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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.
2
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.
3
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.
5
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.
7
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.
11
Höhn, Bernd Robert. "Future Transmissions for Wind Turbines." Applied Mechanics and Materials 86 (August 2011): 18–25. http://dx.doi.org/10.4028/www.scientific.net/amm.86.18.
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Most transmissions for wind turbines are set up by multiple consecutively arranged planetary gear sets and/or normal gear sets. Therefore these transmissions have a constant ratio. In order to feed the electricity produced by the wind turbines into the grid, an electric conversion to a constant frequency of 50 Hz is necessary. FZG developed a new concept for transmissions of wind turbines based on a planetary gear. By superposition of a small electric engine the transmission ratio is continuously variable. This makes an electric conversion unnecessary and thereby increases the efficiency of the wind turbine.
12
Thomas, Benny, K. Sankaranarayansamy, S. Ramachandra, and Suresh Kumar S.P. "Selection of Pressure Angle based on Dynamic Effects in Asymmetric Spur Gear with Fixed Normal Contact Ratio." Defence Science Journal 69, no. 3 (April 30, 2019): 303–10. http://dx.doi.org/10.14429/dsj.69.13636.
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Asymmetric spur gears are finding application in many fields including aerospace propulsion and automobile which demand unidirectional or relatively higher load on one side of the gear flank. Design intend to maximise the load carrying capacity of the drive side of asymmetric gear by increasing the pressure angle is achieved at the expense of coast side capacity. Multiple solution for coast to drive side pressure angle exist for a given contact ratio and each of these have relative merits and demerits. In the present work asymmetric spur gears of theoretically equal contact ratio as that of corresponding symmetric gears are selected to investigate the change in gear tooth static transmission error and dynamic behaviour with coast and drive side pressure angle. Study shows that dynamic factor of normal contact ratio asymmetric spur gears below resonance speed are relatively lower than corresponding symmetric gears of same module, contact ratio, number of teeth, coast side pressure angle and fillet radii. Results also show that, coast and drive side pressure angle can be suitably selected for a given contact ratio to reduce the single tooth and double tooth contact static transmission error and dynamic factor of asymmetric spur gears.
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Yang, Jianwei, Ran Sun, Dechen Yao, Jinhai Wang, and Chuan Liu. "Nonlinear Dynamic Analysis of high speed multiple units Gear Transmission System with Wear Fault." Mechanical Sciences 10, no. 1 (June 7, 2019): 187–97. http://dx.doi.org/10.5194/ms-10-187-2019.
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Abstract. The helical gear system is an important form of transmission in high-speed trains, and helical gear failure has a great impact on the transmission performance. To investigate the influence of wear parameters on the nonlinear dynamics of gear systems, the wear fault parameters of a bending-torsion-shaft coupling mode with six degrees of freedom are established. Using the variable step fourth-order Runge-Kutta numerical integration method, the gear dynamics model with fault parameters is analyzed to get the dynamic response of the helical gear system. The system excitation frequency, evolution of system periodic motion, quasi-periodic motion, and chaotic motion with variable fault parameters are analyzed qualitatively based on the results, including the system status judgment criteria of phase plane graph, Poincaré cross-section graph, bifurcation diagram, and RMS. The results show that wear fault affects the system differently at different frequencies. Finally, the correctness of the conclusion is verified through experiments, and the impact on the actual application process is analyzed.
14
Schleiffer, Jean-Eric, Wilco van Harselaar, Ye Shen, and Stephan Rinderknecht. "Simulative Assessment of Novel Parallel-Hybrid-Electric Powertrains: Consideration of Transmission System Power Losses." Vehicles 2, no. 1 (March 3, 2020): 173–90. http://dx.doi.org/10.3390/vehicles2010010.
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Transmission system power losses influence the efficiency of hybrid powertrains. Well-established parallel-hybrid-electric powertrains employ conventional transmissions that can be treated as single-input-single-output (SISO) systems. Novel parallel-hybrid-electric powertrains, which are not based on conventional transmissions, can increase the systems potential but increase the complexity as the transmission becomes a multiple-input-multiple-output (MIMO) system. For these MIMO-transmission systems, the losses can strongly depend on the selected transmission mode and on the input torques of the power sources. This paper presents a method to automatically model the power losses of such MIMO-transmission systems. This method consists of a mathematical analysis and a design analysis, and obtains the transmission power losses as a function of the selected transmission mode, the rotational speed of the wheels, and the torques of the power sources. The model includes gear meshing losses, gear churning losses, and bearing losses. Furthermore, an extended control strategy is proposed to ensure local optimality including the consideration of the multidimensional transmission power loss characteristics. A case study is presented to demonstrate the developed methods, and shows that the inclusion of the transmission losses in the powertrain model and control strategy can be considered relevant for the simulative assessment of novel parallel-hybrid-electric powertrains.
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Zhao, Fu Qiang, Tie Wang, Rui Liang Zhang, Yu Juan Li, and Jun Shen. "Variable-Grain Optimization Design of High-Speed Transmission Helical Gear." Advanced Materials Research 346 (September 2011): 179–83. http://dx.doi.org/10.4028/www.scientific.net/amr.346.179.
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A variable-grain strategy is proposed to solve the complicated problem of optimization design on high-speed transmission helical gears with multiple objectives and restrictions. Based on the theory of gear meshing noise and the superiority criteria, a multi-objective evaluation index system is brought forward which gives consideration to the increase of the contact ratio and the decrease of the noise generated by the slide ratio of the tooth flank meshing and the mutation of friction torque, and then the variable-grain multi-objective optimization models of high-speed helical gears are established. The coarse-grained model is utilized in the early design to efficiently determine the direction to the optimal solution. Then the grain is refined and the fine-grained model can be utilized to acquire the optimal result.
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Chen, Xingbin, Peng Zhang, Xinhe Min, Nini Li, and Zhanpeng Deng. "Study on power split characteristics of planetary multistage face gear transmission device and its effect to drive efficiency under variable speed working condition." Mechanical Sciences 11, no. 1 (May 27, 2020): 173–82. http://dx.doi.org/10.5194/ms-11-173-2020.
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Abstract. The planetary gear system consists of several concentric single stage face gears symmetrically meshing with multiple cylindrical gears that as the core component of planetary multistage face gears transmission device (PMFGTD), which is the key to realizing shifting and principle innovation that able to flexibly extend the speed ratio region of single stage face gear. The speed ratio distribution mechanism is directly related to the feasibility of the design scheme. The stability, reliability and loading capacity of each power split branch affect the performance of the whole system directly. For the requirements of maximizing drive efficiency and optimizing drive performance under different conditions, this study analyzes the gear matching relationship and driving characteristics by using numerical calculation method basing on the PMFGTD structural characteristics, and calculates the corresponding transmission ratio value. According to the torque equilibrium equation, the torque relation and power ratio relation of each component are established, and then the power distribution relation between system components is calculated. The flow characteristics of system input power and each branch output power under the condition with or without meshing power loss are analyzed. The influence relationship model of power split coefficient on drive efficiency is established to calculate the corresponding rules, thus the dynamic characteristics of PMFGTD on power split under various working conditions are proved by experiments. The result provides reference for the transmission ratio distribution and structure design of planetary multistage face gears transmission.
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Simionescu, P. A., D. Beale, and G. V. Dozier. "Teeth-Number Synthesis of a Multispeed Planetary Transmission Using an Estimation of Distribution Algorithm." Journal of Mechanical Design 128, no. 1 (April 1, 2005): 108–15. http://dx.doi.org/10.1115/1.2114867.
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The gear-teeth number synthesis of an automatic planetary transmission used in automobiles is formulated as a constrained optimization problem that is solved with the aid of an Estimation of Distribution Algorithm. The design parameters are the teeth number of each gear, the number of multiple planets and gear module, while the objective function is defined as the departure between the imposed and the actual transmission ratios, constrained by teeth-undercut avoidance, limiting the maximum overall diameter of the transmission and ensuring proper spacing of multiple planets. For the actual case of a 3+1 speed Ravigneaux planetary transmission, the design space of the problem is explored using a newly introduced hyperfunction visualization technique, and the effect of various constraints highlighted. Global optimum results are also presented.
18
Li, Jianying, Tunglung Wu, Weimin Chi, Qingchun Hu, and Teenhang Meen. "Integrated Analysis of Influence of Multiple Factors on Transmission Efficiency of Loader Drive Axle." Energies 12, no. 23 (November 28, 2019): 4540. http://dx.doi.org/10.3390/en12234540.
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In this study, a loader drive axle digital model was built using 3D commercial software. On the basis of this model, the transmission efficiency of the main reducing gear, the differential planetary mechanism, and the wheel planetary reducing gear of the loader drive axle were studied. The functional relationship of the transmission efficiency of the loader drive axle was obtained, including multiple factors: the mesh friction coefficient, the mesh power loss coefficient, the normal pressure angle, the helix angle, the offset amount, the speed ratio, the gear ratio, and the characteristic parameters. This revealed the influence law of the loader drive axle by the mesh friction coefficient, mesh power loss coefficient, and speed ratio. The research results showed that the transmission efficiency of the loader drive axle increased with the speed ratio, decreased when the mesh friction coefficient and the mesh power loss coefficient increased, and that there was a greater influence difference on the transmission efficiency of the loader drive axle.
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Li, Tong Jie, Ru Peng Zhu, and He Yun Bao. "Study on Dynamic Load Sharing Behavior of Two-Stage Planetary Gear Train Based on a Nonlinear Vibration Model." Applied Mechanics and Materials 86 (August 2011): 611–14. http://dx.doi.org/10.4028/www.scientific.net/amm.86.611.
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The nonlinear torsional vibration model of a two-stage planetary gear system is established taking errors of transmission, time varying meshing stiffness and multiple gear backlashes into account. The solution of the equations is determined by using ODE45. The influences of transmission errors on the load sharing behavior are assessed and some useful theoretical guidelines for the design of planetary gear systems are provided at last.
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Waller, Matthew D., Sean M. McIntyre, and Kevin L. Koudela. "Composite Materials for Hybrid Aerospace Gears." Journal of the American Helicopter Society 65, no. 4 (October 1, 2020): 1–11. http://dx.doi.org/10.4050/jahs.65.042010.
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Hybrid steel-composite gears, which combine steel teeth with a fiber-reinforced polymer composite core, are a rapidly emerging technology for weight reduction in aerospace drivetrain systems. However, power transmission gears—and especially the requirement of rotorcraft gearboxes to operate under loss of lubrication—are a very challenging application for composite materials, due to the combination of mechanical and thermal loads. In this work, composite materials, including newly developed hybrid laminates featuring multiple grades of carbon fiber, are fabricated. Mechanical and thermal testing, along with ply-level finite element analysis, are employed to assess the suitability of these composite materials for hybrid aerospace gear applications. Particular focus is given to high-temperature epoxy and bismaleimide resins and to hybrid laminates reinforced by multiple grades of carbon fiber. This hybrid drivetrain technology would manifest significant weight reductions without compromising gear performance.
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Yang, Yi, Hang Li, and Yiping Dai. "Nonlinear vibration characteristics of spur gear system subjected to multiple harmonic excitations." Proceedings of the Institution of Mechanical Engineers, Part C: Journal of Mechanical Engineering Science 233, no. 17 (June 24, 2019): 6026–50. http://dx.doi.org/10.1177/0954406219858171.
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Due to the complicated working conditions, the gear systems are often subjected to multifrequency excitations in practical situations. This paper is concerned with the nonlinear vibration behaviors of a spur gear pair to excitations that involve multiple frequencies. The spur gear system is described by a typical single degree of freedom model, in which the nonlinear backlash, static transmission error, and multiple harmonic excitations are taken into consideration. With the help of the multi-scale method, the nonlinear frequency–response characteristics of the spur gear system are derived and analyzed. Further, the numerical simulation and the published experimental data are utilized to validate the developed dynamic model of gear pair and to prove the practicality of the analytical method. Results show that the multifrequency excitation-based gear model could be more reliable than the simplified gear model subjected to single-frequency excitation. Thus, the established model in this work would be capable of predicting the nonlinear vibration behaviors of spur gear systems under complicated excitations. The purpose of this study is to provide references that may be of interest to engineers and researchers attempting to handle the nonlinear dynamics of gear systems.
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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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Yao, Lingling, Zhuo Meng, Jianqiu Bu, and Yize Sun. "Investigation of Nonlinear Characteristics of a Gear Transmission System in a Braiding Machine with Multiple Excitation Factors." Shock and Vibration 2020 (March 25, 2020): 1–20. http://dx.doi.org/10.1155/2020/2747204.
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In this study, we attempt to analyze the influence of different excitation factors on the dynamic behavior of a gear transmission system in a braiding machine. In order to observe nonlinear characteristics, a mathematical model is established with a six-degrees-of-freedom gear system for consideration of multiple excitation factors. Iterative results are used to study the nonlinear characteristics of the gear system with respect to contact temperature, varying levels of friction, and disturbance of yarn tension using bifurcation diagrams, maximum Lyapunov exponents, phase diagrams, Poincare maps, and the power spectrum. The numerical results show that excitation factors such as temperature and surface friction, among others, have considerable influence on the nonlinear characteristics of the gear system in a braiding machine, and the model is evaluated to show the key regions of sensitivity. The analysis of associated parameters can be helpful in the design and control of braiding machines.
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Zhang, Yue, Xiang Yu, Lu Lu Guo, and Bing Zhao Gao. "Performance Evaluation of Electric Vehicle with 2-Speed I-AMT." Advanced Materials Research 710 (June 2013): 285–89. http://dx.doi.org/10.4028/www.scientific.net/amr.710.285.
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For a novel electric vehicle equipped with 2-speed Inverse Automated Manual Transmission (I-AMT), optimal design of the gear ratios is carried out using dynamic programming (DP) under vehicle dynamic constraints. Given multiple driving cycles, the design target is to make the electric vehicle obtain the best energy consumption economy. After the gear ratios are determined, the performance of the 2-speed electric vehicle is compared with the same vehicle with a single-speed gear box, and it is shown that the 2-speed transmission has much better performacne in terms of acceleration time, maximum speed and energy economy.
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Qu, Yongzhi, Liu Hong, Xixin Jiang, Miao He, David He, Yuegang Tan, and Zude Zhou. "Experimental study of dynamic strain for gear tooth using fiber Bragg gratings and piezoelectric strain sensors." Proceedings of the Institution of Mechanical Engineers, Part C: Journal of Mechanical Engineering Science 232, no. 21 (November 24, 2017): 3992–4003. http://dx.doi.org/10.1177/0954406217744000.
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It has always been a critical task to understand gear dynamics for gear design and condition monitoring. Many gear models have been proposed to simulate gear meshing dynamics. However, most of the theoretical models are based on simplified gear structure and may contain approximation errors. Direct measuring of gear strain is important for gear design validation, load analysis, reliability assessment, gear condition monitoring, etc. Most of the existing studies of tooth strain measurements are performed under static load condition. In this paper, we investigate new measuring techniques using fiber Bragg grating sensor and piezoelectric strain for gear dynamic strain measurement. We conduct gear dynamic strain measurement under both normal and pitted conditions to evaluate the strain transition process and pitting effect. The experiments are performed on an industrial gearbox with relatively small module gears. Multiple combinations of speed and load conditions are tested and the results are discussed and analyzed. We analyze multiple factors that affect the tooth root stress, including speed, load, extended tooth meshing, etc. It is found that under low operation speed range, the tooth root strain is mainly determined by the torque, while in the medium to high speed range, the tooth root strain is jointly affected by speed and torque. Extended tooth contact is shown in the measurement results with strong evidence. It conforms to earlier founding that the transmission error and dynamic load factor are overestimated for spur gear under heavy load. We also evaluate the change in dynamic strain caused by pitted tooth surface. It is shown that pitting faults lead to decreased bending strain on the tooth, especially in single-tooth contact zone, which represents a loss in torque and possibly reduced mesh stiffness. Numerical simulations are also provided to make comparisons and help to interpret the experimental results.
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Tang, Jinyuan, Zehua Hu, Siyu Chen, and Duncai Lei. "Effects of directional rotation radius and transmission error on the dynamic characteristics of face gear transmission system." Proceedings of the Institution of Mechanical Engineers, Part C: Journal of Mechanical Engineering Science 228, no. 7 (August 27, 2013): 1108–18. http://dx.doi.org/10.1177/0954406213500745.
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The effects of directional rotation radius and transmission error excitation on the nonlinear dynamic characteristics of face gear transmission system are analyzed. First, the accurate time-varying mesh stiffness is calculated using finite element method, and the nonlinear motion equation of the system under static transmission error excitation is proposed. The frequency response curve, time history curve, dynamic mesh force curve and dynamic factor curve are given, and the phenomena of jump, multiple solutions and tooth impact are observed. The numerical results show that the effect of amplitude variation of directional rotation radius on the dynamic characteristics of face gear pair is less conspicuous than that of transmission error but actually existing. The amplitude of the dynamic response of face gear pair reduces to some extent with the uniform distribution of the loading area through enlarging the amplitude variation of directional rotation radius. The static transmission error excitation should be reduced to perfect the transmission property. The system is in periodic motion most of the time, and tooth impact occurs only near [Formula: see text] . Since its dynamic property at low velocity and high velocity is good, the system should get through the resonant area quickly in work.
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CHOY, F. K., H. CHEN, and J. ZHOU. "Identification of Single and Multiple Teeth Damage in a Gear Transmission System." Tribology Transactions 49, no. 3 (September 2006): 297–304. http://dx.doi.org/10.1080/05698190600614882.
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Cao, Zhan, Yong Chen, and Libin Zang. "Model-based transmission acoustic analysis and improvement." Proceedings of the Institution of Mechanical Engineers, Part D: Journal of Automobile Engineering 234, no. 6 (January 21, 2020): 1572–84. http://dx.doi.org/10.1177/0954407019896132.
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A model-based transmission acoustic performance has been studied. Both excitation source and structure-borne noise transfer are investigated. For excitation source, transmission error is the main cause. To reduce transmission error, the most effective method is gear micro-geometry modification. However, there is no direct mathematical model that could reveal the relationship between transmission error and gear micro-geometry parameters, especially in the context of transmission system with shafts, bearings and housings included. By using multiple variable linear regression method, the relationship between transmission error and gear micro-geometry parameters is connected. The optimised transmission error decreases from 9.34 to 5.65 μm at a typical working condition. For structure-borne noise transfer, the housing modal and transmission system modal have been analysed. Based on the simulation results, housing thickness around bearing assembly area is increased, and strengthen ribs are added at weak areas. As a result, the amplitude of housing vibration acceleration is reduced. Finally, the transmission noise sound pressure level at 0.3-m distance has decreased by 4.63 dB on average. The presented model-based transmission acoustic analysis work flow is demonstrated workable and effective.
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Li, Zheng, and Ken Mao. "Frictional Effects on Gear Tooth Contact Analysis." Advances in Tribology 2013 (2013): 1–8. http://dx.doi.org/10.1155/2013/181048.
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The present paper concentrates on the investigations regarding the situations of frictional shear stress of gear teeth and the relevant frictional effects on bending stresses and transmission error in gear meshing. Sliding friction is one of the major reasons causing gear failure and vibration; the adequate consideration of frictional effects is essential for understanding gear contact behavior accurately. An analysis of tooth frictional effect on gear performance in spur gear is presented using finite element method. Nonlinear finite element model for gear tooth contact with rolling/sliding is then developed. The contact zones for multiple tooth pairs are identified and the associated integration situation is derived. The illustrated bending stress and transmission error results with static and dynamic boundary conditions indicate the significant effects due to the sliding friction between the surfaces of contacted gear teeth, and the friction effect can not be ignored. To understand the particular static and dynamic frictional effects on gear tooth contact analysis, some significant phenomena of gained results will also be discussed. The potentially significant contribution of tooth frictional shear stress is presented, particularly in the case of gear tooth contact analysis with both static and dynamic boundary conditions.
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Crispel, Stein, Pablo López-García, Tom Verstraten, Elias Saerens, and Dirk Lefeber. "Introduction of a redundant actuator using planetary gear trains for human centred robotics." MATEC Web of Conferences 317 (2020): 01003. http://dx.doi.org/10.1051/matecconf/202031701003.
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Matching motor efficiency and performance with the load demands can significantly improve the overall efficiency of a driveline. Inspired by the automotive sector -with the high interest of hybrid and electric cars currently-, the authors have studied how state of the art technologies can be used in the relatively new field of collaborative and Human centred robotics. Multiple transmission systems have been considered, among others redundant actuators (both static and kinematic) and continuously variable transmissions. Based on these findings and the experience of the research group on customised planetary gear trains for Human Limb Assistance and Replication, an extensive review of existing redundant actuators is presented in combination with an alternative transmission system which does not need any auxiliary gear transmissions and hence can be lighter and more compact than state of the art drivelines for Human centred robotics. A calculation was performed -including the efficiency model presented by Müller- which shows the high potential of this type of dual-motor actuator.
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Tang, Jin Yuan, Qi Bo Wang, Li Juan Wu, and Si Yu Chen. "Bifurcation Analysis of Impact Model in Gear Transmission System." Applied Mechanics and Materials 86 (August 2011): 479–82. http://dx.doi.org/10.4028/www.scientific.net/amm.86.479.
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Considering the meshing gear system as an impact-contact model, the nonlinear viscoelastic contact force model is introduced to establish the impact dynamic equations. With the application of numerical integration, the bifurcation characteristics and energy dissipation are analyzed. Numeric results show that the system has complex dynamic behaviors: ①during the excitation frequency zone[0.1,1.2], many forms of periodic collisional vibration and chaotic vibration appear alternately, ②excitation frequency being ω>ω7(ω7=1.147), there are significant differences on the value of energy dissipation between the forward bifurcation diagram and backward bifurcation diagram, which indicate that the initial state has great influence on the steady responses, ③the energy dissipation reaches its peaks at ω=0.45 and ω=0.8, corresponding to multiple collisions and large relative deformation.
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Anselma, Pier Giuseppe, Yi Huo, Joel Roeleveld, Ali Emadi, and Giovanni Belingardi. "Rapid optimal design of a multimode power split hybrid electric vehicle transmission." Proceedings of the Institution of Mechanical Engineers, Part D: Journal of Automobile Engineering 233, no. 3 (January 15, 2018): 740–62. http://dx.doi.org/10.1177/0954407017750789.
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This work aims at presenting a design methodology capable of modeling, generating, and testing a large number of multimode power split hybrid electric vehicle transmission designs in a relatively short period of time. Design parameters include the planetary gear ratios, the final drive ratio, the configuration of hookups to link the hybrid powertrain components to the planetary gear sets and the locations of clutch connections between different nodes of the planetary gear sets. The system modeling approach is first presented, including formulations for each component (the vehicle and road load, the engine, the motor/generators and the battery). A rapid and automated modeling procedure is proposed for hybrid electric vehicle transmissions including multiple planetary gear sets and clutch connections. Two algorithms are subsequently presented that enable fast evaluation of fuel economy and acceleration performance of hybrid electric vehicle transmission designs, namely the enhanced Power-Weighted Efficiency Analysis for Rapid Sizing and the Rapid Efficiency-based Launching Performance Analysis algorithms. The developed design methodology is tested by first modeling and evaluating three hybrid electric vehicle designs from the state-of-art. Later, an investigation for optimal designs that can ameliorate the examined benchmarks is performed. Several millions of design options are rapidly generated and tested using the proposed procedure. The methodology is proved effective by quickly coming up with two sub-optimal designs. Fuel economy and acceleration performance are improved by 5.56% and 40.56%, respectively, compared to the corresponding best benchmarks.
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Ou Yang, Tian Cheng, Nan Chen, Cui Cui Ju, Cheng Long Li, and Jiang Hu Li. "Dynamic Analysis of Offset Printing Press Gear-Cylinder-Bearing System under Time-Varying Meshing Stiffness Effect." Key Engineering Materials 656-657 (July 2015): 658–63. http://dx.doi.org/10.4028/www.scientific.net/kem.656-657.658.
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This study propose a new nonlinear model for offset printing press gear-cylinder-bearing system by the lumped parameter approach. The multi-DOF model consists of helical gear pairs and spur gear pairs with time-varying meshing stiffness. Bearing and shaft flexibilities are include in the model as well. The equations of motion are obtained by Darren Bell principle and Runge-Kutta numerical method is used to slove the equations of motion. The results show that meshing stiffness and bearing stiffness significantly affect critical speed, vibration acceleration and meshing force. Multi-body dynamics software are applied to compare with lumped parameter model. The results show that there are many similarities in different aspects. Results of experimental study on offset printing press are also presented for validation of different models. After Discrete Fourier Transform, the graphics display that acceleration peaks frequencies are an integer multiple of the gear mesh frequency. It demonstrate that mechanical vibration is mainly from gear transmission system at high printing speed and gear transmission system lead to nonlinear vibration. This work provide a foundation for further improvement of the dynamics of gear system.
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Li, Baogang, Dongye Sun, Minghui Hu, Xingyu Zhou, Junlong Liu, and Dongyang Wang. "Coordinated control of gear shifting process with multiple clutches for power-shift transmission." Mechanism and Machine Theory 140 (October 2019): 274–91. http://dx.doi.org/10.1016/j.mechmachtheory.2019.06.009.
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Nie, J. F., M. L. Zheng, G. B. Yu, J. M. Wen, and B. Dai. "The Method of Multiple Scales in Solving Nonlinear Dynamic Differential Equations of Gear Systems." Applied Mechanics and Materials 274 (January 2013): 324–27. http://dx.doi.org/10.4028/www.scientific.net/amm.274.324.
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To obtain exact analytical solutions of differential equations of gear system dynamics due to the difficulty of solving complicated differential equations. Only the approximate analytical solutions can be determined. The method of multiple scales is one of the most powerful, popular perturbation methods. The dynamic model which describes the torsional vibration behaviors of gear system has been introduced accurately in this paper. The differential equation of gear system nonlinear dynamics exhibiting combined nonlinearity influence such as time-varying stiffness, tooth backlash and dynamic transmission error (DTE) has been proposed. The theory of multiple scales method has been presented in solving nonlinear differential equations of gear systems and the frequency response equation has been obtained. The fact that the approximate analytical solution by using the method of multiple scales is in good agreement with the exact solutions by numerically integrating differential equations has proved that the method of multiple scales is one of the most frequently used methods in solving differential equations, especially for large and complicated differential equations.
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Sato, Osamu, Yohan Kondo, Sonko Osawa, and Toshiyuki Takatsuji. "Efficient Multiple-Measurement Technique for Rotationally Symmetric Measurands." International Journal of Automation Technology 5, no. 2 (March 5, 2011): 150–55. http://dx.doi.org/10.20965/ijat.2011.p0150.
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Gears are key elements of power transmission systems, and the inspection of their pitch deviation is one of the most important tests done on gears. The specifications of gears are assessed using gear measuring instruments (GMIs) or coordinate measuring machines (CMMs), and the results of the measurements must be validated under an appropriate traceability system. In the traceability system, calibrated gauges whose measuring uncertainties are estimated are necessary. In the case of pitch deviation measurement, special artefacts or gears manufactured with high dimensional accuracy are used as reference gauges. As a calibration method for the pitch deviation standards, authors have proposed themethod based on themultiplemeasurement technique and uncertainty evaluation with analysis of variance (ANOVA). The proposed method performs the accurate calibration for the rotationally symmetric measurands such as pitch deviations; however, the total number of measurements for the calibration tend to be large. In this paper, authors propose a technique for reducing the number of trials based on the symmetry of the measurement for the multiple-measurement technique. First, the evaluation of rotationally symmetric measurands using a multiple-measurement technique and the estimation of its uncertainty based on the analysis of variance are formulated. Second, a technique for reducing the number of measurement trials based on the symmetry of the measurement is discussed. Finally, the proposed calibration method is validated through experiments.
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Chen, Yuan, and Xudong Mou. "Natural characteristics analysis and experimental test of spiral bevel gear pair in the tractor transmission system." Advances in Mechanical Engineering 13, no. 8 (August 2021): 168781402110371. http://dx.doi.org/10.1177/16878140211037120.
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Spiral bevel gear is widely used in various mechanical transmission systems, such as tractor transmission system. Because it is mainly used in the heavy-load conditions, it would most likely resonate within the rated speed, resulting in tooth fatigue damage. In this paper, based on the principle of meshing and gear tooth machining, the spherically involute tooth profile equation of spiral bevel gear is deduced and the precise modeling method based on the CATIA is studied. The natural frequency and modal shape under free vibration are obtained by the finite element method (FEM), the influence of web thickness and web hole on the natural frequency of driven gear plate is analyzed as well. In addition, the experimental modal of bevel gear pair is carried out based on a multiple-reference impact test, Modal Assurance Criterion (MAC) is calculated, the three-dimensional modeling accuracy and the finite element analysis reliability are verified. The results show that the error between the measured frequency of bevel gear pair and the calculated frequency of the finite element simulation are both within 5%, and the MAC is above 0.8. The fourth-order natural frequency is the most sensitive to the web thickness, the second-order natural frequency is the most sensitive to the web hole.
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Sun, Huer, Chao Wu, Xiaohua Liang, and Qunfeng Zeng. "Identification of Multiple Faults in Gearbox Based on Multipoint Optional Minimum Entropy Deconvolution Adjusted and Permutation Entropy." Entropy 20, no. 11 (November 6, 2018): 850. http://dx.doi.org/10.3390/e20110850.
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The weak compound fault feature is difficult to extract from a gearbox because the signal components are complex and inter-modulated. An approach (that is abbreviated as MRPE-MOMEDA) for extracting the weak fault features of a transmission based on a multipoint optimal minimum entropy deconvolution adjustment (MOMEDA) and the permutation entropy was proposed to solve this problem in the present paper. The complexity of the periodic impact signal was low and the permutation entropy was relatively small. Moreover, the amplitude of the impact was relatively large. Based on these advantages, the multipoint reciprocal permutation entropy (MRPE) was proposed to track the impact fault source of the weak fault feature in gearbox compound faults. The impact fault period was indicated through MRPE. MOMEDA achieved signal denoising. The optimal filter coefficients were solved using MOMEDA. It exhibits an outstanding performance for noise suppression of gearbox signals with a periodic impact. The results from the transmission show that the proposed method can identify multiple faults simultaneously on a driving gear in the 4th gear of the transmission.
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Wang, Zhipeng, Yunbo Yuan, Zhiyong Wang, Wei Liu, Yibin Guo, and Donghua Wang. "Lateral-Torsional Coupling Characteristics of a Two-Stage Planetary Gear Rotor System." Shock and Vibration 2018 (May 31, 2018): 1–15. http://dx.doi.org/10.1155/2018/4293475.
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Planetary gears are one part of the whole transmission chain, and the dynamics and vibration characteristics of them are strongly coupled with external rotors. In this paper, to demonstrate the interaction between multistage planetary gears and external rotors as well as investigate the lateral-torsional coupling characteristics of them, a coupling model of a two-stage planetary gear rotor system is proposed. In such a model, the two-stage planetary gear subsystem is established as a lumped-parameter model and the external rotor subsystem is established as a finite element model. The vibration mode distribution properties and lateral-torsional coupling characteristics are both analyzed by modal strain energy. Three different conditions are considered: uncoupled, partially coupled, and fully coupled. The results indicate that the coupling among multiple subsystems and the lateral-torsional coupling mainly exist in the low-mode region. Natural frequencies dominated by the two-stage planetary gear subsystem are sensitive to coupled conditions, whereas natural frequencies dominated by the input rotor subsystem are remarkably insensitive to coupled conditions. Furthermore, the natural frequency of the first torsional mode can be obtained only in the fully coupled condition. Experiments are implemented to obtain natural frequencies, and the experiment results validate the numerical results.
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Du, Jinfu, Jin Mao, Kai Liu, Yahui Cui, and Guorui Zhao. "Load-sharing analysis of two-stage three-branch star gearing based on deformation compatibility." Advances in Mechanical Engineering 10, no. 12 (December 2018): 168781401881954. http://dx.doi.org/10.1177/1687814018819542.
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A load-sharing analysis methodology was proposed for the multiple-branch star gear transmission which is composed of a number of closed-loop power flows. The moment equilibrium and deformation compatibility equations for the two-stage star gearing were derived, which are clearly different from that used in planetary gear transmission. Then the load-sharing analysis model was established and employed to systematically study the load-sharing behavior of the two-stage three-branch star gearing, some untouched aspects were investigated. Results show that the most sensitive directions of the central and star gear assembly errors on load-sharing are along the meshing line. The effects of the size and direction of the central gear–manufacturing errors on load sharing are the same for each branch, the initial directions of the central or a certain star gear–manufacturing errors will have no effect on the load-sharing coefficient of the system, but the initial directions of the assembly errors will. The conditions in which the load distribution curves repeat the first track were also obtained. Finally, a numerical example of a three-branch star gear aviation reducer was adopted to verify the feasibility of this proposed method, and the calculation results show good agreement with a previously published and validated model.
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Wang, Xin Huan, Hong Wei Zhang, and Zi Yi Fu. "Research on Power Balance Control of Multi-Motor Driving Belt Conveyor System Based on Controlled Transmission Device." Applied Mechanics and Materials 719-720 (January 2015): 400–404. http://dx.doi.org/10.4028/www.scientific.net/amm.719-720.400.
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According to the existing problems of driving equipment for belt conveyor, a novel design scheme of controlled transmission which uses hydraulic transmission system driving worm gear to control the output speed of planetary gear mechanism is proposed. The control strategy of multi-motor drive power balance which adopts master-slave structure is designed. The master driver adopts speed closed-loop control with current limiting and the slave drivers adopt power closed-loop control. The given power signal of slave pulley is decided by the master motor. The control system offers multiple communication interfaces which enable the belt conveyor to integrate in coal mine information platform and realize information resource sharing. The controlled transmission device and its power balance control system have characteristics of compact, reliable and high efficiency.
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Li, Xiaotian, and Anlin Wang. "A modularization method of dynamic system modeling for multiple planetary gear trains transmission gearbox." Mechanism and Machine Theory 136 (June 2019): 162–77. http://dx.doi.org/10.1016/j.mechmachtheory.2019.03.002.
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Xie, Xin, Xianliang Jiang, Shixun Fan, and Dapeng Fan. "Compact design of a novel precise cable drive mechanism with high precision and large torque-to-weight ratio." Mechanical Sciences 10, no. 1 (January 11, 2019): 47–56. http://dx.doi.org/10.5194/ms-10-47-2019.
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Abstract. Precise cable drive is an elegant transmission mode and has many advantages of high efficiency, flexible layout, besides being lightweight. Since the common layout, Single-Input Single-Output (SISO) spur gear configuration, suffers from low torque-to-weight ratio and loose structure, this paper proposes a novel transmission configuration with large torque-to-weight and compact size. It combines the advantages of Multiple-Input Single-Output (MISO) configuration and bevel gear configuration. The design methods and transmission kinematics of the novel configuration are studied. An analytical model is developed for characterizing the transmission backlash of the proposed configuration, which is derived by simultaneous satisfying system's constitutive relation, equilibrium, and geometric constraints. Parametric sensitivities are carried out to investigate the influence of the major design parameter on the transmission characteristics. At last, a prototype of MISO with bevel gear configuration cable drive mechanism (MBCDM) is built, with which a series of experiments are carried out. This mechanism could achieve maximum output torque of 3.3 Nm with considerable toque-to-weight ratio of 9.649 Nm kg−1. The experimental results show that the transmission backlash and ripple torque are dominant nonlinear effects in the MBCDM system. It shows that the ripple torque is connected with the rotational displacement, with the highest peak at 694.3 cycle rad−1 and the amplitude of 24.67 µrad. The transmission backlash experimental results are in good agreement with simulation ones, with the error level of 4.14 %.
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Mo, Shuai, Shuai Ma, Guoguang Jin, Yidu Zhang, Chao Lv, and Haruo Houjoh. "Research on Multiple-Split Load Sharing Characteristics of 2-Stage External Meshing Star Gear System in Consideration of Displacement Compatibility." Mathematical Problems in Engineering 2017 (2017): 1–8. http://dx.doi.org/10.1155/2017/1037479.
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This paper studies the multiple-split load sharing mechanism of gears in two-stage external meshing planetary transmission system of aeroengine. According to the eccentric error, gear tooth thickness error, pitch error, installation error, and bearing manufacturing error, we performed the meshing error analysis of equivalent angles, respectively, and we also considered the floating meshing error caused by the variation of the meshing backlash, which is from the floating of all gears at the same time. Finally, we obtained the comprehensive angle meshing error of the two-stage meshing line, established a refined mathematical computational model of 2-stage external 3-split loading sharing coefficient in consideration of displacement compatibility, got the regular curves of the load sharing coefficient and load sharing characteristic curve of full floating multiple-split and multiple-stage system, and took the variation law of the floating track and the floating quantity of the center wheel. These provide a scientific theory to determine the load sharing coefficient, reasonable load distribution, and control tolerances in aviation design and manufacturing.
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Guan, Yuan H., W. Steve Shepard,, and Teik C. Lim. "Direct Hybrid Adaptive Control of Gear Pair Vibration." Journal of Dynamic Systems, Measurement, and Control 125, no. 4 (December 1, 2003): 585–94. http://dx.doi.org/10.1115/1.1636771.
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A direct hybrid adaptive approach based on the Lyapunov stability theorem is proposed for performing active vibration control of a rotational gear pair subject to multiple-harmonic, transmission error disturbances. The analysis applies a reduced single-degree-of-freedom gear pair model of the elastic mesh mode with time-varying tooth mesh stiffness. It is assumed that the resultant actuation force for suppressing the rotational vibration of the gear pair can be directly applied along the tooth contact line-of-action by employing a set of suitably configured inertial actuators. The proposed controller simultaneously adapts both the feedback and feed-forward gains, and only requires knowledge of the fundamental gear mesh frequency that is given by the product of the instantaneous gear rotational speed and the number of gear teeth. The analysis indicates that the proposed controller is insensitive to the gear mesh frequency estimation errors, and the resulting vibration control is more effective than those provided by the adaptive notch filter and filtered-x LMS algorithms. The control theory also incorporates dynamic normalization and leakage enhancements in order to optimize performance and improve robustness. Finally, the salient features are demonstrated in several numerical examples.
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Li, Tongjie, and Rupeng Zhu. "Global Analysis of a Planetary Gear Train." Shock and Vibration 2014 (2014): 1–6. http://dx.doi.org/10.1155/2014/930350.
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By using the Poincaré-like cell-to-cell mapping method and shooting method, the global characteristics of a planetary gear train are studied based on the torsional vibration model with errors of transmission, time-varying meshing stiffness, and multiple gear backlashes. The study results reveal that the planetary with a certain set of parameters has four coexisting periodic orbits, which are P-1, P-2, P-4, and P-8, respectively. P-1 and P-2 motions are not of long-term stability, P-8 motion is of local stability, and P-4 motion is of global stability. Shooting method does not have the capacity of searching coexisting periodic orbits in a global scope, and it is easy to omit some periodic orbits which are far away from the main gropes of periodic orbits.
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Yu, Haidong, Peter Eberhard, Yong Zhao, and Hao Wang. "Sharing behavior of load transmission on gear pair systems actuated by parallel arrangements of multiple pinions." Mechanism and Machine Theory 65 (July 2013): 58–70. http://dx.doi.org/10.1016/j.mechmachtheory.2013.02.010.
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Zhong, Bo, and Rong Chen. "Based on Mechanical Vibration Test Machine V-Belt Transmission Design." Advanced Materials Research 538-541 (June 2012): 2518–21. http://dx.doi.org/10.4028/www.scientific.net/amr.538-541.2518.
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The essay has solved the optimization problem turning multi-objective problem into a single target by using weighting factor to the use of V-belt driving gear. According to engineering requirements, mechanical vibration test machine has determined the coordination of the various coefficients as a single objective optimization function after considering multiple conflicting incommensurability of the objective function, and combining practical experience and computing experience. Conditions on system requirements and relative constraints have been given in the form of constraint functions. Finally, the overall optimal solution has been calculated with the direct method, and an integrated optimal solution can have different numerical values by calculating it for different project objectives and specific requirements.
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Chen, Xihui, Aimin Ji, and Gang Cheng. "A Novel Deep Feature Learning Method Based on the Fused-Stacked AEs for Planetary Gear Fault Diagnosis." Energies 12, no. 23 (November 27, 2019): 4522. http://dx.doi.org/10.3390/en12234522.
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Planetary gear is the key component of the transmission system of electromechanical equipment for energy industry, and it is easy to damage, which affects the reliability and operation efficiency of electromechanical equipment of energy industry. Therefore, it is of great significance to extract the useful fault features and diagnose faults based on raw vibration signals. In this paper, a novel deep feature learning method based on the fused-stacked autoencoders (AEs) for planetary gear fault diagnosis was proposed. First, to improve the data learning ability and the robustness of feature extraction process of AE model, the sparse autoencoder (SAE) and the contractive autoencoder (CAE) were studied, respectively. Then, the quantum ant colony algorithm (QACA) was used to optimize the specific location and key parameters of SAEs and CAEs in deep learning architecture, and multiple SAEs and multiple CAEs were stacked alternately to form a novel deep learning architecture, which gave the deep learning architecture better data learning ability and robustness of feature extraction. The experimental results show that the proposed method can address the raw vibration signals of planetary gear. Compared with other deep learning architectures and shallow learning architecture, the proposed method has better diagnosis performance, and it is an effective method of deep feature learning and fault diagnosis.
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Wu, Zhe, Qiang Zhang, Zeyu Ma, Jialong Lu, and Zhiying Qin. "A New Health Condition Detection Method for Planetary Gears Based on Modified Distributed Compressed Sensing and Multiscale Symbol Dynamic Entropy." Shock and Vibration 2021 (March 29, 2021): 1–15. http://dx.doi.org/10.1155/2021/6681894.
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Planetary gear transmission system is an important transmission part of large machinery and is prone to failure. Aiming at the problem of how to extract fault information from vibration signals of nonlinear and nonstationary planetary gearboxes, a performance degradation evaluation index of planetary gearboxes based on improved distributed compressed sensing and modified multiscale symbolic dynamic entropy (DCSMDE) is proposed. DCSMDE combines distributed compression sensing with modified multiscale symbol dynamic entropy and solves the problem of strong nonlinearity and strong vibration signal coupling of the planetary transmission system from the homologous signals of multiple sensors. A distributed compression sensing parameter optimization algorithm based on Rényi entropy is proposed, which uses improved distributed compression sensing technology to simultaneously sample, compress, and denoise the multisource vibration data of rotating machinery. DCSMDE is used to calculate the reconstructed signal, extract the features with higher recognition characteristics, and use the change trend of the DCSMDE value to judge the working status of the planetary gearbox. Experimental results show that DCSMDE can be applied to dynamic evolution and fault identification of mechanical systems and accurately classify actual fault signals. It provides a new idea for the classification of planetary gear faults and the recognition of performance degradation.