The Coupling Vibration Mechanism of Bearing Installation Misalignment and Rub-Impact in Supercritical Shaft Systems
Academic Background
With the increasing demand for high-speed and lightweight design in the aviation industry, more and more aviation transmission shaft systems have adopted supercritical design. Supercritical design means that the drive shaft must cross its first critical speed, but when crossing the critical speed, the shaft system will produce severe vibration due to imbalance, seriously affecting the safe operation of the system. The dry friction damper effectively limits the vibration amplitude at critical speed through rub-impact between the shaft and the damper. However, the shaft system inevitably faces bearing installation misalignment caused by processing, manufacturing, assembly, and other errors. The coupling effect of bearing installation misalignment and rub-impact may threaten the safe operation of the supercritical shaft system. Therefore, clarifying the coupling vibration mechanism of bearing installation misalignment and rub-impact is of great practical significance for the dynamic design of supercritical shaft systems.
Existing research has not considered the change in rub-impact clearance caused by bearing installation misalignment, resulting in an incomplete understanding of the coupling vibration mechanism. Therefore, this paper establishes a coupling geometric model of bearing installation misalignment and rub-impact, derives the six-degree-of-freedom (6-DOF) rub-impact excitation force, builds a dynamic model of the supercritical shaft system, and reveals the coupling vibration mechanism of bearing installation misalignment and rub-impact. The accuracy of the model is verified through experiments.
Source of the Paper
This paper was co-authored by Chao Zhang, Meijun Liao, Yixi She, Hu Yu, Xiaoyu Che, Liyao Song, Rupeng Zhu, Weifang Chen, and Dan Wang. The authors are from the National Key Laboratory of Science and Technology on Helicopter Transmission at Nanjing University of Aeronautics and Astronautics and the AECC Hunan Aviation Powerplant Research Institute. The paper was accepted on February 13, 2025, and published in the journal Nonlinear Dynamics.
Research Process
1. Dynamic Modeling
a) System Finite Element Model
The supercritical shaft system studied in this paper consists of a spline coupling, shaft, dry friction damper, support, diaphragm group, and other components. The dry friction damper is used to limit the excessive amplitude of the shaft when crossing the critical speed, while the diaphragm group is the main component of the diaphragm coupling, providing flexibility to compensate for misalignment. Based on the structural characteristics of the shaft system, this paper establishes a finite element model of the system and sets nodes at the installation and connection positions of each component as well as at positions of sudden changes in shaft size.
b) Coupling Geometric Model
To describe the misalignment caused by bearing installation misalignment, this paper establishes a coupling geometric model of bearing installation misalignment and rub-impact. The model assumes that the width of the dry friction damper is much smaller than the length of the shaft, thus ignoring variations in misalignment and rub-impact force along the width direction of the dry friction damper. Through this model, the changes in misalignment angle and rub-impact clearance are derived.
c) Bearing Installation Misalignment Excitation Force
The misalignment angle of the diaphragm group introduces misalignment excitation force. This paper establishes a coupling coordinate system and derives the additional reaction forces and moments of the diaphragm group. These forces and moments are applied as periodic loads on the rotating shaft.
d) Rub-Impact Excitation Force
The dry friction damper consists of a rubbing ring, pre-pressing spring, friction washer, shim, bolt, nut, support, and other components. When the shaft system crosses the critical speed, the shaft collides with the rubbing ring, introducing friction damping force. This paper analyzes the mechanism of rub-impact force and derives the expression for rub-impact excitation force.
e) System Dynamic Equation
Based on the rotor dynamic finite element method, this paper assembles the characteristic matrices of the shaft, spline coupling, bearing, and diaphragm group to obtain the mass matrix, stiffness matrix, and gyroscopic matrix of the shaft system. By applying unbalanced excitation force, bearing installation misalignment excitation force, and rub-impact excitation force, the dynamic equation of the supercritical shaft system is established.
2. Results and Discussion
a) Vibration Mechanism of Bearing Installation Misalignment
By analyzing the impact of bearing installation misalignment on the dynamic characteristics of the system, this paper finds that bearing installation misalignment introduces high-order harmonic components, causing the axis trajectory to no longer be regular and stimulating super-harmonic resonance phenomena in the shaft system.
b) Vibration Mechanism of Rub-Impact
Rub-impact significantly increases the critical speed of the shaft system and excites rub-impact frequency components. The rub-impact force reduces the whirling range of the axis trajectory and introduces bending-torsion coupling and bending-axis coupling effects.
c) Coupling Vibration Mechanism of Bearing Installation Misalignment and Rub-Impact
Bearing installation misalignment reduces the rub-impact clearance, increases the rub-impact force, leads to a larger rub-impact range, and may even cause backward whirling, thereby weakening the vibration reduction performance of the dry friction damper. Bearing installation misalignment causes the axis trajectory to deviate with a deflection angle approximately equal to the arctangent of the vertical misalignment and horizontal misalignment, which can be used to analyze the form of bearing installation misalignment.
3. Experimental Verification
To verify the accuracy of the dynamic model of the supercritical shaft system established in this paper, the authors built a dynamic experimental bench and conducted experimental validation. The experimental results show good agreement with the theoretical model, confirming the accuracy of the model.
Research Conclusions
By establishing a coupling geometric model of bearing installation misalignment and rub-impact, deriving the six-degree-of-freedom rub-impact excitation force, and building a dynamic model of the supercritical shaft system, this paper reveals the coupling vibration mechanism of bearing installation misalignment and rub-impact. The accuracy of the model is verified through experiments. The research results indicate that bearing installation misalignment reduces the rub-impact clearance, increases the rub-impact force, leads to a larger rub-impact range, and may even cause backward whirling, thereby weakening the vibration reduction performance of the dry friction damper. The analysis method proposed in this paper provides theoretical and technical support for the dynamic design of supercritical shaft systems.
Research Highlights
- Proposal of the Coupling Geometric Model: This paper is the first to propose a coupling geometric model of bearing installation misalignment and rub-impact, considering the change in rub-impact clearance, providing a new perspective for understanding the coupling vibration mechanism.
- Derivation of Six-Degree-of-Freedom Rub-Impact Excitation Force: This paper derives the six-degree-of-freedom rub-impact excitation force, providing a theoretical foundation for the dynamic modeling of supercritical shaft systems.
- Experimental Verification: This paper validates the accuracy of the dynamic model by building a dynamic experimental bench, providing reliable theoretical support for practical engineering applications.
Research Significance
The research results of this paper not only deepen the understanding of the coupling vibration mechanism of bearing installation misalignment and rub-impact but also provide theoretical basis and technical support for the dynamic design of supercritical shaft systems. This research is of great significance for improving the safety and reliability of aviation transmission shaft systems and also provides new ideas and methods for research in related fields.