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Tolerances on line profiles are used to control cross-sectional shapes of parts, such as turbine blades. A full life cycle for many mechanical devices depends (i) on a wise assignment of tolerances during design and (ii) on careful quality control of the manufacturing process to ensure adherence to the specified

Tolerances on line profiles are used to control cross-sectional shapes of parts, such as turbine blades. A full life cycle for many mechanical devices depends (i) on a wise assignment of tolerances during design and (ii) on careful quality control of the manufacturing process to ensure adherence to the specified tolerances. This thesis describes a new method for quality control of a manufacturing process by improving the method used to convert measured points on a part to a geometric entity that can be compared directly with tolerance specifications. The focus of this paper is the development of a new computational method for obtaining the least-squares fit of a set of points that have been measured with a coordinate measurement machine along a line-profile. The pseudo-inverse of a rectangular matrix is used to convert the measured points to the least-squares fit of the profile. Numerical examples are included for convex and concave line-profiles, that are formed from line- and circular arc-segments.
ContributorsSavaliya, Samir (Author) / Davidson, Joseph K. (Thesis advisor) / Shah, Jami J. (Committee member) / Santos, Veronica J (Committee member) / Arizona State University (Publisher)
Created2013
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Description
This thesis contains the applications of the ASU mathematical model (Tolerance Maps, T-Maps) to the construction of T-Maps for patterns of line profiles. Previously, Tolerance Maps were developed for patterns of features such as holes, pins, slots and tabs to control their position. The T-Maps that are developed in this

This thesis contains the applications of the ASU mathematical model (Tolerance Maps, T-Maps) to the construction of T-Maps for patterns of line profiles. Previously, Tolerance Maps were developed for patterns of features such as holes, pins, slots and tabs to control their position. The T-Maps that are developed in this thesis are fully compatible with the ASME Y14.5 Standard. A pattern of square profiles, both linear and 2D, is used throughout this thesis to illustrate the idea of constructing the T-Maps for line profiles. The Standard defines two ways of tolerancing a pattern of profiles - Composite Tolerancing and Multiple Single Segment Tolerancing. Further, in the composite tolerancing scheme, there are two different ways to control the entire pattern - repeating a single datum or two datums in the secondary datum reference frame. T-Maps are constructed for all the different specifications. The Standard also describes a way to control the coplanarity of discontinuous surfaces using a profile tolerance and T-Maps have been developed. Since verification of manufactured parts relative to the tolerance specifications is crucial, a least squares fit approach, which was developed earlier for line profiles, has been extended to patterns of line profiles. For a pattern, two tolerances are specified, and the manufactured profile needs to lie within the tolerance zones established by both of these tolerances. An i-Map representation of the manufactured variation, located within the T-Map is also presented in this thesis.
ContributorsRao, Shyam Subramanya (Author) / Davidson, Joseph K. (Thesis advisor) / Arizona State University (Publisher)
Created2014
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Description
Dimensional Metrology is the branch of science that determines length, angular, and geometric relationships within manufactured parts and compares them with required tolerances. The measurements can be made using either manual methods or sampled coordinate metrology (Coordinate measuring machines). Manual measurement methods have been in practice for a long time

Dimensional Metrology is the branch of science that determines length, angular, and geometric relationships within manufactured parts and compares them with required tolerances. The measurements can be made using either manual methods or sampled coordinate metrology (Coordinate measuring machines). Manual measurement methods have been in practice for a long time and are well accepted in the industry, but are slow for the present day manufacturing. On the other hand CMMs are relatively fast, but these methods are not well established yet. The major problem that needs to be addressed is the type of feature fitting algorithm used for evaluating tolerances. In a CMM the use of different feature fitting algorithms on a feature gives different values, and there is no standard that describes the type of feature fitting algorithm to be used for a specific tolerance. Our research is focused on identifying the feature fitting algorithm that is best used for each type of tolerance. Each algorithm is identified as the one to best represent the interpretation of geometric control as defined by the ASME Y14.5 standard and on the manual methods used for the measurement of a specific tolerance type. Using these algorithms normative procedures for CMMs are proposed for verifying tolerances. The proposed normative procedures are implemented as software. Then the procedures are verified by comparing the results from software with that of manual measurements.

To aid this research a library of feature fitting algorithms is developed in parallel. The library consists of least squares, Chebyshev and one sided fits applied on the features of line, plane, circle and cylinder. The proposed normative procedures are useful for evaluating tolerances in CMMs. The results evaluated will be in accordance to the standard. The ambiguity in choosing the algorithms is prevented. The software developed can be used in quality control for inspection purposes.
ContributorsVemulapalli, Prabath (Author) / Shah, Jami J. (Thesis advisor) / Davidson, Joseph K. (Committee member) / Takahashi, Timothy (Committee member) / Arizona State University (Publisher)
Created2014
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Description
Design problem formulation is believed to influence creativity, yet it has received only modest attention in the research community. Past studies of problem formulation are scarce and often have small sample sizes. The main objective of this research is to understand how problem formulation affects creative outcome. Three research areas

Design problem formulation is believed to influence creativity, yet it has received only modest attention in the research community. Past studies of problem formulation are scarce and often have small sample sizes. The main objective of this research is to understand how problem formulation affects creative outcome. Three research areas are investigated: development of a model which facilitates capturing the differences among designers' problem formulation; representation and implication of those differences; the relation between problem formulation and creativity.

This dissertation proposes the Problem Map (P-maps) ontological framework. P-maps represent designers' problem formulation in terms of six groups of entities (requirement, use scenario, function, artifact, behavior, and issue). Entities have hierarchies within each group and links among groups. Variables extracted from P-maps characterize problem formulation.

Three experiments were conducted. The first experiment was to study the similarities and differences between novice and expert designers. Results show that experts use more abstraction than novices do and novices are more likely to add entities in a specific order. Experts also discover more issues.

The second experiment was to see how problem formulation relates to creativity. Ideation metrics were used to characterize creative outcome. Results include but are not limited to a positive correlation between adding more issues in an unorganized way with quantity and variety, more use scenarios and functions with novelty, more behaviors and conflicts identified with quality, and depth-first exploration with all ideation metrics. Fewer hierarchies in use scenarios lower novelty and fewer links to requirements and issues lower quality of ideas.

The third experiment was to see if problem formulation can predict creative outcome. Models based on one problem were used to predict the creativity of another. Predicted scores were compared to assessments of independent judges. Quality and novelty are predicted more accurately than variety, and quantity. Backward elimination improves model fit, though reduces prediction accuracy.

P-maps provide a theoretical framework for formalizing, tracing, and quantifying conceptual design strategies. Other potential applications are developing a test of problem formulation skill, tracking students' learning of formulation skills in a course, and reproducing other researchers’ observations about designer thinking.
ContributorsDinar, Mahmoud (Author) / Shah, Jami J. (Thesis advisor) / Langley, Pat (Committee member) / Davidson, Joseph K. (Committee member) / Lande, Micah (Committee member) / Ren, Yi (Committee member) / Arizona State University (Publisher)
Created2015
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Description
A process plan is an instruction set for the manufacture of parts generated from detailed design drawings or CAD models. While these plans are highly detailed about machines, tools, fixtures and operation parameters; tolerances typically show up in less formal manner in such plans, if at all. It is not

A process plan is an instruction set for the manufacture of parts generated from detailed design drawings or CAD models. While these plans are highly detailed about machines, tools, fixtures and operation parameters; tolerances typically show up in less formal manner in such plans, if at all. It is not uncommon to see only dimensional plus/minus values on rough sketches accompanying the instructions. On the other hand, design drawings use standard GD&T (Geometrical Dimensioning and tolerancing) symbols with datums and DRFs (Datum Reference Frames) clearly specified. This is not to say that process planners do not consider tolerances; they are implied by way of choices of fixtures, tools, machines, and operations. When converting design tolerances to the manufacturing datum flow, process planners do tolerance charting, that is based on operation sequence but the resulting plans cannot be audited for conformance to design specification.

In this thesis, I will present a framework for explicating the GD&T schema implied by machining process plans. The first step is to derive the DRFs from the fixturing method in each set-up. Then basic dimensions for the features to be machined in each set up are determined with respect to the extracted DRF. Using shop data for the machines and operations involved, the range of possible geometric variations are estimated for each type of tolerances (form, size, orientation, and position). The sequence of manufacturing operations determines the datum flow chain. Once we have a formal manufacturing GD&T schema, we can analyze and compare it to tolerance specifications from design using the T-map math model. Since the model is based on the manufacturing process plan, it is called resulting T-map or m-map. Then the process plan can be validated by adjusting parameters so that the m-map lies within the T-map created for the design drawing. How the m-map is created to be compared with the T-map is the focus of this research.
ContributorsHaghighi, Payam (Author) / Shah, Jami J. (Thesis advisor) / Davidson, Joseph K. (Committee member) / Ren, Yi (Committee member) / Arizona State University (Publisher)
Created2015