A matrix-based method for searching configurations of planetary gear trains

Dong, Peng; Zuo, Shumiao; Liu, Tianyan; Xu, Xiangyang; Guo, Wei; Liu, Yanfang; Wu, Hongchao; Wang, Shuhan

doi:10.1016/j.mechmachtheory.2022.105161

Cited by 11 publications

(4 citation statements)

References 30 publications

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“…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 effectiveness of the above-mentioned methods can be additionally increased by the matrix notation of the obtained equations [117,187,196].…”

Section: Analysis Of the Kinematics Of Series-parallel Gearsmentioning

confidence: 99%

“…A great facilitation of the analysis of such gear trains, as well as complex and coupled gear transmissions with any possible mobility, is the possibility of their decomposition into elementary subsystems, called blocks, branches, or geared entities [45][46][47][48]64,97]. 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].…”

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

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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Section: Analysis Of the Kinematics Of Series-parallel Gearsmentioning

confidence: 99%

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

View full text Add to dashboard Cite

show abstract

“…Some studies have proposed a program to evaluate the sensitivity of certain characteristics of planetary gear trains-the efficiency and transmission ratio-to small changes in design parameters. This method is only applied to specific transmission systems through examples, rather than through a detailed analysis of numerous gear trains [6][7][8][9][10].…”

Section: Introductionmentioning

confidence: 99%

Motion, Static Force, and Efficiency Analysis of Planetary Gear Transmission Based on Graph Theory

Xue,

2023

Applied Sciences

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This paper employs graph theory to analyze kinematic relationships, static force, and power flow for planetary gear systems. We start from the graphs of these trains to determine all the structurally distinct kinematic inversions. We then obtain all the constructive solutions resulting from every possible combination of gear configuration. Based on the kinematic and static force analysis model, related matrices are acquired. Hence, a kinematic and static force analysis of the planetary gear mechanism is achieved. The link power can be determined by the link speed and torque. Power flow diagrams of each gear are acquired. The efficiency is calculated by the transmission ratio method. This analysis is useful in the design of power transmission applications. A planetary gear system of a 6HP26 automatic transmission is further illustrated for the motion, static force, and efficiency calculations by using graph theory technique and matrix equations. This paper provides a guide for engineers in gear transmission fields to easily finish mechanical transmission design.

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“…T. CIOBOTARU [21] suggested a method for analyzing epicyclic gearboxes by evaluating the speeds, torques, and power of the external elements in epicyclic gear mechanisms, as well as the total ratios of the gear box. A better dynamic and economic performance of vehicles can be produced by increasing the number of gears of planetary gear trains (PGTs), but a more complex structure would be required [22]. In order to increase the competitiveness of railroad transportation and decrease environmental pollution, a more popular design is the single-row star-row split power-coupling mechanism.…”

Section: Introductionmentioning

confidence: 99%

Power-Split Hybrid Train Configuration Design Based on a Single-Row Star Row

Li¹,

Zhang

Qu³

et al. 2023

Applied Sciences

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The fundamental component of a hybrid train system is the hybrid power-coupling mechanism. This paper proposes a single-row star-row power-split arrangement for the power-coupling method in a hybrid train. In order to create input and output power-split configuration schemes for a hybrid train power mechanism, a graphical–theoretical model and a relationship matrix were first established. An electromechanical path power proportion equation was then established to filter out two input power-split configurations. The working states of three developed hybrid power-coupling mechanism schemes were studied to find the scheme that fulfills hybrid train design criteria to meet the power, operating mode, and spatial structural arrangement requirements. Finally, by creating a simulation model for the entire vehicle, the dynamics, battery state of charge (SOC) value, and overall vehicle efficiency for the configuration were simulated and examined. The findings demonstrate that the single-row star-row power-split design technique presented here significantly enhances the train performance.

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A matrix-based method for searching configurations of planetary gear trains

Cited by 11 publications

References 30 publications

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

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

Motion, Static Force, and Efficiency Analysis of Planetary Gear Transmission Based on Graph Theory

Power-Split Hybrid Train Configuration Design Based on a Single-Row Star Row

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