bluuebunny/crossref_metadata_2025 huggingface dataset:
On the Inherent Characteristics of the Dynamics of Robot Manipulators
Authors: Tu Q. , Rastegar J.
Published: April 2021

The inherent characteristics of the (nonlinear) dynamics of robot manipulators are studied. The study is based on a new method, referred to as the trajectory pattern method. The inverse dynamics models of the manipulator are divided into classes of inverse dynamics models, each corresponding to a different trajectory pattern. For each trajectory pattern, the structure of the resulting inverse dynamics model is fixed and is used to study the characteristics of the dynamics of the manipulator by examining the harmonic content of the required actuation torques (forces) and the relative significance of each harmonic. The harmonic content of the actuating torques is shown to be a function of the path length in the joint coordinate space and the harmonic content of the selected trajectory pattern, but is independent of the number of degrees-of-freedom of the manipulator. The relative contribution of each harmonic is a function of the path length, direction of motion, the position of the path of motion within the workspace of the manipulator, and the magnitude of the fundamental frequency. The study provides a systematic approach to path and trajectory planning from the vibration control point of view. As an example, the characteristics of the dynamics of a spatial 3R manipulator is studied for motions with two different path lengths, starting from a specified point and extending in different directions.
Robot Task Oriented Dexterity and Dynamic Performance: A Statistical Approach
Authors: Beretta A. , Marchis V. , Sinatra R.
Published: April 2021

Robot task oriented dexterity has recently reached a well-known acknowledgment for its capability of definig robot arm manipulability figures, over the working space. Because it seemed to the authors that not yet robot dynamic performances have been taken into account in defining its local properties, it has been studied a simple 2R robot arm, in order to identify the most siutable parameters for this scope.

By simulating a mathematical model forced with random input signals (forces), its dynamic behaviour has been investigated with a Monte Carlo approach. Without willing to obtain a complete modal analysis, some numerical parameters have been found as capable to identify system dynamics, e.g. the principal direction of system free oscillations, and its eigenfrequency value. Discussion of the results over the workspace and as a function of system mechanical stiffness properties is also performed.
A Cartesian Workspace Generator for Robot Arm Workcell Obstacle Collision Avoidance
Authors: Luk Tak-Lai Daryl , Sneckenberger John E.
Published: April 2021

Most of the methods for planning collision-free robot manipulator arm morions to accomplish collision-free end-effector paths are based on explicit representation of the sub-space of the robot work space that is free of arm motion with obstacles collision. This sub-space is called the robot arm free space and most path planners represent this free space in joint space. If the robot arm free space is represented in joint space, then each point in the free space corresponds to a robot arm configuration for which no arm-obstacle collision occurs. This paper presents a new approach for generating the robot arm free space for an articulated type robot manipulator. This approach uses an oscillating slider crank mechanism for defining the free-space boundary when certain arm-obstacle collisions occurs. The robot arm free space, importantly, is generated in Cartesian space instead of joint space.
Response of a Rotating Beam Subject to an Accelerating Force
Authors: Argento A. , Scott R. A.
Published: April 2021

A method is given by which the response of a rotating Timoshenko beam subjected to an accelerating fixed direction force can be determined. The beam model includes the gyroscopically induced displacement transverse to the direction of the load. The solution for pinned supports is set up in general form using multi-integral transforms and the inversion is expressed in terms of convolution integrals. These are numerically integrated for a uniformly distributed load having an exponentially varying velocity function. Results are presented for the displacement under the load’s center as a function of position. Comparisons are made between the responses to a constant velocity load and a load which accelerates up to the same velocity.
Spontaneous Sidebanding in High Speed Rotordynamics
Authors: Ehrich Fredric
Published: April 2021

Several observations have been made in the Fourier spectra of high speed rotordynamic response of uniformly spaced frequency spikes on either side of key synchronous or subharmonic or superharmonic response frequencies. In instances where this so-called “sidebanding” could not readily be explained as the nonlinear interaction or combination tones of two distinct responses at slightly different frequencies, we have referred to this class of phenomena as spontaneous sidebanding.

It is invariably noted that the sideband spacing frequency appears to be a whole number fraction (1/J) of the operating speed which suggests that the wave form is periodic and completes a full cycle every J rotations of the rotor. Using a numerical model of a rotor which simulates local contact with a stator in close proximity as a bilinear spring, several studies have been carried out to explore the circumstances for this spontaneous sidebanding. Two general classes of this type of response have been found.

A) For highly nonlinear systems, the chaotic-like response in transition zones between successive orders of subharmonic and superharmonic operation is actually periodic and results in spontaneous sidebands clustered around the key subharmonic or superharmonic frequencies.

B) In trans-critical operation of highly nonlinear and lightly damped systems, a major sideband frequency spike is noted at a frequency which is approximately the system’s natural frequency. Recognition of this fact permits a simple estimate of the repetition index (J).

All these observations from operation of the numerical model have been compared with experimental data derived from incidents of spontaneous sidebanding on aircraft gas turbine rotors. Excellent qualitative agreement has been found in most instances.
Weight-Excited Vibrations of Rotating Curved Beams
Authors: Wauer Jörg
Published: April 2021

Flexural vibrations of a slender rotating beam whose centre line is assumed to be naturally curved are considered. The beam, simply supported and axially restrained rotates at a constant speed about a horizontal axis in a gravity field. In one case, the rotational axis is parallel to the line connecting the centroids of the end cross-sections, and, in the other case, it is perpendicular to that line. A modal truncation of the governing nonlinear boundary value problem yields a set of ordinary gyroscopic differential equations of the Duffing type. For the cases of a cross-section with extremely different bending stiffnesses and a circular cross-section, the vibrational behaviour is analyzed in detail. The steady-state response (neglecting the influence of gravity) and its stability are considered first. A numerical investigation of weight-excited oscillations follows, where both periodic and even chaotic motions may occur. The effect of different damping mechanisms is addressed. A comparison with the dynamic snap-through of a non-rotating arch and the nonlinear vibrations of a rotating straight bar concludes the contribution.
Nonlinear Steady-State Rotordynamic Analysis Using Transfer Coefficient Method
Authors: Kobayashi M. , Saito S. , Yamauchi S.
Published: April 2021

This paper proposes a new method for steady-state, large-order nonlinear rotordynamic calculations: it uses a method called the transfer coefficient method (TCM), which is more convenient than the transfer matrix method. Since TCM calls for only the displacement as the independent variable, whereas both the displacement and the force are needed as the state variables in the conventional transfer matrix method, TCM promises a substantial saving of computation time without incurring loss in the accuracy of calculation. First, the outline of TCM is explained, then the nonlinear calculations for a rotor of many degrees of freedom are presented. This steady-state nonlinear calculation method is based on the discreet Fourier transform (DPT, FFT) and substructure synthesis. As an example, the nonlinear response due to unbalance mass is calculated and discussed in the case of the rotor which is supported by three bearings with two nonlinear squeeze film dampers.
A Slewing Motor-Beam System: Performance, Behavior and Dimensional Analysis
Authors: Sah Jy-Jen F. , Mayne Roger W.
Published: April 2021

This paper considers the behavior of a slewing beam driven by a DC motor. State equations are presented based on a finite element representation of the beam and a dynamic motor model. The equations are nondimensionalized to view the system parameters in dimensionless groups. Attention is particularly focused on a “damping group” which allows beam vibration to be damped by interaction with the motor. Results are presented in both the frequency domain and time domain which show the effects of motor-beam interaction. These include a change in the beam vibration modes from clamped-free to pinned-free and the development of significant first and second mode damping in a frictionless beam representation.
Virtual Balancing of Rotors Supported by Magnetic Bearings
Authors: Chen H. Ming , Ku C. P. Roger
Published: April 2021

A rotor supported by magnetic bearings can be made to spin about its inertia axis, thus greatly attenuating the imbalance forces that are transmitted through the bearings. Conventional control schemes using tracking notch filters to achieve this purpose are sometimes unstable. This paper presents a rotordynamic analysis, in the form of a computer code, to explain and predict stability in systems using these filters. An alternative balancing scheme, called Virtual Balancing, which is used to implement stable balancing with magnetic bearings, is also described. This scheme treats the bearings as balancing planes and applies an influence coefficient method to relate machine casing vibrations to feed-forward control signals injected to the bearings.
A Comparison of Experimental Results and Theoretical Predictions for the Rotordynamic Coefficients of Short (L/D = 1/6) Labyrinth Seals
Authors: Pelletti Joseph M. , Childs Dara W.
Published: April 2021

Experimental results for the rotordynamic coefficients of short (L/D = 1/6) teeth-on-stator and teeth-on-rotor labyrinth seals are presented. The effects that pressure ratio (fluid density), rotor speed, fluid pre-swirl and seal clearance have on these coefficients are studied. Tests were run out to speeds of 16000 rpm with a supply pressure of 17.3 bar and seal clearances ranging from 0.229–0.419 mm. The experimental results are compared with theoretical predictions of a two control volume compressible flow model.

The experimental results show that decreases in pressure ratio and increases in rotor speed are stabilizing while increases in fluid pre-swirl and seal clearance are destabilizing for both seal configurations. The theoretical model correctly predicts the effects of pressure ratio, rotor speed and fluid pre-swirl on the cross-coupled stiffness. It also predicts reasonable values for direct damping for all test conditions. However, the theory incorrectly predicts the effect of seal clearance on these coefficients. Consequently the theoretical predictions are much better for the large clearance seals.
Consistent Modeling of Rotating Timoshenko Shafts Subject to Axial Loads
Authors: Choi S. H. , Pierre C. , Ulsoy A. G.
Published: April 2021

The equations of motion of a flexible rotating shaft have been typically derived by introducing gyroscopic moments, in an inconsistent manner, as generalized work terms in a Lagrangian formulation or as external moments in a Newtonian approach. This paper presents the consistent derivation of a set of governing differential equations describing the flexural vibration in two orthogonal planes and the torsional vibration of a straight rotating shaft with dissimilar lateral principal moments of inertia and subject to a constant compressive axial load. The coupling between flexural and torsional vibration due to mass eccentricity is not considered. In addition, a new approach for calculating correctly the effect of an axial load for a Timoshenko beam is presented based on the change in length of the centroidal line. It is found that the use of either a floating frame approach with the small strain assumption or a finite strain beam theory is necessary to obtain a consistent derivation of the terms corresponding to gyroscopic moments in the equations of motion. However, the virtual work of an axial load through the geometric shortening appears consistently in the formulation only when using a finite strain beam theory.
Rotor System Modeling With Foundation Matrices From Experimental Modal Data
Authors: Stephenson Robert W. , Rouch Keith E.
Published: April 2021

In a rotor system, the bearing housing and foundation structure can have a significant effect on the dynamics of the rotor. A general procedure is presented to include the foundation effects in a rotor system analysis. The procedure uses modal analysis techniques and measured frequency response functions of the actual foundation structure. From this test data, mass, damping, and stiffness matrices are constructed. These matrices can then be assembled with a finite element model of the shaft and bearings to form the overall rotor system model.

Unbalance response and system natural frequencies obtained from a laboratory rotor mounted on a flexible foundation are presented, and compared to results computed from a system model which includes foundation matrices constructed from a dynamic test on the actual foundation.
Rotor Whirl Measurements on a Long Rotating Cylinder Partially Filled With Liquid
Authors: Colding-Jorgensen Jorgen
Published: April 2021

A theoretical analysis of a long flexibly suspended, rotating cylinder partially filled with liquid has been presented earlier (Colding-Jørgensen, 1990). Special emphasis has been placed on dynamic stability, application in centrifuges, and the influence of external damping.

The present paper presents, experimental results for comparison with the theoretical analysis, especially in regard to unstable speed ranges, whirl speed relative to rotational speed, and limit cycle amplitudes with external damping.

The theory agrees quantitatively with regard to speed ranges and whirl frequency ratios but only qualitatively with regard to whirl amplitudes, indicating the need for further development of the non-linear analysis of the fluid motion with external damping.
Determination of Non-Conservative Coupling Loss Factors Between Rotating Machinery Components
Authors: Cuschieri J. M. , Sun J. C. , Journeau F.
Published: April 2021

An expression for calculating the coupling loss factors between non-conservatively coupled substructures is derived based on the characteristics of the coupled substructures and the interface medium. The expressions consists of point mobility functions evaluated on the substructures near or at the junctions and a joint impedance function which represents the interface characteristics. The point mobility functions can be obtained analytically, for simple structures, or experimentally. The joint impedance is modeled by a dissipative stiffness element. The derived expressions for the coupling loss factors simplify to the well known expressions for conservative coupling when the dissipation term tends to zero. This approach is used to estimate the coupling loss factor between a shaft and a bearing liner with an oil film interface. The estimated results for the coupling loss factors are compared to experimental results obtained from a statistical energy analysis model. The estimated results and the experimental results show good agreement which verifies the approach used for the determination of the non-conservative coupling loss factors.
Effect of Backlash on Vibration Spectrum in Spur Gearboxes Incorporating Sleeve Bearings
Authors: El-Saeidy Fawzi M. A.
Published: April 2021

An Analytical model is presented to simulate effect of tooth backlash on vibration spectrum of spur gearboxes incorporating sleeve bearings. Included in the model are: elasticity of shafts, friction between meshing teeth, interaction between gearbox casing and internals, and time-varying tooth backlash (backlash is a function of operating center distance), mesh stiffness (stiffness is calculated based on the strain energies of the tooth that is treated as a cantilever beam of involute shape) and Hertzian mesh damping. The bearing forces are calculated with consideration of bearing radial clearance and system vibrations. The analysis is applied to a single stage gearbox and equations of motion are numerically integrated to obtain system reponse in time domain. This response is transformed into frequency domain (vibration spectrum) using Fast Fourier Transform (FFT) algorithm and samples of the results are shown for different values of tooth backlash. The results show that backlash has a pronounced effect on gearbox vibration and study provides an analysis procedure for predicting such effects.
Fluid Inertia Forces in Squeeze Film Dampers
Authors: El-Shafei A. , Crandall S. M.
Published: April 2021

Fluid inertia forces in Squeeze Film Dampers (SFDs) are obtained for short and long dampers using an energy approximation based on the assumption that the velocity profiles with inertia are the same as those for an inertialess fluid. It is shown that the inertia forces thus obtained are proportional to the usual radial, centripetal, tangential and Coriolis accelerations of the journal, plus an additional nonlinear acceleration. The inertia coefficients of the dampers are obtained, for both uncavitated and cavitated dampers, and are plotted versus the eccentricity ratio for centered, nearly circular whirl. The inertia forces obtained by the energy approximation are compared to an exact linearized solution for centered, circular whirl, and good agreement is found for both short and long dampers in the Reynolds number range of ordinary SFD application.
The Effectiveness of Porous Squeeze Film Dampers for Suppressing Nonsynchronous Motions
Authors: Zhang Shiping , Yan Litang , Li Qihan , Kawazoe Yoshihiko
Published: April 2021

The rotor time domain orbits and the transmissibility trajectories of a rigid rotor supported on squeeze film damper (SFD) and porous squeeze film damper (PSFD) systems were investigated. Under certain system parameters, The SFD system with a centralising spring exhibits excessive nonsynchronous motions with approximate third harmonic frequencies and opposite whirling motions as well as severe transmitted forces. However, under same system parameters and with a porous permeable film outer race PSFD system could effectively attenuate the nonsynchronous motions with very small transmissibilities. The rigid rotor without a centering spring supported on SFD and PSFD systems were also investigated. The highly nonlinear film force characteristics take the major responsibility for the nonsynchronous motions of uncentralized SFD systems, and typical second and third harmonic orbits of SFD system were predicted. While under the same conditions, perfect synchronous orbits of PSFD system were resulted. PSFD through outer race permeability could provide more reasonable film force characteristics, and thus has the capability of suppressing nonsynchronous motions.
Optimal Design of Centered Squeeze Film Dampers
Authors: Nataraj C. , Ashrafiuon Hashem
Published: April 2021

A two degree-of-freedom model, consisting of a rigid rotor supported on rigid bearings which are in turn supported on squeeze film dampers, is considered. Isotropic centering springs are assumed resulting in a steady synchronous centered circular response for the rotor. The resulting nonlinear system is modeled in nondimensional form. The transmissibility ratio of the system as well as the power dissipated are minimized for various values of unbalance and at several speeds, with the squeeze film bearing parameter as the primary design variable. Expressions are derived for linear variational stability of the circular orbit, and are imposed as constraints in the optimization process. The dependence of the optimal configuration on speed and unbalance is discussed.
Experimental Investigation on the Dynamic Pressure and Force Response of a Partially Sealed Squeeze Film Damper
Authors: Meng G. , Andres L. A. San , Vance J. M.
Published: April 2021

The influence of rotational speed, oil temperature and supply pressure on the squeeze film pressure and fluid forces is investigated experimentally for a partially sealed squeeze film damper (SFD) test rig executing circular centered orbits. Experimental Tesults show that the sealed damper produces higher damping forces than an open end SFD, though it is more prone to produce oil cavitation. As a result, the peak-to-peak pressures and the tangential force (damping force) decrease with increasing rotational speed; while, the radial force (stiffhening force) becomes negative due to the large extent of the cavitation zone. The tangential force decreases and the radial force increases with increasing lubricant temperature. The squeeze film pressure and film force increase as the supply pressure rises. The film cavitation onset is determined by the level of supply pressure and rotational speed.
Controllable Squeeze Film Damper: An Application of Electro-Rheological Fluid
Authors: Morishita Shin , Mitsui Jun’ichi
Published: April 2021

A notable characteristic of Electro-Rheological (ER) fluid is the variation of its apparent viscosity with the application of an electric field. The application of this characteristic to the performance of squeeze film damper of a flexible rotor is investigated in this paper. It is shown experimentally that by controlling the supporting damping capacity continuously, rotor vibration can be reduced remarkably in a wide range of rotating speed. Moreover, the study indicates experimentally that there exists an optimum supporting damping for every vibration mode.
Vibrations of Foundations Interacting With Subsoil Experimental Studies and BE Calculations
Authors: Gaul L.
Published: April 2021

Calculation of the dynamic response of sensitive structures like foundations for vibrating machinery requires to take the interaction with subsoil into account. Structures and soil are discretized by boundary elements and coupled by a substructure technique. Viscoelastic constitutive equations contain fractional time derivatives.

Surface waves generated by machine foundations and diffracted by embedded structures and soil inhomogeneities are analyzed by conventional and optoelectronic experimental techniques and calculated by the boundary element method (BEM).
Self-Operating On-Off Type Semi-Active Damper and its Performance Test
Authors: Kim Hyeong-keun , Sung Nak Hoon , Park Youn-sik
Published: April 2021

The semi-active damper idea is not new. Many previous researchers showed that a semi-active damper and an on-off type semi-active damper can each bring about almost die equivalent suspension performance as that of an active suspension system. In this work, a self-operating on-off type semi-active damper idea is devised. The advantage of the self-operating on-off type semi-active damper over the conventional semi-active damper or on-off type semi-active damper is its mechanical simplicity. The self-operating semi-active damper does not need any sensors and logic circuits for on-off control motion and brings about an identical suspension performance. In order to prove the practical applicability of the damper, two prototype dampers are designed, built and tested. As a result, the tested prototype damper shows very good agreement not only with the peak damping forces, but also with the timely self-operating on-off valve motion.
Semiactive Control of Vibrations in Automobiles
Authors: Lieh Junghsen , Haque Imtiaz
Published: April 2021

A seven-DOF vehicle model comprising a full car body and four wheel-axle assemblies is used to investigate the influence of active and semiactive suspensions on ride performance. The active control of car body roll, pitch and bounce is based on an optimal control strategy assuming the tire deflection measurements are not available. The frequency analysis shows a significant attenuation in car body modes but a potential increase in wheel motions. Dissipative dampers with solenoid valves are used as the semiactive control mechanism. Simulation results in the time domain indicate that suboptimal values exist in the damping “on” state and an on-off damping control scheme can effectively reduce the car body motions and suspension travels.
Integral and State Variable Feedback Controllers for Improved Performance in Automotive Vehicles
Authors: ElMadany Mohamed M.
Published: April 2021

An analytical investigation of a half-car model using an integral plus state variable feedback controller for tracking and regulation is performed. The potential benefits of incorporating, actively or semi-actively, such controller to remedy the inherent problems associated with conventional passive suspensions and active suspensions based on state variable feedback controllers are examined. Both random and deterministic roadway inputs as well as deterministic body force and moment disturbances are used. The results demonstrate that an optimal suspension using an integral plus state variable feedback controller retains both excellent ride and attitude control characteristics.
Application of Generalized Polynomial Expansion Method to Nonlinear Rotor Bearing Systems
Authors: Hwang Jon Li , Shiau Ting Nung
Published: April 2021

The Generalized Polynomial Expansion Method (GPEM) is utilized to model a large-order flexible-rotor system with nonlinear supports. With the application of GPEM, a set of nonlinear ordinary differential equations are obtained. A hybrid method which combines the merits of the Harmonic Balance Method (HBM) and the Trigonometric Collocation Method (TCM) is used to solve for the nonlinear response of the system. This hybrid method together with reduction techniques can efficiently solve for the motion of the system. The overall algorithm presented provides a very efficient technique for investigating the periodic response of large-order nonlinear rotor systems. Two examples are used to illustrate the merits of the method. One is the simple Jeffcott rotor which is used to check the accuracy of the present numerical algorithms. The other is a flexible shaft with multiple disks, supported by multiple bearings. It is used to show the advantages of the linkage between GPEM and the presented hybrid numerical algorithm. Some of the support bearings are modeled as a squeeze-film damper associated with a center spring. The center spring is considered to be linear and the squeeze-film damper is nonlinear. The nonlinear hydrodynamic forces are obtained using short-bearing theory.

Based on the example results, the conclusions can be summarized as follows:

(l) For a nonlinear flexible-rotor system, the number of equations needed for the system described by the Generalized Polynomial Expansion Method are always smaller than the number required by the finite element method before applying the condensation technique. This is also true for the linear case which has been discussed by Shiau and Hwang (1989, 1990).

(2) A technique of component mode synthesis has been developed based on the modeling approach of the Generalized Polynomial Expansion Method. It is applied to decouple the nonlinear independent and dependent modal coordinates. With this technique, the number of non-zero elements in the generalized modal-forces vector is equal to the number of nonlinear, dependent modal coordinates. The results indicate that the use of GPEM together with component mode synthesis not only retains its merits in solving a linear rotor-dynamic problem, but also provides attainable solutions for the nonlinear rotor-dynamic problem.

(3) The hybrid numerical algorithm developed in the present study combines both the advantages of the harmonic-balance method and the collocation method. The use of this hybrid method with condensation technique can significantly save computing time. Furthermore, it can be used to predict the periodic response, including the sub-harmonic response and the super-harmonic response, of a nonlinear system.

(4) The time required for the initial formulation processing with this method may be a little more than that required by the finite-element approach. However, it is very small compared to the overall time savings that are accrued.
Nonobstructive Particle Damping (NOPD) Performance Under Compaction Forces
Authors: Panossian H. V.
Published: April 2021

Presented herein are nonobstructive particle damping (NOPD) performance characteristics under forced compaction conditions. NOPD is a new passive vibration damping technique that consists of making small diameter holes (or cavities) at appropriate locations inside the main load-paths of a vibrating structure and filling these holes to appropriate levels with such particles that yield the maximum damping effect. Metallic or nonmetallic particles in powder, spherical, or liquid form (or even mixtures) with different densities, viscosities, and adhesive and cohesive characteristics can be utilized.

In an effort to simulate centrifugal forces on particles placed inside blades of high rotational speed turbomachines, a special test article was made and different particles were tested under various compaction forces and vibration amplitudes. The effectiveness of NOPD was measured and compared with no compaction and no-particle conditions.
Determination of Instability Boundaries for a Highly Flexible Prismatic-Jointed Robot Performing Repetitive Maneuvers
Authors: Buffinton Keith W.
Published: April 2021

Presented in this work are the equations of motion governing the behavior of a simple, highly flexible, prismatic-jointed robotic manipulator performing repetitive maneuvers. The robot is modeled as a uniform cantilever beam that is subject to harmonic axial motions over a single bilateral support. To conveniently and accurately predict motions that lead to unstable behavior, three methods are investigated for determining the boundaries of unstable regions in the parameter space defined by the amplitude and frequency of axial motion. The first method is based on a straightforward application of Floquet theory; the second makes use of the results of a perturbation analysis; and the third employs Bolotin’s infinite determinate method. Results indicate that both perturbation techniques and Bolotin’s method yield acceptably accurate results for only very small amplitudes of axial motion and that a direct application of Floquet theory, while computational expensive, is the most reliable way to ensure that all instability boundaries are correctly represented. These results are particularly relevant to the study of prismatic-jointed robotic devices that experience amplitudes of periodic motion that are a significant percentage of the length of the axially moving member.
Aerodynamics of Moving Belts, Tapes, and Webs
Authors: Chang Y. B. , Fox S. J. , Lilley D. G. , Moretti P. M.
Published: April 2021

The mass of the air surrounding a moving belt leads to a number of forces normal to the belt: hydrodynamically induced inertia, Coriolis force, and centrifugal force. These forces act in concert with those generated by the belt’s own inertia to govern out-of-plane dynamics. Their effect is to reduce stability and limit the safe running speed. These detrimental consequences can be reduced through management of the air flow around the belt. An analysis of the governing partial differential equations is presented; experiments on the aerodynamic interaction terms are reported; and a numerical simulation method for belt dynamics is outlined.
On the Stability of Chain Drive Systems Under Periodic Sprocket Oscillations
Authors: Wang K. W.
Published: April 2021

Experimental observations have shown that periodic torsional oscillations of engine camshafts induced by powertrain loads can cause significant tension variation in the timing chain and magnifies the chain transverse vibrations and noise level. This result indicates that the sprocket dynamic characteristics and the chain vibration behavior are closely coupled. The chain drive models to-date are not able to address these phenomena. This paper presents a nonlinear model of an integrated chain drive system which couples the sprocket motion with the transverse and longitudinal vibration of the axially-moving chain spans. With this model, the effects of the sprocket shaft periodic loads upon the total system are investigated. It is concluded that the sprocket oscillations will cause chain longitudinal vibrations. This could destabilize the system and induce the chains to undergo large transverse vibration. Both the subharmonic and summation types of parametric resonance are found and the instability regions are derived. The effects of various system parameters, such as the sprocket inertia, the chain speed, and the speed dependent excitation frequencies upon the instability regions have been studied. The significance of the gyroscopic terms on the prediction of the stability boundary has been shown. This paper presents an approach that provides new insight to the research of chain drive dynamics.
Dynamic Deflection of Paper Emerging From a Channel
Authors: Stolte James , Benson Richard C.
Published: April 2021

For many machines handling lightweight, flexible sheets, it is necessary for the sheet to transit an open space. Examples include magnetic tape drives, xerographic copiers, and sewing machines. The nonlinear theory of the elastica has often been used to model nonlinear, static deflections. Dynamic modeling is more difficult, and far less studied. Recently, however, L. Mansfield and J.G. Simmonds (1987) have considered the dynamic deflection of a sheet emerging from a horizontal channel at constant velocity and subjected to gravity loading. In this paper, we consider a generalization of that problem to include arbitrary exit angles, and an accelerating “feed” rate. Gravity loading is retained. The resulting nonlinear equations of motion are tractable and are solved numerically.
Dynamic Response of an Axially Moving Beam Coupled to Hydrodynamic Bearings
Authors: Tan C. A. , Yang B. , Mote C. D.
Published: April 2021

The vibration response of a distributed axially moving beam, controlled through distributed hydrodynamic bearing forces, is analyzed by the transfer function method. In the axially moving beam, all modes are affected by the distributed bearing coupling. The bearing force is described in terms of impedance functions. An approximate closed-form transfer function for the coupled beam-bearing system is derived. The transfer function is applicable to all linear, one-dimensional, coupled systems, and it is exact for localized, linear constraint forces. The derivation requires knowledge of the transfer function of the axially moving beam which is not available in the literature. A method for determining the beam transfer function is also presented. The frequency response of the coupled system is illustrated for several beam and bearing design parameters.
On the Stability and Nonlinear Dynamics of a Horizontally Base-Excited Shaker/Mould Structure With Unsymmetric End Stiffnesses
Authors: Cheng John K. H. , Wang K. W.
Published: April 2021

This paper presents a dynamic analysis of a horizontally base -excited shaker/ mould structure with unsymmetric gripper stiffnesses. The study explains the large rotational and transverse vibrations of the mould at specific operating frequencies observed in the experiments. The governing equations consist of a time-dependent coefficient which indicates the existence of parametric excitation effects. It is concluded that differences between the gripper stiffnesses are responsible for this phenomenon and could destabilize the system. The value of the time-varying parameter is related to the horizontal vibration amplitude of the mould and hence is a function of the system parameters and excitation frequency. The mould’s rotational motion is directly parametrically excited while its transverse vibration is excited indirectly through coupling with the rotational motion. A thorough analysis of this class of mechanical systems has not been performed in the past. In this research, studies are conducted to identify the contributions of various system parameters, such as gripper stiffness, damping, mould inertia, and excitation amplitude to the system dynamic characteristics. The results provide new insight and guidelines toward optimizing such mechanical systems.
On the Impact Intensity of Vibrating Axially Moving Roller Chains
Authors: Wang K. W. , Liu S. P. , Hayek S. I. , Chen F. H. K.
Published: April 2021

Experimental observation has shown that the most significant noise source in roller chain drives is from the impacts between the chain and the sprocket during their meshing process. Despite its importance, studies have not been made to thoroughly analyze the chain/sprocket impact dynamics and their interaction with the vibrating, axially moving chain structure. This paper presents a novel analysis which integrates the local meshing phenomena with the global system. An axially moving chain interacting with local impacts has been modelled and the momentum balance method is employed to derive the impulse function. Convergence of the impulse function is examined and a study is carried out to quantify the intensity of subsequent impacts. It is found that the impact intensity is significantly affected by the vibration characteristics and response of the moving chain, and vice versa. The classical quasi-static approach will create errors in predicting the impulse magnitude and system response. This fundamental investigation provides new insight to roller chain dynamics, which is an essential step toward the design of quiet chain drives.
Vibration of Euler-Bernoulli Beams With Arbitrary Boundaries and Intermediate Constraints
Authors: Yong Yan
Published: April 2021

It is an easy task to obtain the analytical solution for a simple Euler-Bernoulli beam. Difficulties, however, do arise when a beam structure has a large number of different-type intermediate constraints, such as exterior simple supports, interior hinges, rollers and other elastic supports. The purpose of this paper is to develop a systematic approach to obtain exact solutions for any kinds of complex beam configurations. The main feature of this approach is that the vibration motion is treated as the result of wave scattering around different media. The discovery of wave scattering phenomena around intermediate constraints sheds the light, for the first time, on the fact that any constraint can serve as a waveguide capable of transmitting and reflecting waves in either directions. This new finding enables us to treat a complex beam structure as a stepped beam which can be handled easily by using the wave propagation approach, previously developed by Yong and Lin (1989) for the analysis of piece-wise periodic structures.
Vibration of a Spinnng Annular Disk With Coupled Rigid Body Motion
Authors: Yang Shih-Ming
Published: April 2021

The vibration of a spinning annular disk with coupled translational and rotational rigid body motion is analyzed. The spinning disk, with one linear spring as transverse load, is free to translate and rotate relative to the shaft axis. The governing equation includes the rigid body translation, rigid body rotation, and flexible disk vibration. Coupling effect between rigid body motion and each annular disk vibration modes is identified. Because of the coupling effects, stable operation of the spinning disk beyond divergence (critical speed) is achieved, the disk loses its stability to flutter. This stability prediction is different from that of a spinning disk without rigid body motion where the disk is unstable at and right after divergence.
Parametric Excitation Under Multiple Excitation Parameters: Asymmetric Plates Under a Rotating Spring
Authors: Shen I. Y. , Mote C. D.
Published: April 2021

A perturbation method is developed to predict stability of parametrically excited dynamic systems containing multiple perturbation parameters. This method, based on the Floquet theorem and the method of successive approximations, results in a nonlinear matrix eigenvalue problem whose eigenvalues are used to predict the system stability. The method is applied to a classical circular plate, containing elastic or viscoelastic inclusions, excited by a linear transverse spring rotating at constant speed. Primary and secondary resonances are predicted. The transition to instability predicted by the perturbation analysis agrees with predictions obtained by numerical integration of the equations of motion.
Coupling Loss Factors and Coupling Damping for Flanged Cylindrical Shells
Authors: Keswick P. R. , Norton M. P.
Published: April 2021

This paper reports on an investigation into an experimental and theoretical evaluation of coupling loss factors and the experimental evaluation of coupling damping for statistical energy analysis of flanged cylindrical shells. It includes the following.

1. An evaluation of the power injection method and the steady state energy method for determining the coupling loss factors of conservative and non-conservatively coupled cylindrical shells. The investigation also establishes if it is necessary to use post processing or additional damping to the subsystems to obtain meaningful loss and coupling loss factors from the power injection method.

2. Establishment of a procedure for measuring coupling damping using the in-situ loss factors measured from the power injection method for non-conservatively coupled systems. The coupling damping estimates are measured for the same non-conservatively coupled cylindrical shell as used for the coupling loss factor experiments.

3. Usage of an elastic wave propagation analysis to obtain theoretical estimates of the coupling loss factors for cylindrical shells connected by a solid flange joint using the Fliigge stress equations for cylindrical shells. The flange joint arrangement is modelled as a ring connecting the two shell halves, where the Love equations are used to develop the in-plane and out-of-plane ring forces and moment. The coupling loss factor is calculated from the power transmitted across the joint and from the stored energy on the incident side.
An Approach to the Vibration Analysis of Confocal Elliptic Annular Plates
Authors: Huang Shyh-Chin , Wang Jaw-Lin
Published: April 2021

An approach is presented for the vibration analysis of annular, confocal, elliptic plate. The approach employs the separation of variables, finite difference, and receptance concept. This method is then expanded to square plate with center crack, or with more complex geometries. The basic idea of this paper is: split the plate into several strips and get the strips’ characteristic values, then compose these strips by the receptance method to get the characteristics value of the plate. Numerical results for certain cases are compared to known data, and precise agreement is met.
Dynamic Continuum Models of Large Platelike Lattice Structures
Authors: Lee Usik
Published: April 2021

A rational and straightforward method is introduced for developing continuum models of large platelike periodic lattice structures based on energy equivalence. The procedure for developing continuum plate models involves the use of existing well-defined finite element matrices for the easy calculation of strain and kinetic energies of a repeating cell, from which the reduced stiffness and mass matrices are obtained in terms of continuum degrees-of-freedom defined in this paper. The equivalent continuum plate properties are obtained from the direct comparison of the reduced matrices for continuum plate with those for lattice plate. Free vibration analyses for the continuum and lattice plates are conducted to evaluate the continuum method proposed in this paper. Numerical results show that the present continuum method gives very reliable structural and dynamic properties compared to other well-recognized methods.
Frequency Spectra of Laminated Piezoelectric Cylinders
Authors: Siao J. C.-T. , Dong S. B. , Song J.
Published: April 2021

A method is given for determining the entire frequency spectra of a cylinder with cylindrical piezoelectric properties for both propagating modes and edge vibrations. Finite element modeling occurs in the radial direction so that layered profiles can be accommodated. In the vector of displacements and electric potential q(r)exp{iξz + nθ + ωt)}, quadratic polynomials are taken for q(r). Two algebraic eigenvalue problems can be deduced from this finite element formulation depending on whether the axial wave number ξ or the frequency ω acts as the eigenvalue. When real wave number ξ are assigned, an eigenvalue problem results for the natural frequency ω. When ω is assigned, then an eigenvalue problem for ξ emerges, where the values for ξ may be real (for propagating waves) or complex conjugate pairs (for edge vibrations in a semi-infinitely long cylinder). Two examples are given to illustrate the method of analysis, viz., a solid piezoelectric cylinder of PZT-4 ceramic material and a two-layer cylinder of PZT-4 covering an isotropic material.
A 3-D Laminated Plate Theory and Nonlinear Impact Modal Analysis
Authors: Chao C. C. , Tung T. P. , Sheu C. C. , Chern H. J.
Published: April 2021

A three-dimensional theory of cross-ply laminated thick plates is developed via an elasticity approach for nonlinear impact modal analysis. The simply supported plate is strictly stress free over all four edges and both lateral surfaces, in addition to stress-loading equilibrium over the patch loading area. The 3-D dynamic displacement fields are expressed in a mixed mode of double Fourier series and cubic polynomials. A system of modified Lagrange’s equations is derived incorporating all surface conditions and interface displacement and stress continuities. Validity of the present 3-D theory is proved in comparison to the only existing exact solutions in the basic cases of statics and free vibration. The nonlinear impact modal analysis is performed using the Hertz contact law in patch loading and Green’s function for small time linearization. The 3-D displacements and stresses are found to predict a tensile crack at the unimpacted side and probably, a delamination at the interface. They are always unsymmetric with respect to the mid-plane in all cases of unidirectional, symmetric and antisymmetric cross-ply laminates due to the one-sided loading.