A universal kinematic analysis of geared mechanisms

Esmail, Essam L.

doi:10.1007/s40430-017-0711-2

Cited by 13 publications

(3 citation statements)

References 24 publications

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“…For any compound planetary gear train consisting of two or more GPEs and/or GTEs, the "velocity ratio" R k i,j between two links (i and j) of a PGT with respect to a third link (k) is written as the following [40]:…”

Section: Velocity Ratio Analysismentioning

confidence: 99%

“…Let us further assume that the efficiencies of the three gear pairs (η 1 , η 2 , η 3 ) are known. By making use of the velocity ratios tabulated in Table 2, we can obtain from Equations (47), (45), (44), (43), (41), (40), (37), and (33), by back substituting the values of the following variables: l, η ð5,4→1Þ , P 1 , l 3 , l 2 , l 1 , P 2 , P 4 , and P 5 , respectively. Case 2.…”

Section: Torque Concluded From Column 6 Assignmentmentioning

confidence: 99%

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Power Flow Simulation for Two-Degree-of-Freedom Planetary Gear Transmissions with Experimental Validation

Hussen

Esmail

Hussen

2020

Modelling and Simulation in Engineering

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The basic relationships among gear ratios, velocity succession, torque directions, power ratios, energy losses, and efficiency are derived from first principles. The techniques presented here can be applied to ordinary, planetary, or mixed gear trains. Also, these techniques provide more insight into how power is flowing through the different parts of the mechanism. Power flow relationships are a helpful tool to study power amplification and power circulation in multipath transmissions. They also provide more insight into how the gear pair entities (GPEs) or gear train entities (GTEs) affect total power losses and allow immediate derivation of the overall efficiency. A representative two-input mechanism is analyzed to demonstrate the effectiveness of improved techniques. The theoretical results are compared with experimental data of previous work. The theoretical and experimental curves exhibit identical trends with a distinct jump in friction loss. The jump is explained by a change in the way of the power flow through the mechanism. The conditions under which power circulation occurs are determined. The results have important implications for understanding how to improve the efficiency of multipath power flow systems.

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Section: Velocity Ratio Analysismentioning

confidence: 99%

Section: Torque Concluded From Column 6 Assignmentmentioning

confidence: 99%

Power Flow Simulation for Two-Degree-of-Freedom Planetary Gear Transmissions with Experimental Validation

Hussen

Esmail

Hussen

2020

Modelling and Simulation in Engineering

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“…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]…”

Section: Analysis Of the Kinematics Of Series-parallel Gearsmentioning

confidence: 99%

Power Flow in Coupled Three-Row Series-Parallel Planetary Gear System, Part I: Without Power Losses

Drewniak,

Kądziołka,

Rysiński

et al. 2023

Energies

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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.

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An Application of Modified Path Matrix Approach for Detection of Isomorphism Among Epicyclic Gear Trains

Mustafa

Hasan

Khan

2020

J. Inst. Eng. India Ser. C

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A universal kinematic analysis of geared mechanisms

Cited by 13 publications

References 24 publications

Power Flow Simulation for Two-Degree-of-Freedom Planetary Gear Transmissions with Experimental Validation

Power Flow Simulation for Two-Degree-of-Freedom Planetary Gear Transmissions with Experimental Validation

Power Flow in Coupled Three-Row Series-Parallel Planetary Gear System, Part I: Without Power Losses

An Application of Modified Path Matrix Approach for Detection of Isomorphism Among Epicyclic Gear Trains

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