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Dynamic analysis of the variable stiffness support rotor system with elastic rings


Elastic rings are common rotor supporting structure, which have been widely used in aeroengine rotor support system. However, large inertia force and gyroscopic moment may occur during the operation of aeroengine, which may lead to contact between elastic ring and bearing pedestal, and then introduce variable stiffness into the rotor support system. In this paper, a mathematical model of variable stiffness of elastic ring is proposed and this model is subsequently verified by comparison with simulation analysis and experimental results. Based on this model, a variable stiffness model of an elastic ring-supported rotor is developed by coupling the kinetic equations of the rotor with the deformation of the combined support. Then, the spectrum cascades are used to analyze the dynamic characteristics of the rotor system. In addition, the influences of the variable stiffness of elastic ring on the critical speed of the system are also examined. Finally, some simulation results are verified by experiments on a combined test bench of an elastic ring-supported rotor.

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Data availability

Data will be made available on reasonable request.


x, y :

Displacements in x and y directions

e :


U i :

Displacement of inner bulges

i :

The ith inner bulge

n :

Number of rotor nodes

I :

Moment of inertia

E :

Elastic modulus

L :

Length of the ring section

b :

Width of the ring

h :

Thickness of the ring

F x, F y :

Force of each ring segment in the x and y directions

K 1 :

Linear segment of the elastic ring

K 2 :

Contact stiffness of the elastic ring

ΔR :

Radius difference between bearing pedestal and elastic ring

h min :

Minimum wall thickness of bearing pedestal

K er :

Variable stiffness of elastic ring

k b :

Stiffness of bearing

k sq :

Stiffness of squirrel cage

m i, m o :

Mass of the inner and outer race of the bearing

u s, u d :

Displacement vector of the shaft, displacement vector of the disk

Q s, Q d :

Excitation vector of the shaft, excitation vector of the disk

\( \boldsymbol{M}_{T}^{S},\boldsymbol{M}_{R}^{S}\) :

Translating inertial matrix of beam element, rotating inertial matrix of beam element

G s, \( \boldsymbol{K}_{B}^{S}\) :

Gyroscopic moment matrix of beam element, stiffness matrix of beam element

\( \boldsymbol{M}_{T}^{d}\), M d R, G d :

Translating inertial matrix of disk element, rotating inertial matrix of disk element, gyroscopic moment matrix of disk element

M r, G r :

Mass matrix of rotor substructure, gyroscopic matrix of rotor substructure

K r, C :

Stiffness matrix of rotor substructure, damping matrix of rotor substructure

F e, F b, F g :

Unbalance vector, bearing force vector, gravity vector

f n 1, f n 2 :

First and second natural frequency of the rotor system

ξ 1, ξ 2 :

First and second modal damping ratios

k B, k sq :

Contact stiffness of bearing, stiffness of squirrel cage

r 0, N b, θ j :

Bearing clearance, number of ball elements, angle location

x r, x o, y r, y o :

Translation of shaft and outer rings of the bearing along the x- and y-axes

w c :

Angular velocity of the cage

R b, r b :

Radius of outer race, radius of inner race

n sq, b sq, h sq, L sq :

Number of cage strips, section width of cage strips, section height of cage strips, length of cage strips

f er x, f er y :

Elastic ring force in the x and y directions

f sq x, f sq y :

Squirrel cage force in the x and y directions

F sq, F er, F b :

Squirrel cage force vector, elastic ring force vector, bearing force vector


Height of the outer bulge

α :

Angle between inner and outer bulge

λ :


δ :

Depth of the contact


Rotational speed


Finite element


Degrees of freedom


Elastic rings


Elastic ring squeeze film damper


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This work was supported by the National Natural Science Foundation of China [Grant Numbers 11872148, U1908217]; The Basic and Applied Basic Research Fund of Guangdong Province [Grant Numbers 2020B1515120015].

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Authors and Affiliations



KS investigated the article, summarized the concepts and methods, wrote the original draft, and verified it with the corresponding software. ZL wrote, reviewed, and edited the article, and provided supervision and analysis. LL carried out software verification and visualization of the article, and managed the data. JL carried out software verification and visualization of the article. FW carried out software verification and visualization of the article.

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Correspondence to Zhong Luo.

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Sun, K., Luo, Z., Li, L. et al. Dynamic analysis of the variable stiffness support rotor system with elastic rings. Nonlinear Dyn (2022).

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  • Variable stiffness
  • Elastic ring
  • Mathematical model
  • Dynamic characteristics
  • Experimental verification