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Journal articles on the topic 'Meshing; Gear mesh stiffness'
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1
Cui, Lingli, Tongtong Liu, Jinfeng Huang, and Huaqing Wang. "Improvement on Meshing Stiffness Algorithms of Gear with Peeling." Symmetry 11, no. 5 (May 1, 2019): 609. http://dx.doi.org/10.3390/sym11050609.
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This paper investigates the effect of a gear tooth peeling on meshing stiffness of involute gears. The tooth of the gear wheel is symmetric about the axis, and its symmetry will change after the gear spalling, and its meshing stiffness will also change during the meshing process. On this basis, an analytical model was developed, and based on the energy method a meshing stiffness algorithm for the complete meshing process of single gear teeth with peeling gears was proposed. According to the influence of the change of meshing point relative to the peeling position on the meshing stiffness, this algorithm calculates its stiffness separately. The influence of the peeling sizes on mesh stiffness is studied by simulation analysis. As a very important parameter, the study of gear mesh stiffness is of great significance to the monitoring of working conditions and the prevention of sudden failure of the gear box system.
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Zhang, Donglin, Rupeng Zhu, Bibo Fu, and Wuzhong Tan. "Mesh Phase Analysis of Encased Differential Gear Train for Coaxial Twin-Rotor Helicopter." Mathematical Problems in Engineering 2019 (July 25, 2019): 1–9. http://dx.doi.org/10.1155/2019/8421201.
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Dynamic excitation caused by time-varying meshing stiffness is one of the most important excitation forms in gear meshing process. The mesh phase relations between each gear pair are an important factor affecting the meshing stiffness. In this paper, the mesh phase relations between gear pairs in an encased differential gear train widely used in coaxial twin-rotor helicopters are discussed. Taking the meshing starting point where the gear tooth enters contact as the reference point, the mesh phase difference between adjacent gear pairs is analyzed and calculated, the system reference gear pair is selected, and the mesh phase difference of each gear pair relative to the system reference gear pair is obtained. The derivation process takes into account the modification of the teeth, the processing, and assembly of the duplicate gears, which makes the calculation method and conclusion more versatile. This work lays a foundation for considering the time-varying meshing stiffness in the study of system dynamics, load distribution, and fault diagnosis of compound planetary gears.
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Muhammad, Arif Abdullah, and Guang Lei Liu. "Time Varying Meshing Stiffness of Cracked Sun and Ring Gears of Planetary Gear Train." Applied Mechanics and Materials 772 (July 2015): 164–68. http://dx.doi.org/10.4028/www.scientific.net/amm.772.164.
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The time varying meshing stiffness of normal and cracked spur gears of planetary gear train is studied by applying the unit normal forces at mesh point on the face width along the line of action of the single gear tooth in FE based software Ansys Workbench 14.5. The tooth deflections due to the applied forces at one mesh point are noted and a deflection matrix is established which is solved using Matlab to get net deflection and finally the meshing stiffness of gear tooth at particular mesh point. The process is repeated for other mesh points of gear tooth by rotating it to get meshing stiffness for whole gear tooth.
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Yin, Jiao. "Analysis of Gear Static Transmission Error and Mesh Stiffness." Applied Mechanics and Materials 365-366 (August 2013): 327–30. http://dx.doi.org/10.4028/www.scientific.net/amm.365-366.327.
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In this paper, the object of study is one pair increasing gear with building a two-dimensional plane model in ANSYS. According to the gears meshing theory, considering the gear deformation, solve the static transmission error and the gear mesh stiffness in different conditions. The influence of the centre errors on static transmission error and mesh Stiffness are basis for modal analysis based on the mesh stiffness of gear and unbalanced harmonic response.
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Huo, Chun Jing, Hui Liu, Zhong Chang Cai, and Ming Zheng Wang. "Non-Linear Vibration Modeling and Simulation of a Gear Pair Based on ADAMS and Simulink." Advanced Materials Research 681 (April 2013): 219–23. http://dx.doi.org/10.4028/www.scientific.net/amr.681.219.
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To set up the virtual prototype of a gear train system in the dynamic analysis software ADAMS, the torsional vibration model of a gear pair was transformed into an equivalent transmission model in which a multi-body model was established in ADAMS and its meshing force solution model was established in Simulink. The time-varying mesh stiffness, gear clearance, meshing errors and other non-linear factors can be included in the gear meshing feedback model, more importantly, the influence of gear speed fluctuation on the time-varying mesh stiffness was taken into consideration. The simulation results contrastively prove the feasibility of co-simulation for obtaining the dynamic characteristics of gear meshing process.
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Wang, Feng, Zong De Fang, and Sheng Jin Li. "Nonlinear Dynamic Analysis of Helical Gear Considering Meshing Impact." Applied Mechanics and Materials 201-202 (October 2012): 135–38. http://dx.doi.org/10.4028/www.scientific.net/amm.201-202.135.
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Comprehensive meshing stiffness and single tooth meshing stiffness are calculated by tooth contact analysis and load tooth contact analysis program. The corner meshing impact model is proposed. Nonlinear dynamic model of helical gear transmission system is established in this paper considering time-varying meshing stiffness excitation, transmission error excitation, corner meshing impact excitation, and the backlash excitation. Take the ship’s helical gear transmission system as an example, the mesh impact force is derived and the primary factors that produce noises are discussed. The effects which the mesh impact brings to vibration characteristics of the gear dynamic system are concluded. Meshing impact has an inevitable effect on the vibration of the dynamic system. Impact excitation costs 8.5% in maximum of vibration acceleration response, 31% in maximum of instantaneous acceleration, and 4.9% in maximum of spectral component amplitude.
7
Wang, J., and I. Howard. "The torsional stiffness of involute spur gears." Proceedings of the Institution of Mechanical Engineers, Part C: Journal of Mechanical Engineering Science 218, no. 1 (January 1, 2004): 131–42. http://dx.doi.org/10.1243/095440604322787009.
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This paper presents the results of a detailed analysis of torsional stiffness of a pair of involute spur gears in mesh using finite element methods. Adaptive meshing has been employed within a commercial finite element program to reveal the detailed behaviour in the change over region from single- to double-tooth contact zones and vice versa. Analysis of past gear tooth stiffness models is presented including single- and multitooth models of the individual and combined torsional mesh stiffness. The gear body stiffness has been shown to be a major component of the total mesh stiffness, and a revised method for predicting the combined torsional mesh stiffness is presented. It is further shown tha the mesh stiffness and load sharing ratios will be a function of applied load.
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Hu, Yu Mei, De Shuang Xue, and Yang Jun Pi. "Effect of Friction Coefficient on the Stiffness Excitation of Gear." Applied Mechanics and Materials 86 (August 2011): 713–16. http://dx.doi.org/10.4028/www.scientific.net/amm.86.713.
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This study addresses the effect of different friction coefficients on the stiffness excitation of gear using finite element technique. Firstly, the simulation model of single pair of gear teeth mesh is established, and the effect of friction coefficient on the composite stiffness values of the teeth meshing is studied. After that, simulation model of multiple pairs of gear teeth meshing is created and the normal load distributions under different friction coefficients in a single meshing cycle are calculated using quasi-static calculation method. Finally, the relationship between friction coefficient and stiffness excitation of gear system is obtained. The investigation results indicate that at the alternation place of single tooth meshing and double teeth meshing, the stiffness excitation of the system is greater under larger friction coefficient when double teeth meshing change into single tooth meshing, while the opposite situation occur when single tooth meshing change into double teeth meshing. The amplitude value of stiffness variation for single pair of teeth meshing under different friction coefficients is 2.12%, while the amplitude value of teeth loads variation for multiple pairs of teeth meshing under different friction coefficients is 22.87%.
9
Xu, Xiangyang, Hongwei Ge, Jijun Deng, Jibo Wang, and Renxiang Chen. "An investigation on dynamic characteristics of herringbone planetary gear system with torsional flexibility between the left and right teeth of the sun gear." Mechanics & Industry 21, no. 6 (2020): 602. http://dx.doi.org/10.1051/meca/2020074.
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Herringbone planetary gear system (HPGS) has high power density and complex structure. The torsional flexibility of the left and right teeth of the sun gear is closely related to the dynamic characteristics of the HPGS. In this research, considering the coordination conditions of both sides torsional stiffness and axial slide of the sun gear, a new dynamic model of the HPGS considering the meshing phase difference between left and right teeth of the sun gear is developed based on the lumped-parameter method, and the influence mechanism of torsional stiffness and axial sliding is studied. Moreover, the dynamic parameters and dynamic characteristics of the HPGS are analyzed in the case of varying torsoinal stiffness and axial slide. The results show that the torsional stiffness of left and right teeth and the axial slide of sun gear have significant impacts on the dynamic parameters and dynamic mesh force response. With the increase of the torsional flexibility (the decrease the torsional stiffness), the sun gear and planet gear meshing stiffness and the maximum tooth surface load are both increased on the left side (input side) and decreased on the right side, but the main peak values and peak frequencies of dynamic response on both sides of the s-p meshing pairs decrease significantly. In addition, when the sun gear slides toward the output side axially, meshing stiffness and dynamic mesh force response main peak values decreased on the left side (input side) and increased on the right side, but the main resonance peaks frequencies keep the same.
10
Lin, Jian, and Robert G. Parker. "Mesh Stiffness Variation Instabilities in Two-Stage Gear Systems." Journal of Vibration and Acoustics 124, no. 1 (September 1, 2001): 68–76. http://dx.doi.org/10.1115/1.1424889.
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Mesh stiffness variation, the change in stiffness of meshing teeth as the number of teeth in contact changes, causes parametric instabilities and severe vibration in gear systems. The operating conditions leading to parametric instability are investigated for two-stage gear chains, including idler gear and countershaft configurations. Interactions between the stiffness variations at the two meshes are examined. Primary, secondary, and combination instabilities are studied. The effects of mesh stiffness parameters, including stiffness variation amplitudes, mesh frequencies, contact ratios, and mesh phasing, on these instabilities are analytically identified. For mesh stiffness variation with rectangular waveforms, simple design formulas are derived to control the instability regions by adjusting the contact ratios and mesh phasing. The analytical results are compared to numerical solutions.
11
Hou, Shaoshuai, Jing Wei, Aiqiang Zhang, Chunpeng Zhang, Junhui Yan, and Changlu Wang. "A Novel Comprehensive Method for Modeling and Analysis of Mesh Stiffness of Helical Gear." Applied Sciences 10, no. 19 (September 24, 2020): 6695. http://dx.doi.org/10.3390/app10196695.
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The mesh stiffness of gear pairs used in aerospace applications, such as geared turbofan, has a vital influence on vibration and noise. To compensate for the deficiencies of the conventional method that does not consider slice coupling and structure coupling simultaneously, a comprehensive mathematical model for computing the mesh stiffness of helical gears is established. In this novel model, the effect of structure coupling and slice coupling between neighboring sliced gears are considered. The effect of the axial component of meshing force is also taken into account simultaneously. The results obtained by the comprehensive model are consistent with the finite element method and it proves that the novel mathematical model is sound. The influences of the helical angle and addendum modification coefficient on mesh stiffness are studied. The results show that the mesh stiffness of helical gears would be decreased in multiteeth regions caused by structure coupling. With or without consideration of the axial component, the relative mean values of mesh stiffness become larger with an increasing helical angle. The fluctuation value of mesh stiffness decreases when a positive addendum modification coefficient is adopted. The addendum modification also changes the phase of mesh stiffness. This study is helpful for a vibration analysis of gear transmission systems.
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Ren, Fei, Da Tong Qin, and Xiao Ling Wu. "Research on the Dynamics of the Double Helical Gear Transmission." Applied Mechanics and Materials 456 (October 2013): 256–59. http://dx.doi.org/10.4028/www.scientific.net/amm.456.256.
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Against the transmission characteristics of the double helical gear pair, considering the time-varying mesh stiffness, the bearing radial and axial stiffness, the tensile and compressive stiffness of the transmission shaft, the bending stiffness of that, error excitations, and corresponding dampings, a double helical gear pair bending-torsion-axis coupling dynamic model was established by using the lumped parameter method based on the gear meshing theory and Lagrange equations. Based on the model, the dynamic response of double helical gear pair was solved, and taking the right side of helical gear as an example, the frequency spectrum characteristics of dynamic meshing force of the right side of helical gear were mainly analyzed. This research establishes the foundation for dynamic performance optimizations and reliability designs of the double helical gear pair transmission system in the future.
13
Liang, Xihui, Ming J. Zuo, and Tejas H. Patel. "Evaluating the time-varying mesh stiffness of a planetary gear set using the potential energy method." Proceedings of the Institution of Mechanical Engineers, Part C: Journal of Mechanical Engineering Science 228, no. 3 (April 24, 2013): 535–47. http://dx.doi.org/10.1177/0954406213486734.
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Time-varying mesh stiffness is a periodic function caused by the change in the number of contact tooth pairs and the contact positions of the gear teeth. It is one of the main sources of vibration of a gear transmission system. An efficient and effective way to evaluate the time-varying mesh stiffness is essential to comprehensively understand the dynamic properties of a planetary gear set. According to the literature, there are two ways to evaluate the gear mesh stiffness, the finite element method and the analytical method. The finite element method is time-consuming because one needs to model every meshing gear pair in order to know the mesh stiffness of a range of gear pairs. On the other hand, analytical method can offer a general approach to evaluate the mesh stiffness. In this study, the potential energy method is applied to evaluate the time-varying mesh stiffness of a planetary gear set. Analytical equations are derived without any modification of the gear tooth involute curve. The developed equations are applicable to any transmission structure of a planetary gear set. Detailed discussions are given to three commonly used transmission structures: fixed carrier, fixed ring gear and fixed sun gear.
14
Shan, Li Jun, Yu Ting Liu, and Wei Dong He. "Analysis of Nonlinear Dynamic Accuracy on RV Transmission System ." Advanced Materials Research 510 (April 2012): 529–35. http://dx.doi.org/10.4028/www.scientific.net/amr.510.529.
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RV (Rotate Vector) transmission is a new precision transmission system. In order to improve its accuracy, we study the RV transmission system. It is researched in comprehensive factors including displacement errors, elastic deformation (static transmission error, design transmission error), gear meshing errors, backlash of gear, time-varying mesh stiffness, mesh damping, bearing stiffness, torsional stiffness of input shaft, etc. The mathematical and mechanical model of dynamic transmission accuracy is established by the concentrated mass method and the dynamic substructure method. Then, the meshing force of each part is analyzed in RV reducer. The motion differential equation of RV drive system is obtained, which lays the foundation for the calculation and analysis of the transmission error.
15
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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Pipitone, Enrico, Christian Maria Firrone, and Stefano Zucca. "Application of Multiple-Scales Method for the Dynamic Modelling of a Gear Coupling." Applied Sciences 9, no. 6 (March 23, 2019): 1225. http://dx.doi.org/10.3390/app9061225.
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Thin-walled gears, designed for aeronautical applications, have shown very rich dynamics that must be investigated in advance of the design phase. One of the signatures of their dynamics is coupling due to the meshing teeth which stand-alone gear models cannot capture. This paper aims to investigate the dynamics of thin-walled gears considering time-varying coupling due to the gear meshing. Each gear is modelled with lumped parameters according to a local rotating reference system and the coupling is modelled by a traveling meshing stiffness. The set of equations of motion is solved by the non-linear Method of Multiple-Time-Scales (MMTS). MMTS is a very powerful technique that is widely used to solve perturbation problems in many fields of mathematic and physics. In the analyzed numerical test case, the relevance of gear coupling is demonstrated as well as the capability of the MMTS to capture the fundamental features of the system dynamics. In this study the analytical methodology, which uses MMTS, allows for the calculation of the forced response of the system made of two meshing gears despite the presence of a parametric quantity, i.e., the mesh stiffness. The calculation is performed in the frequency domain using modal coordinates, which ensures a fast computation. The result is compared with time domain analysis for validation purposes.
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Bettaieb, Mohamed Nizar, Mohamed Maatar, and Chafik Karra. "BIDIMENSIONAL FINITE ELEMENT ANALYSIS OF SPUR GEAR: STUDY OF THE MESH STIFFNESS AND STRESS AT THE LEVEL OF THE TOOTH FOOT." Transactions of the Canadian Society for Mechanical Engineering 33, no. 2 (June 2009): 175–87. http://dx.doi.org/10.1139/tcsme-2009-0016.
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The purpose of this work is to determine the spur gear mesh stiffness and the stress state at the level of the tooth foot. This mesh stiffness is derived from the calculation of the normal tooth displacements: local displacement where the load is applied, tooth bending displacement and body displacement [15]. The contribution of this work consists in, basing on previous works, developing optimal finite elements model in time calculation and results precision. This model permits the calculation of time varying mesh stiffness and the evaluation of stress state at the tooth foot. For these reasons a specific Fortran program was developed. It permit firstly, to obtain the gear geometric parameters (base radii, outside diameter,…) and to generate the data base of the finite element meshing of a tooth or a gear. This program is interfaced with the COSMOS/M finite element software to predict the stress and strain state and calculate the mesh stiffness of a gear system. It is noted that the mesh stiffness is periodic and its period is equal to the mesh period.
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Shweiki, Shadi, Antonio Palermo, and Domenico Mundo. "A Study on the Dynamic Behaviour of Lightweight Gears." Shock and Vibration 2017 (2017): 1–12. http://dx.doi.org/10.1155/2017/7982170.
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This paper investigates the dynamic effects of mass reduction on a pair of spur gears. A one-Degree-of-Freedom (DOF) model of a mechanical oscillator with clearance-type nonlinearity and linear viscous damping is used to perform the investigations. One-dimensional (1D) gear pair models aim at studying the torsional gear vibrations around the rotational axes and can be used to simulate either gear whine or gear rattle phenomena. High computational efficiency is reached by using a spring-damper element with variable stiffness to model the gear meshing process. The angle-dependent mesh stiffness function is computed in a preparation phase through detailed Finite Element (FE) simulations and then stored in a lookup table, which is then interpolated during the dynamic simulation allowing for high computational efficiency. Nonlinear contact effects and influence of material discontinuities due to lightweighting are taken into account by FE simulations with high level of detail. Finally, the influence of gear body topology is investigated through a sensitivity analysis, in which analytical functions are defined to describe the time-varying mesh stiffness.
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Ma, Hui, Jian Yang, Rongze Song, Suyan Zhang, and Bangchun Wen. "Effects of tip relief on vibration responses of a geared rotor system." Proceedings of the Institution of Mechanical Engineers, Part C: Journal of Mechanical Engineering Science 228, no. 7 (August 27, 2013): 1132–54. http://dx.doi.org/10.1177/0954406213500615.
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Considering tip relief, a finite element model of a spur gear pair in mesh is established by ANSYS software. Time-varying mesh stiffness under different amounts of tip relief is calculated based on the finite element model. Then, a finite element model of a geared rotor system is developed by MATLAB software considering the effects of time-varying mesh stiffness and constant load torque. Emphasis is given to the effects of tip relief on the lateral–torsional coupling vibration responses of the system. The results show that as the amount of tip relief increases, the saltation of time-varying mesh stiffness reduces at the position of approach action and transition mesh region from the single tooth to double tooth. A number of primary resonances and some super-harmonic of gears 1 and 2 are excited by time-varying mesh stiffness in amplitude frequency responses. As the amount of tip relief increases, some super-harmonic responses change due to the variation in the higher frequency components of time-varying mesh stiffness. After tip relief, the vibration and meshing force decrease obviously at lower mesh frequency range except at some resonance frequencies; however, tip relief is not effective in reducing the vibration at higher mesh frequency range. The amplitude fluctuation of the vibration acceleration reduces evidently after considering tip relief, which is not remarkable with the increase of meshing frequency.
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Meuleman, P. Klein, D. Walton, K. D. Dearn, D. J. Weale, and I. Driessen. "Minimization of transmission errors in highly loaded plastic gear trains." Proceedings of the Institution of Mechanical Engineers, Part C: Journal of Mechanical Engineering Science 221, no. 9 (September 1, 2007): 1117–29. http://dx.doi.org/10.1243/09544062jmes439.
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Transmission errors (TEs) are an important source of unwanted noise and vibration in gear drives. Errors can result from geometrical inaccuracies and from elastic deformations. Plastic drives are often loaded in a way that produces high deflections relative to steel gears, and the elastic component of TE is relatively more important. Furthermore, plastic gears are often run in mesh with gears made from steel or other metals. In this case there is a large difference in tooth stiffness, which leads to unusual TE problems. The current paper discusses the origins of elastic TEs and means of their calculation. A simple beam model is used to demonstrate the stiffness of a pair of meshing gear teeth. A finite-element analysis is used to refine this model and to run iterative tooth meshing enabling TEs to be accurately characterized. A number of TE traces from gear pairs running under high loads are included and compared with the theoretical predictions. Several different scenarios are proposed including balancing gear tooth stiffness for dissimilar materials and the adjustment of pressure angle to account for tooth deflection. A set of design guidelines are presented in the conclusions. A case study of a precision printer drive is used to illustrate some of the techniques for the minimization of TEs.
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Zhang, Xiu Yan, and Xiao Jun Dai. "Meshing Stiffness Analysis of Four Ring-Plate-Type Pin-Cycloidal Gear Planetary Drive." Applied Mechanics and Materials 229-231 (November 2012): 499–502. http://dx.doi.org/10.4028/www.scientific.net/amm.229-231.499.
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The four ring-plate-type pin-cycloidal gear planetary drive is a new type of the cycloid. Use the new repair tooth profile gap mesh analysis method to Calculate the cycloid mesh stiffness. the mesh stiffness of the cycloid is solved, According to simulation results based on the ANSYS / LS-DYNA. and the results were compared with theoretical calculations, both mutual authentication. It can be use to improve the prototype program at last.
22
Ou Yang, Tian Cheng, Nan Chen, Cui Cui Ju, Cheng Long Li, and Jiang Hu Li. "Dynamic Analysis of Offset Printing Press Gear-Cylinder-Bearing System under Time-Varying Meshing Stiffness Effect." Key Engineering Materials 656-657 (July 2015): 658–63. http://dx.doi.org/10.4028/www.scientific.net/kem.656-657.658.
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This study propose a new nonlinear model for offset printing press gear-cylinder-bearing system by the lumped parameter approach. The multi-DOF model consists of helical gear pairs and spur gear pairs with time-varying meshing stiffness. Bearing and shaft flexibilities are include in the model as well. The equations of motion are obtained by Darren Bell principle and Runge-Kutta numerical method is used to slove the equations of motion. The results show that meshing stiffness and bearing stiffness significantly affect critical speed, vibration acceleration and meshing force. Multi-body dynamics software are applied to compare with lumped parameter model. The results show that there are many similarities in different aspects. Results of experimental study on offset printing press are also presented for validation of different models. After Discrete Fourier Transform, the graphics display that acceleration peaks frequencies are an integer multiple of the gear mesh frequency. It demonstrate that mechanical vibration is mainly from gear transmission system at high printing speed and gear transmission system lead to nonlinear vibration. This work provide a foundation for further improvement of the dynamics of gear system.
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Sun, Xiaoyu, Yongqiang Zhao, Ming Liu, and Yanping Liu. "On Dynamic Mesh Force Evaluation of Spiral Bevel Gears." Shock and Vibration 2019 (October 20, 2019): 1–26. http://dx.doi.org/10.1155/2019/5614574.
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The mesh model and mesh stiffness representation are the two main factors affecting the calculation method and the results of the dynamic mesh force. Comparative studies considering the two factors are performed to explore appropriate approaches to estimate the dynamic meshing load on each contacting tooth flank of spiral bevel gears. First, a tooth pair mesh model is proposed to better describe the mesh characteristics of individual tooth pairs in contact. The mesh parameters including the mesh vector, transmission error, and mesh stiffness are compared with those of the extensively applied single-point mesh model of a gear pair. Dynamic results from the proposed model indicate that it can reveal a more realistic and pronounced dynamic behavior of each engaged tooth pair. Second, dynamic mesh force calculations from three different approaches are compared to further investigate the effect of mesh stiffness representations. One method uses the mesh stiffness estimated by the commonly used average slope approach, the second method applies the mesh stiffness evaluated by the local slope approach, and the third approach utilizes a quasistatically defined interpolation function indexed by mesh deflection and mesh position.
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Suzuki, Daisuke, Shigeru Horiuchi, Jin Hwan Choi, and Han Sik Ryu. "Dynamic Analysis of Contacting Spur Gear Pair for Fast System Simulation." Solid State Phenomena 110 (March 2006): 151–62. http://dx.doi.org/10.4028/www.scientific.net/ssp.110.151.
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The prime source of vibration and noise in a gear system is originated from transmission error between the meshing gears. In this paper, the dynamic modeling method and response of a spur gear pair for the efficient system simulation are investigated by using a detailed contact analysis at each time step. Input values such as time-varying mesh stiffness and static transmission error excitation are not required in this investigation because mesh forces are obtained by contact analysis directly. The efficient contact search kinematics and algorithms in the context of the compliant contact model are developed to detect the interactions between teeth surfaces. In this investigation the compliant force model based on the Herzian law is employed using Coulomb friction force model, and dynamic transmission error (DTE) and mesh frequency values of contacting gear system are also illustrated.
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Sun, Shu Xia, Xiang Jun Zhu, and Ming Ming Wang. "Power Turret the Dynamics Simulation Analysis of Power Turret." Applied Mechanics and Materials 198-199 (September 2012): 133–36. http://dx.doi.org/10.4028/www.scientific.net/amm.198-199.133.
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The dynamic performance of the CNC turret affect the cutting capability and cutting efficiency of the NC machine tool directly, embody the core level of the design and manufacture of the NC machine tool. However, the dynamic performance of the CNC turret mostly decided by the dynamic performance of the power transmission system of the power turret. This passage use Pro/E to set the accurate model of the gears and the CAD model of the gear transmission system and based on this to constitute the ADAMS model of virtual prototype. On the many-body contact dynamics theory basis, dynamic describes the process of the mesh of the gears, work out the dynamic meshing force under the given input rotating speed and loading, and the vibration response of the gear system. The simulation result disclosure the meshing shock excitation and periodical fluctuation phenomena arose by stiffness excitation of the gear transmission. Analyses and pick-up the radial vibration response of the output gear of the gear transmission system as the feasibility analysis data.
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Qiu, Xinghui, Qinkai Han, and Fulei Chu. "Investigation of Parametric Instability of the Planetary Gear under Speed Fluctuations." Shock and Vibration 2017 (2017): 1–14. http://dx.doi.org/10.1155/2017/6851903.
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Planetary gear is widely used in engineering and usually has symmetrical structure. As the number of teeth in contact changes during rotation, the time-varying mesh stiffness parametrically excites the planetary gear and may cause severe vibrations and instabilities. Taking speed fluctuations into account, the time-varying mesh stiffness is frequency modulated, and therefore sideband instabilities may arise and original instabilities are significantly affected. Considering two different speed fluctuations, original and sideband instabilities are numerically and analytically investigated. A rotational lumped-parameter model of the planetary gear is developed, in which the time-varying mesh stiffness, input speed fluctuations, and damping are considered. Closed-form approximations of instability boundaries for primary and combination instabilities are obtained by perturbation analysis and verified by numerical analysis. The effects of speed fluctuations and damping on parametric instability are systematically examined. Because of the frequency modulation, whether a parametric instability occurs cannot be simply predicted by the planet meshing phase which is applicable to constant speed. Besides adjusting the planet meshing phase, speed fluctuation supplies a new thought to minimize certain instability by adjusting the amplitude or frequency of the speed fluctuation. Both original and sideband instabilities are shrunken by damping, and speed fluctuation further shrinks the original instability.
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Xuan, Liang, Chao Xie, Tianmin Guan, Lei Lei, and Heng Jiang. "Research on dynamic modeling and simulation verification of a new type of FT pin-cycloid transmission." Proceedings of the Institution of Mechanical Engineers, Part C: Journal of Mechanical Engineering Science 233, no. 17 (July 10, 2019): 6276–88. http://dx.doi.org/10.1177/0954406219861999.
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A new type of FT pin-cycloid transmission reducer is widely used in the industrial robot field due to the high transmission accuracy. In addition, the complex working conditions bring about vibration, which affects the transmission accuracy of the robot. Therefore, it is necessary to study the dynamic characteristics of FT reducer at the transmission joint. In this paper, based on the analysis of its transmission principle and structure, the dynamic model of FT transmission is established by necessary assumptions. The stiffness mathematical models of different meshing positions are obtained from the dynamic model, and the differential equations of the system are established by Lagrange method. In order to solve the natural frequency of the system, the stiffness of meshing positions of the system is solved, including input shaft torsional stiffness, involute gear meshing stiffness, bearing stiffness, cycloid gear and pin torsional stiffness. Considering the output of FT transmission, a “3+ i” model is proposed to obtain the mesh stiffness between the cycloid gear and output pins. Finally, the correctness of the model is proved by choosing parameters such as transmission ratio and force on parts and components by simulation. The research results will provide theoretical support for the optimal design of FT transmission.
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Peng, Meng, and Hans A. Desmidt. "Torsional Stability of a Face-Gear Drive System." Journal of the American Helicopter Society 60, no. 4 (October 1, 2015): 1–11. http://dx.doi.org/10.4050/jahs.60.042007.
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This paper establishes a structural dynamics model for torsional vibration of gearboxes containing a face-gear drive by considering flexibilities of gear teeth and transmission shafts. This model includes the time-varying gear mesh stiffness resulting from the unique face-gear meshing kinematics and nonunity contact ratio. The face-gear mesh-induced parametric instability phenomena are explored numerically via Floquet theory for various shaft characteristics and system inertia distributions. In addition, Tregold's approximation is employed for face-gear contact ratio calculations to avoid complex numerical computations. For design purposes, a perturbation technique is utilized to analytically predict the parametric instability boundaries for the cases with small time-varying components.
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Jinyuan, Tang, Liu Yang, and Cai Weixing. "The principles of selecting floating members of 2K-H planetary gears for load balancing design." Proceedings of the Institution of Mechanical Engineers, Part C: Journal of Mechanical Engineering Science 231, no. 9 (November 10, 2015): 1589–98. http://dx.doi.org/10.1177/0954406215616420.
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This paper studies the load balancing problems caused by manufacturing and assembly errors of 2K-H planetary gear train. Based on the geometric equivalent relationship and spring mechanical model of load transfer, the relations between the load balancing of planetary gears and the mesh clearance and meshing stiffness are derived. Besides, the vector method is also derived to calculate the meshing clearance which is a result of the deviation of the component center caused by manufacturing errors and assembly errors. On the basis of the meshing clearance calculation formulas, the balanced load structure based on floating members is analyzed, and the results show: 1) when the number of planet gears is [Formula: see text], the floating of the basic members can compensate for the errors of the planet wheels; 2) when the number of planet gears is [Formula: see text], the errors of the planet wheels cannot be compensated by floating the basic components, and the compensation can only be made through the floating of the planetary gear. In addition, a number of recommendations are proposed to improve the performance of the planetary gear train set.
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Dong, Hao, Zhi-Yu Liu, Xiaolong Zhao, and Ya-Hui Hu. "Analysis of dynamic characteristics of power split spiral bevel gear transmission system based on teeth geometric contact analysis." Transactions of the Canadian Society for Mechanical Engineering 43, no. 1 (March 1, 2019): 47–62. http://dx.doi.org/10.1139/tcsme-2017-0128.
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To solve the dynamic load distribution mechanism of the power split transmission system of spiral bevel gears, according to the characteristics of the closed loop of power flow, the deformation coordination condition is deduced. Through the gear teeth geometric contact analysis technique, the time-varying meshing stiffness conditions in the model are solved. The linear time-varying dynamic model of the torsional vibration of the bevel gear split transmission system is established by the lumped mass parameter method. Considering the influence of time-varying mesh stiffness excitation conditions and damping, the dynamic differential equations are treated in a dimensionless way. The dynamic load change and dynamic response characteristics of the system are obtained by numerical solution, and the influence of parameters such as speed and damping on dynamic power flow and dynamic characteristics of the system is revealed. The results show that with an increase of meshing damping ratio, dynamic power flow of each gear pair changes little, and the vibration acceleration and its root mean square value of each gear pair of the system are smaller. With an increase in speed, vibration acceleration and its average amplitude increase.
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Han, Guosheng, Bing Yuan, and Guan Qiao. "Tooth Surface Modification for Helical Gear Pairs considering Mesh Misalignment Tolerance." Shock and Vibration 2021 (April 21, 2021): 1–13. http://dx.doi.org/10.1155/2021/5563648.
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Mesh misalignment in mating the gear tooth surface is common and difficult to be determined accurately because of system deformation and bearing clearances, as well as manufacturing and assembly errors. It is not appropriate to consider the mesh misalignment as a constant value or even completely ignore it in the tooth surface modification design. Aiming to minimize the expectation and variance of static transmission error (STE) fluctuations in consideration of mesh misalignment tolerance, a multiobjective optimization model of tooth surface modification parameters is proposed through coupling the NSGA-II algorithm and an efficient loaded tooth contact analysis (LTCA) model. The modified tooth flank of helical gear pairs is defined using 6 design variables which are related to profile modification, lead modification, and bias modification. The influences of mesh misalignment on time-dependent meshing stiffness (TDMS) and STE of unmodified and modified helical gear pairs are investigated. Then, the dynamic transmission error (DTE) of modified helical gears in consideration of mesh misalignment is discussed. The results indicate that the designed modified tooth surface shows good robustness to mesh misalignment.
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Xu, Kai, Ping Jia, Ming Qiu, and Jian Jun Yang. "Planetary Gear Train Used in Wind Driver Generator Based on TCA." Applied Mechanics and Materials 672-674 (October 2014): 251–54. http://dx.doi.org/10.4028/www.scientific.net/amm.672-674.251.
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By the disadvantage of the speed fluctuations to the gear noise and vibration spectrum in time domain, a new method to measuring the periodic signal was put forward in pulse time domain. The multi-channel simultaneous measurement model were brought out, aimed at analyzing the gear meshing state and its frequency characteristics. Then, the 14 DOF nonlinear vibration equations was derived from kinetic analysis on the planetary gear pair meshing model, which was solved and simulated in Matlab software, containing with transmission error, time-varying mesh stiffness, clearance and other factors. Finally, an integrated platform was constructed for measuring gear noise, vibration and transmission error to verify the effectiveness and feasibility of the analytical.
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Zhou, Zhi Gang, Da Tong Qin, Jun Yang, and Hui Tao Chen. "Study on Dynamic Characteristics of Wind Turbine Planetary Gear System Coupled with Bearing at Varying Wind Speed." Applied Mechanics and Materials 86 (August 2011): 653–57. http://dx.doi.org/10.4028/www.scientific.net/amm.86.653.
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The sparse least squares support vector machines (SL-SVM) is used to simulate wind speed of real wind field, and time-varying wind load caused by stochastic wind speed is then obtained. A coupling gear-bearing dynamical model of planetary gear transmission system of wind turbine is built using lumped-parameter method, in which the varying wind load, time-vary mesh stiffness of gear pair and time-vary stiffness of rolling element bearing are taken into account. Numerical method is used to simulate the dynamic performance of planetary gear transmission of multibrid technology wind turbine (MTWT) with 1.5MW rated power, the vibration displacement responses of gears and dynamic meshing forces of gear pairs as well as nonlinear bearing forces in the transmission system are obtained, and the influence rules of external varying wind load on the vibration characteristics of transmission system of wind turbine are studied. The research results lay a foundation for dynamic performance optimization and reliability design of gear transmission system of wind turbine.
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Fan, Rong, Chao Sheng Song, Zhen Liu, and Wen Ji Liu. "Coupled Dynamic and Vibration Analysis of Beveloid Geared System." Applied Mechanics and Materials 215-216 (November 2012): 917–20. http://dx.doi.org/10.4028/www.scientific.net/amm.215-216.917.
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Dynamic modeling of beveloid gears is less developed than that of spur gears, helical gears and hypoid gears because of their complicated meshing mechanism and 3-dimsional dynamic coupling. In this study, a nonlinear systematic coupled vibration model is created considering the time-varying mesh stiffness, time-varying transmission error, time-varying rotational radius and time-varying friction coefficient. Numerical integration applying the explicite Runge-Kutta formula and the implicit direct integration is used to solve the nonlinear dynamic model. Also, the dynamic characteristics of the marine gear system are investigated.
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Huang, Kang, Fengwei Xu, Yangshou Xiong, Meng Sang, and Yong Yi. "Nonlinear dynamic analysis of a microsegment gear system with a time-varying base circle." Transactions of the Canadian Society for Mechanical Engineering 44, no. 2 (June 1, 2020): 279–93. http://dx.doi.org/10.1139/tcsme-2019-0086.
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A systematic dynamic analysis of a microsegment gear system with a time-varying base circle, time-varying mesh stiffness, and gear backlash is carried out in this paper. By discretizing the meshing process, a six degree-of-freedom nonlinear dynamic model of a microsegment gear pair is established. To study the dynamic response of the microsegment gear and involute gear under various operating conditions, the numerical integration method is adopted. The dynamic transmission error (DTE) of the two gears is analysed in terms of time history charts, phase diagrams, fast Fourier transformation spectra, and Poincaré maps. The effects of support damping and support stiffness on radial vibration are also investigated. Results reveal that, compared with the involute gear system, the microsegment gear system is more stable at the high-speed condition and has a smaller amplitude of DTE under medium-speed and heavy-load, high-speed, and heavy-load conditions. The support damping and support stiffness have great effects on the resonant peak in the radial direction of the microsegment gear. Both the proposed model and numerical results are expected to provide a useful source of reference for the dynamic design of the microsegment gear system.
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Chen, Xingbin, Qingchun Hu, Zhongyang Xu, and Chune Zhu. "Numerical modeling and dynamic characteristics study of coupling vibration of multistage face gearsplanetary transmission." Mechanical Sciences 10, no. 2 (September 24, 2019): 475–95. http://dx.doi.org/10.5194/ms-10-475-2019.
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Abstract. A novel transmission with multistage face gears as the core component achieves variable speeds via differential gear shifting. Single/multistage coupled vibration models have been established in this study to derive the coupled vibration equation in order to accurately solve the load distribution between the meshing teeth and the vibration shock between the shifting stages in the transmission process, improve the transmission smoothness of the face gears during the shifting processing, suppress the resonance of face gears meshing, reduce the noise, and optimize the power transmission performance. The characterization relationships of the key parameters such as equivalent mass, rotational inertia, equivalent mesh stiffness, support stiffness, and meshing damping coefficient to dynamic characteristics were investigated. The linear and nonlinear dynamic characteristics of coupled vibration differential equations were solved. The influence rules of factors such as integrated transmission error, dynamic load, tooth surface friction, loading speed, and load on the transmission system were analyzed. The results of the study provide a theoretical basis for the expansion of field of application of transmission devices.
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Chen, Ying Chung, Chung Hao Kang, and Siu Tong Choi. "Dynamic Analysis of a Geared Rotor-Bearing System with Time-Varying Gear Mesh Stiffness and Pressure Angle." Applied Mechanics and Materials 284-287 (January 2013): 461–67. http://dx.doi.org/10.4028/www.scientific.net/amm.284-287.461.
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The dynamic analysis of a geared rotor-bearing system with time-varying gear mesh stiffness and pressure angle is presented in this paper. Although there are analyses for both of the gear and rotor-bearing system dynamics, the coupling effect of the time-varying mesh and geared rotor-bearing system is deficient. Therefore, the pressure angle and contact ratio of the geared rotor-bearing system are treated as time-varying variables in the proposed model while they were considered as constant in previous models. The gear mesh stiffness is varied with different contact ratios of the gear pair in the meshing process. The nonlinear equations of motion for the geared rotor-bearing system are obtained by applying Lagrange’s equation and the dynamic responses are computed by using the Runge-Kutta numerical method. Numerical results of this study indicated that the proposed model provides realistic dynamic response of a geared rotor-bearing system.
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Zhu, Zengbao, Longchao Cheng, Rui Xu, and Rupeng Zhu. "Impacts of Backlash on Nonlinear Dynamic Characteristic of Encased Differential Planetary Gear Train." Shock and Vibration 2019 (May 27, 2019): 1–15. http://dx.doi.org/10.1155/2019/9347925.
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A multifreedom tensional nonlinear dynamic equation of encased differential planetary gear train with multibacklash and time-varying mesh stiffness was developed in the present research. The nonlinear dynamic response was obtained by solving the formulated nonlinear dynamic equation, and the impacts of backlash on dynamic characteristics of the gear train were then analyzed by combining time process diagram, phase diagram, and Poincaré section. The results revealed that bilateral shock in meshing teeth was caused due to smaller backlash, thus causing dramatic changes in meshing force; hence, the gears were found to be in a chaotic state. Further, during stable motion state, no contact between intermeshing teeth with bigger backlash was noticed; thus, they were in a stable quasiperiodic motion state in the absence of teeth exciting force. Therefore, in order to avoid a bilateral shock in gears as well as to maintain gear teeth lubrication, a slightly bigger backlash is required. The backlash change in any transmission stage caused significant impacts on gear force and the motion state of its own stage; however, the impact on gear force of another stage was quite small, whereas the impact on the motion state of another stage was quite large.
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Rincon, Alfonso Fernandez del, Fernando Viadero, Miguel Iglesias, Ana de-Juan, Pablo Garcia, and Ramon Sancibrian. "Effect of cracks and pitting defects on gear meshing." Proceedings of the Institution of Mechanical Engineers, Part C: Journal of Mechanical Engineering Science 226, no. 11 (February 1, 2012): 2805–15. http://dx.doi.org/10.1177/0954406212437104.
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The development of vibration-based condition monitoring techniques, especially those focused on prognosis, requires the development of better computational models that enable the simulation of the vibratory behaviour of mechanical systems. Gear transmission vibrations are governed by the so-called gear mesh frequency and its harmonics, due to the variable stiffness of the meshing process. The fundamental frequency will be modulated by the appearance of defects which modify the meshing features. This study introduces an advanced model to assess the consequences of defects such as cracks and pitting on the meshing stiffness and other related parameters such as load transmission error or load sharing ratio. Meshing forces are computed by imposing the compatibility and complementarity conditions, leading to a non-linear equation system with inequality constraints. The calculation of deformations is subdivided into a global and a local type. The former is approached by a finite element model and the latter via a non-linear Herztian-based formulation. This procedure enables a reduced computational effort, in contrast to conventional finite element models with contact elements. The formulation used to include these defects is described in detail and their consequences are assessed by a quasi-static analysis of a transmission example.
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Liu, Zhifeng, Tao Zhang, Yongsheng Zhao, and Shuxin Bi. "Time-varying stiffness model of spur gear considering the effect of surface morphology characteristics." Proceedings of the Institution of Mechanical Engineers, Part E: Journal of Process Mechanical Engineering 233, no. 2 (May 12, 2018): 242–53. http://dx.doi.org/10.1177/0954408918775955.
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The nonuniform cantilever beam and Hertzian contact model have been widely used to derive the mesh stiffness of spur gear assuming that the contact surface is absolutely frictionless. However, studies have confirmed that machined surfaces are rough in microscale and can be simulated by the Weierstrass–Mandelbort function. In order to get a reasonable and precise mesh stiffness model, the M-B contact model and finite element method are combined to express the local contact stiffness Kh. Through the simulation and comparison, the analytical finite element method is proved to be consistent with the traditional models and introduces the roughness parameters of machined tooth surface into the meshing process. Furthermore, the results also show that it is advantageous to improve the total mesh stiffness by increasing the fractal dimension D and input torque T as well as decreasing the roughness parameter G. In this paper, a relationship is built between the total mesh stiffness of gear sets with tooth surface characters and input torque, which can be a guidance in the design of the tooth surface parameters and the choice of the processing method in the future.
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Wang, Jungang, Shinan Yang, Yande Liu, and Ruina Mo. "Analysis of Load-Sharing Behavior of the Multistage Planetary Gear Train Used in Wind Generators: Effects of Random Wind Load." Applied Sciences 9, no. 24 (December 13, 2019): 5501. http://dx.doi.org/10.3390/app9245501.
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Load-sharing behavior is very important for power-split gearing systems. Taking the multistage planetary gear train transmission of an Million Watt (MW) wind generator as the investigation object, and based on the gear transmission system of a wind generator in a complex and changing load environment, a random wind model of a wind farm is built by using the two-parameter Weibull distribution. According to the realistic working region of the wind generator, the random wind speed is changed into time-varying input speed of the wind generator gear box. Considering the internal excitation, such as mesh stiffness, mesh damping of gear pairs and the meshing error, a dynamic model for a multistage planetary gear transmission system is built by using the lumped parameter method. The load-sharing coefficients are obtained for each planet gear pair in the same meshing period of the transmission system that is under the interaction of time-varying input speed and internal excitation. It is shown that the degree of load-sharing coefficient fluctuation for each planet gear pair of the first- and second-stage planetary gear train is significantly affected by time-varying input speed. The research results can lay a theoretical foundation for optimization and reliability of planetary gear transmission systems of wind generators.
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Nikolic-Stanojevic, Vera, Ljiljana Veljovic, and Cemal Dolicanin. "A New Model of the Fractional Order Dynamics of the Planetary Gears." Mathematical Problems in Engineering 2013 (2013): 1–14. http://dx.doi.org/10.1155/2013/932150.
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A theoretical model of planetary gears dynamics is presented. Planetary gears are parametrically excited by the time-varying mesh stiffness that fluctuates as the number of gear tooth pairs in contact changes during gear rotation. In the paper, it has been indicated that even the small disturbance in design realizations of this gear cause nonlinear properties of dynamics which are the source of vibrations and noise in the gear transmission. Dynamic model of the planetary gears with four degrees of freedom is used. Applying the basic principles of analytical mechanics and taking the initial and boundary conditions into consideration, it is possible to obtain the system of equations representing physical meshing process between the two or more gears. This investigation was focused to a new model of the fractional order dynamics of the planetary gear. For this model analytical expressions for the corresponding fractional order modes like one frequency eigen vibrational modes are obtained. For one planetary gear, eigen fractional modes are obtained, and a visualization is presented. By using MathCAD the solution is obtained.
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Hou, Jingyu, Shaopu Yang, Qiang Li, and Yongqiang Liu. "Nonlinear dynamic analysis of spur gear system based on fractional-order calculus." Modern Physics Letters B 34, no. 36 (September 1, 2020): 2050420. http://dx.doi.org/10.1142/s0217984920504205.
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In this paper, nonlinear dynamic model of spur gear pairs with fractional-order damping under the condition of time-varying stiffness, backlash and static transmission error is established. The general formula of fractional-order damping term is derived by using the incremental harmonic balance method (IHBM), and the approximate analytical solution of the system is obtained by use of the iterative formula. The correctness of the results is verified by comparing with the numerical solutions in the existing literature. The effects of mesh stiffness, internal excitation amplitude and fractional order on the dynamic behavior of the system are analyzed. The results show that changing the fractional order can effectively control the resonance position and amplitude in the meshing process. Both the mesh stiffness and internal excitation can control the collision state and the stability.
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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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Liu, Dawei, Dandan Gu, and Zhijia Liu. "Coupled vibration modeling and dynamic characteristics of noncircular face gear drive system with time-varying instantaneous center excitation." Proceedings of the Institution of Mechanical Engineers, Part C: Journal of Mechanical Engineering Science 233, no. 14 (April 8, 2019): 4947–59. http://dx.doi.org/10.1177/0954406219841085.
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Noncircular face gear drive is a new type of variable transmission ratio mechanism with advantages of light weight, high interchangeability, and convenient installation. Based on its transmission principle, the excitation pattern of the time-varying instantaneous center of the noncircular face gear drive system is investigated. A torsional–lateral–axial coupled dynamic model of the noncircular face gear system is presented under the compound parametric excitations of the time-varying instantaneous center and the mesh stiffness. By using Runge–Kutta numerical integration method, the dynamic responses of the system are derived to analyze the vibration features of the noncircular face gear under compound parametric excitations and the effect of the design parameters on the coupled vibration. The analytical results indicate that there exist multifrequency components in the dynamic responses of the system, including the instantaneous center frequency f1, the meshing one f2, nf1, mf2, and mf2 ± nf1. In addition, the dynamic performance of the noncircular face gear drive can be improved by decreasing the amplitude coefficient of the instantaneous center and the mesh stiffness or increasing their mean values.
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Liu, Chao, Zong-de Fang, Xuan Liu, and Sheng-yang Hu. "Multibody dynamic analysis of a gear transmission system in electric vehicle using hybrid user-defined elements." Proceedings of the Institution of Mechanical Engineers, Part K: Journal of Multi-body Dynamics 233, no. 1 (July 29, 2018): 30–42. http://dx.doi.org/10.1177/1464419318789185.
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Considering flexibility of the support shafts as well as bearing supports, the effect of meshing impact force and meshing stiffness on the dynamic behavior of a gear transmission system in electric vehicle is investigated in this paper using the proposed hybrid user-defined element method. First, a structured grid generation method is introduced to establish accurate mesh models of the pinion and gear teeth. Second, coupling the tooth mesh models and the flexible shafts as well as bearings, two finite element models are, respectively, constructed for the two helical gear pairs of the electric vehicle reduction unit to calculate the meshing impact force. Next, the basic mechanism of meshing impact is explained in detail according to the finite element results, and the impact force is determined as one of the main internal excitations substituted into the dynamic model established by the hybrid user-defined element method. Under 50 N m input torque and 12,010 r/min rotational speed of the input shaft, the simulation results by the hybrid user-defined element method indicate that the example system reaches a steady state and the vibrations primarily occur at the meshing frequencies. With an increment of 600 r/min of the input rotational speed, it is also concluded from the results that (1) the calculated impact force approximately presents linear growth with the increase of the input shaft rotational speed and (2) the root mean square values of the vibration acceleration generally grow with the increase of the speed.
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Qiao, Li Xia, and Jun Ting Zhang. "The Research on Modeling and Dynamic Simulation of Gear Box Virtual Prototype Based on Pro/E and ADAMS." Advanced Materials Research 681 (April 2013): 115–20. http://dx.doi.org/10.4028/www.scientific.net/amr.681.115.
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In this paper, the combination of Pro\/E and ADAMS to build a virtual prototype model of gear transmission, the dynamic simulation of the gear meshing process, study on dynamic speed, mesh force bearing load, where, for the gear box of the engineering analysis and optimization design. A 3D modeling and designing software, established a parametric model of a gear box of the rack and pinion drive mechanism, which is used in large gantry milling machine XK2425-600. The data interface module MECHANISM/Pro is used to convert the Pro/E model data to ADAMS, and then the virtual prototype is built in it. The rotational speeds, meshing forces, and reactive loads at bearings are obtained by dynamic simulation of the virtual prototype, which can be used in finite element analysis as boundary condition, helped to calculate the strength and stiffness of the box.
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Guo, Fang, Zongde Fang, Xijin Zhang, and Yanmei Cui. "Influence of the Eccentric Error of Star Gear on the Bifurcation Properties of Herringbone Star Gear Transmission with Floating Sun Gear." Shock and Vibration 2018 (2018): 1–32. http://dx.doi.org/10.1155/2018/6014570.
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Taking a herringbone star gear transmission (HSGT) with floating sun gear as an example, the system bifurcation characteristics with the changing of the eccentric error of star gear and the working frequencies are analyzed. For this analysis, a generalized dynamic model of HSGT considering the manufacturing eccentric errors, time-varying mesh stiffness, and load balancing mechanism is established and solved by numerical method. The floating process of sun gear is explained. In this paper, there are seven cases about the eccentric errors of star gears which are calculated, respectively. To study the effect of the working frequencies (including meshing frequency and rotation frequency), the calculation is done at three kinds of input speed in which the working frequencies are close to the system natural frequencies. The results are demonstrated in detail by the bifurcation diagrams, phase plane plots, and Poincare maps. The system bifurcation characteristics are particularly analyzed and compared in every case. This work provides important guidance to the engineering of HSGT.
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Wang, Jingyue, Haotian Wang, Lixin Guo, and Diange Yang. "Modeling and fault identification of the gear tooth surface wear failure system." International Journal of Nonlinear Sciences and Numerical Simulation 22, no. 3-4 (March 1, 2021): 341–51. http://dx.doi.org/10.1515/ijnsns-2018-0221.
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Abstract In order to detect the gear tooth surface wear fault, this paper presents a new fault diagnosis method based on Symlets wavelet family multi-structure element difference morphological denoising and frequency slice wavelet transform (FSWT). Besides considering the gear backlash, time-varying mesh stiffness, gear error and bearing longitudinal response, and low frequency excitation caused by the torque fluctuation, random disturbance of damping gear ratio, gear backlash, excitation frequency, and meshing stiffness are also considered. Dynamics equations of a three degrees of freedom spur gear transmission system with tooth surface wear fault are established according to Newton’s laws. The 4–5 order variable step Runge–Kutta method has been used for solving the equations to get the vibration signal of the system. Then, the proposed method is applied to extract the wear fault signal, which verifies the feasibility and effectiveness of the proposed method.
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Xiao, Zhengming, Jinxin Cao, and Yinxin Yu. "Mathematical Modeling and Dynamic Analysis of Planetary Gears System with Time-Varying Parameters." Mathematical Problems in Engineering 2020 (March 16, 2020): 1–9. http://dx.doi.org/10.1155/2020/3185624.
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Planetary gears are widely used in automobiles, helicopters, heavy machinery, etc., due to the high speed reductions in compact spaces; however, the gear fault and early damage induced by the vibration of planetary gears remains a key concern. The time-varying parameters have a vital influence on dynamic performance and reliability of the gearbox. An analytical model is proposed to investigate the effect of gear tooth crack on the gear mesh stiffness, and then the dynamical model of the planetary gears with time-varying parameters is established. The natural characteristics of the transmission system are calculated, and the dynamic responses of transmission components, as well as dynamic meshing force of each pair of gear are investigated based on varying internal excitations induced by time-varying parameters and tooth root crack. The effects of gear tooth root crack size on the planetary gear dynamics are simulated, and the mapping rules between damage degree and gear dynamics are revealed. In order to verify the theoretical model and simulation results, the planetary gear test rig was built by assembling faulty and healthy gear separately. The failure mechanism and dynamic characteristics of the planetary gears with tooth root crack are clarified by comparing the analytical results and experimental data.