齿轮传动效率

article info
Article history: Received 10 March 2011 Received in revised form 5 April 2012 Accepted 5 September 2012 Available online 4 October 2012
Keywords: Epicyclic gear train Power flow Efficiency Split power
Mechanism and Machine Theory 59 (2013) 96–106
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Mechanism and Machine Theory
journal homepage: www.elsevier.com/locate/mechmt
2. Compound gear train with split power
The epicyclic gear train shown in Fig. 1 is a one-dof train with one planetary carrier as the input shaft. This is a compound gear system with split power. There are six elements including ground. The geometric constraints are given by
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0094-114X/$ – see front matter © 2012 Elsevier Ltd. All rights reserved. http://dx.doi.org/10.1016/j.mechmachtheory.2012.09.004
The rest of this work is organized as follows. The kinematics of the compound gear train with split power [16] is studied in Section 2. The directions of power flows are analyzed in Section 3, where the split-power ratio and the virtual split-power ratio are introduced for the first time. Power losses and the total efficiency of the train are derived analytically in Section 4, where the
The previous efforts in computing the efficiency of simple epicyclic trains can be found in [4–8,3,9–11]. Power flow study of compound gear trains can be found in [12,13], with numeric results reported. All the above methods in deriving the formulas of efficiency were based on the torque balance of the whole system, by considering independent overall efficiencies. However, we found that the overall efficiencies are in fact coupled together. The approach proposed in [14] provides detailed power flow patterns of simple one-dof epicyclic trains. In [15], the concepts of virtual motors and generators were introduced into the framework of virtual power analysis, which significantly simplify the procedure of power analysis.
C. Chen / Mechanism and Machine Theory 59 (2013) 96–106
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efficiency formula is verified. Further, the phenomenon oቤተ መጻሕፍቲ ባይዱ self-lock in this train is disclosed based on the efficiency analysis. Suggestions on design of this train, to avoid self-lock and improve the total efficiency, are also given in Section 4.
abstract
The analytical efficiency expression of a compound epicyclic gear train with split power is derived via the approach based on virtual power. New concepts, the split-power ratio and the virtual split-power ratio, are introduced to handle the compound gear train. The efficiency formula is verified by a particular condition. The phenomenon of self-lock is disclosed in this compound gear train. It is observed that the power loss on one planet is dominant. This dominant power loss is caused by the immense virtual power passing through one gear mesh. Based on the analytical results, suggestions on design are given to avoid self-lock and increase the total efficiency.
Power flow and efficiency analysis of epicyclic gear transmission with split power
C. Chen ⁎
Department of Mechanical and Aerospace Engineering, Monash University, Clayton, Australia, 3802
r23 ¼ r32; r25 ¼ r52
ð3Þ
The kinematics relations are given by w3n34 þ w4n43 ¼ 0 w5n54 þ w4n45 ¼ 0 ðw3−w1Þ−w2 ¼ 0 ðw5−w1Þ þ w2 ¼ 0
ð4aÞ ð4bÞ ð4cÞ ð4dÞ
where wi, for i = 1, 3, 4, 5, is the angular velocity of Link i with respect to the ground, while w2 is the angular velocity of Link 2 with respect to Link 1.
However, when dealing with compound gear trains with split power, the approach in [15] is no longer sufficient. The major reason is that the virtual power ratios do not yield enough equations to solve for all branch powers. Here, we introduce new relations in compound system: the split-power ratio and the virtual split-power ratio. Upon these relations, a typical compound epicyclic train in [16] is analyzed.
n43 þ n34 ¼ 1 n45 þ n54 ¼ 1
ð2aÞ ð2bÞ
where 0 b nijb 1. In the following discussion, we assume r43> r45, and the planets on Link 2 are 45° bevel gears. Hence,
© 2012 Elsevier Ltd. All rights reserved.
1. Introduction
Epicyclic gear trains have broad applications in automobile, aerospace, mill, and automation industries, such as [1,2]. Predetermining internal power flows of an epicyclic gear train is critical to a successful design, because the internal power flows may yield significant power losses at gear meshes and fail the concept. It was reported in [3] that the mechanical efficiency of an epicyclic system could be much lower than that of a simple gear train. The cause of this phenomenon is commonly believed to be the internal power circulation and amplification. Principal power sinks in gear trains are: sliding friction between meshing tooth surfaces, oil churning, and friction in shaft support bearings [4]. Here, we focus on the power losses due to the gear-mesh sliding friction.
r43 þ r34 ¼ d
ð1aÞ
r45 þ r54 ¼ d
ð1bÞ
where rij is the radius of the gear on Link i, engaged with Link j, and d is the distance between the rotation axes of Link 1 and Link 4. To simplify the notation, we introduce nij= rij/d, so that Eqs. (1a) and (1b) can be written as