bluuebunny/crossref_metadata_2025 huggingface dataset:
The Dual Inertia Operator and Its Application to Robot Dynamics
Authors: Brodsky V. , Shoham M.
Published: June 2008

The principle of transference states that when dual numbers replace real ones all laws of vector algebra, which describe the kinematics of rigid body with one point fixed, are also valid for motor algebra, which describes a free rigid body. No such direct extension exists, however, for dynamics. Rather, the inertia binor is used to obtain the dual momentum, from which the dual equations of motion are derived. This raises the dual dynamic equations to six dimensions, and in fact, does not act on the dual vector as a whole, but on its real and dual parts as two distinct real vectors. Moreover, in order to obtain the dual force as a derivative of the dual momentum in a correct order, real and dual parts have to be artificially interchanged. In this investigation the dual inertia operator, which allows direct relation of dual momentum to dual velocity, is introduced. It gives the mass a dual property which has the inverse sense of Clifford’s dual unit, namely, it reduces a motor to a rotor proportional to the vector part of the former. In a way analogous to the principle of transference, the same equation of momentum and its time derivative, which holds for a linear motion, holds for both linear and angular motion of a rigid body if dual force, dual velocity, and dual inertia replace their real counterparts. It is shown that by systematic application of the dual inertia for derivation of the dual momentum and the dual energy, both Newton-Euler and Lagrange formulations of equations of motion are obtained in a complete three-dimensional dual form. As an example, these formulations are used to derive the inverse dual dynamic equations of a robot manipulator.
Instability and Chaos in Quadruped Gallop
Authors: Nanua P. , Waldron K. J.
Published: June 2008

A dynamic model for the two-dimensional quadruped has been developed. The main body is modelled as a rigid bar and each leg consists of a constant stiffness spring, a viscous damper and a force actuator. Based on symmetry principles, a controller has been devised that will enable the quadruped to gallop at constant speed. The controller consists of two parts: an energy controller which will apply the required amount of force through the legs, and the speed controller that will control the forward speed by appropriately placing the legs. It will be shown that the body pitch need not be explicitly controlled. The stability of this controller will be examined using Poincare maps. Stable systems show either periodic or quasi-periodic response. This system also exhibits chaotic behavior and chaotic response results in instability. The stability of the system with changes in the initial conditions, as well as variations in the system parameters, will also be examined. It will be shown that the system is stable for a range of leg stiffnesses. Outside this range, the system shows chaotic behavior.
Direct Position Kinematics of the 3-1-1-1 Stewart Platforms
Authors: Husain M. , Waldron K. J.
Published: June 2008

In this work, a closed from solution for the direct position kinematics problem of a special class of Stewart Platform is presented. This class of mechanisms has a general feature that the top platform is connected to the six limbs at four locations. Three limbs connect at one location and the remaining limbs connect to the top platform singly at three separate locations. The base platform is connected at six different locations as is the case in the general platform. This particular class of mechanism is termed as 3-1-1-1 mechanism in this paper. It has been shown that there are a maximum of sixteen real assembly configurations for the direct position kinematics problem. This has been verified using a geometric argument also. The numerical example solved in this paper demonstrates that it is possible to obtain a set of solutions which are all real.
Kinematic Analysis and Design of Two-Input, Five-Bar Mechanisms Driven by Relatively Small Cranks
Authors: Basu P. S. , Farhang K.
Published: June 2008

Single-input mechanisms driven by relatively small cranks have been shown to have output link motions, describable as approximately simple harmonic functions of the input crank angular displacement. This paper presents a mathematical formulation for the approximate analysis and design of two-input, small-crank five-bar mechanisms for function generation. A perturbation technique is employed for the derivation of the approximate equations. Coefficients of the harmonic terms in the equations for an output link motion are obtained from the mechanism geometry and application of the perturbation technique. The output link motion is shown to be approximately described by a linear combination of two simple harmonic functions, in terms of the two input crank angles. Two mechanism design examples are presented to demonstrate the utility of the analytical development in the synthesis of five-bar mechanisms for function generation.
Reliability-Based Optimal Design of a Bistable Compliant Mechanism
Authors: Howell L. L. , Rao S. S. , Midha A.
Published: June 2008

Compliant mechanisms obtain at least some of their motion from the deflection of their flexible members. Advantages of such mechanisms include the reduction of manufacturing and assembly cost and time. Bistable mechanisms are particularly useful in applications where two stable equilibrium positions are required, such as switches, gates, and closures. Fatigue is a major concern in many compliant mechanisms due to the cyclic stresses induced on the flexible members. In this paper, a method for the probabilistic design of a bistable compliant slider-crank mechanism is proposed. Link lengths, material properties, and cross-section dimensions are taken as random variables. Probabilistic constraints on the maximum and minimum required input torque, location of stable equilibrium position, and overall size are included. The objective function is the maximization of the mechanism reliability in fatigue. Several design studies are performed to gain further insight into the nature of the problem.
Synthesis of Six-link, Slider-crank and Four-link Mechanisms for Function, Path and Motion Generation Using Homotopy with m-homogenization
Authors: Dhingra A. K. , Cheng J. C. , Kohli D.
Published: June 2008

This paper presents solutions to the function, motion and path generation problems of Watt’s and Stephenson six-link, slider-crank and four-link mechanisms using homotopy methods with m-homogenization. It is shown that using the matrix method for synthesis, applying m-homogeneous group theory, and by defining auxiliary equations in addition to the synthesis equations, the number of homotopy paths to be tracked is drastically reduced. To synthesize a Watt’s six-link function generator for 6 through 11 precision positions, the number of homotopy paths to be tracked to obtain all possible solutions range from 640 to 55,050,240. For Stephenson-II and -III mechanisms these numbers vary from 640 to 412,876,800. It is shown that slider-crank path generation problems with 6, 7 and 8 prescribed positions require 320, 3840 and 17,920 paths to be tracked, respectively, whereas for four-link path generators with 6 through 8 specified positions, these numbers range from 640 to 71, 680. The number of homotopy paths to be tracked to body guidance problems of slider-crank and four-link mechanisms is exactly the same as the maximum number of possible solutions given by Burmester-Ball theories. Numerical examples dealing with the synthesis of slider-crank path generators for 8 precision positions, and six-link Watt and Stephenson-III function generators for 9 prescribed positions are also presented.
Graphical Synthesis for Limit Positions of a Four-Bar Mechanism Using the Triangle Inequality Concept
Authors: Norton T. W. , Midha A. , Howell L. L.
Published: June 2008

An innovative methodology is presented for a set of synthesis problems in which the mobility angle between limit positions of a side link of a four-bar mechanism is necessarily prescribed. The principles used in synthesis are derived from a graphical interpretation of the triangle inequality concept. The derived principles give valuable insight to the solution space by dividing it into two separate regions. One region yields only Grashofian mechanisms, and the other region yields only non-Grashofian mechanisms. This information gives the designer a method for generating all possible mechanisms which satisfy the limit position and mechanism type constraints. A major advantage of the graphical technique is that is uses simple geometric objects, and therefore it can be easily implemented on most CAD packages. Several examples are used to demonstrate the concepts.
Closed-Form Direct Kinematics Solution of a New Parallel Minimanipulator
Authors: Tahmasebi F. , Tsai L.-W.
Published: June 2008

Closed-form direct kinematics solution of a new three-limbed six-degree-of-freedom minimanipulator is presented. Five-bar linkages and inextensible limbs are used in synthesis of the minimanipulator to improve its positional resolution and stiffness. All of the minimanipulator actuators are base-mounted. Kinematic inversion is used to reduce the direct kinematics of the mimimanipulator to an eighth-degree polynomial in the square of tangent of half-angle between one of the limbs and the moving platform. Hence, the maximum number of assembly configurations for the minimanipulator is sixteen. Furthermore, it is proved that the sixteen solutions are eight pairs of reflected configurations with respect to the plane passing through the lower ends of the three limbs. A numerical example is also presented and the results are verified by an inverse kinematics analysis.
Computer-Aided Structure Modification of Electromechanical Systems Using Singular Value Decomposition
Authors: Rai S. , Asada H.
Published: June 2008

A computer-aided design method for modifying the mechanical structure of electromechanical systems, e.g., robots and positioning systems, is presented in this paper. The pole-zero locations and other characteristics are represented in relation to the structural geometry by using the finite element method. The inverse problem of determining a geometry which will yield better dynamic characteristics is formulated and solved. Based on sensitivity analysis and the singular value decomposition of the sensitivity matrix, useful information is provided to the designer for making effective design changes and understanding trade-offs among multiple system characteristics to be improved. This decomposition also provides us with a new type of geometric design mode-shapes that characterizes all possible design changes affecting system characteristics. The design methodology is implemented to develop a computer-aided structure modification system. A design example of a flexible robot arm demonstrates the usefulness of the system.
Effects of Rim Thickness on Spur Gear Bending Stress
Authors: Bibel G. D. , Reddy S. K. , Savage M. , Handschuh R. F.
Published: June 2008

Thin rim gears find application in high-power, lightweight aircraft transmissions. Bending stresses in thin rim spur gear tooth fillets and root areas differ from the stresses in solid gears due to rim deformations. Rim thickness is a significant design parameter for these gears. To study this parameter, a finite element analysis was conducted on a segment of a thin rim gear. The rim thickness was varied and the location and magnitude of the maximum bending stresses reported. Design limits are discussed and compared with the results of other researchers.
A Study on a High-Speed NC Gear Grinding Machine Using a Screw-Shaped CBN Wheel
Authors: Emura T. , Wang L. , Arakawa A.
Published: June 2008

This paper describes a basic study for designing a high-speed NC gear grinding machine using a screw-shaped CBN wheel. Gear grinding machines using screw-shaped grinding wheels are quite prevalent. However, their productivity is not high, because the rotary speed of their spindles is very low. Therefore, the authors raised the maximum rotary speeds of the grinding spindle and the workspindle to 12,000 rpm and 3,000 rpm, respectively, in order to use a high-speed multithread CBN wheel. A magnetic scale whose wave length is long but pitch accuracy is high enough was used for detecting such a high-speed rotation. Since the wave length of the scale is long, a high-resolution interpolation using two-phase type PLL proposed by Emura was used. Both spindles are direct-drive type for removing backlash. When we grind gears, the initial setting between rotary angles of grinding wheel and work is required. The authors tried to automatically set the initial rotary angles by using a CCD camera.
A Comparison of the Performance of Nonlinear Equation Solvers for Machine Design Problems
Authors: Agrawal R. , Sridhar N. , Kinzel G. L.
Published: June 2008

Often, the mathematical modeling of mechanical components leads to a set of nonlinear equations which have to be solved in order to compute the design variables. This paper discusses the performance of six different nonlinear, algebraic-equation solvers useful for machine design problems. Problems from spring design are taken as test cases for the purpose of evaluation.
Use of Resultants and the Bernshtein Formula in the Dimensional Synthesis of Linkage Components
Authors: Lin Chuen-Sen , Jia Bao-Ping
Published: June 2008

The applications of resultants and the Bernshtein formula for the dimensional synthesis of linkage components for finite precision positions are discussed. The closed-form solutions, which are derived from systems of polynomials in multiple unknowns by applying resultant theory, are in forms of polynomial equations of a single unknown. For the case of two compatibility equations, the closed form solution is a sixth degree solution polynomial. For the case of three compatibility equations, the solution is a fifty-fourth degree solution polynomial. For each case, the Bernshtein formula is applied to calculate the number of solutions of the system of polynomial equations. The calculated numbers of solutions match the degrees of the solution polynomials for both cases.
Instantaneous Invariants and Curvature Analysis of a Planar Four-Link Mechanism
Authors: Yang An Tzu , Pennock G. R. , Hsia Lih-Min
Published: June 2008

This paper shows that the canonical system and the instantaneous invariants for a moving plane, which is connected to the fixed plane by a revolute-revolute crank, are functions of the derivatives of the crank angle. Then closed-form expressions are derived for the curvature ratios of the path generated by an arbitrary point fixed in the moving plane, in terms of the coordinates of the point and the instantaneous invariants of the plane. For illustrative purposes, numerical results are presented for the instantaneous invariants (up to the fourth-order) of the coupler of a specified crank-rocker mechanism, as a function of the input angle. In addition, the paper shows the variation in the first and second curvature ratios of an arbitrary coupler curve during the complete operating cycle of the mechanism. The authors hope that, based on the results presented here, a variety of useful tools for the kinematic design of planar mechanisms, with a rotary input, will be developed for plane rigid body guidance as well as curve generation.
Comparison of Weibull Strength Parameters from Flexure and Spin Tests of Brittle Materials
Authors: Holland F. A. , Zaretsky E. V.
Published: June 2008

Fracture data from five series of four-point bend tests of beams and spin tests of flat annular disks were reanalyzed. Silicon nitride and graphite were the test materials. The experimental fracture strengths of the disks were compared with the predicted strengths based on both volume flaw and surface flaw analyses of four-point bend data. Surface flaw analyses resulted in good correlation with experimental results in those test series where all tested specimens were obtained from the same material batch. The Weibull slopes (moduli) and characteristic gage strengths for the disks and beams were also compared. Differences in the experimental Weibull slopes were not statistically significant. It was shown that results from the beam tests can predict the fracture strength of rotating disks under well controlled conditions.
An Intelligent Real Time Design Methodology for Component Selection: An Approach to Managing Uncertainty
Authors: Bradley S. R. , Agogino A. M.
Published: June 2008

An Intelligent Real Time Design (IRTD) methodology is presented for component selection applications under the reality of uncertain and incomplete information. A decision analytic approach is developed with the goal of assisting designers in making decisions that balance the cost of the limited resources consumed during the design process, such as the designer’s time, against the benefit to be derived from the utilization of those resources in terms of expectations of an improved design. This approach is shown to complement other formal methods for design based on interval arithmetic and qualitative optimization, and a general methodology is proposed for performing component selection utilizing a combination of these methods. An example application to the selection of rolling element bearings is presented to clarify the methodology and demonstrate its effectiveness in providing guidance to designers when selecting elements from a component database.
Optimal Design of a Nonhomogeneous Annular Disk Under Pressure Loadings
Authors: Gau Chung-Yun , Manoochehri Souran
Published: June 2008

A method for the design of nonhomogeneous, variable-thickness, annular disks under internal and external pressures satisfying Tresca yield criterion is presented in this paper. The effects of varying the disk thickness and stiffness properties to achieve a fully stressed design are investigated. Analytical solutions for distributions of Young’s modulus and disk thickness variations have been developed for the case of fully stressed designs. Examples are given for three different cases, namely, constant thickness with variable Young’s modulus, variable thickness with constant Young’s modulus, and variable thickness with variable Young’s modulus. In the last case, due to the existence of many alternative solutions, optimal design techniques have been utilized. Application of the developed methodology for optimal designs of short fiber composites with random fiber orientations is discussed. The optimization results of fiber volume fraction distributions and thickness variations for a disk made of nylon 66 matrix with E glass fiber are given under specified pressure loadings.
Structural Configuration Examples of an Integrated Optimal Design Process
Authors: Chirehdast M. , Gea H.-C. , Kikuchi N. , Papalambros P. Y.
Published: June 2008

Structural optimization procedures usually start from a given design topology and vary proportions or boundary shapes of the design to achieve optimality of an objective under various constraints. This article presents examples of the application of a novel approach for initiating formal structural optimization at an earlier stage, where the design topology is rigorously generated. A three-phase design process is used. In Phase I, an optimal initial topology is created by a homogenization method as a gray-scale image. In Phase II, the image is transformed to a realizable design using computer vision techniques. In Phase III, the design is parameterized and treated in detail by conventional size and shape optimization techniques. Fully-automated procedures for optimization of two-dimensional solid structures are outlined, and several practical design problems for this type of structures are solved using the proposed procedure, including a crane hook and a bicycle frame.
Motion of Unbalanced Balls in High-Speed Angular Contact Ball Bearings
Authors: Kawamura H. , Touma K.
Published: June 2008

This paper reports on an experimental study of the three-dimensional ball motion of an unbalanced ball in a 50-mm bore angular contact ball bearing operating at high speeds under axial loads. One bearing ball, which was unbalanced by making a small hole in it, was magnetized and the motion of the ball was determined using Hall-elements. The bearing was tested under various loads and speeds up to 12,000 rpm. The influence of unbalance eccentricity on the unbalanced ball’s motion was investigated.
Dynamic Characteristics of Gas-Lubricated Slider Bearings Under High Knudsen Number Conditions
Authors: Hayashi T. , Fukui S. , Ohkubo T. , Kaneko R.
Published: June 2008

This paper presents numerical analyses of the dynamic characteristics of gas-lubricated slider bearings under high Knudsen number conditions using a generalized lubrication equation based on the the Boltzmann equation. These analyses are compared with those of the slip flow approximation equations and the differences are clarified. The present analysis is applied to the dynamic response of flying head sliders for magnetic disk storage devices. For a small slider with ultra-thin spacing, the deviations of the slip flow approximation equations are remarkable in regard to steady flying characteristics, but insignificant in regard to dynamic characteristics.
Experimental and Analytical Research on Floating-Ring Bearings for Engine Applications
Authors: Dong X. , Zhao Z.
Published: June 2008

This study deals with whether floating-ring journal bearings can be applied to engine bearings or not. The performance of floating-ring journal bearings with nonstationary load is analyzed. The main bearings of a S195 4-stroke diesel engine are replaced by floating-ring bearings and an experiment is carried out with success. After the engine starting, the ring lifts off when crankshaft speeds approach seven hundred and forty rpm. The ring maintains its rotation until crankshaft speeds decrease to two hundred rpm, during its deceleration to a stop. Once the ring lifts off it remains in normal working order. It is possible for floating-ring bearings to be used in engines where the load is nonstationary. It is hoped that a further reduction in the ring starting speed will be provided by lessening the difference between dynamic and static frictional coefficients in friction pair and an increase in lifetime will be provided by the floating-ring journal bearing.
A Thermal Hydrodynamic Lubrication Analysis for Entrained Film Thickness in Cold Strip Rolling
Authors: Yuan K. , Chern B. C.
Published: June 2008

A thermal hydrodynamic lubrication analysis which takes account of temperature-dependent viscosity variation along as well as across the film thickness is developed for the entrained film thickness in cold strip rolling using generalized Reynolds equation (Dowson, 1962). The results are compared with that of the two approximate models (i.e., the effective viscosity model and thermal Reynolds equation model) being widely used in metal forming lubrication literature. It is found that neither of the two approximate models is more accurate than the other and that neither can deal with the effect of surface temperature difference of the roll and strip adequately.
Designing Miniature Plastic Bearings
Authors: Rymuza Z.
Published: June 2008

Designing procedure for miniature steel-polymer journal bearings is presented. The formulas useful for selecting main features of the polymeric bearing bush and enabling predicting tribological behavior including wear of the bearings discussed are given. The procedure presented may be also applicable at designing steel-polymer journal bearings used in machines.
Hydrostatic Damper for the Space Shuttle Main Engine (SSME) High Pressure Oxidizer Turbopump (HPOTP)
Authors: Goggin D. G. , Scharrer J. K. , Beatty R. F.
Published: June 2008

Alternative methods were evaluated for increasing rotor damping on the SSME HPOTP to reduce bearing dynamic loads and extend their useful life. A unique application of a hydrostatic damper was developed by incorporating a hydrostatic element between stationary turbine bearing support components. Damper design is shown to be dependent on accurate rotordynamic response analysis. Optimization to achieve maximum damper performance under high loading conditions and limited supply flow is discussed. Damping levels approaching critical damping were achieved without major modifications. Bearing dynamic loads are reduced up to 70 percent and rotor mode logarithmic decrement was increased from 0.085 to as much as 1.0. Possible opportunities for further improvements in damper performance are also discussed.
Friction at a Lubricated Line Contact Operating at Oscillating Sliding Velocities
Authors: Hess D. P. , Soom A.
Published: June 2008

Although many contacts operate under unsteady loading and sliding conditions, friction behavior under such conditions is still not well understood. In this paper we report on a series of experiments that were run to examine friction-velocity characteristics of line contacts operating under unsteady sliding velocities in the mixed, elastohydrodynamic and hydrodynamic lubrication regimes. A periodic, time-varying velocity component was superimposed on a steady sliding speed in such a way that all three lubrication regimes could be covered in a cycle. It was found that as the frequency of oscillation was increased, a multi-valued friction coefficient appeared as a loop about the average (steady state) friction-velocity relation. It is shown that this behavior can be modeled by a characteristic time lag between a changing velocity and the corresponding steady state friction. The latter is described by a single equation that was matched to measured average friction data. In the mixed lubrication regime, which is where this lag most significantly affects friction behavior, the lag time increases with normal load and lubricant viscosity. It is shown that the time shift is not associated with a fixed characteristic distance. The observed delay arises due to entrainment and normal approach, which includes squeeze-films combined with rough surface contact deformations.
Lubrication of a Lightly Loaded Sliding Cylinder in Normal Motion
Authors: You H. I.
Published: June 2008

The hydrodynamic characteristics of a cylinder-plane bearing in normal motion is investigated by using the Reynolds equation in conjunction with the Coyne-Elrod rupture model. It is seen that the solutions of the pressure distribution as well as the rupture point are more acceptable than those found using the Reynolds boundary conditions. It is found that the squeeze effect cancels the entraining effect as the approach velocity is large. The entraining effect becomes important as the velocity of the normal approach is reduced, and a significant negative pressure region occurs in the downstream divergent space.
Predictive Models for the Design of Profile Bore Bearings
Authors: Gethin D. T.
Published: June 2008

A comparative study of three theoretical models for predicting the thermal behavior of a tilted three lobe profile bore bearing is presented. It is based on a simple heat balance, an integrated energy equation, and a rigorous thermohydrodynamic approach. For a given eccentricity ratio the models predict load carrying capacities that are in close agreement. The remaining parameters of torque reaction and effective and maximum film temperature do not illustrate such complete agreement. An integrated model generally gives the highest maximum film temperature since it does not account for heat removal from the film by conduction through the bearing components.
Friction and Wear of Ceramics for Magnetic Recording Applications: Part I—A Review
Authors: Chandrasekar S. , Bhushan Bharat
Published: June 2008

The friction and wear of ceramics under lightly-loaded, marginally-lubricated sliding-contact conditions are reviewed. The mechanism of ceramic friction and wear and the factors influencing them in these situations are identified and discussed with reference to the results presented in the literature. The implications to slider-material and thin-film rigid-disk overcoat material selection in magnetic recording devices are discussed.
Rolling Bearing Life Prediction-Correction for Materials and Operating Conditions—Part III: Implementation in Bearing Dynamics Computer Codes
Authors: Gupta P. K. , Tallian T. E.
Published: June 2008

Models for the correction of classical fatigue life for material imperfections and severity of operating conditions in rolling bearings are implemented in a bearing dynamics computer code. The significance of life correction factors is then demonstrated for both ball and cylindrical roller bearings over a range of operating conditions.
Tribological Studies of Ion-Implanted Steel Constituents Using an Oscillating Pin-on-Disk Wear Tester
Authors: Wei R. , Wilbur P. J. , Sampath W. S. , Williamson D. L. , Qu Yi , Wang Li
Published: June 2008

Wear tests of ferrite (pure α-Fe) and austenite (AISI 304 stainless steel) implanted with nitrogen have been conducted using a unique oscillating pin-on-disk test machine. The results show that nitrogen implantation at elevated temperatures to high doses dramatically improves the adhesive wear resistance of ferrite and the critical load at which the wear mechanism changes from mild to severe adhesive wear for austenite. The wear resistance of nitrogen implanted ferrite is determined by the nitride formed. Ranked from most to least wear resistant the nitrides observed are γ’-Fe4N, ε-Fe3N, and ζ-Fe2N. No evidence of nitride break-up and attendant nitrogen migration during wear testing is found. Nitrogen does diffuse into both ferrite and austenite rapidly when they are implanted at an elevated temperature and this enhances their wear resistances.
Theoretical Analysis of the Effects of Instantaneous Charge Leakage on Roller Tracks of Roller Bearings Lubricated With High Resistivity Lubricants Under the Influence of Electric Current
Authors: Prashad Har
Published: June 2008

An analysis is presented for determining the effects of instantaneous charge leakage on the rise of contact temperature between rollers and roller track of races of roller bearings lubricated with high resistivity lubricant. Analysis is also given for the contact stresses on the races which lead to initiation of craters by the arcing effect on the roller tracks and subsequent damage to the roller bearing. Estimates of the leakage of charge between roller tracks and rollers during momentary asperity contacts along with an expression for the instantaneous contact resistance between roller and race was used to establish heat generated and instantaneous temperature rise in the contact zone on the roller tracks in each shaft revolution. Using this temperature rise, the contact stresses were determined and the minimum number of cycles was calculated before craters are initiated on the roller track of the races. The number of cycles thus determined corresponds, within the reasonable limits, to the appearance of the craters on the roller track of the inner race of a roller bearing, operated under the influence of electric current. Subsequently, the ratio of reduction in bearing life with that of the bearing operated under rolling friction without the influence of electric current is established. This paper gives general guidance for determination of instantaneous temperature rise due to charge leakage in the contact zone and makes it possible to predict the life of a roller bearing lubricated with high resistivity lubricant under the influence of electric current before the craters appear on the roller tracks.
An Efficient, Robust, and Time Accurate Numerical Scheme Applied to a Cavitation Algorithm
Authors: Vijayaraghavan D. , Keith T. G.
Published: June 2008

In this paper, an implicit numerical scheme, based on an approximate factorization technique, is applied to a cavitation algorithm. The algorithm is a modified version of the Elrod cavitation algorithm, which automatically predicts film rupture and reformation in bearings. At each time step, Newton iterations are performed to achieve time accurate solutions for unsteady problems. This numerical scheme is applied in both orthogonal and nonorthogonal grid arrangements. An aligned finite grooved bearing and a flared, misaligned line grooved bearing are analyzed using this new approach. The predictions are compared with the results obtained with procedures currently being used. The new scheme is robust, quickly convergent, and provides time accurate solutions with a minimum expenditure of CPU time.
Grid Transformation and Adaption Techniques Applied in the Analysis of Cavitated Journal Bearings
Authors: Vijayaraghavan D. , Keith T. G.
Published: June 2008

An existing cavitation algorithm (a numerical procedure that automatically predicts film rupture and reformation in bearings) is modified in this paper. Second order upwinding is used to difference the shear induced flow terms in the cavitated region. A grid transformation procedure using a body fitted coordinate system and grid adaption techniques are applied to the algorithm. Four statically loaded finite journal bearing cases are analyzed. The results are compared with the results obtained using a conventional grid. The advantage of these methods is demonstrated by obtaining equal or better accuracy with a coarser grid and by the consumption of smaller amounts of computer time.
Analysis of a Finite Grooved Misaligned Journal Bearing Considering Cavitation and Starvation Effects
Authors: Vijayaraghavan D. , Keith T. G.
Published: June 2008

The effect of journal misalignment on the predicted performance of a finite grooved journal bearing is analyzed in this paper. The numerical procedure used incorporates a cavitation algorithm, which automatically predicts film rupture and reformation in the bearings. The misalignment considered varies in magnitude and direction with reference to the boundaries of the bearing. In addition to the misalignment, the effect of lubricant starvation at the groove is also considered and compared with flooded inlet conditions. The effects of various degrees of starvation, or higher lubricant supply pressure, bearing length to diameter ratio and groove size are also investigated.
Wear Experiments on Glassy-Carbon Based Materials
Authors: Burton Ralph A. , Burton R. Gaines
Published: June 2008

Friction and wear are reported for monolithic glassy carbon and a composite made of copper fibers in a glassy carbon matrix. The friction coefficient is shown to be comparable to reported values for typical graphitic and copper-graphite specimens, and the wear is shown to be exceptionally low. Replacement of ambient oxygen by nitrogen does not lead to accelerated wear or dusting.
Stability of a Rigid Rotor Supported on Rough Oil Journal Bearings
Authors: Majumdar B. C. , Ghosh M. K.
Published: June 2008

This investigation deals with the stability of rigid rotors supported on finite rough oil journal bearings using perturbation method. The effect of various surface roughness parameters, viz., composite surface roughness, roughness orientation pattern and variance ratio on the stability has been studied. In general, surface roughness effect when incorporated into the analysis does not show a significant change in the stability for surfaces having same roughness structure. However, the effect of variance ratio (i.e., surfaces having different roughness structure) on stability is quite marked.
A Database for Interpolation of Poiseuille Flow Rates for High Knudsen Number Lubrication Problems
Authors: Fukui S. , Kaneko R.
Published: June 2008

This paper proposes the use of a Poiseuille flow rate database for rapid calculation of a generalized lubrication equation for high Knudsen number gas films. The database is created by numerical calculations based on the linearized Boltzmann equation. The proposed interpolation method is verified to reduce calculation time to several tenths of that required to perform rigorous calculations with the same accuracy.
A Subroutine Package for Solving Slider Lubrication Problems
Authors: Sun D. C.
Published: June 2008

The paper presents a subroutine package that solves the inverse problem of slider lubrication considering such features as finite bearing width, squeeze action, and starvation. The underlying analysis and computational algorithm are described. A representative example of piston ring and cylinder bore contact is used to demonstrate the use of the subroutine package.
Study of Direct Measuring of Lubricant Condition in Rolling Element Bearings With Microcomputer Technique
Authors: Zhao Dongchu
Published: June 2008

A method for measuring the lubricant condition with strain gage in rolling element bearings and the instrument used are introduced. In order to illustrate the method and the instrument, the theory of measuring lubricant films in rolling element bearings using strain technique, test apparatus, microcomputer hardware as well as software, flow charts for the main program and subprograms, are first described in detail. In addition, the lubricant film thickness is measured for several different lubricants and results are compared with theoretical ones. It is demonstrated that using the method and the instrument introduced in this paper, one can measure the lubricant condition inside bearings very accurately.
A Finite Element Approach to Pad Flexibility Effects in Tilt Pad Journal Bearings: Part I—Single Pad Analysis
Authors: Earles L. L. , Palazzolo A. B. , Armentrout R. W.
Published: June 2008

A general method of incorporating pad flexibility effects into tilting pad isothermal bearing analysis is developed. The pad assembly approach is extended using 2-dimensional finite elements to determine pad deformations of a single pad. The pad deformations are represented by a single degree of freedom, the change in the pad radius of curvature, thus the current method is an approximate approach. The equations to calculate frequency reduced coefficients for a single pad are presented. Synchronously reduced coefficients for a single pad are in agreement with previous curved beam approximate methods and a more rigorous iterative approach. The finite element pad model provides more versatility in modeling nonuniform pad dimensions and the skewed boundary conditions which occur at the spherical pivot-pad socket interfaces.
A Finite Element Approach to Pad Flexibility Effects in Tilt Pad Journal Bearings: Part II—Assembled Bearing and System Analysis
Authors: Earles L. L. , Palazzolo A. B. , Armentrout R. W.
Published: June 2008

Pad flexibility effects are studied in an actual bearing. This flexibility is shown to decrease the predicted instability onset speed of the rotor bearing system. The use of complex eigenvalue dependent bearing coefficients as compared with using synchronously reduced coefficients is seen to produce a more significant decrease in the instability onset speed. Further reductions in the instability onset speed are obtained by including pivot stiffness in the complex eigenvalue dependent bearing coefficients.
Effects of Two Film Rupture Models on the Thermal Analysis of a Journal Bearing
Authors: Knight J. D. , Niewiarowski A. J.
Published: June 2008

A model for the thermal behavior of lubricant in the cavitated regions of a journal bearing is presented. The model assumes a bubbly mixture of liquid and air and includes the calculation of local mixture properties for the fluid film. Temperature in the film is calculated by a first order approximate energy equation that includes heat transfer between the film and its boundaries. A second order profile is assumed to represent the temperature distribution across the film. The classical Reynolds equation is applied, using a viscosity that does not vary across the film. Results of calculations are compared with published experimental results and with a prior theory that uses an effective length calculation in the cavitation zone. Results are found to be in good agreement with experiment at two different speeds, predicting the peak temperature of the bearing wall within 10 to 20 percent of the total temperature rise. The model predicts the temperature in the cavitated zone with much greater accuracy than the effective length model, with all theoretical values within 2 C of the measured values.
Thermal Elastohydrodynamic Lubrication of Rolling/Sliding Contacts
Authors: Sadeghi F. , Sui P. C.
Published: June 2008

A complete numerical solution of thermal compressible elastohydrodynamic lubrication of rolling/sliding contacts has been obtained. The Newton-Raphson technique is used to solve the simultaneous system of Reynolds and elasticity equations. The control volume finite element modeling was employed to solve the energy equation and its boundary conditions. The effects of various loads, speeds, and slip conditions on the lubricant temperature, film thickness, and friction force have been investigated. The results indicate that the temperature effects are significant and cannot be neglected.
An Annular Gas Seal Analysis Using Empirical Entrance and Exit Region Friction Factors
Authors: Elrod D. A. , Childs D. W. , Nelson C. C.
Published: June 2008

Wall shear stress results from stationary-rotor flow tests of five annular gas seals are used to develop entrance and exit region friction factor models. The friction factor models are used in a bulk-flow seal analysis which predicts leakage and rotor-dynamic coefficients. The predictions of the analysis are compared to experimental results and to the predictions of Nelson’s analysis (1985). The comparisons are for smooth-rotor seals with smooth and honeycomb-stators. The present analysis predicts the destabilizing cross-coupled stiffness of a seal better than Nelson’s analysis. Both analyses predict direct damping well and direct stiffness poorly.
Role of Fractal Geometry in Roughness Characterization and Contact Mechanics of Surfaces
Authors: Majumdar A. , Bhushan B.
Published: June 2008

A proper characterization of the multiscale topography of rough surfaces is very crucial for understanding several tribological phenomena. Although the multiscale nature of rough surfaces warrants a scale-independent characterization, conventional techniques use scale-dependent statistical parameters such as the variances of height, slope and curvature which are shown to be functions of the surface magnification. Roughness measurements on surfaces of magnetic tape, smooth and textured magnetic thin film rigid disks, and machined stainless steel surfaces show that their spectra follow a power law behavior. Profiles of such surfaces are, therefore, statistically self-affine which implies that when repeatedly magnified, increasing details of roughness emerge and appear similar to the original profile. This paper uses fractal geometry to characterize the multiscale self-affine topography by scale-independent parameters such as the fractal dimension. These parameters are obtained from the spectra of surface profiles. It was observed that surface processing techniques which produce deterministic texture on the surface result in non-fractal structure whereas those producing random texture yield fractal surfaces. For the magnetic tape surface, statistical parameters such as the r.m.s. peak height and curvature and the mean slope, which are needed in elastic contact models, are found to be scale-dependent. The imperfect contact between two rough surfaces is composed of a large number of contact spots of different sizes. The fractal representation of surfaces shows that the size-distribution of the multiscale contact spots follows a power law and is characterized by the fractal dimension of the surface. The surface spectra and the spot size-distribution follow power laws over several decades of length scales. Therefore, the fractal approach has the potential to predict the behavior of a surface phenomenon at a particular length scale from the observations at other length scales.
Liquid-Mediated Adhesion at the Thin Film Magnetic Disk/Slider Interface
Authors: Bhushan B. , Dugger M. T.
Published: June 2008

The adhesive force between magnetic-recording heads and thin film disks in a direction normal to the interface has been measured for a variety of loads, contact times, separation rates, and relative humidities with and without a layer of perfluoropolyether lubricant at the interface. At low humidities, the adhesive force due to the lubricant film alone is small for the lubricant thickness and disk surface roughness used. We find that the major component of the adhesive force between the slider and the disk in humid environments may be attributed to an adsorbed water film which can displace the lubricant (if the disk is lubricated) at sufficiently high loads, during tangential sliding, or after extended exposure to high concentrations of water vapor and create menisci around individual asperity contacts. The adhesive force was found to increase with contact duration on the unlubricated disk, but was essentially independent of contact duration on the lubricated disk. For both lubricated and unlubricated disks, the adhesive force increased with increasing relative humidity and loading rate, but was independent of applied normal load.
An Approximate THD Theory for Journal Bearings
Authors: Gupta G. , Hammond C. R. , Szeri A. Z.
Published: June 2008

The aim of this paper is to make available to the industrial designer results of the thermohydrodynamic theory of journal bearings, by providing a simplified, yet accurate model of journal bearing lubrication that can be implemented on a personal computer and be used in an interactive mode. The simplified THD theory we propose consists of two coupled ordinary differential equations for pressure and energy and an algebraic equation for viscosity, which are to be solved iteratively. Bearing load capacity, maximum bearing temperature, maximum pressure, coefficient of friction and lubricant flow rate calculated from this simplified theory compare well with results from a more sophisticated model. We also make comparisons with experimental data on full journal bearings, demonstrating substantial agreement between experiment and simplified theory.
Numerical Study of Film Thickness Averaging in Compressible Lubricating Films Incurring Stationary Surface Roughness
Authors: Mitsuya Y. , Hayashi T.
Published: June 2008

The compressibility effects of lubricating films incurring a roughness on film thickness averaging were studied numerically with a focus on the physical interpretation of the roughness effects. A numerical comparison between load-carrying capacities resulting from rough film thickness and from averaged film thickness are presented for a wide range of bearing numbers up to 107. It is found that currently indicated particular features such as the appearance of the maximum or minimum load-carrying capacity can be induced from the superimposition of local compressibility effects (LCEs) caused by individual unit roughness on compressibility effects owing to averaged film thickness. The most noticeable difference between the case of small LCEs and that of saturated LCEs is that the roughness phase results in a minimal effect with the increasing wave number for the former, while it creates a dominant effect for the latter. The results confirm that the same averaging method as that for incompressible films can be applied for small LCEs, and that Greengard’s method is applicable for nearly saturated LCEs. It should be noted that the averaged film thickness can be determined physically for small LCE regions, while it is defined mathematically for nearly saturated LCE regions.
Friction, Wear, and Interfacial Chemistry in Thin Film Magnetic Rigid Disk Files
Authors: Dugger M. T. , Chung Y. W. , Bhushan B. , Rothschild W.
Published: June 2008

We present results of a study of hemispherical pins of manganese-zinc ferrite sliding against rigid disks composed of thin films of a sputtered cobalt-nickel-platinum alloy and carbon, with perfluoropolyether as the topical lubricant. The contact life, as marked by the total distance slid to the point at which the coefficient of friction increases rapidly over the steady state value, is much longer in air with 50 percent relative humidity than in dry air or vacuum. The wear debris generated in humid air is much finer and is enriched with cobalt on its surface. In dry air and vacuum, the debris is substantially larger than one micron and tends to be enriched with nickel on its surface. We present a hypothesis which explains the wear mechanisms in various operating environments.