Use Of Influence Coefficients Research Articles

Characteristics of oil film nonlinearity in bearings and its effects in rotor balancing

Since unbalance is inherent to any rotating machine, and some effects like coupling misalignment and thermal bow, which are not taken into account in pre-balancing, can lead to changes in unbalance distribution, in-field rotor balancing is sometimes a necessary action. Traditionally, the influence coefficients method has been used as the main balancing procedure, and due to the low accessibility in assembled rotating machinery, generally only the journal displacements inside hydrodynamic bearings are available for the balancing procedure. However, influence coefficients method assumes linearity of rotor response and it is known that hydrodynamic bearings can sometimes present a strong nonlinear relationship between bearing forces and journal displacements, making balancing difficult or even impossible. Otherwise, the bearing housing vibrations are directly proportional to the bearing forces and are independent of the journal displacements, therefore avoiding problems related to oil film nonlinearities. This paper proposes the use of bearing housing accelerations as influence coefficients and verifies experimentally that balancing can be successful also in highly nonlinear oil film bearing conditions. First, the oil film nonlinear characteristics are introduced by means of a simple analytical model. Then, different behaviors have been experimentally investigated by means of a test rig rotor supported by three hydrodynamic bearings, designed to enhance oil film nonlinear effects. Nonlinear effects are quantified through deviations with respect to linear behavior and development of higher harmonics in the response of the oil film. It is shown that these effects can seriously affect the possibility of balancing with the use of influence coefficients. Finally, it has been verified experimentally that balancing with the use of bearing housing acceleration to calculate influence coefficients was successful, as expected.

Influence Coefficients of Stress Intensity Factors for Curved Tubing With a Semi-Elliptical Crack

The boundary element method is employed to determine polynomial influence coefficients of stress intensity factors, KI, for a semi-elliptical crack in internally pressurized thick-walled curved tubing. Numerical results of these coefficients are obtained for a wide range of geometric parameters; they are the bend radius ratio, cross-sectional radius ratio, angular extent of the bend, and relative crack depth. The use of influence coefficients allows KI solutions to be determined for different load cases without repetitive 3D stress analysis of the cracked body. This is demonstrated for the case of autofrettage where the effects on KI of the residual stresses arising from it are presented.

A new calculation method for the worst case tolerance analysis and synthesis in stack-type assemblies

Productivity and industrial product quality improvements entail a rational tolerancing process to be applied as early as product design. Once functional conditions are defined, an optimal specification for each component in a mechanical system is to be developed. Despite numerous studies in this area, the problem is still far from solved. It may be decomposed into two stages: development of specifications based on standards, or qualitative synthesis, and calculation of tolerances. To the extent that these two sets of problems are related, we propose to address them in parallel. In this paper, we present an original method that enables us to solve these two problems for the case of serial assembly (stacking) without clearances. This method is based on the use of influence coefficients to obtain the relationship between the functional tolerance and the tolerances associated with the geometry of the mechanism’s interface surfaces. We will describe a calculation algorithm that helps obtain influence coefficients solely from the assembly’s geometric definition. Then, we will show that under our working hypothesis, this relationship is piecewise linear.

Numerical Model of a Reciprocating Hydraulic Rod Seal

A numerical model of an elastomeric reciprocating hydraulic rod seal has been constructed. The model consists of coupled fluid mechanics, deformation mechanics, and contact mechanics analyses, with an iterative computational procedure. The fluid mechanics analysis consists of the solution of the Reynolds equation, using flow factors to account for surface roughness. Deformation of the seal is computed through the use of influence coefficients, obtained from an off-line finite element analysis. The contact mechanics analysis uses the Greenwood and Williamson model. The seal model is used to predict leakage rate, friction force, fluid and contact pressure distributions, and film thickness distribution. Results for a typical seal show that the seal operates with mixed lubrication, and the seal roughness plays an important role in determining whether or not the seal leaks.

Use of Cm and cross product coefficients in influence coefficient algorithms for quantitative XRF analysis

AbstractThe use of influence coefficients in algorithms for the correction of matrix effects in quantitative XRF analysis is discussed. In principle, multi‐element influence coefficients should be used. In practice, many algorithms are based on the use of binary influence coefficients, even when dealing with multi‐component specimens. This involves approximations which may affect the accuracy of the analysis. It is shown that the effects of this approximation can be reduced, provided that the binary influence coefficients are calculated for the correct composition (this involves the use of Cm, where Cm is the sum of the concentrations of the matrix elements, i.e. Cm = 1 − Ci) and by applying cross‐product coefficients. Copyright © 2004 John Wiley & Sons, Ltd.

The concordance of algorithms and influence coefficients for the correction for matrix effects in XRF

The development of influence coefficient algorithms has retained the attention of XRF analysts given that their goal seeks to combine the theoretical exactness of the fundamental parameters approach for quantifying fluorescence missions and the flexibility of simple mathematical models that convert experimentally measured fluorescence intensities to concentrations. By definition, the purpose underlying the use of influence coefficients is to quantify or condense in one value the magnitude of absorption and/or enhancement effects. This presentation examines the concordance underlying a number of algorithms and their influence coefficients which have been proposed over some 50 years. Initially, influence coefficients were defined only in the context of binary absorption and monochromatic excitation sources. Subsequently, the coefficients were defined explicitly for the more comprehensive context, namely, polychromatic excitation sources, absorption and enhancement effects defined separately or combined as 'matrix effects' in multi-element specimens. Thus, on close examination, it can be shown that contrary to algorithms, influence coefficients are direct explicit functions of analytical contexts and that algorithms, often contested when interpreted in the original context for which they were developed, retain their validity when subsequent advancements in the definition of influence coefficients are taken into consideration.

Why The Fundamental Algorithm is So Fundamental

In X-ray fluorescence (XRF) analysis, one of the major problems is the correction for matrix effects (absorption and enhancement). One of the solutions proposed was the use of influence coefficients, which are numerical coefficients that correct for the effect of each matrix element on the analyte. For many years, these coefficients were considered as an empirical approach having little connection with X-ray fluorescence theory. They were considered useful only when no other alternative was available to solve the problem of matrix effect.

A Review of Some Aspects of the Prediction of Mechanical Seal Coning

Knowledge of the taper angle of the lubricating film of a rotary mechanical seal is fundamental to understanding seal performance. Whilst the literature contains numerous reports of mechanical seal distortion analysis, these usually deal with specific seal designs. This paper addresses the analysis procedures more generally, giving a detailed discussion of factors affecting prediction of seal ring distortions, especially heat partitioning, locating reaction diameters and estimation of heat transfer coefficients. The “face locking” concept is discussed. Use of influence coefficients is discussed and an extension of this concept for distributed interfacial pressure is presented. Finally a typical analysis sequence is outlined.

New free-wake analysis of rotorcraft hover performance using influence coefficients

Free-wake analyses of helicopter rotor wakes in hover using time stepping have been shown to encounter instabilities which preclude convergence to valid free-vortex solutions for rotor-wake geometries. Previous work has demonstrated that these convergence difficulties can be overcome by implementing a new free-wake analysis method based on the use of influence coefficients. The present paper reviews this approach and documents its incorporation into a hover performance analysis called Evaluation of Hover Performance using Influence Coefficients (EHPIC). The technical principles underlying the EHPIC code are described with emphasis on steps taken to develop the single-filament wake models used in previous work into a multifilament wake valid for realistic hover performance predictions. The coupling of the wake model to a lifting surface loads analysis is described, and sample problems are solved that illustrate the robustness of the method. Performance calculations are also undertaken for hover to illustrate the utility of EHPIC in the analysis of rotorcraft performance.

The vibration of a multi-bearing rotor

A numerical method based on the use of influence coefficients is described for the free and forced vibration analysis of a general rotor/bearing system. The method is found to combine the numerical speed of the transfer matrix method with the accuracy and versatility of the finite element method. The paper describes the prediction of the vibration performance of a four-bearing rotor with which experimental results compare satisfactorily.

XCII. A theoretical investigation of the compression of a ductile material between smooth flat dies

Summary A theory is suggested to describe the distribution of stress and velocity in a block of ductile material symmetrically indented on opposite sides by two smooth flat dies. The theory is two- dimensional and an ideal plastic-rigid material is assumed. Slip-line fields are proposed for all ratios of width of dies to height of block greater than one. It is found that the velocity field transforms into its corresponding slip-line field. Other plane plastic problems where this correspondence occurs are cited. Since the velocities are known along only one slip-line boundary, the usual numerical procedure for calculating the field has to be modified and the use of influence coefficients is introduced. Solutions are computed for width/height ratios between one and two, and it is observed that simple analytical relations hold between these ratios and the corresponding velocity discontinuities in the field. The calculated mean pressures on the dies are compared with upper and lower bound curves derived by Hill on the basis of extremum principles. The deformation after different finite indentations is illustrated by photographs of experiments using (a) plasticine models, and (b) aluminium alloy strip. Similar fields are proposed for extrusion or drawing through a wedge-shaped die with large reductions, but no solutions have been computed.

Aileron Reversal Speed by Influence Coefficients and Matrix Iteration

Methods most frequently used in determining the aileron reversal speed are briefly reviewed. An alternative method of determining the reversal speed, making use of influence coefficients and matrix iteration, is presented.