Natural Frequencies and Modes Shapes of Two Mistuned Bladed Discs on the Shaft (original) (raw)

Natural frequencies of tuned and mistuned bladed discs on a shaft

The dynamic behaviour of a rotor consisting of two tuned and mistuned bladed discs on a solid shaft is considered. The effect of the shaft's flexibility on the dynamic characteristics of the bladed discs and the coupling effects between the shaft and bladed disc modes are investigated. Results show clearly the coupling effects in a bladed disc-shaft system. Interference diagrams are developed, from which the dynamic behaviour of a bladed disc can be predicted for varying flexibility relationships between solid shafts and bladed discs. The global rotating mode shapes of flexible tuned and mistuned bladed disc-shaft assemblies are calculated. Rotational effects, such as centrifugal stiffening, are accounted for and all the possible couplings between the flexible parts are allowed. Calculated natural frequencies obtained from the blade, the bladed disc and the shaft with two discs are checked to discover resonance conditions and coupling effects. It is shown that blade mistuning st...

Multistage coupling of eight mistuned bladed discs on a solid shaft with 1% mistuning

Mechanics and Mechanical Engineering, 2011

Considered here was the effect of multistage coupling on the dynamics of a rotor consisting of eight mistuned bladed discs on a solid shaft. Free and forced vibrations were examined. In this study, the global rotating mode shapes of flexible mistuned bladed discs–shaft assemblies were calculated, taking into account rotational effects, such as centrifugal stiffening. The thus obtained natural frequencies of the blade, the shaft, the bladed disc, and the entire shaft with discs were carefully examined to discover resonance conditions and coupling effects.

Multistage Coupling of Eight Bladed Discs on a Solid Shaft

Volume 6: Structures and Dynamics, Parts A and B, 2010

Considered here was the effect of multistage coupling on the dynamics of a rotor consisting of eight bladed discs on a solid shaft. Each bladed disc had a different number of rotor blades. Free vibrations were examined using finite element representations of rotating single blades, bladed discs, and the entire rotor. In this study, the global rotating mode shapes of flexible tuned bladed discs-shaft assemblies were calculated, taking into account rotational effects, such as centrifugal stiffening. The thus obtained natural frequencies of the blade, the shaft, the bladed disc, and the entire shaft with discs were carefully examined to discover resonance conditions and coupling effects. This study found that the flexible modes of the tuned bladed discs affected by shaft motion were those with zero, one and two nodal diameters. In these modes the shaft deflection was clearly visible. In forced vibration analysis a different EO excitation was applied for each stage. Comparisons of forced analysis were carried out both in the real life situation, where the eight bladed discs have a different numbers of rotor blades on each disc, and also in the case of a simplified model where the number of rotor blades is the same on each disc.

The Assumed Mode Method in Structural Dynamics of Bladed-Disk-Shaft Systems

Volume 5: Manufacturing Materials and Metallurgy; Ceramics; Structures and Dynamics; Controls, Diagnostics and Instrumentation; General, 1990

Analytical investigation into the effect of transverse bending of continuous flexible shafts is presented. While the blades are allowed both in-plane and out-ofplane deformations, the considered disk is rigid, and the shaft is allowed to bend in two planes. The assumed mode method is used to express flexible blade and shaft deformations, and the Lagrangian approach is used to derive the governing equations of motion for the considered structure. Stiffness and inertia properties of an actual experimental rotor, typical of a fan stage, are used in the analysis. Calculations are performed for three different disk-shaft configurations, and results are presented for different shaft stiffness and inertia parameters, as well as for a wide range of rotational speed. NOMENCLATURE a n (t),b n (t) Generalized coordinates used to describe shaft's flexible deformation. (EI) x ,(EI) y Bending rigidity of the shaft along the X and Y directions. I bd Mass moment of inertia for the bladed-disk. Kb Modal stiffness of the blade, associated with the fundamental blade bending mode. KM Ratio of the shaft's mass to the mass of the bladed-disk. KS Ratio of the shaft's length to the radius of blade tip. Mbd Mass of the bladed-disk. M O P) Modal mass of the shaft.

GT-2006-90158 Forced Vibration of Several Bladed Discs on the Shaft

The effect of multistage coupling on the dynamics of a rotor consisting of eight bladed discs on a solid shaft is considered. Free vibrations are examined using finite element representations of rotating single blades, bladed discs, and the complete rotor. In this study, the global rotating mode shapes of flexible tuned bladed discs-shaft assemblies are calculated. Rotational effects, such as centrifugal stiffening are accounted for. The calculated natural frequencies obtained from the blade, the shaft, the bladed disc, and the complete shaft with discs are carefully examined to discover resonance conditions and the coupling effects. It was found that the flexible modes of the tuned bladed discs affected by shaft motion are those with zero, one and two nodal diameters. In these modes the shaft deflection is clearly visible. Different EO excitation is applied for particular stages in forced vibration analysis.

The Influence of Shaft’s Bending on the Coupling Vibration of a Flexible Blade-Rotor System

Mathematical Problems in Engineering, 2017

The influence of shaft bending on the coupling vibration of rotor-blades system is nonignorable. Therefore, this paper analyzed the influence of shaft bending on the coupling vibration of rotor-blades system. The vibration mode function of shaft under elastic supporting condition was also derived to ensure accuracy of the model as well. The influence of the number of blades, the position of disk, and the support stiffness of shaft on critical speed of system was analyzed. The numerical results show that there were two categories of coupling mode shapes which belong to a set where the blade's first two modes predominate in the system: shaft-blade (SB) mode and interblade (BB) mode due to the coupling between blade and shaft. The BB mode was of repeated frequencies of (− 2) multiplicity for number blades, and the SB mode was of repeated frequencies of (2) multiplicity for number blades. What is more, with the increase of the number of blades, natural frequency of rotor was decreasing linearly, that of BB mode was constant, and that of SB mode was increasing linearly. Natural frequency of BB mode was not affected while that of rotor and SB mode was affected (changed symmetrically with the center of shaft) by the position of disk. In the end, vibration characteristics of coupling mode shapes were analyzed.

Free vibrations analysis of shrouded bladed discs with one loose blade

2006

Abstract: As a failure of rotor blades in a gas turbine was reported, the rotating-mode shapes of flexible shrouded bladed disc assemblies were calculated using a finite element approach. Rotational effects, such as centrifugal stiffening were accounted for, and all couplings between the flexible parts were allowed. The spin softening effects were neglected. A dynamic analysis of the shrouded bladed disc demonstrated that it was designed with a sufficient safety region of resonance. In case of one blade getting loose, it is vibrating in resonance.

Study on the Coupled Vibration Characteristics of a Two-Stage Bladed Disk Rotor System

Applied Sciences, 2021

This paper conducts a coupled vibration analysis of a two-stage bladed disk rotor system. According to the finite element method, the bladed disk rotor system is established. The substructure modal synthesis super-element method (SMSM) with a fixed interface and free interface is presented to obtain the vibration behaviors of the rotor system. Then, the free vibration results are compared with the ones calculated by the cyclic symmetry analysis method to validate the analysis in this paper. The results show that the modes of the two-stage bladed disk not only include the modes of the first- and second-stage bladed disk, but also the coupled modes of the two-stage bladed disk.

Dynamic Response Predictions of Tuned and Mistuned Bladed Discs Using Finite Element Method

The power production of any country plays a vital role in its economy. One such promising power production methods is by means of gas turbines. The effects of random blade mistuning on the dynamics of advanced industrial turbine rotor, using a finite element formulation for tuned and mistuned bladed discs are studied. The technique uses modal data obtained from finite element model to create computationally in expensive models of mistuned bladed disc in a systematic manner.

Shaft flexibility effects on the forced response of a bladed-disk assembly

Journal of Sound and Vibration, 1990

A modal analysis approach is used to study the forced response of an actual flexible bladed-disk-shaft system. Both in-plane and out-of-plane flexible deformations of the bladed-disk assembly are considered, in addition to its rigid-body translations and rotations, resulting from the bending of the supporting flexible shaft in two orthogonal planes. The effects of Coriolis forces and structural coupling between flexible and rigid disk motions on the system's response are investigated. Aerodynamic loads acting on the rotating and vibrating bladed-disk assembly are accounted for through a simple quasisteady representation, to evaluate their influence, combined with shaft flexibility and Coriolis effects.