Diagnostics of the presence of a fatigue crack in the compressor blade using the spectrum of vibration amplitudes at the superharmonic resonance

In this study, the solution of the forced vibration response of a structural element with a fatigue crack was carried out using the finite element method to determine the influence of its presence on the flexural forced vibration behaviour of the compressor blade airfoil at the superharmonic resonance of the order 1/2. The blade airfoil with a low twisted angle was used as an object of investigation to perform the computational analysis. Its vibrations in the plane of minimum stiffness were excited by the kinematic displacement of root edge elements. The fatigue crack was modelled as a mathematical cut. Two locations of the crack were investigated – on the leading edge and convex side of the blade airfoil. The nonlinearity due to the intermittent contact of the crack surfaces, which is caused by the opening and closing of the crack during each vibration cycle, was taken into account by solving the contact problem. To quantify this kind of nonlinear dynamic behaviour, the vibration diagnostic parameter was defined as the displacement amplitude ratio of the dominant harmonics at the superharmonic resonance of the order 1/2. Based on the results of the calculations it has been found that regardless of the crack location, the ratio nature is the same for all vibration axes. However, with vibrations in the plane of minimum stiffness, the crack on the convex side of the airfoil has an opening mode propagation, which makes it possible to fix its location due to a sharp change in the ratio of the amplitudes of the dominant harmonics along the corresponding axis.

Nonlinear Dynamics of Cutting Process considering Higher-Order Deformation of Composite Cutting Tool

In this paper, the nonlinear dynamic analysis of the cutting process of composite cutting tool is performed. The cutting tool is simplified to a nonplanar bending rotating shaft. The higher-order bending deformation, structural damping, and gyroscopic effect of cutting tool are considered. It is assumed that cutting tool is subjected to a regenerative two-dimensional cutting force containing the first and second harmonic components. Based on the Hamilton principle, the motion equation of nonlinear chatter of the cutting system is derived. The nonlinear ordinary differential equations in the generalized coordinates are obtained by Galerkin method. In order to analyze the nonlinear dynamic response of cutting process, the multiscale method is used to derive the analytical approximate solution of the forced response for the cutting system under periodic cutting forces. In the forced response analysis, four cases including primary resonance and superharmonic resonance, i.e., Ω ¯ = ω 1 , Ω ¯ = ω 2 , 2 Ω ¯ = ω 1 , and 2 Ω ¯ = ω 2 , are considered. The influences of ratio of length to diameter, structural damping, cutting force, and ply angle on primary resonance and superharmonic resonance are investigated. The results show that nonlinearity due to higher-order bending deformation significantly affects the dynamic behavior of the milling process and that the effective nonlinearity of the cutting system is of hard type. Multivalued resonance curves and jump phenomenon are presented. The influences of various factors, such as ratio of length to diameter, ply angle, structural damping, cutting force, and rotating speed, are thoroughly discussed.

VIBRATION DIAGNOSTICS OF FATIFUE DAMAGE IN STRUCTURAL ELEMENTS OF GAS TURBINE ENGINES AT THE REPAIR STAGE

Vibration diagnostics of damage belongs to the class of non-destructive methods, which usually do not take long time. However, the main problem of vibration diagnostics is relatively low sensitivity to the critical damage of fatigue crack type, which arises because of long time accumulation of plastic deformation. To improve the sensitivity and reliability of vibration diagnostics of damage two methods were considered. First method was based on the fact, that a characteristic feature of vibrations of structural elements with fatigue crack is the occurrence of non-linear resonances (sub- and super-harmonic) and significant non-linearity of vibration response at these resonances. Secon one – on the fact, that quite noticeable in certain cases increase of damping characteristic caused by a crack can be observed. Analytical and experimental studies of these methods were carried out as applied to the blades of aircraft gas turbine engines. As a result of the studies, the intensity of change in parameter of super-harmonic resonance and in damping characteristics at different parameters of crack was determined. Besides, the experimental techniques for vibration testing of turbine blades were developed. There was demonstrated, that the sensitivity of both considered methods of vibration diagnostics is several orders of magnitude higher than the sensitivity of conventional methods based on the change in natural frequencies and mode shapes, and they can be effectively used for the diagnostics of blades on the stage of engine repair. All the other conditions being equal, second-order superharmonic resonance demonstrates a higher sensitivity to the presence of cracks than the damping characteristic. The smallest crack with an area of 0.2% considered in the work causes a reliably recorded non-linearity of vibration response at superharmonic resonance of order of 2/1. At this the change of damping characteristic slightly exceeds the error of experiment.

Semi-numerical analysis of a two-stage series composite planetary transmission considering incremental harmonic balance and multi-scale perturbation methods

This study conducts an analytical investigation of the dynamic response characteristics of a two-stage series composite system (TsSCS) with a planetary transmission consisting of dual-power branches. An improved incremental harmonic balance (IHB) method, which solves the closed solution of incremental parameters passing through the singularity point of the analytical path, based on the arc length extension technique, is proposed. The results are compared with those of the numerical integration method to verify the feasibility and effectiveness of the improved method. Following that, the multi-scale perturbation (MsP) method is applied to the TsSCS proposed in this subject to analyze the parameter excitation and gap nonlinear equations and then to obtain the analytical frequency response functions including the fundamental, subharmonic, and superharmonic resonance responses. The frequency response equations of the primary resonance, subharmonic resonance, and superharmonic resonance are solved to generate the frequency response characteristic curves of the planetary gear system (PGS) in this method. A comparison between the results obtained by the MsP method and the numerical integration method proves that the former is ideal and credible in most regions. Considering the parameters of TsSCS excitation frequency and damping, the nonlinear response characteristics of steady-state motion are mutually converted. The effects of the time-varying parameters and the nonlinear deenthing caused by the gear teeth clearance on the amplitude–frequency characteristics of TsSCS components are studied in this special topic.

Applying System Dynamics of Discrete Supported Track to Analyze the Rail Corrugation Causation on Curved Urban Railway Tracks

Urban rail corrugation on curved tracks with small radii causes strong howling during operation, which has been bothering subway operating companies for many years. Therefore, revealing its causes and growth is important for the comfort and safety of subway operation. Current studies believe that the occurrence of rail corrugation is largely due to the resonant vibration of the wheel-rail system. However, little attention has been paid to the key causes of the track resonance and the practical prediction of the occurrence probability of rail corrugation on the certain track. This paper intends to solve these above issues. Firstly, the practical model of predicting the rail corrugation growth is proposed based on the wheel-rail coupling interaction, the key causes of corrugation are investigated, and the sensitivity analysis is carried out, while the corrugation superposition model is introduced to the analyze the corrugation evolution as well as to validate the corrugation growth from the aspect of material friction and wear. Secondly, the impact of the key causes on the initiation and development of the rail corrugation is investigated based on the cosimulation. Finally, case studies validate the proposed theory model and method. The results show that the practical prediction model for the rail corrugation growth proposed in this paper is able to estimate the occurrence possibility of rail corrugation on a specific track, and the superharmonic resonance of the track directly excited by passing vehicles eventually leads to rail corrugation. It is also found that shortwave corrugation develops more rapidly, and adjusting the support stiffness or sleeper spacing leads to fluctuations in the corrugation wavelength and its wear rate.