Formal Modelling of Process Planning in
Combined Additive and Subtractive Manufacturing
Behnood Afsharizand 1, Aydin Nassehi 1, Vimal Dhokia 1, Stephen T. Newman 1
1
Department of Mechanical Engineering, University of Bath, BA2 7AY, Bath, United Kingdom,
Tel.: +44(01225)384049, E-Mail: B.Afshari@bath.ac.uk
Abstract
Decision-making models for manufacturing technologies are becoming increasingly complex due to on-going rapid
developments in additive and subtractive (Addtractive) manufacturing. Decision-making in manufacturing technologies
should be based on machine and resource capabilities. Currently, multi-process manufacturing models have many
shortcomings when describing machining capabilities, and in some cases, modelling approaches used in decisionmaking are ambiguous and poorly constrained. In this research, a formal modelling approach is proposed to facilitate
modelling of machining capability and associated Addtractive operations. This mathematically based formal method
allows system properties to be described in a well-defined manner. The ISO-standardised Z notation (named after
Zermelo-Fraenkel set theory) has been utilised to build a state-oriented formalism model for machining capabilities and
associated operations.
Keywords:
Manufacturing decision-making; Machine capability; formal modeling
1
INTRODUCTION
Decision-making has been emerged as a dominant factor in
process planning of combined additive and subtractive
manufacturing (Addtractive manufacturing) for achieving the goal of
providing products in a shorter time and at a lower cost. Addtractive
terminology has been used to categorize a subset of manufacturing
processes and resources that have capabilities beyond those in the
previous generations [1,2]. Developing new technologies for layered
manufacturing known as rapid prototyping (RP) is now becoming
evident that the classic manufacturing technologies are not capable
of coping shortages with industrial needs. Process planning for
Addtractive manufacturing requires detail investigation on a
machine’s capability profile to corporate manufacturing
technologies, which minimize cost and time of production.
Currently, there is no model that exists, for modelling multi-process
manufacturing steps by describing the machining capabilities
constraints. The modelling approaches should be capable of
describing machining status in each single operation
comprehensively to facilities decision-making modelling considering
resource limitations. Ambiguous and poorly defined models
suppress decision makers finding the best machining scenarios.
The informal methods such as data flow diagram and CASE tools
provide few criteria to determine whether a design is correct, or to
choose the best of several plausible designs. Formal method’s were
developed in the late 1970’s by Oxford University programming
research group, and was used for the first time to specify the IBM
customer information control system (CICS). Also, a qualitative
survey was conducted on twelve industrial applications (such as an
airline collision avoidance system, ship’s engine monitoring system
and altitude control of the satellite), which developed formal
methods, shows satisfaction results [3]. Formal method’s is the
area of computer science that is concerned with the application of
mathematical techniques to the design and implementation of
complex systems [4]. The data model, which is built by formal
techniques uses the Z language [5], and is comprehensive and
precise enough for defining the system components. In this paper, a
formal model has been developed for decision-making in
Addtractive manufacturing systems followed by two case studies
presenting the fitness of the model.
2
PROCESS PLANNING IN MANUFACTURING SYSTEMS
Process planning is the decision making process that decides on
how to manufacture a part according to its design specification and
the selection of parameters and necessary production methods in
order to transform raw material into a part. A process plan specifies
the machines, setups, tool specifications, operation time estimates,
etc. required to convert raw material into a finished part [6]. In
effective process planning and scheduling, the trade off among
cost, time and quality should be taken into consideration [7].
Through manufacturing organisations considering Addtractive
manufacturing, there is the possibility to compress the time to
manufacture and inspect products compared to today’s processes.
Figure 1 shows a simple comparison of the current manufacturing’s
schema towards this Addtractive vision.
Figure 1: Manufacturing shifts towards multi process production
There have also been a number of developments following
international standards/initiatives for facilitating the process
planning within manufacturing systems [8]:

ISO14649 [9] informally known as STEP-NC: uses highlevel hierarchical manufacturing information model for
process planning and CAD/CAM interoperability.

ISO10303-AP238: [10] links between ISO14649 and
application interpreted model for broader part definition.
5th International Conference on Changeable, Agile, Reconfigurable and Virtual Production (CARV2013), Munich, Germany 2013

ISO6983 [11] and RS274D [12]: uses low-level machining
instructions for G-codes generation.
The STEP-NC standards of ISO 146489 and AP238 consider
different processes based on the same data schema, and the
authors believe that this could be a valuable starting point for multiprocess manufacturing and Addtractive manufacturing. In this
paper, decision-making within process planning has been
considered in regards to the Addtractive concept introduced above.
2.1
Additive and subtractive process planning
Subtractive technology deals with material removal manufacturing
techniques. For operations using this technology, material is
removed from a single workpiece, forming a new workpiece with
examples including metal cutting (i.e. milling, drilling, turning etc.).
Additive technology deals with operations where either material is
added to an existing workpiece or deposited to form a new
workpiece. (i.e. fused filament fabrication, selective laser sintering,
etc.). The well-defined integration of additive and subtractive
techniques optimizes the resources utilized during manufacturing
time. Decision-making for Addtractive production of a part considers
manufacturing capabilities for the part geometry using both additive
and subtractive techniques. The modelling approach used for
formulating Addtractive technology has to be comprehensive and
precise enough for defining the complex manufacturing process.
For instance, Figure 2 shows the possible combinations of additive
and subtractive manufacturing techniques used for machining a
designed test part.
upper level classes. In this research formal methods are used to
construct a new type of model for Addtractive manufacturing
processes.
3
USING Z NOTATION FOR PROCESS PLANNING
Formal methods are mathematical based methods for describing
system properties in a well-defined and non-ambiguous manner [5].
In this research Z has been selected as the formal method of choice
as it allows some aspects of a system to be defined without it being
necessary for the other aspects to be specified in any manner. It is
also noteworthy that the Z notation has been standardized as
ISO/EIC 13568 [19]. Z notation forms an abstract and analytical
description of the system under study. The abstract model built
based on the formal specification can be checked with peers,
clients and against other formal specifications and standards to
make sure that the problem and specifications are correct. It is
possible to check that solution against the formal specifications to
make sure that the proposed solution will correctly solve the
problem. If not, the abstract problem model and the methods can be
changed until the solution meets the specifications. Formal
declarations such as Z are distinguished from less formal notations
such as data flow diagrams [20] because they have a formal
semantics that assigns a precise meaning to any formula in the
declaration [5]. The fundamentals of Z, as required to enable the
logic of this research to be understood can be summarised as
follows:
  is used to denote there is a unique object exists with a certain
property.
  is used to denote that a property holds true for at least one
object of a certain type.
 , and \ are used to denote union, intersection and
subtraction respectively.
  is used to show that set is a subset of another set.
  is used to denote a power set. The power set of a given set,
contains all of the subsets of that set as elements.
  is used to show occurrence of an object in a certain type.
  is used to denote changes in the state of a system.
Figure 2: Possible combinations of additive and subtractive
manufacturing techniques
The optimum selection of different manufacturing scenarios has to
be done in an innovative mathematical formulation considering the
complexity of Addtractive process planning and the diversity of
manufacturing background [13].
2.2
  is the set of all total functions from one set to another.
Every entity in Z forms a certain type and it is only possible to
compare entities from the same type. For defining a new type in
correct declaration, writing its name between square brackets has
been used. The framework developed for the Addtractive process
with formal methods is depicted in Figure 3. A CAD model of the
part to be manufactured represented within the abstract data model.
Analytical modelling of process plans
Previous studies in building analytical modelling for process
planning has been done in several layers, which each layer
representing different process knowledge about the specific
manufacturing technologies [14,15]. Others have adopted
prototype-oriented definitions for multi process manufacturing,
which uses hierarchical modelling techniques [16,17]. Some
researchers have limited the multi process manufacturing definition
to the combination of various material removal technologies [18].
Process planning for manufacturing needs to be defined clearly and
comprehensively, as a system with inter-connected classes. Each
class represents information about the process retrieved from the
Figure 3: Formal model development for Addtractive
The abstract model constructs with the geometric representation of
the solid model. An extended version of the abstract model requires
information about machining capabilities and manufacturing
technologies. After analysing all combinations of additive and
subtractive techniques, the best scenario for manufacturing the part
will be selected at final stage.
3.1
Schema structure in manufacturing
The new primitives that are used for creating the machining
capability are machine and resources. Machine is a type of machine
tools use for manufacturing a part. The single machine tool may use
different manufacturing techniques for producing finished parts.
Resources are defined as tools, auxiliary devices, human expertise
and everything else apart from the raw workpiece and machine tool
that are required for performing a manufacturing operation.
To avoid the unstructured application of Z language, which results
in a description that is difficult to understand, a schema language
has been used. Each schema includes a constraint on the object
that is being defined. For instance, the format of a schema definition
expressing that “for every object x of type s the predicate p holds
true” is as follows:
3.2
Formulating additive and subtractive manufacturing
A manufacturing process is a sequence of operations that can take
place on a set of workpieces, which are ultimately transformed into
another set of workpieces. So, an effective operation on the
workpiece and process is defined as below:
Before building a model for subtractive and additive process, some
primitives need to be defined. The only parameter that changes
during machining a solid model is a set of Cartesian points. The
points are influenced by each sequence of operations and
constructed new shape. So, a Cartesian point’s basic type, which
presents the actual cutting locations, has been defined as follows:
Consequently, The workpiece should be expressed as a solid
shape, which is defined by all its subsets of points. Completion of
any manufacturing techniques may result in a workpiece changing
to another workpiece.
Finally, the optimum scenario for producing a part is determined by
the lowest machining time. So, the following Z notations identify
optimum process:
Subtractive manufacturing has been perceived as a cause of
changing the workpiece into a new workpiece while cutting the
material out of its surface. So, changes in workpiece and Cartesian
points type including constraints may be defined as follows:
4
Consequently, the additive process may be defined as it shown
below:
CASE STUDY ONE
The designed test workpiece has been tried out for the fitness of the
approach. The workpiece has been designed so as to find the best
scenario of machining with the efficient process planning. The
optimum scenario is the one, which consumes less machining time.
Machining resources have been neglected in this research for
simplicity, but it will be possible to extend the abstract model for
more details. Figure 4 shows the design used for model evaluation.
The test workpiece includes a positive cylinder and a negative
pocket. The model formulation has been done for each feature
based on the Cartesian coordination position in that shape. The
formal definition of the workpiece has been used for the designed
test piece.
5
CASE STUDY TWO
The second case study has been designed with 4 different
machining operations for the multi-feature test workpiece presented
in Figure 5. The finished part includes one open slot, one closed
pocket and two steps on each side. Similar to the previous case,
machining resources and machining technology have been
neglected for simplicity, but it will be possible to consider those by
adding more details to the abstract model.
Figure 4: 3D view of the designed test piece
Regardless to the additive technology used for machining the
cylinder, the Cartesian points are transferred to their new position
for shaping a cylinder. So, the formal definition of the additive
process has been defined as follow:
Figure 5: 3D view of the test workpiece
Similarly, milling the pocket causes the same changes in the
negative direction.
A similar procedure to the previous case study has been formalized
for modelling designed artefacts. Regardless of the additive
technology used for manufacturing the block, it has been assumed
that the Cartesian points are transferred to their new position for
shaping the block, and other features are to be machined out of the
block in next steps. So, the formal definition of the additive process
has been defined as follow:
Since each line consists of an infinite numbers of points, the length
and width of the pocket has been defined as sets of points. Also,
dadd and dsub denote the height of cylinder and depth of pocket
respectively.
To demonstrate that the shape has been machined on the surface
of the block, it needs to be illustrated that created feature and
workpiece have common points. So, the last predicate added at the
end of each schema for constructing a single solid shape.
Based on the manufacturing scenario presented, the formal model
has been built for specific Addtractive operation on the workpiece.
Finally, The problem associated with finding optimized process
plans for producing a part correlated with different manufacturing
scenarios could be generated from the above schema.
Subtractive operations have been modelled by considering the fact
that finite numbers of points have been machined out of the added
block in the negative direction. So, for subtracting the open slot,
closed pocket and steps following schemas have been developed:
notation has been shown as a possible method for building an
abstract mathematical model for describing the process planning for
Addtractive manufacturing. The proposed formal framework was
logically proven with a well-designed test piece correlated with
machining capability analysis and time restrictions. This research
can be interfaced with object-oriented modelling and programming
for further extension by developing Addtractive manufacturing
technology databases for different feasible scenarios.
Machining scenario has been modelled based on the formal
specification defined by Z as follow:
8
ACKNOWLEDGMENTS
The research leading to these results has received funding from the
European Union's Seventh Framework Programme managed by
REA Research Executive Agency (FP7/2007-2013) under grant
agreement n286962.
9
Having defined suitable models to describe the geometrical
representation of the features shown in Figures 4 and 5, the next
stage of the research shall address the need to identify optimal
process plans with respect to manufacturing time. Various
mathematical techniques could be used for testing different process
sequences, and finding the optimum solution. The general
optimization problem can be defined as follow:
6
7
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DISCUSSION
The proposed formal framework has the unique ability to deal with
the complexity of the Addtractive process. However, the
mathematical model presented here was an abstract model while
real implementation of the approach needs more detailed
knowledge about the Addtractive operations itself, this process is
called refinement in Z notation. Furthermore, a quantitative analysis
needs to be done according to manufacturing capability and
process comprehension for discovering the feasibility of formal
methods. Adding more classes to the abstract model, which is one
of the benefits of using this method, may extend the presented
model. Also, a more classified model increases the appropriateness
of Z notation for being applicable in multi-process manufacturing.
CONCLUSION
The combining of manufacturing processes enables shorter delivery
times for manufactured parts, and provides greater manufacturing
flexibility. Process planning for combined additive and subtractive
manufacturing has emerged as a potential improvement of current
manufacturing techniques. Finding the best scenario for
manufacturing a part requires innovative mathematical method
covering the complexity of Addtractive manufacturing concepts. Z
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