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In the present paper, kinematical analysis of an automotive gear is described. Versatile graph based methods have been utilized for this purpose. An application of mixed, contour and bond graphs gives the same results. It allows the detection of possible mistakes as well as a deeper insight into the designed artifact. The graphs can also be used fo...
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... and reverse drive, respectively. The mixed graphs are considered, i.e., a simple graph where a clique is drawn as a shaded polygon (according to Hsu's idea) and the directed path from an input to an output is considered. The double-line edges symbolize connections where the gear element (encoded by one edge end vertex) is stopped, e.g., arm j in Fig.2a (low gear). The other rules of graph drawing and assignment are collected in Tab.2. The graphs in Fig.2b and c are transformed (simplified) graphs, i.e., all redundant elements are neglected. The graph for a top gear is omitted because the ratio is equal to 1, so the reverses (rotational velocities) and power are passed directly from an input to ...
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... other rules of graph drawing and assignment are collected in Tab.2. The graphs in Fig.2b and c are transformed (simplified) graphs, i.e., all redundant elements are neglected. ...
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... only the description 4 was used because just this wheel is in mesh. The formulas (3.2b) were created upon the f-cycles (formulas (3.2a)). ...
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... the case of the second gear, according to the data given in Tab.1, the input is connected to element 3 and the output is performed via element J. The adequate mixed graph is shown in Fig.2b. Therefore upon f- cycles (3.5a) we can write the system of Eq.(3.5b) ...
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... the ratio is as follows . In the case of the reverse gear, the mixed graph is shown in Fig.2c. Based on this graph, one can write the cycles (3.8a) and Eq. ...
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... contour graphs are built according to the related methods given in Marghitu (2005). The graphs collected in Fig.2 are assigned to the same drives as previously. ...
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... graphs collected in Fig.2 are assigned to the same drives as previously. For example, the double circle vertex in the contour graph (Fig.2a) is equivalent to the double line in the mixed graph: (j, 5) ↔j (case a i.e.: low gear, arm j is braked). Some chosen rules and remarks for all three graphs are collected in Tab.2. ...
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Citations
... In order to determine the directions of the flow of power streams and to estimate the power losses in the meshing, it is necessary to determine the magnitudes and directions of the angular velocity vectors of the gears and carriers of each gear subsystem in advance (blocks, units, or branches) [195]. In practice, the Willis formula [12][13][14][15][16][17]163,178] is often used for this purpose, although graph methods (linear, contour, signal flow, bond graphs, matroids, and hypergraphs) are gaining more and more recognition, thanks to their advantages [143,162,[164][165][166][167][168][169][171][172][173][174][175][176][177][179][180][181][182][183][184][185][186]189,192,194]. The nomograph method and, especially, the lever analogy are also promising as universal methods for kinematics, statics, and power flow analysis of the most complex PSHEV planetary transmission [88,[118][119][120][121]126,[128][129][130]160,161,164,188]. ...
So far it is believed that, for every series-parallel planetary gear system (PGS), as a coupled gear, a very harmful phenomenon of power circulation must occur in at least one of its closed circuits. In this paper (Part I) and in the next two (Part II and Part III), it will be shown that it is possible to construct a three-row series-parallel PGS in which this phenomenon can be avoided. For this purpose, in Part I, a detailed analysis of the kinematics and statics of a planetary gear with power circulation inside a closed loop was carried out. The determination of the angular velocities of gears and carriers is carried out using Willis formulas and the graphical-analytical method (for verification), while the torques are determined using free body diagrams. The magnitudes of angular velocities and torques were used to determine the directions of power flows with improved energy balance equations in the reference frame related to the stationary gear body and, additionally, only to verify the energy balance equation in the mobile reference frame related to the carrier hi (i=2,5,8). The improvement of the methods was based on the use of the original concept of distinguishing active torque from reactive torque, as well as active power from reactive power, which made it very easy to determine the directions of the power flow. The determined paths of the power flow, including the power circulation in the analysed PGS, are presented graphically.
Comparisons of power flows and efficiencies in two structurally quite similar cylindrical series-parallel planetary gear systems (PGSs) were performed in three separate parts of this paper. Each of these single degree of freedom (DoF) systems consists of three different 2KH subsystems connected in series-parallel. The main goal was to prove that apart from complex, structurally and dynamically coupled PGSs, there are also complex and only structurally coupled PGSs, in which the phenomenon of power flow circulation inside closed loops does not occur. Such a half-coupled type of PGS is herein called pseudo-coupled. Therefore, Part I discusses in detail the geometry, kinematics and statics of coupled PGSs in order to determine power flow paths. A comparison of the directions of power flow in both types of PGSs can be made in Part II after determining the power flow paths in the second planetary gear in a similar way. The directions of power flow in both types of PGSs were determined in a relatively simple way, thanks to the distinction between active and passive torques and thus active and passive shafts of individual subsystems. The efficiency comparison made in Part III will show whether power circulation has an influence on the efficiency value, at least in these two types of PGSs.
The modeling and simulation of gearboxes is important for analyzing the dynamic characteristics and designing control strategies of transmission systems. Variable-speed gearboxes include compound planetary gear trains and clutches, which complicates dynamic modeling. Here, a procedural bond graph-based modeling method that considers many uncertainties is proposed. The proposed method yields a constant system–structure model. First, bond graph models of the two most common planetary gears were summarized, and were used as sub-models of a compound planetary gear train. Then, the Karnopp friction sub-model of the friction clutch and a relative angular displacement sub-model of the one-way clutch were constructed. Based on the dynamic coupling between the sub-models, the modeling steps of the gearbox, including the compound planetary gear train friction clutch one-way clutch coupling system, are described in detail. Next, the main sources of uncertainties of gearbox were analyzed and the simulation methods were given. Finally, the novel uncertain bond graph model was used to simulate the double planetary gearbox; the transmission ratio before and after the shift was 2.42 and 1.72, compared with the design values of 2.41 and 1.71, respectively; the deviation is within 5.8%; The average rotating speeds of the output shaft fluctuated by 6 and 2.5% respectively, which was within a reasonable range, so the effectiveness of the method is verified.
Planetary gears are applied in a wide range of applications. For example power supply of airplane auxiliaries or hybrid electric vehicles benefit from suchlike gears. Thus heavy truck hybrid propulsion based on epicyclic four-speed gears guarantees internal combustion engine optimal working point. Assuming that generic power split modelling for this gear type marks a research focus for some time already. The Bond Graph method as a member of a very closely related power flow modelling tool family is especially very well suitable to meet this aim. The paper argues this message not via common analysis but via synthesis, introduces folding operation as natural effective means for getting vectorial models, shows variants and illustrates generalization via simulation results and numerical examples. Synthesis approach suggested can also serve as a starting point for generation of more detailed models or research and comparison of new epicyclic gear constructions.
The chapter is dedicated to the achievements of Professor Józef Wojnarowski, polish IFToMM activist, who had originated graph-based modelling of mechanical systems in Poland in the 70’s of the twentieth century. He simultaneously, attracted a group of co-workers as well as other Polish scientists to this idea. All together they wrote a bunch of papers and a few books related to graph theory application. He also initiated and organized two international conferences “Graphs and Mechanics”. So, He could be recognized as a very important scientists whose output is fully in accordance with the goals of the present book and the IFToMM mission.
Dynamic system modeling is prerequisite in research of automatic transmissions (AT) controls and failure diagnostic. New generation of AT includes a large number of Planetary Gear Trains which leads to increasing difficulty for dynamic system modeling. A Modularization method for Planetary Gear Trains System Modeling is proposed to standardize the modeling procedure. Transmission gearbox system is decomposed into three kinds of subsystem with Bond graph Causality Definition: PGT (Planetary Gear Trains), Clutch and Inertial Rotator. A component tables listing procedure is introduced to convert the gearbox transmission schematic into subsystem connection diagram. Subsystems can be assembled by this diagram and the gearbox dynamic model can be achieved. This research presents a standard modeling process which can be used to model complicate vehicle planetary gearbox, and can be used on study about automatic transmission control and failure diagnostic.
The article is devoted to a graph method of dataware that will form a system of construction spiroid gearboxes, based on search algorithms. Stages of the data are considered that form, from existing structures, an analysis to generalize graph structure synthesis. It is an informational base for further synthesis of new structures.
