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

Author(s):  
Gaurav Ameta ◽  
Joseph K. Davidson ◽  
Jami J. Shah

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.

Author(s):  
Y. He ◽  
J. K. Davidson ◽  
N. J. Kalish ◽  
Jami J. Shah

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.


Author(s):  
Utpal Roy ◽  
Bing Li

Abstract This paper presents a scheme for establishing geometric tolerance zones for polyhedral objects in solid modelers. The proposed scheme is based on a surface-based variational model. Variations are applied to a part model by varying each surface’s model variables. Those model variables are constrained by some algebraic relations derived from the specified geometric tolerances. For size tolerance, two types of tolerance zones are considered in order to reflect two different types of size tolerances. For any other geometric tolerance (form, orientation or positional), the resultant tolerance zone is defined by the combination of size tolerance and that particular geometric tolerance specifications. Appropriate algebraic constraints (on the model variables) are finally used to establish the tolerance zone boundaries in the surface-based variational model.


Author(s):  
W. H. ElMaraghy ◽  
Z. Wu ◽  
H. A. ElMaraghy

Abstract This paper focuses on the development of a procedure and algorithms for the systematic comparison of geometric variations of measured features with their specified geometric tolerances. To automate the inspection of mechanical parts, it is necessary to analyze the measurement data captured by coordinate measuring machines (CMM) in order to detect out-of-tolerance conditions. A procedure for determining the geometric tolerances from the measured three dimensional coordinates on the surface of a cylindrical feature is presented. This procedure follows the definitions of the geometric tolerances used in the current Standards, and is capable of determining the value of each geometric tolerance from the composite 3-D data. The developed algorithms adopt the minimum tolerance zone criterion. Nonlinear numerical optimization techniques are used to fit the data to the minimum tolerance zone. Two test cases are given in the paper which demonstrate the successful determination of geometric tolerances from given simulated data.


2012 ◽  
Vol 53 (1-3) ◽  
pp. 53-68
Author(s):  
László Vikárius

Bartók’s “Six Dances in Bulgarian Rhythm,” the only formally self-contained set within the Mikrokosmos, is the crowning series of pieces in this huge compendium of the composer’s later piano music. Since Bartók recorded all six of them in 1940, they are ideal for an investigation of performance issues. The recordings from the Mikrokosmos, although relatively late, are fortunately close to the composition of most of the pieces, which makes these recordings all the more “authentic.” The essay, however, focuses on the concept of the series as a series revisiting the compositional manuscripts, discussing the evolution of the individual pieces and the emergence of the idea of the set (first intended to comprise only five pieces) and Bulgarian rhythm as a pedagogical issue within the series. The “Six Dances” also bear a somewhat enigmatic dedication to the British pianist of Jewish descent, Harriet Cohen, obviously not an accidental choice. The dedication might be considered with what Bartók said in an interview in 1940 about the “hibridity” of national musical types in his “Bulgarian” pieces as well as with his article “Race Purity in Music” (1942) in mind. The significance of order and ordering in Bartók’s creative work, a hitherto little discussed common central element in the various fields of his activity, collecting, performing and composing, are also discussed.


differences ◽  
2020 ◽  
Vol 31 (2) ◽  
pp. 1-29
Author(s):  
Nell Wasserstrom

Through a close reading of Freud’s last major work, Moses and Monotheism (1939), this article considers the socio-political and literary stakes of a central element of Freud’s oeuvre, which reaches its fullest elaboration in the Moses text: belatedness. Belatedness, or deferred action (Nachträglichkeit), which structures the movement of repression and return in the individual psychology of Freud’s earlier work, is aggravated and intensified in this late modernist text. Now, it is an entire people (the Jews) and (Judeo-Christian) civilization founded upon the temporal predicament of trauma, latency, and the return of the repressed. What is most innovative about Moses—its fragmentary style, its rewriting of biblical origins, its daring conjectures and methods of recording history—gestures back, after all, to the singular problem that both Freudian psychoanalysis and modernism are destined to repeat: the constitutive belatedness of all experience.


10.14201/3033 ◽  
2009 ◽  
Vol 15 ◽  
Author(s):  
Antonio Bernal Guerrero

RESUMEN: En este estudio, replanteamos, vinculándolo a su dimensión moral, el problema de la identidad personal. Analizamos los elementos esenciales para la comprensión del fenómeno moral y proponemos el reconocimiento de la identidad en sentido formal, fundamento para el reconocimiento de la identidad de los demás, como alternativa a la tradicional perspectiva sustancializadora y al enfoque posmoderno que propone su disolución. Desde esta fundamentación del constructo identidad personal, se plantea la posibilidad de la construcción de la dimensión moral como parte central de la configuración positiva, humanizadora, de la identidad de la persona. Como componente esencial de un proyecto de educación moral, tratamos de delimitar las competencias generales que configuran la identidad moral del sujeto. Desde un enfoque educativo que asume la complejidad y la incertidumbre de los fenómenos humanos, las competencias propuestas se dirigen a la construcción posible de una persona moralmente autónoma.ABSTRACT: This study approaches the problem of personal identity linked to its moral dimension. We analyse the elements that are essential for understanding the moral phenomenon and we propose the recognition of identity in a formal sense, the basis for the recognition of the identity of others as an alternative to the traditional substantialising focus and to the post-modern focus that proposes its dissolution. From this basis for the personal identity construct, we propose the possibility of constructing the moral dimension as a central element of the positive, humanising configuration of the individual. As an essential component of a moral education project, we try to define the general responsibilities that configure the subject's moral identity. The proposed responsibilities are directed towards the possible construction of a morally autonomous individual from an educational approach that is fully aware of the unpredictable nature of human phenomena.SOMMAIRE: Dans cette étude, nous posons une fois de plus, en le rattachant à sa dimension morale, le problème de l'identité personnelle. Nous analysons les éléments essentiels en vue de la compréhension du phénomène moral et nous proposons la reconnaissance de l'identité dans son sens formel, comme fondement de la reconnaissance de l'identité des autres, comme alternative au point de vue substancialisateur et d'une optique post-moderne qui propose sa dissolution. À partir du fondement de la constructivité de l'identité personnelle, on envisage la possibilité de la construction de la dimension morale comme partie centrale de la configuration positive, humanisatrice, de l'identité de la personne. Comme compétence essentielle d'un projet d'éducation morale, nous essayons de délimiter les compétences générales qui configurent l'identité morale du sujet. D'un point de vue éducatif qui assume la complexité et l'incertitude des phénomèmes humains, les compétences proposées visent à la construction possible d'une personne moralement autonome.


2010 ◽  
Vol 9 (1) ◽  
Author(s):  
Juliani Dyah Trisnawati ◽  
Ema Andajani ◽  
Budhiman Setyawan

This study describes the tolerance zone for the assessment of service quality cellular phone card providers in the city of Surabaya. Variables which refer to the variables used in the variable service quality (SERVQUAL) Zeithaml, Parasuraman, and Berry (1990) which includes dimensions reliability, assurance, tangible, Empathy, and responsiveness. Furthermore, the analysis obtained questionnaires aimed to describe the MSS (Measure of Service Superiority), namely the gap between service perceptions and service desired, and MSA (Measure of Adequate Service) is the gap between service perceptions and service adequate, and the tolerance zone is the gap between desire service and adequate service. Moreover, tolerance zone is used to explore customer satisfaction to the individual transaction, or service Encounters, and customer satisfaction for services provided by mobile phone providers in the city of Surabaya as a whole.


Author(s):  
Ioana Olariu

The current paper is a theoretical approach to the management of territories according to sales force, which has an important role in the realization of distribution. The central element is the way in which agents split their efforts between the activities and routes they are responsible with. A related issue is that of establishing what comes first – defining the sales territory or performing the selling. The effects of the interaction between the number of distribution representatives and the delimiting of the territory they cover influence the measurement of the individual elements that contribute to achieving commercial performance.


Author(s):  
S. B. Savaliya ◽  
J. K. Davidson ◽  
Jami J. Shah

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].


Sign in / Sign up

Export Citation Format

Share Document