SAFE Diagram Research Articles

Modeling and dynamic analysis of a full flexible shaft–disk–blades system with nonlinear energy sinks (NESs) using modified SAFE diagram

Modeling and dynamic analysis of a full flexible shaft–disk–blades system with nonlinear energy sinks (NESs) using modified SAFE diagram

Modal Verification and Strength Analysis of Bladed Rotors of Turbine in Rated Working Conditions

The Top-pressure Recovery Turbine (TRT) uses the blast furnace gas generated in the iron and steel manufacturing process to push the turbine which drives the generator to generate electricity, and the generated electric energy is supplied to in-plant equipment. In this paper, we investigate the aerodynamic force, centrifugal force, and maximum stress on the structure of the TRT rotor in rated working conditions and the positions of occurrence using the Finite Element Method (FEM), as well as discuss the dynamic characteristics of bladed disks during TRT operation through Campbell and SAFE diagrams. To confirm the effectiveness of the finite element models, the mode shapes and natural frequencies in the FEA-based modal analysis of the TRT rotor will be captured and compared with those of the practical structures through the Experimented Modal Analysis (EMA). To verify the agreement between the mode shapes of the finite element analysis and those of the actual structure, the Modal Assurance Criterion (MAC) is introduced here to confirm the reliability of the finite element model. The stress distribution on the structure in the rotation is obtained by centrifugal force analysis. The TRT rotor is driven as the blast furnace top pressure pushes the moving blade; when the rotor rotates, the moving blade bears centrifugal and periodic aerodynamic forces. The stress distribution is investigated on the structure when these forces act simultaneously using aerodynamic analysis. To discuss whether the bladed disks will resonate with the external force under the operating conditions, Campbell and SAFE diagrams are used for evaluation, and the modal parameters obtained from the EMA are used to estimate the strength and durability of the blades. According to the analysis results when the TRT rotor is in working conditions, the fatigue failure may occur at the maximum stress existing on the dovetail slot.

A novel modal vibration reduction of a disk-blades of a turbine using nonlinear energy sinks on the disk

This study evaluates the application of nonlinear energy sinks (NESs), mounted on the disk of a real packeted bladed disk, for an indirect passive vibration attenuation of blades. To this end, the finite element analysis is used to extract the natural modes and SAFE diagram. The cyclic symmetry property reduces the size of the system to the degrees of freedom (DOFs) in a sector containing only one packet and a disk slice. In addition, a 2-DOF reduced order model (ROM) is obtained for the two first modes of the bladed disk. The NES with an essential nonlinear stiffness and a linear damping is added to this ROM to suppress the blades vibration. Then, theoretical and numerical analyses are followed by employing the perturbation and Runge-Kutta methods to solve the system motion equations. Finally, the occurrence of Saddle-Node (SN) and Hopf bifurcations and responses like periodic and strongly modulated responses are surveyed. The results demonstrate a good performance of NESs at the second nodal diameter (ND) of the first mode due to a strong coupling between blades and the disk in out-of-plane modes and a poor performance at the second mode due to a weak coupling in in-plane ones.

Determination of fracture parameter and prediction of structural fracture using various concrete specimen types

Concrete tensile strength and fracture toughness are two important material constants that should be independent of specimen size, geometry or type. In this study, on the basis of the improved boundary effect model, independent tensile strength and fracture toughness of concrete, which are unaffected by the specimen type, were determined by using various specimens, e.g., three-point-bending and wedge-splitting specimens. The concrete structural failure was fully predicted using independent material constants, and the constructed safe design diagrams with upper and lower limits (±15%) can cover all experimental results. The theoretical minimum size of the concrete meeting the linear elastic fracture mechanics were quantified, and the peak loads of concrete specimens were predicted using various average fictitious crack growth length.

Automated Experimental Modal Analysis of Bladed Wheels with an Anthropomorphic Robotic Station

Experimental modal analysis is challenging when the component has a highly three-dimensional shape, since a great number of measurement points are needed with accurate positioning. An anthropomorphic robotic station is proposed to automate this analysis, specifically on bladed wheels. This provides a reliable control of the spot location and of the beam orientation of a Laser Doppler Vibrometer. The modal frequencies were obtained along with the vibrational shapes and their spatial resolution was managed by exploiting the programming flexibility of the robotic station. The SAFE diagram was easily obtained by measuring a single point for each sector, and an extension of this diagram was demonstrated for the splitter blade wheels. The use of multiple measurement points, for each wheel sector, significantly improved the characterization of the modes having the same number of nodal diameters, hence the same shape coordinate on the SAFE diagram.

Research on the Rotor of a Ducted Fan Propulsion System of MOSUPS Aircraft Taking into Account Self-Balance during Operation

The work concerns the research of a propulsion system for an unmanned aerial vehicle MOSUPS in joined wing configuration. Modeling, analysis and experimental research of a statically unbalanced rotor of a ducted fan propulsion system has been conducted.The aim of the analysis was to determine the critical rotational speeds of the rotor due to the probable excitation of oscillations. Due to the complex geometry, Finite Element Method has been used for the calculations. In the study, the critical frequencies (and also rotational speeds) of the rotor as well as precessional instability, flexibly mounted in the bearings have been calculated. Campbell and SAFE diagrams have been presented.Furthermore, the paper presents the idea for a device for automatic dynamic balancing of the mentioned rotor. A mechanism for changing the position of the correction weights has been developed, allowing for a long term operation of rotating parts without the need to stop the unit and correcting the unbalance.The main motivation for work was to fully understand the working conditions of the propulsion system and dynamic properties of the rotor in order to carry out a proper assessment of their impact on the safe operation of the aircraft.

3D MODELING AND DYNAMIC CHARECTARIZATION OF STEAM TURBINE PACKET BLADE AND CYCLIC SYMMETRIC ANALYSIS

A rotating turbine blade (bucket) is the component, which converts the kinetic energy of the flowing fluid into mechanical energy. Thus the reliability of these blades is very important for the successful operation of a turbine. Turbine blades experience fluctuating forces when they pass through non-uniform fluid flow from the stationary vanes. The basic design consideration is to avoid or to minimize the dynamic stresses produced by the fluctuating forces. The aim of the project is to estimate the stresses occurring in the packet blade of steam turbine in last stage due to centrifugal forces and steam bending forces. The blade, root and disc are modeled separately in ANSYS package and they are assembled using constrained equations. After giving the constrain equations cyclic symmetric analysis conditions are applied and then static and model analysis are carried out. After that Campbell and safe diagrams are plotted.

The times they are a‐changin’: time to change glaucoma management

The times they are a‐changin’: time to change glaucoma management

노즐 분사력에 의해 가진되는 다중 패킷 블레이드계의 과도 진동 해석

A modeling method for the modal and the transient vibration analysis of a multi-packet blade system excited by nozzle jet forces is presented in this paper. Blades are idealized as cantilever beams and the elastic structures like disc and shroud connecting blades are modeled as coupling stiffnesses. A modified Campbell diagram is proposed to identify true resonance frequencies of the multi-packet blade system. Different from the SAFE diagram that employs three dimensional space, the modified Campbell diagram Proposed in this study employs a plane to find the true resonance frequencies. To verify the existence of true resonance frequencies, nozzle jet forces are modeled as periodic forces and transient vibration analysis were performed with the modeling method.

Reliability Evaluation of Shrouded Blading Using the SAFE Interference Diagram

The SAFE Interference Diagram is shown to be useful in the design reliability evaluation of shrouded blading, including long-arc shrouding construction. This method provides an alternate method to the widely used Campbell diagram and also brings in more information for easier design evaluation. The SAFE diagram uses the natural frequencies of an entire bladed disk rather than individual blade or packet frequencies. In addition, it compares frequencies, mode shapes, and speed to evaluate whether a resonance occurs. Theoretical arguments are provided for the validity of the SAFE Diagram and its usefulness is shown by practical examples. This method provides an easier means to show why long-arc shrouding works and also when it might not.