MATHEMATICAL MODEL OF SIZE TOLERANCE FOR PLANE BASED ON MATHEMATICAL DEFINITION

2001 ◽  
Vol 37 (09) ◽  
pp. 12 ◽  
Author(s):  
Yusheng Liu
Keyword(s):  
Mathematical Model ◽  
Mathematical Definition ◽  
Size Tolerance

Geometric tolerances: A new application for line geometry and screws

2002 ◽  
Vol 216 (1) ◽  
pp. 95-103 ◽  
Author(s):  
J K Davidson ◽  
J J Shah
Keyword(s):  
Mathematical Model ◽  
Cylindrical Surface ◽  
Line Geometry ◽  
Tolerance Zone ◽  
New Model ◽  
Plücker Coordinates ◽  
Geometric Tolerances ◽  
Size Tolerance

A new mathematical model is introduced for the tolerances of cylindrical surfaces. The model is compatible with the ISO/ANSI/ASME standard for geometric tolerances. Central to the new model is a Tolerance-Map®†, a hypothetical volume of points that corresponds to all possible locations and variations of a segment of a line (the axis) that can arise from tolerances on size, location and orientation of the cylindrical surface. Each axis in a tolerance zone will be represented with the six Plücker coordinates. Cylindrical surfaces in a tolerance zone for the same hole can then be treated by attaching a size tolerance to each of the lines, thereby forming a screw. Relationships for the content of line solids for a tolerance zone are developed to correspond to the variations of locations. These are then used to obtain a measure for the increment in cost when a more refined tolerance is specified. This model is one part of a bilevel model that is under development for geometric tolerances.

The Effects of Different Specifications on the Tolerance-Maps for an Angled Face

2004 ◽  
Author(s):  
Gaurav Ameta ◽  
Joseph K. Davidson ◽  
Jami J. Shah
Keyword(s):  
Mathematical Model ◽  
Convex Set ◽  
Angular Size ◽  
Linear Size ◽  
New Model ◽  
Iso Standards ◽  
Geometric Tolerances ◽  
Dimensioning And Tolerancing ◽  
Level Model ◽  
Size Tolerance

A new mathematical model for representing geometric tolerances is applied to a part with an angled face and is extended to show its sensitivity to different specifications for dimensioning and tolerancing the part. The model is compatible with the ASME/ISO Standards for geometric tolerances. Central to the new model is a Tolerance-Map®, a hypothetical volume of points that corresponds to all possible locations and variations of a segment of a plane which can arise from tolerances on size, position, form, and orientation. Every Tolerance-Map is a convex set. This model is one part of a bi-level model that we are developing for geometric tolerances. The new model makes stackup relations apparent in an assembly, and these can be used to allocate size and orientational tolerances; the same relations also can be used to identify sensitivities for these tolerances. All stackup relations can be met for 100% interchangeability or for a specified probability. This paper develops several Tolerance-Maps for a part with an angled end face for different tolerance specifications. These specifications are linear size, angularity, angular size, “linear size & angularity” and “linear & angular size” tolerance. Comparison of Tolerance-Maps for their content for these specifications led to the following conclusions: a) only angular size tolerance is not sufficient for tolerancing an angled face; b) if the value of tolerance remains the same, the allowable variation is more in a part having only an angularity tolerance than in one having only a size tolerance.

Mathematical model of hit phenomena and its application to movie advertisement

2008 ◽  
Author(s):  
Ishii Akira ◽  
Yoshida Narihiko ◽  
Hayashi Takafumi ◽  
Umemura Sanae ◽  
Nakagawa Takeshi
Keyword(s):  
Mathematical Model
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