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Nonlinear thermo-mechanic coupling effect of a dual-rotor system with an intershaft bearing

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Abstract

The nonlinear thermo-mechanic coupling effect refers to the interaction between the nonlinear dynamic characteristics of a dual-rotor system and the thermal effect of an intershaft bearing. In this paper, the nonlinear thermo-mechanic coupling effect of the dual-rotor system is proposed and studied by the operating radial clearance and dynamic load of the intershaft bearing. A nonlinear dynamic model of the dual-rotor system under the thermal effect of the intershaft bearing is established by considering nonlinear factors such as the Hertzian contact force and the operating radial clearance of the intershaft bearing. The dynamic load of the intershaft bearing is obtained based on the dynamic responses of the system. Based on this, a thermal effect model of the intershaft bearing considering the nonlinear dynamic characteristics of the system is proposed. The operating radial clearance of the intershaft bearing is attained according to the temperature field of the intershaft bearing. The thermo-mechanic coupling model of the dual-rotor system is presented by connecting the dynamic model and the thermal effect model. The results solved by numerical iteration show that the nonlinear dynamic characteristics of the dual-rotor system are deeply coupled with the thermal effect of the intershaft bearing, and become weaker. In turn, a complex nonlinear thermal effect affects the bearing due to the nonlinear dynamic characteristics of the system. Furthermore, the operating radial clearance of the intershaft bearing is closely related to the thermo-mechanic coupling effect of the system. The operating radial clearance decreases with increasing temperature, decreases with decreasing initial radial clearance, and decreases sharply in the resonance regions. Thus, the “negative clearance” may affect the operating radial clearance of the intershaft bearing, which endangers the operation of the rotor system. Moreover, the nonlinear characteristics of the thermo-mechanic coupling effect become stronger as the ambient temperature increases. The results presented in this paper provide insight into the mechanism of the nonlinear thermo-mechanic coupling effect and new theoretical guidances for the dynamic and thermodynamic design of the intershaft bearing in the dual-rotor system.

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All data generated or analyzed during this study are included in this published article.

Abbreviations

M :

The friction torque

Q :

The friction heat generation

T :

The temperature

ΔT :

The temperature rise

R :

The thermal resistance

f :

The friction coefficients of the bearing

d :

The diameter

D :

The diameter

r :

The radius

a r :

The length of the roller

B :

The width of the bearing

v :

The line speed

V :

The line speed

L :

The characteristic length

k steel :

Thermal conductivity of steel

c steel :

The specific heat capacity of steel

ν :

The viscosity of the lubricant

α :

The thermal diffusivity

A :

The area

Nu :

The Nusselt number

Re :

The Reynolds number

Pr :

The Prandtl number

Ta :

The Taylor number

Bi :

The Biot number

Pe :

The Peclet number

ω :

The rotation speed

λ :

The rotation speed ratio

F x :

The nonlinear restoring force of the intershaft bearing in the vertical direction

F y :

The nonlinear restoring force of the intershaft bearing in the horizontal direction

F b :

The dynamic load

x :

The translation displacement in the vertical direction

y :

The translation displacement in the horizontal direction

θ x :

The rotational angle of the LP rotor around the x-axis

θ y :

The rotational angle of the LP rotor around the y-axis

φ x :

The rotational angle of the HP rotor around the x-axis

φ y :

The rotational angle of the HP rotor around the y-axis

m :

The mass

J d :

The diameter rotational inertia

J p :

The polar rotational inertia

e :

The unbalance

k :

The stiffness coefficient of the support

c :

The damping coefficient of the support

δ ▪ :

The virtual displacement

θ k :

The angular location

l :

The length of rotors

n b :

The number of loaded rollers

N b :

The number of cylindrical rollers

K b :

The Hertz contact stiffness

ξ :

The linear thermal expansion coefficient

ε :

The radial thermal expansion

δ k :

The elastic deformation between the roller and raceways

δ 0 :

The initial radial clearance

δ t :

The operating radial clearance

Δω :

The bistable interval

ΔA:

The jump amplitude

ΔB:

The jump amplitude

ω A :

The resonance frequency

ω B :

The resonance frequency

r A :

The resonance peak

r B :

The resonance peak

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Acknowledgements

We acknowledge the financial support from the National Natural Science Foundation of China (Grant Nos. 11972129, 12102011, 12102084).

Funding

The funding was provided by the National Natural Science Foundation of China (Grant Nos. 11972129, 12102011, 12102084).

Author information

Authors and Affiliations

  1. School of Intelligent Manufacturing, Nanjing University of Science and Technology, Nanjing, 210094, People’s Republic of China

    Peng Gao

  2. Department of Mechanical and Automation Engineering, The Chinese University of Hong Kong, Shatin, New Territories, Hong Kong, People’s Republic of China

    Peng Gao

  3. Department of Mechanics, Tianjin University, Tianjin, 300354, People’s Republic of China

    Zhiyong Zhang

  4. Department of Mechanical Engineering, Beijing Technology and Business University, Beijing, 100048, People’s Republic of China

    Qiyi Dai

  5. School of Mechanical Engineering, Southwest Jiaotong University, Chengdu, 611756, People’s Republic of China

    Yulin Jin

  6. School of Astronautics, Harbin Institute of Technology, Harbin, 150001, People’s Republic of China

    Lei Hou & Yushu Chen

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  1. Peng Gao
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Correspondence to Peng Gao.

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Gao, P., Zhang, Z., Dai, Q. et al. Nonlinear thermo-mechanic coupling effect of a dual-rotor system with an intershaft bearing. Nonlinear Dyn 111, 15933–15953 (2023). https://doi.org/10.1007/s11071-023-08709-y

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