Journal of Vibration Engineering & Technologies

, Volume 7, Issue 6, pp 565–577 | Cite as

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

  • Guanghu JinEmail author
  • Wei Ren
  • Rupeng Zhu
  • Fengxia Lu
Original Paper



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.


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 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.


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


Face gear Split torque Load sharing Dynamic load coefficient 

List of Symbols




Meshing damping

cDm, cifp, cijsjh

Torsional damping of the corresponding shaft


Eccentric error


Gap function

Fifx, Fify, Fifz

Component forces of the meshing force of the face gear pairs

Fijx, Fijy

Component force on the split shaft

Finmf, Finpjs,FinBjh

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

Fipx, Fipy, Fipz

Component forces on duplicate shaft


Meshing force

Fmx, Fmz

Component force on the input shaft

FBx, FBy

Component force on the output shaft


Dynamic load coefficient

Im, Iif, Iip, Iijs, Iijh, IB

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


Average meshing stiffness


Variation amplitude of meshing stiffness

KDm, Kifp, Kijsjh, KBo

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


Meshing stiffness

Kipx, Kipy, Kipz

Support stiffness of duplicate shaft

Kinmf, Kinpjs, KinBjh

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

Kmx, Kmz

Support stiffness of input shaft

mm, mif, mip, mijs, mijh, mB

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


Static load of gear pairs

Ωimf, Ωijs, Ωijh

Load sharing coefficient

ribp, ribjs, ribjh, rbB

Base circle radius of Zip, Zijs, Zijh and ZB


Equivalent meshing radius of face gear

rifp, rijsjh

Equivalent radius of duplicate shaft and split shaft


Radius of pitch circle of Zm

rDm, rBo

Equivalent radius of the input shaft and output shaft

TD, To

Input torque and the load

Xinp, Yinp, Zinp

Displacement of duplicate shaft along the coordinate direction

Xij, Yij

Transverse displacement of split shaft

Xnm, Znm

Transverse and axial displacement of input shaft


Transverse displacement of output shaft

Zif, Zijh

Face gear, the pinion of power confluence stage

Zip, Zijs

Driving and driven gear of split torque stage

φD, φm, φB, φo

Torsional displacement of input, Zm, ZB and output

φif, φip, φijs, φijh

Torsional displacement of gear Zif, Zip, Zijs and Zijh

θip, θij, θiB, θB

Installation angle


R, L


1, 2


inmf, inpjs and inBjh



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


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Copyright information

© Krishtel eMaging Solutions Private Limited 2019

Authors and Affiliations

  1. 1.National Key Laboratory of Science and Technology on Helicopter TransmissionNanjing University of Aeronautics and AstronauticsNanjingChina

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