Nomographs for Kinematics, Statics and Power Flow Analysis of Epicyclic Gear Trains

Esmail, Essam L.; Hussen, Hamed A.

doi:10.1115/imece2009-10789

Cited by 5 publications

(6 citation statements)

References 21 publications

(31 reference statements)

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“…Considering the field of Machine Mechanics and Design over the last 30 years, we found several works on nomograms for gear train design (Esmail & Hussen, 2010;Esmail, 2013Esmail, , 2016Esmail et al, 2018); they are also still used for the design of planar (Hassaan, 2015) or spherical (Hwang & Chen, 2007;Lu, 1999) linkages, for optimizing motion laws in cams (de Freitas Avelar et al, 2021), for the analysis of the efficiency of a kinematic chain (Aleksandrov, 2011), for studying tire dynamics in a vehicle (Zotov & Balakina, 2007), and for the design of hollow springs (Bagaria et al, 2017).…”

Section: Resurgence? 1990-todaymentioning

confidence: 99%

Nomograms in the History and Education of Machine Mechanics

Mottola

Cocconcelli

2023

Found Sci

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Computing formulae and solving equations are essential elements of scientific analysis. While today digital tools are almost always applied, analog computing is a rich part of the larger history of science and technology. Graphical methods are an integral element of computing history and still find some use today. This paper presents the history of nomograms, a historically-relevant tool for solving mathematical problems in various branches of science and engineering; in particular, we consider their role in mechanical engineering, especially for education, and discuss their mathematical properties. Each nomogram is a graphical description of a specific mathematical equation, designed such that the solution can be found through a simple geometric construction that can be performed with a straightedge. By design, using nomograms requires little skills and can be done even in adverse environments; a solution of sufficient accuracy for most purposes can then be found in a very short time. Another important advantage of nomograms is that they offer clear insight on the relationships between the variables, an insight which can be lost by looking at a complex equation. First introduced in the late 19 th century, nomograms were used by engineers and scientists due to their speed with respect to manual calculations, before being superseded by computers. While now mostly obsolete in practice, nomograms can still prove useful in workshops and teaching classes: we thus also discuss their educational applications and present a few original examples.

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Section: Resurgence? 1990-todaymentioning

confidence: 99%

Nomograms in the History and Education of Machine Mechanics

Mottola

Cocconcelli

2023

Found Sci

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“…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]. The...…”

Section: Analysis Of the Kinematics Of Series-parallel Gearsmentioning

confidence: 99%

“…In the first modified version of the analytical method used in this paper, the kinematics and statics are analysed using the matrix method, which makes the form of the equations which are used more compact and the computer calculations easier to perform [116,117]. In an equally popular variant, angular velocities and torques are determined using the lever analogy method and nomograms [118][119][120][121][122][123][124][125][126][127][128][129][130]. Also very interesting is the combined method of determining the power flow and efficiency epicyclic transmission presented in references [131][132][133][134][135][136][137][138][139][140], where the Lagrange multipliers and kinematic constraints are used to determine the power flow and to verify the normal power flow balance.…”

Section: Introductionmentioning

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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“…In the particular case of EGTs, a nomograph can be constructed using three or more vertical parallel axes [19,27]. Traditionally, the velocity ratio is used to study the velocity relations among the different links of an EGT [3].…”

Section: Nomographs and Geometry Relations For Seven-link Ravigneaux mentioning

confidence: 99%

“…Because there are four coaxial links and link four is preassigned as the output link, this gear train can provide six overall velocity ratios [27,28]. Figure 6 shows the clutching sequence nomograph for this mechanism.…”

Section: Enumeration Of All Feasible Clutching Sequencesmentioning

confidence: 99%

Nomographs and Feasibility Graphs for Enumeration of Ravigneaux-Type Automatic Transmissions

Esmail

2013

Advances in Mechanical Engineering

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Although there are many epicyclic-type automatic transmissions in production, the related configuration design methods are still tedious and borne to human error. A simple methodology for the systematic design of the Ravigneaux-type epicyclic gear transmissions needs to be developed. First, fundamentals and gear-shifting of four-speed and six-speed epicyclic-type automatic transmissions are illustrated to establish the design requirements. Second, based on the kinematic nomographs of the corresponding basic gear ratios, a simple clutching-sequence method is proposed and illustrated. Next, a planar-graph representation is presented to arrange the desired clutches for each possible clutching sequence into the epicyclic gear mechanism. Then, with the above methods, the systematic designs of the epicyclic gear mechanisms are given for demonstrating the feasibility of the proposed methodology. The result of this work shows that the seven-, eight-, and nine-link two-DOF Ravigneaux-type epicyclic gear mechanisms could reach four-, six-, and eight-forward speeds at most, respectively. New five-, six-, seven-, and eight-velocity automatic transmissions are enumerated from the two-ring eight-and nine-link Ravigneaux gear mechanisms. It is a major breakthrough to design completely satisfactory eight-speed automatic transmissions from the nine-link Ravigneaux gear mechanism.

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Nomographs for Kinematics, Statics and Power Flow Analysis of Epicyclic Gear Trains

Cited by 5 publications

References 21 publications

Nomograms in the History and Education of Machine Mechanics

Nomograms in the History and Education of Machine Mechanics

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

Nomographs and Feasibility Graphs for Enumeration of Ravigneaux-Type Automatic Transmissions

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