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Dynamic model of planetary gearbox
Půst, Ladislav ; Pešek, Luděk ; Radolfová, Alena
Influence of planetary gears flexible pins on the dynamic properties of planetary gearing box is investigated. This flexibility of planets pins enable better power flow distribution in planet subsystems and increase the input torque density. Analysis of proposed simple mathematical model explains basic dynamical properties of planetary gearing with flexible pins, influence of pins’ stiffness on frequencies and on modes of free vibrations as well as on the response curves at external harmonic excitation.
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Free vibration of planetary gearing
Půst, Ladislav ; Pešek, Luděk ; Radolfová, Alena
Planetary gear drives have important advantages over parallel axis gears due to theirs compact design an great torque-to-weight ratio, but dynamic properties of such gearings are more complicated and they need deep dynamic analysis. For improving load sharing among planet wings, the application of flexible planetary pins or using free central wheel is needed. Presented paper is oriented on mathematical model design. The plane type of gearings with four planetary subsystems and fixed planet carrier has been selected. Used helical gearing has an essential smaller variation of contact stiffness against the direct spur gearings. Therefore this stiffness variability is not taken into account. Frequency and modal spectrums of such a dynamic mathematical model of planetary gearing set is presented and influences of design parameters are analysed.
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Planetary differential system - simulation model
Hortel, Milan ; Škuderová, Alena
The system of motion equations of mathematical-physical model of the planetary gear differential system with three double satellites with the front straight teeth prepared on the basis of a mass discretization and Lagrangian theory, which expresses, in a compact form, motions with regard to the possible impact effects in gearing, was transferred to the explicit form for the second derivatives of the generalized coordinates. For the rebuilt system of 42 weakly and strongly nonlinear parametric differential equations describing the motion in individual gear meshes, in their bearings and motion of the satellite carrier is built the first version of the simulation model in Matlab / Simulink, which allows, for given parameters, the analysis of the dynamic characteristics of the modeled gear systems .
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Dynamics of nonlinear parametric planetary systems with kinematic constraints
Hortel, Milan ; Škuderová, Alena
The report thoroughly discusses the theory of dynamics of planar mathematical-physical models of planetary differential and special cases of pseudoplanetary transmission systems. Due to the existence of the tooth backlashes, the system is seen as a discrete nonconservative strongly nonlinear parametric and multifrequency excited system with many degrees of freedom. The equations of motion are derived and compiled on the basis of the Lagrangian theory in a compact form and express the three areas of the gear mesh, ie. the range of normal gear mesh, gear backlash area and the area of the inverse gear mesh. After the rebound meshing gear profiles in the region of the side gear backlash, the impact effects occur when re contacting tooth flanks in both normal as well as during the eventual inverse mesh, depending on the size of the dynamic forces in the gearing.
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The test of the time-difference method for the torsion vibration of the rottating shaft
Pešek, Luděk ; Bula, Vítězslav ; Cibulka, Jan
The contribution deals with testing of the time difference method by using the encoder for evaluation of the torsion vibration of the rotating shaft under dynamic torque moment excitation. The testing of accuracy of this method was first performed on the numerical simulations of the pulse signals and then on the real experimental data gained from the encoder. Then the method was implemented into dSPACE control system for on-line processing. The achieved experimental results are in accordance with the numerical assumptions.
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