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To the analytical dynamic analysis of non-linear parametric systems with gears
Hortel, Milan ; Škuderová, Alena
In contrast to the mathematical methods of solution of the linear dynamic problems are the analytical solution methods and the analysis of non-linear at that the analysis of the time heteronymous, i.e. parametrical, problems more complicated and difficult. In these systems can occur the various dynamic behaviour, where appear, in the certain sensible areas of the tuning, the new often unexpected phenomena, such as the patterns of the solution ambiguity, the bifurcation and the splitting of the resonance characteristics, the change over the regular motions into the irregular, up to the motions with deterministic chaotic character etc. The above mentioned and the another phenomena can occur at the more precise physical modelling in the category of the high-parametrical, i.e. in the light high-speed structures, for example in the aeronautical propjets, where today the revolutions of the driving turbines are reaching the 80000 rpm. For the analysis of the mentioned phenomena of the relativ
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K vlivu nelineárního tlumení na bifurkační jevy v záběru ozubení v jedné větvi výkonového toku pseudoplanetové převodové soustavy
Hortel, Milan ; Škuderová, Alena
The aim of this contribution is the analysis of damping properties both the material of gear mechanics in the mesh and the lubricating oil film in the tooth space at the tooth profile contact bounces into the area of the technological gear backlash. The damping influence over gear mesh stability is pursued on the special case of the simulation model of the system with split power flow for the selected frequency range of the resonance characteristics. The nonlinear damping in gear mesh and in gear system is concerned significantly in the amplitude progress, greatness and phase shift of relative motion towards stiffness function alternatively towards its modify form in gear mesh.
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K numerické analýze singularit v rezonančních charakteristikách nelineárních parametrických systémů s rázovými jevy v záběru ozubení
Hortel, Milan ; Škuderová, Alena
The impact effects in gear mesh represent specific phenomena in the dynamic investigation of highspeed light transmission systems with kinematic couplings. They are caused of greater dynamic than static-elastic deformations in meshing gear profiles. In term of internal dynamics they are influenced among others by time heteronomous stiffness functions in gear mesh and resonance tuning of stiffness level. The damping in gear mesh and in gear system is concerned significantly in the amplitude progress, greatness and phase shift of relative motion towards stiffness function alternatively towards its modify form in gear mesh. In consequence of these and another actions rise above resonance characteristics certain singular locations with jump amplitude course.
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To some dynamic properties of parametric - heteronomous systems with internal kinematic couplings and split power flow
Hortel, Milan ; Škuderová, Alena
The contribution deals partly with the problems of influence of material damping of gearing by normal and inverse mesh and the effect of viscous damping of lubricant surrounding, i.e. the influence of oil during cog contact bounce in the gap - technological backlash and partly with the analysis of issue causation of sharp discontinuity locality in the resonance characteristics, which is associated with the cog contact bounce with the impact effects in dependence with given resonance tuning, the gear mesh duration term on stiffness level of the parametric stiffness function or the modify stiffness function, inclusive the time phase shifts of relative motion towards these stiffness function.
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To influence of damping on impact effects in gear mesh
Hortel, Milan ; Škuderová, Alena
The motion equations of nonlinear parametric system of kinematic pair with elastic supported cog wheels were assembled on the basis of analytical Lagrange’s theory of mechanics, principle of virtual work, d’Alembert’s principle of conversion of kinetics problem onto statics and Lagrange’s release principle and analytical solved by means of equivalent nonlinear integrodifferential equations with solved kernels in the form of split Green’s resolvent. The influence of linear and nonlinear damping in the several phasis of gear engagement onto impact effects in gear mesh is solved in the contribution by means of numerical simulation in MATLAB/Simulink.
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Influence of linear and nonlinear damping on the stability of motion of kinematic pairs of gears
Hortel, Milan ; Škuderová, Alena
The damping of dynamic phenomena in the structural complicated mechanical systems with different i.e. rigid or liquid substances of elements is the matter till this time generally recondite. The contribution deals therefore both qualitative and quantitative with the model of different combinations of linear and nonlinear - quadratic and cubic - damping both in the phase of normal gear mesh and in the phase of dynamic tuning when happens to contact bounces of tooth faces in gear mesh and to following contacts with impacts.
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