Search

This study investigates the determination approach of distorted scaling laws for predicting the dynamic characteristic of an aero engine’s blisk. Based on the dynamic scaling laws of typical thin-w...

A Jeffcott rotor system with surface coatings capable of describing the mechanical vibration resulting from unbalance and rub-impact is formulated in this article. A contact force model proposed recently to describe the impact force between the disc and casing with coatings is employed to do the dynamic analysis for the rotor system with rubbing fault. Due to the variation of penetration, the contact force model is correspondingly modified. Meanwhile, the Coulomb friction model is applied to simulate the friction characteristics. Then, the case study of rub-impact with surface coatings is simulated by the Runge-Kutta method, in which a linear interpolation method is adopted to predict the rubbing instant. Moreover, the dynamic characteristics of the rotor system with surface coatings are analyzed in terms of bifurcation plot, waveform, whirl orbit, Poincare map and spectrum plot. And the effects of the hardness of surface coatings on the response are investigated as well. Finally, compared with the classical models, the modified contact force model is shown to be more suitable to solve the rub-impact of aero-engine with surface coatings.

Similitude design plays a vital role in the analysis of vibration and shock problems encountered in large engineering equipment. Similitude design, including dimensional analysis and governing equation method, is founded on the dynamic similitude theory. This study reviews the application of similitude design methods in engineering practice and summarizes the major achievements of the dynamic similitude theory in structural vibration and shock problems in different fields, including marine structures, civil engineering structures, and large power equipment. This study also reviews the dynamic similitude design methods for thin-walled and composite material plates and shells, including the most recent work published by the authors. Structure sensitivity analysis is used to evaluate the scaling factors to attain accurate distorted scaling laws. Finally, this study discusses the existing problems and the potential of the dynamic similitude theory for the analysis of vibration and shock problems of structures.

A dual-rotor system dynamics model is established for simulating the aero-engine vibration with unbalance-partial rubbing coupled faults. The main characteristics of the dual-rotor model are as follows: (1) the compressor disc and turbine disc are considered in both low pressure rotor and high pressure rotor; (2) two eccentricities exist in the LP and HP turbine discs, respectively; (3) two convex points exist in the casing and then fixed-point rubbing may occur in the LP and HP turbine discs, respectively; (4) coatings are painted on the surfaces of all the discs and casing. Taking into account the soften characteristics of coatings, the Lankarani-Nikravesh model is used to describe the impact forces between two convex points and two turbine discs. Then, the case of two fixed-point rubbings is simulated by the Runge-Kutta method. At different rotational speeds, the responses of the dual-rotor system are analyzed by spectrum cascades and waveforms. Meanwhile, the effects of rotational speed ratio, initial clearance and curvature radius of convex point on the dynamic characteristics and impact force are discussed. Finally, the experiment performed on a dual-rotor test rig proves the validity of the dynamics model.

For theoretical and experimental research on the fixed point rubbing of aero-engine, a dual-rotor system capable of describing the mechanical vibration resulting from two imbalances and fixed point rubbing is established in this paper. Considering the effects of the softer coatings painted on the discs and casing, the Lankarani–Nikravesh model is applied to describe the impact force between the compressor disc of the low pressure rotor and the casing convex point. Meanwhile, the Coulomb model is used to simulate the frictional characteristics. Then the motion equations of the dual-rotor system with fixed point rubbing are solved by the Runge–Kutta method and the complicated responses at different rotational speeds are analyzed by the 3D waterfall plot, waveform and frequency spectrum. To verify the effectiveness of the dual-rotor system dynamic model, the experiment of fixed point rubbing is performed on a dual-rotor test rig. The vibration displacement of the low pressure rotor is obtained from the data measured in the impact experiment. The numerical results and experimental results indicate that for the dual-rotor system without rub-impact, the phenomena of beat vibration occur at the certain rotational speed ratio. Moreover, for the case of fixed point rubbing, several combination frequencies in the responses of the dual-rotor system are identified as the particular fault frequencies.

Rotor unbalance and rub-impact are major concerns in rotating machinery. In order to study the dynamic characteristics of these machinery faults, a dual-disc rotor system capable of describing the mechanical vibration resulting from multi-unbalances and multi-fixed-point rub-impact faults is formulated using Euler beam element. The Lankarani–Nikravesh model is used to describe the nonlinear impact forces between discs and casing convex points, and the Coulomb model is applied to simulate the frictional characteristics. To predict the moment of rub-impact happening, a linear interpolation method is carried out in the numerical simulation. The coupling equations are numerically solved using a combination of the linear interpolation method and the Runge–Kutta method. Then, the dynamic behaviours of the rotor system are analysed by the bifurcation diagram, whirl orbit, Poincare map and spectrum plot. The effects of rotating speed, phase difference of unbalances, convex point of casing and initial clearance on the responses are investigated in detail. The numerical results reveal that a variety of motion types are found, such as periodic, multi-periodic and quasi-periodic motions. Moreover, the energy transfer between the compressor disc and the turbine disc occurs in the multi-fixed-point rubbing faults. Compared with the parameters of the turbine disc, those of the compressor disc can affect the motion of the rotor system more significantly. That is, the responses exhibit simple 1T-periodic motion in the wide range of rotating speed under the conditions of sharp convex point and larger initial clearance. These forms of dynamic characteristics can be effectively used to diagnose the fixed-point rub-impact faults.

A novel hysteretic force model is proposed to describe the contact force for the impact analysis of the rotor blade and casing of an aero-engine in this article. Firstly, the structural stiffness of both the flexible blade and casing, as well as the local stiffness of coating painted on both the blade tip and casing are taken into consideration in the formulation of the impact stiffness. Moreover, energy loss during the process of impact is expressed by introducing the nonlinear hysteretic damping. Then, the hysteretic impact force model for both soft and hard coating is obtained. In order to estimate the values of parameters in the contact force model and show the effectiveness of the model, impact experiments are performed at different rotating speeds on a rotor test rig. The impact force and the displacement at the contact point are obtained from the data measured in the experiment. According to the theory of the least square method, the ranges of curvature radius and coefficient of restitution are given respectively. At different rotating speed in certain range, simulation results are compared with the actual experimental results to illustrate the validity and accuracy of the contact force model.

In the present study, a new method of predicting the dynamic behavior of a variable thickness (VT) cantilever plate by using a thin plate scaled model is proposed. The thin plate model, defined as the model thin (MT) plate, is designed by using the newly proposed similitude design method. The method is derived based on the transfer matrix of both the stepped thickness (ST) plate that is simplified by the VT plate and the thin plate. The thickness of the MT plate is calculated by introducing the equivalent thickness corresponding to each VT plate’s vibration modals, such that a series of accurate distorted scaling laws are provided to predict each corresponding property. Moreover, an algorithm of designing the MT plate is proposed and a design process is summarized in steps. Finally, an example, where the prototype VT plate is made of 42 CrMo and the MT plate is made of NO. 45 steel, is discussed to validate the proposed design method, showing that the MT plate, which is designed by using the proposed method, can accurately predict the dynamic properties of the prototype VT plate, and showing its significance in engineering practice.

This study investigates new dynamic scaling laws of geometrically distorted models in predicting the dynamic characteristics of a cantilever plate. The significance of this study is to provide new scaling laws and rules for selecting dynamic scaling laws, which guide the design of distorted models. By considering the size effect of different orders’ vibration, a governing equation and the method of sensitivity analysis are employed to establish dynamic scaling laws between the model and the prototype. Both approximate and accurate scaling laws are investigated and the processes for determining these scaling laws are summarized. After that, a commonly used titanium alloy plate is analyzed as a prototype to compare the accuracy of the approximate scaling laws and the accurate scaling laws. Finally, the applicability of these new scaling laws is validated by experimental data. The results indicate that, by using the new scaling laws, the distorted models can predict the characteristics of the titaniu...

For the applicability of dynamic similitude models of thin walled structures, such as engine blades, turbine discs, and cylindrical shells, the dynamic similitude design of typical thin walled structures is investigated. The governing equation of typical thin walled structures is firstly unified, which guides to establishing dynamic scaling laws of typical thin walled structures. Based on the governing equation, geometrically complete scaling law of the typical thin walled structure is derived. In order to determine accurate distorted scaling laws of typical thin walled structures, three principles are proposed and theoretically proved by combining the sensitivity analysis and governing equation. Taking the thin walled annular plate as an example, geometrically complete and distorted scaling laws can be obtained based on the principles of determining dynamic scaling laws. Furthermore, the previous five orders’ accurate distorted scaling laws of thin walled annular plates are presented and numerically validated. Finally, the effectiveness of the similitude design method is validated by experimental annular plates.