Journal articles: 'Gear mesh stiffness'

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Olanipekun, K. A. "Estimation of a Planetary Gear Mesh Stiffness: An Approach Based on Minimising Error Function." European Journal of Engineering and Technology Research 6, no. 3 (April 30, 2021): 164–69. http://dx.doi.org/10.24018/ejers.2021.6.3.2416.

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The mesh stiffness of gear teeth is one of the major sources of excitation in gear systems. Many analytical and finite element methods have been proposed in order to determine the mesh stiffness of gears especially parallel axis spur gears. Most of these methods are not trivial because they involve complicated analyses which incorporate parameters like gear tooth error, gear spalling sizes and shapes, nonlinear contact stiffness and sliding friction before mesh stiffness can be determined. In this work, a method is proposed to determine the sun-planet and ring-planet mesh stiffnesses of a planetary gear system. This approach involves fitting a relationship between the measured natural frequencies from an experimental modal test and natural frequencies predicted using an analytical model of a planetary gear. This method is relatively easier compared to the existing methods which involve complicated analyses. For this study, the average mesh stiffness estimated is 12.5 MN/m.

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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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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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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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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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Chen, Ying Chung, Chung Hao Kang, and Siu Tong Choi. "Dynamic Analysis of a Spur Geared Rotor-Bearing System with Nonlinear Gear Mesh Stiffness." Advanced Materials Research 945-949 (June 2014): 853–61. http://dx.doi.org/10.4028/www.scientific.net/amr.945-949.853.

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The gear mesh stiffnesses have been regarded as constants in most previous models of geared rotor-bearing systems. In this paper, a dynamic analysis of a spur geared rotor-bearing system with nonlinear gear mesh stiffness is presented. The nonlinear gear mesh stiffness is accounted for by bending, fillet-foundation and contact deflections of gear teeth. A finite element model of the geared rotor-bearing system is developed, the equations of motion are obtained by applying Lagrange’s equation, and the dynamic responses are computed by using the fourth-order Runge-Kutta numerical method. Numerical results indicate that the proposed gear mesh stiffness provides a realistic dynamic response for spur geared rotor-bearing system.

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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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Zhang, Dongsheng, and Shiyu Wang. "Parametric vibration of split gears induced by time-varying mesh stiffness." Proceedings of the Institution of Mechanical Engineers, Part C: Journal of Mechanical Engineering Science 229, no. 1 (April 23, 2014): 18–25. http://dx.doi.org/10.1177/0954406214531748.

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Time-varying mesh stiffness is a significant excitation source within gear systems. Split gear (or laminated gear, phase gear) is an interesting design using equally phased gear-slices, which can remarkably reduce the mesh stiffness fluctuation like helical gears but completely avoid the axial force. This work examines a split gear pair to address the suppression of the mesh stiffness fluctuation and rotational vibration thereof, especially the relationship between the key design parameters including the number of slice, contact ratio, and damping, and the parametric vibration. For these aims, this work develops a purely rotational model, based on which the multi-scale method is employed to determine stability boundaries. The results imply that the unstable zones are related to the mesh phase determined by the number of slices and contact ratio, and these zones can be diminished by the damping. The analytical predictions are numerically verified by Floquet theory.

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Gu, Cheng Zhong, and Xin Yue Wu. "Study of the Modeling of the Gear Dynamics Considering Mesh Stiffness and Sliding Friction." Applied Mechanics and Materials 29-32 (August 2010): 618–23. http://dx.doi.org/10.4028/www.scientific.net/amm.29-32.618.

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Time- varying mesh stiffness and sliding friction between teeth are the great excitation for vibration and noise in gears system. But, there are rarely studies on this topic. This paper proposes a new dynamic modeling of gear system, which is effect of mesh stiffness variation, sliding friction and distribution of load. Firstly, the expression of time-varying mesh stiffness is gained, which is a period function. Secondly, a new friction modeling has the same period as mesh stiffness, is proposed. Thirdly, friction torque of each gear pair is calculated respectively, which is considering the distribution of load and time-varying friction arm. Finally, because all parameter have the same cycle, it is easy to get the approximate analytical solution to non-line model of gear dynamic by fourier transform.

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Zhang, K.-Z., H.-D. Yu, X.-X. Zeng, and X.-M. Lai. "Numerical simulation of instability conditions in multiple pinion drives." Proceedings of the Institution of Mechanical Engineers, Part C: Journal of Mechanical Engineering Science 225, no. 6 (May 25, 2011): 1319–27. http://dx.doi.org/10.1177/2041298310392649.

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Multiple pinion drives, parallel arrangements of the pinions for large torque transmission, are widely utilized in various heavy-duty industrial applications. For such multi-mesh gear systems, periodic mesh stiffnesses could possibly cause parametric instabilities and server vibrations. Based on the Floquet–Lyapunov theory, numerical simulations are conducted to determine the parametric instability status. For rectangular waveforms assumption of the mesh stiffness variations, the primary, secondary, and combination instabilities of the multiple pinion drives are studied. The effects of mesh stiffness parameters, including mesh frequencies, stiffness variation amplitudes, and mesh phasing, on these instabilities are yielded. Unstable regions are also indicated for different gear pair configurations. Instability conditions of three-pinion drives are obtained and compared with those of the three-stage gear train.

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Wang, Yanzhong, Delong Dou, E. Shiyuan, and Jianjun Wang. "Comparison on torsional mesh stiffness and contact ratio of involute internal gear and high contact ratio internal gear." Proceedings of the Institution of Mechanical Engineers, Part C: Journal of Mechanical Engineering Science 234, no. 7 (December 11, 2019): 1423–37. http://dx.doi.org/10.1177/0954406219893721.

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The mesh stiffness and contact ratio of gear drive are very important factors which have a great impact on the dynamic load. Contact ratio also affects the fluctuation and the mode of change of the mesh stiffness. In this research, a novel high contact ratio internal gear with a circular arc contact path is introduced. However, the irregular tooth profile of non-involute gear usually causes the numerical calculation to be more complex. To get the torsional mesh stiffness of a pair of internal spur gear, the two-dimensional finite element models of involute internal gear and high contact ratio internal gear are presented and compared. In addition, the influence of input torque on torsional mesh stiffness and contact ratio are analyzed. The mesh stiffness of a single tooth pair and the effect of different engagement positions on mesh stiffness are obtained and compared. Finally, experimental measurement of contact ratio is established by strain gauge technique. It is shown that the torsional mesh stiffness increases with the increase of input torque, and the greater the contact ratio, the smoother the gear drive.

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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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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.

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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.

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Hedlund, J., and A. Lehtovaara. "A parameterized numerical model for the evaluation of gear mesh stiffness variation of a helical gear pair." Proceedings of the Institution of Mechanical Engineers, Part C: Journal of Mechanical Engineering Science 222, no. 7 (July 1, 2008): 1321–27. http://dx.doi.org/10.1243/09544062jmes849.

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One of the most common challenges in gear drive design is to determine the best combination of gear geometry parameters. These parameters should be capable of being varied effectively and related to gear mesh stiffness variation in advanced excitation and vibration analysis. Accurate prediction of gear mesh stiffness and transmission error requires an efficient numerical method. The parameterized numerical model was developed for the evaluation of excitation induced by mesh stiffness variation for helical gear design purposes. The model uses linear finite-element (FE) method to calculate tooth deflections, including tooth foundation flexibility. The model combines Hertzian contact analysis with structural analysis to avoid large FE meshes. Thus, mesh stiffness variation was obtained in the time and frequency domains, which gives flexibility if comparison is made with measured spectrums. Calculations showed that a fairly low number of elements suffice for the estimation of mesh stiffness variation. A reasonable compromise was achieved between design trends and calculation time.

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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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Yuan, Bing, Shan Chang, Geng Liu, Lan Liu, and Lehao Chang. "Sensitivity Analysis of Helical Gears with Tooth Surface Modification to Applied Torque and Gear Misalignment." Xibei Gongye Daxue Xuebao/Journal of Northwestern Polytechnical University 36, no. 6 (December 2018): 1085–92. http://dx.doi.org/10.1051/jnwpu/20183661085.

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

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Ma, Hui, Rongze Song, Xu Pang, and Bangchun Wen. "Fault Feature Analysis of a Cracked Gear Coupled Rotor System." Mathematical Problems in Engineering 2014 (2014): 1–22. http://dx.doi.org/10.1155/2014/832192.

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Considering the misalignment of gear root circle and base circle and accurate transition curve, an improved mesh stiffness model for healthy gear is proposed, and it is validated by comparison with the finite element method. On the basis of the improved method, a mesh stiffness model for a cracked gear pair is built. Then a finite element model of a cracked gear coupled rotor system in a one-stage reduction gear box is established. The effects of crack depth, width, initial position, and crack propagation direction on gear mesh stiffness, fault features in time domain and frequency domain, and statistical indicators are investigated. Moreover, fault features are also validated by experiment. The results show that the improved mesh stiffness model is more accurate than the traditional mesh stiffness model. When the tooth root crack appears, distinct impulses are found in time domain vibration responses, and sidebands appear in frequency domain. Amplitudes of all the statistical indicators ascend gradually with the growth of crack depth and width, decrease with the increasing crack initial position angle, and firstly increase and then decrease with the growth of propagation direction angle.

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Gao, Nan, Chanannipat Meesap, Shiyu Wang, and Dongsheng Zhang. "Parametric vibrations and instabilities of an elliptical gear pair." Journal of Vibration and Control 26, no. 19-20 (February 14, 2020): 1721–34. http://dx.doi.org/10.1177/1077546320902543.

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Parametric vibrations and instabilities can be induced in an elliptical gear pair. This study examined the effects of basic parameters on vibration instability. Geometric parameters and time-variant mesh stiffness are calculated. A torsional dynamic model is established by introducing the lumped parameter assumption. Based on the model, the parametric vibrations caused by the excitations of eccentricity and time-variant mesh stiffness are investigated, and the additive and difference combination resonances are identified. Comparison between the elliptical and circular gears implies that the vibration amplitude at mesh frequency of the elliptical gears is lower than that of the regular circular gears. The vibrations caused by load torque are also examined. The results show that the vibrations with different frequencies are coupled with each other. The inherent reason behind the coupling is the interaction between the eccentricity, time-variant stiffness, and load.

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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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Yinong, Li, Li Guiyan, and Zheng Ling. "Influence of Asymmetric Mesh Stiffness on Dynamics of Spiral Bevel Gear Transmission System." Mathematical Problems in Engineering 2010 (2010): 1–13. http://dx.doi.org/10.1155/2010/124148.

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An 8-DOF (degrees-of-freedom) nonlinear dynamic model of a spiral bevel gear pair which involves time-varying mesh stiffness, transmission error, backlash, and asymmetric mesh stiffness is established. The effect of the asymmetric mesh stiffness on vibration of spiral bevel gear transmission system is studied deliberately with numerical method. The results show that the mesh stiffness of drive side has more effect on dynamic response than those of the coast side. Only double-sided impact region is affected considerably by mesh stiffness of coast side while single-sided impact and no-impact regions are unchanged. In addition, the increase in the mesh stiffness of drive side tends to worsen the dynamic response of the transmission system especially for light-load case.

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Li, Zheng Min Qing, Qing Bin Zhao, and Xiao Zhen Li. "Prediction of Spur Gear Mesh Stiffness Associated with the Tooth Corrosion." Applied Mechanics and Materials 799-800 (October 2015): 570–75. http://dx.doi.org/10.4028/www.scientific.net/amm.799-800.570.

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In this study, a mesh stiffness model of spur gear drives considering the tooth corrosion effect, which is based on Ishikawa model, is proposed. The fidelity of mesh stiffness based on the proposed model is checked by comparing the result with a benchmark result from the reference and the effect of the tooth corrosion on mesh stiffness is analyzed. The prediction indicates mesh stiffness is insensitive to the tooth corrosion, but this conclusion has a signification for assessing the stability of inherent properties of a spur gear drive when the tooth corrosion is produced.

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Ambarisha, Vijaya Kumar, and Robert G. Parker. "Suppression of Planet Mode Response in Planetary Gear Dynamics Through Mesh Phasing." Journal of Vibration and Acoustics 128, no. 2 (February 10, 2005): 133–42. http://dx.doi.org/10.1115/1.2171712.

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This work analytically derives design rules to suppress certain harmonics of planet mode response in planetary gear dynamics through mesh phasing. Planet modes are one of three categories of planetary gear vibration modes. In these modes, only the plantes deflect while the carrier, ring, and sun gears have no motion (Lin, J., and Parker, R. G., 1999, ASME J. Vib. Acoust., 121, pp. 316–321;J. Sound Vib, 233(5), pp. 921–928). The dynamic mesh forces are not explicitly modeled for this study; instead, the symmetry of planetary gear systems and gear tooth mesh periodicity are sufficient to establish rules to suppress planet modes. Thus, the conclusions are independent of the mesh modeling details. Planetary gear systems with equally spaced planets and with diametrically opposed planet pairs are examined. Suppression of degenerate mode response in purely rotational degree-of-freedom models achieved in the limit of infinite bearing stiffness is also investigated. The mesh phasing conclusions are verified by dynamic simulations of various planetary gears using a lumped-parameter analytical model and by comparisons to others’ research.

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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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Arafa, M. H., and M. M. Megahed. "Evaluation of spur gear mesh compliance using the finite element method." Proceedings of the Institution of Mechanical Engineers, Part C: Journal of Mechanical Engineering Science 213, no. 6 (June 1, 1999): 569–79. http://dx.doi.org/10.1243/0954406991522509.

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This paper presents a finite element (FE) modelling technique to evaluate the mesh compliance of spur gears. Contact between the engaging teeth is simulated through the use of gap elements. Analysis is performed on several gear combinations and the variation in tooth compliance along the contact location is presented in a non-dimensional form. Results are compared with earlier predictions based on analytical, numerical and experimental methods. Load sharing among the mating gear teeth is discussed, and the overall gear mesh stiffness together with its cyclic variation along the path of contact is evaluated.

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Yang, Yong, Jiaxu Wang, Qinghua Zhou, Yanyan Huang, Jinxuan Zhu, and Wanyou Yang. "Mesh stiffness modeling considering actual tooth profile geometry for a spur gear pair." Mechanics & Industry 19, no. 3 (2018): 306. http://dx.doi.org/10.1051/meca/2018026.

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Some tooth profile geometric features, such as root fillet area, flank modification and wear are of nonnegligible importance for gear mesh stiffness. However, due to complexity of analytical description, their influence on mesh stiffness was always ignored by existing research works. The present work derives analytical formulations for time-varying gear mesh stiffness by using parametric equations of flank profile. Tooth geometry formulas based upon a rack-type tool are derived following Litvin's vector approach. The root fillet area and tooth profile deviations can therefore be fully considered for spur gear tooth stiffness evaluation. The influence of gear fillet determined by tip fillet radius of the rack-type tool is quantified parametrically. The proposed model is validated to be effective by comparing with a finite element model. Further, the model is applied to investigate the stiffness variations produced by tooth addendum modification, tooth profile nonuniform wear and modification.

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Zhang, Ruiliang, Kaida Wang, Yandong Shi, Xiuquan Sun, Fengshou Gu, and Tie Wang. "The Influences of Gradual Wears and Bearing Clearance of Gear Transmission on Dynamic Responses." Energies 12, no. 24 (December 11, 2019): 4731. http://dx.doi.org/10.3390/en12244731.

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Gears are important components of the transmission system. Tooth wear and bearing clearance are significant factors affecting the dynamics of the gear system. In order to reveal the effects of gradual wears and bearing clearance on the gear system dynamics, a six-degrees-of-freedom bending-torsion coupled model of gear-rotor-bearing which considers surface wear, bearing clearance and backlash is established. The Rung-Kutta method is used to solve the nonlinear dynamic system, and the dynamic responses of the system are obtained. The results show that the time-varying mesh stiffness decreases with the tooth surface from the unworn phase to severe wear phase. At the same time, the change of the mesh stiffness in the double-tooth mesh area and single-tooth area are different. Moreover, the amplitude of the X-displacement, Y-displacement and relative gear mesh displacement will be enlarged slightly with the increase of wear depth or bearing clearance. By analyzing variation tendency in the frequency domain, the different order harmonics show the different change characteristic with the variation of the wear phases or bearing clearances. This study provides a theoretical basis for improving the transmission performance and the selection of the bearing clearances in the gear system.

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Xiang, Ling, Chaohui An, and Aijun Hu. "Nonlinear Dynamic Characteristics of Wind Turbine Gear System Caused by Tooth Crack Fault." International Journal of Bifurcation and Chaos 31, no. 10 (August 2021): 2150148. http://dx.doi.org/10.1142/s0218127421501480.

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Crack in gears impacts the dynamic response of wind turbine multistage gear system, which also influences the safe operation of wind turbine. A translational–torsional nonlinear dynamic model of the multistage gear system is proposed with root crack fault. The model considers the effects of sun gear support, time-varying mesh stiffness, gear backlash and other factors. The mesh stiffness with root crack is analyzed by using potential energy method. Based on the Runge–Kutta method, the system responses are obtained with multiple parameters changing. The nonlinear dynamic features of the cracked and normal system are compared by bifurcation diagram, time series, phase trajectory, Poincaré map, spectrum diagram and corresponding three-dimensional diagrams. The analyses show the effects of input torque, backlash, crack occurrence and evolution on the system dynamic behaviors, and the effect of crack fault on the gear system response is further verified by experiment. The results provide a theoretical basis for the cognition of fault mechanism and fault diagnosis of wind turbine gearbox.

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Skrickij, Viktor, and Marijonas Bogdevičius. "VEHICLE GEARBOX DYNAMICS: CENTRE DISTANCE INFLUENCE ON MESH STIFFNESS AND SPUR GEAR DYNAMICS." TRANSPORT 25, no. 3 (September 30, 2010): 278–86. http://dx.doi.org/10.3846/transport.2010.34.

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Vehicle gearbox dynamics is characterized by time varying mesh stiffness. The paper presents a survey of methods used for determining mesh stiffness and the analysis of the centre distance influence on it. The refined mathematical transmission model presenting the centre distance as a variable is presented. The centre distance error as well as backlash and bearing flexibility is defined and the influence of these factors on mesh stiffness and spur gear dynamics is investigated. The results obtained from this paper may be used in gear‐box diagnostics.

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Wang, Jun, and Teik C. Lim. "On the Boundary between Nonlinear Jump Phenomenon and Linear Response of Hypoid Gear Dynamics." Advances in Acoustics and Vibration 2011 (May 26, 2011): 1–13. http://dx.doi.org/10.1155/2011/583678.

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A nonlinear time-varying (NLTV) dynamic model of a hypoid gear pair system with time-dependent mesh point, line-of-action vector, mesh stiffness, mesh damping, and backlash nonlinearity is formulated to analyze the transitional phase between nonlinear jump phenomenon and linear response. It is found that the classical jump discontinuity will occur if the dynamic mesh force exceeds the mean value of tooth mesh force. On the other hand, the propensity for the gear response to jump disappears when the dynamic mesh force is lower than the mean mesh force. Furthermore, the dynamic analysis is able to distinguish the specific tooth impact types from analyzing the behaviors of the dynamic mesh force. The proposed theory is general and also applicable to high-speed spur, helical and spiral bevel gears even though those types of gears are not the primary focus of this paper.

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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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33

Yang, Xu Juan, Guang Heng Xu, Zhao Jun Li, and Ru Gui Wang. "Dynamic Modeling and Response Analysis of Lateral-Torsional Coupling Vibration of the Slewing Mechanism of a Hydraulic Excavator." Advanced Materials Research 753-755 (August 2013): 1755–59. http://dx.doi.org/10.4028/www.scientific.net/amr.753-755.1755.

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A lateral-torsional coupled vibration model of the slewing mechanism of a hydraulic excavator is developed with consideration of the effect of lateral vibration and torsional vibration of sun gear and planetary gear on mesh displacement, the mesh stiffness of gear pairs, the bearing stiffness of the planetary and the coupling relationship of two stage planetary gear trains. The dynamic response of the slewing mechanism of a hydraulic excavator is obtained. Compared to the pure torsional vibration, the lateral-torsional vibration model is more reasonable.

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Zhou, Chi, Qi Wang, Weiqi Ding, Liangjin Gui, and Zijie Fan. "Numerical simulation of drive axles considering the nonlinear couplings between gears and bearings." Proceedings of the Institution of Mechanical Engineers, Part D: Journal of Automobile Engineering 233, no. 4 (April 18, 2018): 851–61. http://dx.doi.org/10.1177/0954407018755598.

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The drive axle is the core of the powertrain in automotive vehicles, and numerical simulation is a common and effective approach for designing and analysing drive axles. This article develops a new numerical simulation method for drive axles considering the nonlinear couplings between gears and bearings. Two types of models are proposed and integrated: a reduced model with nonlinear bearing elements and equivalent gear elements, which is efficient for nonlinear bearing simulation, and a gear contact analysis model with equivalent bearing stiffnesses, which can accurately reflect the gear mesh conditions and system deflection. The equivalent gear mesh parameters used in the reduced model are derived from the contact analysis model, and the linear equivalent bearing stiffness matrices used in the contact analysis model are derived from the reduced model. Therefore, the static equilibrium condition of the entire drive axle system is obtained through an iterative calculation process involving the two models under the same load condition. The good correlation between the numerical and experimental results of the gear-loaded contact pattern indicates that the proposed method is reliable.

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35

Han, Lin, Lixin Xu, and Fujun Wang. "Study on torsional stiffness of transmission employed in a rotary table." Proceedings of the Institution of Mechanical Engineers, Part C: Journal of Mechanical Engineering Science 230, no. 19 (August 8, 2016): 3541–55. http://dx.doi.org/10.1177/0954406215613116.

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Torsional stiffness of a rotary table plays an important role in the static and dynamic characteristics of a rotary feed drive system. This paper proposes an effective approach to estimate the torsional stiffness of a worm geared transmission usually employed in rotary table. First, the stiffness models of each component used in the transmission are extracted. Then, an expression for the coefficient relating angular displacements is derived and a general torsional stiffness model for the rotary feed drive is developed, taking the time-varying mesh stiffness into account. Finally, a stiffness test scheme is presented and conducted to verify the proposed stiffness model. Furthermore, the influences of the gear’s parameters on the resultant torsional stiffness are investigated based on the developed model. Results indicate the necessity to incorporate a time-varying mesh stiffness when the torsional stiffness of the rotary table is under estimation. Also, a high-frequency variation in profile of torsional stiffness is induced by the mesh stiffness of gear pairs at the high-speed stage. Parametric studies show that tooth width and number of teeth of the driven gear at low-speed stage are more sensitive to stiffness than those at high-speed stage. However, the number of teeth of the driving gears introduces different effects onto the torsional stiffness. The presented model can be used to estimate the torsional stiffness of a rotary feed system efficiently, especially during the preliminary design stage.

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Zhu, CaiChao, XiangYang Xu, Teik Chin Lim, XueSong Du, and MingYong Liu. "Effect of flexible pin on the dynamic behaviors of wind turbine planetary gear drives." Proceedings of the Institution of Mechanical Engineers, Part C: Journal of Mechanical Engineering Science 227, no. 1 (May 4, 2012): 74–86. http://dx.doi.org/10.1177/0954406212447029.

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Flexible pins eliminate the need for straddle mounting, and therefore enable the maximum possible number of planets to be used for any particular epicyclic ratio of power transmission systems. Having more planet gears will significantly increase the input torque density. In this type of design, the pin stiffness and position tolerances are important parameters as they affect the dynamic performances significantly. The present study addresses this issue by modeling, the design of double cantilevered flexible pin, and analyzing the contributions of pin stiffness and misalignment applying the lumped parameter approach. The proposed model formulates the coupled lateral-torsional dynamic response of a planetary spur gear, including the effects of mesh stiffness and phasing as a function of pin error. The resultant equations of motion are applied to examine the effects of pin stiffness and position errors on the natural modes and structural dynamic response. The effects of pin stiffness on deviation of the tooth contact forces of the sun-planet and ring-planet gear pairs are analyzed to understand the relationship between mesh characteristic and input speed variations. The calculated supporting forces of the planet gear are examined to understand the load sharing characteristic due to pin errors, pin stiffness and input load of the power transmission system.

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Batinic, Vojislav. "Determination of gear mesh stiffness in planetary gearing." Vojnotehnicki glasnik 56, no. 2 (2008): 227–36. http://dx.doi.org/10.5937/vojtehg0802227b.

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Xiong, Yangshou, Kang Huang, Fengwei Xu, Yong Yi, Meng Sang, and Hua Zhai. "Research on the Influence of Backlash on Mesh Stiffness and the Nonlinear Dynamics of Spur Gears." Applied Sciences 9, no. 5 (March 12, 2019): 1029. http://dx.doi.org/10.3390/app9051029.

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In light of ignoring the effect of backlash on mesh stiffness in existing gear dynamic theory, a precise profile equation was established based on the generating processing principle. An improved potential energy method was proposed to calculate the mesh stiffness. The calculation result showed that when compared with the case of ignoring backlash, the mesh stiffness with backlash had an obvious decrease in a mesh cycle and the rate of decline had a trend of decreasing first and then increasing, so a stiffness coefficient was introduced to observe the effect of backlash. The Fourier series expansion was employed to fit the mesh stiffness rather than time-varying mesh stiffness, and the stiffness coefficient was fitted with the same method. The time-varying mesh stiffness was presented in terms of the piecewise function. The single degree of freedom model was employed, and the fourth order Runge–Kutta method was utilized to investigate the effect of backlash on the nonlinear dynamic characteristics with reference to the time history chart, phase diagram, Poincare map, and Fast Fourier Transformation (FFT) spectrogram. The numerical results revealed that the gear system primarily performs a non-harmonic-single-periodic motion. The partially enlarged views indicate that the system also exhibits small-amplitude and low-frequency motion. For different cases of backlash, the low-frequency motion sometimes shows excellent periodicity and stability and sometimes shows chaos. It is of practical guiding significance to know the mechanisms of some unusual noises as well as the design and manufacture of gear backlash.

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Hu, Youmin, Jikai Fan, and Jin Yu. "Study of the Influences of Transient Crack Propagation in a Pinion on Time-Varying Mesh Stiffness." Shock and Vibration 2016 (2016): 1–13. http://dx.doi.org/10.1155/2016/6928686.

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Cracks in a cracked gear may further propagate by a tiny length in a very short time for several reasons, such as material fatigue and load fluctuations. In this paper, this dynamic process is defined as transient propagation of cracks. This research aims to calculate the time-varying mesh stiffness of gears when transient propagation of cracks arises, which has not been extensively studied in existing literatures. The transient propagation of cracks is modelled. An improved potential energy method is proposed by incorporating the propagation model into the potential energy method. The improved method can also be utilised to calculate the mesh stiffness of gears when transient propagation of cracks arises. Different transient propagation models are considered to simulate the propagation of cracks in a short amount of time. Different deterioration levels of cracks before transient propagation and different lengths and models of transient propagation are also examined. The variation rules of mesh stiffness caused by the transient propagation of cracks are summarised. The influence of the deterioration level of cracks on mesh stiffness variation when transient propagation arises is obtained. Simulation results show that the proposed method accurately calculates time-varying mesh stiffness when transient propagation of cracks arises. Furthermore, the method improves the monitoring of further propagation of cracks in gears from the perspective of time-varying mesh stiffness.

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40

Fokas, Nikolaos. "A Lightweight Model for Gear Mesh Dynamics Incorporating Variable Mesh Stiffness." MATEC Web of Conferences 28 (2015): 02003. http://dx.doi.org/10.1051/matecconf/20152802003.

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41

Xu, Lijiao, and Nan Chen. "Nonlinear dynamic study and vibration reduction of a power turret gear train with modified design parameters." Proceedings of the Institution of Mechanical Engineers, Part C: Journal of Mechanical Engineering Science 229, no. 10 (August 12, 2014): 1745–59. http://dx.doi.org/10.1177/0954406214547092.

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This work presents the nonlinear dynamic characteristics and vibration reduction of a numerical control power turret three-stage gear transmission system composed of four spur gears. Considering translational and rotational motions, the nonlinear lumped-parameter and multi-degrees of freedom models of modified and unmodified transmission systems are introduced to study the dynamic behavior while the time-varying mesh stiffness and backlash of gear mesh pairs are involved as internal excitations. For the requirement of high speed and low vibration, high contact ratio by modifying design parameters is suggested in this study. By numerical method, the dynamic vibration responses are calculated. Results in the time and frequency domains show that the vibration amplitudes and mesh forces are efficiently decreased after modification. The influences of key parameters, such as mesh stiffness, damping, backlash, and torque on the dynamic response are also studied here. To demonstrate the effectiveness of the proposed model, the vibration tests are conducted by two physical prototypes of the power turret. The values of vibration acceleration at different tests points and speeds are obtained and analyzed. Experimental results validate that the vibration of turret is decreased by the design improvement of gear system.

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42

Park, Chan Il. "Initial Behavior of Speed Increasing Helical Gears by Torque Fluctuation." Applied Mechanics and Materials 86 (August 2011): 813–16. http://dx.doi.org/10.4028/www.scientific.net/amm.86.813.

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This work studied initial impact behavior of speed increasing helical gears with backlash and the change of mesh stiffness by torque fluctuation. For this purpose, single degree of freedom equations of motion of helical gears with the periodical change of mesh stiffness and backlash, and its dimensionless form were derived. The Newmark beta method and the Newton-Raphson method were used to obtain nonlinear behavior of helical gears. Many excitation frequencies initially caused the tooth separation and single-sided impacts of the gear pair and eventually led to the normal tooth contact. However, some special excitation frequencies caused the single-sided impacts in the entire time. Damping increase reduced the initial transient period. Backlash increase extended the duration of single-sided impacts and also increased mesh force.

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43

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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Chang, Le Hao, Geng Liu, Li Yan Wu, and Zhong Hong Bu. "Research on Vibration Influence Chart of Planetary Gear Systems." Applied Mechanics and Materials 86 (August 2011): 747–51. http://dx.doi.org/10.4028/www.scientific.net/amm.86.747.

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The common definition of vibration influence chart is proposed in this study. A 46 degree-of-freedom time-varying dynamic model with coupled translation-rotation effect is developed to simulate the vibration of an encased differential planetary gear system using lumped mass method. With the dynamic load and the acceleration on gears and bearings as references, the dynamic responses in different load cases are investigated to search the change law of concerned parameters. The parameters considered include mesh stiffness, structure stiffness, gear mass and moment of inertia. The good and poor regions for vibration are evidently presented in figures, which is convenient to conduct the parameters design of planetary gear systems.

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Liu, De-Shin, Chuen-Ren Wang, Ting-Nung Shiau, Kuo-Hsuan Huang, and Wei-Chun Hsu. "Bifurcation Analysis of Gear Pair with Continuous and Intermittent Mesh Stiffness Using Enhanced Compliance Method." International Journal of Bifurcation and Chaos 30, no. 10 (August 2020): 2050156. http://dx.doi.org/10.1142/s0218127420501564.

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The nonlinear dynamics of a multigear pair with the time-varying gear mesh stiffness are investigated using an enhanced compliance-based methodology. In the proposed approach, Lagrangian theory and Runge–Kutta method are used to derive the equation of motion of the multigear pair and solve its dynamic response for various values of the gear mesh frequency, respectively. The simulation results obtained for the dynamic behavior of the multigear pair are compared with those obtained by using continuous (cosine, sine and offset sine function) and intermittent representations of the time-varying gear mesh stiffness. It is shown that periodic, quasi-periodic, aperiodic and chaos motions are induced at different values of the gear mesh frequency. In addition, the bifurcation diagram reveals the occurrence of both nonimpact motion and single-sided impact motion, and Lyapunov exponent can easily diagnose the chaos phenomenon of system.

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46

Daniewicz, S. R., J. A. Collins, and D. R. Houser. "The Stress Intensity Factor and Stiffness for a Cracked Spur Gear Tooth." Journal of Mechanical Design 116, no. 3 (September 1, 1994): 697–700. http://dx.doi.org/10.1115/1.2919438.

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The stiffness of a spur gear tooth mesh controls load sharing in an operating gearset as well as vibratory properties which further dictate fatigue resistance and gear noise. A spur gear mesh consisting of a pinion with a single cracked tooth and an uncracked gear is considered. Expressions are presented which allow the determination of stress intensity factors for small through face width fatigue cracks in spur gear teeth. Predictions of tooth pair stiffness for a cracked pinion tooth and uncracked gear tooth pair are made using an analytical model. The model is based on elastic energy methods and fracture mechanics principles. The model employs a conformal mapping technique from elasticity theory, often denoted in spur gear applications as the complex potential method, in which a gear tooth is mapped onto on elastic half-plane.

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Yang, Fu Chun, Qi Lin Huang, Yong Wang, and Jun Gang Wang. "Research on Dynamics of Double-Mesh Helical Gear Set." Applied Mechanics and Materials 215-216 (November 2012): 1021–25. http://dx.doi.org/10.4028/www.scientific.net/amm.215-216.1021.

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A dynamic model of double-mesh helical gear set was established including the torsional vibration, axial vibration and time varying mesh stiffness. The natural modes were systematically analyzed and classified into three types: rotational vibration mode, axial vibration mode and overall vibration mode. The influence of time varying mesh stiffness and the dynamic responses of the gear set were also investigated. The results showed that several natural frequencies are excited in the dynamic response and there is a frequency sensitive area which may cause large dynamic load.

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Liu, Gang, and Robert G. Parker. "Nonlinear, parametrically excited dynamics of two-stage spur gear trains with mesh stiffness fluctuation." Proceedings of the Institution of Mechanical Engineers, Part C: Journal of Mechanical Engineering Science 226, no. 8 (May 17, 2012): 1939–57. http://dx.doi.org/10.1177/0954406212447509.

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This work studies the nonlinear, parametrically excited dynamics of two spur gear pairs in a two-stage counter-shaft configuration. The dynamic model includes parametric excitations and contact loss of both tooth meshes with two different mesh frequencies. The time-varying mesh stiffnesses and nonlinear tooth separation functions are reformulated into forms suitable for perturbation analysis. The periodic steady-state solutions are obtained by the method of multiple scales and compared against a semi-analytical harmonic balance method as well as numerical integration for fundamental and subharmonic resonances for ranges of system parameters. The interaction of the two meshes is found to depend strongly on the relation of the two mesh periods. The dynamic influences of design parameters, such as shaft stiffness, mesh stiffness variations, contact ratios, and mesh phasing, are discussed. The closed-form solutions provide design guidelines in terms of the system parameters.

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Jin, Guanghu, Wei Ren, and Rupeng Zhu. "Influence of torsional stiffness on load sharing coefficient of a power split drive system." MATEC Web of Conferences 211 (2018): 17002. http://dx.doi.org/10.1051/matecconf/201821117002.

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A dynamic model of power split transmission system with face gear and cylindrical gear is established. The factors including time-varying mesh stiffness, torsional stiffness, supporting stiffness, and clearance are considered in the model. The influence of the torsional stiffness of compound gear shaft on the load sharing coefficient is analyzed. The results show that the influence of the torsional stiffness of the compound gear shaft is obvious. Because the torsional stiffness of the output gear components is larger and the torsional stiffness of the input gear is smaller, so the input stage's deformation coordination ability is strong. Therefore, with the increase of the torsional stiffness of the compound gear shaft, the load sharing coefficient of the power input stages is improved, but the load sharing coefficient of the split torque stages and power confluence stages is worse. Hence, the torsional stiffness ratio of the transmission shaft should be rationally allocated under the condition that the torsional stiffness of the compound shaft is small.

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Jia, Shengxiang, Ian Howard, and Jiande Wang. "The Dynamic Modeling of Multiple Pairs of Spur Gears in Mesh, Including Friction and Geometrical Errors." International Journal of Rotating Machinery 9, no. 6 (2003): 437–42. http://dx.doi.org/10.1155/s1023621x03000423.

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This article presents a dynamic model of three shafts and two pair of gears in mesh, with 26 degrees of freedom, including the effects of variable tooth stiffness, pitch and profile errors, friction, and a localized tooth crack on one of the gears. The article also details howgeometrical errors in teeth can be included in a model. The model incorporates the effects of variations in torsional mesh stiffness in gear teeth by using a common formula to describe stiffness that occurs as the gears mesh together. The comparison between the presence and absence of geometrical errors in teeth was made by using Matlab and Simulink models, which were developed from the equations of motion. The effects of pitch and profile errors on the resultant input pinion angular velocity coherent-signal of the input pinion's average are discussed by investigating some of the common diagnostic functions and changes to the frequency spectra results.

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Journal articles on the topic 'Gear mesh stiffness'

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