scholarly journals ‘Open-loop’ tracking interferometer for machine tool volumetric error measurement—Two-dimensional case

2014 ◽  
Vol 38 (3) ◽  
pp. 666-672 ◽  
Author(s):  
Soichi Ibaraki ◽  
Goh Sato ◽  
Kunitaka Takeuchi
Keyword(s):  
Machine Tool ◽  
Open Loop ◽  
Dimensional Case ◽  
Error Measurement ◽  
Two Dimensional ◽  
Volumetric Error ◽  
Tracking Interferometer

A Low Cost and Efficient Volumetric-Error Measurement Method for Five-Axis Machine Tools

2013 ◽  
Vol 284-287 ◽  
pp. 1723-1728
Author(s):  
Shih Ming Wang ◽  
Han Jen Yu ◽  
Hung Wei Liao
Keyword(s):  
Machine Tool ◽  
Error Compensation ◽  
Machine Tools ◽  
Measurement Method ◽  
Low Cost ◽  
Machining Accuracy ◽  
Error Measurement ◽  
Volumetric Error ◽  
Volumetric Errors ◽  
Five Axis

Error compensation is an effective and inexpensive way that can further enhance the machining accuracy of a multi-axis machine tool. The volumetric error measurement method is an essential of the error compensation method. The measurement of volumetric errors of a 5-axis machine tool is very difficult to be conducted due to its complexity. In this study, a volumetric-error measurement method using telescoping ball-bar was developed for the three major types of 5-axis machines. With the use of the three derived error models and the two-step measurement procedures, the method can quickly determine the volumetric errors of the three types of 5-axis machine tools. Comparing to the measurement methods currently used in industry, the proposed method provides the advantages of low cost, easy setup, and high efficiency.

The formation of gas hydrates under shock wave impact on the bubble media (two-dimensional case)

2010 ◽  
Vol 7 ◽  
pp. 90-97
Author(s):  
M.N. Galimzianov ◽  
I.A. Chiglintsev ◽  
U.O. Agisheva ◽  
V.A. Buzina
Keyword(s):  
Shock Wave ◽  
Gas Hydrates ◽  
Hydrate Formation ◽  
Dimensional Case ◽  
Two Dimensional ◽  
Wave Impact ◽  
Bubble Liquid ◽  
One Dimensional ◽  
Bubble Media ◽  
Main Factors

Formation of gas hydrates under shock wave impact on bubble media (two-dimensional case) The dynamics of plane one-dimensional shock waves applied to the available experimental data for the water–freon media is studied on the base of the theoretical model of the bubble liquid improved with taking into account possible hydrate formation. The scheme of accounting of the bubble crushing in a shock wave that is one of the main factors in the hydrate formation intensification with increasing shock wave amplitude is proposed.

Regions-based Two-dimensional Continua: The Euclidean Case

2018 ◽  
Author(s):  
Geoffrey Hellman ◽  
Stewart Shapiro
Keyword(s):  
Mathematical Induction ◽  
Dimensional Case ◽  
Two Dimensional ◽  
Entire Space ◽  
Euclidean Case ◽  
Free Basis ◽  
One Dimensional ◽  
Archimedean Property ◽  
The One

This chapter develops a Euclidean, two-dimensional, regions-based theory. As with the semi-Aristotelian account in Chapter 2, the goal here is to recover the now orthodox Dedekind–Cantor continuum on a point-free basis. The chapter derives the Archimedean property for a class of readily postulated orientations of certain special regions, what are called “generalized quadrilaterals” (intended as parallelograms), by which the entire space is covered. Then the chapter generalizes this to arbitrary orientations, and then establishes an isomorphism between the space and the usual point-based one. As in the one-dimensional case, this is done on the basis of axioms which contain no explicit “extremal clause”, and we have no axiom of induction other than ordinary numerical (mathematical) induction.

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