bluuebunny/crossref_metadata_2025 huggingface dataset:
Mold Tool Configuration to Minimize Undercuts
Authors: Weinstein Marc , Manoochehri Souran
Published: March 2021

This paper presents a methodology for obtaining mold configurations, defined by cavity and core geometries, with a minimum number of undercuts in a molded part. The methodology identifies optimal draw directions and associated parting line locations that minimize the number of undercuts thereby obtaining a good mold configuration. The interaction of the allowable draw ranges of the concave regions of the part determines the allowable draw direction range for the part. The allowable draw range for each concave region depends on how the constituent surfaces are grouped. This grouping determines whether the surfaces are formed by one or two mold halves, depending on the draw direction. The grouping also identifies which surfaces, if any, form an undercut regardless of draw direction. This last grouping identifies which surfaces require modification so that either a side core or a mold halves can form the surfaces. The allowable draw direction range for the part and its interaction with surfaces within the convex region defines the parting line location for the part. Once the draw ranges and parting line locations are identified, an algorithm selects the optimum draw direction and parting line location that minimizes the number of undercuts and results in a mold that is easy to make.
Experimental Developments Toward Multi-Material Micron Scale Rapid Prototyping
Authors: Maxwell James L. , Pegna Joseph
Published: March 2021

Rapid prototyping of millimeter- to micron-scale mechanical parts was obtained by selective Laser Induced Chemical Vapor Deposition (LCVD) onto a computer controlled five degree of freedom substrate. A description of Rensselaer’s experimental apparatus for 3-dimensional rapid prototyping is given. Details of the (LCVD) system are presented as well as the experimental approach taken. We illustrate our purpose with sample carbon micro-structures obtained during system calibration. By virtue of the process selected, the range of material that can be deposited is as large as there are organometallic precursors for them. Many ceramics, intermetallics, metals, and possibly some polymers can be grown via this method.
Design of a Nanometric Position Sensor Based on Computational Metrology of the Circle
Authors: Pegna Joseph , Guo Chi , Hilaire Thierry P.
Published: March 2021

The work presented in this paper derives from the design of a position sensing interferometer, in which circular fringe patterns are automatically analyzed by a computer vision system. Central to this process is a circle fitting problem in the sense of least Linfinity norm, also known as Chebichev or MinMax fit. The problem at hand can be formulated as follows: Given a set of points in the plane, find the pair of concentric circles with minimum radial gap enclosing all the points.

The solution to this problem is elegantly given by common computational geometry tools, indeed the center of such a circle is necessarily a vertex of the Nearest Point Voronoi Diagram (NVD), a vertex of the Farthest Point Voronoi Diagram (FVD), or an intersection of edges from both diagrams.

An algorithm for determining the Chebichev circular fit is presented and illustrated on the basis of that observation. Applications and potential extensions of this method to soft gauging and image metrology will also be discussed.
Computer Aided Analysis of Functional Couplings in Structural Axiomatic Design
Authors: Johannesson H. L.
Published: March 2021

Creating product structure models is an important task in design, as different such models are needed during the product design process. Depending on what theoretical model or methodology for product design that is used during the process, structure models of different kinds are developed.

In structural axiomatic design, functional requirement structure models and physical solution structure models are essential. These are hierarchial tree structure models which are developed during the process by zigzagging between the functional domain and the physical solution domain from the highest to the lowest hierarchical structure level. While doing this, functional couplings, making it harder to fulfill a certain functional requirement without affecting others, are built into the structure.

The theory of axiomatic design provides tools to identify such couplings. In this work, the so called design equation in the axiomatic design theory, has been given a graphical interpretation. This has made it possible to use a computer based structure modeling tool, with a graphic user interface, to directly identify and analyze functional couplings in the structure model on the graphical screen.
The Preliminary Design of Mechanical Drive and Transmission Components
Authors: Yeh Jung-Hua , Liou F. W.
Published: March 2021

Selecting the appropriate components for a mechanical drive and transmission system is complicated not only by the inherent nature of the system designed, but also by the wide varieties of components available from a multitude of manufacturers. The integration of these components is more important when designing a working system where specific constraints have been imposed. Presented in this paper is an investigation of component relationship in the form of a knowledge-based-system which provides a practical algorithm for preliminary design of mechanical drive and transmission system. A design abstraction and an integration attributes in the power transmission components are addressed. The development of the matrix table for optimizing component design is also presented.
Determination of Maximum Possible Contact Ratios for Spur Gear Drives With Small Number of Teeth
Authors: Arikan M. A. Sahir
Published: March 2021

Maximum possible contact ratios which can be obtained by making use of x-zero gear pairs are determined for spur gear drives with small number of teeth. Rack cutter tip fillet radius and rack cutter geometry are taken into consideration in the analysis. Results for gear drives with various numbers of teeth and cut by rack cutters standardized by ISO and AGMA are given in forms of tables. Results are also compared with addendum modification coefficients recommended by ISO.
Computerized Design and Simulation of Meshing of Worm-Gear Drive With Longitudinally Localized Bearing Contact
Authors: Litvin Faydor L. , Seol I. H. , Kim K.
Published: March 2021

The design and simulation of meshing of a single-enveloping worm-gear drive with a localized bearing contact is considered. The bearing contact has a longitudinal direction. The purpose of localization is to reduce the sensitivity of the worm-gear drive to misalignment. The authors’ approach for localization of bearing contact is based on the proper mismatch of the sufaces of the hob and the drive worm. The developed computer program allows the investigation of the influence of misalignment on the shift of the bearing contact and allows determination of the transmission errors. The developed approach is applicable for all types of single-enveloping worm-gear drives. The developed theory is illustrated with a numerical example.
Finite Element Analysis and Design of a Trochoidal-Type Machine Without Apex Seals
Authors: Venkatesh Kannan , Shung John B.
Published: March 2021

A two-dimensional model for a trochoidal-type machine without apex seals using finite element method has been developed with the help of Cosmos/M V1.65, and is evaluated by using a classical free-body technique. The minimum running clearance required to avoid contact between rotor and chamber is determined by an iterative procedure using the finite element model. The variation in the minimum required running clearance with the variation in the design parameters is studied. Guidelines for using the results of this study for an optimal design of a trochoidal-type machine without apex seals are presented.
Kinematic Analysis on Running Clearance in a Trochoidal-Type Machine
Authors: Shung John B. , Zhang Yi
Published: March 2021

A methodology to design tight running clearance between rotor and chamber in a trochoidal-type machine is presented. A mathematical model to describe the running clearance is developed. Only kinematic design parameters are considered. The effect of the mean values and tolerances of the design parameters on the running clearance is studied by applying robust design. Mean values of design parameters which provide running clearance to be less sensitive to the tolerances are obtained. The effect of the upper bound of the running clearance on the tolerance is also studied by applying the probabilistic optimal design. Optimum tolerances which minimize a cost function are obtained. Therefore, one can apply this methodology to design running clearance by choosing appropriate mean values and tolerances of the design parameters.
On Inverse Kinematics of a Rolling Disk Between Two Manipulators
Authors: Liang Zhongming
Published: March 2021

The present paper addresses two questions: (1) how to define an inverse kinematic problem of a rolling disk between two manipulators; (2) what is the number of solutions of the inverse problem. Two solution procedures and their examples are also given.
Analysis of Interference Zone for Dual-Arm Robots
Authors: Xu Li Ju , Wang Qiang , Yao Jin , An Xiao Yu
Published: March 2021

An analytical method to evaluate time zones of interference for a dual-arm robot is presented with the consideration of shape and volume of links in the case, when the robot arms move along two given continuous trajectories in three-dimensional space respectively. The formulations and criteria to determine interference zones are derived. The method is applicable to general dual-arm robots with not only revolute joints, but also prismatic joints. A numerical example is presented for illustration.
Needle Fatigue Analysis for High-Speed Knitting Machines
Authors: Lyon Richard H. , Malinin Leonid M.
Published: March 2021

In modern, high capacity circular knitting machines, the small and fragile latch needles are often a performance-limiting machine element (Schuler, 1980). For these machines, the operating circumferential speed may exceed 1.5 m/sec. Due to the kinematics of the process, the cam driven needles are exposed to periodic excitation with frequency proportional to the speed. Increase in rotational speed gives rise to needle head fatigue breakages unless special design measures are undertaken. Frequencies up to 15 kHz have been observed and up to 60 kHz may be expected in the vibration spectrum. To understand what particular features of needle design may be responsible for their longevity, several techniques were developed to apply Finite Element Analysis software to estimating the fatigue life under a non-harmonic periodic loading.

The known FEA packages handle dynamics of a system with such loading as a general non-stationary problem, whereas much more efficient solution can be constructed by combining the analytical solution for a one DOF system under recurring impulses (5-functions of amplitude A) at the moments 0, T, 2T, …, and the natural modes of the system (with the driving point fixed) provided by FEA. As applied to the system in question, from the broad frequency range of the excitation forces and displacements, only frequencies close to those providing maxima to the transfer functions from the driving point to the head of the needle were selected. These frequencies are referred to further on as the response frequencies. Then the time history simulating polyharmonic stresses in the dangerous area was generated and processed according to the chosen fatigue criteria (a corrected linear hypothesis of damage summation, see below). Thus for any given node of the needle a point on the S-N diagram was obtained.

A wide spread desktop package, ALGOR, was selected as a Linear Stress Analysis solver. The described procedure is built on top of this package and allows design engineers to make judgements as to what design is more advantageous for needle longevity.
Dynamic Impact Upon Steel Target Plate: Experimental and Theoretical Analysis
Authors: Al-Obaid Y. F.
Published: March 2021

This paper gives complete analysis of the local failure of steel target plate subjected to shot impact by using three-dimensional dynamic finite element analyses in which provision is made for the simulation of impact loads, plasticity and cracking of steel target. An assessment is made for perforation. Three computer programmes NONSAP, MARC and OBAID have been used for comparison. The analytical results are well compared with those available from a model test.
Reasoning With Shapes: Some Observations From a Case Study
Authors: Chakrabarti Amaresh , Wolf Burkhard
Published: March 2021

Reasoning with shapes plays an essential role in mechanical design. Therefore, developing methods and techniques for supporting this activity is an important goal of design research. As a pre-requisite to this, it is crucial to understand how designers create, modify and consolidate shapes, and based on these, to identify areas where they need to be, and can be supported.

The goal of this paper is to report some observations about the influencing factors and processes involved in reasoning with shapes, based on a case study of an in-house design project. Three questions were asked: (i) where did the initial ideas originate and why, (ii) what were the reasons for changing/modifying these, and how these changed, and, (iii) where did this stop and why.

This paper provides a description and the results of the case study, involving observations and analyses of the above steps. The observations indicate that shape generation and modification is more significantly influenced by (i) the initial state of the design, (ii) identification, contextualisation and selection of criteria to apply for evaluation of that design state, and (iii) on the quality of evaluation of the design state, than by the generative changes, which often are simple adaptations of existing solutions.
A Spectral Optimization Algorithm for Multi-Objective Prototype Selection
Authors: Dong Andy , Agogino Alice M.
Published: March 2021

In design synthesis, engineering prototypes make an ideal representation medium for preliminary designs. Unlike parametric design wherein a pre-specified design is parametrically varied, design synthesis demands artistic creativity and engineering experience to transform the previously known components, relationships and designs into a new form. The process compels the designer to ascertain which prototypes will, in some sense, best satisfy the design task. The challenge in this assignment lies in selecting the “right” design prototype. This selection process typically entails an objective evaluation of different designs that perform the same functions or have similar intended behavior and comparing trade-offs between alternate designs. This paper introduces a multi-objective spectral optimization algorithm for the selection of design prototypes based upon their functional representations. The optimization algorithm returns an index of rank, scoring the functional similarity of the proposed design to the goal design. Two illustrative examples apply the algorithm to the selection of a heat fin and beam.
Benchmarking Within the Product Development Process
Authors: Meeker David G. , Thornton Anna C.
Published: March 2021

One cannot design in a vacuum; the goodness of a product is almost always (except in the case of a novel design) measured with respect to an existing design. It is logical, therefore, to have a design process that takes competitors into account. Competitor’s hardware is a rich source of design information providing concept and design solutions, current market trends, cost and quality drivers, missing functionality and unwanted functionality. This paper presents a methodology to systematically evaluate existing designs using a process called benchmarking. In addition, a methodology for incorporating the benchmark information into the specification, concept, embodiment, detail design phases of the product development process is described.
Design Education: A Fifty Year View
Authors: Smith Charles O.
Published: March 2021

Design education of engineering students is an important, integral component of design for the present and for the future. This paper presents one view of how design education in the United States has changed over the past fifty years. Recent changes in accreditation are discussed.

Some on-going experiments in revised curricula and manufacturing engineering by corsortia are also discussed.
Interactive Feature Recognition Using Multi-Processor Methods
Authors: Regli William C. , Gupta Satyandra K. , Nau Dana S.
Published: March 2021

The availability of low-cost computational power is enabling development of increasingly sophisticated CAD software. Automation of design and manufacturing activities poses many difficult computational problems. Design is an interactive process and speed is a critical factor in systems that enable designers to explore and experiment with alternative ideas. As more downstream manufacturing activities are considered during the design phase, computational costs become problematic. Achieving interactivity requires a sophisticated allocation of computational resources in order to perform realistic design analyses and generate feedback in real time.

This paper presents our initial efforts to use distributed algorithms to recognize machining features from solid models of parts with large numbers of features and many geometric and topological entities. Our goal is to outline how significant improvements in computation time can be obtained using existing hardware and software tools. An implementation of our approach is discussed.
Dynamic Response of a Rotor Landed on Auxiliary Bearings
Authors: Wang Xinchao , Noah Sherif
Published: March 2021

This study concerns the dynamic response of a rotor landed on auxiliary (catcher) bearings in an Active Magnetic Bearing (AMB) supported rotor, following postulated loss of power or overload of the AMB.

An analytical model involving disk, shaft and auxiliary bearings on damped flexible supports is constructed and appropriate equations of the nonlinear dynamic system are developed. The equations include a switch function to indicate contact/noncontact events and determine the existence of contact normal forces and tangential friction forces between the shaft and the bearings.

Steady state solutions are obtained. An analytical method was formulated and used to yield solutions for cases with well balanced rotors, in absence of any side forces. The Fixed Point Algorithm (FPA) is used to obtain steady state periodic solutions for various parameters. The FPA is used to determine the stability of the periodic solution and the type of bifurcations involved. Multiple periodic solutions, quasiperiodic and chaotic responses are detected and discussed. A set of preliminary guidelines for selection of the parameters of the catcher bearings are given.
Experimental Periodic Localized Motions in Coupled Beams With Active Nonlinearities
Authors: King Melvin E. , Aubrecht Johannes , Vakakis Alexander F.
Published: March 2021

Steady-state nonlinear motion confinement is experimentally studied in a system of weakly coupled cantilever beams with active stiffness nonlinearities. Quasi-static swept-sine tests are performed by periodically forcing one of the beams at frequencies close to the first two closely-spaced modes of the coupled system, and experimental nonlinear frequency response curves for certain nonlinearity levels are generated. Of particular interest is the detection of strongly localized steady-state motions, wherein vibrational energy becomes spatially confined mainly to the directly excited beam. Such motions exist in neighborhoods of strongly localized anti-phase nonlinear normal modes (NNMs) which bifurcate from a spatially extended NNMs of the system. Steady-state nonlinear motion confinement is an essentially nonlinear phenomenon with no counterpart in linear theory, and can be implemented in vibration and shock isolation designs of mechanical systems.
Dynamical Behaviour of Hysteretic Systems Under Harmonic Forces
Authors: Capecchi Danilo , Maslani Renato , Vestroni Fabrizio
Published: March 2021

The study of the response of hysteretic systems to harmonic forces is formulated in a suitable phase space in which an originally multi-valued restoring force is represented by proper functions. The asymptotic response can thus be studied using an approach which derives from the Poincaré map concept and avoids approximate analytical techniques. On account of the peculiarity of the hysteretic systems considered, based on Masing rules, the dynamics are studied in a reduced dimension phase space using an efficient solution algorithm. Only the periodic response is taken into account, which is described by frequency response curves at various intensities of the excitation and by the frequency content. The results presented mainly refer to a two d.o.f. system with two linear frequencies in a ratio of 1:3 and 1:4.

The response is highly complex with numerous peaks corresponding to higher harmonics. The range of frequency in which the effects of internal resonance are evident is much larger than the nonlinear elastic case. In particular the coupling produces a strong modification of the frequency response curves and of the oscillation shape of the structure.
Discrete Evolutionary Spectra of Discretized Beams and Plates Under Time-Frequency Modulated Random Excitations
Authors: To C. W. S. , Hung H. W.
Published: March 2021

Various methods that employed the theory of evolutionary spectral density of Priestley (1965) have been proposed for the non-stationary random response analysis of linear time-invariant multi-degree-of-freedom systems (Hammond, 1968, Fugimori and Lin, 1973, To, 1982, Shihab and Preumont, 1987, To and Hung, 1989).

In this paper the method presented earlier by the authors (1989) is further applied to discrete or discretized systems under time-frequency moduated random excitations in which the white noise processes are replaced by band-limited white noise processes and Kanai-Tajimi models. Applications of the method to beam and plate structures discretized by the finite element method are made so as to illustrate its capability in dealing with practical engineering systems under intensive transient disturbances that may be modelled as such time-frequency modulated random excitations.
Efficient Computation of the Statistics of Reciprocating Engine Dynamics With Dimensional Tolerances
Authors: Zhang F. , Sinha A. , Gilmore B. J.
Published: March 2021

Using the alternating frequency/time domain technique and statistical analysis, an efficient analytical technique has been developed to compute the mean values and variances of the crank’s angular speed and driving torque for a stochastically defined internal combustion (I.C) engine. The I. C. engine is represented by a slider-crank mechanism with a discontinuous force on the piston due to the time-varying gas pressure in the cylinder. The tolerances on link lengths and radial clearances and uncertainties in pin location are treated as random variables. The validity of analytical technique is established by comparison with results from Monte Carlo simulation. The results from parametric studies are also presented.
Analysis of Beam-Like Structures With Displacement-Dependent Friction Forces: Part I — Single-Degree-of-Freedom Model
Authors: Whiteman Wayne E. , Ferri Aldo A.
Published: March 2021

The dynamic behavior of a beam-like structure undergoing transverse vibration and subjected to a displacement-dependent dry friction force is examined. In Part I, the beam is modeled by a single mode while Part II considers multi-mode representations. The displacement dependence in each case is caused by a ramp configuration that allows the normal force across the sliding interface to increase linearly with slip displacement. The system is studied first by using first-order harmonic balance and then by using a time integration method. The stick-slip behavior of the system is also studied. Even though the only source of damping is dry friction, the system is seen to exhibit “viscous-like” damping characteristics. A strong dependence of the equivalent natural frequency and damping ratio on the displacement amplitude is an interesting result. It is shown that for a given set of parameter values, an optimal ramp angle exists that maximizes the equivalent damping ratio. The appearance of two dynamic response solutions at certain system and forcing parameter values is also seen. Results suggest that the overall characteristics of mechanical systems may be improved by properly configuring frictional interfaces to allow normal forces to vary with displacement.
Theoretical Dynamic Analysis of a Cantilever Beam Damped by a Dry Friction Damper
Authors: Korkmaz I. , Barrau J. J. , Berthillier M. , Creze S.
Published: March 2021

The dynamic behavior of a cantilever beam damped by dry friction has been studied The beam is represented partly by its effective modal parameters, obtained from a finite element model. The Coulomb friction law is used and a temporal integration of the dynamic response is performed. A detailed parametric study, highlighting the influence of the static and the dynamic friction coefficients, the viscous damping coefficient, the contact stiffness and the position of the damper along the span, on the dynamic response has been conducted. A better understanding of the damping mechanism by dry friction has been obtained. The numerical results have been compared to experimental results, and a good agreement was found. The results could be applied to a turbine blade with a blade to ground damper.
Carbon Brake Friction Model Parameter Identification Using Genetic Algorithms
Authors: von Doenhoff Roger C. , Streifel Robert J. , Marks Robert J.
Published: March 2021

A model of the friction characteristics of carbon brakes is proposed to aid in the understanding of the causes of brake vibration. The model parameters are determined by a genetic algorithm in an attempt to identify differences in friction properties between brake applications during which vibration occurs and those during which there is no vibration. The model computes the brake torque as a function of wheelspeed, brake pressure, and the carbon surface temperature. The surface temperature is computed using a five node temperature model. The genetic algorithm chooses the model parameters to minimize the error between the model output and the torque measured during a dynamometer test. The basics of genetic algorithms and results of the model parameter identification process are presented.
Extraction of Impulse Response Data via Wavelet Transform for Structural System Identification
Authors: Robertson A. N. , Park K. C. , Alvin K. F.
Published: March 2021

This paper presents a wavelet transform-based method of extracting the impulse response characteristics from the measured disturbances and response histories of linear structural dynamic systems. The proposed method appears to have alleviated some of the most pronounced deleterious aspects of both the time-domain methods that suffer from the matrix ill-conditioning of the input signals and FFT-based methods that must cope with erraneous auto and cross-correlation functions, unless the input signals are rich enough in frequency content The method is found to be effective in capturing very low frequency response components and also far insensitive to output noises than existing methods. The present method has been applied to a variety of problems, which show significant improvements over existing impulse response function extraction methods, especially for limited harmonic excitations and input/output data contaminated with noises.
Adaptivity and Three Dimensional Hierarchical Boundary Elements for Rigid Acoustic Scattering Problems
Authors: Newhouse Steven J. , Mathews Ian C.
Published: March 2021

The boundary element method is an established numerical tool for the analysis of acoustic pressure fields in an infinite domain. There is currently no well established method of estimating the surface pressure error distribution for an arbitrary three dimensional body. Hierarchical shape functions have been used as a highly effective form of p refinement in many finite and boundary element applications. Their ability to be used as an error estimator in acoustic analysis has never been fully exploited.

This paper studies the influence of mesh density and interpolation order on several acoustic scattering problems. A hierarchical error estimator is implemented and its effectiveness verified against the spherical problem. A coarse cylindrical mesh is then refined using the new error estimator until the solution has converged. The effectiveness of this analysis is shown by comparing the error indicators derived during the analysis to the solution generated from a very fine cylindrical mesh.
Patching Model for Acoustoelastic Scattering
Authors: Sachs David A.
Published: March 2021

Faceting models have long been used in electromagnetic scattering to achieve target shape generality. An analogous approach to acoustoelastic scattering from submerged shells has been developed. Generalized asymptotic (ray) solutions of the thin shell equations for smooth shells, developed by Norris and Rebinsky, are applied to a discretized geometry representation to analyze the membrane wave contributions to the scattered field from shells excited by incident plane acoustic waves. Example results for a finite cylindrical shell with spherical endcaps are compared to Finite Element calculations. Limitations of the Norris and Rebinsky theory and of the patching methodology are discussed. A major prerequisite for further progress is a hybrid ray/numerical approach to treat the common practical problem of adjoining and interacting ray and non-ray zones.
Acoustic Design of a Local Scatterer in a Phase-Space
Authors: McCoy John J. , Steinberg Ben Zion
Published: March 2021

A spatially local region of mechanical property heterogeneity is a source of scattering, by which a structure-borne mechanical wavefield is released as sound, to a surrounding fluid. We consider the case of a scatterer which is of the order of the size of the wavelength of a plate-wave field for a frequency which is below coincidence. A design strategy for reducing the strength of the scattered sound field in the fluid, at far-field distances from the scatterer, by adding a small-scale structure to the heterogenity, is presented. The design is accomplished in a wavelet-based phase-space. Emphasized is a significant distinction required of the added structure, depending on the heterogeneity applying to a measure of the local mass density or the local bending stiffness.
Bifurcation and Stability Analysis of Parabolic Ray Equations for Acoustic Wave Propagation in an Underwater Sound Channel
Authors: Wiercigroch Marian , Badiey Mohsen , Simmen Jeffrey , Cheng Alexander H.-D.
Published: March 2021

The non-linear dynamic behavior of acoustic wave propagation in underwater sound channel is studied by a parabolic ray theory using Munk’s sound speed profile. The Hamiltonian system of the ray trajectory is forced by a single mode sinusoidal internal wave. The amplitude and wave length of this excitation are used in a bifurcation analysis. The regions of instability are located by numerical simulations and visualized through a sequence of phase diagrams and Poincaré maps.
Scattering of a Plane Acoustic Wave by a Spherical Elastic Shell Near a Free Surface
Authors: Huang H. , Gaunaurd G. C.
Published: March 2021

The acoustic scattering by a submerged spherical elastic shell near a free surface, and insonified by plane waves at arbitrary angles of incidence is analyzed in an exact fashion using the classical separation of variables technique. To satisfy the boundary conditions at the free surface as well as on the surface of the spherical elastic shell, the mathematical problem is formulated using the image method. The scattering wave fields are expanded in terms of the classical modal series of spherical wave functions utilizing the translational addition theorem. Quite similar to the problem of scattering by multiple spheres, the numerical computation of the scattered wave pressure involves the solution of an ill-conditioned complex matrix system the size of which depends on how many terms of the modal series are required for convergence. This in turn depends on the value of the frequency, and the proximity of the spherical elastic shell to the free surface. The ill-conditioned matrix equation is solved using the Gauss-Seidel iteration method and Twersky’s method of successive iteration double checking each other. Backscattered echoes from the spherical elastic shell are extensively calculated and displayed. The result also demonstrates that the large amplitude low frequency resonances of the echoes of the submerged elastic shell shift upward with proximity to the free surface. This can be attributed to the decrease of added mass for the shell vibration.
Scatter, Radiation and Attenuation of Acoustic Waves in Discontinuous Structures
Authors: Wendlandt B. C. H.
Published: March 2021

The acoustic response of inhomogeneous viscous-plastic elastomer layers which are usually described in terms of impedance and resonance behaviour of the major acoustic structures commonly found in sound attenuating layers as applied to underwater structures is discussed with the visco-elastic wave element approach. The ability of the wave element approach to describe conversion of dilatational waves into flexural waves at two and three dimensional structural intersections, including of the type used to support heavy machinery, is demonstrated theoretically and supported by experimentation. Normal and angular reflection, and underwater radiation properties of such systems are discussed. Understanding the acoustic behaviour of such systems and layers is important in developing approaches to quieten sound transmitting structures and reducing echoes from structures underwater.
On the Influence of Coating Discontinuity on Sound Radiation of Submerged Structures
Authors: Pyshin Alexandr V.
Published: March 2021

Rubber based coatings are successfully used to reduce sound radiation of submerged structures. In some cases it is impossible to put coating continuously on the surface of a complex structure. The existing relations of architectural acoustics estimate the effect of a coating with broken continuity at high frequencies and do not work correctly at low frequencies. The solution of the task of sound radiation from a surface with given vibration and a coating layer with discontinuities is presented. New expressions for estimating an influence of coating discontinuities on the coating effect at low frequencies are obtained. It is shown that at low frequencies coating discontinuities can cause an additional gain of the noise reduction. The explanation of this phenomenon is given and the conditions of its existence are formulated. Sound radiation in dependence of the area of uncoated surface parts and the loss factor of coating material is studied.
Acoustic Finite Element Analysis of Coupled Cavities Having Bulk-Reacting Absorbing Materials
Authors: Qian A. , Ballinger R. S.
Published: March 2021

This research presents the finite element formulation of a bulk-reacting sound absorbing material for use in interior cavity solutions. The bulk properties of the absorbing material are represented by complex density and complex propagation speed. Coupling between the vibrating cavity structure and the acoustic medium is considered. The continuity of sound pressure and the particle velocity at the interface between the acoustic domains having different properties is satisfied. Two case studies, a one-dimensional duct and a three-dimensional cavity, are considered. Analytical solutions and experimental results are compared to the finite element results. Excellent agreement has been achieved.
Acoustic Scattering by Rigid or Elastic Structures: Case of a Shell With a “Line” Shape
Authors: Trad A. , Ravel P.
Published: March 2021

A modified Werner’s method is used to study, at any real arbitrary frequency, the scattering problem of full axisymetric elastic structures and for any axisymetric elastic shell. It leads to a coupled system of integral equations on the surface of the structure which governs the scattering pressure and the normal component of the displacement vector on the boundary’s structure. A finite element method is computed to calculate the scattering of elastic structures for low and medium frequency ranges. Then this method is tested on the case of a steel made sphere in a radial field and applied to a « LINE » shaped structure, which is a right cylinder ended by two half spheres on its extremities.
Friction Induced Instabilities and Sound Generation
Authors: Raous M. , Barbarin S. , Vola D. , Martins J. A. C.
Published: March 2021

This paper deals with the characterization of occurrence of instabilities during the sliding of a deformable body on a rigid obstacle. We focus here on the analysis of the mechanical phenomenon which leads to local microshocks that could induce noise by exciting some eigenmodes of the structure. A model with constant friction coefficient is presented to characterize the occurrence of instabilities related to friction during a quasi-static sliding by using various instability criteria : energetic (power rate) criterion, dynamic divergence instability, dynamic flutter instability. Models and numerical processes are given. A first example concerns the characterization of stress waves and friction force jumps for a photoelastic solid sliding on a plane. A second exemple is related to the noise generation during the sliding of a rubber licker on a car window. The model is applied to an experiment conducted so as to characterize the friction coefficient of the material and where instabilities have been observed in some cases.
Modeling of Rotor Shafting for Lower Mode Accuracy: Influence of Section L/D
Authors: Kirk R. G. , Baheti S. , Ramesh K.
Published: March 2021

The transfer matrix and finite element methods are currently widely used to model rotor shafting for calculation of critical speeds, forced response, and stability. For many rotors, long uniform shafting sections occur on the ends of the rotors which could be treated without consideration of section L/D. The use of finite element continuous mass models makes it possible to consider longer sections than previously considered using lumped inertia models. This paper will review a major mass reduction technique which has been used for transfer matrix lumped mass models and compares the results to those obtained by the continuous mass finite element method. The required section L/D for desired accuracy of the lowest eight modes of a uniform shaft (4 forward, 4 backward) will be studied for both simple property splitting and a modified major mass reduction technique. The necessary section L/D for desired accuracy for varying bearing to shaft stiffness ratios will be presented. A comparison of the finite element method required section L/D to that of the transfer matrix major mass method is presented for both a uniform shafting geometry and a typical centrifugal compressor model.

Conclusions and recommendations will be given concerning the required section L/D for improved rotor system analysis accuracy when using lumped inertia rotor models.
Prediction of Periodic Response of Rotor Dynamic Systems With Nonlinear Supports
Authors: Wang Yu
Published: March 2021

A numerical-analytical method for estimating steady-state periodic behavior of nonlinear rotordynamic systems is presented. Based on a finite element formulation in the time domain, this method transforms the nonlinear differential equations governing the motion of large rotor dynamic systems with nonlinear supports into a set of nonlinear algebraic equations with unknown temporal nodal displacements. A procedure is proposed to reduce the resulting problem to solving nonlinear algebraic equations in terms of the coordinates associated with the nonlinear supports only. The result is a simple and efficient approach for predicting all possible fundamental and sub-harmonic responses. Stability of the periodic response is readily determined by a direct use of Floquet’s theory. The feasibility and advantages of the proposed method are illustrated with two examples of rotor-bearing systems of deadband supports and squeeze film dampers, respectively.
Rotor Bearing System Design on Magnetic Bearings
Authors: De Choudhury Pranabesh
Published: March 2021

The rotordynamic analysis of a high speed multistage centrifugal compressor supported on radial magnetic bearings, which has been running successfully in the field for 9000 hours to date, is presented. Iterations required to achieve an acceptable rotor configuration using magnetic bearings are discussed. The results of the rotor-bearing system on standard fluid film five shoe tilting pad journal bearings are compared to the dynamics of the rotor on magnetic bearings.

Correlation of the observed peak responses with those predicted on magnetic bearings is presented. The actual orbit plots and frequency plots during the coastdown of the rotor-bearing system on auxiliary ball bearings are discussed.
Asymptotic Analysis of the Torsional Vibrations in Reciprocating Machinery
Authors: Ashrafiuon Hashem , Whitman Alan M.
Published: March 2021

A class of two degree of freedom reciprocating machines is analysed and simple asymptotic expressions for both the steady state and transient vibration levels are obtained. The results are compared with those of a standard numerical modeling package, and are found to be in good agreement for parameter values typical of real machines. This happens because real machines are designed so that the vibration levels are small, thereby satisfying the conditions for the validity of the approximation.
Entrance Effects in Annular Seal Flows
Authors: Arghir Mihai , Frene Jean
Published: March 2021

The paper presents the theoretical results for a test case proposed by Staubli (1993) that allows testing the procedures for predicting rotordynamic coefficients of plain annular seals. The calculations were made using the time averaged Navier-Stokes equations. The results underline the weaknesses of the traditional turbulence models. Comparisons with a thin fluid film based procedure show that the entrance zone in the seal, where the flow is not a parallel one, influences the radial force and so the direct dynamic stiffness coefficient.
Studies on Determination of Natural Frequencies of Industrial Turbine Blades
Authors: Bhat Mahesh M. , Ramamurti V. , Sujatha C.
Published: March 2021

Steam turbine blade is a very complex structure. It has geometric complexities like variation of twist, taper, width and thickness along its length. Most of the time these variations are not uniform. Apart from these geometric complexities, the blades are coupled by means of lacing wire, lacing rod or shroud. Blades are attached to a flexible disc which contributes to the dynamic behavior of the blade. Root fixity also plays an important role in this behavior. There is a considerable variation in the frequencies of blades of newly assembled turbine and frequencies after some hours of running. Again because of manufacturing tolerances there can be some variation in the blade to blade frequencies. Determination of natural frequencies of the blade is therefore a very critical job. Problems associated with typical industrial turbine bladed discs of a 235 MW steam turbine are highlighted in this paper.
Modal Analysis of a Laminated Stator Core
Authors: Dias M. , Weber H. I.
Published: March 2021

One of the main reasons for the acoustical noise and vibrations in electrical machines is the excitation of the stator due to the presence of magnetic harmonics in motors and generators. During the design of these machines one must care that the frequencies of the excitation forces do not coincide with the natural frequencies of the stator, which would increase considerably the acoustic noise levels and the vibrations.

This work concerns the study of dynamic behavior of segmented (laminated) structures that will define the natural frequency of stators. Our main interest consists in the longitudinal modes of cylindrical segmented shells where the effect of discontinuous layers is more concentrated. A comparison of proposals for modelling of stators is done with the results of experimental modal analysis of a stack of metal sheets, clamped with tie rods and with the clamping pressure controled through strain gages. A study of these structures considered orthotropic (and not isotropic as one normally assumes) is done.
Vibration Control in Turbomachinery Blading Using Lacing Wires
Authors: Wang Robert X. , Chapman Graham M.
Published: March 2021

In turbomachinery practice the use of inter-blade coupling is an accepted procedure. The use of lacing wires in highly stressed short blading introduces damping and also modifies the vibration characteristics of the blading. This paper reports on a study into the dynamic characteristics of single blades with a lacing wire. Vibration analysis is carried out using finite element modelling. The theoretical results are verified using Electronic Speckle Pattern Interferometry technique (ESPI).
Adaptive Virtual Autobalancing for a Magnetic Rotor With Unknown Mass Imbalance: Part I — Static Balancing
Authors: Lum Kai-Yew , Bhat Sanjay P. , Bernstein Dennis S. , Coppola Vincent T.
Published: March 2021

An adaptive control scheme is proposed for stabilizing a planar rotor mounted on a magnetic bearing. The control strategy involves the concept of virtual autobalancing, where the control algorithm emulates the dynamics of a mechanical autobalancer by applying forces that are equivalent to the action of the autobalancer on the rotor. Equations of motion for a planar, torque-free, elastically suspended rotor equipped with an autobalancer are derived. Based on these equations, an adaptive controller for the magnetic rotor is formulated. The results are demonstrated in simulation.
Analytical Study of Dispersion of Stress Waves in a Weakly Coupled Layered System
Authors: Vakakis A. F. , Cetinkaya C.
Published: March 2021

Dispersion of transient stress waves in the first layer of a weakly coupled semi-infinite bi-layered system is carried out. Fourier transform inversions are performed analytically by making use of the fact that the weakly coupled system possesses small propagation zones (PZs) in the frequency domain. Low- and high-frequency asymptotic approximations to the transient waves are computed, taking into account frequency components of the transfer function in the first and second PZs, respectively. The derived analytic expressions are superpositions of non-oscillating terms and convolution integrals with decaying oscillatory kernels. Depending on the frequency and the amplitude of the convolution kernels, the dispersed waves overshoot or undershoot the applied impulsive excitation. This result is of significant practical importance in the design of layered systems as stress attenuators.
Vibration Localization in Rotating Shafts: Part I — Theory
Authors: Ulsoy A. Galip , Pierre Christophe , Choi Suhyun
Published: March 2021

This paper presents a theoretical study of vibration localization in single-span, flexible, rotating shafts. A non-circular cross-section of the rotating shaft, leading to dissimilar lateral moments of inertia, can introduce disorder. Internal coupling between the principal directions of vibration is provided by the rotational speed through the gyroscopic moments. It is shown, using both exact and perturbation solutions, that directional vibration localization can occur for certain appropriate combinations of disorder and coupling.