Modeling of Geometric Variations for Line-Profiles

2012 ◽  
Vol 12 (4) ◽  
Author(s):  
Joseph K. Davidson ◽  
Jami J. Shah
Keyword(s):  
Two Dimensional ◽  
Line Profiles ◽  
Tolerance Zone ◽  
Geometric Tolerances ◽  
True Profile ◽  
Profile Tolerance ◽  
On Line ◽  
Model Features ◽  
Tolerance Accumulation ◽  
First Time

The geometric variations in a tolerance-zone can be modeled with hypothetical point-spaces called Tolerance-Maps (T-Maps) for purposes of automating the assignment of tolerances during design. The objective of this paper is to extend this model to represent tolerances on line-profiles. 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. In this paper, the Tolerance-Map (Patent No. 6963824) is a hypothetical volume of points that captures all the positions for the true profile, and those curves parallel to it, which can reside in the tolerance-zone. The model is compatible with the ASME/ANSI/ISO Standards for geometric tolerances. T-Maps have been generated for other classes of geometric tolerances in which the variations of the feature are represented with a plane, line or circle, and these have been incorporated into testbed software for aiding designers when assigning tolerances for assemblies. In this paper the T-Map for line-profiles is created and, for the first time in this model, features may be either symmetrical or nonsymmetrical simple planar curves, typically closed. To economize on length of the paper, and yet to introduce a method whereby T-Maps may be used to optimize the allocation of tolerances for line-profiles, the scope of the paper has been limited to square, rectangular, and triangular shapes. An example of tolerance accumulation is presented to illustrate this method.

Modeling of Geometric Variations for Line-Profiles

2011 ◽  
Author(s):  
Joseph K. Davidson ◽  
Jami J. Shah
Keyword(s):  
Two Dimensional ◽  
Line Profiles ◽  
Tolerance Zone ◽  
Geometric Tolerances ◽  
True Profile ◽  
Profile Tolerance ◽  
On Line ◽  
Model Features ◽  
Tolerance Accumulation ◽  
First Time

The geometric variations in a tolerance-zone can be modeled with hypothetical point-spaces called Tolerance-Maps (T-Maps) for purposes of automating the assignment of tolerances during design. The objective of this paper is to extend this model to represent tolerances on line-profiles. 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. In this paper, the Tolerance-Map (Patent No. 6963824) is a hypothetical volume of points that captures all the positions for the true profile, and those curves parallel to it, which can reside in the tolerance-zone. The model is compatible with the ASME/ANSI/ISO Standards for geometric tolerances. T-Maps have been generated for other classes of geometric tolerances in which the variation of the feature are represented with a plane, line or circle, and these have been incorporated into testbed software for aiding designers when assigning tolerances for assemblies. In this paper the T-Map for line-profiles is created and, for the first time in this model, features may be either symmetrical or non-symmetrical simple planar curves, typically closed. To economize on length of the paper, and yet to introduce a method whereby T-Maps may be used to optimize the allocation of tolerances for line-profiles, the scope of the paper has been limited to square, rectangular, and triangular shapes. An example of tolerance accumulation is presented to illustrate this method.

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].

Modeling of Geometric Variations Within a Tolerance-Zone for Circular Runout

2009 ◽  
Author(s):  
Patrick J. Clasen ◽  
Joseph K. Davidson ◽  
Jami J. Shah
Keyword(s):  
Cross Section ◽  
Transverse Cross Section ◽  
Tolerance Zone ◽  
Iso Standards ◽  
Geometric Tolerances ◽  
Short Cylinder ◽  
Tolerance Zones ◽  
First Time

The geometric variations in a tolerance-zone can be modeled with hypothetical point-spaces called Tolerance-Maps (T-Maps) for purposes of automating the assignment of tolerances during design. The objective of this paper is to extend this model to represent tolerances on circular runout which limit geometric manufacturing variations to a specified tolerance-zone. Such a zone is an annular area at one transverse cross-section for spherical, conical, or cylindrical objects (features), but it is a short cylinder when the feature is a round or annular segment of a plane. Depending on the kind of feature and the tolerances that are specified for it, the model may be used to represent variations within tolerance-zones for circular runout, size, position, orientation, and form. In this paper, the Tolerance-Map (T-Map) is a hypothetical volume of points that captures all the circular variations that can arise from these tolerances. The model is compatible with the ASME/ANSI/ISO Standards for geometric tolerances. T-Maps have been generated for other classes of geometric tolerances in which the variation of the feature are represented with a plane or line, and these have been incorporated into testbed software for aiding designers when assigning tolerances for assemblies. In this paper the T-Map for circular runout is created and, for the first time, circles are used to represent the geometric variations of a feature in tolerance-zones.

Tolerance-Maps Applied to a Point-Line Cluster of Features

2006 ◽  
Vol 129 (8) ◽  
pp. 782-792 ◽  
Author(s):  
Gaurav Ameta ◽  
Joseph K. Davidson ◽  
Jami J. Shah
Keyword(s):  
Dimensional Space ◽  
Local Level ◽  
Two Dimensional ◽  
Relative Location ◽  
Global Level ◽  
Tolerance Zone ◽  
Geometric Tolerances ◽  
Cluster A ◽  
Point Line ◽  
Picture Frame

In this paper, groups of individual features, i.e., a point, a line, and a plane, are called clusters and are used to constrain sufficiently the relative location of adjacent parts. A new mathematical model for representing size and geometric tolerances is applied to a point-line cluster of features that is used to align adjacent parts in two-dimensional space. First, tolerance-zones are described for the point-line cluster. A Tolerance-Map® (Patent no. 69638242), a hypothetical volume of points, is then established which is the range of a mapping from all possible locations for the features in the cluster. A picture frame assembly of four parts is used to illustrate the accumulations of manufacturing variations, and the T-Maps® provide stackup relations that can be used to allocate size and orientational tolerances. This model is one part of a bilevel model that we are developing for size and geometric tolerances. At the local level the model deals with the permitted variations in a tolerance zone, while at the global level it interrelates all the frames of reference on a part or assembly.

Application of on-line two-dimensional liquid chromatography in comparative proteome analysis of antlers with different growing stages

2010 ◽  
Vol 28 (2) ◽  
pp. 146-151 ◽  
Author(s):  
Liang GAO ◽  
Xiaoqiang QIAO ◽  
Zhen LIANG ◽  
Lihua ZHANG ◽  
Yushu HUO ◽  
...  
Keyword(s):  
Liquid Chromatography ◽  
Proteome Analysis ◽  
Two Dimensional ◽  
On Line

scholarly journals Influence of a Standing Wave Flow-Field on the Dynamics of a Spray Diffusion Flame

Fluids ◽  
2021 ◽  
Vol 6 (1) ◽  
pp. 27
Author(s):  
J. Barry Greenberg ◽  
David Katoshevski
Keyword(s):  
Liquid Phase ◽  
Flow Field ◽  
Standing Wave ◽  
Diffusion Flame ◽  
Stokes Number ◽  
Flame Height ◽  
Wave Flow ◽  
Two Dimensional ◽  
Governing Equations ◽  
First Time

A theoretical investigation of the influence of a standing wave flow-field on the dynamics of a laminar two-dimensional spray diffusion flame is presented for the first time. The mathematical analysis permits mild slip between the droplets and their host surroundings. For the liquid phase, the use of a small Stokes number as the perturbation parameater enables a solution of the governing equations to be developed. Influence of the standing wave flow-field on droplet grouping is described by a specially constructed modification of the vaporization Damkohler number. Instantaneous flame front shapes are found via a solution for the usual Schwab–Zeldovitch parameter. Numerical results obtained from the analytical solution uncover the strong bearing that droplet grouping, induced by the standing wave flow-field, can have on flame height, shape, and type (over- or under-ventilated) and on the existence of multiple flame fronts.

scholarly journals Tetrazine molecules as efficient electronic diversion channel in 2D organic-inorganic perovskites

2021 ◽  
Author(s):  
Ferdinand Lédée ◽  
Pierre Audebert ◽  
Gaëlle Trippé-Allard ◽  
Laurent Galmiche ◽  
Damien Garrot ◽  
...  
Keyword(s):  
Organic Component ◽  
Two Dimensional ◽  
Diversion Channel ◽  
Halide Perovskites ◽  
First Time

We present the synthesis of two novel two-dimensional (2D) hybrid organic-inorganic halide perovskites incorporating for the first time 100% of a photoactive tetrazine derivative as the organic component. With this...

scholarly journals Exfoliation in a low boiling point solvent and electrochemical applications of MoO3

2020 ◽  
Vol 11 ◽  
pp. 662-670
Author(s):  
Matangi Sricharan ◽  
Bikesh Gupta ◽  
Sreejesh Moolayadukkam ◽  
H S S Ramakrishna Matte
Keyword(s):  
Energy Storage ◽  
Electrode Material ◽  
Electronic Devices ◽  
High Specific Capacitance ◽  
Two Dimensional ◽  
Energy Storage Devices ◽  
Intrinsic Nature ◽  
Storage Devices ◽  
Scan Rate ◽  
First Time

MoO3 is a versatile two-dimensional transition metal oxide having applications in areas such as energy storage devices, electronic devices and catalysis. To efficiently utilize the properties of MoO3 arising from its two-dimensional nature exfoliation is necessary. In this work, the exfoliation of MoO3 is carried out in 2-butanone for the first time. The achieved concentration of the dispersion is about 0.57 mg·mL−1 with a yield of 5.7%, which are the highest values reported to date. These high values of concentration and yield can be attributed to a favorable matching of energies involved in exfoliation and stabilization of MoO3 nanosheets in 2-butanone. Interestingly, the MoO3 dispersion in 2-butanone retains its intrinsic nature even after exposure to sunlight for 24 h. The composites of MoO3 nanosheets were used as an electrode material for supercapacitors and showed a high specific capacitance of 201 F·g−1 in a three-electrode configuration at a scan rate of 50 mV·s−1.

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