Predictions of input pinion floating on concentric face gear transmission static load sharing

Si Li1 , Zhengminqing Li2 , Xin Tang3 , Wenlin Zhu4 , Meijun Liao5

1, 2National Key Laboratory of Science and Technology on Helicopter Transmission, Nanjing University of Aeronautics and Astronautics, Nanjing, 210016, China

3, 4, 5Science and Technology on Helicopter Transmission Laboratory, AECC Hunan Aviation Powerplant Research Institute, Zhuzhou, 412002, China

2Corresponding author

Vibroengineering PROCEDIA, Vol. 28, 2019, p. 236-240. https://doi.org/10.21595/vp.2019.21010
Received 12 September 2019; accepted 26 September 2019; published 19 October 2019

Copyright © 2019 Si Li, et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
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Abstract.

A static load sharing analysis model of concentric face gear transmission associated with the input pinion floating is constructed, and the calculation method of static load sharing is proposed. The influence of the input pinion floating on static load sharing is predicted. The results show the input pinion floating stiffness reduction could benefit for the concentric face gear transmission static load sharing.

Predictions of input pinion floating on concentric face gear transmission static load sharing

Highlights
  • A static load sharing model of concentric face gear transmission is constructed.
  • The calculation method of concentric face gear transmission is proposed.
  • The influences of floating support stiffness on static load sharing is simulated.

Keywords: concentric face gear transmission, input pinion floating, static load sharing.

1. Introduction

The concentric face gear transmission shows the advantages in weight, transmission efficiency and reliability, compared with the traditional gear torque split transmission. Therefore, it is focused by the helicopter transmission researchers.

For the gear split torque transmission, uneven load distribution on gears is one of the key problems for the split transmission design. Therefore, many scholars studied the load sharing behavior of various split transmission, such as planetary gear transmissions [1-5], cylindrical gear split torque transmissions [6-12] and traditional face gear split torque transmissions [13-15]. However, there are few studies on the concentric face gear transmission. Thus, in the paper, the static load sharing of the concentric face gear transmission is studied. A static load sharing analysis model and a static load sharing calculation method associated with the input pinion floating are constructed. Then, the influence of the floating support stiffness on the static load sharing of the system is simulated. The results would be helpful to the concentric face gear transmission design.

2. Analysis model and calculation method constructions

The concentric face gear transmission is composed of two coaxial face gears, two input pinions and two idler gears, as show in Fig. 1. In the system, torque split to upper and lower face gears by two input pinions, the low face gear transfers torque to the up face gear by the idler gears, and the torque is output by the upper face gear finally. The static load sharing model associated with the input pinion floating is proposed, as shown in Fig. 2.

Illustrated in Fig. 2., Z1 and Z2 are the input pinions, Z3 and Z4 are the idlers, ZU and ZL are the upper and lower face gears, T1 and T2 are the input torques, TO is the output torque, kt is the floating support stiffness, kij is the mesh stiffness. Moreover, Fij is defined as the mesh force between gear j and gear i.

Based on the equilibrium conditions, the static load sharing equation is obtained by:

(1)
F 1 U + F 1 L c o s α = T 1 / r b 1 , F 2 U + F 2 L c o s α = T 2 / r b 1 , F 3 U - F L 3 = 0 , F 4 U - F L 4 = 0 , - F 1 L - F 2 L + F L 3 + F L 4 c o s α = 0 ,

and the floating support equation could be derived by:

(2)
F 1 U - F 1 L - k t s 1 = 0 , F 2 U - F 2 L - k t s 2 = 0 ,

and the gear meshing force could be expressed as:

(3)
F i j = k i j r b i φ i j ,

where, rib is the gear i base circle radius, and φij is the deflection angle between the gear i and the gear j.

Fig. 1. The concentric face gear transmission

 The concentric face gear transmission

Fig. 2. The static load sharing model

 The static load sharing model

For static load sharing of input pinions, the distribution ratio and maximum distribution ratio between upper and lower face gears could be obtained by:

(4)
Ω i U = F i U T i / r b i , Ω i L = F i L T i / r b i ,         i = 1 ,   2 ,
(5)
Ω m a x = m a x Ω i U , Ω i L .

3. Simulations

In order to predict the influence of floating support stiffness on static load sharing of the concentric face gear transmission, the parameters of an example case are listed in Table 1.

Table 1. Parameters of system

Symbol name
Value
Unit
Modulus / m
4
mm
Pressure angle / α
20
°
Tooth number of face gear / zf
86
Tooth number of cylindrical gears / zp
24
Tooth number of shaper / zt
25
Addendum coefficient / ha*
1
Clearance coefficient / c*
0.25

Fig. 3. Static load sharing with different floating support stiffness

 Static load sharing with different floating support stiffness

a) Without floating (1)

 Static load sharing with different floating support stiffness

b) Floating support stiffness 109N/m (2)

 Static load sharing with different floating support stiffness

c) Floating support stiffness 108N/m (3)

 Static load sharing with different floating support stiffness

d) Floating support stiffness 107N/m (4)

 Static load sharing with different floating support stiffness

e) Floating support stiffness 106N/m (5)

According to the static load sharing model and calculation method, as well as the parameters listed in Table 1, the influences of the input pinion floating on the static load sharing are simulated. The results are shown in Fig. 3 and Fig. 4.

Fig. 4. Maximum static load sharing under different floating support stiffness

 Maximum static load sharing under different floating support stiffness

a) Input pinion 1

 Maximum static load sharing under different floating support stiffness

b) Input pinion 2

4. Conclusions

The works of the issue are as follows:

1) The static load sharing model and calculation method of the concentric face gear transmission associated with the input pinion floating are proposed.

2) The influences of floating support stiffness on static load sharings are simulated, and the results indicate the floating support stiffness reduction is benefit for static load sharings.

These contributions would be helpful to the concentric face gear transmission design.

Acknowledgements

The authors are grateful for the financial support provided by the National Natural Science Foundation of China under No. 51775264, and by National Key Laboratory of Science and Technology on Helicopter Transmission (Nanjing University of Aeronautics and Astronautics) (Grant No. HTL-A-19G06). In addition, the authors declare that there is no conflict of interests regarding the publication of this article.

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