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.

Comparison of Modelling Methods for Hydraulic Valve Gear

1987 ◽  
Author(s):  
H. Shang ◽  
G. K. Matthew ◽  
W. Luo
Keyword(s):  
Lumped Parameter Model ◽  
Distributed Parameter ◽  
Distributed Parameter Model ◽  
Lumped Parameter ◽  
Comparison Results ◽  
Hydraulic Valve ◽  
Modelling Methods ◽  
Measured Response ◽  
Valve Gear

Abstract A combined lumped/distributed parameter model for the follower system of a hydraulically operated valve is compared to a lumped parameter model of the same system. Since previous results show excellent correspondence between the lumped/distributed parameter model and measured response, it is natural to attempt to simplify the model and to again perform a comparison. Results of several examples are shown.

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.

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.

scholarly journals An Improved Lumped Parameter Model for a Piezoelectric Energy Harvester in Transverse Vibration

2014 ◽  
Vol 2014 ◽  
pp. 1-12 ◽  
Author(s):  
Guang-qing Wang ◽  
Yue-ming Lu
Keyword(s):  
Correction Factor ◽  
Transverse Vibration ◽  
Energy Harvester ◽  
Lumped Parameter Model ◽  
Distributed Parameter ◽  
Piezoelectric Energy ◽  
Distributed Parameter Model ◽  
Lumped Parameter ◽  
Lumped Parameter Models ◽  
Tip Mass

An improved lumped parameter model (ILPM) is proposed which predicts the output characteristics of a piezoelectric vibration energy harvester (PVEH). A correction factor is derived for improving the precisions of lumped parameter models for transverse vibration, by considering the dynamic mode shape and the strain distribution of the PVEH. For a tip mass, variations of the correction factor with PVEH length are presented with curve fitting from numerical solutions. The improved governing motion equations and exact analytical solution of the PVEH excited by persistent base motions are developed. Steady-state electrical and mechanical response expressions are derived for arbitrary frequency excitations. Effects of the structural parameters on the electromechanical outputs of the PVEH and important characteristics of the PVEH, such as short-circuit and open-circuit behaviors, are analyzed numerically in detail. Accuracy of the output performances of the ILPM is identified from the available lumped parameter models and the coupled distributed parameter model. Good agreement is found between the analytical results of the ILPM and the coupled distributed parameter model. The results demonstrate the feasibility of the ILPM as a simple and effective means for enhancing the predictions of the PVEH.

scholarly journals The effect of a hydrological model structure and rainfall data on the accuracy of flood description in an upland catchment

2015 ◽  
Vol 47 (4) ◽  
pp. 305-320 ◽  
Author(s):  
Andrzej Wałęga ◽  
Leszek Książek
Keyword(s):  
Hydrological Model ◽  
Model Performance ◽  
Rainfall Data ◽  
Lumped Parameter Model ◽  
Distributed Parameter ◽  
Model Structure ◽  
Related Data ◽  
Distributed Parameter Model ◽  
Lumped Parameter ◽  
Starting Point

Abstract The effect of a hydrological model structure and rainfall data on the accuracy of flood description in an upland catchment. The aim of this paper was to determine the influence of a hydrological model structure and rainfall- -related data on flood parameters obtained from a simulation. The study included an upland river Stobnica, right tributary of the Wisłok. The following assumptions were investigated: (i) the greater number of rainfall stations, the more accurate a flood description, i.e. the resulting hydrograph much better describes the actual flood, (ii) a distributed parameter model provides a more precise description of a catchment response to rainfall than a lumped parameter model. All calculations were performed using HEC-HMS 3.4 software. The analyses showed that increasing the number of rainfall stations slightly improved the model performance (by on average 4.1%). Furthermore, it was showed that in the catchment characterized by low topographical variability and stable land use, more reliable flood simulation results were obtained in the lumped parameter model than in the distributed parameter model. Considering the calibration process slightly improved the model performance, irrespective of its structure and the number of rainfall stations. Multivariate analysis of variance (MANOVA) revealed that the resulting differences in the model efficiency for individual variants were not significant. Considering limited empirical evidence on rainfall-runoff episodes, uncertainty of these results is probably high and thus they should be treated as a starting point for further studies.

An asymmetric magnetic-coupled bending-torsion piezoelectric energy harvester: modeling and experimental investigation

2021 ◽  
Author(s):  
Huirong Zhang ◽  
Wentao Sui ◽  
Chongqiu Yang ◽  
Leian Zhang ◽  
Rujun Song ◽  
...  
Keyword(s):  
Energy Harvester ◽  
Average Power ◽  
Harmonic Excitation ◽  
Lumped Parameter Model ◽  
Distributed Parameter ◽  
Piezoelectric Energy ◽  
Distributed Parameter Model ◽  
Piezoelectric Beam ◽  
Lumped Parameter ◽  
Torsion Energy

Abstract This paper presents a detailed investigation on an asymmetric magnetic-coupled bending-torsion piezoelectric energy harvester based on harmonic excitation. There is an eccentricity between the shape center of moving magnets and the axis of the piezoelectric beam, which results in the bending and torsion simultaneously in working condition. The distributed mathematical model is derived from the energy method to describe the dynamic characteristics of the harvester, and the correctness of the model is verified by experiments. To further demonstrate the improvement performance of the proposed energy harvester, the bending-torsion energy harvester (i.e. magnetic-coupled was not configured) is experimented and compared. The theoretical and experimental results indicate that the average power increases about 300% but the resonance frequency decreases approximately 2 Hz comparing to the harvester without magnetic-coupled. According to the characteristic of distributed parameter model, the magnetic force and the size of the piezoelectric beam are investigated respectively. And the lumped-parameter model is introduced to analyze the steady-state characteristic. Accordingly, this paper provides a feasible method to improve performance for piezoelectric energy harvester.

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