Functional dimensioning and tolerancing software for concurrent engineering applications M.N. Islam * Department of Mechanical Engineering, Pohang University of Science and Technology, San 31 Hyoja-dong, Nam-gu, Pohang, Kyungbuk 790-784, South Korea Received 18 September 2002; accepted 13 September 2003 Abstract This paper describes the development of a prototype software package for solving functional dimensioning and tolerancing (FD&T) problems in a Concurrent Engineering environment. It provides a systematic way of converting functional requirements of a product into dimensional specifications by means of the following steps: firstly, the relationships necessary for solving FD&T problems are represented in a matrix form, known as functional requirements/dimensions (FR/D) matrix. Secondly, the values of dimensions and tolerances are then determined by satisfying all these relationships represented in a FR/D matrix by applying a comprehensive strategy which includes: tolerance allocation strategies for different types of FD&T problems and for determining an optimum solution order for coupled functional equations. The prototype software is evaluated by its potential users, and the results indicate that it can be an effective computer-based tool for solving FD&T problems in a CE environment. # 2003 Elsevier B.V. All rights reserved. Keywords: Functional dimensioning and tolerancing; Concurrent engineering; Tolerance allocation 1. Introduction Functional Dimensioning and Tolerancing (FD&T) is a concept widely used for specifying dimensions and tolerances of the component parts and sub-assem- blies of a product according to their functional requirements. These functional requirements arise from all life cycle issues, such as manufacturing, assembly and inspection. Concurrent Engineering (CE) is an engineering and management philosophy, which also deals with the life cycle issues of a product. CE is based on the idea of carrying out as many stages of product development concurrently as possible, rather than in a sequential order. It calls for the formation of a cross-functional product development team, which includes people from a wide range of departments, such as: product planning, design, man- ufacture, assembly, quality assurance, marketing, sales and finance. Dimensions and tolerances influence almost all aspects of product development which are of interest to CE team members who consider all the life cycle issues of a product during its design stage. Therefore, a CE approach will be ideal for selection of dimensions and tolerances through applications of FD&T metho- dology. Furthermore, FD&T can serve as a common link between all members of the CE team; hence it can enhance the CE team performance [1,2]. It is also argued in [3] that CE offers the best option for finding the values of dimensions and tolerances using informal optimization methods because the data required for Computers in Industry 54 (2004) 169–190 * Tel.: þ82-54-279-8639; fax: þ82-54-279-5899. E-mail address: [email protected] (M.N. Islam). 0166-3615/$ – see front matter # 2003 Elsevier B.V. All rights reserved. doi:10.1016/j.compind.2003.09.006
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Functional dimensioning and tolerancing software forconcurrent engineering applications
M.N. Islam*
Department of Mechanical Engineering, Pohang University of Science and Technology, San 31 Hyoja-dong,
Nam-gu, Pohang, Kyungbuk 790-784, South Korea
Received 18 September 2002; accepted 13 September 2003
Abstract
This paper describes the development of a prototype software package for solving functional dimensioning and tolerancing
(FD&T) problems in a Concurrent Engineering environment. It provides a systematic way of converting functional requirements
of a product into dimensional specifications by means of the following steps: firstly, the relationships necessary for solving
FD&T problems are represented in a matrix form, known as functional requirements/dimensions (FR/D) matrix. Secondly, the
values of dimensions and tolerances are then determined by satisfying all these relationships represented in a FR/D matrix by
applying a comprehensive strategy which includes: tolerance allocation strategies for different types of FD&T problems and for
determining an optimum solution order for coupled functional equations. The prototype software is evaluated by its potential
users, and the results indicate that it can be an effective computer-based tool for solving FD&T problems in a CE environment.
# 2003 Elsevier B.V. All rights reserved.
Keywords: Functional dimensioning and tolerancing; Concurrent engineering; Tolerance allocation
1. Introduction
Functional Dimensioning and Tolerancing (FD&T)
is a concept widely used for specifying dimensions
and tolerances of the component parts and sub-assem-
blies of a product according to their functional
requirements. These functional requirements arise
from all life cycle issues, such as manufacturing,
assembly and inspection. Concurrent Engineering
(CE) is an engineering and management philosophy,
which also deals with the life cycle issues of a product.
CE is based on the idea of carrying out as many stages
of product development concurrently as possible,
rather than in a sequential order. It calls for the
formation of a cross-functional product development
team, which includes people from a wide range of
departments, such as: product planning, design, man-
ufacture, assembly, quality assurance, marketing,
sales and finance.
Dimensions and tolerances influence almost all
aspects of product development which are of interest
to CE team members who consider all the life cycle
issues of a product during its design stage. Therefore, a
CE approach will be ideal for selection of dimensions
and tolerances through applications of FD&T metho-
dology. Furthermore, FD&T can serve as a common
link between all members of the CE team; hence it can
enhance the CE team performance [1,2]. It is also
argued in [3] that CE offers the best option for finding
the values of dimensions and tolerances using informal
optimization methods because the data required for
This is a length dimension problem represented by a
single functional equation; therefore, the LengthSol-
ver module was used for the solution. This assembly
contains three purchased parts; their dimensions are
non-negotiable and were taken out of both basic size
and tolerance equations. Fig. 7 shows the initially the
CE team proposed turning operation with IT grade 9
and capability index 1.33 for manufacture of the
remaining features. However, this proposal is not
acceptable because of negative residual tolerance
(�0.0177 mm). Fig. 7 also reveals that the problem
could be rectified by changing the process used for
Fig. 6. Shaft and bearing assembly [25].
M.N. Islam / Computers in Industry 54 (2004) 169–190 181
Fig. 7. Screen print showing the intervention strategy of LengthSolver.
Fig. 8. Screen print showing ‘what-if’ capability of LengthSolver.
182 M.N. Islam / Computers in Industry 54 (2004) 169–190
producing dimensions B or E by 1 IT grade (24%
reduction), whereas for achieving the same goal the IT
grade for the process used for the manufacture of
dimension D or F had to be reduced by 3 (68%
reduction). On this basis the CE team decided to
change the manufacturing operation for producing
the dimension B to fine turning with IT grade 8 and
capability index 1.33. Fig. 8 illustrates that where the
proposed manufacturing processes are acceptable
(residual tolerance þ0.093 mm), some of the proposed
tolerance values (d and f) are not compatible with the
process capability tolerances. At this stage the CE
team was able to do a ‘what if’ analysis, by trying out
different scenarios and finally came up with an accep-
table solution. The final results from the LengthSolver
are given in Fig. 9.
6.2. Problem no. 2
Fig. 10 illustrates a belt drive unit dimensioning and
tolerancing problem adopter from Williams [27]. The
following functional requirements are to be met (all
dimensions are in mm):
FR1: Fit 1, 2: Cmin ¼ 0, Cmax ¼ 0:092.
FR2: Fit 3, 4: MF ¼ �0:018 � 0:017.
FR3: Fit 5, 6: should be a ‘normal running’ fit.
FR4: Fit 7, 8: Cmin ¼ 0, Cmax ¼ 0:092.
FR5: The end play of the spindle is not to be less
than 0.06 and is not to exceed 0.188.
FR6: The distance Z1 is to be controlled within
65:� 0:064 taking into account the end play.
FR7: The distance Z2 is to be between 14.08 and
13.92 taking account the end play.
Calculate the values of the dimensions and toler-
ances to be placed on the drawing to satisfy the above
functional requirements.
6.2.1. Solution
The loop equations are as follows (see Fig. 11):
FR1: Fitting feature problem with type 2 target
value.
FR2: Fitting feature problem with type 3 target
value.
FR3: Fitting feature problem with type 1 target
value.
FR4: Fitting feature problem with type 2 target
value.
FR5: End play ¼ B � A.
FR6: Z1 ¼ B þ C
FR7: Z2 ¼ B � A þ D.
Fig. 9. Print showing final results of LengthSolver.
M.N. Islam / Computers in Industry 54 (2004) 169–190 183
The initial choices of the CE team for manufacture
of the different features in the proposed design are
given in Table 3.
This problem consists of seven functional equations;
the problem was firstly represented in the matrix format
with the help of MatrixSolver. Then the functional
requirements were grouped into five groups according
to the interrelationships among the variables. The soft-
ware then provided an optimum solution order. The first
four functional requirements are independent func-
tional requirements and were solved first. As FR1 to
FR4 are fitting feature problems, FitSolver module was
used for finding their solutions. Fig. 12 illustrates a fit
ranking table used in the process of solving FR2. The
final results from MatrixSolver are depicted in Fig. 13.
Note that the solution order of functional requirements
in Group no. 5 were changed from FR5 > FR6 > FR7
to FR6 > FR5 > FR7. The effectiveness of the proto-
type software becomes more evident with an increase in
the number of functional equations with more compli-
cated interrelationships. However, such problems were
not chosen here due to space constraints.
7. Software evaluation
The primary characteristic of the CE concept is its
team approach to product development; the prototype
software was designed with this in mind. However,
the evaluating of software for team work is difficult
[28] because it is difficult to create the dynamics of
interactions between individual team members in the
laboratory; it is also time-consuming, because team
interactions usually unfold over a relatively long period
of time. Anticipating these difficulties, the prototype
software was not evaluated in a CE environment. The
two evaluation processes followed are described below.
7.1. Software evaluation against selected criteria
First the requirements of a FD&T tool suitable for
a CE environment were formulated by considering
Fig. 10. Belt drive unit [27].
Table 3
Initial choices of the CE for manufacture of belt drive unit
Part name Feature name Dimension symbol Design size Material Manufacturing process Difficulty level
Pulley Hole diameter D2 10.00 Cast iron – –
Bush External diameter D4 20.00 Bronze – –
Spindle Bearing diameter D6 12.00 Steel – –
Gear Hole diameter D8 10.00 Steel – –
Housing Hub depth A 36.00 Cast iron Turning Moderate
Spindle Bearing length B 36.00 Steel Turning Moderate
Pulley Hub offset C 29.00 Cast iron Turning Moderate
Gear Boss depth D 14.00 Steel Turning Moderate
184 M.N. Islam / Computers in Industry 54 (2004) 169–190
various requirements for such a tool as reported
in the literature. Details of this establishment process
can be found in [13]. FDT was then evaluated
against these criteria and the evaluation results
are summarized in Table 4, with brief explanations in
subsequent paragraphs.
R1: The proposed methodology helps to describe or
quantify the functional requirements of the design
with the help of some existing CE tools, such as
QFD and tree diagram. However, this aspect of the
Fig. 11. Loop equations: belt drive unit.
Fig. 12. Screen print showing fit ranking table in FitSolver.
M.N. Islam / Computers in Industry 54 (2004) 169–190 185
methodology has not been integrated into the pro-
totype software. Software packages are available for
QFD analysis, e.g. QFD/CAPTURE developed by
International Technical Group [32] and for construc-
tion of Tree Diagrams, e.g. Microsoft Visio [33].
R2: FDT helps to develop functional equations in a
structured way, although the actual equations are
not generated.
R3: FDT tries to find economic solutions by
applying an informal optimization strategy.
Fig. 13. Screen print showing final results from MatrixSolver.
186 M.N. Islam / Computers in Industry 54 (2004) 169–190
R4: FDT considers assembly and inspection
requirements when specifying functional require-
ments in form of functional equations and
manufacturing requirements during finding a
solution for functional equations.
R5: FDT helps in decision making at multiple
stages of product development.
R6: FDT is easy to use and does not require
advanced technical knowledge.
R7: FDT is interactive and has an attractive
Graphic User Interface.
R8: FDT runs on Windows which is the most
widely used computer platform.
R9: FDT is easy to learn; many other usability
attributes are built into it.
R10: FDT has a structured methodology which
helps the user in solving FD&T problems through
step by step instructions.
R11: It can solve four commonly occurring types
of 1D, FD&T problems, viz. fitting feature
problems, length dimension problems, mixed-type
problems, and surface texture problems as well
as coupled loop equations for these types of
problems.
R12: The results obtained from the prototype
software were compared with the results obtained
through manual calculations and they matched
one another. This indicates that the results are
credible.
From the foregoing, its appears that the prototype
software has satisfied most of its requirements at a
satisfactory level and it has the potential to be an
effective tool for solving FD&T problems in a CE
environment. As the above evaluation was per-
formed by the developer there might be a perceived
bias in the evaluation findings. In this case, the
evaluation findings should be treated as the devel-
oper’s claims about the prototype and a survey of
the opinions of independent potential users was
undertaken.
7.2. Software evaluation by its potential users
The prototype software was evaluated by 15
volunteers chosen from the staff and students of
the School of Mechanical and Manufacturing Engi-
neering, The University of New South Wales, Aus-
tralia. Participants had varying degrees of familiarity
with FD&T problems. Evaluation sessions were run
within a lab environment with one participant at a
time. At the beginning of each session each partici-
pant was briefed on the evaluation procedure; cap-
abilities of the prototype software were demonstrated
by the evaluator solving some sample problems.
Participants were then individually asked to solve
some exercise problems and were monitored during
their use of the software and any difficulties faced by
them were noted as well any questions or additional
Table 4
Evaluation summary of the prototype software against selected criteria
Req. No Description Source Findings
R1 It should help the user to describe and quantify the functional requirements of the design [29] No
R2 It should help the user to develop functional equations [29] Yesa
R3 It should provide and economic solution to the functional equations [29,19] Yesb
R4 It should consider manufacturing, assembly, and inspection requirements in tolerance selection [29,30] Yes
R5 It should help in decision making at multiple stages of product development [30] Yes
R6 It should be suitable for team members from different tecchnical backgrounds [29,30] Yes
R7 It should be interactive [29] Yes
R8 It should run on a platform that is easily accessible [31] Yes
R9 It should be easy to learn [31] Yes
R10 It should be based on a structured methodology [31] Yes
R11 It should be applicatble to a wide range of products [31] Noc
R12 It should be provide credible results [31] Yes
a It helps but does not generate loop equations automatically.b It does this indirectly.c It can solve certain types of 1D problems and is capable of solving coupled requirements.
M.N. Islam / Computers in Industry 54 (2004) 169–190 187
information they requested. At the completion of
the tasks by each participant a short interview was
then recorded.
About 2 h of conversation was recorded, transcribed
and then evaluated. Details of the evaluation can be
found in [13]. From the analysis it appears that except
for three participants all were very satisfied with
the performance of the software. One participant
expressed reservations about its practical use. Another
participant felt that due to the sequential nature of the
program, making changes might be difficult. Some of
the participants praised its capability of making a
‘what-if’ analysis and were impressed with the good
use of colors. Others found the ability to produce fast
results most useful.
The prototype software required a great amount of
manual input. This problem will be rectified once it is
interfaces with a CAD system for which collaboration
of the CAD supplier is required. The inability of the
prototype software to illustrate the whole matrix on a
single screen was identified as the single most con-
cerning issue throughout the evaluation process. How-
ever, this is a common problem in most computer
programs and could be solved by displaying the screen
on a wall. This solution is particularly useful in a CE
environment where the members of the CE team
would be able to get a ‘total’ picture of the problem
being solved.
8. Discussion
FDT is FD&T software in its true sense. It is based
on a structured FD&T methodology that leads the user
towards an optimum solution for common 1D dimen-
sioning and tolerancing problems. The emphasis of
most of the commercially available packages has been
tolerance analysis. Therefore, during FD&T the CE
team members are only able to test the validly of their
selection using these packages. Still, the tolerance
values should not be changed on the basis of simula-
tion results only, which analyses the assembly require-
ments only, whereas FD&T involves the fulfillment of
a number of other requirements, such as manufactur-
ing and inspection. Furthermore, the statistical data
required by these packages, such as distributions of
input tolerances, are often not available at an early
design stage.
The use of a matrix or spreadsheet format for
organizing dimensioning and tolerancing problems
is not new; designers have been using different
custom-made formats for years. Some of the commer-
cially available packages, e.g. CATS-1D XL, also use
such format. However, their representation is not
meaningful. The format used by FDT is unique and
it represents the complexity of the FD&T problem of
product.
FDT increases the efficiency of the solution
search process, firstly, by dividing the whole
FD&T problem of a product into groups and then
by providing solution orders for functional require-
ments in each group. In a real life problem the
number of requirements and the number of variables
will be high and a way of storing and managing all
this information is required. Any FD&T tool suita-
ble for the CE environment should provide all of
these facilities.
FD&T requires frequent use of different types of
data which is catered for in FDT in form of a database.
The accessibility of the database from any part of the
software is of enormous help to its user. The upgrading
facility of the process capability data to reflect the
capability of actual manufacturing processes being
used is another plus.
FDT is PC-based and has an attractive GUI which
makes it very easy to use. It is a much simpler tool than
those available commercially. It does not require a
high level of technical knowledge, thus is suitable for
all members of a CE team, especially the non-tech-
nical members. It produces fast results, indeed almost
instantly, after entering required input data. It provides
a ‘what-if’ analysis facility for rapid evaluation of
different design alternatives. A number of error avoid-
ance measures are built into the software which pre-
vents the user from making any error in the first place
and if any error is made its step back facility allows
easy correction. It allows the user to save the project
data so that the user can come back to it later. It gives
attractive print-outs (both in graphical and text form)
which are useful for presenting results.
9. Concluding remarks
Evaluation of the prototype software indicated
that it can be a useful tool for solving FD&T
188 M.N. Islam / Computers in Industry 54 (2004) 169–190
problems, though its interface needs some improve-
ments. Although the prototype software was not
evaluated in a CE environment, the evaluations
results indicate that it could be an effective tool
for solving FD&T problems in a CE environment.
The evaluation results of the prototype software
presented in this paper are based on qualitative
evaluation only which highlighted some problems
areas. These problem areas should be further inves-
tigated through quantitative evaluation. Finally,
copies of the prototype software should be made
available to the members of the CE team for evalua-
tion, and the feedback should be incorporated into
further refinements.
Acknowledgements
The work presented in this paper was carried out
in the School of Mechanical and Manufacturing
Engineering, University of New South Wales,
Australia under the supervision of Dr. L. E. Farmer.
The author would like to thank Dr. Farmer for
his input and the Department of Employment, Train-
ing, and Youth Affairs, Government of Common-
wealth of Australia, for their financial support
through the provision of an Australian Postgraduate
Award.
References
[1] L.E. Farmer, Function Oriented Dimensioning Enhances Con-
current Engineering Performance, Proceedings of ACME’93,
I.E. Aust., 1993.
[2] R.G. Wilhem, S.C.Y. Lu, Tolerance synthesis to support