Automating Linear Tolerance Analysis Across Assemblies

1992 ◽  
Vol 114 (1) ◽  
pp. 174-179 ◽  
Author(s):  
N. P. Juster ◽  
P. M. Dew ◽  
A. de Pennington
Keyword(s):  
Mathematical Model ◽  
Manufacturing Process ◽  
Tolerance Analysis ◽  
Mathematical Framework ◽  
Worst Case ◽  
Experimental Software

One of the tests carried out by designers in an attempt to check whether an assembly of components will function correctly is tolerance analysis. Tolerance analysis, although relatively straightforward, is liable to be time consuming and error prone. It cannot be automated unless a suitable mathematical framework is developed to model the variations introduced by the manufacturing process. The designer allows for the variations by means of tolerances attached to the dimensions. This paper describes a suitable mathematical model and shows how it may be used to automate linear worst case tolerance analysis across assemblies. Experimental software has been written, based on the theory.

scholarly journals Geometrical and dimensional tolerance analysis for the radial flux type of permanent magnet generator design

2021 ◽  
Vol 12 (2) ◽  
pp. 68-80
Author(s):  
Muhammad Fathul Hikmawan ◽  
Agung Wibowo ◽  
Muhammad Kasim
Keyword(s):  
Permanent Magnet ◽  
Manufacturing Process ◽  
Cumulative Effect ◽  
Tolerance Analysis ◽  
Air Gap ◽  
Tolerance Allocation ◽  
Design Stage ◽  
Worst Case ◽  
Radial Flux ◽  
Permanent Magnet Generator

Mechanical tolerance is something that should be carefully taken into consideration and cannot be avoided in a product for manufacturing and assembly needs, especially in the design stage, to avoid excessive dimensional and geometric deviations of the components made. This paper discusses how to determine and allocate dimensional and geometric tolerances in the design of a 10 kW, 500 rpm radial flux permanent magnet generator prototype components. The electrical and mechanical design results in the form of the detailed nominal dimensions of the generator components, and the allowable air gap range are used as input parameters for tolerance analysis. The values of tolerance allocation and re-allocation process are carried out by considering the capability of the production machine and the ease level of the manufacturing process. The tolerance stack-up analysis method based on the worst case (WC) scenario is used to determine the cumulative effect on the air gap distance due to the allocated tolerance and to ensure that the cumulative effect is acceptable so as to guarantee the generator's functionality. The calculations and simulations results show that with an air gap of 1 ± 0.2 mm, the maximum air gap value obtained is 1.1785 mm, and the minimum is 0.8 mm. The smallest tolerance value allocation is 1 µm on the shaft precisely on the FSBS/SRBS feature and the rotor on the RPMS feature. In addition, the manufacturing process required to achieve the smallest tolerance allocation value is grinding, lapping, and polishing processes.

Tolerance Analysis and Allocation for Design of a Self-Aligning Coupling Assembly Using Tolerance-Maps

2013 ◽  
Vol 135 (3) ◽  
Author(s):  
Gagandeep Singh ◽  
Gaurav Ameta ◽  
Joseph K. Davidson ◽  
Jami J. Shah
Keyword(s):  
Mathematical Model ◽  
Statistical Study ◽  
Tolerance Analysis ◽  
Worst Case ◽  
Iso Standards ◽  
Statistical Measures ◽  
Geometric Tolerances ◽  
Different Types ◽  
The Future ◽  
Tolerance Assignment

A self-aligning coupling is used as a vehicle to show that the Tolerance-Map (T-Map) mathematical model for geometric tolerances can distinguish between related and unrelated actual mating envelopes as described in the ASME/ISO standards. The coupling example illustrates how T-Maps (Patent No. 6963824) may be used for tolerance assignment during design of assemblies that contain non-congruent features in contact. Both worst-case and statistical measures are obtained for the variation in alignment of the axes of the two engaged parts of the coupling in terms of the tolerances. The statistical study is limited to contributions from the geometry of toleranced features and their tolerance-zones. Although contributions from characteristics of manufacturing machinery are presumed to be uniform, the method described in the paper is robust enough to include different types of manufacturing bias in the future. An important result is that any misalignment in the coupling depends only on tolerances, not on any dimension of the coupling.

scholarly journals ANALYSIS OF GEOMETRICAL SPECIFICATION IN DECANTER CENTRIFUGE MACHINE

2018 ◽  
Vol 8 (2) ◽  
pp. 29-47
Author(s):  
Bagus Budiwantoro ◽  
Indra Djodikusumo ◽  
Ade Ramdan
Keyword(s):  
Statistical Method ◽  
Manufacturing Process ◽  
Tolerance Analysis ◽  
Mean Value ◽  
Case Method ◽  
3D Design ◽  
Worst Case ◽  
Production Phase ◽  
Performance Requirements ◽  
Decanter Centrifuge

A decanter centrifuge machine has been developed and currently at a complete stage of a preliminary 3D design layout. The next phase is a production phase. In the production phase, an ideal component that is identical with the 3D model will never be realized. Every manufacturing process has unavoidable variations. If they are accumulated, they can be immense and may cause serious problems. The machine may fail. Thus, the analysis of geometry specification is necessary to be conducted. The main objective of this study is to design the geometry specification which includes their tolerance to assure that the machine will work and achieve its performance, considering variation in manufacturing process. The study consists of four stages, they are: (1) reviewing the 3D design layout, (2) identifying functional key characteristics, (3) analyzing each requirement to determine the geometric dimensioning and tolerancing schemes and (4) allocating tolerances. Every scheme was built through six steps, establish the performance requirements, draw a loop diagram, converting dimension to mean dimension, calculate mean value with stack tolerance, determine the method of tolerance analysis and calculate the variation of performance requirements. The tolerance analysis uses the worst case and statistical methods. They involve 45 fixed tolerances and 38 variable tolerances. The calculated variation data output of every requirement is elaborated to finalize tolerance value that will meet all requirements. Finally, the final tolerance values are allocated and set to component geometry. This analysis concludes that every final tolerance of variable tolerance values must be tighter for the worst case method, and only 42% for statistical method. Probability of machine will work and achieve its performance is 100% for the worst case method and 99.73% for the statistical method.

Using Tolerance-Maps to Generate Frequency Distributions of Clearance and Allocate Tolerances for Pin-Hole Assemblies

2007 ◽  
Vol 7 (4) ◽  
pp. 347-359 ◽  
Author(s):  
Gaurav Ameta ◽  
Joseph K. Davidson ◽  
Jami J. Shah
Keyword(s):  
Mathematical Model ◽  
Statistical Method ◽  
Frequency Distribution ◽  
Probabilistic Representation ◽  
Worst Case ◽  
Frequency Distributions ◽  
One Dimensional ◽  
Material Condition ◽  
Geometric Tolerances ◽  
Case Basis

A new mathematical model for representing the geometric variations of lines is extended to include probabilistic representations of one-dimensional (1D) clearance, which arise from positional variations of the axis of a hole, the size of the hole, and a pin-hole assembly. The model is compatible with the ASME/ ANSI/ISO Standards for geometric tolerances. Central to the new model is a Tolerance-Map (T-Map) (Patent No. 69638242), a hypothetical volume of points that models the 3D variations in location and orientation for a segment of a line (the axis), which can arise from tolerances on size, position, orientation, and form. Here, it is extended to model the increases in yield that occur when maximum material condition (MMC) is specified and when tolerances are assigned statistically rather than on a worst-case basis; the statistical method includes the specification of both size and position tolerances on a feature. The frequency distribution of 1D clearance is decomposed into manufacturing bias, i.e., toward certain regions of a Tolerance-Map, and into a geometric bias that can be computed from the geometry of multidimensional T-Maps. Although the probabilistic representation in this paper is built from geometric bias, and it is presumed that manufacturing bias is uniform, the method is robust enough to include manufacturing bias in the future. Geometric bias alone shows a greater likelihood of small clearances than large clearances between an assembled pin and hole. A comparison is made between the effects of choosing the optional material condition MMC and not choosing it with the tolerances that determine the allowable variations in position.

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.

Parametric Kinematic Tolerance Analysis of Planar Pairs With Multiple Contacts

1996 ◽  
Author(s):  
Elisha Sacks ◽  
Leo Joskowicz
Keyword(s):  
Efficient Algorithm ◽  
Tolerance Analysis ◽  
Parametric Model ◽  
Worst Case ◽  
Multiple Contacts ◽  
Work Cycle ◽  
Computer Aided ◽  
Kinematic Models ◽  
Range Of Variation ◽  
Different Parts

Abstract We present an efficient algorithm for worst-case limit kinematic tolerance analysis of planar kinematic pairs with multiple contacts. The algorithm extends computer-aided kinematic tolerance analysis from mechanisms in which parts interact through permanent contacts to mechanisms in which different parts or part features interact at different stages of the work cycle. Given a parametric model of a pair and the range of variation of the parameters, it constructs parametric kinematic models for the contacts, computes the configurations in which each contact occurs, and derives the sensitivity of the kinematic variation to the parameters. The algorithm also derives qualitative variations, such as under-cutting, interference, and jamming. We demonstrate the algorithm on a 26 parameter model of a Geneva mechanism.

scholarly journals A Branching Process to Characterize the Dynamics of Stem Cell Differentiation

2015 ◽  
Author(s):  
david miguez
Keyword(s):  
Mathematical Model ◽  
Cell Cycle ◽  
Stem Cell ◽  
Cycle Length ◽  
Branching Process ◽  
Stem Cell Differentiation ◽  
Stem Cell Population ◽  
Mathematical Framework ◽  
Average Cell ◽  
Cell Cycle Length

The understanding of the regulatory processes that orchestrate stem cell maintenance is a cornerstone in developmental biology. Here, we present a mathematical model based on a branching process formalism that predicts average rates of proliferative and differentiative divisions in a given stem cell population. In the context of vertebrate spinal neurogenesis, the model predicts complex non-monotonic variations in the rates of pp, pd and dd modes of division as well as in cell cycle length, in agreement with experimental results. Moreover, the model shows that the differentiation probability follows a binomial distribution, allowing us to develop equations to predict the rates of each mode of division. A phenomenological simulation of the developing spinal cord informed with the average cell cycle length and division rates predicted by the mathematical model reproduces the correct dynamics of proliferation and differentiation in terms of average numbers of progenitors and differentiated cells. Overall, the present mathematical framework represents a powerful tool to unveil the changes in the rate and mode of division of a given stem cell pool by simply quantifying numbers of cells at different times.

Defining Flexibility and Sewability in Conductive Yarns

2002 ◽  
Vol 736 ◽  
Author(s):  
Margaret Orth
Keyword(s):  
Mathematical Model ◽  
Stainless Steel ◽  
Manufacturing Process ◽  
Permanent Deformation ◽  
Stress And Strain ◽  
Lateral Stress ◽  
Electronic Textiles ◽  
Qualitative Properties ◽  
Textile Manufacturing ◽  
Conductive Yarns

ABSTRACTIn order for electronic textiles to truly qualify as textiles, they must maintain one of the intrinsic qualities of textiles, flexibility, or the ability to resist permanent deformation under bending, lateral stress and strain. Flexibility will allow electric textiles to be intimate, soft, wearable, conformable and durable. Unfortunately, flexibility is poorly understood by many researchers who come from a traditional electronics background. This paper presents some common terminology of textiles, and different approaches to understanding flexibility in fibers and yarns. Because one of the most mechanically stressful textile manufacturing process is machine sewing and embroidery, this paper defines the necessary properties of machine sewable yarns and demonstrates a formal Curl Test for judging the sewability and flexibility of stainless steel yarns. This paper also examines flexibility in yarns and fibers, historically and based on a mathematical model and more qualitative properties.

Process Capability Based Tolerance Allocation in Pneumatic Percussive Riveting

2020 ◽  
Author(s):  
Hua Wang ◽  
Jialei Zhang ◽  
Junyang Yu
Keyword(s):  
High Efficiency ◽  
Load Transfer ◽  
Process Capability ◽  
Tolerance Analysis ◽  
Tolerance Allocation ◽  
Hole Drilling ◽  
Case Method ◽  
Pneumatic Hammer ◽  
Worst Case ◽  
Mating Conditions

Abstract Pneumatic percussive riveting is an important way to join the sheet metals. In order to ensure the load transfer and the fatigue performance of riveted joint, the interference of the rivet/hole is strictly specified. The interference of the rivet/hole is highly correlated with the process capability of the pneumatic hammer and the diameter of the pre-hole. It is a critical step to choose the appropriate pneumatic hammer to ensure the interference requirements. Energy per blow of the pneumatic hammer is a proclaimed parameter from the riveting hammer manufacturer. It is difficult for the designer to choose the riveting hammer in practical riveting scheme based on energy per blow. Tolerance analysis is an efficient way to model the manufacturing variation and implement process control. This paper presents the tolerance allocation of the pneumatic percussive riveting based on the process capability of the pneumatic hammer. In order to obtain the designed interferences of the rivet/hole, a tolerance chain is built with the process capability of the pneumatic hammer, the diameter of the pre-hole and the diameter of the rivet shank. The process capability of the pneumatic hammer is represented with the interferences of the rivet/hole after riveting. It is an intuitive parameter for the designer to choose the riveting hammer in practical riveting scheme. The process capability of the pneumatic hammer is obtained from the designed riveting experiments with the pneumatic percussive riveting platform. The diameter of the pre-hole affects the interference of the rivet/hole also. The tolerance for manual hole-drilling should be determined to assure the interference requirements and high drilling operation efficiency simultaneously. The variation of the pre-hole is obtained from the manual drilling experiments and diameter measurements. Different hole-drilling results in different mating conditions between the pre-hole and the rivet. The fit conditions of different pre-holes are modeled and the final interferences after riveting are analyzed. Worst case method and statistical analysis method are two common methods for tolerance analysis. For the manual hole-drilling and the pneumatic percussive riveting, worst case method is employed to analyze the constructed tolerance chain in order to accomplish the interferences of the rivet/hole. The different analyzed dimensions, rivet-hole clearances and pre-hole drilling variation, are investigated respectively. The reported work enhances the understanding of the tolerance allocation for the pneumatic percussive riveting. The interference based process capability of the pneumatic hammer provides good reference for pneumatic hammer choosing in riveting scheme. The reported tolerance chain of the interference could be used for the tolerance determination of manual hole-drilling with good quality and high efficiency.

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