Numerical modeling and dynamic characteristics study of coupling vibration of multistage face gearsplanetary transmission

Abstract

Abstract. A novel transmission with multistage face gears as the core component achieves variable speeds via differential gear shifting. Single/multistage coupled vibration models have been established in this study to derive the coupled vibration equation in order to accurately solve the load distribution between the meshing teeth and the vibration shock between the shifting stages in the transmission process, improve the transmission smoothness of the face gears during the shifting processing, suppress the resonance of face gears meshing, reduce the noise, and optimize the power transmission performance. The characterization relationships of the key parameters such as equivalent mass, rotational inertia, equivalent mesh stiffness, support stiffness, and meshing damping coefficient to dynamic characteristics were investigated. The linear and nonlinear dynamic characteristics of coupled vibration differential equations were solved. The influence rules of factors such as integrated transmission error, dynamic load, tooth surface friction, loading speed, and load on the transmission system were analyzed. The results of the study provide a theoretical basis for the expansion of field of application of transmission devices.

Elastic Damping Mechanism Optimization by Indefinite Lagrange Multipliers

“…The obtained equations, as well as the equations of constraints ( 5) and (6) equated to zero, has formed the system of equations (14)(15)(16)(17)(18), where there were expressed all the variables х (x1, x2, x3, x4, x5) through λ2 and λ3 (which are L2 и L2 in the program).…”

“…For example, in order to improve gearbox shifting, some researchers have designed a dynamic transmission model, analyzed gear shifting processes, and developed coordinated strategies for controlling these processes with the replacement of several clutches during tractor field operations [16]. Other researchers have developed a numerical model of dynamic performance for a new transmission with multi-stage wheel gears as the main component [17]. There has been developed a simulation model of the all-synchromesh gearbox, which differs from other models by its simplicity and quality, which can be calculated in real-time [18].…”

“…Two-stage adjustable throttle (15) is installed in pressure main (10). Safety valve (17) and control valve (18) are connected to input (16). Damper valve (19) is connected in parallel with the throttle (15).…”

Mathematical Modeling of a Multi-Inert Oscillatory Mechanism

“…Разработаны осцилляторы с другим характером энергообмена, например, преобразованием кинетической энергии груза в энергию магнитного поля соленоида или энергию электрического поля конденсатора. Все эти колебательные системы и подобные им [3][4][5][6][7][8][9][10][11][12][13][14][15][16][17][18][19][20] явились предпосылкой создания биинертного осциллятора, в котором ускорение одного груза происходит за счет торможения другого, т. е. происходит обмен только кинетическими энергиями.…”

Study on Impact Characteristics of Multistage Double Crown Face Gear Pairs considering Ratio Switching under Variable Conditions

“…However, to analyze contact impact states of face gears, accurate models of real application conditions are built. During dynamic meshing, the transmission systems generate impact, vibration and noise due to large conditions fluctuating, elastoplastic deformation and sliding friction load in acceleration, deceleration, variable torque, and ratio shifting [2,3]. erefore, it is of great significance to study the impact characteristics of face gear for the vibration noise reduction mechanism and dynamic design of transmission system.…”