Contact analysis of a flexible bladed-rotor

doi:10.1016/j.euromechsol.2006.11.002

European Journal of Mechanics - A/Solids

Volume 26, Issue 3, May–June 2007, Pages 541-557

https://doi.org/10.1016/j.euromechsol.2006.11.002 Get rights and content

Abstract

This paper presents a model of fully flexible bladed rotor developed in the rotating frame. An energetic method is used to obtain the matrix equations of the dynamic behaviour of the system. The gyroscopic effects as well as the spin softening effects and the centrifugal stiffening effects, taken into account through a pre-stressed potential, are included in the model. In the rotating frame, the eigenvalues' imaginary parts of the latter matrix equation give the Campbell diagram of the system and its stability can be analysed through its associated eigenvalues' real parts. The turbo machine casing is also modelled by an elastic ring in the rotating frame through an energetic method. Thus, in some rotational speed ranges the contact problem between the rotor and the stator can be treated as a static problem since both structures are stationary to each other. Prior to the study of the complete problem of contact between the flexible blades of the rotor and the flexible casing, a simple model of an elastic ring having only one mode shape, excited by rotating loads is developed in the rotating frame too, in order to underline divergence instabilities and mode couplings. Then, the complete problem of frictionless sliding contact between the blades and the casing, without rubbing, is studied. The stable balanced static contact configurations of the structure are found as function of the rotational speed of the rotor. Finally, the results are compared to these of the simple model of rotating spring-masses on an elastic ring, showing good adequacy. The present model of rotor appears thus particularly adapted to the study of blades-casing contacts and highlighted an unstable phenomenon near the stator critical speed even in case of frictionless sliding.

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Aiming at the phenomenon that blade bending deformation and coating wear are rarely considered in existing rubbing force models, a blade-casing rubbing model based on the Archard wear model was established in this paper. First, the bending deformation of the blade was deduced according to the torque balance relationship, the equivalent deformation of the coated casing was analysed using the equivalent stiffness method, and the clearance between the blade and casing was calculated with the consideration of coating wear based on the Archard model. Second, the influences of the casing stiffness, blade size, and Young's modulus of the coating on the rubbing force were analysed and compared with the existing rubbing force models. Subsequently, a rubbing force characterisation test bench was built considering the AlSi-polyester coating. A strain gauge was used to analyse the blade deformation, the rubbing force was compensated based on the acceleration sensor, and a grating displacement sensor was used to measure the penetration depth, which made the relative error between the experimental and simulation results was less than 15%. Finally, the rubbing force model was applied to the rotor–blade–casing system, and the influence of coating and coating wear on the dynamic characteristics of the rotor system is analyzed. The results show that the model proposed in this paper is more suitable for the rub-impact faults of the elastic blade with an abradable coating on the casing surface. The rubbing force model considering the coating wear is beneficial to accurately predict the rubbing force.
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Citation Excerpt :
However, more rubbing types need to be further studied. A rotor–blade–casing model with six blades was established by Lesaffre et al. [26,27], their study found that blades involved in rubbing were different at different speeds, however, no further research was done on the rubbing process. Wang et al. [28,29] established a finite element model of the dual-rotor–blade–casing system considering the intermediary bearing and gyro torque and analyzed the vibration characteristics of the rotor and casing.
Rubbing is a common phenomenon in aero engines. Serious rubbing will cause failure, and even lead to accidents. Blade–casing rubbing is complicated, the rubbing process, rubbing positions, and rubbing forms are important factors to describe the rubbing of blade and casing. The details of these problems are lacking in published works. This paper aims to gain insight into the process and characteristics of blades participating in rubbing and propose an experimental method for quantitatively judging the blades with rub-impact faults. Firstly, a rotor–blade–casing dynamic model with the consideration of the flexibility of blades is established. After that, using Poincaré sections and bifurcation diagrams of the rotor, the influence of the number of blades involved in rubbing on the motion behavior of the rotor is discussed. Then, the process of the blades participating in the rubbing, the rubbing forms, and rubbing positions under the speed-up condition are analyzed. Besides, the influence of the gravity of the system on the rubbing process and the motion state of the rotor is analyzed. Finally, a test rig with four blades is built. Based on the strain signals of four blades, an evaluation index that can quantitatively judge the blades involved in rubbing is defined to verify the complex rubbing process. The results show that the rubbing between blades and casing will undergo complex rubbing forms; different forms of rubbing have different rubbing parts; the number of blades involved in rubbing will affect the motion behavior and the smooth operation of the rotor system. This research can provide some reference for rubbing fault diagnosis in engineering.
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In a gas turbine, the multistage bladed drum rotor often operates under high time-varying ambient temperature. Thermal deformations of the thin drum could lead to the rub-impact fault between multistage blade rows and the outer casing, which may cause damage to the blades or even the whole machine. Due to the complexity of the thermoelastic coupling solution, rub-impact characteristics of this kind of rotor system are not clear. This study develops a multistage bladed drum rotor model with the rub-impact fault induced by high time-varying temperature. A solution process for the thermoelastic dynamics analysis of the multistage bladed drum rotor system is proposed, combining experimental, numerical, and analytical methods. According to temperature characteristics in a gas turbine, the effect of the high-temperature environment, heating, fluctuating temperature rise, and cooling on the rub-impact fault is the main emphasis of the study. The high-temperature environment could cause a rub-impact fault for the multistage bladed drum rotor. The sudden increase of the exhaust temperature leads to paroxysmal vibrations, which could induce tip rub or make a slight rub-impact fault into a severe accident. Large fluctuation during temperature rise induces the rub-impact fault and even leads to the continuous aggravation of the rub-impact fault. Fortunately, reducing an appropriate exhaust temperature can eliminate or weaken the rub-impact fault and avoid shock vibrations induced by the sudden drop of the high ambient temperature at the same time. Besides, more blade rows could aggravate this kind of rub-impact phenomenon for the multistage bladed drum rotor.
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This article focuses on the stability assessment of mechanical systems featuring a nonlinear interface on which are applied unilateral contact constraints. The regularized-Lanczos harmonic balance method is used to compute periodic solutions for each system. For each considered mechanical system, the implementation of distinct stability assessment numerical algorithms (including the Newmark $2 n$ -pass method and Hill’s method using eigenvalue sorting) relying on Floquet theory allows for an in-depth investigation of their convergence and accuracy. From a single-degree of freedom impactor impacting a fixed obstacle to the industrial finite element model of a transonic compressor blade impacting a deformed casing, the gradually increasing complexity of the considered mechanical systems provides new insight on which stability assessment numerical algorithm may be the best suited when dealing with contact nonlinearities. From a numerical standpoint, attention is paid to specific developments that were identified as key for enhancing the numerical efficiency of the stability assessment process including the iterative solver, the computation of analytical derivatives, the scaling of the problem and the use of fast Fourier transforms. Particular attention is also paid to the influence of the Lanczos filtering procedure and its implications in terms of stability assessment. While it is found that both the Newmark $2 n$ -pass method and Hill’s method with eigenvalue sorting can be successfully applied on large industrial systems featuring a nonlinear interface, the faster convergence of Hill’s method is underlined and suggests it may be a better option for an accurate and efficient stability assessment on which Lanczos filtering has a negligible influence.
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To achieve the objective, it is necessary to establish the disk-shaft-blade model with tip-rub. Lesaffre [3] simplified a full set of flexible blades to Euler–Bernoulli beams to investigate the rubbing dynamics of a flexible bladed-rotor. Using uniform cantilever beams.
In turbo-machinery, wide-chord blades are widely used due to the advantages of improving fan efficiency and aerodynamic performance. The rotor with multiple wide-chord blades is spaced from the outer casing. The small clearance may cause rub-impact fault between wide-chord blades and the casing, which induces different damage severity or the destruction of the whole machine. Numerical simulation is necessary to analyze this kind of rub-impact fault, but the solution process becomes complicated because of the coupling of geometric nonlinearity, local vibrations of wide-chord blades and gyroscopic motion of the rotor. This paper develops a rubbing rotor model with multiple wide-chord blades considering the gyroscopic effect and geometric nonlinearity induced by rub-impact. Based on the rub-impact model established for wide-chord blades, the high-order nonlinear governing equations of the bladed rotor are derived. Vibration responses are solved, and a series of dynamic characteristic analysis is carried out. The results reveal that high-order nonlinearity has a little effort on vibrations during slight rub-impact. But with the increase of transverse deformation induced by severe tip-rub, its influence cannot be ignored. Besides, localized rub-impact phenomenon of blades induced by external synchronous forces is found. Instead, external asynchronous force makes all blades rub, one after another along the circumferential direction of the disk, and there is a phase difference $Δ φ = 2 π / [(Ω \pm ω) N_{b}]$ between the vibration responses of adjacent blades. Then, we found that the swing motion intensifies the difference of transverse deformations along the chord direction of wide-chord blades with tip-rub, which may induce the edge failures. Also, the swing motion intensifies the steady rub-impact fault. It could weaken or eliminate its divergence and instability when the rotor with multiple wide-chord blades is unstable. The gyroscopic effect could weaken the swing motion, and then weakens the stable rub-impact fault.

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Contact analysis of a flexible bladed-rotor

Abstract

Journal of Sound and Vibration

Journal of Sound and Vibration

Chaos Solitons & Fractals

Chaos Solitons & Fractals

Wear

Wear

Journal of Sound and Vibration

Journal of Sound and Vibration

Journal of Sound and Vibration

Turbomachinery Rotordynamics: Phenomena, Modelling and Analysis

Rotordynamics

Resonant whirling of aircraft propeller-engine systems

Journal of Applied Mechanics

Handbook of Rotordynamics