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Experimental evaluation of the gear windage loss and thermal load of a gear tooth
Kordík, Jozef ; Dobiáš, Jiří ; Hrubý, Jan
The report is written for the needs of the project no. TA04011656 (Research and development of new type of high-speed planetary gear unit with the flexible pin technology to support the planet wheels enabling the transmission of high outputs.). The first part of the report targets the topic of windage losses of a rotating toothed wheel, the experiments with testing gearbox Alfa II are introduced here, as well. The experiments included measurements of windage losses and temperature measurements along a wheel tooth width. Three geometrical configurations differing in wheel enclosure distance were tested, the case without the enclosure was tested too. The outcome of this part is an extension of the previous windage loss model for real geometry configuration: a wheel with an enclosure opened at place of oil outflow and at place of meshing with pinion.\nThe second part of the report targets the thermal load of a wheel tooth and presents experimental results of measurements of temperature distribution along the tooth. This part also contains the details concerning the numerical modeling of this problematic. The numerical analysis included (i) development of methodology for modeling of tooths meshing, (ii) development of the computational model, (iii) development of methodology for assessment of unknown values of some parameters of the model, (iv) development of algorithm. \n
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Eigen-modes of four-planets gearing box
Půst, Ladislav ; Pešek, Luděk ; Radolfová, Alena
The report is oriented on influence analysis of planet pins compliance on the frequency and modal spectrums of gearing box. The assumptions of mathematical model of four-planets gearing are: Lumped, stiff bodies of gear wheels, linear stiffness of planet’s pins as well as all wheel axes. Contact stiffness in gearings are modelled by average values with neglecting of periodic variability. All wheels moves in plane. Frequency spectrum of dynamic model with 16 degrees of freedom contains multiple eigen-frequencies. Computations of frequency and modal spectra are realized in the programme base Matlab.
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Methodology for evaluation of the gear windage loss and thermal load of a tooth
Bauer, Petr ; Bartoš, Ondřej ; Hrubý, Jan ; Kordík, Jozef ; Krátký, Tomáš ; Sedlář, Milan
This report contains results of experiments identifying thermo-physical properties of a gearbox oil mist. The main part of the report studies a dependency of a gear wheel windage power loss on the radial and axial gap between the wheel and its enclosure. This parametric study relies primarily on the results coming from numerical simulations (CFD analysis). For the default enclosure configuration the evaluated power dissipation is compared with the values obtained using theoretical relationships. The theory is based on one-dimensional turbulent velocity profiles over smooth and rough surfaces. A summary of the theoretical analysis and the derivations are also included in the report.\nThe influence of a tooth shape on the windage power loss is also studied using the numerical simulations. A change of a tooth top surface angle is technologically easily realizable adjustment, and can have a positive effect on the power loss reduction. In the report there are performed simulations for varying angles of this surface and the expected improvements in aerodynamic properties are confirmed.\nThe last part of the report contains the formulation of boundary conditions for numerical evaluation of gear wheel heat balance. This information is documented more in detail in related research reports.\n
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Generalization of the methodology for evaluation of the gear windage loss
Bauer, Petr ; Kordík, Jozef ; Krátký, Tomáš ; Sedlář, Milan
The first part of the report proposes a methodology for gear windage loss evaluation using CFD analysis. The methodology includes simplification of gearbox complex geometry and the toothed wheel and pinion are replaced by a rough-walled disks with additional braking volume forces. The values of volume forces were determined using auxiliary computations with a real gear geometry (a gear segment with periodical boundary conditions). The computations included configuration of the gear wheel meshing with the pinion, while distance of wheel enclosure was a variable parameter (the case without enclosure was tested as well). The cases without pinion were computed too, they were compared with earlier results obtained with the gear segment geometry.\nThe second part of the report contains a revision of the earlier proposed analytical approach. The approach can serve for approximate gear windage loss evaluation and its idea dwells in smooth connection of logarithmic velocity profiles. The gear windage loss values obtained from the analytical approach were compared with the results based on CFD analysis. A good agreement between both methods was concluded.\n
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Dynamic model of planetary gearbox with four satellites and standing planet carrier
Hortel, Milan ; Škuderová, Alena
The precised mathematical and physical weakly and strongly nonlinear parametric dynamic model pseudoplanetary transmission system with kinematic couplings, ie. four satellites with front straight toothing and standing planet carrier (model Wikov type PP) with 28 degrees of freedom was compiled within the project TAČR TA04011656 follow-up to previous research reports Z-1512/14, Z-1521/14, Z-1537/15. Model respects both elastic supports of all gears and by means Heaviside functions possible contact bounces of meshing gear profiles in the area of the lateral tooth clearances. There are a impact effects upon re-contact of tooth flanks both in normal and during the eventual inverse gear meshes, depending on the size of dynamic forces in gearing. Based on the explicit expression of Lagrange equations of this model, the simulation model of transmission system is prepared in MATLAB / Simulink.
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Experimental modal analysis of four-planet gear-box in a steady state
Pešek, Luděk ; Bula, Vítězslav ; Šulc, Petr ; Cibulka, Jan
This research report deals with a description and presentation of results of experimental modal analysis of non-rotating four-planet gear-box specific by planets placed on flexible pins designed and fabricated by Wikov Gear. The analysis deals with an evaluation of frequency domain behavior and localization of the main inner resonances of gear-box. The results of the experiment will be used for validation and tuning of developed numerical models in IT AS CR for vibrodiagnostic purposes and description of the gear-box behavior under rotation and with additional aggregates, i.e. engine, add-on bear-box and brake.\n
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The refined model of dynamics of planetary gearbox
Hortel, Milan ; Škuderová, Alena
The study continues the research report Z 1521/14, which describes the first version of the simulation model of system 42 weakly and strongly nonlinear parametric differential equations, solving motions in individual gear meshes, their bearing including moving the carrier satellites in Matlab / Simulink. The study complements and refines the simulation model of the transmission system by the physical description and modelling of time-varying values and geometric parameters occuring in the motion equations of mathematical and physical model of the planetary differential gear system with three double satellites with straight teeth.
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Dynamic model of planetary gearbox with braked satellite-gear carrier
Půst, Ladislav ; Pešek, Luděk ; Radolfová, Alena
The report is focused on theoretical-numerical analysis of influence of flexible planetary pins and of planetary gearbox connection with external driving and braking aggregates. Introducing of the compliance of planetary pins and releasing of sun wheel requires complicated differential equations of motion containing new radial coordinates and negative radial stiffness of tooth mesh. Eigen-frequencies of separated gearbox and of three-aggregates-set are ascertain for different values of torsion stiffness of external aggregates. It was shown that there exist several multi-fold eigen-frequencies.
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