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A finite element model of the cantilever combined support rotor included two discs established in this paper to predict and explain the nonlinear vibration phenomenon. The model considered local nonlinear support force generated by the combined support and the coupling effects of the rotor with the combined support. The nonlinear factors contained the clearance, the Hertz contact force and the vibration of the rolling bearing and the nonlinear force of the squeeze film damper. The combined support included bearing, squeeze film damper and squirrel cage elastic support. Finally, the high-dimensional partial differential equations with local nonlinearity were derived and solved by Newmark- $$\upbeta $$ combined with Runge–Kutta method. Based on the above theoretical results, the bifurcation phenomenon of vibration response at different positions was analysed and the dynamic response of the rotor system at different positions due to the rotational speed was compared.

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.

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 designing the test model of thin-walled cylindrical shells, geometrically distorted models are widely used. This study investigates a method of designing a distorted cylindrical shell model by considering the strength requirement, which means the test model should reflect the strength situation or even failures of the prototype. The significance of this study is that it provides an acceptable process which guides the design of test models. First, governing equations are employed to derive the scaling law of the natural frequency. The harmonic response is calculated in order to obtain the scaling law of the vibration response amplitude. As the study is based on governing equations of elastic cylindrical shells, only elastic behavior is discussed. Then considering the different materials’ ultimate stress, an excitation force ratio is defined. An applicable size interval is investigated and the range of the excitation force is obtained. Finally, an aluminium alloy cylindrical shell is used as a prototype and a NO. 45 steel scaled down cylindrical shell is used as a distorted test model. The accuracy of the prediction is verified by using simulation data.

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.

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.

This study investigates a method of designing a simplified cylindrical shell model. This model accurately predicts the dynamic characteristics of a prototype cylindrical shell with sealing teeth accurately. The significance of this study is that it provides an acceptable process which guides the design of test models. Firstly, an equivalent cylindrical shell with rectangular rings is designed by combining the energy equation and numerical analysis. Then the transfer matrixes of the stiffened cylindrical shell and the cylindrical shell are employed to calculate the equivalent thickness of the simplified cylindrical shell commonly used in model tests. Further, the equivalent thicknesses are normalized by introducing an average equivalent thickness. The distorted scaling laws and size applicable intervals are investigated to reduce the errors caused by the normalization. Finally, a 42CrMo cylindrical shell with sealing teeth is used as a prototype and a number 45 steel scaled-down cylindrical shell is used as a distorted test model. The accuracy of the prediction is verified by using experimental data, and the results indicate that the distorted model can predict the characteristics of the stiffened cylindrical shell prototype with good accuracy.