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SPECIFICATION OF GEOMETRIC TOLERANCES, REVIEW THE RECENT

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 9th International Quality Conference
June 2015
Center for Quality, Faculty of Engineering, University of Kragujevac

SPECIFICATION OF GEOMETRIC
Dragan Lazarević1)
Milan Mišić1) TOLERANCES, REVIEW THE RECENT
Živče Šarkoćević1) DEVELOPMENT
Zlatibor Lekić2)
Abstract: The way of specifying tolerances on manufactured
Bojan Stojčetović1) products has progressively changed during the last two
decades. In traditional practice, allowable variation limits
1) Higher Technical School were simply assigned to dimensions regarded as critical for fit
of Professional Studies and function (linear tolerancing). This is no longer sufficient,
Zvecan, since the advent of Geometric Dimensioning and Tolerancing
(GD&T) has put forward the idea that part features need to
2) Faculty of Technical be controlled in many different geometric characteristics
Sciences, (size, form, orientation, location, profile, runout).
Kosovska Mitrovica Specification is less studied than allocation and analysis,
lazarevicddragan@yahoo.com because it was not an issue with linear tolerancing and is
m.misic@vts-zvecan.edu.rs actually inherent to the geometric approach. It can be viewed
zivcesarkocevic@yahoo.com as a missing link in the tolerancing chain, which provides the
zlatibor.lekic@pr.ac.rs two downstream tasks with a correct and complete geometric
bstojcetovic@yahoo.com description of design requirements in the GD&T language.
Available knowledge for the solution of the specification
problem comes from tolerance standards and technical
handbooks in the form of rules and application examples. This
paper reviewed the recent development of specification of
geometric tolerances, new standards and technologies.
Keywords: Tolerancing, Tolerance specification, Geometric
tolerances, Standard ISO 1101

1. INTRODUCTION conflict with the functional requirements. In order

to guarantee the intended functions and assembly
Recent development in computer-based relationships, tolerances are specified, which
manufacturing and inspection has necessitated define the permissible variations from the ideal
extended knowledge and usage of geometric part given in the drawing. This is because it is
tolerances as carriers of design intent. The aim of almost impossible to produce a part with perfect
applying geometrical tolerances in design is to size and form as indicated in the drawing. Size
provide function-oriented precise description of variations are given by the size tolerances that are
part geometry where the conventional size traditionally accepted to be sufficient to guarantee
tolerance system fails to address. In view of the fulfilment of functional requirements.
current development of computer-aided systems, Nowadays manufacturing industries are
applying geometric tolerances opens a new under intense pressure from the ever-increasing
research front. competition demanding products to be produced
Mechanical design is by nature a synthesis within tighter tolerances, shorter time to market
work intended to give precise description of the and more accurate communication with design
part on engineering drawings using pictures, intent [1]. This has made many companies to
texts, numbers and symbols. The design recognize the importance of having competence
specifications transfer the design intent stated as in tolerating their drawings with geometric
the geometrical and material characteristics, the tolerances. The existing manufacturing practice
critical function relationships among features in on the workshop floor indicates that there are two
part and the assembly requirements. The design main challenges to make smooth flow of design
specifications are not unique in nature, but valid intent. Primarily, the practical use of the rules,
within permissible ranges that should not come in symbols and concepts of geometric tolerances is
not well established. In view of the extended use

9th IQC June, 2015 317

of computers in almost every activity involved in 2. GEOMETRIC TOLERANCE
a product’s life cycle, the ability to represent a
design model that is complete, consistent, According to ISO 1101 [2] and ASME 14.5
meaningful and unambiguous is absolutely [3], geometric tolerance is defined as ‘‘an
necessary. As the interpretation of the standards international language of symbols placed on
is not easy, companies are doing significant technical drawings to adequately describe the
investment on training their engineers and allowable variation of part geometry.’’ In other
technicians so that the geometric tolerance words, the purpose of geometric tolerances is to
concepts given by the standards are well establish smooth communication between the
understood and applied. Secondly, computer users of the standard. Accordingly, the geometric
representation of geometric tolerances, i.e., the tolerance language uses welldefined set of
symbols and textual rules, demands development symbols, rules, definitions and conventions to
of complex algorithms. It is crucial that the enable the required smooth communication.
design representations including the tolerance The geometric tolerance characteristics and
information allow easy modification and design symbols are basically categorized into three main
optimization. The ability to transfer both the groups: form, orientation and location. However,
dimensional model data and the associated this paper would like to group the parameters (14
tolerances including the providing functional in number) into five categories. This is becoming
requirements from computer-aided design (CAD) the practice in most recent publications and
model is important for future progress of textbooks in the field. Figure 1 shows the
computeraided inspection systems. In the process geometric tolerance categories, the parameters
of developing common neutral files for data under each category and the symbols [4]. The
transfer, recent development in the standard for geometric characteristic symbol (S), i.e., one of
the exchange of product model data is widely the symbols in Figure 1, and the tolerance value
expected as the most promising tool to solve the (t) are given in a rectangular tolerance frame with
constraints on transfer of design data. at least two compartments (for single features)
and up to five compartments (for related
features). A typical tolerance frame with
examples of modifying parameters is illustrated
in Figure 2.

Figure 1 - Overview of the basic geometric tolerance parameters and simbols [4]

Two major principles, the maximum geometric tolerances. While the MMC principle
material condition (MMC) principle and the attempts to contain the form variations within the
independence principle (ISO 8015), lay the worst case boundary, the independence principle
foundation of modern tolerating principle using provides clear distinction between size and form

318 D., Lazarević, M., Mišić, Ž., Šarkoćević, Z., Lekić, B.,Stojčetović
tolerances unless a specific relationship is
defined.

2.1 Standardization of geometric tolerances

The guidelines of specifying geometric

tolerances are standardized in two main
international standards: ASME and ISO
standards. ASME adopts the American Y14.5
national standard (previous ANSI standard) and
introduces some other concepts, definitions, rules
and symbols.

Figure 3 - Examples omitted former practices of

indicating (a) geometric tolerances and (b)datum
triangle with datum letter on kommon axes

Due to the difficulties in mathematical

modeling and representation, implementing the
standards in the seamless linking of CAD and
manufacturing (CAD/CAM) system has not been
straightforward. Furthermore, the standards are
frequently revised with introduction of some new
concepts, symbols and conventions while some
are removed from the standards. For instance,
Figure 3 shows some of the design conventions
that used to be part of former practices as given
by ISO 1101:1983, but omitted in the 2004
version. The measures clearly improve the
existing ambiguities in the standard. Closer
review of the literature also shows that the
research on how geometric tolerance information
Figure 2 - Illustration on reference frame (a), can be represented is not progressing with the
and examples of modifaying symbols (b) same speed as the representation and integration
of geometric modeling and manufacturing data.
The most recent main revision of the
standard is ASME Y15.5: 2009 [3]. Geometric 2.2 Tolerance zone
tolerances in ISO are given by ISO 1101 in which
the recent updated version is ISO 1101:2004. In The tolerance zone specifies the region
addition, ISO has issued a series of documents on within which the part feature (axis, point, line,
geometric tolerances and other engineering surface or median plane) deviation is constrained.
drawing standards. According to this standard [2], This zone has different forms partly depending on
a geometric tolerance applied to a feature defines the type of the geometric tolerance parameter and
the tolerance zone within which the feature shall partly basing on the specifications given in the
be contained. Due to the difficulties in tolerance frame. In other words, some of the
mathematical modeling and representation, geometric tolerance properties are defined by
implementing the standards in the seamless specific form of the tolerance zone while some
linking of CAD and manufacturing (CAD/CAM) are dictated by the specifications given by the
system has not been straightforward. designer. For instance, a flatness tolerance is
Furthermore, the standards are frequently revised defined only between two parallel lines (in 2D) or
with introduction of some new concepts, symbols three parallel planes (in 3D). Thus modification
and conventions while some are removed from of the tolerance zone in the tolerance frame is not
the standards.

9th IQC June, 2015 319

allowed. In a similar way, a cylindricity error is
bounded by a condition that points of a revolution
surface are equidistant from a common axis, thus
its tolerance zone is bounded by two concentric
cylinders. The tolerance feature may be of any
form or orientation within the defined tolerance
zones unless restricted by other specifications.
Figure 4 shows the various forms of the available
tolerance zones for geometric tolerances, both in
2D and 3D. Most tolerance zones are in 3D, but
the 2D versions that are the projections of the 3D
space on a plane are more intuitionistic in
tolerance analysis.

Figure 5 - Tasks involved in geometric

tolerancing [5]

Specification is less studied than allocation

and analysis, because it was not an issue with
linear tolerancing and is actually inherent to the
Figure 4 - Sample forms of tolerance zones
geometric approach. It can be viewed as a
missing link in the tolerancing chain, which
Tolerance zone formulation is one of the
provides the two downstream tasks with a correct
early attempts to achieve computer-based
and complete geometric description of design
representation of geometric tolerances
requirements in the GD&T language.

3. TOLERANCE SPECIFICATION
4. REVIEW THE RECENT
The methods developed can be classified DEVELOPMENT
into the following three categories, related to the
main design tasks of geometric tolerancing As noted in a recent survey [6], tolerance
(illustrated in Figure 5): specification has often been referred to by
different names to emphasize its distinction from
 tolerance specification: the types of
allocation (qualitative tolerancing) or the need for
tolerances on functional features and the
a modeling of design requirements (tolerancing
datum reference frame are chosen for each
for function, tolerancing for assembly). Its role
part;
within the tolerancing process and its
 tolerance allocation: the values of all relationships to downstream tasks have been
specified tolerances are determined by either clarified in some early papers [7,8]. Although it
refining empirical tentative values or involves detailed part design, it should be
optimizing them according to cost–tolerance anticipated to the earlier stage of assembly design
functions; as suggested in [9,10]. Acceptance conditions on
 tolerance analysis: the stackup of errors the tolerances generated by a specification
allowed by selected tolerance values is procedure include the unambiguous positioning
evaluated and compared to design of part features [11,12] and the compliance to
requirements (possibly more than once syntax rules stated by technical standards.
during the allocation procedure). Tolerance values are not specified as they will be
To date, little support exists for tolerance optimized in the allocation task along with
specification and allocation, while software tools possible alternative choices for tolerance types
for tolerance analysis are available on a growing and datum reference frames.
number of CAD platforms. The basic input for tolerance specification is
the nominal product geometry as it could be

320 D., Lazarević, M., Mišić, Ž., Šarkoćević, Z., Lekić, B.,Stojčetović
extracted from a geometric modeler, although according to predefined rules. Clusters are then
only a few studies report a true CAD integration. aggregated in a final step by considering the
The processing of geometric data involves a whole set of assembly relations of the product.
preliminary selection of the features to be In the function decomposition method [28],
toleranced. In most cases, these are classified the strategy based on assembly relations is
according to the types of assembly relations with combined with an explicit treatment of design
features of mating parts. requirements. Each functional requirement input
Input data can be completed with additional by the user is decomposed into a hierarchy of part
precision requirements set by the designer. In features, from which a subset of critical features
linear tolerancing, requirements are mainly is selected according to reasoning rules on feature
related to tolerance chains as widely discussed in types and associated directions. From critical
[13]. In the context of GD&T this concept is features, other rules allow to choose datums and
better specialized with the definition of key geometric tolerances on features. The method has
characteristics, delivered by chains of geometric been enhanced with rules for the identification of
relations identified by means of flowdown functional requirements from high-level
procedures [14]. Alternative ways proposed to mechanical functions [29] and for the choice of
represent design requirements include assembly modifiers from the assembly sequence [30]. A
geometric tolerances [15], pseudo-TTRS [16], further extension based on the small displacement
virtual boundary requirements [17], functional– torsor concept has also been proposed for the
structural models [18] and hierarchies of generation of tolerance specifications in the early
hypergraphs [19]. phases of product development [31].
The first method of generative specification The method of variational loop circuit
is based on the TTRS model of tolerance [32,33] combines the focus on design
representation [20]. By recognizing loops in the requirements with an explicit classification of
graph of assembly relations, an iterative tolerancing cases. For each requirement, a graph-
algorithm creates associations between features of based model links the involved features and the
individual parts. This results in a hierarchy of related associated entities (e.g. axes) through
feature associations for each part, which are parameters and equations. An output graph is
completed with geometric tolerances according to built upon it by adding geometric tolerances
the above cited classification of cases. The extracted from the classification, as well as
method has been further developed into an functional equations which can help the
interactive software tool [21], enhanced with integrated treatment of tolerance allocation and
rules for loop selection [22] and integrated in analysis.
commercial CAD packages. Similar approaches
have been used to select datum reference frames
for individual parts [23,24] and to transfer 5. CONCLUSIONS
geometric tolerances into detailed specifications
along the steps of a machining process. Some considerations on existing methods
Another method connected to a classification help to identify opportunities for further work on
of tolerancing cases is based on the degree-of- tolerance specification. They apply to three
freedom representation model [11, 25, 26]. A aspects: the treatment of design requirements, the
global model of feature relations is used to use of assembly process data and the traceability
generate directional relations between pairs of of generated tolerances.
features, which are later converted into geometric The computer-aided tools in the future of
tolerances selected from classified cases. The design engineering are expected to establish a
claimed benefits of the approach include the system that operates intelligently and performs
identification of datum precedences and a better better than before. However, the existing
verification of the correct positioning of machines and operations in the area are still
toleranced features with respect to datums. unable to mimic some basic human capabilities
The method proposed in [27] is based on such as adjusting appropriately to the dynamic
mirrors, i.e. planar surfaces involved in assembly environment, understanding some of the human
relations, which are expected to have a special readable symbols and texts, etc. It is only when
influence on part tolerancing. Each mirror is such human actions and other natural reactions
selected as a datum and forms the basis for a local are ‘‘learned’’ that the system is said to be
cluster of features, which are toleranced intelligent. This requires both hardware and

9th IQC June, 2015 321

software used in the area that have the ability to provided by a software tool will probably be
adapt to the dynamic changes. modified and adapted to corporate standards and
Regardless of the method, one of the practices. The chance of establishing a logical
possible limitations of a specification procedure path from the assembly sequence through design
is the limited traceability of generated tolerances, requirements to specified tolerances can help to
i.e. the difficulty to convey the rationale of their trace specification results back to underlying
selection to the designer. A ‘‘canned’’ tolerance technical reasons.
specification is likely to be of little use in a real-
world design environment, where the results

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