An improved rotor-blade dynamic model is developed based on our previous works (Ma et al. in J Sound Vib, 337:301–320, 2015; J Sound Vib 357:168–194, 2015). In the proposed model, the shaft is discretized using a finite element method and the effects of the swing of the rigid disk and stagger angles of the blades are considered. Furthermore, the mode shapes of rotor-blade systems can be obtained based on the proposed model. The proposed model is more accurate than our previous model, and it is also verified by comparing the natural frequencies obtained from the proposed model with those from the finite element model and published literature. By simplifying the casing as a two degrees of freedom model, the single- and four-blade rubbings are studied using numerical simulation and experiment. Results show that for both the single- and four-blade rubbings, amplitude amplification phenomena can be observed when the multiple frequencies of the rotational frequency $$(f_\mathrm{r})$$
 coincide with the conical and torsional natural frequencies of the rotor-blade system, natural frequencies of the casing and the bending natural frequencies of the blades. In addition, for the four-blade rubbing, the blade passing frequency (BPF, $$4f_\mathrm{r})$$
 and its multiple frequency components also have larger amplitudes, especially, when they coincide with the natural frequencies of the rotor-blade system or casing; the four-blade rubbing levels are related to the rotor whirl, and the most severe rubbing happens on the blade located at the right end of the whirl orbit.

Nonlinear vibration response analysis of a rotor-blade system with blade-tip rubbing

Blade–casing interaction/rubbing can occur under the small blade-tip clearance, which may lead to the rubbing damage, excessive wear of the abradable coating, and efficiency loss caused by the increasing tip leakage flow. Moreover, the rubbing process involves complicated dynamic phenomena, such as friction-induced wear and heat, coupling vibration of the blade and elastic casing, which has recently received a great concern. This paper provides a review on the dynamic characteristics of blade, rotor, and casing as well as the mechanism of coating wear when the rubbing between the blade and bare or coating casing occurs. Firstly, the modeling methods for blade–casing rubbing are categorized into three types in accordance with different casing types, namely models for the rubbing between the blade and bare casing, models for the rubbing between the blade and coating casing without considering wear, and models for the rubbing between the blade and coating casing considering wear. Then, the simulated blade–casing dynamic characteristics due to rubbing are described for both bare and coating casings. After that, the experimental results of the blade–casing rubbing are reviewed and summarized for the bare and coating casings, respectively. Finally, the open problems for blade–casing rubbings are stated, and some recommendations for future research are also pointed out.

A review on dynamic characteristics of blade–casing rubbing

A cyclic sector corresponding to blade-disk structure with dovetail connection (1/38 blade-disk) is studied and the finite element (FE) model of this structure is established based on ANSYS software. A revised normal rubbing force model is developed and a pulse force model is established to simulate the local rubbing phenomenon between the blade and elastic casing based on the revised model. The effects of the rubbing under different rotating speeds and penetration depths on the blade vibration response and contact behaviors of dovetail interface are analyzed. The results show that the rubbing will cause amplitude amplification phenomenon when the multiple frequency components are close to the first bending and first torsion natural frequencies. The arch bending of the blade caused by blade-tip rubbing can be identified by evaluating the displacement and stress of the blade in the radial direction (y-direction). The dynamic stress in the process of rubbing gradually changes from alternation between tensio...

Vibration response analysis of blade-disk dovetail structure under blade tip rubbing condition

A dynamic model for simulating rubbing between blade and flexible casing

The rotor–stator rubbing in rotating machinery generated as a consequence of rotor imbalance, shaft misalignment, and casing deformation is a potential threat to the machinery that seriously affects its performance. Timely prediction and correction of the rubbing are essential for the prolonged life of the machinery and its overall performance. A complete understanding of the system behavior during interaction is a great challenge for researchers working in the field of rotor dynamics. Rubbing phenomena involve complex contact nonlinearities and associated thermal effects, which makes the analysis very difficult. Research works in this field are started with the analysis of simple two degree-of-freedom models and now dealing with extensive three-dimensional finite element models. This paper provides a comprehensive review of different numerical models of rotor–stator rubbing with respect to their ability in simulating the actual response characteristics. A detailed description of contact modeling is also presented with the advantages and disadvantages of each model. Different methods for solving the numerical models are briefly explained. In addition, a commentary on different emerging techniques of rub identification is also reported. Finally, some informed recommendations on future directions are made by stating what lacks in the current research activities.

The numerical modeling of rotor–stator rubbing in rotating machinery: a comprehensive review

Based on finite element (FE) method, a dynamic model of a single span blade-rotor-casing coupling system is established. The bearings, bladed rotor, discs and casing are simulated using spring-damping element, beam element, shell element and beam element suitable for curved beam separately (the casing stiffness and damping using spring-damping element). The blade-casing rub-impact is simulated using point-point contact elements; here the corresponding nodes of the blades and the casing are identified as the contact points. To deal with contact constraint conditions and simulate blade-casing frictional characteristics, the augmented Lagrangian method and the coulomb friction model are adopted, respectively. The responses of the system are analyzed under two loading conditions by using variable-step Newmark-β integral method combined with Newton-Raphson iteration. The results show that the rub-impact at the second critical speed (case 2) is more serious than that at the first critical speed (case 1). 4× (× denotes the rotating frequency) and its edge frequency components, combination frequency components about 1× can be viewed as distinguishable rub-impact features for cases 1 and 2, respectively. Results can provide theoretical basis for rub-impact diagnosis in blade-rotor-casing coupling systems.

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Hui Ma

Papers

Numerical research on rub-impact fault in a blade-rotor-casing coupling system