Abstract
In this paper, a systematic approach for the dynamic modeling of complex planetary gear sets is presented. The approach relies upon a set of rules for building the system matrices and vectors of the system full dynamic model for any planetary gear set. A congruent state-space transformation is applied to obtain a reduced-order rigid model of the system, which allows for faster simulations. The behavior of the tangential forces accounting for the gears interactions is proven to be obtained from the reduced-order model. Furthermore, the kinematic relations of the considered planetary gear set are automatically generated when developing the reduced-order rigid model. As an example, two systems of interest in the vehicle industry are then modeled with the proposed approach and simulated in Matlab/Simulink: a Ravigneaux planetary gear set and a double-stage planetary gear set.
Highlights
T HE trend in the development of modern road transportation systems is strongly oriented toward the hybridization of propulsion systems, since this represents the most promising solution allowing to limit the exhaust emissions
Fixed-step simulations are enabled by the reduced-order model, because the fast dynamics associated with the tangential springs are no longer present
The first one is suitable for accurately simulating the system, whereas the second one is suitable for fixed-step simulations which are needed for real-time execution
Summary
T HE trend in the development of modern road transportation systems is strongly oriented toward the hybridization of propulsion systems, since this represents the most promising solution allowing to limit the exhaust emissions. Different works can be found in the literature regarding the modeling of power-split HEVs, including planetary gear sets and all the main elements of the transmission system. ZANASI AND TEBALDI: MODELING OF COMPLEX PLANETARY GEAR SETS USING POWER-ORIENTED GRAPHS in-contact gears; c) the comparison of the proposed method with the well-known Lever Analogy; d) new considerations about the possible operating conditions of planetary gear sets; e) the presentation of a new case study and its simulation in a power-split HEV; f) the extension of a case study, which was previously shown in our previous work [22], with the introduction of the relative friction coefficients; g) new considerations about the energy and the angular momentum of the system.
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