The Optimal Tolerance Assignment With Less Than Full Acceptance

1982 ◽  
Vol 104 (4) ◽  
pp. 855-860 ◽  
Author(s):  
W. Michael ◽  
J. N. Siddall
Keyword(s):  
Nonlinear Optimization ◽  
Manufacturing Process ◽  
Mathematical Theory ◽  
Production Cost ◽  
Engineering System ◽  
Important Distinction ◽  
Lower Limits ◽  
The Relationship ◽  
Tolerance Assignment ◽  
General Mathematical Theory

This paper proposes an approach that integrates the relationship between design and production engineers through the theory of nonlinear optimization. It attempts to cope with the problem of optimally allocating tolerances in a manufacturing process. The upper and lower limits of the random variables of an engineering system are allocated so as to minimize production cost, with allowance for the system scrap percentage. The approach is illustrated by an example, and the general mathematical theory is also provided. An important distinction between the design and the manufacturing scrap is introduced, and the cell technique is utilized to estimate efficiently the system scrap.

PIOPLE. INFORMATION. DEGRADATION

2019 ◽  
pp. 44-53
Author(s):  
Andrey Varlamov ◽  
Vladimir Rimshin
Keyword(s):  
Information Theory ◽  
Mathematical Theory ◽  
Maximum Information ◽  
Building Models ◽  
Man And Nature ◽  
History Of ◽  
Nature And Society ◽  
Relationship Of ◽  
Link Information ◽  
The Relationship

Considered the issues of interaction between man and nature. Noted that this interaction is fundamental in the existence of modern civilization. The question of possible impact on nature and society with the aim of preserving the existence of human civilization. It is shown that the study of this issue goes towards the crea-tion of models of interaction between nature and man. Determining when building models is information about the interaction of man and nature. Considered information theory from the viewpoint of interaction between nature and man. Noted that currently information theory developed mainly as a mathematical theory. The issues of interaction of man and nature, the availability and existence of information in the material sys-tem is not studied. Indicates the link information with the energy terms control large flows of energy. For con-sideration of the interaction of man and nature proposed to use the theory of degradation. Graphs are pre-sented of the information in the history of human development. Reviewed charts of population growth. As a prediction it is proposed to use the simplest based on the theory of degradation. Consideration of the behav-ior of these dependencies led to the conclusion about the existence of communication energy and information as a feature of the degradation of energy. It justifies the existence of border life ( including humanity) at the point with maximum information. Shows the relationship of energy and time using potential energy.

A N. Bourbaki Type General Theory and the Properties of Contracting Symbols and Corresponding Contracted Forms

1999 ◽  
Vol 6 (2) ◽  
pp. 179-190
Author(s):  
SH. Pkhakadze
Keyword(s):  
General Theory ◽  
Mathematical Theory ◽  
General Mathematical Theory

Abstract A system of contracting symbols is introduced for a N. Bourbaki type general mathematical theory corresponding to a general classical mathematical theory .

The Changing Views of a Philosopher of Chemistry on the Question of Reduction

2016 ◽  
Author(s):  
Eric R. Scerri
Keyword(s):  
Quantum Mechanics ◽  
Mathematical Theory ◽  
Approximate Solutions ◽  
Electron Systems ◽  
Atomic Systems ◽  
Quantum Mechanical Description ◽  
The Subject ◽  
The Moment ◽  
The Relationship

The question of the reduction of chemistry to quantum mechanics has been inextricably linked with the development of the philosophy of chemistry since the field began to develop in the early 1990s. In the present chapter I would like to describe how my own views on the subject have developed over a period of roughly 30 years. A good place to begin might be the frequently cited reductionist dictum that was penned in 1929 by Paul Dirac, one of the founders of quantum mechanics. . . . The underlying laws necessary for the mathematical theory of a larger part of physics and the whole of chemistry are thus completely known, and the difficulty is only that exact applications of these laws lead to equations, which are too complicated to be soluble. (Dirac 1929) . . . These days most chemists would probably comment that Dirac had things backward. It is clear that nothing like “the whole of chemistry” has been mathematically understood. At the same time most would argue that the approximate solutions that are afforded by modern computers are so good as to overcome the fact that one cannot obtain exact or analytical solutions to the Schrödinger equation for many-electron systems. Be that as it may, Dirac’s famous quotation, coming from one of the creators of quantum mechanics, has convinced many people that chemistry has been more or less completely reduced to quantum mechanics. Another quotation of this sort (and one using more metaphorical language) comes from Walter Heitler who together with Fritz London was the first to give a quantum mechanical description of the chemical bond. . . . Let us assume for the moment that the two atomic systems ↑↑↑↑ . . . and ↓↓↓↓ . . . are always attracted in a homopolar manner. We can, then, eat Chemistry with a spoon. (Heitler 1927) . . . Philosophers of science eventually caught up with this climate of reductionism and chose to illustrate their views with the relationship with chemistry and quantum mechanics.

A simple mathematical theory of finite distortional latent hardening in single crystals

1977 ◽  
Vol 358 (1692) ◽  
pp. 47-70 ◽  
Keyword(s):  
Tensile Test ◽  
Single Crystals ◽  
Finite Deformation ◽  
Mathematical Theory ◽  
Slip Systems ◽  
Plastic Crystals ◽  
Hardening Law ◽  
Infinitesimal Strain ◽  
Latent Hardening ◽  
General Mathematical Theory

A simple (one-parameter) hardening law is proposed which accounts for the perpetuation of finite single slip, beyond the symmetry line, in the tensile test of f. c. c. crystals and reduces to Taylor’s rule at infinitesimal strain. This new law emerges as the simplest case of a general mathematical theory of finite deformation of elastic-plastic crystals. The fully anisotropic finite-distortional hardening of latent slip systems predicted by the simple theory is in qualitative agreement with experiment.

Free Abrasive Machining in Slicing Brittle Materials With Wiresaw

2000 ◽  
Vol 123 (3) ◽  
pp. 254-259 ◽  
Author(s):  
Fuqian Yang ◽  
Imin Kao
Keyword(s):  
Process Parameters ◽  
Manufacturing Process ◽  
Brittle Materials ◽  
Stochastic Approach ◽  
Abrasive Machining ◽  
Photovoltaic Applications ◽  
Indentation Crack ◽  
Microelectronics Fabrication ◽  
The Relationship ◽  
Free Abrasive

Wiresaw has emerged as a leading technology in wafer preparation for microelectronics fabrication, especially in slicing large silicon wafers (diameter⩾300 mm) for both microelectronic and photovoltaic applications. Wiresaw has also been employed to slice other brittle materials such as alumina, quartz, glass, and ceramics. The manufacturing process of wiresaw is a free abrasive machining (FAM) process. Specifically, the wiresaw cuts brittle materials through the “rolling-indenting” and “scratch-indenting” processes where the materials removal is resulting from mechanical interactions between the substrate of the workpiece and loss abrasives, which are trapped between workpiece and wire. Built upon results of previous investigation in modeling of wiresaw, a model of wiresaw slicing is developed based on indentation crack as well as the influence of wire carrying the abrasives. This model is used to predict the relationship between the rate of material removal and the mechanical properties of the workpiece together with the process parameters. The rolling, indenting, and scratching modes of materials removal are considered with a simple stochastic approach. The model provides us with the basis for improving the efficiency of the wiresaw manufacturing process based on the process parameters.

Engineering System Fault Detection Using Particle Filters

2009 ◽  
Author(s):  
B. Samanta
Keyword(s):  
Fault Detection ◽  
Bayesian Learning ◽  
Particle Filters ◽  
State Space Model ◽  
Engineering System ◽  
Process Noise ◽  
Machine Vibration ◽  
Relationship Of ◽  
The Relationship ◽  
Train System

This paper presents an approach to machinery fault detection using particle filters (PF). The machine vibration signals are processed using morphological signal processing (MSP) to extract a novel entropy based health index (HI) characterizing the signal shape-size complexity. The evolution of HI is approximated as a nonlinear state space model using a computational intelligence (CI) technique. PF is used to estimate the progression of HI in presence of observation and process noise. The PF based approach is illustrated for estimation of state and parameters of a chaotic system. The feasibility of the approach is demonstrated through vibration dataset of a helicopter drive-train system gearbox. The results help understand the relationship of the system condition, the corresponding HI, the level of degradation and its progression in a stochastic environment using Bayesian learning.

Effect of fiber length and blending method on the tensile properties of ring spun chitosan–cotton blend yarns

2016 ◽  
Vol 87 (2) ◽  
pp. 244-257 ◽  
Author(s):  
Ngan Yi Kitty Lam ◽  
Meng Zhang ◽  
Hui-fen Guo ◽  
Chu Po Ho ◽  
Li Li
Keyword(s):  
Tensile Properties ◽  
Textile Industry ◽  
Fiber Length ◽  
Production Cost ◽  
Materials Science ◽  
Rapid Development ◽  
Blending Method ◽  
Potential Applications ◽  
Chitosan Fiber ◽  
The Relationship

Chitosan has been widely studied for use in many areas, such as for its applications in the biomedical, engineering and pharmaceutical fields, as well as in industry, because of its unique properties, including biodegradability, antimicrobial activity, polycationic nature and biocompatibility. Thanks to the rapid development of materials science, chitosan applications are now possible in textiles. However, there are still many limitations of chitosan fibers in terms of their high electrostaticity, poor mechanical properties and high cost, which are obstacles that inhibit potential applications of chitosan fiber in the industry. Generally, in order to achieve the best performance with chitosan and enhance its commercial value, chitosan fibers are usually blended with long cotton fibers in the textile industry. Therefore, based on preliminary experiments and feedback from the industry, this study was carried out to further investigate the relationship between fiber length, fiber interaction and yarn performance. The results of this study would therefore help to reduce the production cost of yarns with the blending parameters used and also expand the utilization and applications beyond medical applications to fashion-based functional wear. The sliver-blending method offers better tensile properties of yarn samples, while the fiber-blending method offers higher uniformity of fiber distribution. This study would help to reduce the production cost of yarns by blending and also to expand the utilization and application not limited to fashion-based functional wear.

Relationship between Mean Value and Fourier Coefficients of a Time-Varying Function with Half-Period Rests: Theory and Application

1994 ◽  
Vol 116 (1) ◽  
pp. 26-30
Author(s):  
Jun-Yao Yu
Keyword(s):  
Fourier Coefficient ◽  
Mathematical Theory ◽  
Fourier Coefficients ◽  
Mean Value ◽  
Time Function ◽  
Half Period ◽  
Time Varying ◽  
Ic Engine ◽  
The Mean ◽  
The Relationship

The Fourier coefficients are investigated for such a periodic time function whose magnitude keeps constant during the time of every half-period. In this case the relationship between the mean value and the Fourier coefficients is achieved using appropriate mathematical theory. It was applied successfully to the study of torsional harmonic excitations due to gas pressure in a four-cycle IC engine. A formula relating the truncated Fourier coefficient series to MIP has been established with very little error. The series simulation of Fourier coefficients is utilized in the determination and analysis of excitations.

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