Nondestructive Evaluation of Parts With Degenerate Modes Using Pseudorepeated Roots

2004 ◽  
Vol 126 (3) ◽  
pp. 498-508 ◽  
Author(s):  
Brandon J. Jellison ◽  
Harold R. Kess ◽  
Douglas E. Adams ◽  
David C. Nelson
Keyword(s):  
Raw Materials ◽  
Element Model ◽  
Lumped Parameter Model ◽  
Mass Distributions ◽  
Lumped Parameter ◽  
Fabrication Procedure ◽  
Modes Of Vibration ◽  
Systemic Problems ◽  
Vibration Tests ◽  
Degenerate Modes

The modes of vibration of manufactured parts can be good indicators of the overall quality of the manufacturing process. That is, deviations in the modal frequencies or modal vectors of mechanical parts can help to identify outlier or systemic problems in the raw materials or fabrication procedure. A novel method for characterizing nonuniformities in homogeneous symmetric parts using pseudorepeated modal frequencies is discussed in this paper. It is demonstrated that the spacing between pseudorepeated roots in dominantly symmetric manufactured parts is a direct indicator of nonuniformities (i.e., inclusions, voids) in the stiffness or mass distributions. Smaller differences between split-peaks indicate less nonuniformity, and hence, higher quality parts. A simple fourth-order lumped parameter model is used to elaborate on this technique analytically, a representative finite element model is used to further this development, root locus techniques are used to study the sensitivity to nonuniformities, and acceleration response data from impact vibration tests on deep drawn hemispherical shells are used to verify the approach experimentally.

Vibration-Based NDE Technique for Identifying Non-Uniformities in Manufactured Parts With Degeneracies

2002 ◽  
Author(s):  
B. J. Jellison ◽  
H. R. Kess ◽  
D. E. Adams ◽  
D. C. Nelson
Keyword(s):  
Lumped Parameter Model ◽  
Modal Parameter ◽  
Mass Distributions ◽  
Response Data ◽  
Lumped Parameter ◽  
Novel Method ◽  
Vibration Tests ◽  
Vibration Modal ◽  
Impact Vibration ◽  
Hemispherical Shells

A novel method for characterizing non-uniformities in homogeneous precision symmetric parts using pseudo-repeated modal frequencies is discussed in this paper. It is demonstrated that the spacing between pseudo-repeated roots (modal frequencies) in dominantly symmetric manufactured parts is a direct indicator of non-uniformities (i.e. asymmetries) in the stiffness or mass distributions. Smaller differences between split-peaks indicate less non-uniformity, and hence, higher quality-greater precision parts. By establishing a tolerance for precision manufactured parts based on a collection of vibration modal parameter data from acceptable parts for a given process, this work shows that poorly manufactured parts with density discontinuities (e.g. inclusions, voids) can be identified based on the degree to which their pseudo-repeated roots are separated. A simple low-order lumped parameter model is used to develop this technique analytically and acceleration response data from impact vibration tests on deep drawn hemispherical shells is used to verify the validity of the approach experimentally.

Vibration and Analysis of Multi-Disk Friction Systems

1998 ◽  
Author(s):  
Henric Larsson ◽  
Kambiz Farhang
Keyword(s):  
Frictional Contact ◽  
Vibration Characteristics ◽  
Lumped Parameter Model ◽  
Stick Slip ◽  
Friction Forces ◽  
Lumped Parameter ◽  
Modes Of Vibration ◽  
The Coefficient Of Friction ◽  
Slip Region ◽  
Stiffness And Damping

Abstract The paper presents a lumped parameter model of multiple disks in frictional contact. The contact elastic and dissipative characteristics are represented by equivalent stiffness and damping parameters in the axial as well as the torsional directions. The formulation accounts for the coupling betwen the axial and angular motions by viewing the contact normal force to be the result of axial behavior of the system. The frictional contact of two disks in contact is modeled in two dynamic states (i.e. sticking and slipping state) having individual lumped parameter models and the conditions that control the switching between the two states are established. The friction forces are represented by assuming the coefficient of friction to be a function of the sliding velocity, varying exponentially from its static value at zero relative velocity to its kinetic value at high velocities. A computer simulation of an eight-rotor disk assembly is presented. The torsional vibration characteristics and how it is liked to the axial modes of vibration is analyzed. The vibration characteristics in the transient, steady-state and stick-slip region is compared. In the stick-slip region, the angular velocity of the interfaces in frictional contact is depicted and the sticking and slipping states are defined. It is shown that the duration of slip is approximately constant and the duration of stick increases almost exponentially until a final sticking is achieved.

scholarly journals The Development of a Tympanic Membrane Model and Probabilistic Dose-Response Risk Assessment of Rupture Because of Blast

2020 ◽  
Vol 185 (Supplement_1) ◽  
pp. 234-242
Author(s):  
Anthony E Iyoho ◽  
Kevin Ho ◽  
Philemon Chan
Keyword(s):  
Tympanic Membrane ◽  
Dose Response ◽  
Injury Risk ◽  
Element Model ◽  
Lumped Parameter Model ◽  
Unintended Effects ◽  
Response Curves ◽  
Membrane Rupture ◽  
Lumped Parameter ◽  
Dose Response Curves

ABSTRACT Introduction There is no dose-response model available for the assessment of the risk of tympanic membrane rupture (TMR), commonly known as eardrum rupture, from exposures to blast from nonlethal flashbangs, which can occur concurrently with temporary threshold shift. Therefore, the objective of this work was to develop a fast-running, lumped parameter model of the tympanic membrane (TM) with probabilistic dose-dependent prediction of injury risk. Materials and Methods The lumped parameter model was first benchmarked with a finite element model of the middle ear. To develop the dose-response curves, TMR data from a historic cadaver study were utilized. From these data, the binary probability response was constructed and logistic regression was applied to generate the respective dose-response curves at moderate and severe eardrum rupture severity. Results Hosmer-Lemeshow statistical and receiver operation characteristic analyses showed that maximum stored TM energy was the overall best dose metric or injury correlate when compared with total work and peak TM pressure. Conclusions Dose-response curves are needed for probabilistic risk assessments of unintended effects like TMR. For increased functionality, the lumped parameter model was packaged as a software library that predicts eardrum rupture for a given blast loading condition.

Non-linear dynamic simulation of mechanical periodicity of end-diastolic volume of left ventricle under the influence of baroreflex

2006 ◽  
Vol 220 (3) ◽  
pp. 357-366 ◽  
Author(s):  
Q Wang ◽  
S Xu ◽  
D Chen ◽  
M Collins
Keyword(s):  
Left Ventricle ◽  
Vascular System ◽  
Element Model ◽  
Baroreceptor Reflex ◽  
Lumped Parameter Model ◽  
Linear Dynamic ◽  
End Diastolic Volume ◽  
Lumped Parameter ◽  
Non Linear ◽  
Mechanical Periodicity

Mechanical periodicity (MP) of the end-diastolic volume (EDV) of the left ventricle (LV) is closely associated with cardiovascular pathophysiology. On the basis of the Starling's law of the LV and Burattini and Gnudi's four-element model of the vascular system, and considering baroreceptor reflex, a non-linear dynamic lumped-parameter model is proposed. This simulates the MP phenomena of the EDV by solving a series of one-dimensional discrete non-linear dynamic equations. The results demonstrate that excessive deviations of some physiological parameters often induce MP - the unstable phenomena of EDV - and verify that the effects of baroreceptor reflex enhance the ability of the human physiological system to maintain stability.

scholarly journals Analysis of Fly Fishing Rod Casting Dynamics

2011 ◽  
Vol 18 (6) ◽  
pp. 839-855
Author(s):  
Gang Wang ◽  
Norman Wereley
Keyword(s):  
Finite Element ◽  
Initial Boundary ◽  
Element Model ◽  
Nonlinear Finite Element ◽  
Lumped Parameter Model ◽  
Parameter Method ◽  
Line System ◽  
Fly Fishing ◽  
Lumped Parameter ◽  
Rigid Rod

An analysis of fly fishing rod casting dynamics was developed comprising of a nonlinear finite element representation of the composite fly rod and a lumped parameter model for the fly line. A nonlinear finite element model was used to analyze the transient response of the fly rod, in which fly rod responses were simulated for a forward casting stroke. The lumped parameter method was used to discretize the fly line system. Fly line motions were simulated during a cast based on fly rod tip response, which was used as the initial boundary condition for the fly line. Fly line loop generation, propagation, and line turn-over were simulated numerically. Flexible rod results were compared to the rigid rod case, in which the fly tip path was prescribed by a given fly rod butt input. Our numerical results strongly suggest that nonlinear flexibility effects on the fly rod must be included in order to accurately simulate casting dynamics and associated fly line motion.

The Mechanism on Prediction of Transient Maximum Amplitude for Tuned and Mistuned Blisks

2020 ◽  
Vol 142 (5) ◽  
Author(s):  
Luohui Ouyang ◽  
Hai Shang ◽  
Hua Chen ◽  
Qingzhen Bi ◽  
Li-Min Zhu
Keyword(s):  
Damping Ratio ◽  
Maximum Amplitude ◽  
Element Model ◽  
Forced Response ◽  
Lumped Parameter Model ◽  
Fundamental Parameter ◽  
Reduced Order ◽  
Lumped Parameter ◽  
Engine Order ◽  
Acceleration And Deceleration

Abstract Blisks are subjected to frequent acceleration and deceleration, which leads to a transient forced response; however, there is limited understanding of this response. In this work, the mechanism on prediction of transient maximum amplitude is found. An analytical link is proposed between the transient maximum amplitude and a fundamental dimensionless parameter which combines the damping ratio, natural frequency, acceleration, and engine order of the system to reveal the mechanism of the transient maximum amplitude. Therefore, the transient maximum amplitudes of tuned and mistuned blisks are predicted analytically. First, a lumped parameter model is used to study the mechanism of the transient maximum amplitude for a tuned blisk, and an approximated analytical expression is derived between the fundamental parameter and the transient amplification factor of a 1DOF (degree-of-freedom) model. The relationship is also applicable to a reduced order, tuned finite element model (FEM). Second, the mechanism of the transient response for a mistuned blisk is studied in the decoupled modal space of the blisk, based on the 1DOF transient relationship. The transient maximum amplitude in a reduced order, mistuned FEM is predicted. Two lumped parameter models and a FEM are employed to validate the prediction.

Advances in simulation of gerotor pumps: An integrated approach

2017 ◽  
Vol 231 (7) ◽  
pp. 1221-1236 ◽  
Author(s):  
Giorgio Altare ◽  
Massimo Rundo
Keyword(s):  
Fluid Dynamics ◽  
Computational Fluid Dynamics ◽  
Integrated Approach ◽  
Element Model ◽  
Lumped Parameter Model ◽  
Lumped Parameter ◽  
Pump Flow Rate ◽  
Incomplete Filling ◽  
Pressure Ripple ◽  
Dynamics Simulations

The paper describes a multi-domain simulation of a gerotor oil pump. Three different analysis tools have been used in synergy to predict the pump flow rate, in both conditions of complete and incomplete filling, and the pressure ripple. The computational fluid dynamics software PumpLinx® has been used for the determination of the discharge coefficients, while a finite element model analysis performed with ANSYS® has allowed the evaluation of the deflection of the pump cover under the action of the delivery pressure. The data calculated with the 3D tools have been utilized as input for a lumped parameter model of the pump developed in LMS Amesim® with customized libraries. The aim of the study is to supply the guidelines for tuning the models using a reduced number of computational fluid dynamics simulations. The results collected in the experimental campaign have demonstrated that a lumped parameter approach can be suitable, if properly calibrated, to predict the pressure oscillations in conditions of defective filling. Moreover, it was found that the cover deflection has a significant importance not only on the leakages, but also on the pressure ripple.

Biomimetic idealization of a mechanically coupled acoustic sound sensing mechanism

SIMULATION ◽  
2017 ◽  
Vol 94 (2) ◽  
pp. 131-143 ◽  
Author(s):  
Jin-Hyuk Lee
Keyword(s):  
Material Properties ◽  
Element Model ◽  
Lumped Parameter Model ◽  
Test Cases ◽  
Acoustic Sensor ◽  
Micro Fabrication ◽  
Lumped Parameter ◽  
Commercial Software Package ◽  
Two Degree Of Freedom ◽  
Force Equilibrium

This paper presents the idealization of a mechanically coupled acoustic sensor mechanism for directivity with the use of polysilicon, which has ideal mechanical and electrical material properties in terms of micro-fabrication. A mathematical model related to mechanical sensitivity is developed as a function of the material properties and geometry of the sensor, which evaluates the characteristics of a two-degree-of-freedom-based lumped parameter model. A challenge in such a study is that the model needs to be simple but sufficiently sophisticated to capture the characteristics of the sensor mechanism. Eigen modes and frequencies of the mechanically coupled acoustic sensor mechanism are determined by an energy method using mode functions applicable to the complete system that are from admissible the mode functions chosen for the component elements of the system. The synthesis is accomplished by using equations of constraint that follow conditions imposed by force equilibrium and deflection compatibility at the junctions. Finally, the results are compared with those obtained by a full-scale finite element model developed in a commercial software package. The predicted first and second natural frequencies differed by less than 10% and 3%, respectively, in all test cases.

Comparison of Golf Ball/Driver Impact Models With Respect to Mechanical Impedance Matching Theory

2009 ◽  
Author(s):  
Willem Petersen ◽  
Armaghan Salehian ◽  
John McPhee
Keyword(s):  
Impedance Matching ◽  
Mechanical Impedance ◽  
Element Model ◽  
Golf Ball ◽  
Lumped Parameter Model ◽  
Matching Theory ◽  
Beam Equation ◽  
Distributed Parameter ◽  
Piecewise Constant ◽  
Lumped Parameter

Three models of a golf ball and a golf clubhead are created to investigate the efficiency of the collision with respect to the theory of mechanical impedance matching, normally derived from oversimplified models. While the results obtained from a lumped-parameter model do validate the mechanical impedance matching theory, the results obtained from a finite element model used to investigate this phenomenon with more fidelity by varying the clubface flexibility disagree. Therefore, a distributed-parameter model is developed. In this model, the clubface is modelled using the Euler-Bernoulli beam equation with clamped-clamped boundary conditions, and the golf ball is modelled using a 3-piece rod with piecewise constant material properties representing the multiple layers of a real golf ball. The number of modes considered in the calculations is varied to determine the influence of the complexity of the model. The results obtained from this model are compared against those from the previous approaches and from the mechanical impedance matching theory.

Research on Suppressing Vibration of Mistuning Cyclic-Periodic Structure

2018 ◽  
Vol 0 (0) ◽  
Author(s):  
Pengcheng Deng ◽  
Lin Li ◽  
Chao Li
Keyword(s):  
Periodic Structure ◽  
Vibration Suppression ◽  
Vibration Reduction ◽  
Element Model ◽  
Lumped Parameter Model ◽  
Modal Assurance Criterion ◽  
Suppression Effect ◽  
Lumped Parameter ◽  
Two Systems ◽  
Aero Engines

Abstract This paper deals with the cyclic-periodic structure with piezoelectric shunt circuits or a parallel piezoelectric network. The objective is to obtain the vibration suppression effect of them on the cylic-periodic structure. The background of the research is about vibration reduction of bladed disks in aero-engines, and the system is simulated by a lumped parameter model. The tuned and mistuned dynamic equations of the system are derived. The method of equivalent blisk model (EBM) is used to identify the lumped parameters of a finite element model, which is related to the experimental model. Then the Modified Modal Assurance Criterion (MMAC) is used to evaluate the vibration suppression ability of shunt circuits and the network. The numerical results show that both of these two systems can control vibration well, even the mechanical and electrical mistuning level are up to 10 %, and there is an optimal resistance which can be used to design the system to get a good performance of vibration suppression. An experiment is performed to validate the analytical results. The experimental results demonstrate that the ability of vibration suppression for both two systems are almost the same, but the piezo-network has an advantage in vibration delocalization of the mistuned system.

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