Corner Reproduction Accuracy in Electro-Chemical Drilling (ECD) of Blind Holes

1984 ◽  
Vol 106 (1) ◽  
pp. 55-61 ◽  
Author(s):  
V. K. Jain ◽  
Vinod Kumar Jain ◽  
P. C. Pandey
Keyword(s):  
Experimental Data ◽  
Mathematical Model ◽  
Regression Analysis ◽  
Dimensional Analysis ◽  
Analysis Of Variance ◽  
Process Parameters ◽  
Important Process ◽  
Electrochemical Drilling ◽  
Experimental Findings ◽  
Shape And Size

Little information is available about the corner shape and size produced in electrochemical drilling of blind holes. On this account prediction of the complete anode shape analytically, in ECD, is not possible. This paper reports the experimental findings regarding the shape and size of the corners copied, in the anode during electrochemical drilling of blind holes using a tool of specified geometry. An equation evolved by regression analysis of experimental data has been suggested for this purpose. With a view to improve results, an equation based on dimensional analysis has also been presented. Finally, a comprehensive mathematical model accounting for the independent, higher order, and the interaction effects of different important process parameters on the yield (anode radius) has been proposed and its adequacy has been tested by the analysis of variance and accuracy against experimental data.

Mathematical Model of the Sintering Process of Iron-Copper Bearings

2007 ◽  
Vol 23 ◽  
pp. 119-122
Author(s):  
Cristina Teișanu ◽  
Stefan Gheorghe ◽  
Ion Ciupitu
Keyword(s):  
Experimental Data ◽  
Mechanical Properties ◽  
Mathematical Model ◽  
Regression Analysis ◽  
Function Optimization ◽  
Chemical Compositions ◽  
Sintering Process ◽  
Molybdenum Disulphide ◽  
Iron Copper ◽  
Antifriction Properties

The most important features of the self-lubricating bearings are the antifriction properties such as friction coefficient and wear resistence and some mechanical properties such as hardness, tensile strength and radial crushing strength. In order to improve these properties new antifriction materials based on iron-copper powders with several additional components (tin, lead and molybdenum disulphide) have been developed by PM techniques. To find the optimal relationship between chemical compositions, antifriction and mechanical properties, in this paper a mathematical model of the sintering process is developed, which highlighted the accordance of the model with data by regression analysis. For the statistical processing of the experimental data the VH5 hardness values of the studied materials were considered. The development of mathematical model includes the enunciation of the model, the establishment of the performance function (optimization) and the establishment of the model equations and verifying. The accordance of the model with experimental data has been highlighted by regression analysis

scholarly journals Specific residue: application of orthogonal contrasts when heteroscedasticity is present

2010 ◽  
Vol 67 (1) ◽  
pp. 117-125
Author(s):  
Maria Cristina Stolf Nogueira
Keyword(s):  
Experimental Data ◽  
Mathematical Model ◽  
Analysis Of Variance ◽  
Residue Analysis ◽  
Sum Of Squares ◽  
Block Designs ◽  
Mean Square ◽  
Orthogonal Contrasts ◽  
Variance Homogeneity ◽  
Analyze Data

When experimental data are submitted to analysis of variance, the assumption of data homoscedasticity (variance homogeneity among treatments), associated to the adopted mathematical model must be satisfied. This verification is necessary to ensure the correct test for the analysis. In some cases, when data homoscedascity is not observed, errors may invalidate the analysis. An alternative to overcome this difficulty is the application of the specific residue analysis, which consists of the decomposition of the residual sum of squares in its components, in order to adequately test the correspondent orthogonal contrasts of interest between treatment means. Although the decomposition of the residual sum of squares is a seldom used procedure, it is useful for a better understanding of the residual mean square nature and to validate the tests to be applied. The objective of this review is to illustrate the specific residue application as a valid and adequate alternative to analyze data from experiments following completely randomized and randomized complete block designs in the presence of heteroscedasticity.

Research on the Zero Drift of Sensor Based on Data Fusion Technology

2012 ◽  
Vol 546-547 ◽  
pp. 696-701
Author(s):  
Xiao Ming Li ◽  
Zhi Shu Feng ◽  
Zhong Chun Cai ◽  
Bin Xie ◽  
Chang Jie Liu
Keyword(s):  
Experimental Data ◽  
Mathematical Model ◽  
Regression Analysis ◽  
Data Fusion ◽  
Zero Drift ◽  
Two Dimensional ◽  
Fusion Technology ◽  
Input Output ◽  
Influence Of Temperature ◽  
Fusion Methods

The zero drift of sensor and its solution are presented in this paper. The basic principle of data fusion with two-dimensional regression analysis is expounded and the experimental data of any pressure sensor are fused with the two-dimensional regression analysis. Besides, the input-output mathematical model of sensor under the influence of temperature is established. At last, the linear, fitting and fusion methods are compared.

A Study on the Grindability of Engineering Plastics and Metals

2016 ◽  
Vol 686 ◽  
pp. 137-142 ◽  
Author(s):  
Ondřej Bílek ◽  
Jitka Baďurová ◽  
Jiří Čop
Keyword(s):  
Surface Quality ◽  
Analysis Of Variance ◽  
Process Parameters ◽  
Functional Relation ◽  
Experimental Results ◽  
Surface Grinding ◽  
Important Process ◽  
Research Directions ◽  
Engineering Plastics

In this study, the surface grinding was performed at different feed rates and depth of cuts. Grindability of engineering thermoplastics and metals was evaluated. Further, important process parameters influencing surface quality were determined using analysis of variance (ANOVA). Experimental results compared two significantly different groups of materials in order to emphasize common variables. Finally, further research directions were presented to seek for functional relation between process parameters and grindability.

Study of Factors Effecting Surface Roughness and Tool Tip Temperature in Step Turning Using Factorial Technique

2015 ◽  
Vol 15 (4) ◽  
pp. 319-326
Author(s):  
Kondapalli Siva Prasad
Keyword(s):  
Mathematical Model ◽  
Surface Roughness ◽  
Regression Analysis ◽  
Process Parameters ◽  
Depth Of Cut ◽  
Turning Process ◽  
Nose Radius ◽  
Five Factors ◽  
The Mathematical Model ◽  
Anova Technique

AbstractThe paper focuses on the effect of various process parameters like spindle speed, feed, depth of cut, nose radius and machining condition on the Tool tip temperature and surface roughness in step turning process is investigated by using Factorial Technique. Five factors- Two levels are used and total 32 experiments are performed. The coefficients are calculated by using regression analysis and the model is constructed. The adequacy of the developed model is checked using Analysis of Variance (ANOVA) technique. By using the mathematical model the main and interaction effect of various process parameters on tool tip temperature and surface roughness are studied.

scholarly journals Port-Hamiltonian Mathematical Model of a Fluid Ring Attitude System

Energies ◽  
2021 ◽  
Vol 14 (21) ◽  
pp. 6906
Author(s):  
Juan Cristobal Alcaraz Alcaraz Tapia ◽  
Carlos E. Castañeda ◽  
Héctor Vargas-Rodríguez
Keyword(s):  
Experimental Data ◽  
Mathematical Model ◽  
Regression Analysis ◽  
Linear Regression ◽  
Turbulent Flows ◽  
Linear Regression Analysis ◽  
Hamiltonian Formalism ◽  
System Model ◽  
Energy Shaping ◽  
Spatial Environment

In this article, we propose a mathematical model using the port-Hamiltonian formalism for a satellite’s three-axis attitude system comprising fluid rings. Fluid rings are an alternative to reaction wheels used for the same purpose, since, for the same mass, they can exert a greater torque than a reaction wheel as the fluid can circulate the periphery of the satellite. The port-Hamiltonian representation lays the foundation for a posterior controller that is feasible, stable, and robust based on the interconnection of the system to energy shaping and/or damping injection components, and by adding energy routing controllers. The torques exerted by the fluid rings are modeled using linear regression analysis on the experimental data got from a prototype of a fluid ring. Since the dynamics of turbulent flows is complex, the torques obtained by the prototype lead to a simpler first approach, leaving its uncertainties to a controller. Thus, the attitude system model could be tested in a future prototype before considering a spatial environment.

Impairment of blood volume restitution after large hemorrhage: a mathematical model

1996 ◽  
Vol 270 (5) ◽  
pp. R1163-R1177 ◽  
Author(s):  
D. E. Carlson ◽  
M. D. Kligman ◽  
D. S. Gann
Keyword(s):  
Experimental Data ◽  
Mathematical Model ◽  
Cell Membrane ◽  
Capillary Pressure ◽  
Blood Volume ◽  
Extracellular Space ◽  
Progressive Failure ◽  
Plasma Osmolality ◽  
Water Move ◽  
Experimental Findings

A mathematical model tests possible mechanisms for the progressive failure of blood volume restitution seen after larger hemorrhages ( > 26%) with increasing changes in plasma osmolality. After 10% hemorrhage, the model requires a decrease in net hydrostatic capillary pressure, the release of solute into the extracellular space, and the release of Na+ and K+ from a bound pool in equilibrium with the interstitium to match the experimental data. The solute and released cations expand the interstitium to drive the restitution of volume and protein from 3 to 24 h. After 30% hemorrhage, the best prediction of the average experimental responses occurs when the Na(+)-K(+)-adenosinetriphosphatase (ATPase) in the cell membrane is inhibited by 38.7% from 0.8 to 3 h, and the proportionality between capillary pressure and blood volume is reduced by 68% from its value for 10% hemorrhage. When the change in plasma osmolality is doubled after 30% hemorrhage, an increase in the inhibition of the ATPase to 85% and extension of its duration to 24 h are necessary to match experimental findings. The associated defect in sodium transport may occur after large hemorrhage so that sodium and water move into cells. This response may oppose osmotically driven expansion of the interstitium and thus account for the failure of restitution.

scholarly journals CONSTRUCTION OF MATHEMATICAL MODELS USING THE METHODS OF CORRELATION AND REGRESSION ANALYSIS

2021 ◽  
pp. 29-36
Author(s):  
Olga Prishchenko ◽  
Nadezhda Cheremskaya ◽  
Tetyana Chernogor
Keyword(s):  
Experimental Data ◽  
Mathematical Model ◽  
Regression Analysis ◽  
Functional Relationship ◽  
Functional Dependence ◽  
Mathematical Expression ◽  
Regression Equation ◽  
Statistical Hypothesis ◽  
Correlation And Regression Analysis ◽  
The Relationship

The article discusses the construction of a mathematical model using the methods of correlation and regression analysis in determining the functional relationship between the quantities. When conducting an experiment, it is often necessary to establish the interdependence between two or more quantities in order to obtain an empirical formula. In some cases, this is a simple task, because these connections are almost obvious or known in advance. As a rule, to establish the relationship between different indicators, factors and characteristics is not a trivial task. There is a need to use some hypothesis in the form of functional dependence. In other words, it is necessary to replace this functional dependence with a fairly simple mathematical expression. Such a mathematical expression can be a linear equation or a polynomial. In order to use such experimental data to determine such a mathematical or functional relationship between variables, the methods of correlation and regression analysis are used. Correlation analysis provides an answer to the statistical hypothesis of the absence or presence of a relationship between variables with some predetermined confidence probability. Determination of the functional dependence between different values on their experimental values is carried out using regression analysis. It is based on the well-known method of least squares. Proposing one or another regression equation, the researcher determines both the very existence of the relationship between variables and its mathematical form. Regression analysis considers the relationship between the dependent quantity and non-dependent variables. This relationship is represented using a mathematical model, that is, an equation that connects the dependent and independent variables. Processing of experimental data using correlation and regression analysis allows us to build a statistical mathematical model in the form of a regression equation. Thus, the methods of correlation and regression analysis are closely related.

The substantiation of the formalized estimation of effectiveness of technological and production systems

2018 ◽  
Vol 15 (1) ◽  
pp. 169-181
Author(s):  
M. I. Sidorov ◽  
М. Е. Stavrovsky ◽  
V. V. Irogov ◽  
E. S. Yurtsev
Keyword(s):  
Experimental Data ◽  
Mathematical Model ◽  
Production Systems ◽  
Van Der Pol

Using the example of van der Pol developed a mathematical model of frictional self-oscillations in topochemically kinetics. Marked qualitative correspondence of the results of calculation performed using the experimental data of researchers.

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