has to be taken to avoid modeling errors from significantly influencing the result. When the application area is nonlinear, such as when modeling contact problems or fracture analysis, etc, the 2D assumption must be used cautiously. In this paper, a large number of 2D and three-dimensional (3D) gear models were investigated using finite element analysis. The models included contact analysis between teeth in mesh, a gear body (disk), and teeth with and without a crack at the tooth root. The model results were compared using parameters such as the torsional (mesh) stiffness, tooth stresses and the stress intensity factors that are obtained under assumptions of plane stress, plane strain, and 3D analysis. The models considered variations of face width of the gear from 5 mm to 300 mm. This research shows that caution must be used especially where 2D assumptions are used in the modeling of solid gears.
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Dai, Guang Hao, Ai Jun Zhao, Hai Fu Zhang, and Chang Wei Gao. "Research on Relationship between Modulus and Tooth Number of Transmitting Gear and Vibration Noise." Applied Mechanics and Materials 86 (August 2011): 192–95. http://dx.doi.org/10.4028/www.scientific.net/amm.86.192.
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The dynamic model of gear driving system is built using centralized mass method in this paper. On the base of frequency domain and time domain results of model derived from equation of Fourier series, the example of a certain gearbox is calculated. Through adjusting the parameters of modulus and tooth number of gearbox, the dynamics computation is completed. The relationship between diversification of modulus and tooth number of gear and vibration noise is gained by comparatively analyzing the calculation results.
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Cheng, Yuping, and Teik C. Lim. "Dynamics of Hypoid Gear Transmission With Nonlinear Time-Varying Mesh Characteristics." Journal of Mechanical Design 125, no. 2 (June 1, 2003): 373–82. http://dx.doi.org/10.1115/1.1564064.
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The coupled translation-rotation vibratory response of hypoid geared rotor system due to loaded transmission error excitation is studied by employing a generalized 3-dimensional dynamic model. The formulation includes the effects of backlash nonlinearity as well as time-dependent mesh position and line-of-action vectors. Its mesh coupling is derived from a quasi-static, 3-dimensional, loaded tooth contact analysis model that accounts for the precise gear geometry and profile modifications. The numerical simulations show significant tooth separation and occurrence of multi-jump phenomenon in the predicted response spectra under certain lightly loaded operating conditions. Also, resonant modes contributing to the response spectra are identified, and cases with super-harmonics are illustrated. The computational results are then analyzed to quantify the extent of non-linear and time-varying factors.
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Velex, P., and L. Flamand. "Dynamic Response of Planetary Trains to Mesh Parametric Excitations." Journal of Mechanical Design 118, no. 1 (March 1, 1996): 7–14. http://dx.doi.org/10.1115/1.2826860.
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An extended three-dimensional model is used for calculating dynamic tooth loads on a planetary gear set. Time dependent mesh stiffnesses are determined and an original Ritz method aimed at solving large parametrically excited differential systems is proposed. Results from the Ritz method compare favorably with those given by direct integrations for highly reduced computation times. The difference between local critical speeds (for one individual mesh) and global critical speeds (for sun or ring gear-planet meshes) on a sequential spur gear train is pointed out. Finally, it is shown that, for linear behaviors, mesh stiffnesses are largely controlling dynamic tooth loads while the influence of a floating sun or ring gear is less important.
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Zeng, Qing-liang, Zhi-yuan Sun, Li-rong Wan, Yang Yang, Han-zheng Dai, and Zhi-kuan Yang. "Research and Comparative Analysis of Flow Field Characteristics and Load-Independent Power Losses of Internal and External Gear Pairs." Mathematical Problems in Engineering 2020 (December 9, 2020): 1–19. http://dx.doi.org/10.1155/2020/8860588.
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Power loss analysis of gear transmission in a transmission system is of great significance to improve the efficiency of the power system, and load-independent power losses are an important part of the power losses of gear transmission. Based on the computational fluid dynamics (CFD) method, the hydrodynamic models of internal and external gear pairs are established. By analyzing the pressure field and the velocity field, the windage and squeezing power losses and the pressure and viscous power losses, the influence of rotation speed and tooth width on flow field characteristics, and load-independent power losses of internal gear pair are studied. In addition, we compare the flow field characteristics and the load-independent power losses between external and internal gear pairs and discuss the difference between them. The results show that the pressure and fluid velocity in the meshing area of the gear pair are greatly affected by rotation speed and tooth width, and the load-independent power losses increase with the increase of rotation speed and tooth width. At the same rotation speed, the transmission ratio and number of teeth, windage, and squeezing power losses of the external gear pair are smaller than those of the internal gear pair. Compared with the internal gear pair, the external gear pair has more advantages in controlling the load-independent power losses. The difference of the load-independent power losses of the two meshing modes mainly comes from the viscous power losses of the wheel gear of internal gear pair. This paper provides a basis for the selection of the gear meshing mode and the analysis of load-independent power losses of the transmission system.
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Wang, Jianhong, Jian Wang, and Teik C. Lim. "Influence of assembly error and bearing elasticity on the dynamics of spur gear pair." Proceedings of the Institution of Mechanical Engineers, Part C: Journal of Mechanical Engineering Science 230, no. 11 (April 27, 2015): 1805–18. http://dx.doi.org/10.1177/0954406215584632.
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The elasticity and geometrical errors of precision elements are one of the major factors affecting vibration responses in geared transmission systems. In this study, the influences of assembly error and bearing elasticity on the spur gear dynamic behavior are analyzed. A lumped parameter model for spur gear pair is formulated by representing the bearing elasticity with infinitesimal spring elements and tooth stiffness time function as rectangular waveform. The nonuniform tooth contact load is also considered. The severity of assembly error is assumed to be sufficiently small such that no partial loss of tooth contact occurs. A harmonic balance method is applied to the resultant second-order partial differential equation governing the gear pair dynamic behavior. The variations of dynamic transmission error and tooth contact load with respect to mesh frequency for a set of bearing stiffness are analyzed. The influences of bearing stiffness on the dynamic transmission error are also evaluated. The variation of actual cross angle, an indicator on the tooth meshing state, is examined with respect to nominal cross angle and bearing stiffness. The analysis shows that the presence of bearing elasticity and assembly error can degenerate tooth contact significantly, and hence the appropriate specifications of bearing and mesh stiffness are critical at gearbox design stage. The analysis demonstrates that the proposed lumped parameter model can provide detailed contact information like finite element model, but it avoids finite element model’s prohibitive computation burden and can be completed easily and be computed quickly.
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Duan, Zhenyun, Ning Wang, Jingshun Fu, Wenhui Zhao, Boqiang Duan, and Jungui Zhao. "High Precision Edge Detection Algorithm for Mechanical Parts." Measurement Science Review 18, no. 2 (April 1, 2018): 65–71. http://dx.doi.org/10.1515/msr-2018-0010.
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AbstractHigh precision and high efficiency measurement is becoming an imperative requirement for a lot of mechanical parts. So in this study, a subpixel-level edge detection algorithm based on the Gaussian integral model is proposed. For this purpose, the step edge normal section line Gaussian integral model of the backlight image is constructed, combined with the point spread function and the single step model. Then gray value of discrete points on the normal section line of pixel edge is calculated by surface interpolation, and the coordinate as well as gray information affected by noise is fitted in accordance with the Gaussian integral model. Therefore, a precise location of a subpixel edge was determined by searching the mean point. Finally, a gear tooth was measured by M&M3525 gear measurement center to verify the proposed algorithm. The theoretical analysis and experimental results show that the local edge fluctuation is reduced effectively by the proposed method in comparison with the existing subpixel edge detection algorithms. The subpixel edge location accuracy and computation speed are improved. And the maximum error of gear tooth profile total deviation is 1.9 μm compared with measurement result with gear measurement center. It indicates that the method has high reliability to meet the requirement of high precision measurement.
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Ali, Yasir Hassan, Roslan Abd Rahman, and Raja Ishak Raja Hamzah. "Artificial Neural Network Model for Monitoring Oil Film Regime in Spur Gear Based on Acoustic Emission Data." Shock and Vibration 2015 (2015): 1–12. http://dx.doi.org/10.1155/2015/106945.
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The thickness of an oil film lubricant can contribute to less gear tooth wear and surface failure. The purpose of this research is to use artificial neural network (ANN) computational modelling to correlate spur gear data from acoustic emissions, lubricant temperature, and specific film thickness (λ). The approach is using an algorithm to monitor the oil film thickness and to detect which lubrication regime the gearbox is running either hydrodynamic, elastohydrodynamic, or boundary. This monitoring can aid identification of fault development. Feed-forward and recurrent Elman neural network algorithms were used to develop ANN models, which are subjected to training, testing, and validation process. The Levenberg-Marquardt back-propagation algorithm was applied to reduce errors. Log-sigmoid and Purelin were identified as suitable transfer functions for hidden and output nodes. The methods used in this paper shows accurate predictions from ANN and the feed-forward network performance is superior to the Elman neural network.
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Lias, M. R., M. Awang, M. N. Talib, A. R. Senawi, and M. A. Samad. "Investigation of Axial Misalignment Effects to the Gear Tooth Strength Properties Using FEM Model." JOURNAL OF MECHANICAL ENGINEERING AND SCIENCES 12, no. 2 (June 30, 2018): 3581–92. http://dx.doi.org/10.15282/jmes.12.2.2018.5.0317.
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Lias, M. R., M. Awang, M. N. Talib, A. R. Senawi, and M. A. Samad. "Investigation of Axial Misalignment Effects to the Gear Tooth Strength Properties Using FEM Model." JOURNAL OF MECHANICAL ENGINEERING AND SCIENCES 12, no. 2 (June 30, 2018): 3581–92. http://dx.doi.org/10.15282/jmes.12.2.2018.5.317.
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Mo, Shuai, Shuai Ma, Guoguang Jin, Yidu Zhang, Chao Lv, and Haruo Houjoh. "Research on Multiple-Split Load Sharing Characteristics of 2-Stage External Meshing Star Gear System in Consideration of Displacement Compatibility." Mathematical Problems in Engineering 2017 (2017): 1–8. http://dx.doi.org/10.1155/2017/1037479.
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This paper studies the multiple-split load sharing mechanism of gears in two-stage external meshing planetary transmission system of aeroengine. According to the eccentric error, gear tooth thickness error, pitch error, installation error, and bearing manufacturing error, we performed the meshing error analysis of equivalent angles, respectively, and we also considered the floating meshing error caused by the variation of the meshing backlash, which is from the floating of all gears at the same time. Finally, we obtained the comprehensive angle meshing error of the two-stage meshing line, established a refined mathematical computational model of 2-stage external 3-split loading sharing coefficient in consideration of displacement compatibility, got the regular curves of the load sharing coefficient and load sharing characteristic curve of full floating multiple-split and multiple-stage system, and took the variation law of the floating track and the floating quantity of the center wheel. These provide a scientific theory to determine the load sharing coefficient, reasonable load distribution, and control tolerances in aviation design and manufacturing.
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Yang, Kai Ming, Zhao Zhao Liu, Wei Fang Wang, and Li Wen Guan. "Accurate Mathematical Model of Profile Curve Generated by Pre-Grinding Hob and Three-Dimensional Simulation of the Gear Generation." Advanced Materials Research 842 (November 2013): 612–19. http://dx.doi.org/10.4028/www.scientific.net/amr.842.612.
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This paper illustrates a method to establish the theoretical equations of profile curve of gear teeth generated by the pre-grinding hob. Matrix computation and differential geometry are employed to derive the equations. Graphics of numerical examples based on the mathematical equations are interpreted using Matlab. The proposed model draws the conclusion about the proper parameters of the teeth profile for the optimization of hob design for industrial application. Furthermore, a three-dimensional model of the pre-grinding hob is built with Pro/E in parametric form as a supplementary approach. It is a descriptive-geometry-based method to generate the gear directly without mathematical derivation. By changing parameters that affect the geometry of a hob tooth profile the hobbing cutter can be constructed to generate any conjugated gear through the motion simulation. With the aid of exact mathematical model and computer program, efficiency of gear machining can be improved by eliminating the traditional trial and error procedure. Keywords-pre-grinding hob; antenna; differential geometry; theoretical equation; parametric design; simulation of generation.
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Nguyen, Cong Dai, Alexander E. Prosvirin, Cheol Hong Kim, and Jong-Myon Kim. "Construction of a Sensitive and Speed Invariant Gearbox Fault Diagnosis Model Using an Incorporated Utilizing Adaptive Noise Control and a Stacked Sparse Autoencoder-Based Deep Neural Network." Sensors 21, no. 1 (December 22, 2020): 18. http://dx.doi.org/10.3390/s21010018.
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Gearbox fault diagnosis based on the analysis of vibration signals has been a major research topic for a few decades due to the advantages of vibration characteristics. Such characteristics are used for early fault detection to guarantee the enhanced safety of complex systems and their cost-effective operation. There exist many fault diagnosis models that have been developed for classifying various fault types in gearboxes. However, the classification results of the conventional fault classification models degrade when they are applied to gearbox systems with multi-level tooth cut gear (MTCG) faults operating under variable shaft speeds. These conditions cause difficulty in discriminating the gear fault types. Due to the improved computational capabilities of modern systems, the application of deep neural networks (DNNs) is getting popular in a variety of research fields, such as image and natural language processing. DNNs are capable of improving the classification results even when addressing complex problems such as diagnosing gearbox MTCG faults. In this research, an adaptive noise control (ANC) and a stacked sparse autoencoder–based deep neural network (SSA-DNN) are used to construct a sensitive fault diagnosis model that can diagnose a gearbox system with MTCG fault types under varying shaft rotation speeds, despite its complicatedness. An ANC is applied to gear vibration characteristics to remove a significant level of noise along the frequency spectrum of vibration signals to fix the most fault-informative components of each fault case. Next, the autoencoder learns the gear faults characteristic features from these fault-informative components to separate the fault types considered in this study. Furthermore, the implementation of the SSA-DNN is substituted for feature extraction, feature selection, and the classification processes in traditional fault diagnosis schemes by high-performance unity. The experimental results show that the proposed model outperforms conventional methodologies with higher classification accuracy.
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Lu, Fengxia, Meng Wang, Weizhen Liu, Heyun Bao, and Rupeng Zhu. "CFD-based calculation method of convective heat transfer coefficient of spiral bevel gear in intermediate gearbox under splash lubrication." Industrial Lubrication and Tribology 73, no. 3 (January 19, 2021): 470–76. http://dx.doi.org/10.1108/ilt-07-2020-0233.
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Purpose This paper aims to propose a numerical method to calculate the convective heat transfer coefficient of spiral bevel gears under the condition of splash lubrication and to reveal the lubrication and temperature characteristics between the gears and the oil-air two-phase flow. Design/methodology/approach Based on computational fluid dynamics, the multiple reference frames (MRF) method was used to simulate the rotational characteristics of gears and the motions of their surrounding fluid. The lubrication and temperature characteristics of gears were studied by combining the MRF method with the volume of the fluid multiphase flow model. Findings The convective heat transfer coefficient can be improved by increasing the rotational speed and the oil immersion depth. Moreover, the temperature of the tooth surface having a large convective heat transfer coefficient is also found to be low. A large convection heat transfer coefficient could lead to a good cooling effect. Originality/value This method can be used to obtain the convective heat transfer coefficient values at different meshing positions, different radii and different tooth surface positions. It also can provide research methods for improving the cooling effect of gears under the condition of splash lubrication. Peer review The peer review history for this article is available at: https://publons.com/publon/10.1108/ILT-07-2020-0233/
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Li, Chang, Guang Bing Zhao, and Xing Han. "A Method of Reliability Sensitivity Analysis for Gear Drive System." Applied Mechanics and Materials 130-134 (October 2011): 2311–15. http://dx.doi.org/10.4028/www.scientific.net/amm.130-134.2311.
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Based on profile involutes equation and tooth easement curve equation of standard gear, parameterization three dimensional finite element model of the gear drive system is built up in ANSYS, and numerical computation of the working process is taken in ANSYS/LS-DYNA, then contact stress of and pressure distribution are got. It creates an ultimate state equation of every system parameter (input) converting to output (response), considering different system random error synthetically, sample points locations in input variable sampling space are fixed with the method of matrix experiment design, which was used in series of deterministic fitting test. In the test, least-squares procedure regression analysis of the ultimate state equation is taken to fix the items and coefficients after multiple fitting test. Using this ultimate state equation, system reliability level and reliability sensitivity of different variables can be calculated which provides theoretical bases for dynamic optimum design of gear drive system.
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Potočnik, Roki, Jože Flašker, Bostjan Zafošnik, and Srečko Glodež. "The Parametric Study of the Crack Growth in the Lubricated Rolling-Sliding Contact Problems." Key Engineering Materials 348-349 (September 2007): 689–92. http://dx.doi.org/10.4028/www.scientific.net/kem.348-349.689.
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A two-dimensional numerical model is used to describe the crack path in the lubricated rolling-sliding contact problems. The model assumes that the crack is initiated in a pre-existing micro pit, which resulted from the crack growth on the surface of a gear tooth flank. The lubricated rolling-sliding contact problem is modelled using the Hertz theory of contact, the Coulomb's law of friction and hydraulic pressure mechanism with constant pressure which simulates the effect of lubricant trapped into the crack. Different load cases are used to simulate the moving of a contact load. The crack propagation path is evaluated by a maximum tangential stress criterion and modified maximum tangential stress criterion which considers the stress intensity factors KI and KII, the T-stress, the critical distance ahead the crack tip rc, and the stress on the crack surfaces. The computational results show that the consideration of the T-stress has a significant influence on the crack path in the lubricated rolling-sliding contact problems.
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Budzik, Grzegorz, Bogdan Kozik, and Jacek Pacana. "Defining influence of load conditions on distribution and value of stresses in dual-power-path gear wheels applying FEM." Aircraft Engineering and Aerospace Technology 85, no. 6 (October 14, 2013): 453–59. http://dx.doi.org/10.1108/aeat-10-2012-0197.
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Purpose – The analysis, carried out for this publication, concerned checking the nature of mating of gear wheels with different load conditions. The computation was made applying FEM in Abaqus 6.10-1 program and concerned spur gears in dual-power-path gears made of ABS. The same geometrical models, material parameters and boundary conditions were assumed for all the analysed stages of the computation. However, the values of torque transmitted from active wheels to passive wheel of the gearing were changed. The paper aims to discuss these issues. Design/methodology/approach – Observing changes of stress levels for toothed wheel and pinions allows to state that for relatively low load values, bending stresses at tooth root change proportionally to the change of the applied load. Findings – Values of contact stresses on mating teeth flanks were also defined for the most loaded part of the dual-power-path gearing, namely for a pinion. In case of contact stresses, it was observed that together with constant increase of torque value, the values of stresses change but the nature of these changes is not proportional to the applied load. Out of all the analysed variants, the most favourable, from the point of view of durability, was the situation in initial (theoretical) model with regular power division on all mating wheels. Originality/value – Conclusions drawn as a result of numerical computation are helpful in defining the nature of work of dual-power-path gearing in different load conditions and will be compared to results of stand tests of the analysed gearing.
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Xiao, Yancai, Jinyu Xue, Mengdi Li, and Wei Yang. "Low-Pass Filtering Empirical Wavelet Transform Machine Learning Based Fault Diagnosis for Combined Fault of Wind Turbines." Entropy 23, no. 8 (July 29, 2021): 975. http://dx.doi.org/10.3390/e23080975.
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Fault diagnosis of wind turbines is of great importance to reduce operating and maintenance costs of wind farms. At present, most wind turbine fault diagnosis methods are focused on single faults, and the methods for combined faults usually depend on inefficient manual analysis. Filling the gap, this paper proposes a low-pass filtering empirical wavelet transform (LPFEWT) machine learning based fault diagnosis method for combined fault of wind turbines, which can identify the fault type of wind turbines simply and efficiently without human experience and with low computation costs. In this method, low-pass filtering empirical wavelet transform is proposed to extract fault features from vibration signals, LPFEWT energies are selected to be the inputs of the fault diagnosis model, a grey wolf optimizer hyperparameter tuned support vector machine (SVM) is employed for fault diagnosis. The method is verified on a wind turbine test rig that can simulate shaft misalignment and broken gear tooth faulty conditions. Compared with other models, the proposed model has superiority for this classification problem.
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Du, Jin Fu, Zong De Fang, Min Xu, Xing Long Zhao, and Yu Min Feng. "Mathematical Model of Klingelnberg Cyclo-Palloid Hypoid Gear." Applied Mechanics and Materials 341-342 (July 2013): 572–76. http://dx.doi.org/10.4028/www.scientific.net/amm.341-342.572.
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The geometry of the tooth surface is important for tooth contact analysis, load tooth contact analysis and the ease-off of gear pairs. This paper presents a mathematical model for the determination of the tooth geometry of Klingelnberg face-hobbed hypoid gears. The formulation for the generation of gear and pinion tooth surfaces and the equations for the tooth surface coordinates are provided in the paper. The surface coordinates and normal vectors are calculated and tooth surfaces and 3D tooth geometries of gear and pinion are obtained. This method may also applied to other face-hobbing gears.
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Wang, Cheng. "Dynamic model of a helical gear pair considering tooth surface friction." Journal of Vibration and Control 26, no. 15-16 (January 14, 2020): 1356–66. http://dx.doi.org/10.1177/1077546319896124.
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The tooth surface friction is one of the main sources of gear vibration and noise. The current challenging problems in research of a helical gear pair dynamics considering tooth surface friction include the following: (1) Calculation accuracy of the tooth surface friction factor needs to be improved. (2) The meshing process of a helical gear pair has not been fully taken into account in a dynamic model. To solve these problems, a dynamic model of a helical gear pair considering tooth surface friction is proposed in this article. First, based on the tooth contact analysis and loaded tooth contact analysis of a helical gear pair, excitation of time-varying meshing stiffness, the sliding friction coefficient on tooth surface, and the arm of friction force are preliminarily calculated. Second, the dynamic model of a helical gear pair considering tooth surface friction is built and solved, in which the dynamic meshing force/speed/displacement is calculated. The sliding friction coefficient on tooth surface, arm of friction force, and dynamic equations form a coupled system. By decoupling calculation, the model system equations are solved. Finally, an example is presented to verify the proposed model.
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Wang, Qibin, and Yimin Zhang. "A model for analyzing stiffness and stress in a helical gear pair with tooth profile errors." Journal of Vibration and Control 23, no. 2 (August 8, 2016): 272–89. http://dx.doi.org/10.1177/1077546315576828.
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A model is introduced for analyzing the influence of tooth shape deviations and assembly errors on the helical gear mesh stiffness, loaded transmission error, tooth contact stress and tooth root stress. The helical gear is approximated as a series of independent spur gear slices along axial direction whose face-width is relatively small. The relative position relationships among those sliced teeth in mesh are developed with tooth profile errors and the stiffness of the sliced tooth is calculated by the potential energy method. From the equilibriums of the forces, gear mesh stiffness, loaded transmission error, tooth contact stress and tooth root stress are calculated. Then two cases are presented for validation of the model. It is demonstrated that the model is effective for calculating the stiffness of helical gear pairs. Finally, the effects of the tooth tip reliefs, lead crown reliefs and misalignments on the gear mesh stiffness, transmission error, tooth contact stress and tooth root stress are analyzed. The results show that mesh stiffness decreases, loaded transmission error, the maximum tooth contact stress and the maximum tooth root stress grow with the increasing tooth tip relief, lead crown relief and misalignment. And tooth edge has concentrated tooth contact stresses with a gear misalignment.
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Wang, Huiliang, Xiaozhong Deng, Jianhai Han, Jubo Li, and Jianjun Yang. "Mathematical Model of Helical Gear Topography Measurements and Tooth Flank Errors Separation." Mathematical Problems in Engineering 2015 (2015): 1–10. http://dx.doi.org/10.1155/2015/176237.
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During large-size gear topological modification by form grinding, the helical gear tooth surface geometrical shape will be complex and it is difficult for the traditional scanning measurement to characterize the whole tooth surface. Therefore, in order to characterize the actual tooth surfaces, an on-machine topography measurement approach is proposed for topological modification helical gears on the five-axis CNC gear form grinding machine that can measure the modified gear tooth deviations on the machine immediately after grinding. Combined with gear form grinding kinematics principles, the mathematical model of topography measurements is established based on the polar coordinate method. The mathematical models include calculating trajectory of the centre of measuring probe, defining gear flanks by grid of points, and solving coordinate values of topology measurement. Finally, a numerical example of on-machine topography measurement is presented. By establishing the topography diagram and the contour map of tooth error, the tooth surface modification amount and the tooth flank errors are separated, respectively. Research results can serve as foundation for topological modification and tooth surface errors closed-loop feedback correction.
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Wang, Wen Jin, Jing Zhang, Zhi Qiang Zhang, J. Zhao, L. L. Zhang, and Tai Yong Wang. "Mathematical Model and Tooth Surface Representation of Face-Gear Drive with Curvilinear-Tooth Cylindrical Gear." Advanced Materials Research 426 (January 2012): 93–96. http://dx.doi.org/10.4028/www.scientific.net/amr.426.93.
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A tilted head-cutter is considered the generating tool for the generation of the proposed face-gear and a mathematical model of face-gear with curvilinear shaped teeth is developed according to the differential geometry and meshing theory. The generation of a conjugated pinion is based on application of a tilted head-cutter as well. Computer graphs of the gear with curvilinear shaped teeth are presented based on the developed gear’s mathematical model, and then the equation of the gear-tooth surface is deduced. An example is presented to demonstrate the application of the proposed mathematical model.