An integrated process planning and robust fixture design system 5

81
Chapter 5
Optimal Set-up Planning




5.1 Introduction

Set-up planning is a function of both process planning and fixture design (Ong and
Nee, 1994). Its task is to determine the number and sequence of set-ups, the features to
be machined in each set-up, and the part orientation and locating features of each set-
up. The purpose of a set-up plan is to locate and fix a part in a specific manner on a
machine tool so that machining can take place according to design specifications.

Two factors have to be considered in set-up planning, design specifications and
manufacturing resources. Design specifications include workpiece geometry,
dimension, tolerance, and features which can be both functional and aesthetic.
Manufacturing resources include production requirements, available machines, cutting
tools, and fixtures. A set-up plan which considers all these factors optimally can ensure
to deliver the product with not only high quality but also high throughput rate and low
cost.

From published work, these two factors of set-up planning are treated separately. Most
research attempted to satisfy the first factor, i.e., analysis of the design specifications,
including tolerance analysis, precedence constraint satisfaction, geometric data
analysis, and tool access direction verification. The main objective of these studies is
Chapter 5 Optimal Set-up Planning

82
to reduce the locating error and minimize the number of set-ups. The second factor was
normally considered at the optimization stage in terms of cost, quality and lead time,
and under an assumption of the availability of certain machine tools.

Different set-up plans can be generated in a different manufacturing environment.
Different set-up plans may also lead to different locating methods and manufacturing
cost, and different fixture configurations can result in different locating stack-up errors
and stability. Machining accuracy and the capability of available machine tools would
need to be considered simultaneously during set-up planning in order to achieve a
higher level of optimization. An optimized set-up plan can eliminate unnecessary
machining error stack-up, improve product quality and reduce production cost.

In this chapter, an optimized set-up planning approach which considers machining
error stack-up and the capability of available machine tools simultaneously is
addressed. It is assumed that a machining environment contains several machine
resources which include 3-, 4- or 5-axis machine centers, and can be distributed and
located in different places. A tolerance cost factor, which will be applied in the case of
a stack-up, has been introduced. The strategies are achieved by minimizing a cost
model among the distributed machine resources.





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5.2 Set-up Planning System

5.2.1 Consideration of Design Specifications
Set-up planning should satisfy the design specifications, i.e., geometric, dimensional
and tolerance requirements, precedence constraint satisfaction, and tool approach
direction (TAD) verification. Product design information in a CAD model would need
to be recognized and extracted before set-up planning.

In this research, hole and plane machining features, which commonly exist on a cast
part, are considered. The heuristics used for reasoning the hole and plane features are
shown in Table 3.2 in Chapter 3. The TAD of a feature is determined by searching for
any intersection entities in the candidate direction with a ray which has a radius similar
to the cutter. If the result is negative, the candidate direction can be considered as a
TAD. Otherwise, this candidate direction should be discarded. For a hole feature, the
candidate directions are the two directions of the hole axis. For a plane feature, the
candidate direction is the direction of the face normal.

Tolerances, which represent the characteristics and relationships of features on a part,
serve as functional description of the design requirements which should be satisfied
during manufacturing processes. Tolerances can usually be classified into self-
tolerances and relative-tolerances. Self-tolerance is the tolerance reflecting the size
deviation of a feature. It is related to the operations, but not directly related to other
features. The examples are the straightness for feature B and flatness for feature A in
Figure 5.1. Both are typical casting features. The form tolerances described in Chapter
4 are self-tolerances. Relative-tolerance reflects the position tolerance in relation to
Chapter 5 Optimal Set-up Planning


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the other features, such as feature C, which is a machining feature having dimension
tolerances with A and B respectively, which are shown in Figure 5.1. The dimensional

tolerances described in Chapter 4 are relative-tolerances. Relative-tolerance can be
used to identify the locating datum of a feature. For example, in Figure 5.1, to
guarantee the dimensions of C, it is logical to use A and B as the locating datum.
Otherwise, tolerance stack-ups would arise and tolerance compression might happen.


Figure 5.1 Self and relative tolerances

Tolerance compression means a feature has to be machined with higher tolerances
compared with the blueprint values, and therefore a more accurate machining centre or
operation may be needed. Tolerance compression can happen between set-ups and
within a set-up. The tolerance compression between set-ups usually happens due to
tolerance stack-up. Figure 5.2 shows an example of how the compression of
operational tolerances happens. In Figure 5.2, dimension 10±0.10 is to be obtained
from the previous operation. To obtain dimension 5±0.05, if it is machined having B as
the base, the tolerance for dimension 10 has to be compressed to less than 0.05 by
Chapter 5 Optimal Set-up Planning


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considering the tolerance stack-up. For a process plan with multiple set-ups, this could
happen quite frequently.

For a CNC machine, no chain analysis is needed for the relative and positional
relationships between the geometry surfaces in a set-up because they can be
programmed accurately. If the specified tolerances cannot be obtained, nothing can be
done in the sequence unless a machining method or a machine tool with a higher
process capacity is adopted or a higher rate of scrap can be accepted. For example,
assuming the two dimensions in Figure 5.2 have to be achieved in a set-up. A more
accurate machining method may be used for dimension 10±0.10 comparing with

obtaining it in separate set-ups. In a multi-axis machine tool environment where
multiple operations can be carried out in a single set-up and the design datum cannot
always coincide with the set-up datum, tolerance compression would occur quite
frequently.

Figure 5.2 Tolerance compression

The compression of operational tolerances will lead to an increase of the
manufacturing lead time and production costs and should be taken into consideration
during set-up planning.
Chapter 5 Optimal Set-up Planning


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5.2.2 Consideration of Real-Time Machine Resources
For set-up planning, the application of set-up datum may vary according to different
machining environment, e.g., 3-, 4- or 5-axis machining centre, whether vertical or
horizontal. The number of set-ups and the selection of the machining features in each
set-up depend on the machine tool configuration, that is, the number of axes and the
orientation of the axes.

In set-up planning, features are grouped into set-ups according to the type of
machining centres. For a 3-axis machining centre, the machining features are grouped
based on their TADs. Features with the same TADs are assigned to the same group. In
this case, the number of set-ups is determined by the number of TADs of the
machining features. For a 4/5-axis machining centre, the machining features are
grouped based on the Tool Orientation Space (TOS) of the machining centre. Features
with TADs within the machining centre’s TOS are assigned to the same group. In this
case, the number of set-ups is determined by both the TOSs of the machining centres

and the TADs of machining features. To determine the locating features for a set-up,
the position tolerances for the machining features in a set-up are verified.

In this research, it is assumed that a machining environment contains several
machining centres which could be distributed and located in different places. Each
machine has different capabilities (rigidity, power, accuracy, etc.), schedule, tooling,
operation cost, with unique machine type, configuration, table size, main axis direction,
machine ID code and location. For a particular distributed environment, the database
also includes the information of the traveling distance between the places where the
Chapter 5 Optimal Set-up Planning


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machine resources are located. Among them, the schedules of machining centres are
very important during set-up planning. From a technical viewpoint, a set-up plan may
appear to be good, but by taking into account the schedules of candidate machining
centres, it may not be the most economical.

Machine resources are provided in a database in the managing module. A user
interface is developed to provide a way for the user to configure and update the
machining environment in real-time, i.e., the currently available machining resources
along with their capabilities, attributes and their operating schedules. It is integrated
with the database and therefore each time the user updates the manufacturing
environment using this interface, the database will be updated accordingly. The
process planning module will read information from this database when performing
set-up planning. Therefore, the set-up planning is performed with the machining
resources with real-time response, which takes into account the production schedule
and some unexpected events, such as the machine tool breakdown and an urgent job
which needs to be handled immediately.

5.2.3 Tolerance Analysis
Depending on the accuracy of the machine tool, features machined in a single set-up
can be maintained in accurate relationship with respect to the machine tool coordinate
system. This position will be lost if the part is dismounted from the machine tool and
remounted again in a different fixture. The errors in the alignment of the part and
fixture on the machine tool can be equal to or even larger than the accuracy
requirements of small-tolerance relations. As a result, the position accuracy of a
feature machined in a previous set-up can be insufficient to realize the required
Chapter 5 Optimal Set-up Planning


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accuracy in the relation to the features to be machined in the present set-up. Even in a
single set-up, when the set-up datum is different with the design datum, the required
position tolerances of a feature may not be guaranteed. It is necessary to check the
blueprint tolerances during set-up planning to ensure the set-up to be used is a feasible
one.

Case 1: Dimension datum coincides with set-up datum
If the set-up datum coincides with a feature’s dimension datum, it is not necessary to
check the tolerance for this feature. It is based on the assumption that the selected
machining process and fixturing method can guarantee the dimensions and tolerances.

Case 2: Dimension datum does not coincide with set-up datum
In this case, it is necessary to take into consideration the stack-up error. For example,
in the workpiece illustrated in Figure 5.3, the position dimensions clearly state that the
centre of the hole (a machining feature) should be at the distance X from face A and Y
from face C. Consequently, face A and face C must be used as datum to locate the
workpiece while drilling this hole. This would ensure that the hole is at the specified
distances from face A and face C. If one uses face B as a stopper, the deviation in

length X1 between faces A and B would cause inaccuracies in the position of the hole.
If length X1 is oversized by 1mm, the centre of the hole will be at (X+1) mm away
from face A. If the length X1 is undersized, the hole would shift towards face A and
would be nearer than distance X from face A. However, if location is on face A, the
hole would always be at the same distance from face A irrespective of the variation in
length X1. Similarly, the same situation will occur when locating with face D instead
of face C for dimension Y.
Chapter 5 Optimal Set-up Planning


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To satisfy the dimension requirements, sometimes a more accurate process or even a
more accurate operation has to be chosen, and it would be more expensive. To reflect
the additional cost if a higher accuracy machining process/operation is required, a
tolerance cost factor (f) is introduced, which will be applied when calculating the
machining time. Each operation can achieve a typical tolerance, and it is always within
a certain range (Figure 5.4). Machining processes operating under normal conditions
would produce parts within the tolerances as indicated in Figure 5.4 (a). Figure 5.4 (b)
indicates the ANSI B4.1 Standard Tolerances. According to blueprint tolerances
specified on a workpiece, suitable machining processes will be selected to generate the
machining features.


Figure 5.3 Tolerance chain

To calculate f, it is first assumed that the operation selection for a machining feature is
according to the lowest tolerance which this operation can achieve. For example, if
there is a hole with tolerance around 0.25mm, a drilling operation with the lowest
tolerance 0.254 as shown in Figure 5.4 is chosen for this. The tolerance range is

defined as grades, and a grade represents a cell in Figure 5.4 (a). For example, for the
drilling process, the tolerance range can be divided into four grades: grade 10 to grade
Chapter 5 Optimal Set-up Planning


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13. f is calculated based on the grade. The initial value f is set to 1. If the tolerance
jumps to a new grade, f is increased by the number of grades jumped. If the jump is in
between the grades, half a jump is used. If a selected machining operation cannot
achieve this higher tolerance, a more accurate process will be selected.








(a) Tolerance grades









(b) ANSI B4.1 standard tolerances
Figure 5.4 Dimensional tolerance capabilities of operations

(www.engineeringtoolbox.com)

Chapter 5 Optimal Set-up Planning


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5.2.4 Cost Model
One of the ultimate goals of an enterprise is to be profitable. Hence, every company
has the mandate to reduce cost and increase profit margin, which can be achieved more
effectively at the design planning stage rather than the manufacturing stage. In this
research, set-up planning is performed based on a cost model and an optimization
methodology is formulated to minimize the overall cost of machining all the features
on a workpiece. It justifies the machining overhead with machining time, and
considers the tolerance requirements simultaneously.

Depending on how the features are to be located on the faces of a workpiece, they can
be grouped into different TADs. Usually, the smallest number of TAD groups would
be the best as the cost of set-ups will be lower. However, that is not always true
because the grouping is dependent on the type of tooling used. The schedules and the
locations of different machine resources will result in different machining times thus
the manufacturing costs. A planned machine tool with a schedule requiring additional
waiting time to start work will cost more considering the wasted waiting time, and a
machine tool located elsewhere may cost more than one which is nearby, considering
the transport cost. In addition, different machine tools have different fixturing
methods, leading to different costs. For example, for a 5-axis machining centre, fewer
set-ups are needed, so the total machining time would be less. However, there may be
a trade-off between reduced machining time and a higher overhead on a 5-axis
machine. In addition, since the fixturing method is likely to be more complex, it will
cost more. Conducting tolerance analysis of a set-up incurs additional steps and this
will move up the manufacturing cost. Therefore, the cost model considers all those

factors and is a composite of: (1) machine tool overhead; (2) cutter cost due to wear
and tear; (3) fixture cost; (4) schedule-based cost per unit time; (5) set-up time cost; (6)
Chapter 5 Optimal Set-up Planning


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tool change time cost; (7) transport cost. Using this cost model as the optimization
objective function for the algorithm, feasible set-up plans with the minimum cost can
be found. The above seven cost factors are described in detail in the following.

Machine tool cost per unit time (MCP) The machine tool cost per unit time is the
summation of the operating cost per unit time and the fixed investment cost amortized
over time. It is a constant for a machine.

Cutter cost per unit time (CCP) Similar to MCP, the cost of a cutter per unit time is the
summation of the operating cost per unit time and fixed investment cost amortized
over time. It can be considered a constant for a cutter when machining the features on a
specific part with a particular material.

Fixture cost per unit time (FCP) It is the summation of the operating cost per unit time
and fixed investment cost amortized over time. Modular fixtures are considered and
used in this research for all types of machine tools.

Schedule-based cost per unit time (SCP) Schedule-based cost occurs when a machine
is needed to wait for some time to perform the operations planned. It is based on the
schedule of a machine tool.

Set-up change cost per unit time (SCCP) Set-up change is required when a machine
tool change is needed which will also require a new fixture.

Cutter change cost per time (CCCP) Cutter change is required when two adjacent
operations performed on the same machine tool use different cutters. In addition,
Chapter 5 Optimal Set-up Planning


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machine tool change may also result in cutter change. The cutter change cost incurred
between any two operations.

Transport Cost per unit distance (TCP) Transport is required when operations on the
same workpiece have to be performed on different machine tools which are located in
different places.

For different manufacturing environments, the values of MCP, CCP, FCP, SCP,
SCCP, CCCP and TCP may be different. Therefore, when performing set-up planning,
different database of the machine resources would need to be used.

A set-up plan usually contains several set-ups. Each set-up contains resources which
include a machine tool, a fixture, and different cutters to complete the machining
processes in this set-up. The cost for the tooling is calculated using the machining
times of machining the features in this set-up. The set-up change cost and the cutter
change cost is based on the change times. The transport cost depends on the distance of
the current machine to the next machine. Therefore, the cost model can be formulated
as in the following:


(5.1)

Where,




KJ
kj
Machining
kj
kj
Machining
k
Machining
ij
IJ
ij
ij
Machining
i
TfTTfT ,
TCPDNCCCPNSCCPTSCP
TCCPTFCPMCP
I
i
mncs
I
i
Waiting
i
Machining

k
K
k
k
I
i
Machining
iii




)(
Chapter 5 Optimal Set-up Planning


94
Machining
i
T

machining time for
th
i machine tool, a summation of
operations’ machining time having on this machine
Machining
k
T machining time for
th
k cutter, a summation of operations’

machining time having on this cutter
Machining
ij
T

machining time for
th
j
operation performed on
th
i machine
Waiting
i
T

waiting time for
th
i machine tool, determined by the schedule
of this machine tool
Machining
kj
T

machining time for
th
j
operation performed on
th
k cutter
ij

f

tolerance cost factor for
th
j
operation performed on
th
i
machine
kj
f

tolerance cost factor for
th
j
operation performed on
th
k cutter
s
N
number of set-ups in the current set-up plan
c
N
number of tool changes in the current set-up plan
mn
D
distance between
th
m and
th

n machine,
nminm  ,,

i
MCP
machine cost per unit time for
th
i machine
i
CCP
tool cost per unit time for
th
i machine
i
FCP
fixture cost per unit time for
th
i machine
I
number of machines selected in the current set-up plan
J
number of operations selected in the current set-up plan
K
number of cutters selected in the current set-up plan

For a specific machine, the machining time, which considers the tolerance cost factor f,
is computed by calculating and summing the individual operation times for all the
operations performed on a particular machine in a set-up plan. The individual
Chapter 5 Optimal Set-up Planning

95
operation time is estimated by computing the volume of material removed in that
operation divided by the material removal rate. The tool approach time and other
travelling time from feature to feature where no materials are removed are not
considered. The volume of material removed in an operation can be obtained from the
machining feature geometry, while the material removal rate can be computed from
tool geometry and processing parameters.

In this study, it is assumed that a machining feature can be generated in an operation
with a specific cutter. In this way, the number of set-ups can be obtained after the
completion of the set-up plan, and the total number of cutter changes is the summation
of the cutter changes in each set-up.

The distances between the locations of the machine tools and their schedules can be
obtained from the machine resource database. Cost factors can be used either
individually or collectively as a compound cost factor based on the actual requirement
and the data availability of the machine resources in a machining environment.

5.3 System Implementation
As set-up planning is a NP-complete problem, optimization techniques are commonly
employed to achieve an optimal or near-optimal set-up plan. ACO is an efficient
approach and it has been applied successfully to solve NP-complete problems. The
ACO meta-heuristic frame work describes the scheduling of several processes and is
presented in Figure 5.5.


Chapter 5 Optimal Set-up Planning

96




Figure 5.5 The ACO meta-heuristic framework

Construct solution: This process is responsible for the construction of new solutions.
This is achieved using probabilistic stepwise solution construction. The probability of
a particular solution component being added to a growing solution is based on a
combination of problem specific (heuristic) information and learned (pheromone)
information of how well this component is used in the past solutions. The exact
combination of this information and the greediness of the selection mechanism are
important implementation specific details.

Pheromone trail update and decay: Once solutions have been evaluated, they can
influence the pheromone matrix through a pheromone update process. To allow the
replacement of old information with new information, a pheromone decay process is
also employed that removes the influence of past solutions over multiple successive
algorithm cycles.

In this study, the feasibility of using the ACO algorithm is studied to address the set-up
planning problem.

Extract Problem
Information
Initialize
Heuristic Values
Construct
Solutio

n
Initialize
Pheromon
Update
Pheromone
Pheromone
Matrix
Decay
Pheromone
Chapter 5 Optimal Set-up Planning


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5.3.1 System Structure
Set-up planning starts with extracting workpiece information from the raw and final
CAD parts. A file, recording the extracted information inclusive of machining features,
tolerances, datum, etc., is generated for subsequent searching use. The extracted
information can be displayed in an interface through which users can check and
modify, and can also add other necessary information, such as form tolerances, to
certain features. Figure 5.6 shows the overall flowchart of this developed system.









Figure 5.6 Overall system flowchart

An interface which links with the machine resource database is provided. Through this,
users can check, modify and update the machining environment. In this way, the
machine resources used in the search is able to reflect the current resource status and
make the set-up planning more reliable. During the ACO optimizing process, tolerance
analysis is conducted, and the cost is evaluated for each solution based on the cost
model. Finally, an optimal or near-optimal result can be obtained.

Design Information
Start
Extract Design Specifications
Read Machine Resources
Tool Information
Machine
Resource
Database
ACO Search
Tolerance Analysis
Cost Model
End
Chapter 5 Optimal Set-up Planning


98
The extracted design information is saved in a structure as follows. The ideal datum is
the datum obtained through tolerance definition.

{Feature Name, TAD, Self_tolerance, Relative_tolerance, Operation, Ideal Datum,
Length (L), depth, Machining_time, tolerance_cost_factor}

Features can be machining features and cast features. For cast features, only
self_tolerance is saved, other attributes are set to null. The machining time is
calculated as:

)/()/( CutofDepthDepthfnLT
Machining
 (5.2)

where, L is the length of a machining feature. f is feed and n is the rotation speed. The
technical parameters other than L are taken based on the average capability of given
machine resources. The machining time of each machining feature is calculated based
on the machine resource selected for them during the set-up planning.

The machine resources are saved in a structure as:

{Machine Name, f, n, cut of depth, schedule, TOS, MCP, FCF}
{Cutter ID, CCP, Type, Radius}

Schedule indicates the available time of the machine tool. If it is zero, it means the
machine tool is available currently. If it is larger than zero, it means the machine tool is
only available at a later time. If tasks are assigned to this machine tool now, a waiting
Chapter 5 Optimal Set-up Planning


99
time is required. Each operation is performed with a cutter, and each has a unique
CCP. A planner can select suitable cutters for operations to be performed. In this
study, the machine tools are assumed to be located in different places to reflect the
distributed manufacturing environment in the real world. Therefore, if workpieces are
machined on machine tools in different locations, they have to be transported from one

place to another and transport cost will occur. The transport cost depends on the
distances (d
ij
) between the locations of machine tools. An example of the distance
matrix for n machine tools is shown in Table 5.1, where, d
ij
= d
ji
; d
ij
= d
ji
=0, if i=j.
The values of the distances in the matrix can be extracted from the database of the
machine resource.

SCCP, CCCP, SCP and TCP are saved outside the machine tool structure as they are
applied at the set-up level.

Table 5.1 Distance matrix between machine tools
M
1
M
2
M
3
… M
n

M

1
0 d
12
d
13
… d
1n

M
2
d
21
0 d
23
… d
2n

M
3
d
31
d
32
0 … d
3n

… … … … 0 …
M
n
d

n1
d
n2
d
n3
… 0

5.3.2 ACO Based Set-up Planning
The set-up planning process can be divided into three stages: preliminary set-up
planning, tolerance planning and optimal set-up planning. During the preliminary set-
up planning stage, each machining feature is assigned certain machine resource based
Chapter 5 Optimal Set-up Planning


100
on their TADs and the TOSs from the available machine resources. During the
tolerance planning stage, the machining features are grouped into set-ups based on the
machine tool assigned and their TADs, and the machining datum for each set-up is
determined. The determination is performed according to the two rules: 1) If there are
more than two machining features sharing the same ideal datum, this datum is taken as
the set-up datum. 2) If Rule 1) cannot be applied, choose the ideal datum of a
machining feature with tighter blueprint tolerances. After that, the set-ups are
sequenced. Next the blueprint tolerances of the machining features are checked based
on their ideal datum and the set-up datum, and a tolerance cost factor is generated
according to the rules described in Section 5.3.3. During the optimal set-up planning
stage, the manufacturing cost of each set-up plan is evaluated based on the cost model
described in Section 5.3.4. The set-up plan which has the least cost is taken as the final
result. This set-up planning process is adopted in the ACO algorithm which is
described as follows.


Pheromone structure
During set-up planning, a machining feature on a given workpiece is assigned to a set-
up based on its TAD, operation type, and the TOSs of machine tools, linked to a
specific operation for the processing of this feature on a chosen machine tool (M),
using a suitable cutter (T) and fixture (F), and in a particular set-up orientation (TAD).
It can be represented by the set of M, T, F and TAD. Given a particular job shop with
available machine tools, cutters and fixtures, a set of alternative operation methods can
be generated for a feature by traversing all the possible combinations of M, T, F and
TAD that can be used to perform the operation. Thus, the method to process a
machining feature can be represented as a set of feasible combinations of M/T/F/TAD.
Chapter 5 Optimal Set-up Planning


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A set-up plan can be specified as a linking of the operation methods for machining all
the features on a given part. Therefore, the pheromone dimension can be determined
by the number of the machining features. In this study, it is assumed, when a machine
tool is selected for a machining feature, its fixture is decided since a machine tool
would correspond to a particular fixture in a set-up. The cutter would need to be
selected among the available cutters. Thus, the pheromone has two levels. One is the
machine tool level which contains all the information exclusive of the cutters, and the
other is the cutter level.

Initialize Pheromone
The design information and machine resources are loaded. The pheromone dimension
is assigned accordingly and the heuristic variables on the machine level and cutter
level are initialized. Matrix structures M and T (Table 5.2 and Table 5.3) are used to
represent the pheromone values at the machine tool level and cutter level respectively.
They are initialized with a zero value and will be updated during the searching

procedure.

Table 5.2 Pheromone matrix at the machine tool level
M1 M2 M3 … Mn
M1 0 m
12
m
13
… m
1n

M2 m
21
0 m
23
… m
2n

M3 m
31
m
32
0 … m
3n

… … … … 0 …
Mn m
n1
m
n2

m
n3
0



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Table 5.3 Pheromone matrix at the cutter level
T
1
T
2
T
3
… T
n

T
1
0 t
12
t
13
… t
1n

T

2
t
21
0 t
23
… t
2n

T
3
t
31
t
32
0 … t
3n

… … … … 0 …
T
n
t
n1
t
n2
t
n3
0


Construct Solution

Solution construction is the preliminary set-up planning. Each machining feature is
taken as a region that an ant has to visit. At each region, the ant has to select a machine
tool with a cutter from the loaded machine resource. The fixture information can be
obtained from the attribute of the machine tool. Figure 5.7 presents a graph that an ant
travels. It contains eight regions, i.e., eight machining features in the design space.
Tool selection is based on the TAD of the machining feature and the TOS of available
machine tools. The TAD of the machining feature must be inside the TOS of the
selected machine tool. The cutter is selected according to the dimension and operation
of the machining feature and the radius and type of the cutter. The radius of a cutter
should be smaller than the dimension of the machining feature. The type of the cutter
should also match with the operation of the machining feature.

Refinement of Solution
The constructed solutions are analyzed at this stage. Set-ups together with set-up
datum are determined, and the set-ups are sequenced. A tolerance analysis is
conducted, and a tolerance cost factor is generated for each machining feature. A set-
up plan is generated for each solution.
Chapter 5 Optimal Set-up Planning


103
M,
T
M,
T
M,T
M,
T
M,
T

M,T
M,T
M,T
End
Start
F1
F2 F3
F4
F5
F6F7
F8
Machine
Resources






Figure 5.7 An example of traveling graph

Upon satisfying the above rules, the machine tools and cutters are selected based on
probability. The probability with which ant k on node i chooses the next node j at the
current iteration h, is according to the State Transition Rule (Dorigo et al, 1996)
equation 5.3. It is directed by both the pheromone amount and the heuristic value.

K
iijijijij
k
ij

Njhhhp 

 ,)())(()())(()(


(5.3)

where,
h: iteration index
ij

: pheromone value between nodes i and j
ij

: heuristic value between nodes i and j
ij
p
: probability to travel from node i to node j
K
i
N : nodes not yet traversed in the ant-tour thus far


where,
),1(, nji 
, n is the number of nodes. Parameters α and β are used to tune the
relative importance of the pheromone and the heuristic distance in decision making.
Chapter 5 Optimal Set-up Planning

104
The heuristic value at the machine level is determined from equation 5.4 and the
heuristic value at the cutter level is determined from equation 5.5.

)/(1
ijii
m
ij
dTCPFCPMCP 

(5.4)

i
c
ij
CCP/1

(5.5)


Evaluate Solution
The feasible solutions are evaluated based on the objective function equation 5.1
described in Section 5.3.4. The parameters in equation 5.1 are obtained as follows:

•
s
N : it is obtained from the set-up plan of each constructed solution.
•
c
N : the number of cutters selected in a solution is obtained first, and then the

tool change number is obtained.
• MCP/CCP/FCP/Distance/Schedule: these parameters are obtained from the
attributes of the machined tools.
• SCCP/TCCP/TCP: these parameters are obtained from the machine resource
database.
• Tolerance cost factor: it is obtained from the attributes of the machining feature,
which have been stored in the machining feature data structure during the
solution refinement stage.




Chapter 5 Optimal Set-up Planning


105
Update Pheromone
After each iteration, an updating process is triggered if there are better solutions in the
population which is used to store the global best results. The pheromone values are
updated at both the machine level and the cutter level. It is based on equation 5.6.

)(1)(),()()1( hChhhh
S
s
s
best
ij
best
ij
ijij




(5.6)

where, S is the number of solutions at the current iteration that are better than anyone
in the population, C
s
is the cost of a solution, and ρ is the pheromone evaporation rate.


5.4 System Performance

5.4.1 Illustration of an Example Part
An example part is presented in this section to demonstrate the proposed approach and
present the test results. It is a simplified front knuckle of an automotive chassis system,
and it is cast followed by machining. Figure 5.8 gives the details of the cast and
machined parts. The input CAD model, which contains the dimensions and tolerance
information, is constructed using Inventor
®
.