scholarly journals On-machine precision truing of ultrathin arc-shaped diamond wheels for grinding aspherical microstructure arrays

2021 ◽  
Author(s):  
Shimeng Yu ◽  
Peng Yao ◽  
Chuanzhen Huang ◽  
Dongkai Chu ◽  
Hongtao Zhu ◽  
...  
Keyword(s):  
Machine Precision

Solution of Kepler’s Equation with Machine Precision

2020 ◽  
Vol 64 (12) ◽  
pp. 1060-1066
Author(s):  
M. K. Abubekerov ◽  
N. Yu. Gostev
Keyword(s):  
Machine Precision ◽  
Kepler's Equation ◽  
Kepler’S Equation

Stageless evaluation for a vector Preisach model based on rotational operators

2017 ◽  
Vol 36 (5) ◽  
pp. 1501-1516
Author(s):  
Michael Nierla ◽  
Alexander Sutor ◽  
Stefan Johann Rupitsch ◽  
Manfred Kaltenbacher
Keyword(s):  
Design Methodology ◽  
Computational Cost ◽  
Direct Application ◽  
Preisach Model ◽  
Machine Precision ◽  
Content Type ◽  
Model Based ◽  
Evaluation Scheme ◽  
Computational Resources ◽  
Rotational Operator

Purpose This paper aims to present a novel stageless evaluation scheme for a vector Preisach model that exploits rotational operators for the description of vector hysteresis. It is meant to resolve the discretizational errors that arise during the application of the standard matrix-based implementation of Preisach-based models. Design/methodology/approach The newly developed evaluation uses a nested-list data structure. Together with an adapted form of the Everett function, it allows to represent both the additional rotational operator and the switching operator of the standard scalar Preisach model in a stageless fashion, i.e. without introducing discretization errors. Additionally, presented updating and simplification rules ensure the computational efficiency of the scheme. Findings A comparison between the stageless evaluation scheme and the commonly used matrix approach reveals not only an improvement in accuracy up to machine precision but, furthermore, a reduction of computational resources. Research limitations/implications The presented evaluation scheme is especially designed for a vector Preisach model, which is based on an additional rotational operator. A direct application to other vector Preisach models that do not rely on rotational operators is not intended. Nevertheless, the presented methodology allows an easy adaption to similar vector Preisach schemes that use modified setting rules for the rotational operator and/or the switching operator. Originality/value Prior to this contribution, the vector Preisach model based on rotational operators could only be evaluated using a matrix-based approach that works with discretized forms of rotational and switching operator. The presented evaluation scheme offers reduced computational cost at much higher accuracy. Therefore, it is of great interest for all users of the mentioned or similar vector Preisach models.

COMPUTATIONAL STUDIES OF DISCRETE BREATHERS — FROM BASICS TO COMPETING LENGTH SCALES

2006 ◽  
Vol 16 (06) ◽  
pp. 1645-1669 ◽  
Author(s):  
SERGEJ FLACH ◽  
ANDREY GORBACH
Keyword(s):  
Initial Conditions ◽  
Computational Studies ◽  
Machine Precision ◽  
Algebraic Decay ◽  
Computational Tools ◽  
Length Scales ◽  
Localized Excitations ◽  
Long Range Interactions ◽  
Discrete Breathers ◽  
Anharmonic Interactions

This work provides a description of the main computational tools for the study of discrete breathers. It starts with the observation of breathers through simple numerical runs, the study uses targeted initial conditions, and discrete breather impact on transient processes and thermal equilibrium. We briefly describe a set of numerical methods to obtain breathers up to machine precision. In the final part of this work we apply the discussed methods to study the competing length scales for breathers with purely anharmonic interactions — favoring superexponential localization — and long range interactions, which favor algebraic decay in space. As a result, we observe and explain the presence of three different spatial tail characteristics of the considered localized excitations.

Device for Training of Machine Tool Diagnostic Routines under Various Conditions

2015 ◽  
Vol 808 ◽  
pp. 3-8
Author(s):  
Miroslav Císar ◽  
Ivan Kuric ◽  
Vasile Adrian Ceclan
Keyword(s):  
Machine Tool ◽  
Environmental Impacts ◽  
Machine Tools ◽  
Experimental Device ◽  
Training Process ◽  
Machine Precision ◽  
Geometrical Errors ◽  
Wide Scale

The article deals with diagnostics of machine tool precision and necessity to train basic routines of measurement and its preparation. Such training is essential for efficiency of diagnostic processes as preparation is usually the most time-consuming and skill-demanding part of overall measurement. The article roughly describes simulation of machine tool errors on proposed experimental device and its implementation into the training process in order to gain experiences with measurement on machine tools in wide scale of conditions. Described device is designed to simulate several geometrical errors, inaccuracies and environmental impacts on precision of positioning which affects not only machine precision but also effectivity of measurement itself.

HIGH-ORDER OUT-OF-PLANE EXPANSION FOR 3D FIELDS

2011 ◽  
Vol 26 (10n11) ◽  
pp. 1807-1821 ◽  
Author(s):  
K. MAKINO ◽  
M. BERZ ◽  
C. JOHNSTONE
Keyword(s):  
Fixed Point Problem ◽  
Precise Determination ◽  
Point Problem ◽  
Detailed Knowledge ◽  
Machine Precision ◽  
Out Of Plane ◽  
3D Fields ◽  
Finite Element Schemes ◽  
Careful Assessment

The precise determination of the dynamics in accelerators with complicated field arrangements such as Fixed Field Alternating Gradient accelerators (FFAG) depends critically on the ability to describe the appearing magnetic fields in full 3D. However, frequently measurements or models of FFAG fields postulate their behavior in the midplane only, and rely on the fact that this midplane field and its derivatives determine the field in all of space. The detailed knowledge of the resulting out-of-plane fields is critical for a careful assessment of the vertical dynamics. We describe a method based on the differential algebraic (DA) approach to obtain the resulting out-of-plane expansions to any order in an order-independent, straightforward fashion. In particular, the resulting fields satisfy Maxwell's equations to the order of the expansion up to machine precision errors, and without any inaccuracies that can arise from conventional divided difference or finite element schemes for the computation of out-of-plane fields. The method relies on re-writing the underlying PDE as a fixed point problem involving DA operations, and in particular the differential algebraic integration operator. We illustrate the performance of the method for a variety of practical examples, and obtain estimates for the orders necessary to describe the fields to a prescribed accuracy.

An on-machine precision measurement method for API threads

2019 ◽  
Vol 30 (8) ◽  
pp. 085006 ◽  
Author(s):  
Zhixu Dong ◽  
Xingwei Sun ◽  
Changzheng Chen ◽  
Heran Yang
Keyword(s):  
Precision Measurement ◽  
Measurement Method ◽  
Machine Precision

Envelope grinding of micro-cylinder array lenses using a near arc-profile wheel without on-machine precision truing

2021 ◽  
Vol 289 ◽  
pp. 116927
Author(s):  
Wei Wang ◽  
Zhen Zhang ◽  
Peng Yao ◽  
Xiangyu Wang ◽  
Zongbo Zhang ◽  
...  
Keyword(s):  
Machine Precision ◽  
Cylinder Array

scholarly journals Grain growth for astrophysics with Discontinuous Galerkin schemes

2020 ◽  
Author(s):  
Maxime Lombart ◽  
Guillaume Laibe
Keyword(s):  
Numerical Modelling ◽  
Galerkin Method ◽  
Grain Growth ◽  
Discontinuous Galerkin ◽  
Discontinuous Galerkin Method ◽  
Chemical Reactions ◽  
Dust Grains ◽  
Machine Precision ◽  
Accurate Treatment ◽  
Coagulation Equation

Abstract Depending on their sizes, dust grains store more or less charges, catalyse more or less chemical reactions, intercept more or less photons and stick more or less efficiently to form embryos of planets. Hence the need for an accurate treatment of dust coagulation and fragmentation in numerical modelling. However, existing algorithms for solving the coagulation equation are over-diffusive in the conditions of 3D simulations. We address this challenge by developing a high-order solver based on the Discontinuous Galerkin method. This algorithm conserves mass to machine precision and allows to compute accurately the growth of dust grains over several orders of magnitude in size with a very limited number of dust bins.

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