This document provides an overview of ASME Y14.5.1, which establishes a mathematical definition of dimensioning and tolerancing principles. It introduces key concepts such as datum reference frames, vectors, and common tolerance zones like circularity, cylindricity, and flatness. Mathematical definitions are provided for these concepts. It also covers topics like the assumptions behind datum reference frames, interpreting true position tolerances, and profile tolerances for lines and surfaces.
GD&T is an international way of describing a part accurately. It is used widely in all manufacturing sectors for part dimensioning. This ppt contains basic overview of GD&T. The detailed version will be uploaded soon.
This slide describes two essential elements in machining operations:
cutting-tool materials and cutting fluids.
° The slide opens with a discussion of the types and characteristics of cutting tool materials.
° The properties and applications of high-speed steels, carbides, ceramics, cubic boron nitride, diamond, and coated tools are described in detail.
The types of cutting fluids in common use are then described, including their functions and how they affect the machining operation.
° Trends in near-dry and dry machining are also discussed, and their importance with respect to environmentally friendly machining operations are explained.
The selection of cutting-tool materials for a particular application is among the most important factors in machining operations, just as the selection of mold and die
materials was critical for forming and shaping processes . We will discuss throughout this slide the relevant properties and performance characteristics of all major types of cutting-tool materials, which will help us in tool selection.
However, as it will become apparent, the complex nature of this subject does not always render itself to the determination of appropriate tool materials; hence, we also must rely on general guidelines and recommendations that have been accumulated in industry over many years.More detailed information on tool material recommendations for specific workpiece materials and machining operations will be presented.
As noted, the cutting tool is subjected to
(a) high temperatures,
(b) high contact stresses, and
(c) rubbing along the tool-chip interface and along the machined surface.
Consequently, the cutting-tool material must possess the following characteristics:
° Hot hardness, so that the hardness, strength, and wear resistance of the tool are maintained at the temperatures encountered in machining operations. This property ensures that the tool does not undergo any plastic deformation and thus retains its shape and sharpness.
Toughness and impact strength (or mechanical shock resistance), so that impact forces on the tool that are encountered repeatedly in interrupted cutting operation (such as milling and turning a splined shaft on a lathe) or forces due to vibration and chatter during machining do not chip or fracture the tool.
Thermal shock resistance, to withstand the rapid temperature cycling encountered in interrupted cutting.
Wear resistance, so that an acceptable tool life is obtained before replacement is necessary.
Chemical stability and inertness with respect to the material being machined, to avoid or minimize any adverse reactions, adhesion, and tool-chip diffusion that would contribute to tool wear.
GD&T is an international way of describing a part accurately. It is used widely in all manufacturing sectors for part dimensioning. This ppt contains basic overview of GD&T. The detailed version will be uploaded soon.
This slide describes two essential elements in machining operations:
cutting-tool materials and cutting fluids.
° The slide opens with a discussion of the types and characteristics of cutting tool materials.
° The properties and applications of high-speed steels, carbides, ceramics, cubic boron nitride, diamond, and coated tools are described in detail.
The types of cutting fluids in common use are then described, including their functions and how they affect the machining operation.
° Trends in near-dry and dry machining are also discussed, and their importance with respect to environmentally friendly machining operations are explained.
The selection of cutting-tool materials for a particular application is among the most important factors in machining operations, just as the selection of mold and die
materials was critical for forming and shaping processes . We will discuss throughout this slide the relevant properties and performance characteristics of all major types of cutting-tool materials, which will help us in tool selection.
However, as it will become apparent, the complex nature of this subject does not always render itself to the determination of appropriate tool materials; hence, we also must rely on general guidelines and recommendations that have been accumulated in industry over many years.More detailed information on tool material recommendations for specific workpiece materials and machining operations will be presented.
As noted, the cutting tool is subjected to
(a) high temperatures,
(b) high contact stresses, and
(c) rubbing along the tool-chip interface and along the machined surface.
Consequently, the cutting-tool material must possess the following characteristics:
° Hot hardness, so that the hardness, strength, and wear resistance of the tool are maintained at the temperatures encountered in machining operations. This property ensures that the tool does not undergo any plastic deformation and thus retains its shape and sharpness.
Toughness and impact strength (or mechanical shock resistance), so that impact forces on the tool that are encountered repeatedly in interrupted cutting operation (such as milling and turning a splined shaft on a lathe) or forces due to vibration and chatter during machining do not chip or fracture the tool.
Thermal shock resistance, to withstand the rapid temperature cycling encountered in interrupted cutting.
Wear resistance, so that an acceptable tool life is obtained before replacement is necessary.
Chemical stability and inertness with respect to the material being machined, to avoid or minimize any adverse reactions, adhesion, and tool-chip diffusion that would contribute to tool wear.
jigs and fixtures, types of fixtures, definition of jigs and fixtures, types of jigs, application of jigs and fixtures, difference between jigs and fixtures
Roll forming Long parts with constant complex cross-sections; good surface finish; high
production rates; high tooling costs.
Stretch forming
Large parts with shallow contours; suitable for low-quantity production; high
labor costs; tooling and equipment costs depend on part size.
Drawing Shallow or deep parts with relatively simple shapes; high production rates;
high tooling and equipment costs.
Stamping Includes a variety of operations, such as punching, blanking, embossing,
bending, flanging, and coining; simple or complex shapes formed at high
production rates; tooling and equipment costs can be high, but labor costs
are low.
Rubber-pad
forming
Drawing and embossing of simple or complex shapes; sheet surface protected
by rubber membranes; flexibility of operation; low tooling costs.
Spinning Small or large axisymmetric parts; good surface finish; low tooling costs, but
labor costs can be high unless operations are automated.
Superplastic
forming
Complex shapes, fine detail, and close tolerances; forming times are long,
and hence production rates are low; parts not suitable for high-temperature
use.
Peen forming Shallow contours on large sheets; flexibility of operation; equipment costs
can be high; process is also used for straightening parts.
Explosive
forming
Very large sheets with relatively complex shapes, although usually axisymmetric;
low tooling costs, but high labor costs; suitable for low-quantity
production; long cycle times.
Magnetic-pulse
forming
Shallow forming, bulging, and embossing operations on relatively lowstrength
sheets; most suitable for tubular shapes; high production rates;
requires special tooling.
Fundamentals of Metal cutting and Machining Processes
MACHINING OPERATIONS AND MACHINING TOOLS
Turning and Related Operations
Drilling and Related Operations
Milling
Machining Centers and Turning Centers
Other Machining Operations
High Speed Machining
jigs and fixtures, types of fixtures, definition of jigs and fixtures, types of jigs, application of jigs and fixtures, difference between jigs and fixtures
Roll forming Long parts with constant complex cross-sections; good surface finish; high
production rates; high tooling costs.
Stretch forming
Large parts with shallow contours; suitable for low-quantity production; high
labor costs; tooling and equipment costs depend on part size.
Drawing Shallow or deep parts with relatively simple shapes; high production rates;
high tooling and equipment costs.
Stamping Includes a variety of operations, such as punching, blanking, embossing,
bending, flanging, and coining; simple or complex shapes formed at high
production rates; tooling and equipment costs can be high, but labor costs
are low.
Rubber-pad
forming
Drawing and embossing of simple or complex shapes; sheet surface protected
by rubber membranes; flexibility of operation; low tooling costs.
Spinning Small or large axisymmetric parts; good surface finish; low tooling costs, but
labor costs can be high unless operations are automated.
Superplastic
forming
Complex shapes, fine detail, and close tolerances; forming times are long,
and hence production rates are low; parts not suitable for high-temperature
use.
Peen forming Shallow contours on large sheets; flexibility of operation; equipment costs
can be high; process is also used for straightening parts.
Explosive
forming
Very large sheets with relatively complex shapes, although usually axisymmetric;
low tooling costs, but high labor costs; suitable for low-quantity
production; long cycle times.
Magnetic-pulse
forming
Shallow forming, bulging, and embossing operations on relatively lowstrength
sheets; most suitable for tubular shapes; high production rates;
requires special tooling.
Fundamentals of Metal cutting and Machining Processes
MACHINING OPERATIONS AND MACHINING TOOLS
Turning and Related Operations
Drilling and Related Operations
Milling
Machining Centers and Turning Centers
Other Machining Operations
High Speed Machining
Modeling and Structural Analysis of a Wing [FSI ANSYS&MATLAB] BahaaIbrahim10
In our study, analyzing aircraft’s wing with the old assumptions will not give an exact solution but
this solution (total deformation) changes according to the geometry of the cross-section of the beam, so
the total deformation of the beam may be greater or lower than the exact solution. In these two cases,
the solution is not acceptable as in the first case which the deformation is greater than the exact solution
will make more weight and cost, and Engineers design aircraft at minimum weight and less cost. But in
the second case which will make lower deformation than exact solution will be much risky as the aircraft
could fail at any time, and this case much dangerous because it threatens the life of people.
This presentation is about electromagnetic fields, history of this theory and personalities contributing to this theory. Applications of electromagnetism. Vector Analysis and coordinate systems.
This first lecture describes what EMT is. Its history of evolution. Main personalities how discovered theories relating to this theory. Applications of EMT . Scalars and vectors and there algebra. Coordinate systems. Field, Coulombs law and electric field intensity.volume charge distribution, electric flux density, gauss's law and divergence
The presentation deals with the basics of Dimensional Metrology.
The presentation includes the basic terminologies , including the following:
Measurement uncertainty: Understanding how to evaluate and report measurement uncertainty, which is the level of confidence in a measurement result.
Statistical analysis: Knowledge of basic statistical concepts, such as mean, standard deviation, and normal distribution, and their use in dimensional metrology.
Tolerance analysis: Understanding of tolerance limits, and how to apply them in dimensional measurements to determine if a part is acceptable or not.
Measurement systems analysis: Knowledge of how to evaluate the performance of measurement systems and identify sources of error.
The presentation depicted herein presents briefly an introduction of acceptance sampling along with some major differences amongst the widely used sampling standards.
Acceptance Sampling standards comparison. MIL-STD-105E, MIL-STD-1916, ISO 2859, ISO 3951. About AQLs and OC Curves.
Uncertainty of Coordinate Measuring MachinesHassan Habib
The presentation was delivered in the presentation of a conference paper at ICAYS (International Conference in Aerospace for Young Scientists) at Beihang University, Beijing, China. The topic takes into account the critical factors that effect the CMM measurements. The presentation represents the way of Guide to Expression of Uncertainty Measurement (GUM). All the formulas taken for the calculation are based on literature review.
The presentation takes into account widely used surface finishing processes including electroplating, anodizing, alodining, cadmium plating, zinc plating, phosphating, passivation
Calibration of Coordinate Measuring Machines (CMM)Hassan Habib
This presentation is made in an effort to impart information regarding the techniques used for the calibration of coordinate measuring machines. These versatile machines are today being used for the inspection of very precise and accurate mechanical components manufactured by keeping in view advanced geometrical dimensioning and tolerancing techniques.
It is a rudimentary emphasis on the importance of Child Labor. It concerns itself with some of the labor laws of Pakistan and points out how great the issue is world wide.
About
Indigenized remote control interface card suitable for MAFI system CCR equipment. Compatible for IDM8000 CCR. Backplane mounted serial and TCP/Ethernet communication module for CCR remote access. IDM 8000 CCR remote control on serial and TCP protocol.
• Remote control: Parallel or serial interface.
• Compatible with MAFI CCR system.
• Compatible with IDM8000 CCR.
• Compatible with Backplane mount serial communication.
• Compatible with commercial and Defence aviation CCR system.
• Remote control system for accessing CCR and allied system over serial or TCP.
• Indigenized local Support/presence in India.
• Easy in configuration using DIP switches.
Technical Specifications
Indigenized remote control interface card suitable for MAFI system CCR equipment. Compatible for IDM8000 CCR. Backplane mounted serial and TCP/Ethernet communication module for CCR remote access. IDM 8000 CCR remote control on serial and TCP protocol.
Key Features
Indigenized remote control interface card suitable for MAFI system CCR equipment. Compatible for IDM8000 CCR. Backplane mounted serial and TCP/Ethernet communication module for CCR remote access. IDM 8000 CCR remote control on serial and TCP protocol.
• Remote control: Parallel or serial interface
• Compatible with MAFI CCR system
• Copatiable with IDM8000 CCR
• Compatible with Backplane mount serial communication.
• Compatible with commercial and Defence aviation CCR system.
• Remote control system for accessing CCR and allied system over serial or TCP.
• Indigenized local Support/presence in India.
Application
• Remote control: Parallel or serial interface.
• Compatible with MAFI CCR system.
• Compatible with IDM8000 CCR.
• Compatible with Backplane mount serial communication.
• Compatible with commercial and Defence aviation CCR system.
• Remote control system for accessing CCR and allied system over serial or TCP.
• Indigenized local Support/presence in India.
• Easy in configuration using DIP switches.
TECHNICAL TRAINING MANUAL GENERAL FAMILIARIZATION COURSEDuvanRamosGarzon1
AIRCRAFT GENERAL
The Single Aisle is the most advanced family aircraft in service today, with fly-by-wire flight controls.
The A318, A319, A320 and A321 are twin-engine subsonic medium range aircraft.
The family offers a choice of engines
Saudi Arabia stands as a titan in the global energy landscape, renowned for its abundant oil and gas resources. It's the largest exporter of petroleum and holds some of the world's most significant reserves. Let's delve into the top 10 oil and gas projects shaping Saudi Arabia's energy future in 2024.
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Student information management system project report ii.pdfKamal Acharya
Our project explains about the student management. This project mainly explains the various actions related to student details. This project shows some ease in adding, editing and deleting the student details. It also provides a less time consuming process for viewing, adding, editing and deleting the marks of the students.
COLLEGE BUS MANAGEMENT SYSTEM PROJECT REPORT.pdfKamal Acharya
The College Bus Management system is completely developed by Visual Basic .NET Version. The application is connect with most secured database language MS SQL Server. The application is develop by using best combination of front-end and back-end languages. The application is totally design like flat user interface. This flat user interface is more attractive user interface in 2017. The application is gives more important to the system functionality. The application is to manage the student’s details, driver’s details, bus details, bus route details, bus fees details and more. The application has only one unit for admin. The admin can manage the entire application. The admin can login into the application by using username and password of the admin. The application is develop for big and small colleges. It is more user friendly for non-computer person. Even they can easily learn how to manage the application within hours. The application is more secure by the admin. The system will give an effective output for the VB.Net and SQL Server given as input to the system. The compiled java program given as input to the system, after scanning the program will generate different reports. The application generates the report for users. The admin can view and download the report of the data. The application deliver the excel format reports. Because, excel formatted reports is very easy to understand the income and expense of the college bus. This application is mainly develop for windows operating system users. In 2017, 73% of people enterprises are using windows operating system. So the application will easily install for all the windows operating system users. The application-developed size is very low. The application consumes very low space in disk. Therefore, the user can allocate very minimum local disk space for this application.
Hybrid optimization of pumped hydro system and solar- Engr. Abdul-Azeez.pdffxintegritypublishin
Advancements in technology unveil a myriad of electrical and electronic breakthroughs geared towards efficiently harnessing limited resources to meet human energy demands. The optimization of hybrid solar PV panels and pumped hydro energy supply systems plays a pivotal role in utilizing natural resources effectively. This initiative not only benefits humanity but also fosters environmental sustainability. The study investigated the design optimization of these hybrid systems, focusing on understanding solar radiation patterns, identifying geographical influences on solar radiation, formulating a mathematical model for system optimization, and determining the optimal configuration of PV panels and pumped hydro storage. Through a comparative analysis approach and eight weeks of data collection, the study addressed key research questions related to solar radiation patterns and optimal system design. The findings highlighted regions with heightened solar radiation levels, showcasing substantial potential for power generation and emphasizing the system's efficiency. Optimizing system design significantly boosted power generation, promoted renewable energy utilization, and enhanced energy storage capacity. The study underscored the benefits of optimizing hybrid solar PV panels and pumped hydro energy supply systems for sustainable energy usage. Optimizing the design of solar PV panels and pumped hydro energy supply systems as examined across diverse climatic conditions in a developing country, not only enhances power generation but also improves the integration of renewable energy sources and boosts energy storage capacities, particularly beneficial for less economically prosperous regions. Additionally, the study provides valuable insights for advancing energy research in economically viable areas. Recommendations included conducting site-specific assessments, utilizing advanced modeling tools, implementing regular maintenance protocols, and enhancing communication among system components.
Welcome to WIPAC Monthly the magazine brought to you by the LinkedIn Group Water Industry Process Automation & Control.
In this month's edition, along with this month's industry news to celebrate the 13 years since the group was created we have articles including
A case study of the used of Advanced Process Control at the Wastewater Treatment works at Lleida in Spain
A look back on an article on smart wastewater networks in order to see how the industry has measured up in the interim around the adoption of Digital Transformation in the Water Industry.
Immunizing Image Classifiers Against Localized Adversary Attacksgerogepatton
This paper addresses the vulnerability of deep learning models, particularly convolutional neural networks
(CNN)s, to adversarial attacks and presents a proactive training technique designed to counter them. We
introduce a novel volumization algorithm, which transforms 2D images into 3D volumetric representations.
When combined with 3D convolution and deep curriculum learning optimization (CLO), itsignificantly improves
the immunity of models against localized universal attacks by up to 40%. We evaluate our proposed approach
using contemporary CNN architectures and the modified Canadian Institute for Advanced Research (CIFAR-10
and CIFAR-100) and ImageNet Large Scale Visual Recognition Challenge (ILSVRC12) datasets, showcasing
accuracy improvements over previous techniques. The results indicate that the combination of the volumetric
input and curriculum learning holds significant promise for mitigating adversarial attacks without necessitating
adversary training.
2. Mathematical Definition of
Dimensioning and Tolerancing
Principles
Introduction - ASME Y14.5.1
Mathematical Possibilities of
DRFs
Datum Reference Frames
Vectors, Addition, Subtraction,
Scalar Product, Vector Product
Some Mathematics
Circularity, Cylindricity,
Flatness Mathematical
Definition
Common Tolerance Zones
Definition, Use and
Interpretation of Position,
Profile of Line and Surface
Circular and Total Runout
Overview of Location
Lessons Learned
References
Conclusions
Table Of Contents
3. Introduction - ASME Y14.5.1
Developments of 1980s
GIDEP Alert 1988
National Science Foundation
ASME Meetings (1989~)
Introduction to the Standard
- Mathematical Definition of
Dimensioning and Tolerancing
Principles
Important Considerations
4. Introduction - ASME Y14.5.1
Developments of 1980s
Advent of Computers in Manufacturing Industry
Decreasing Costs of CMMs
Integration with PCs
Invention of Touch Trigger Probes
Versatile Software Development
Mismatch Between Different Proprietary Software
5. Introduction - ASME Y14.5.1
GIDEP ALERT, 1988
Government Industry Data Exchange Program (GIDEP)
Walker, 1988 tested CMM Software (Form Tolerances)
Repeatability (Sampling, Strategy, stability, force)
Flatness, Parallelism, Straightness, Perpendicularity
Data set = Graphically solvable
Qty=05 CMMs tested
6. Introduction - ASME Y14.5.1
GIDEP ALERT, 1988
Results were shocking
37% worse than actual, 50% better than actual
Mr. Walker did not hide, he published the results
Specification crises
Grant from National Science Foundation
ASME Board on Research and Development
Recommended mathematical definition of mechanical tolerances
7. Introduction - ASME Y14.5.1
ASME Meetings, 1989
ASME sub committee meeting in 1989
Establishment of Ad hoc ASME Y14.5.1
15 meetings – 5 years
Publication of ASME Y14.5.1 in 1994
First Ever Endeavor in this area
Reiterated in 1999, 2004
8. Introduction - ASME Y14.5.1
Introduction - Mathematical Definition of Dimensioning and
Tolerancing Principles
Reiteration of textual tolerance definitions of Y14.5
Definition of geometric constraints
Construction of mathematical DRFs
Easy conversion to programming code
9. Introduction - ASME Y14.5.1
Important Considerations
Distinction between “measured” and “actual” values
“Actual” Value is inherently true (Measured perfectly)
Perfect value can never be obtained
“Measured” value is the estimated value generated by a
measurement system
It has Uncertainty associated with it
10. Introduction - ASME Y14.5.1
Important Considerations
Standard is based on “Actual” Values
Applies to conceptual design phase
Compromise between Unique Specification of tolerance &
eventual measurement method
12. Mathematics
Vectors
Vector is an abstract geometric entity that has length and
magnitude
In comparison with scalar
Represented by an arrow on capital letters
𝐴, 𝐵, etc.
15. Mathematics
Unit & Position Vectors
Unit Vector is of unit length, describes the direction of a
vector in a coordinate system
Represented by Hat on Alphabets
𝐴, 𝐵, etc.
Position Vector is a vector that describes position of a point
in reference coordinate system
22. Datum Reference Frames (DRFs)
Introduction
Degrees of Freedom
Assumptions
Mathematical Possibilities
Aggregated Possibilities
23. Datum Reference Frames (DRFs)
Introduction
Definition:
“A coordinate system that is located and oriented on the
datum features of the part, and from which the location and
orientation of other part features are controlled”
26. Datum Reference Frames (DRFs)
Assumptions
Two reasons DRF can yield more than 1 physical datum
Referenced at MMC and is manufactured b/w MMC & LMC
Inherent Form Errors
Therefore, multitude of candidate datum reference frames
Conclusion, Search for a DRF that yields features within defined
tolerance zones
27. Datum Reference Frames (DRFs)
Assumptions
Datum is established before a feature is evaluated
Smoothing of part surface is implied in this standard
For distinguishing dimension from surface texture, roughness,
material microstructure etc.
Rule # 1: Size controls the form applies
Variation of size is based on “spine”
28. Datum Reference Frames (DRFs)
Assumptions
Spine is a simple non intersecting curve
0-Dimensional spine is ‘point’
1-Dimensional spine is a ‘curve’ in space (cylindrical feature)
2-Dimensional spine is a surface (two Parallel planes)
ASME Y 14.5M- 1994 establishes a mathematical model of perfect planes,
cylinders, axes, etc. that interact with the infinite point set of imperfectly-
formed features.
29. Datum Reference Frames (DRFs)
Assumptions
Part is fixed in space DRFs are established in relation to the part
In contrast, ASME Y14.5 assumes that DRF is fixed and part is moved into
the DRF
Does not apply to screw threads, gears, splines, or mathematically defined
surfaces (Sculptured Surfaces)
36. Common Tolerance Zones
Overview of Form Tolerances
Form tolerances refine the inherent form control imparted by a size tolerance
They are not referenced from a datum reference frame
They are not specified on a nominal feature
Form tolerances are dependent on the on the characteristics of the tolerance
feature itself
37. Common Tolerance Zones
Circularity
Circularity controls the form error of a sphere or
any other feature that has nominally circular
cross sections
Cross sections exist on a spine
Spine is a curve in space with continuous slope
(1st Derivative)
Tolerance zone is on annular area on the cross
section plane, centered on spine
38. Common Tolerance Zones
Circularity
Definition puts constraint on points denoted by 𝑃
Point 𝐴 is on spine
𝑇 is a unit vector (Tangent to the spine at 𝐴)
Points are defined by:
𝑇 • (𝑃- 𝐴) = 0
𝑇 is ⊥ to 𝐴
(𝑃- 𝐴) points from 𝐴 to 𝑃
To restrict these points in tolerance zone t
||𝑃- 𝐴| - r | ≤
𝑡
2
39. Common Tolerance Zones
Cylindricity
Cylindricity tolerance controls the form error of
cylindrically shaped features.
Consists of a set of points existing in a pair of
coaxial cylinders
Axis of the cylinder does not have any defined
orientation
40. Common Tolerance Zones
Cylindricity
Definition puts constraint on points denoted by 𝑃
Point 𝐴 is position vector for axis
𝑇 is a unit vector (Defines cylindricity axis at 𝐴)
Points are defined by:
|| 𝑇 x (𝑃- 𝐴) | - r | ≤
𝑡
2
41. Common Tolerance Zones
Flatness
Flatness tolerance zone controls the form error
of a nominally flat feature
Surface to be constrained by two parallel
planes
42. Common Tolerance Zones
Flatness
Definition puts constraint on points denoted by 𝑃
Point 𝐴 is an arbitrary locating point
𝑇 is a unit vector (Defines normal to plane)
Points are defined by:
| 𝑇 • (𝑃- 𝐴) | ≤
𝑡
2
43. Overview of Location
Assumptions, Definition, & Interpretation of
True Position
Profile of Line & Surface
Circular and Total Runout
44. Overview of Location
Assumptions, Definition, & Interpretation of TP
Assumptions:
Surface Interpretation
Surface of the actual feature
Resolved Geometry Interpretation
Size and resolved geometry (Center Point, Axis,
or center plane) of applicable (Mating or Minimum
Material) actual envelope
45. Overview of Location
Consider the hole with 0 TP at MMC
The MMC VC has a Dia equal to MMC Dia of Hole
Assume that manufactured hole is within limits of size
(LOS) (Does not violate LOS)
It would be acceptable as per surface interpretation
As per resolved geometry interpretation it would be
rejected (Hole is further away from TP than allowed
by combined effects of TP (zero) and bonus tolerance
resulting from actual mating size of hole
Assumptions, Definition, & Interpretation of TP
46. Overview of Location
Conversely, consider the opposite
Shaft is controlled by TP = t at MMC
Radius of shaft = rAM and MMC radius is rMMC
Radius of tolerance zone = rMMC-rAM+t/2
Height of shaft = h
Axis of actual shaft is tilted to extreme
As per resolved geometry interpretation, the part is
acceptable
Points 𝑃 lie outside the tolerance as per surface
interpretation
Assumptions, Definition, & Interpretation of TP
47. Overview of Location
For the purposes of this standard all tolerances of location are
considered to apply to pattern of features (PLTZF)
Definition
A positional tolerance can be explained in terms of a zone
within which the resolved geometry (center point, axis or
center plane) of a Feature of Size is permitted to vary
from TP
Notation r(𝑃) denotes the distance of points 𝑃 to the TP
Assumptions, Definition, & Interpretation of TP
48. Overview of Location
In terms of Surface of a Feature
Definition
For a Pattern of Feature of Size, a TP specifies that the
surface of each actual feature must not violate the
boundary of a corresponding TP zone
Each TP is volume defined by all points 𝑃 that satisfy:
b = radius or half width
Assumptions, Definition, & Interpretation of TP
49. Overview of Location
In terms of Surface of a Feature
Assumptions, Definition, & Interpretation of TP
50. Overview of Location
In terms of Surface of a Feature
Conformance
Assumptions, Definition, & Interpretation of TP
51. Overview of Location
In terms of Resolved Geometry of Feature
Definition
For features within a pattern, a position tolerance specifies
that the resolved geometry (center point, axis, or center
plane, as applicable) of each actual mating envelope (for
features at MMC or RFS) or actual minimum material
envelope (for features at LMC) must lie within a
corresponding positional tolerance zone
Each TP is volume defined by all points 𝑃 that satisfy r(𝑃) ≤ b
Assumptions, Definition, & Interpretation of TP
52. Overview of Location
In terms of Resolved Geometry of Feature
Definition
Assumptions, Definition, & Interpretation of TP
53. Overview of Location
In terms of Resolved Geometry of Feature
Conformance
Assumptions, Definition, & Interpretation of TP
54. Overview of Location
Conical Tolerance Zones
Bi-Directional Tolerance Zone
Polar Bi-Directional Tolerance Zone
Assumptions, Definition, & Interpretation of TP
55. Overview of Location
A profile is the outline of an object in a given plane (2D
figure). Profiles are formed by projecting a 3D figure onto a
plane or taking cross sections through the figure. The
elements of a profile are straight lines, arcs, and other curved
lines. With profile tolerancing, the true profile may be defined
by basic radii, basic angular dimensions, basic coordinate
dimensions, basic size dimensions, un-dimensioned
drawings, or formulas
Profile of Line & Surface
56. Overview of Location
Definition:
A profile tolerance zone is an area (profile of a line) or a
volume (profile of a surface) generated by offsetting each
point on the nominal surface in a direction normal to the
nominal surface at that point.
Profile of Line & Surface
57. Overview of Location
For a given point 𝑃N on a nominal surface there is a unit
vector 𝑁, normal to the nominal surface either into or out of
material.
A profile tolerance t consists of sum of two intermediate
tolerances t+ and t-. +ve and –ve disposition of tolerance in
surface normal 𝑁 at 𝑃N
Profile of Line & Surface
58. Overview of Location
Conformance:
Surface conforms to profile tolerance t0 if all points 𝑃S of the surface
conform to either of intermediate tolerances t+ or t- disposed about
some corresponding point 𝑃N on nominal surface
𝑃S conforms to t+ if 𝑃S is between 𝑃N and 𝑃N + 𝑁t+
𝑃S conforms to t- if 𝑃S is between 𝑃N and 𝑃N − 𝑁t+
2 values are necessarily calculated: 1 for surface variations in positive
direction and 1 for negative direction. Actual value is the smallest
intermediate tolerance to which the surface conforms
Profile of Line & Surface
59. Overview of Location
Runout is a composite tolerance used to control the functional
relationship of one or more features of a part to a datum axis. The
types of features controlled by runout tolerances include those
surfaces constructed around a datum axis1 and those
constructed at right angles to a datum axis2
The mathematical definition of 1 and 2 are different
Runout
60. Overview of Location
Evaluation
Total Runout on tapered or contoured surfaces require establishment
of actual mating normal. Nominal Diameters, lengths, radii, and
angles establish cross sectional desired contour having perfect form
and orientation. It:
may be translated axially and/or radially
May not be tilted/scaled with respect to a datum axis
When a tolerance band is equally disposed about this contour and
then revolved around datum axis, a volumetric tolerance zone is
generated.
Runout
61. Overview of Location
Circular Runout
Surfaces constructed at right angles to a datum axis
The tolerance zone for each circular element on a surface
constructed at right angles to a datum axis is generated by revolving
a line segment about the datum axis.
Runout
62. Overview of Location
For a surface point 𝑃S, a circular runout tolerance is a set of points
𝑃 satisfying ∶
| 𝐷1 𝑥(𝑃- 𝐴) | = r and
| 𝐷1 • (𝑃- 𝐵) | ≤
𝑡
2
Runout
63. Overview of Location
Circular Runout
Surfaces constructed around a Datum Axis
The tolerance zone for each circular element on a surface
constructed around a datum axis is generated by revolving a line
segment about the datum axis.
Runout
64. Overview of Location
For a surface point 𝑃S, a datum axis [ 𝐴 , 𝐷1 ] and a given mating
surface, a circular runout tolerance is a set of points 𝑃 satisfying ∶
𝐷1•(𝑃− 𝐵)
|𝑃− 𝐵|
= 𝐷1 • 𝑁 and
| |𝑃− 𝐵|-d| ≤
𝑡
2
𝑁 • (𝑃s− 𝐵) > 0
Runout
66. Overview of Location
Total Runout
Surfaces constructed at right angles to a datum axis
A total runout tolerance for a surface constructed at right angles to a
datum axis specifies that all points of the surface must lie in a zone
bounded by two parallel planes perpendicular to the datum axis and
separated by the specified tolerance
Runout
67. Overview of Location
For a surface constructed at right angles to a datum axis, total runout
zone is a volume consisting of point 𝑃 satisfying ∶
| 𝐷1 • (𝑃- 𝐵) | ≤
𝑡
2
𝐷1 = direction vector for datum axis
𝐵 = Position vector locating midplane of tolerance zone
t = size of tolerance zone
Runout
68. Overview of Location
Total Runout
Surfaces constructed around a datum axis
A total runout tolerance zone for a ,surface constructed around a
datum axis is a volume of revolution generated by revolving an area
about the datum axis.
Runout
69. Overview of Location
For a surface point 𝑃S, a datum axis [ 𝐴 , 𝐷1 ], Let 𝐵 be a point on
datum axis locating one end of desired contour and r is distance from
datum axis to desired contour. Then for given 𝐵 and r, C(𝐵 ,r) denotes
the desired contour. For each C(𝐵 ,r) runout zone is a set of points
𝑃 satisfying ∶
|𝑃− 𝑃′| ≤
𝑡
2
𝑃′ = projection of 𝑃 onto surface generated by rotating C(𝐵 ,r) about
datum axis
t = size of tolerance zone
Runout
71. Conclusions
This standard is a mathematical translation of ASME Y14.5
It is a guideline for software developers and users to understand how the
calculations are made
The information helps in better comprehending the design intent in later
stages of product development, specially manufacturing and inspection
The understanding helps in better decisions regarding “Acceptable” and
“Conforming” parts.
It takes into account the theoretical calculations used to establish definitions
GD&T as defined in Y14.5
It does not take into account measureability
Lessons Learned
72. Conclusions
Basic Theme is a courtesy of SlideModel
Dimensioning and tolerancing handbook by Paul J. Drake
https://betterexplained.com/articles/cross-product/
https://www.grc.nasa.gov/WWW/K-12/airplane/vectpart.html
https://en.wikipedia.org/wiki/Multiplication_of_vectors
References