scholarly journals Rapid Evaluation for Position-Dependent Dynamics of a 3-DOF PKM Module

2014 ◽  
Vol 6 ◽  
pp. 238928 ◽  
Author(s):  
Hai-wei Luo ◽  
Hui Wang ◽  
Jun Zhang ◽  
Qi Li
Keyword(s):  
Natural Frequencies ◽  
Mode Shapes ◽  
Parallel Kinematic Machine ◽  
Computationally Efficient ◽  
Element Analysis ◽  
Reduction Techniques ◽  
Modal Reduction ◽  
Governing Differential Equation ◽  
Parallel Kinematic ◽  
Analytical System

Based on the substructure synthesis and modal reduction technique, a computationally efficient elastodynamic model for a fully flexible 3-RPS parallel kinematic machine (PKM) tool is proposed, in which the frequency response function (FRF) at the end of the tool can be obtained at any given position throughout its workspace. In the proposed elastodynamic model, the whole system is divided into a moving platform subsystem and three identical RPS limb subsystems, in which all joint compliances are included. The spherical joint and the revolute joint are treated as lumped virtual springs with equal stiffness; the platform is treated as a rigid body and the RPS limbs are modelled with modal reduction techniques. With the compatibility conditions at interfaces between the limbs and the platform, an analytical system governing differential equation is derived. Based on the derived model, the position-dependent dynamic characteristics such as natural frequencies, mode shapes, and FRFs of the 3-RPS PKM are simulated. The simulation results indicate that the distributions of natural frequencies throughout the workspace are strongly dependant on mechanism's configurations and demonstrate an axial-symmetric tendency. The following finite element analysis and modal tests both validate the analytical results of natural frequencies, mode shapes, and the FRFs.

A Comparison of Two Finite Element Reduction Techniques for Mistuned Bladed-Disks

2000 ◽  
Author(s):  
François Moyroud ◽  
Torsten Fransson ◽  
Georges Jacquet-Richardet
Keyword(s):  
Finite Element ◽  
Mode Shapes ◽  
Finite Element Models ◽  
Computationally Efficient ◽  
Bladed Disks ◽  
Mode Localization ◽  
Reduced Order ◽  
Bladed Disk ◽  
Reduction Techniques ◽  
Modal Reduction

The high performance bladed-disks used in today’s turbomachines must meet strict standards in terms of aeroelastic stability and resonant response level. One structural characteristic that can significantly impact on both these area is that of bladed-disk mistuning. To predict the effects of mistuning, computationally efficient methods are necessary to make it feasible, especially in an industrial environment, to perform free vibration and forced response analyses of full assembly finite element models. Due to the size of typical finite element models of industrial bladed-disks, efficient reduction techniques must be used to systematically produce reduced order models. The objective of this paper is to compare two prevalent reduction methods on representative test rotors, including a modern design industrial shrouded bladed-disk, in terms of accuracy (for frequencies and mode shapes), reduction order, computational efficiency, sensitivity to inter-sector elastic coupling, and ability to capture the phenomenon of mode localization. The first reduction technique employs a modal reduction approach with a modal basis consisting of mode shapes of the tuned bladed-disk which can be obtained from a classical cyclic symmetric modal analysis. The second reduction technique is based on a Craig and Bampton substructuring and reduction approach. The results show a perfect agreement between the two reduced order models and the non-reduced finite element model. It is found that the phenomena of mode localization is equally well predicted by the two reduction models. In terms of computational cost, reductions from 1 to 2 orders of magnitude are obtained for the industrial bladed-disk, with the modal reduction method being the most computationally efficient approach.

Nonstationary Vibration of a Fully Flexible Parallel Kinematic Machine

2007 ◽  
Vol 129 (5) ◽  
pp. 623-630 ◽  
Author(s):  
Zili Zhou ◽  
Chris K. Mechefske ◽  
Fengfeng Xi
Keyword(s):  
Natural Frequencies ◽  
Kinematic Model ◽  
Inertial Force ◽  
Mode Shapes ◽  
Absolute Amount ◽  
Hard Material ◽  
Parallel Kinematic Machine ◽  
Damping Matrix ◽  
Nonstationary Vibration ◽  
Parallel Kinematic

This paper studies the problem of the nonstationary vibration of a fully flexible parallel kinematic machine (PKM) that has flexibilities both in links and in joints. In the stationary case, the PKM was treated as a varying structure and the natural frequencies and mode shapes changed with the changes in the PKM configuration, without consideration of the PKM nominal motion. In the nonstationary case as studied in this paper, the nominal motion is included to investigate how it would affect the natural frequencies and mode shapes. To do so, a nonstationary model is developed using the elasto-dynamics method. First, a kinematic model is built based on rigid links and ideal joints, which is used to solve the PKM nominal motion. Second, the kinetic model is developed considering the flexibilities in the links and joints. In this case, the vibration equations would contain the Coriolis and gyroscopic damping matrix and the tangential and normal stiffening matrix, which are the terms resulting from the nominal motion. The instantaneous eigensolutions are obtained from the nonstationary eigenequations. The results show that (i) the slider velocity affects the instantaneous natural frequencies more than the slider acceleration; and (ii) the nominal motion has an effect on the system eigencharacteristics (e.g., the nonstationary frequencies can be higher or lower than the stationary ones) but the effect is small in an absolute amount (within 2.1Hz in natural frequencies presented at set nominal motions of the studied PKM prototype). This is because the extra inertial force from the nominal motion is always much smaller than the stiffness force in the system bodies as long as the bodies are made of hard material. The method presented is more convenient to use for the multibody system with flexible joints than other methods.

Characteristic Equation-Based Dynamic Analysis of a Three-Revolute Prismatic Spherical Parallel Kinematic Machine

2015 ◽  
Vol 10 (2) ◽  
Author(s):  
Jun Zhang ◽  
Jian S. Dai ◽  
Tian Huang
Keyword(s):  
Dynamic Model ◽  
Dynamic Characteristics ◽  
Natural Frequencies ◽  
Eigenvalue Decomposition ◽  
Mode Shapes ◽  
Design Parameters ◽  
Parallel Kinematic Machine ◽  
Characteristic Equations ◽  
Parallel Kinematic ◽  
Compliance Model

A three-revolute prismatic spherical (3-RPS) parallel kinematic machine (PKM) module is proposed as an alternative solution for high-speed machining (HSM) tool. Considering the PKM as a typical compliant parallel device, whose three limb assemblages have bending, extending, and torsional deflections, this paper applies screw theory to establish an analytical compliance model for the device. The developed compliance model is then combined with the energy method to deduce a comprehensive dynamic model of the 3-RPS module. The solution for the characteristic equations of the dynamic model leads to the modal properties of the PKM module. Based on the eigenvalue decomposition of the characteristic equations, a modal analysis is conducted. The natural frequencies and corresponding mode shapes at typical and nontypical configurations are analyzed and compared with finite element analysis (FEA) results. With an algorithm of workspace partitions combining with eigenvalue decompositions, the distributions of natural frequencies throughout the workspace are predicted to reveal a strong dependency of dynamic characteristics on mechanism's configurations. At the last stage, the effects of some design parameters on system dynamic characteristics are investigated with the purpose of providing useful information for the conceptual design and performance improvement for the PKM.

A Numerical Method for the Dynamic Analysis of Rotating Flexible Blade-Disc-Shaft Assemblies

1995 ◽  
Author(s):  
Georges Jacquet-Richardet ◽  
Guy Ferraris ◽  
Pierre Rieutord
Keyword(s):  
Finite Element Analysis ◽  
Numerical Method ◽  
Natural Frequencies ◽  
Mode Shapes ◽  
Rotating System ◽  
Dynamic Interactions ◽  
Element Analysis ◽  
Modal Reduction ◽  
Rotating Shafts

Abstract A numerical method is proposed to compute the natural frequencies and mode shapes of rotating flexible blade-disc-shaft assemblies The formulation is based on a modal finite element analysis of the rotating system. The mode shapes used for the modal reduction are those associated to the global non-rotating undamped structure. To compute these modes, the size of the problem is reduced using both wave propagation and component mode techniques. An application is presented. The results obtained show that the chosen reductions do not reduce the quality of the model and illustrate its capability to deal with rotating shafts usually calculated using the rotordynamic approach. Finally, the possible dynamic interactions between shaft and disc components are described.

scholarly journals NASTRAN Analysis of a Turbine Blade and Comparison With Test and Field Data

1975 ◽  
Author(s):  
J. M. Allen ◽  
L. B. Erickson
Keyword(s):  
Turbine Blade ◽  
Natural Frequencies ◽  
Beam Theory ◽  
Mode Shapes ◽  
Stress Distributions ◽  
Free Standing ◽  
Element Analysis ◽  
Metallographic Examination ◽  
Stiffening Effect ◽  
Generalized Beam Theory

A NASTRAN finite element analysis of a free standing gas turbine blade is presented. The analysis entails calculation of the first four natural frequencies, mode shapes, and relative vibratory stresses, as well as deflections and stresses due to centrifugal loading. The stiffening effect of the centrifugal force field was accounted for by using NASTRAN’s differential stiffness option. Natural frequencies measured in a rotating test correlated well with computed results. Areas of maximum vibratory stress (fundamental mode) coincided with the three zones of crack initiation observed in a metallographic examination of a fatigue failure. Airfoil stress distributions were found to be significantly different from that predicted by generalized beam theory, especially near the airfoil-platform junction.

Updating of Non-Conservative Systems Using Inverse Methods

1997 ◽  
Author(s):  
Ladislav Starek ◽  
Milos Musil ◽  
Daniel J. Inman
Keyword(s):  
Analytical Model ◽  
Degrees Of Freedom ◽  
Ad Hoc ◽  
Natural Frequencies ◽  
Eigenvalue Problems ◽  
Model Updating ◽  
Analytical Models ◽  
Mode Shapes ◽  
Element Analysis ◽  
Modal Data

Abstract Several incompatibilities exist between analytical models and experimentally obtained data for many systems. In particular finite element analysis (FEA) modeling often produces analytical modal data that does not agree with measured modal data from experimental modal analysis (EMA). These two methods account for the majority of activity in vibration modeling used in industry. The existence of these discrepancies has spanned the discipline of model updating as summarized in the review articles by Inman (1990), Imregun (1991), and Friswell (1995). In this situation the analytical model is characterized by a large number of degrees of freedom (and hence modes), ad hoc damping mechanisms and real eigenvectors (mode shapes). The FEM model produces a mass, damping and stiffness matrix which is numerically solved for modal data consisting of natural frequencies, mode shapes and damping ratios. Common practice is to compare this analytically generated modal data with natural frequencies, mode shapes and damping ratios obtained from EMA. The EMA data is characterized by a small number of modes, incomplete and complex mode shapes and non proportional damping. It is very common in practice for this experimentally obtained modal data to be in minor disagreement with the analytically derived modal data. The point of view taken is that the analytical model is in error and must be refined or corrected based on experimented data. The approach proposed here is to use the results of inverse eigenvalue problems to develop methods for model updating for damped systems. The inverse problem has been addressed by Lancaster and Maroulas (1987), Starek and Inman (1992,1993,1994,1997) and is summarized for undamped systems in the text by Gladwell (1986). There are many sophisticated model updating methods available. The purpose of this paper is to introduce using inverse eigenvalues calculated as a possible approach to solving the model updating problem. The approach is new and as such many of the practical and important issues of noise, incomplete data, etc. are not yet resolved. Hence, the method introduced here is only useful for low order lumped parameter models of the type used for machines rather than structures. In particular, it will be assumed that the entries and geometry of the lumped components is also known.

Investigation of stiffness of small wind turbine blade based on vibration analysis technique

2019 ◽  
Vol 44 (1) ◽  
pp. 49-59
Author(s):  
Nilesh Chandgude ◽  
Nitin Gadhave ◽  
Ganesh Taware ◽  
Nitin Patil
Keyword(s):  
Finite Element Analysis ◽  
Finite Element ◽  
Wind Turbine ◽  
Natural Frequency ◽  
Vibration Analysis ◽  
Natural Frequencies ◽  
Mode Shapes ◽  
Element Analysis ◽  
Finite Element Software ◽  
Small Wind Turbine

In this article, three small wind turbine blades of different materials were manufactured. Finite element analysis was carried out using finite element software ANSYS 14.5 on modeled blades of National Advisory Committee for Aeronautics 4412 airfoil profile. From finite element analysis, first, two flap-wise natural frequencies and mode shapes of three different blades are obtained. Experimental vibration analysis of manufactured blades was carried out using fast Fourier transform analyzer to find the first two flap-wise natural frequencies. Finally, the results obtained from the finite element analysis and experimental test of three blades are compared. Based on vibration analysis, we found that the natural frequency of glass fiber reinforced plastic blade reinforced with aluminum sheet metal (small) strips increases compared with the remaining blades. An increase in the natural frequency indicates an increase in the stiffness of blade.

The Use of Interference Diagrams to Avoid Impeller Resonance: An Application to IGV Design

2009 ◽  
Author(s):  
Marco Ferioli
Keyword(s):  
Centrifugal Compressor ◽  
Natural Frequencies ◽  
Mode Shapes ◽  
Common Source ◽  
Operating Speed ◽  
Element Analysis ◽  
Exciting Frequency ◽  
Combine Information ◽  
The Impact

Interference diagrams can be used to avoid the potential excitation of a particular mode of vibration for centrifugal compressor impellers, thus reducing the risk of fatigue failures. Such diagrams are an excellent tool to combine information on impeller natural frequencies and mode shapes, excitation sources and operating speed of the machine on the same graph. Once the impeller design has been finalized in terms of aerodynamic performance, structural assessments and therefore geometry, Finite Element Analysis can be used to predict its natural frequencies and mode shapes (i.e. nodal diameters). Results can therefore be shown on a chart, together with the operating speed range of the machine. The need to plot on a single diagram this whole set of data arises from the mathematical evidence to consider the frequency of vibration together with the mode shape and the shape of the exciting force, while analyzing resonances. Typical Campbell diagrams are unable to provide this information at a glance. A common source of excitation for the first impeller of centrifugal compressors is the IGV set. Inlet Guide Vanes produce an exciting frequency that is directly proportional to the number of vanes N, where N represents also the shape of the excitation. The interference diagram can therefore be used: • to design and optimize the IGV for a new machine; • to choose between two different designs; • to evaluate the impact of a new IGV for the impeller of an existing compressor. A case study will be introduced, in order to show the application of interference diagrams to avoid potentially dangerous resonances between an IGV set and the first impeller during the re-design phase for a centrifugal compressor already in operation.

Free Vibration Analysis of PZT Glide Heads

1999 ◽  
Vol 121 (4) ◽  
pp. 984-988 ◽  
Author(s):  
Alex Y. Tsay ◽  
Jin-Hui Ouyang ◽  
C.-P. Roger Ku ◽  
I. Y. Shen ◽  
David Kuo
Keyword(s):  
Finite Element Analysis ◽  
Finite Element ◽  
Natural Frequencies ◽  
Laser Doppler Vibrometer ◽  
Free Vibration Analysis ◽  
Mode Shapes ◽  
Element Analysis ◽  
The Finite Element Analysis ◽  
Bonding Length ◽  
Measured Displacement

This paper studies natural frequencies and mode shapes of a glide head with a piezoelectric transducer (PZT) through calibrated experiments and a finite element analysis. In the experiments, the PZT transducer served as an actuator exciting the glide head from 100 kHz to 1.3 MHz, and a laser Doppler vibrometer (LDV) measured displacement of the glide head at the inner or outer rail. The natural frequencies were measured through PZT impedance and frequency response functions from PZT to LDV. In the finite element analysis, the glide head was meshed by brick elements. The finite element results show that there are two types of vibration modes: slider modes and PZT modes. Only the slider modes are important to glide head applications. Moreover, natural frequencies predicted from the finite element analysis agree well with the experimental results within 5% of error. Finally, the finite element analysis identifies four critical slider dimensions whose tolerance will significantly vary the natural frequencies: PZT bonding length, wing thickness, slider thickness, and air bearing recess depth.

scholarly journals Model Updating of Friction Stir Welding for Aluminium and Magnesium Plate Structure

2018 ◽  
Vol 150 ◽  
pp. 04004 ◽  
Author(s):  
Nazrotul Afina Nazri ◽  
Mohd Shahrir Mohd Sani ◽  
Muhammad Nasiruddin Mansor ◽  
Siti Norazila Zahari
Keyword(s):  
Friction Stir Welding ◽  
Natural Frequencies ◽  
Model Updating ◽  
Mode Shapes ◽  
Average Error ◽  
Element Analysis ◽  
Structural Dynamic ◽  
Friction Stir ◽  
Dissimilar Friction Stir Welding ◽  
Al 7075

Friction stir welding (FSW) of aluminium and magnesium alloys face high demands in automotive and aerospace application due to its advanced and lightweight properties. FSW is an emerging solid state joining process in which the material that is being welded does not melt and recast. The main objectives of this project are to perform model updating based on finite element analysis (FEA) and experimental modal analysis (EMA) of dissimilar material of aluminium alloy AL 7075 and magnesium alloy AZ 31B. Modal properties such as natural frequencies, mode shapes are obtained and compared between FEA and EMA. The discrepancies of first five modes natural frequencies are below than 10% and the model updating have been conducted to minimize the error between two methods. This model updating are based on sensitivity analysis in order to make sure which parameters are given more influence in this structural dynamic analysis. Young’s modulus and Poisson’s ratio both materials are selected in the model updating process. After perform model updating, total average error of the natural frequencies of dissimilar friction stir welding plate is improved significantly.

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