Planetary Gear Modeling Using the Power-Oriented Graphs Technique

Abstract

In this paper, the Power-Oriented Graphs (POG) technique is used to model Planetary Gear transmission systems. The full elastic dynamic model of the system is obtained using a fast and direct method which can be easily applied to any type of planetary gear. The rigid and reduced dynamic model of the system when the stiffness coefficients go to infinity is then obtained using a POG congruent state space transformation allowing the user to select which angular speeds are to be maintained in the reduced model. Another interesting aspect of the presented method is that the obtained reduced model is still able to provide the time behaviors of the tangential forces present between each couple of gears of the considered planetary gear system. The presented fast and direct method is then applied to two practical case studies, and simulative results in Matlab/Simulink showing the effectiveness of the method are finally reported and commented.

Modeling of Complex Planetary Gear Sets Using Power-Oriented Graphs

“…The reduced-order rigid system (22) no longer contains any information regarding the force vector F. Nevertheless, vector F can be obtained from the reduced-order rigid system (22), as described by Prop. 3 illustrated in the following.…”

“…The time behavior of the force vector F can be obtained from the state vector x 1 and the input vector u = τ of the reduced rigid system (22) using the following relation:…”

“…The POG is a graphical modeling technique which relies on power and energy variables to describe the energy exchanges between the physical elements present in the system. Some examples showing the application of the POG technique in the automotive field can be found in [20]- [22].…”

“…In this paper, it is our intent to present an extension of the systematic approach for modeling planetary gear sets introduced in [22]. The contributions of this paper compared to our previous work are: a) formal proofs of the model properties; b) the introduction of the relative friction coefficients present between two 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. The presented approach is deemed more effective than the current state of the art for the following reasons:…”

Modeling and Control of a Power-Split Hybrid Propulsion System

“…The planetary gear shown in Fig. 1 has been modeled by using the systematic and effective approach exploiting the POG technique described by the authors in [10].…”