Form Defects Consideration in Polytope-Based Tolerance Analysis

2019 ◽  
Vol 141 (6) ◽  
Author(s):  
Ting Liu ◽  
Laurent Pierre ◽  
Nabil Anwer ◽  
Yanlong Cao ◽  
Jiangxin Yang
Keyword(s):  
Tolerance Analysis ◽  
Significant Loss ◽  
Minkowski Sum ◽  
Skin Model ◽  
Model Combining ◽  
Perfect Form ◽  
Finite Set ◽  
Physical Shape ◽  
Polytope Model

The polytope-based tolerance analysis in design process uses a finite set of constraints to represent specifications and propagates these constraints to any objective point in the Euclidean space. The operations of Minkowski sum and intersection on polytopes are well suited to serial and parallel assemblies. The polytope model has been applied to complex assemblies which contain a large number of joints and geometrical tolerances. However, the previous studies on this model consider toleranced features as surfaces of perfect form. The ignorance of form defects in tolerance analysis would result in a significant loss in accuracy and reliability. In this paper, an extension of the polytope model for tolerance analysis considering form defects is described in which the skin model shape representing the physical shape of the product is adopted to simulate the actual toleranced feature in place of the substitute one used conventionally. The combination of polytope model and skin model shape is expected to inherit many of the advantages of each model, combining easy-to-use tolerance propagation and form defects representation with accuracy guarantees. To demonstrate the method and its respective application, a case study of an assembly is illustrated in detail. The proposed method further enhances the capability of the polytope model in handling form defects and provides more realistic assembly results that approximate the actual assembly conditions for design evaluation.

Tolerance Analysis With Polytopes in HV-Description

2017 ◽  
Vol 17 (4) ◽  
Author(s):  
Santiago Arroyave-Tobón ◽  
Denis Teissandier ◽  
Vincent Delos
Keyword(s):  
Open Source ◽  
Open Source Software ◽  
Dual Space ◽  
Tolerance Analysis ◽  
Minkowski Sum ◽  
Duality Property ◽  
Finite Set ◽  
Minkowski Sums

This article proposes the use of polytopes in HV-description to solve tolerance analysis problems. Polytopes are defined by a finite set of half-spaces representing geometric, contact, or functional specifications. However, the list of the vertices of the polytopes is useful for computing other operations as Minkowski sums. Then, this paper proposes a truncation algorithm to obtain the V-description of polytopes in ℝn from its H-description. It is detailed how intersections of polytopes can be calculated by means of the truncation algorithm. Minkowski sums as well can be computed using this algorithm making use of the duality property of polytopes. Therefore, a Minkowski sum can be calculated intersecting some half-spaces in the dual space. Finally, the approach based on HV-polytopes is illustrated by the tolerance analysis of a real industrial case using the open source software politocat and politopix.

Tolerance Analysis With Polytopes in HV-Description

2016 ◽  
Author(s):  
Santiago Arroyave-Tobón ◽  
Denis Teissandier ◽  
Vincent Delos
Keyword(s):  
Open Source ◽  
Open Source Software ◽  
Dual Space ◽  
Tolerance Analysis ◽  
Minkowski Sum ◽  
Duality Property ◽  
Finite Set ◽  
Minkowski Sums

This article proposes the use of polytopes in HV-description to solve tolerance analysis problems. Polytopes are defined by a finite set of half-spaces representing geometric, contact or functional specifications. However, the list of the vertices of the poly-topes are useful for computing other operations as Minkowski sums. Then, this paper proposes a truncation algorithm to obtain the V-description of polytopes in ℝn from its H-description. It is detailed how intersections of polytopes can be calculated by means of the truncation algorithm. Minkowski sums as well can be computed using this algorithm making use of the duality property of polytopes. Therefore, a Minkowski sum can be calculated intersecting some half-spaces in the dual space. Finally, the approach based on HV-polytopes is illustrated by the tolerance analysis of a real industrial case using the open source software PolitoCAT and politopix.

Probability Tolerance Maps: A New Statistical Model for Non-Linear Tolerance Analysis Applied to Rectangular Faces

2010 ◽  
Author(s):  
Nadeem S. Khan ◽  
Jami J. Shah ◽  
Joseph K. Davidson
Keyword(s):  
Probability Distribution ◽  
Statistical Model ◽  
Ray Tracing ◽  
Delaunay Triangulation ◽  
Point Cloud ◽  
Tolerance Analysis ◽  
Minkowski Sum ◽  
Joint Probability Distribution ◽  
Statistical Parameters ◽  
Perfect Form

A new statistical model for the tolerance analysis based upon joint probability distribution of the trivariate normal distributed variables involved in the construction of Tolerance-maps (T-Maps) for rectangular face is presented. Central to the new model is a Tolerance-Map (T-Map) (Patent No. 69638242). It is the range of points resulting from a one-to-one mapping from all the variational possibilities of a perfect-form feature, within its tolerance-zone, to a specially designed Euclidean point-space. The model is fully compatible with the ASME/ANSI/ISO Standard for geometric tolerances. In this research, 4D probability T-Maps (prob T-Maps) have been developed in which the probability value of a point in space is represented by the size of the marker and the associated color. Additionally, 3D prob T-Maps (3D cross sections of the 4D prob T-Maps at pre specified values) are used to represent the probability values of two variables at a time for a constant value of the third variable on a plane. Superposition of the probability point cloud with the T-Map clearly identifies which points are inside and which are outside the T-Map. This represents the pass percentage for parts manufactured with the statistical parameters such as mean and standard deviation as of the assumed trivariate probability distribution. The effect of refinement with form and orientation tolerance is highlighted by calculating the change in pass percentage with the pass percentage for size only. Delaunay triangulation and ray tracing algorithms have been used to automate the process of identifying the points inside and outside the T-Map. Proof of concept software has been implemented to demonstrate this model and to determine pass percentages for various cases. The model is further extended to assemblies by employing convolution algorithms on two trivariate statistical distributions to arrive at the statistical distribution of the assembly. Accumulation T-Maps generated by using Minkowski Sum techniques on the T-Maps of the individual parts is superimposed on the probability point cloud resulting from convolution. Delaunay triangulation and ray tracing algorithms are employed to determine the assemleability percentages for the assembly.

Reports From the Field: “Vini Ansanm” Come Together for Inclusive Community Music Development in Port-au-Prince, Haiti

2020 ◽  
pp. 273-289
Author(s):  
Donald DeVito ◽  
Gertrude Bien-Aime ◽  
Hannah Ehrli ◽  
Jamie Schumacher
Keyword(s):  
Social Media ◽  
Inclusive Education ◽  
Children With Disabilities ◽  
Small Population ◽  
Significant Loss ◽  
Community Music ◽  
Music Learning ◽  
Loss Of Life

Haiti has experienced a series of catastrophic natural disasters in recent decades, resulting in significant loss of life and long-term damage to infrastructure. One critical outcome of these disasters is that there are approximately 400,000 orphans in the small population of just over 10 million. Throughout Haiti, children with disabilities are often considered cursed, and thus are rejected by the community in which they live. Haitian children with disabilities need creative and educational activities that will help them grow, develop, enjoy their lives, and become accepted members of the community. This chapter on the Haitian Center for Inclusive Education presents a case study of social media engagement and music learning, with an emphasis on social justice that has contributed to sustainable efforts.

scholarly journals Nutrient retention behind a tropical mega-dam: a case study of the Sardar Sarovar Dam, India

2021 ◽  
Vol 3 (1) ◽  
Author(s):  
Harish Gupta ◽  
S. Kiran Kumar Reddy ◽  
Mounika Chiluka ◽  
Vamshikrishna Gandla
Keyword(s):  
Arabian Sea ◽  
Inorganic Nitrogen ◽  
Nutrient Retention ◽  
Significant Loss ◽  
N Removal ◽  
Narmada River ◽  
Sardar Sarovar ◽  
The Impact

AbstractIn this study, we demonstrate the impact of the construction of a mega-dam on the nutrient export regime of a large tropical river into the Arabian Sea. Long-term (11 years) fortnight nutrient parameters, upstream and downstream to Sardar Sarovar (SS) Dam, were examined to determine the periodical change in nutrient fluxes from the Narmada River, India. During this 11-year period, the average discharge of the Narmada River upstream to Rajghat (35.3 km3 year−1) was higher than that of downstream at Garudeshwar (33.9 km3 year−1). However, during the same period, the suspended sediment load was reduced by 21 million tons (MT) from 37.9 MT at Rajghat to 16.7 MT at Garudeshwar. Similarly, mean concentrations of dissolved silica (DSi) reduced from 470 (upstream) to 214 µM (downstream), dissolved inorganic phosphate (DIP) from 0.84 to 0.38 µM, and dissolved inorganic nitrogen (DIN) from 43 to 1.5 µM. It means that about 54%, 55%, and 96% flux of DSi, DIP, and DIN retained behind the dam, respectively. The estimated denitrification rate (80,000 kg N km−2 year−1) for the reservoir is significantly higher than N removal by lentic systems, globally. We hypothesize that processes such as biological uptake and denitrification under anoxic conditions could be a key reason for the significant loss of nutrients, particularly of DIN. Finally, we anticipated that a decline in DIN fluxes (by 1.13 × 109 mol year−1) from the Narmada River to the Arabian Sea might reduce the atmospheric CO2 fixation by 7.46 × 109 mol year−1.

Process Signature Modeling for Tolerance Analysis

2010 ◽  
Vol 10 (2) ◽  
Author(s):  
R. Ascione ◽  
W. Polini ◽  
Q. Semeraro
Keyword(s):  
Concurrent Engineering ◽  
Manufacturing Process ◽  
Tolerance Analysis ◽  
Actual Surface ◽  
Contact Points ◽  
Geometric Tolerances ◽  
Systematic Pattern ◽  
Process Signature ◽  
Nominal Surface

Many well-known approaches exist in the literature for tolerance analysis. All the methods proposed in the literature consider the dimensional and the geometric tolerances applied to some critical points (contact points among profiles belonging to couples of parts) on the surface of the assembly components. These points are generally considered uncorrelated since the nominal surface is considered. Therefore, the methods proposed in the literature do not consider the actual surface due to a manufacturing process. Every manufacturing process leaves on the surface a signature, i.e., a systematic pattern that characterizes all the features machined with that process. The aim of the present work is to investigate the effects of considering the manufacturing signature in solving a tolerance stack-up function. A case study involving three parts has been defined and solved by means of a method of the literature, the variational method, with and without considering the correlation among the points of the same surface due to the manufacturing signature. This work represents a first step toward the integration of the design and the manufacturing in a concurrent engineering approach.

Statistical Tolerance Analysis With Sensitivities Established With Tolerance-Maps

2018 ◽  
Author(s):  
Aniket N. Chitale ◽  
Joseph K. Davidson ◽  
Jami J. Shah
Keyword(s):  
Tolerance Analysis ◽  
Minkowski Sum ◽  
Coordinate Frame ◽  
Target Feature ◽  
Functional Feature ◽  
Design Function ◽  
Statistical Tolerance ◽  
The One ◽  
The Relationship ◽  
Statistical Tolerance Analysis

The purpose of math models for tolerances is to aid a designer in assessing relationships between tolerances that contribute to variations of a dependent dimension that must be controlled to achieve some design function and which identifies a target (functional) feature. The T-Maps model for representing limits to allowable manufacturing variations is applied to identify the sensitivity of a dependent dimension to each of the contributing tolerances to the relationship. The method is to choose from a library of T-Maps the one that represents, in its own local (canonical) reference frame, each contributing feature and the tolerances specified on it; transform this T-Map to a coordinate frame centered at the target feature; obtain the accumulation T-Map for the assembly with the Minkowski sum; and fit a circumscribing functional T-Map to it. The fitting is accomplished numerically to determine the associated functional tolerance value. The sensitivity for each contributing tolerance-and-feature combination is determined by perturbing the tolerance, refitting the functional map to the accumulation map, and forming a ratio of incremental tolerance values from the two functional T-Maps. Perturbing the tolerance-feature combinations one at a time, the sensitivities for an entire stack of contributing tolerances can be built. For certain classes of loop equations, the same sensitivities result by fitting the functional T-Map to the T-Map for each feature, one-by-one, and forming the overall result as a scalar sum. Sensitivities help a designer to optimize tolerance assignments by identifying those tolerances that most strongly influence the dependent dimension at the target feature. Since the fitting of the functional T-Map is accomplished by intersection of geometric shapes, all the T-Maps are constructed with linear half-spaces.

Integrated Quality Function Deployment as a Tool for Quality Achievement in Healthcare

2012 ◽  
Vol 1 (2) ◽  
pp. 80-92 ◽  
Author(s):  
Chintala Venkateswarlu ◽  
A. K. Birru
Keyword(s):  
Analytic Hierarchy Process ◽  
Quality Function Deployment ◽  
Healthcare Services ◽  
Relative Importance ◽  
Analytic Hierarchy ◽  
Direct Evaluation ◽  
Quality Function ◽  
Model Combining ◽  
Hierarchy Process

Quality function deployment (QFD) is a methodology that extracts client demands (CDs) and inducting them in the final service/product. Once CDs are extracted from client the traditional QFD approach uses absolute importance to identify the degree of importance for each CD. Direct evaluation of CDs based on absolute weighting without tradeoffs is easy to perform, but may lead to serious deviations from reality. An alternative to avoid this problem is to adopt the analytic hierarchy process (AHP) approach. In this paper, an integrated model combining AHP and QFD has been delineated as a quality achievement tool in healthcare. A case study is performed on the healthcare services provided by government general hospital, Indore District, Madhya Pradesh, India and data has been analyzed to benchmark the proposed framework by computing the degree of relative importance for CDs through AHP and incorporating them in subsequent deployment matrices.

A Reinforcement Learning - Great-Deluge Hyper-Heuristic for Examination Timetabling

2010 ◽  
Vol 1 (1) ◽  
pp. 39-59 ◽  
Author(s):  
Ender Özcan ◽  
Mustafa Misir ◽  
Gabriela Ochoa ◽  
Edmund K. Burke
Keyword(s):  
Reinforcement Learning ◽  
Complete Solution ◽  
Examination Timetabling ◽  
Low Level ◽  
Termination Criteria ◽  
Candidate Solution ◽  
Wide Range ◽  
Finite Set ◽  
Different Characteristics

Hyper-heuristics can be identified as methodologies that search the space generated by a finite set of low level heuristics for solving search problems. An iterative hyper-heuristic framework can be thought of as requiring a single candidate solution and multiple perturbation low level heuristics. An initially generated complete solution goes through two successive processes (heuristic selection and move acceptance) until a set of termination criteria is satisfied. A motivating goal of hyper-heuristic research is to create automated techniques that are applicable to a wide range of problems with different characteristics. Some previous studies show that different combinations of heuristic selection and move acceptance as hyper-heuristic components might yield different performances. This study investigates whether learning heuristic selection can improve the performance of a great deluge based hyper-heuristic using an examination timetabling problem as a case study.

A Method for Integrating Form Errors Into Geometric Tolerance Analysis

2005 ◽  
Author(s):  
Robert Scott Pierce ◽  
David Rosen
Keyword(s):  
Manufacturing Process ◽  
High Speed ◽  
Tolerance Analysis ◽  
Analysis Model ◽  
Geometric Tolerance ◽  
Form Errors ◽  
Product Function ◽  
Component Models ◽  
Insight Into

In this research we describe a computer-aided approach to geometric tolerance analysis for assemblies and mechanisms. This new tolerance analysis method is based on the “generate-and-test” approach. A series of as-manufactured component models are generated within a NURBS-based solid modeling environment. These models reflect errors in component geometry that are characteristic of the manufacturing processes used to produce the components. The effects of different manufacturing process errors on product function is tested by simulating the assembly of these imperfect-form component models and measuring geometric attributes of the assembly that correspond to product functionality. A tolerance analysis model is constructed by generating-and-testing a sequence of component variants that represent a range of manufacturing process capabilities. The generate-and-test approach to tolerance analysis is demonstrated using a case study that is based on a high-speed stapling mechanism. As-manufactured models that correspond to two different levels of manufacturing precision are generated and assembly between groups of components with different precision levels is simulated. Misalignment angles that correspond to functionality of the stapling mechanism are measured at the end of each simulation. The results of these simulations are used to build a tolerance analysis model and to select a set of geometric form and orientation tolerances for the mechanism components. It is found that this generate-and-test approach yields insight into the interactions between individual surface tolerances that would not be gained using more traditional tolerance analysis methods.

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