Relevant bibliographies by topics / Multiple gear transmission

Contents

  1. Journal articles
  2. Dissertations / Theses
  3. Book chapters
  4. Conference papers

Academic literature on the topic 'Multiple gear transmission'

Author: Grafiati
Published: 28 June 2021
Last updated: 14 February 2022

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Journal articles on the topic "Multiple gear transmission"

1

Sommer, Andrew, Jim Meagher, and Xi Wu. "Gear Defect Modeling of a Multiple-Stage Gear Train." Modelling and Simulation in Engineering 2011 (2011): 1–8. http://dx.doi.org/10.1155/2011/754257.

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This study demonstrates the transient and steady state dynamic loading on teeth within a two-stage gear transmission arising from backlash and geometric manufacturing errors by utilizing a nonlinear multibody dynamics software model. Backlash between gear teeth which is essential to provide better lubrication on tooth surfaces and to eliminate interference is included as a defect and a necessary part of transmission design. Torsional vibration is shown to cause teeth separation and double-sided impacts in unloaded and lightly loaded gearing drives. Vibration and impact force distinctions between backlash and combinations of transmission errors are demonstrated under different initial velocities and load conditions. The backlash and manufacturing errors in the first stage of the gear train are distinct from those of the second stage. By analyzing the signal at a location between the two stages, the mutually affected impact forces are observed from different gear pairs, a phenomenon not observed from single pair of gears. Frequency analysis shows the appearance of side band modulations as well as harmonics of the gear mesh frequency. A joint time-frequency response analysis during startup illustrates the manner in which contact forces increase during acceleration.
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Cristescu, Ana, Bogdan Cristescu, and Laurenţia Andrei. "Designing Multispeed Gear Pitch Curves." Applied Mechanics and Materials 657 (October 2014): 480–84. http://dx.doi.org/10.4028/www.scientific.net/amm.657.480.

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As special mechanical systems within transmissions of unconventional motions, noncircular gears still offer multiple research opportunities due to their various geometries and kinematics characteristics. Investigation on noncircular gears highlights the lack of information on gears with combination of constant and variable speed, also named multispeed gears, recommended for industrial applications that require uniform speeds for different parts of a cycle, with a smooth transition between the parts. Therefore, in this paper the design of multispeed gears pitch curves is taken into account, as the first important step in the gear design procedure. Specific original algorithms are dedicated to multispeed gear pitch curve modeling, based on the definition of gear transmission ratio variation law. The next step of the multispeed gear design, the teeth generation, accessible through solid modeling or analytical procedure, will be approached in a future study.
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Yao, Lingling, Zhuo Meng, Jianqiu Bu, and Yize Sun. "Non-Linear Dynamic Feature Analysis of a Multiple-Stage Closed-Loop Gear Transmission System for 3D Circular Braiding Machine." Symmetry 12, no. 11 (October 28, 2020): 1788. http://dx.doi.org/10.3390/sym12111788.

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Aiming at the particularity of a multiple-stage closed-loop gear transmission system for 3D circular braiding machine, the model of gear transmission system in radial braiding machine was simplified. The non-linear dynamic equations of a n-elements closed-loop gear transmission system with symmetrical structure including static transmission error, the random disturbance of meshing damping and backlash were considered. For convenience of calculation n = 3, the equations were solved numerically by using Runge-Kutta. The dynamic transmission error(DTE) with different backlash, dynamic meshing forces with and without the random disturbance of meshing damping, the amplitude of dynamic transmission error at n = 1000 r/min and b = 2.65 × 10−5 m, root mean square(RMS) of DTE and the mean value of DTE of the first pair of gears were analyzed. The simulation results show that different backlash and the random disturbance of meshing damping have a great influence on the dynamic displacement error and meshing force of the gear pair, and RMS and the mean value of DTE changes at different rotational speeds. The results will provide a reference for realizing the smoothness of the closed-loop gear transmission system with symmetrical structure for 3D braiding machine and have great practical significance for improving the braiding quality.
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Mu, Xiao Kai, Yu Guang Li, Dian Hua Chen, and Cheng Chao Li. "Failure Analysis and Transmission Parameters Optimization Design of WN Gears Drive." Applied Mechanics and Materials 229-231 (November 2012): 449–52. http://dx.doi.org/10.4028/www.scientific.net/amm.229-231.449.

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This paper taking the high strength of WN gears drive as target, which makes the WN gear device has light weight and compact size. The WN gears drive optimization design model of actual project is put forward by multiple-factor comprehensive failure analysis. The research is to solve nonlinear constrained optimization problems by the method of sequence quadratic programming (SQP) in MATLAB optimization toolbox. Using the optimization program of engineering design examples to analyze the relationship about gear drive parameters on contact and bending fatigue strength, thus the engineering design method of the WN gears drive is improved. This research not only achieved the optimization design of WN gears drive, but also revealed that the interactions between transmission parameters and strength design of the gear, which improved design efficiency and provided application foundation for CAD design of WN gears driving.
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Choy, F. K., D. H. Mugler, and J. Zhou. "Damage Identification of a Gear Transmission Using Vibration Signatures." Journal of Mechanical Design 125, no. 2 (June 1, 2003): 394–403. http://dx.doi.org/10.1115/1.1564571.

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Important advancements in preventive maintenance of rotor-craft gear transmission systems are currently being sought for the development of an accurate machine health diagnostic system. Such a diagnostic system would use vibration or acoustic signals from the gear transmission system for (1) rapid on-line evaluation of gear wear or damage status, and (2) prediction of remaining gear life. Such health diagnostic capabilities would be essential for effective machine event/life management and advance warning before critical component failures. This paper demonstrates the use of vibration signature analysis procedures for health monitoring and diagnostics of a gear transmission system. The procedures used in this paper include (i) the numerical simulation of the dynamics of a gear transmission system with single and multiple tooth damage, (ii) the application of the Wigner-Ville Distribution (WVD) and the Wavelet transform in damage identification and quantification of damaged tooth based on the numerically generated vibration signal, and (iii) the application of both WVD and the Wavelet transform on experimental data at various stage of gear failure obtained from an accelerated gear damage test rig. This paper demonstrates that the developed signature analysis procedure can successfully detect faulty gears in both numerically simulated and experimental tested transmission system. General conclusions on identification and quantification of gear tooth damage are drawn based on the results of this study.
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Cristescu, Ana, Mircea Niculescu, and Laurenţia Andrei. "The Influence of Kinematics Variation on Multispeed Gears Meshing." Applied Mechanics and Materials 809-810 (November 2015): 962–67. http://dx.doi.org/10.4028/www.scientific.net/amm.809-810.962.

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Multispeed gears are noncircular gears whose kinematics varies during a rotational period, alternating uniform and variable motions. Due to the limited information on multispeed gears design and performance, the paper presents i) the generation of multispeed gears, using the design hypothesis of the transmission ratio variation and ii) investigations on meshing conditions, as a qualitative information on gears contact. To generate multispeed gears, the gears transmission ratio are defined by hybrid multiple parameters functions with parabolic and trigonometric variations. Virtual models of the multispeed gears, produced by the Matlab-PHP-MySQL-AutoCAD interference, are further used for the gear meshing analysis, the theoretical static contact evolution and distribution along the teeth being investigated and compared for both kinematics. It was found that the trigonometric variation of the gears transmission ratio improves the gears meshing in gear concave zones, while the parabolic variation has benefits on tooth contact pattern in zones where the gears centrodes geometry is changed from circular to noncircular shapes.
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Liang, Mingxuan, Ying Wang, and Tian Zhao. "Optimization on Nonlinear Dynamics of Gear Rattle in Automotive Transmission System." Shock and Vibration 2019 (December 24, 2019): 1–12. http://dx.doi.org/10.1155/2019/4056204.

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Recently, gear rattle noise is gradually becoming a nonignorable issue involving comfortableness in automotive transmission for a car. Generally, the rattle noise is influenced by nonlinear dynamic of multiple pairs of idler gears in the multistage gear transmission system. Optimization methods based on nonlinear rattle dynamic analysis are worthy of further study to control the noise. In this research, an equivalent rattle dynamic model of the idler gear is proposed, and the nonlinear rattle dynamic responses are solved based on the integral method. The effect laws of key factors on nonlinear dynamic performance are investigated by using a bifurcation diagram, spectrum map, and Poincaré map. Finally, the gear backlash, equivalent mass, and rotational speed are optimized based on Kriging surrogate model (KSM) and differential evolution (DE) algorithm by taking the minimization of the maximum rattle noise as the optimal object. It can be concluded that the rattle dynamics of the idler gear show rich nonlinear characteristics as the parameters change. The proposed method can not only reduce the sound pressure level of rattle noise but also provide a viable path and reference value for the low-noise design of the gear transmission system.
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Hu, Shengyang, Zongde Fang, Yingqiang Xu, Yabin Guan, and Rui Shen. "Meshing impact analysis of planetary transmission system considering the influence of multiple errors and its effect on the load sharing and dynamic load factor characteristics of the system." Proceedings of the Institution of Mechanical Engineers, Part K: Journal of Multi-body Dynamics 235, no. 1 (January 10, 2021): 57–74. http://dx.doi.org/10.1177/1464419320986285.

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The meshing impact on transmission system and internal meshing gear pair and its impact on the load sharing and dynamic characteristics of the system are not well understood yet. In this paper, the meshing impact models of internal gear pairs and planetary transmission system were successfully constructed, and the meshing impact point, meshing impact time and meshing impact force were accurately obtained. Meshing impact in gear transmission system is obviously affected by eccentricity error, installation error, and other errors. Due to the difference in error of each component, the internal and external gears of each branch lead to different meshing positions, which causes the constant change in meshing impact point, meshing impact time and meshing impact force. This creates difficulties in the analysis of meshing impact characteristics of gear transmission system. Load Tooth Contact Analysis (LTCA) method can be used to accurately analyse the change in position of gear tooth under load condition. Through the dynamic model of planetary transmission system, the influence in component errors on the contact position of tooth surface is obtained. Combining the loaded transmission error of the tooth surface under load and the geometric transmission errors under the influence of component errors, the model of meshing impact for accurately solving the system is deduced, and the influence of meshing impact on the system's load sharing coefficient and dynamic load factor coefficient is analysed. By comparing the planetary transmission system before and after considering the meshing impact of the system, it is found that the system's load-sharing coefficient increases slightly, dynamic load factor coefficient fluctuates significantly, and meshing force becomes more clutter after considering meshing impact.
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Yu, Haidong, Chunzhang Zhao, Hao Wang, and Yong Zhao. "Experimental and numerical analysis on load-sharing behavior of gear set with simultaneously actuated pinions." Proceedings of the Institution of Mechanical Engineers, Part C: Journal of Mechanical Engineering Science 230, no. 7-8 (April 2016): 1198–208. http://dx.doi.org/10.1177/0954406216642472.

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The load-sharing behavior is important for the gear set actuated by multiple parallel pinions to avoid the excessive wear and fatigue failure. A lumped parameter dynamic model of gear set driven by three pinions simultaneously is established, in which their support stiffness and mounted positions of gear pairs are considered. A load-sharing index is defined as the ratio of the maximal and the minimal transmission loads of three gear pairs. The load-sharing behavior of gear set is numerically investigated with four distributions of three pinions. A corresponding testing device was presented. The load-sharing behavior of gear set with various mounted positions of three pinions was studied experimentally and compared with numerical results. The similar behavior denotes that the load transmission of various gear pairs has close relation with the mounted positions of pinions. Then, the load-sharing behavior of the gear set driven by three pinions is discussed in which the contact ratios and the support stiffness of pinions are considered. The results show that the increase of the contact ratios and the decrease of the support stiffness may worsen the load-sharing behavior of gear set actuated by multiple pinions. Suitable mechanical parameters of gear systems are important for the load transmission and dynamic behavior of multiple gear pairs.
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Tang, Zhaoping, Min Wang, Xiaoying Xiong, Manyu Wang, Jianping Sun, and Li Yan. "Optimal design of noise reduction and shape modification for traction gears of EMU based on improved BP neural network." Noise Control Engineering Journal 69, no. 4 (July 1, 2021): 373–88. http://dx.doi.org/10.3397/1/376934.

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Under high-speed operating conditions, the noise caused by the vibration of the traction gear transmission system of the Electric Multiple Units (EMU) will distinctly reduce the comfort of passengers. Therefore, analyzing the dynamic characteristics of traction gears and reducing noise from the root cause through comprehensive modification of gear pairs have become a hot research topic. Taking the G301 traction gear transmission system of the CRH380A high-speed EMU as the research object and then using Romax software to establish a parametric modification model of the gear transmission system, through dynamics, modal and Noise Vibration Harshness (NVH) simulation analysis, the law of howling noise of gear pair changes with modification parameters is studied. In the small sample training environment, the noise prediction model is constructed based on the priority weighted Back Propagation (BP) neural network of small noise samples. Taking the minimum noise of high-speed EMU traction gear transmission as the optimization goal, the simulated annealing (SA) algorithm is introduced to solve the model, and the optimal combination of modification parameters and noise data is obtained. The results show that the prediction accuracy of the prediction model is as high as 98.9%, and it can realize noise prediction under any combination of modification parameters. The optimal modification parameter combination obtained by solving the model through the SA algorithm is imported into the traction gear transmission system model. The vibration acceleration level obtained by the simulation is 89.647 dB, and the amplitude of the vibration acceleration level is reduced by 25%. It is verified that this modification optimization design can effectively reduce the gear transmission.
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Dissertations / Theses on the topic "Multiple gear transmission"

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Košík, Matej. "Koncepční návrh převodového ústrojí pro užití v elektromobilu." Master's thesis, Vysoké učení technické v Brně. Fakulta strojního inženýrství, 2021. http://www.nusl.cz/ntk/nusl-444969.

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This diploma thesis deals with designing electric vehicle gearbox. Gearbox should serve as virtual replacement for actual transmission of VW ID.3 EV. Designed gearbox has two gears. In the first section there is an extensive search processed of drivetrain and transmission of battery electric vehicles. Next section contains choice of transmission concept and analyses solving of individual structural nodes – gear wheels, band breaks (components that engage individual gears), carriers, shaft, bearing. In the conclusion of diploma thesis, the two-gear planetary transmission is evaluated.
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Sommer, Andrew Patrick. "VIBRATION-BASED HEALTH MONITORING OF MULTIPLE-STAGE GEAR TRAIN AND DIFFERENTIAL PLANETARY TRANSMISSION INVOLVING TEETH DAMAGE AND BACKLASH NONLINEARITY." DigitalCommons@CalPoly, 2011. https://digitalcommons.calpoly.edu/theses/631.

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The objective of this thesis is to develop vibration-based fault detection strategies for on-line condition monitoring of gear transmission systems. The study divides the thesis into three sections. First of all, the local stresses created by a root fatigue crack on a pinion spur gear are analyzed using a quasi-static finite element model and non-linear contact mechanics simulation. Backlash between gear teeth which is essential to provide better lubrication on tooth surfaces and to eliminate interference is included as a defect and a necessary part of transmission design. The second section is dedicated to fixed axis power trains. Torsional vibration is shown to cause teeth separation and double-sided impacts in unloaded and lightly loaded gearing drives. The transient and steady-state dynamic loading on teeth within a two stage crank-slider mechanism arising from backlash and geometric manufacturing errors is investigated by utilizing a non-linear multi-body dynamics software model. The multi-body model drastically reduces the computation time required by finite element methods to simulate realistic operation. The gears are considered rigid with elastic contact surfaces defined by a penalty based non-linear contact formulation. The third section examines a practical differential planetary transmission which combines two inputs and one output. Planetary gears with only backlash errors are compared to those containing both backlash and tooth defects under different kinematic and loading conditions. Fast Fourier Transform (FFT) analysis shows the appearance of side band modulations and harmonics of the gear mesh frequency. A joint time-frequency analysis (JTFA) during start-up reveals the unique vibration patterns for fixed axis gear train and differential planetary gear, respectively, when the contact forces increase during acceleration.
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Book chapters on the topic "Multiple gear transmission"

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Li, Shengbo Eben, Yang Zheng, Yougang Bian, and Keqiang Li. "Distributed receding horizon control of a platoon of multiple CAVs with discontinuous-gear transmissions." In Advanced Vehicle Control AVEC’16, 111–18. CRC Press/Balkema, P.O. Box 11320, 2301 EH Leiden, The Netherlands, e-mail: Pub.NL@taylorandfrancis.com, www.crcpress.com – www.taylorandfrancis.com: Crc Press, 2016. http://dx.doi.org/10.1201/9781315265285-19.

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Zhou, Z. G., and F. Xu. "Wind load calculation and compiling spectrum of a wind turbine gear transmission system under multiple excitation sources." In Power Engineering, 265–70. CRC Press, 2016. http://dx.doi.org/10.1201/9781315386829-41.

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Conference papers on the topic "Multiple gear transmission"

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Kartik, V., and Donald R. Houser. "Analytical Predictions for the Transmission Error Excitation in Various Multiple-Mesh Gear-Trains." In ASME 2003 International Design Engineering Technical Conferences and Computers and Information in Engineering Conference. ASMEDC, 2003. http://dx.doi.org/10.1115/detc2003/ptg-48066.

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Transmission error has long been considered the primary exciter of gear whine noise. Previous work has resulted in the development of an analytical procedure for contact analysis of gear meshing based on plate deflection models. This procedure has been demonstrated to give good accuracy while being much less computationally intensive than finite element models. This paper extends this procedure to predict the load distribution and transmission error in multiple-mesh gear-trains. The model takes into account the effect of the load distribution at one mesh, on the load distribution and transmission error on the other meshes. The local compliance at the meshes is calculated and the kinematic constraints are used to determine the contact points. The equations of contact are linearized and solved using a modified simplex algorithm. The effect of the ‘phasing’ of the meshes is also considered. Application areas of this analysis procedure include idler gears, planetary gear-trains and split-path transmissions.
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Hebbale, Kumar, Dongxu Li, Jing Zhou, Chengwu Duan, Chi-Kuan Kao, Farzad Samie, Chunhao Lee, and Robert Gonzales. "Study of a Non-Circular Gear Infinitely Variable Transmission." In ASME 2014 Dynamic Systems and Control Conference. American Society of Mechanical Engineers, 2014. http://dx.doi.org/10.1115/dscc2014-6083.

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Improving automobile fuel efficiency is an important research and development effort in the automotive industry. In the transmission area, it is generally understood that optimum fuel economy can be achieved via a combination of highly efficient power transfer (gears, for example) and an ability to transmit power at an infinite number of ratios (CVT, for example). In this paper, a geared infinitely variable transmission (IVT) is analyzed for efficiency through static analysis. This IVT is based on a non-circular gear concept described in [1, 2]. This IVT consists of multiple function generators with each function generator comprising two sets of non-circular gear sets whose outputs are combined with a summing planetary gear set. Each function generator provides the desired gear ratio for only a part of the driving rotation. So, multiple function generators are combined along with multiple one-way clutches to provide an infinitely variable transmission. This paper first explains the operating principle of the geared IVT. A static analysis of the IVT powerflow is derived and it is shown that this powerflow exhibits a torque recirculation phenomenon, which is not desired. This recirculation phenomenon is expected to be present in all similarly arranged IVTs where two inputs are combined using a planetary gear set to provide infinite gear ratio capability. The efficiency of the IVT is calculated based on assumed individual component efficiency and it is shown that, owing to torque recirculation, the efficiency of this transmission may not compare well with that of current automatic transmissions for a passenger car application.
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Azzouz, Salim, and Guy Bernard. "A Gear-Chain Based Transmission for the Machine Elements Design Laboratory." In ASME 2018 International Mechanical Engineering Congress and Exposition. American Society of Mechanical Engineers, 2018. http://dx.doi.org/10.1115/imece2018-87107.

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This project describes the collaboration of two instructors, one from the mechanical engineering department and one from the mathematics department with a group of mechanical engineering students to build and analyze a new type of transportation transmission. Current transmissions have torque limitations when working at various vehicle loading conditions. The ideal vehicle transmission is a continuously variable transmission that delivers optimum torque at any loading condition. The motivation for this research project is to design a new transmission that would increase the number of gear ratios using a chain element, and consequentially, increasing the number of available torques to achieve better overall vehicle performance. The new transmission consists of two planetary gears systems linked by a chain. It includes multiple inputs and outputs with the possibility of using one of the outputs to drive other engine components. The system is currently investigated for all possible gear ratios and usable torque configurations. The gear ratios are determined using Willis’s formula for planetary gear systems. All possible gear combinations are investigated and their gear ratios mathematically determined. A prototype was designed and built. It is being automatized, currently.
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Mucino, Victor H., James E. Smith, Pradeep K. Sharma, Ben Cowan, and Marek Kmicikiewicz. "A Double Planetary Gear Train-CVT Transmission with Multiple Applications." In International Congress & Exposition. 400 Commonwealth Drive, Warrendale, PA, United States: SAE International, 1995. http://dx.doi.org/10.4271/950094.

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Zou, Shuaidong, Guangjian Wang, and Li Yu. "Research on Calculation of Unloaded Transmission Error of Planetary Gear Train Caused by Eccentricity." In ASME 2017 International Design Engineering Technical Conferences and Computers and Information in Engineering Conference. American Society of Mechanical Engineers, 2017. http://dx.doi.org/10.1115/detc2017-67463.

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In this paper, calculation of no-load transmission error (TE) of planetary gear train is studied. The theory computational model of the eccentric planetary gear train with single planet gear (SPG) under no-load conditions is constructed initially for acquiring the formulas of no-load transmission ratio error and unloaded transmission error (UTE) of internal and external gear pairs. Then computational formula of the UTE of planetary gear train with SPG caused by eccentricity is presented. Through simulation TE and the developed formula of UTE, the eccentricities and initial phasing are uncoupled by curve fitting. Simultaneously, formula of UTE of planet gear train with SPG is validated. At the same time, different groups of initial phasing are analyzed to acquire the relatively good initial phasing group. In addition, the UTE of planetary gear train with multiple planet gears (MPG) caused by eccentricity is developed.
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Zhou, X. X., P. D. Walker, N. Zhang, B. Zhu, and F. Ding. "The Influence of Transmission Ratios Selection on Electric Vehicle Motor Performance." In ASME 2012 International Mechanical Engineering Congress and Exposition. American Society of Mechanical Engineers, 2012. http://dx.doi.org/10.1115/imece2012-85906.

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Increasingly electric vehicle design is looking forward the application of multiple ratio transmissions in place of traditional single ratio gearboxes. The choice of gear ratio has significant influence on vehicle performance, including range, acceleration, and gradeability. To study the impact of different transmissions on EV’s dynamic and economic performance, mathematical models of an EV is presented which is applicable to both single and multiple ratio transmissions. These transmission variants are then studied under different operating conditions to investigate how operating conditions in the motor work efficiency change with different transmissions. Here comparisons are made between 2-speed and single speed transmission. Then the reasons for the results are analysed.
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Majumder, Gargi, and Rajiv Tiwari. "Vibration Control of Spur Geared Rotor Systems With Transmission Errors by Active Magnetic Bearings." In ASME 2019 International Design Engineering Technical Conferences and Computers and Information in Engineering Conference. American Society of Mechanical Engineers, 2019. http://dx.doi.org/10.1115/detc2019-97176.

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Abstract Dynamic forces between the mating gears are generated due to the mesh deformation, gear eccentricities, transmission error, and gear run-out, which cause excessive vibration and noise. Study and control of these forced vibrations in gear box are vital to prevent any adverse effects on the gears and its supporting structures. Hence, this work presents a novel concept of active vibration control by introducing Active Magnetic Bearings (AMBs) on the shaft of a spur gearbox having conventional bearings as well. The AMB suppresses the response of the system by generating controlled electromagnetic forces based on the gear shaft vibration measurement. The AMB force is applied without any physical contact as opposed to mechanical forces in conventional bearings. A coupled torsional-lateral vibration analysis has been simulated with the effects of mesh deformation, gear eccentricities, transmission error, and gear run-out. The electromagnetic actuator is designed in such a way that a resultant radial control force can be developed with the help of forces in two mutually perpendicular directions. With a feedforward PID controller, the transverse vibration amplitude is observed to be suppressed to a considerable level. The frequency domain analysis is done using a full spectrum, which shows that multiple harmonics of gear mesh frequency is minimized simultaneously.
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Yu, Bowen, and Kwun-lon Ting. "Compensated Conjugation and Gear Tooth Modification." In ASME 2013 International Design Engineering Technical Conferences and Computers and Information in Engineering Conference. American Society of Mechanical Engineers, 2013. http://dx.doi.org/10.1115/detc2013-13409.

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This paper rigorously presents a new theory called compensated conjugation for gear transmission error balance. The proposed theory is a systematic study based on conjugation equation and transmission function. The basic idea is that conjugation is essentially impaired by loading condition but can be compensated by modifying transmission function. In contrast to the traditional method which is mainly applicable for planar involute gears, the new idea generally applies for all conjugation types based on the same concept of transmission. Multiple Concepts of conjugation and transmission are rigorously modeled and defined by screw theory. A theorem about the continuity of motion and conjugate geometries is presented and proved in order for desirable modification. The proposed theory is consistent with the standard manufacturing process for tooth modification. Tooth geometries and cutter geometries can be obtained after the theoretical transmission error function is designed. For the most important application — planar involute gear design, a practically convenient method with a direct rack-cutter modification is proposed and rigorously analyzed by kinematics and differential geometry. Examples show the effectiveness of the methodology.
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Zhang, Yi, and Zhi Wu. "A Simple Method for Gear Ratio and Torque Analysis of Planetary Train Systems." In ASME 1998 Design Engineering Technical Conferences. American Society of Mechanical Engineers, 1998. http://dx.doi.org/10.1115/detc98/ptg-5793.

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Abstract Planetary gear train systems are widely used in automotive transmissions due to their compactness, large reduction ratios and degrees of freedom available for the selection of gear ratios. The analysis of gear ratios and torque relations among the elements of a planetary train system is often difficult due to the complexity of the planetary train structure. This is especially the case for automotive transmissions using planetary train system where the members for input and output and the members that are fixed or interconnected must be changed in the clutch engagement schedule to obtain multiple transmission speeds. This paper proposes a systematic approach that simplifies the gear ratio and torque analysis based on the basic planetary train characteristics. The approach can be effectively used for the analysis of gear ratio and static torques for power transmissions consisting of parallel planetary trains. A case study of multi-speed automotive transmission based on the approach is included in the paper.
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Xun, Chao, Xinhua Long, and Hongxing Hua. "The Effects of Multi-Mesh Tooth Profile Modifications on Planetary Gear Vibration." In ASME 2016 International Mechanical Engineering Congress and Exposition. American Society of Mechanical Engineers, 2016. http://dx.doi.org/10.1115/imece2016-65780.

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In this paper, the different effects of tooth profile modifications (TPMs) for the sun-planet and the ring-planet meshes on the first two rotational modes are investigated with the consideration of tooth thickness errors. A nonlinear model with multiple degree of freedoms is built to descript the rotational vibration of the planetary gears. In contrast to the majority of the models in the literature, the variable mesh stiffness, TPM, manufacturing error, and loss of contact in both of the sun-planet and ring-planet meshes are introduced in the analysis. Multiple scale method is used to analyze dynamic response and transmission errors. Numerical integrations are carried to verify the perturbation results and explore the nonlinear phenomena in the planetary gears. The frequency response curves of dynamic transmission error (DTE) obtained for different TPM with different tooth thickness errors are presented. Results indicate the TPM not only affects the amplitude of response but also results into the change of the margin of contact between sun gear and planet gears and the margin of contact between the ring gear and planet gears. In addition, the optimal TPM for the first mode may induce high level vibration on the second or higher order modes. These mean one need to consider the effects of TPM on the response amplitude and the margin of the loss of contact for both rotational modes to get an optimal TPM among the teeth of sun gear, planet gears, and ring gear. This provides guidance for practical design and tolerance standard for the planetary gears.
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