scholarly journals Vibration and Stability of a Spinning Disk in Contact With Evenly-Spaced Stationary Load Systems

1998 ◽  
Vol 120 (1) ◽  
pp. 301-302
Author(s):  
Jen-San Chen ◽  
Cheng-Chou Wong
Keyword(s):  
Finite Element ◽  
Natural Frequency ◽  
Critical Speed ◽  
Complex Conjugate ◽  
Element Calculation ◽  
Modal Interactions ◽  
Reflected Wave ◽  
Spinning Disk ◽  
Divergence Instability ◽  
The Difference

The titled problem is studied numerically by finite element calculation. Attention is focused on the behavior of modal interactions when two modes are almost degenerate. In the case when the difference between the numbers of nodal diameters of these two modes is equal to a multiple of the number of the stationary load systems, the frequency loci may merge together (when one of these two modes is a reflected wave) or veer away (when both modes are non-reflected). Otherwise, the natural frequency loci simply cross each other and no instability is induced. When a backward wave meets its complex conjugate at the critical speed, it is found that divergence instability is induced when two times the number of nodal diameters is equal to a multiple of the number of stationary springs.

scholarly journals Divergence Instability of a Spinning Disk With Axial Spindle Displacement in Contact With Evenly Spaced Stationary Springs

1995 ◽  
Vol 62 (2) ◽  
pp. 544-547 ◽  
Author(s):  
Jen-San Chen ◽  
Cheng-Chou Wong
Keyword(s):  
Finite Element ◽  
Eigenfunction Expansion ◽  
Coupled System ◽  
Finite Element Calculation ◽  
Element Calculation ◽  
Spinning Disk ◽  
Divergence Instability

The titled problem is studied numerically by finite element calculation and analytically by three-mode eigenfunction expansion. It is found that divergence instability of the coupled system is induced only when two times the number of nodal diameters 2n is equal to a multiple of the number of stationary springs N, but n itself is not a multiple of N.

Vibration and Stability of a Spinning Disk Under Stationary Distributed Edge Loads

1996 ◽  
Vol 63 (2) ◽  
pp. 439-444 ◽  
Author(s):  
Jen-San Chen
Keyword(s):  
Natural Frequency ◽  
Natural Frequencies ◽  
Modal Interaction ◽  
Reflected Waves ◽  
Reflected Wave ◽  
Nonzero Integer ◽  
Spinning Disk ◽  
The Difference

The vibration and stability of a spinning disk under conservative distributed edge tractions are studied both numerically and analytically. The edge traction is circumferentially stationary in the space. When the compressive traction is uniform, it is found that no modal interaction occurs and the natural frequencies of all nonreflected waves decrease, while the natural frequencies of the reflected waves increase. When the spinning disk is under distributed traction in the form of cos kθ, where k is a nonzero integer, it is found that the eigenvalue only changes slightly under the edge traction if the natural frequency of interest is well separated from others. When two modes are almost degenerate, however, modal interaction may or may not occur. It is observed that when the difference between the number of nodal diameters of these two modes is equal to ±k, frequency veering occurs when both modes are nonreflected, and merging occurs when one of these two modes is a reflected wave. In applying this rule, the number of nodal diameters of the forward and the reflected wave is considered as negative.

scholarly journals Effect of Torsional Element towards High-Speed Rotating Shaft’s Critical Speed at Different Boundary Conditions

2019 ◽  
Vol 8 (4) ◽  
pp. 6787-6792
Keyword(s):  
Finite Element ◽  
Boundary Conditions ◽  
High Speed ◽  
Critical Speed ◽  
Element Model ◽  
Accurate Estimation ◽  
Fe Model ◽  
Rotating Shaft ◽  
Different Boundary Conditions ◽  
The Difference

Efficiency improvement that can be provided by the high-speed rotating equipment becomes a concern for designers nowadays. Since the high-speed rotating machinery was capable of rotating at very near to critical speed, the accurate estimation of critical speed needs to be considered. This paper investigated the effect of torsional element towards critical speed of high-speed rotating shaft system for pinned-pinned (P-P), clamped-free (C-F) and clamped-free (C-F) boundaries condition. The Nelson’s finite element model that considers the torsional effect was developed for formulating the finite element (FE) model. This FE model was used to derive Mathieu-Hill’s equation and then solved by applying the Bolotin’s theory. From the solution, the Campbell’s diagram of the high-speed shaft was plotted. It was found that torsional motion has significant effect on the critical speed for different boundary conditions. The difference between critical speed of 4DOF and 5DOF models can be as high as 6.91 %.

Research on Vibration Characteristics and Fault Diagnosis of 34CrMo1 Generator with Poor Heat Treatment

2019 ◽  
Vol 893 ◽  
pp. 27-32
Author(s):  
Qing Meng Zeng ◽  
Bao Tong Chai ◽  
Hao Chen
Keyword(s):  
Heat Treatment ◽  
Finite Element ◽  
Fault Diagnosis ◽  
Manufacturing Process ◽  
Critical Speed ◽  
Treatment Process ◽  
Original Data ◽  
First Order ◽  
Response Characteristics ◽  
The Difference

Poor heat treatment of the generator may cause cracks during operation. The presence ofcracks on the rotor causes the rotor to vibrate. The paper establishes a finite element modeling of aunit. The model is used to study the vibration response characteristics of the shafting system when thesupport characteristics of the generator are similar and the difference is significant. When thedifference in support characteristics between the two ends of the generator is large, the first-orderunbalance of the generator not only causes a large in-phase vibration at the first-order critical speed ofthe generator, but also causes a large reverse component. Finally, the reliability of the conclusion isfurther verified by combining the abnormal vibration diagnosis and processing cases of a generator.The innovation of the paper is to diagnose the possible cracks in the generator through the vibration ofthe generator, and then look at the original data in the generator manufacturing process to find that theheat treatment process of the generator rotor is poor.

scholarly journals Stability Analysis of a Spinning Elastic Disk Under a Stationary Concentrated Edge Load

1994 ◽  
Vol 61 (4) ◽  
pp. 788-792 ◽  
Author(s):  
Jen-San Chen
Keyword(s):  
Stability Analysis ◽  
Traveling Waves ◽  
Critical Speed ◽  
Natural Frequencies ◽  
Transverse Component ◽  
Membrane Stress ◽  
Reflected Wave ◽  
Spinning Disk ◽  
Elastic Disk ◽  
Stationary Type

The natural frequencies and stability of a spinning elastic disk subjected to a stationary concentrated edge load are investigated both numerically and analytically. It is found that a stationary, conservative, compressive edge load decreases the natural frequencies of the forward and backward traveling waves, but increases the natural frequency of the so-called reflected wave. It is also found that the significance of the effect of the conservative edge load on the natural frequencies and stability of the spinning disk is solely through the transverse component of the edge load on the boundary, and not through the membrane stress field it produces inside the disk. In addition, the compressive edge load induces a stationary-type instability before the critical speed, and induces a merged-type instability after the critical speed when a reflected wave meets a forward or a backward wave. The expression for the derivative of the eigenvalues of the spinning disk with respect to the edge load is derived to verify the numerical results.

scholarly journals A New Mixed Functional-probabilistic Approach for Finite Element Accuracy

2020 ◽  
Vol 20 (4) ◽  
pp. 799-813
Author(s):  
Joël Chaskalovic ◽  
Franck Assous
Keyword(s):  
Finite Element ◽  
Finite Elements ◽  
Asymptotic Relation ◽  
Probabilistic Approach ◽  
Random Variable ◽  
High Order ◽  
Relative Accuracy ◽  
The Difference ◽  
New Perspective

AbstractThe aim of this paper is to provide a new perspective on finite element accuracy. Starting from a geometrical reading of the Bramble–Hilbert lemma, we recall the two probabilistic laws we got in previous works that estimate the relative accuracy, considered as a random variable, between two finite elements {P_{k}} and {P_{m}} ({k<m}). Then we analyze the asymptotic relation between these two probabilistic laws when the difference {m-k} goes to infinity. New insights which qualify the relative accuracy in the case of high order finite elements are also obtained.

Effect of crack on free vibration of a pre-stressed curved plate

2021 ◽  
pp. 095440622199486
Author(s):  
Can Gonenli ◽  
Hasan Ozturk ◽  
Oguzhan Das
Keyword(s):  
Finite Element ◽  
Free Vibration ◽  
Natural Frequency ◽  
Present Model ◽  
Mode Shapes ◽  
Load Parameter ◽  
Flexible Plate ◽  
Cantilever Plate ◽  
Finite Element Software ◽  
Aspect Ratios

In this study, the effect of crack on free vibration of a large deflected cantilever plate, which forms the case of a pre-stressed curved plate, is investigated. A distributed load is applied at the free edge of a thin cantilever plate. Then, the loading edge of the deflected plate is fixed to obtain a pre-stressed curved plate. The large deflection equation provides the non - linear deflection curve of the large deflected flexible plate. The thin curved plate is modeled by using the finite element method with a four-node quadrilateral element. Three different aspect ratios are used to examine the effect of crack. The effect of crack and its location on the natural frequency parameter is given in tables and graphs. Also, the natural frequency parameters of the present model are compared with the finite element software results to verify the reliability and validity of the present model. This study shows that the different mode shapes are occurred due to the change of load parameter, and these different mode shapes cause a change in the effect of crack.

Optimum Design for the Frame of Open Type Abrasive Flow Polish Machine

2012 ◽  
Vol 497 ◽  
pp. 89-93
Author(s):  
Liang Liang Yuan ◽  
Ke Hua Zhang ◽  
Li Min
Keyword(s):  
Finite Element ◽  
Natural Frequency ◽  
Finite Element Methods ◽  
Optimization Design ◽  
Low Cost ◽  
Three Dimensional ◽  
Force Model ◽  
Optimization Analysis ◽  
Open Type ◽  
Set Up

In order to process heterotype hole of workpiece precisely, an open abrasive flow polish machine is designed, and the optimization design of machine frame is done for low cost. Firstly, basing on the parameters designed with traditional ways, three-dimensional force model is set up with the soft of SolidWorks. Secondly, the statics and modal analysis for machine body have been done in Finite element methods (FEM), and then the optimization analysis of machine frame has been done. At last, the model of rebuild machine frame has been built. Result shows that the deformation angle value of machine frame increased from 0.72′ to 1.001′, the natural frequency of the machine decreased from 75.549 Hz to 62.262 Hz, the weight of machine decreased by 74.178 Kg after optimization. It meets the strength, stiffness and angel stiffness requirement of machine, reduces the weight and cost of machine.

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