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Influence of Backlash on Load Sharing and Dynamic Load Characteristics of Twice Split Torque Transmission System

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Abstract

Introduction

Based on the characteristics of the helicopter main reduction gearbox, and combined with the advantages of face gear and cylindrical gear power dividing, a new configuration of helicopter main gearbox with twice split paths is proposed. A bending–torsional coupled dynamic model of the system is developed through the lumped parameter method, and the influence of stiffness, damping and backlash are considered.

Methods

The dynamic equation is solved by Runge–Kutta method, and the load sharing and the dynamic load coefficients are obtained, as well as their variation with the backlash.

Results

Results show that with the increase of the backlash, the load-sharing coefficient decreases, the dynamic load coefficient increases, but the other drive stages are almost unaffected. Compared with split torque stages and power confluence stages, the load sharing and dynamic load coefficient of power input stages are the most sensitive to the backlash of the power input stage, and the appropriate increase of the backlash can effectively improve the dynamic properties.

Conclusion

Therefore, in order to obtain better dynamic performance, it is necessary to allocate the backlash reasonably.

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Abbreviations

b :

Backlash

c :

Meshing damping

c Dm, c ifp, c ijsjh :

Torsional damping of the corresponding shaft

e :

Eccentric error

f l(Y t):

Gap function

F ifx, F ify, F ifz :

Component forces of the meshing force of the face gear pairs

F ijx, F ijy :

Component force on the split shaft

F inmf, F inpjs,F inBjh :

Meshing forces of Zm and Zif, Zip and Zijs, ZB and Zijh

F ipx, F ipy, F ipz :

Component forces on duplicate shaft

F l :

Meshing force

F mx, F mz :

Component force on the input shaft

F Bx, F By :

Component force on the output shaft

Gl :

Dynamic load coefficient

I m, I if, I ip, I ijs, I ijh, I B :

Moment of inertia of Zm, Zif, Zip, Zijs, Zijh and ZB

k m :

Average meshing stiffness

k 0 :

Variation amplitude of meshing stiffness

K Dm, K ifp, K ijsjh, K Bo :

Torsional stiffness of the input shaft, duplicate shaft, split shaft and output shaft

K l,:

Meshing stiffness

K ipx, K ipy, K ipz :

Support stiffness of duplicate shaft

K inmf, K inpjs, K inBjh :

Time-varying meshing stiffness of Zif and Zm, Zip and Zijs, ZB and Zijh

K mx, K mz :

Support stiffness of input shaft

m m, m if, m ip, m ijs, m ijh, m B :

Lumped mass of Zm, Zif, Zip, Zijs, Zijh and ZB

P l :

Static load of gear pairs

Ωimf, Ωijs, Ωijh :

Load sharing coefficient

r ibp, r ibjs, r ibjh, r bB :

Base circle radius of Zip, Zijs, Zijh and ZB

r if :

Equivalent meshing radius of face gear

r ifp, r ijsjh :

Equivalent radius of duplicate shaft and split shaft

r m :

Radius of pitch circle of Zm

r Dm, r Bo :

Equivalent radius of the input shaft and output shaft

T D, T o :

Input torque and the load

X inp, Y inp, Z inp :

Displacement of duplicate shaft along the coordinate direction

X ij, Y ij :

Transverse displacement of split shaft

X nm, Z nm :

Transverse and axial displacement of input shaft

X B, Y B :

Transverse displacement of output shaft

Z if, Z ijh :

Face gear, the pinion of power confluence stage

Z ip, Z ijs :

Driving and driven gear of split torque stage

φ D, φ m, φ B, φ o :

Torsional displacement of input, Zm, ZB and output

φ if, φ ip, φ ijs, φ ijh :

Torsional displacement of gear Zif, Zip, Zijs and Zijh

θ ip, θ ij, θ iB, θ B :

Installation angle

i :

R, L

j :

1, 2

l :

inmf, inpjs and inBjh

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Acknowledgements

The work is fully supported by National Natural Science Foundation of PRC (Grant No. 51475226).

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Authors and Affiliations

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

    Guanghu Jin, Wei Ren, Rupeng Zhu & Fengxia Lu

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  1. Guanghu Jin
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  2. Wei Ren
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  3. Rupeng Zhu
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  4. Fengxia Lu
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Correspondence to Guanghu Jin.

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Jin, G., Ren, W., Zhu, R. et al. Influence of Backlash on Load Sharing and Dynamic Load Characteristics of Twice Split Torque Transmission System. J. Vib. Eng. Technol. 7, 565–577 (2019). https://doi.org/10.1007/s42417-019-00150-z

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  • DOI: https://doi.org/10.1007/s42417-019-00150-z

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