Tolerance-Maps for Line-Profiles Formed by Intersecting Kinematically Transformed Primitive Tolerance-Map Elements

2016 ◽  
Vol 16 (2) ◽  
Author(s):  
Y. He ◽  
J. K. Davidson ◽  
N. J. Kalish ◽  
Jami J. Shah
Keyword(s):  
Line Profile ◽  
Comprehensive Treatment ◽  
Solid Model ◽  
Line Profiles ◽  
Tolerance Zone ◽  
Math Model ◽  
Subsequent Formation ◽  
Point Space ◽  
Map Construction ◽  
Global Reference Frame

For the purposes of automating the assignment of tolerances during design, a math model, called the Tolerance-Map (T-Map), has been produced for most of the tolerance classes that are used by designers. Each T-Map is a hypothetical point-space that represents the geometric variations of a feature in its tolerance-zone. Of the six tolerance classes defined in the ASME/ANSI/ISO Standards, profile tolerances have received the least attention for representation in computer models. The objective of this paper is to provide a comprehensive treatment of T-Map construction for any line-profile by using primitive T-Map elements and their Boolean intersection. The method requires (a) decomposing a profile into segments, each of constant curvature; (b) creating a solid-model T-Map primitive for each in a common global reference frame; and (c) combining these by Boolean intersection to generate the T-Map for a complete line-profile of any shape. Freeform portions of a profile are modeled as a series of closely spaced points and subsequent formation of short circular arc-segments, each formed from the circle that osculates to three adjacent points.

Tolerance-Maps for Line-Profiles Constructed From Boolean Operations on Primitive T-Map Elements

2013 ◽  
Author(s):  
Y. He ◽  
J. K. Davidson ◽  
Jami J. Shah
Keyword(s):  
Line Profile ◽  
Line Profiles ◽  
Tolerance Zone ◽  
Compressor Blades ◽  
Cross Sectional ◽  
Math Model ◽  
True Profile ◽  
Profile Tolerance ◽  
On Line ◽  
Computer Automation

For purposes of automating the assignment of tolerances during design, a math model, called the Tolerance-Map (T-Map), has been produced for most of the tolerance classes that are used by designers. Each T-Map is a hypothetical point-space that represents the geometric variations of a feature in its tolerance-zone. Of the six tolerance classes defined in the ASME/ANSI/ISO Standards, only one attempt has been made at modeling line-profiles [1], and the method used is an intuitive kinematic description of the allowable displacements of the middle-sized profile within its tolerance-zone. The objective of this paper is to describe an alternative method of construction, one that is much more amenable to computer automation, to obtain the T-Map of any line-profile. Tolerances on line-profiles are used to control cross-sectional shapes of parts, even mildly twisted ones such as those on turbine or compressor blades. Such tolerances limit geometric manufacturing variations to a specified two-dimensional tolerance-zone, i.e. an area, the boundaries to which are curves parallel to the true profile. The single profile tolerance may be used to control position, orientation, and form of the profile. The new method requires decomposing a profile into segments, creating a solid-model T-Map primitive for each, and then combining these by the Boolean intersection to generate the T-Map for a complete line profile of any shape. To economize on length, the scope of this paper is limited to line-profiles having any polygonal shape.

Using Planar Kinematics to Construct the Full 4-D Tolerance-Map for a Line-Profile

2013 ◽  
Author(s):  
S. B. Savaliya ◽  
J. K. Davidson ◽  
Jami J. Shah
Keyword(s):  
Companion Paper ◽  
Line Profiles ◽  
Tolerance Zone ◽  
Compressor Blades ◽  
Cross Sectional ◽  
Math Model ◽  
True Profile ◽  
Triangular Profile ◽  
On Line ◽  
The Common

Tolerances on line-profiles are used to control cross-sectional shapes of parts, even mildly twisted ones such as those on turbine or compressor blades. Such tolerances limit geometric manufacturing variations to a specified two-dimensional tolerance-zone, i.e. an area, the boundaries to which are curves parallel to the true profile. The single profile tolerance may be used to control position, orientation, and form of the profile. For purposes of automating the assignment of tolerances during design, a math model, called the Tolerance-Map (T-Map), has been produced for most of the tolerance classes that are used by designers. Each T-Map is a hypothetical point-space that represents the geometric variations of a feature in its tolerance-zone. Of the six tolerance classes defined in the ASME/ANSI/ISO Standards, only one attempt has been made at modeling line-profiles [1], and the method used is a kinematic description, based largely on intuition, of the allowable displacements of the middle-sized profile within its tolerance-zone. The result presented is a 4-D double pyramid having a 3-D shape for the common base. Allowable small changes in size represent the fourth dimension in the altitude-direction of the pyramids. However, that work is limited to square, rectangular, and right-triangular profile shapes for which the 3-D transverse sections (called hypersections) of the 4-D T-Map are all geometrically similar to the base because the boundaries are doubly traced. For more generally shaped profiles, [2] the hypersections are not geometrically similar to the base. The objective of this paper is to expand the kinematic description of a profile in its tolerance-zone to include the changing constraints that take place as size is incremented or decremented within the allowable tolerance-range. It provides validation of a different method that is described in a companion paper [3].

Allocating Tolerances Statistically With Tolerance-Maps and Beta Distributions: The Target a Planar Face

2005 ◽  
Author(s):  
Gaurav Ameta ◽  
Joseph K. Davidson ◽  
Jami J. Shah
Keyword(s):  
Probability Density Function ◽  
Beta Distribution ◽  
Central Element ◽  
Tolerance Zone ◽  
Math Model ◽  
Point Space ◽  
Geometric Tolerances ◽  
Acceptable Range ◽  
The Individual ◽  
New Math

A new math model for geometric tolerances is used to build the frequency distribution for clearance in an assembly of parts, each of which is manufactured to a given set of size and orientation tolerances. The central element of the new math model is the Tolerance-Map® (T-Map®); it is the range of points resulting from a one-to-one mapping from all the variational possibilities of a feature, within its tolerance-zone, to a specially designed Euclidean point-space. A functional T-Map represents both the acceptable range of 1-D clearance and the acceptable limits to the 3-D variational possibilities of the target face consistent with it. An accumulation T-Map represents all the accumulated 3-D variational possibilities of the target which arise from allowable manufacturing variations on the individual parts in the assembly. The geometric shapes of the accumulation and functional maps are used to compute a measure of all variational possibilities of manufacture of the parts which will give each value of clearance. The measures are then arranged as a probability density function over the acceptable range of clearance, and a beta distribution is fitted to it. The method is applied to two examples.

scholarly journals The Kinematics of Quasar Broad Emission Line Regions Using a Disk-Wind Model

2017 ◽  
Vol 34 ◽  
Author(s):  
Suk Yee Yong ◽  
Rachel L. Webster ◽  
Anthea L. King ◽  
Nicholas F. Bate ◽  
Matthew J. O’Dowd ◽  
...  
Keyword(s):  
Emission Line ◽  
Line Profile ◽  
Inclination Angle ◽  
Opening Angle ◽  
Line Profiles ◽  
Wind Model ◽  
Disk Wind ◽  
Reverberation Mapping ◽  
Broad Emission ◽  
Line Region

AbstractThe structure and kinematics of the broad line region in quasars are still unknown. One popular model is the disk-wind model that offers a geometric unification of a quasar based on the viewing angle. We construct a simple kinematical disk-wind model with a narrow outflowing wind angle. The model is combined with radiative transfer in the Sobolev, or high velocity, limit. We examine how angle of viewing affects the observed characteristics of the emission line. The line profiles were found to exhibit distinct properties depending on the orientation, wind opening angle, and region of the wind where the emission arises.At low inclination angle (close to face-on), we find that the shape of the emission line is asymmetric, narrow, and significantly blueshifted. As the inclination angle increases (close to edge-on), the line profile becomes more symmetric, broader, and less blueshifted. Additionally, lines that arise close to the base of the disk wind, near the accretion disk, tend to be broad and symmetric. Single-peaked line profiles are recovered for the intermediate and equatorial wind. The model is also able to reproduce a faster response in either the red or blue sides of the line profile, consistent with reverberation mapping studies.

Ca II Emission from Late-type Stars

1983 ◽  
Vol 5 (2) ◽  
pp. 152-157 ◽  
Author(s):  
L. E. Cram
Keyword(s):  
Line Profile ◽  
Strong Correlation ◽  
Velocity Fields ◽  
Line Profiles ◽  
Late Type ◽  
Wide Range ◽  
Cool Stars ◽  
Visual Magnitude ◽  
The Absolute ◽  
Emission Core

Two recent observational surveys of the Ca II resonance lines (Zarro and Rodgers 1983; Linsky et al. 1979) illustrate the great diversity of line profile shapes found in the spectra of cool stars. This diversity reflects a corresponding wide range in the underlying chromospheric properties of the stars. There are, however, three well-marked systematic trends in the shapes of Ca II line profiles which presumably reflect systematic trends in chromospheric properties. One of these, the Wilson-Bappu effect (Wilson and Bappu 1957), describes the strong correlation betweeen the width of the emission core (see Figure 1) and the absolute visual magnitude of the star. Despite much work, it is still not clear whether this is due primarily to systematic changes of velocity fields (e.g. Hoyle and Wilson 1958) or optical depths (e.g. Jefferies and Thomas 1959) in stellar chromospheres.

scholarly journals New Progress in Mode Detection and Identification in δ Scuti Stars by the Analysis of Line Profile Variations

2000 ◽  
Vol 176 ◽  
pp. 463-464
Author(s):  
L. Mantegazza ◽  
E. Poretti ◽  
M. Bossi ◽  
N. S. Nuñez ◽  
A. Sacchi ◽  
...  
Keyword(s):  
High Resolution ◽  
Line Profile ◽  
High Resolution Spectroscopy ◽  
Line Profiles ◽  
Powerful Technique ◽  
Mode Detection ◽  
Detection And Identification ◽  
Scuti Stars ◽  
Δ Scuti Stars ◽  
Nonradial Pulsation

Abstractδ Sct stars are among the most promising targets to perform ground-based asteroseismology. High resolution spectroscopy offers us a powerful technique to identify radial and nonradial pulsation modes, since we can easily detect oscillations and travelling features in the line profiles.

scholarly journals MOBSTER – III. HD 62658: a magnetic Bp star in an eclipsing binary with a non-magnetic ‘identical twin’

2019 ◽  
Vol 490 (3) ◽  
pp. 4154-4165 ◽  
Author(s):  
M E Shultz ◽  
C Johnston ◽  
J Labadie-Bartz ◽  
V Petit ◽  
A David-Uraz ◽  
...  
Keyword(s):  
Magnetic Field ◽  
Magnetic Fields ◽  
Light Curve ◽  
Line Profile ◽  
Longitudinal Magnetic Field ◽  
Stellar Structure ◽  
Line Profiles ◽  
Dipole Strength ◽  
Rotational Modulation ◽  
Brightness Modulation

ABSTRACT HD 62658 (B9p V) is a little-studied chemically peculiar star. Light curves obtained by the Kilodegree Extremely Little Telescope (KELT) and Transiting Exoplanet Survey Satellite (TESS) show clear eclipses with a period of about 4.75 d, as well as out-of-eclipse brightness modulation with the same 4.75 d period, consistent with synchronized rotational modulation of surface chemical spots. High-resolution ESPaDOnS circular spectropolarimetry shows a clear Zeeman signature in the line profile of the primary; there is no indication of a magnetic field in the secondary. PHOEBE modelling of the light curve and radial velocities indicates that the two components have almost identical masses of about 3 M⊙. The primary’s longitudinal magnetic field 〈Bz〉 varies between about +100 and −250 G, suggesting a surface magnetic dipole strength Bd = 850 G. Bayesian analysis of the Stokes V profiles indicates Bd = 650 G for the primary and Bd < 110 G for the secondary. The primary’s line profiles are highly variable, consistent with the hypothesis that the out-of-eclipse brightness modulation is a consequence of rotational modulation of that star’s chemical spots. We also detect a residual signal in the light curve after removal of the orbital and rotational modulations, which might be pulsational in origin; this could be consistent with the weak line profile variability of the secondary. This system represents an excellent opportunity to examine the consequences of magnetic fields for stellar structure via comparison of two stars that are essentially identical with the exception that one is magnetic. The existence of such a system furthermore suggests that purely environmental explanations for the origin of fossil magnetic fields are incomplete.

scholarly journals First Detection of a Frequency Multiplet in the Line Profile Variations of RR Lyrae: Towards an Understanding of the Blazhko Effect

2000 ◽  
Vol 176 ◽  
pp. 286-290 ◽  
Author(s):  
K. Kolenberg ◽  
C. Aerts ◽  
M. Chadid ◽  
D. Gillet
Keyword(s):  
Line Profile ◽  
Theoretical Models ◽  
Theoretical Modelling ◽  
Line Profiles ◽  
Multiplet Structure ◽  
Complete Understanding ◽  
Period Analysis ◽  
Essential Step ◽  
Rr Lyrae ◽  
Blazhko Effect

AbstractWe provide the first detection of a frequency multiplet in the line profile variations of RR Lyrae. Performing a period analysis on 669 high resolution line profiles obtained with the spectrograph ELODIE at OHP, we clearly detect a multiplet structure, with a separation equal to the Blazhko frequency, around the main frequency and its harmonics. The triplet components are very prominent; additional observations are needed to decide about the existence of a quintuplet. The complete understanding of the origin of the Blazhko effect still needs further theoretical modelling and better observations. Our detection of the frequency multiplet in the line profile variations is a first essential step towards a decisive confrontation between the theoretical models and the observations.

scholarly journals Measurement of line profiles

1986 ◽  
Vol 118 ◽  
pp. 401-412
Author(s):  
David F. Gray
Keyword(s):  
Spectral Line ◽  
High Precision ◽  
Line Profile ◽  
Line Profiles ◽  
Spectral Line Profile ◽  
The University

The basic requirements for high precision spectral line profile measurements are reviewed, with the observatory at the University of Western Ontario serving to illustrate several of the points.

Profile Tolerances Modeling: A Unified Framework for Representing Geometric Variations for Line Profiles

2015 ◽  
Author(s):  
Jiao Chen ◽  
Yuan Li ◽  
Jianfeng Yu ◽  
Wenbin Tang
Keyword(s):  
Line Profile ◽  
Assessment Method ◽  
Maximum Deviation ◽  
Unified Framework ◽  
Tolerance Zone ◽  
Type 1 Error ◽  
Split Point ◽  
Type 2 Error

Tolerance modeling is the most basic issue in Computer Aided Tolerancing (CAT). It will negatively influence the performance of subsequent activities such as tolerance analysis to a great extent if the resultant model cannot accurately represent variations in tolerance zone. According to ASME Y14.5M Standard [1], there is a class of profile tolerances for lines and surfaces which should also be interpreted correctly. Aim at this class of tolerances, the paper proposes a unified framework called DOFAS for representing them which composed of three parts: a basic DOF (Degrees of Freedom) model for interpreting geometric variations for profiles, an assessment method for filtering out and rejecting those profiles cannot be accurately represented and a split algorithm for splitting rejected profiles into sub profiles to make their variations interpretable. The scope of discussion in this paper is restricted to the line profiles; we will focus on the surface profiles in forthcoming papers. From the DOF model, two types of errors result from the rotations of the features are identified and formulized. One type of the errors is the result of the misalignment between profile boundary and tolerance zone boundary (noted as type 1); and if the feature itself exceeds the range of tolerance zone the other type of errors will form (noted as type 2). Specifically, it is required that the boundary points of the line profile should align with the corresponding boundary lines of the tolerance zone and an arbitrary point of the line profile should lie within the tolerance zone when line profile rotates in the tolerance zone. To make DOF model as accurate as possible, an assessment method and a split algorithm are developed to evaluate and eliminate these two type errors. It is clear that not all the line features carry the two type errors; as such the assessment method is used as a filter for checking and reserving such features that are consistent with the error conditions. In general, feature with simple geometry is error-free and selected by the filter whereas feature with complex geometry is rejected. According to the two type errors, two sub-procedures of the assessment process are introduced. The first one mathematically is a scheme of solving the maximum deviation of rotation trajectories of profile boundary, so as to neglect the type 1 error if it approaches to zero. The other one is to solve the maximum deviation of trajectories of all points of the feature: type 2 error can be ignored when the retrieved maximum deviation is not greater than prescribed threshold, so that the feature will always stay within the tolerance zone. For such features rejected by the filter which are inconsistent with the error conditions, the split algorithm, which is spread into the three cases of occurrence of type 1 error, occurrence of type 2 error and concurrence of two type errors, is developed to ease their errors. By utilizing and analyzing the geometric and kinematic properties of the feature, the split point is recognized and obtained accordingly. Two sub-features are retrieved from the split point and then substituted into the DOFAS framework recursively until all split features can be represented in desired resolution. The split algorithm is efficient and self-adapting lies in the fact that the rules applied can ensure high convergence rate and expected results. Finally, the implementation with two examples indicates that the DOFAS framework is capable of representing profile tolerances with enhanced accuracy thus supports the feasibility of the proposed approach.

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