Skip to main content
SpringerLink
Log in

Dynamic Analysis of Planetary Gear Transmission System Considering the Flexibility of Internal Ring Gear

  • Research Paper
  • Published:
Iranian Journal of Science and Technology, Transactions of Mechanical Engineering Aims and scope Submit manuscript

Abstract

A rigid-flexible coupled dynamic model of the planetary gear transmission system was developed considering the flexibility of the internal ring gear (flexible internal ring gear) and the sun shaft based on the shell theory and Timoshenko beam theory, respectively. For the dynamic modeling, the time-varying meshing stiffness and static transmission error excitations were considered and the Runge–Kutta numerical algorithm was applied to calculate the dynamic response. The results indicate that the flexibility of internal ring gear sharply decreases the dynamic factor between the internal ring gear and the planet gear, and it also shows significant positive influences on the system load-sharing performance. For the fixed internal ring gear, the maximum stress is located on the midpoint along the axial direction. The maximum dynamic deformations appear at the ends of the tooth surface along width direction, and the dynamic deformation shows a decremental trend from the tooth top edge to the tooth root edge. The load-sharing coefficient decreases rapidly with the increase in the thickness, as the support stiffness is small. The misalignment of one of the planet pins and various static transmission errors have a negative influence on the load-sharing coefficient of the planetary gear transmission system.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Fig. 1
Fig. 2
Fig. 3
Fig. 4
Fig. 5
Fig. 6
Fig. 7
Fig. 8
Fig. 9
Fig. 10
Fig. 11
Fig. 12

Similar content being viewed by others

Abbreviations

M :

Mass

C d :

Damping

K :

Stiffness

α :

Pressure angle

β :

Helical angle

e :

Static transmission error

e:

Natural constant

X :

Displacement

A, B, C :

Fourier expanded coefficients

U v :

Elastic strain energy

P sp :

Potential energy

T :

Kinetic energy

ρ :

Density

E :

Young’s modulus

μ :

Poisson’s ratio

R 0 :

Addendum circle radius of the ring gear

R 1 :

Outer radius of the ring gear

B :

Tooth with of the ring gear

x, θ, r :

Cylindrical coordinates in the axial, circumferential and radial directions

h :

Thickness of the ring gear

\( \bar{r} \) :

\( \bar{r} = r - R_{0} \)

u, v, w :

Displacement components

U, V, W :

Robust form of the Fourier series expansions

δ :

Equivalent displacement

ω :

Natural frequency

b:

Base circle

c:

Carrier

i :

Ordinal number

je:

Pitch circle

p:

Planet gear

r:

Ring gear

s:

Sun gear

l, g, q :

Supplement coefficient

References

  • Abousleiman V, Velex P (2006) A hybrid 3D finite element/lumped parameter model for quasi-static and dynamic analyses of planetary/epicyclic gear sets. Mech Mach Theory 41(6):725–748

    MATH  Google Scholar 

  • Abousleiman V, Velex P, Becquerelle S (2007) Modeling of spur and helical gear planetary drives with flexible ring gears and planet carriers. J Mech Des 129(1):95–106

    Google Scholar 

  • Ambarisha VK, Parker RG (2006) Suppression of planet mode response in planetary gear dynamics through mesh phasing. J Vib Acoust 128(2):133–142

    Google Scholar 

  • Ambarisha VK, Parker RG (2007) Nonlinear dynamics of planetary gears using analytical and finite element models. J Sound Vib 302(3):577–595

    Google Scholar 

  • Cervantes-Sánchez JJ, Rico-Martínez JM (2009) Simulation of planetary gear trains, modeling and numerical validation. Proc Inst Mech Eng K J Multibody Dyn 223:53–71

    Google Scholar 

  • Chen ZG, Shao YM, Su DZ (2013) Dynamic simulation of planetary gear set with flexible spur ring gear. J Sound Vib 332(26):7191–7204

    Google Scholar 

  • Chen SY, Tang JY, Li YP et al (2016) Rotordynamics analysis of a double-helical gear transmission system. Meccanica 51(1):251–268

    MathSciNet  MATH  Google Scholar 

  • Cooley CG, Parker RG (2014a) Vibration of high-speed rotating rings coupled to space-fixed stiffnesses. J Sound Vib 333(12):2631–2648

    Google Scholar 

  • Cooley CG, Parker RG (2014b) A review of planetary and epicyclic gear dynamics and vibrations research. Appl Mech Rev 66(4):040804

    Google Scholar 

  • Cooley CG, Parker RG (2015) Limitations of an inextensible model for the vibration of high-speed rotating elastic rings with attached space-fixed discrete stiffnesses. Eur J Mech A Solids 54:187–197

    MathSciNet  MATH  Google Scholar 

  • Erkaya S, Su Ş, Uzmay İ (2007) Dynamic analysis of a slider–crank mechanism with eccentric connector and planetary gears. Mech Mach Theory 42(4):393–408

    MATH  Google Scholar 

  • Gawande S, Kokare DK (2017) Experimental investigations of vibration reduction in spur gear pair by method of phasing. J Vib Eng Technol 5(6):13

    Google Scholar 

  • Gawande SH, Shaikh SN (2014) Experimental investigations of noise control in planetary gear set by phasing. J Eng 2014:1–11

    Google Scholar 

  • Guo Y, Parker RG (2010) Sensitivity of general compound planetary gear natural frequencies and vibration modes to model parameters. J Vib Acoust 132(1):647–670

    Google Scholar 

  • Guo Y, Keller J, Parker RG (2014) Nonlinear dynamics and stability of wind turbine planetary gear sets under gravity effects. Eur J Mech A Solids 47:45–57

    Google Scholar 

  • Helsen J, Vanhollebeke F, De Coninck F et al (2011) Insights in wind turbine drive train dynamics gathered by validating advanced models on a newly developed 13.2 MW dynamically controlled test-rig. Mechatronics 21(4):737–752

    Google Scholar 

  • Helsen J, Peeters P, Vanslambrouck K et al (2014) The dynamic behavior induced by different wind turbine gearbox suspension methods assessed by means of the flexible multibody technique. Renewable Energy 69:336–346

    Google Scholar 

  • Liu CG, Cooley CG, Parker RG (2017) Parametric instability of spinning elastic rings excited by fluctuating space-fixed stiffnesses. J Sound Vib 400:533–549

    Google Scholar 

  • Parker RG, Wu X (2010) Vibration modes of planetary gears with unequally spaced planets and an elastic ring gear. J Sound Vib 329(11):2265–2275

    Google Scholar 

  • Parker RG, Wu XH (2012) Parametric instability of planetary gears having elastic continuum ring gears. J Vib Acoust 134(4):1–11

    Google Scholar 

  • Qiu XH, Han QK, Chu FL (2015) Load-sharing characteristics of planetary gear transmission in horizontal axis wind turbines. Mech Mach Theory 92:391–406

    Google Scholar 

  • Sun T, Hu HY (2003) Nonlinear dynamics of a planetary gear system with multiple clearances. Mech Mach Theory 38(12):1371–1390

    MATH  Google Scholar 

  • Sun W, Li X, Wei J et al (2015) A study on load-sharing structure of multi-stage planetary transmission system. J Mech Sci Technol 29(4):1501–1511

    Google Scholar 

  • Wang SY, Huo MN, Zhang C et al (2011) Effect of mesh phase on wave vibration of spur planetary ring gear. Eur J Mech A Solids 30(6):820–827

    MATH  Google Scholar 

  • Wei S, Zhao JS, Han QK et al (2015) Dynamic response analysis on torsional vibrations of wind turbine geared transmission system with uncertainty. Renewable Energy 78:60–67

    Google Scholar 

  • Wu XH (2010) Vibration of planetary gears having an elastic continuum ring gear dissertation. Ph.D. thesis, Ohio State University, USA

  • Ye TG, Jin GY, Shi SX et al (2014) Three-dimensional free vibration analysis of thick cylindrical shells with general end conditions and resting on elastic foundations. Int J Mech Sci 84:120–137

    Google Scholar 

  • Yi PX, Zhang C, Guo LJ et al (2015) Dynamic modeling and analysis of load sharing characteristics of wind turbine gearbox. Adv Mech Eng 7(3):1–16

    Google Scholar 

  • Zhai HF, Zhu CC, Song CS et al (2015) Dynamic modeling and analysis for transmission system of high-power wind turbine gearbox. J Mech Sci Technol 29(10):4073–4082

    Google Scholar 

  • Zhai HF, Zhu CC, Song CS et al (2016) Influences of carrier assembly errors on the dynamic characteristics for wind turbine gearbox. Mech Mach Theory 103:138–147

    Google Scholar 

  • Zhang J, Liu XZ (2014) Multibody dynamic modeling and analysis for a helical planetary gear train. J Vib Shock 33(7):11–17

    Google Scholar 

  • Zhu CC, Xu XY, Liu HJ et al (2014) Research on dynamical characteristics of wind turbine gearboxes with flexible pins. Renewable Energy 68(7):724–732

    Google Scholar 

  • Zhu CC, Chen S, Song CS et al (2015) Dynamic analysis of a megawatt wind turbine drive train. J Mech Sci Technol 29(5):1913–1919

    Google Scholar 

Download references

Acknowledgements

The authors appreciate the financial support from the National Natural Science Foundation of China (Grant Nos. 51405043, 51575060) and Chongqing Innovation Program (Nos. cstc2015zdcy-ztzx70010, cstc2015zdcy-ztzx70012).

Author information

Authors and Affiliations

  1. The State Key Laboratory of Mechanical Transmissions, Chongqing University, Chongqing, 400044, China

    Zhixin Fan, Caichao Zhu & Chaosheng Song

Authors
  1. Zhixin Fan
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Caichao Zhu
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Chaosheng Song
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Caichao Zhu.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Fan, Z., Zhu, C. & Song, C. Dynamic Analysis of Planetary Gear Transmission System Considering the Flexibility of Internal Ring Gear. Iran J Sci Technol Trans Mech Eng 44, 695–706 (2020). https://doi.org/10.1007/s40997-019-00290-3

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s40997-019-00290-3

Keywords

Search

Navigation