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Procedia CIRP 00 (2023) 000–000 www.elsevier.com/locate/procedia
56th CIRP Conference on Manufacturing Systems
Multi-operation blank localization with hybrid point cloud and feature-based
representation
Tam´
as Csertega,b,, Andr´
as Kov´
acsa, J´
ozsef V´
anczaa,c
aEPIC Centre of Excellence, Institute for Computer Science and Control (SZTAKI), E¨otv¨os Lor´and Research Network, Budapest H-1111, Hungary
bDoctoral School of Informatics, ELTE E¨otv ¨os Lor ´and University, Budapest H-1117, Hungary
cDepartment of Manufacturing Science and Technology, Budapest University of Technology and Economics, Budapest H-1111, Hungary
* Corresponding author. E-mail address: cserteg.tamas@sztaki.hu
Abstract
Sustainability objectives, including the endeavor to reduce waste, energy consumption and machining effort gave rise to the near net shape (NNS)
machining concept, which requires the initial rough blank to be as close to the final machined product as possible. Nevertheless, the opportunity
of savings in material, energy and effort come with a risk of manufacturing scrap even in case of a very small geometrical error of the blank. This
issue is addressed by blank localization, i.e., the act of placing the final machined product in the geometry of the rough blank. Multi-operation
blank localization was proposed recently to exploit tolerances in the product design to compensate potential geometrical errors of the blank. It
places each feature group, machined together in the same operation, separately in the blank. When tolerances connecting different feature groups
allow, these feature groups can be moved slightly according to the measured actual blank geometry. This paper proposes a novel multi-operation
blank localization approach that models the rough blank as a free-form geometry, capturing all possible geometrical errors, whereas represents the
final product using a feature-based model. The problem of blank localization for minimizing tolerance errors while leaving sufficient allowance is
formulated and solved as a convex quadratically constrained quadratic program (QCQP). In a case study from the automotive industry, it is shown
that the proposed multi-operation approach outperforms earlier methods that handle the product as a single solid geometry.
©2023 The Authors. Published by Elsevier Ltd.
This is an open access article under the CC BY-NC-ND license (http://creativecommons.org/licenses/by-nc-nd/4.0/)
Peer-review under responsibility of the scientific committee of the 56th CIRP Conference on Manufacturing System.
Keywords: blank localization; free-form machining; point clouds; quadratic programming; optimization
1. Introduction
This research was motivated by the concept of near net
shape machining, which aims to improve the sustainability and
cost efficiency of subtractive manufacturing techniques by pre-
shaping the blank as close to the final product geometry as pos-
sible. This reduces material use and machining effort, and there-
fore, energy consumption and manufacturing costs. Yet, it also
implies that upon even a minor, within-tolerance deviation of
the blank, the machining process parameters may have to be
adjusted to the actual blank geometry to receive a final product
that complies with the design specifications.
Workpiece localization (or workpiece referencing) has al-
ways been an engineering problem to be solved as part of sub-
tractive machining processes; it involves locating the to-be-
machined workpiece in the workspace of the machine. In the
early days of machining, contact-based solutions were the only
available methods and those are still a popular choice, even in
combination with modern production technologies like additive
manufacturing [6]. Non-contact methods based on vision sys-
tems [7] or 3D measurements [2,13,16] are popular because of
their versatility, speed and high accuracy.
The problem of reconstructing the product geometry from
point cloud data is a classical field of reverse engineering [8].
The overall procedure is typically subdivided into four basic
phases: (1) data capture using contact or non-contact measure-
ment methods, (2) pre-processing including noise filtering and
registration, (3) segmentation and fitting of surface models by
finding the parameters that match the measurements the best,
and when required, (4) the creation of the CAD model (e.g.,
stitching the fitted surfaces together using appropriate blend-
ing surfaces). Current challenges in feature recognition include
identifying the underlying part or surface function in addition
to mere geometry [11], as well as the recognition and classifi-
cation of potential geometrical defects [10].
Blank localization is a special case of workpiece localiza-
tion that focuses on ensuring sufficient machining allowance
2212-8271 ©2023 The Authors. Published by Elsevier Ltd.
This is an open access article under the CC BY-NC-ND license (http://creativecommons.org/licenses/by-nc-nd/4.0/)
Peer-review under responsibility of the scientific committee of the 56th CIRP Conference on Manufacturing System.
T. Cserteg et al. /Procedia CIRP 00 (2023) 000–000 2
for the subtractive process. It can be described as placing the
nominal geometry of the machined part or its features entirely
inside the actual blank geometry. To ensure that allowance is
uniformly distributed along the surface of products with com-
plex shapes, [15] proposes an iterative workpiece localization
process that utilizes rotational and translational registration ma-
trices. Other objectives for maximizing allowance include least
squares, minimax and maximin criteria [5,9,14].
All the above papers place the entire final product in the
blank as a single solid geometry. The idea of placing individ-
ual machining features separately, while considering the di-
mensional tolerances between them, was originally proposed
in [3], and elaborated further in [4]. This approach, called multi-
operation blank localization can achieve more robust manufac-
turing processes by achieving a higher machining allowance.
In [4], the authors focused on applications where the challenge
was compensating the deviation of the feature positions on the
blank, and accordingly, actual blank geometry could be de-
scribed using perfectly shaped features. Compared to that, the
main novelty of the current approach is applying a point cloud
characterization of the blank geometry, which allows compen-
sating local geometrical errors of the individual features as well.
This paper is structured as follows. In Section 2, the optimal
blank localization problem is defined formally. The proposed
solution approach, including geometrical models and computa-
tions, as well as the mathematical model for finding the optimal
placement of the machined features are presented in detail in
Section 3. First experimental results for a sample automotive
component (see Figure 1) are presented and discussed in Sec-
tion 4, whereas conclusions are drawn and directions for future
research are proposed in Section 5.
2. Problem statement
The objective of the blank localization problem is placing
the final product, characterized via its machined features, in the
the actual blank geometry. This must be performed by consid-
ering the precise shape of the blank, the allowance between the
machined features and the blank, all dimensional tolerances be-
tween machined features or rough surfaces, as well as the struc-
ture of the NC code used during machining.
The actual geometry of the blank is captured by a point
cloud, which can be partitioned according to machined features:
each measured point of the blank surface must be either as-
signed to the machined feature that removes the given surface
area from the blank, or classified as unmachined surface.
The final product is created from the blank by establishing
a set of machined features. Face and hole features, and cor-
respondingly drilling and face milling are considered in this
study. The final product conforms to the design specifications
if the placement of every feature satisfies the following two cri-
teria. First, every machined feature must be placed entirely in-
side the blank, leaving sufficient machining allowance between
the rough surface of the blank and the final machined feature
surface to ensure proper surface finishing even in case of poten-
tial errors during measurement and machining. The allowance
Fig. 1. Sample workpiece machined on four sides by four operations, with 10
drilled holes and 10 machined face (2 of 4 part zeros are shown).
for a given feature is defined as the smallest distance between
the machined feature surface and a measured point assigned to
that feature. Second, all dimensional tolerances must be satis-
fied. In addition to dimensional accuracy, these tolerances are
also important because they ensure the desired fit with other
products. Each dimensional tolerance defines a minimum and a
maximum distance between two notable points, both of which
can be either a feature point of a machined feature (placed dur-
ing blank localization) or a point on the rough surface of the
blank (given in the input). Tolerances between two points on
the rough surface can be disregarded, since the solution of the
blank localization problem has no impact on the satisfaction of
those tolerances.
Machined features are created using a given CNC code.
The code consists of two major sections: (1) the definition of
the machined features w.r.t. a local reference frame, and (2)
the location of those reference frames called part zeros in the
workspace of the machine. Any modification of the first sec-
tion is possible only with the permission of the customer after
extensive quality assurance procedures. At the same time, the
adjustment of the part zeros is regarded as a safe modification
of the CNC code, which can be performed whenever needed for
achieving a final product that conforms to design specifications.
In this paper, an operation is defined as machining the group of
features assigned to the same part zero.
Hence, formally, solving the blank localization problem con-
sists in computing the position of the part zeros in the CNC code
in such a way that the given lower bound on the machining al-
lowance, as well as all dimensional tolerances are satisfied. The
objective is minimizing the average tolerance error over all di-
mensional tolerances, where an error of 0% corresponds to the
center, and 100% to the limits of the tolerance interval. The fol-
lowing assumptions are made:
•A product defined by machined face and hole features, as
well as unmachined blank surfaces is considered.
•The nominal geometries of the rough and machined fea-
tures are available.
•Actual blank geometry is characterized by a measured
point cloud, where each point can be assigned to a feature
or classified as unmachined rough surface.
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T. Cserteg et al. /Procedia CIRP 00 (2023) 000–000 3
•Each machined feature is assigned to a part zero in the
CNC code.
•The rotation of each part zero is fixed w.r.t. the workpiece
datum frame. The axes of the machined holes, as well as
the surface normals of the machined faces are parallel to
the zaxis of the corresponding part zero.
•All tolerance requirements can be encoded into the form
of dimensional tolerances that prescribe a minimum and a
maximum distance between the feature points of two ma-
chined features, or the feature point of a machined feature
and a measured point on the blank.
•The only allowed modification of the CNC code is the
adjustment of the part zeros.
A further assumption is that a calibrated machine model is
available, thus the geometric transformation between the lo-
cal workpiece coordinates and machine workspace coordinates
is available. Consequently, the optimization problem can be
solved independently of the machine in the coordinate frame
of the workpiece datum, which is defined as a physically or vir-
tually measurable point on the workpiece where the workpiece
and its fixture make contact.
3. Solution approach
This paper proposes an approach whose application takes
place in two different stages of the product life cycle. In the
preparation stage, once for each new product, a machining cell
model is built and calibrated, involving the machine, the fixture,
and the fixture-workpiece relation. The feature-based product
model is constructed, including machined features (Section 3.1)
and tolerances (Section 3.3). Finally, the process of blank mea-
surements up to the segmented point cloud representation is
planned (Section 3.2).
In the production stage, once for each lot of blanks or each
individual workpiece, the blank is measured and the resulting
point cloud is processed. The mathematical model of optimal
blank localization is constructed automatically from the mea-
sured data and solved (Sections 3.4 and 3.5). Finally, the com-
puted part zeros are applied on the machine and the workpiece
is machined.
3.1. Feature-based representation of nominal geometry
Afeature-based model for the nominal blank and the final
product geometries is employed. The current implementation
supports two types of machining features: holes and faces. The
machined hole feature refers to the cylindrical surface of the
hole. If the front face of the hole needs to be machined as well,
then it is represented by a separate face feature. In order to re-
flect the characteristics of 3D and 4D machining centers, it is
assumed that the surface normals of the faces, as well as the
axes of machined holes are parallel to the zaxis of the corre-
sponding part zero, and the positive zdirection points outwards
from the product geometry.
Each feature can have two states, a rough and a machined
state. The rough state on the blank is produced with a non-
subtractive shaping process (e.g., casting, forging, or 3D print-
ing), and it is characterized by a nominal geometry (e.g., draw-
ing or CAD model) that describes its ideal shape. After the pro-
duction of the blank, the actual geometry of the rough feature
can be reconstructed by appropriate measurement techniques,
resulting in a point cloud representation. The machined state of
the feature describes the desired geometry on the final product,
which is specified by the CAD model and the CNC code used
for machining.
Regarding the states actually taken by each feature, the fol-
lowing three cases are possible: (1) the feature has a pre-shaped
surface on the blank and it must be machined, i.e., it takes both
a rough and a machined state; (2) the feature does not have a
pre-shaped surface, but it must be machined, i.e., it takes only
the machined state; or (3) the feature is shaped on the blank di-
rectly to its final geometry, i.e., it does not have to be machined
and it takes only a rough state.
3.2. Point cloud representation of actual rough geometry
While the nominal geometry of rough features can be de-
scribed by the feature-based model with perfect geometrical
shapes, their actual geometry can deviate from this ideal model.
The actual geometry is captured by a point cloud representa-
tion. In order to assign individual points to the given rough
features, the point cloud is filtered and segmented by exploit-
ing the known nominal geometry. The nominal geometry of the
rough blank may differ from the machined geometry, as in the
case of casting, when cast holes are cones, while the drilled
holes are cylinders. As the nominal rough geometry is only used
for the point cloud segmentation, this difference does not im-
pact later stages of the process. For each feature, points around
the surface of the nominal geometry are searched for. For hole
features, points that are within a ±ϵband of the cylindrical or
conical surface are assigned to the rough geometry of the fea-
ture. For face features, a bounding box is considered around the
Fig. 2. Measured point cloud segmented by features. Points associated with
holes (respectively, faces) are displayed in green (red). Two operations on two
different sides of the workpiece are shown: the first involves one face and one
hole, while the other includes five holes and four face features.
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T. Cserteg et al. /Procedia CIRP 00 (2023) 000–000 4
plane with well-chosen edge lengths. The edge lengths and the
value of ϵneed to be specified manually.
Commercially available measurement systems often readily
provide a processed, triangulated mesh representation of the
blank. This mesh can be exploited for refining the assignment
of points further by comparing the surface normals of the tri-
angles to the nominal geometry. A given point on the mesh
is included in the partition if the surface normal of the mesh
and the nominal geometry are within an αangle band. This
method is inspired by the compatibility measures used in the Ef-
ficient RANSAC algorithm [12]. The results of assignment for
the sample product are shown in Figure 2, where the segments
of the mesh corresponding to individual features provided by
the measurement system are displayed.
3.3. Dimensional tolerances
Dimensional tolerances are defined on the 3D distance be-
tween the so-called feature points of two features. They are usu-
ally defined between two machined features, while occasionally
between a machined and a rough feature.
For machined features, the location of the feature point is de-
termined during the solution of the blank localization problem.
The feature point for a machined hole is the intersection of its
axis and front face, whereas for a face, it is an arbitrary point in
the plane of the face.
In contrast, the location of the feature point of a rough fea-
ture is fixed on the blank. The method for computing the loca-
tion from the actual geometry is defined by industrial standards
according to the type of the feature and the tolerance. In the
case study presented in this paper, the feature point of rough
faces is computed as the center of gravity of the corresponding
point cloud segment.
3.4. Machining allowance
Machining allowance, δ, is the smallest distance between the
points of a rough feature and the corresponding (nominal) ma-
chined feature surface. Accordingly, allowance is defined only
for features that take both a rough and a machined state. To
lighten the computational burden on the solver, it is sufficient to
consider points of the rough surface that, for some values of the
part zeros, may become the closest points, and therefore, define
an active constraint in the optimization model.
For face features, by the convention on the direction of the
zaxis and the surface normal, the single relevant point is the
one with the lowest zcoordinate. Since the direction of the z
axis is known in advance, the point can be chosen during pre-
processing.
For hole features, the allowance equals the distance between
an assigned point and the cylindrical surface, which is always
perpendicular to the axis of the hole. This axis is parallel to the z
axis of the part zero. Consequently, the allowance can be calcu-
lated in the xy plane of the part zero. Moreover, it is easy to see
that only the points located on the convex hull in the xy plane
can define active constraints. Accordingly, the set of points can
be reduced to those on the convex hull in xy. This procedure is
visualized in Fig. 3. These filtering steps are performed before
solving the optimal blank localization problem.
3.5. Optimal blank localization
With a given segmented and filtered point cloud for describ-
ing the actual blank geometry and a given feature-based model
of the final product, the optimal blank localization problem can
be formulated as a convex quadratically constrained quadratic
program (QCQP) as displayed in Fig. 4. The notation is defined
in Table 1, where vectors and matrices are highlighted with bold
font, and abbreviation hv denotes a homogeneous vector.
The objective (1) is to minimize the average tolerance er-
ror, relative to the center of the tolerance field for each dimen-
sional tolerance. Constraint (2) computes the distance between
the two feature points connected by the dimensional tolerances.
Depending on the feature states, either the position of the ma-
chined feature point (defined w.r.t. the corresponding part zero
in the CNC code, and then transformed into the workpiece da-
tum frame) or the rough feature point (given directly in the
workpiece datum) is considered. The objective function in itself
does not guarantee that all tolerances respect their lower and
upper bounds; hence constraint (3). Allowance is calculated for
each point in the segment assigned to a rough feature. There-
fore, in equation (4), the distance of a point and the correspond-
ing machined feature point is calculated. The distance vector is
computed in the part zero coordinate frame of the feature, be-
cause then the radial and axial distance, and subsequently the
allowance can be calculated easily. For hole features, the radial
distance is calculated from the xy distance by constraint (5),
and then the machined radius is subtracted to ensure appropri-
ate allowance (6). For face features, the axial distance must be
greater than the allowance (7).
All constraints of the above model are linear, except for
equality (5), which is a convex quadratic constraint. This is
thanks to the known rotation matrix Rpof the part zeros. Ac-
cordingly, the proposed optimization model is a convex QCQP,
which can be solved efficiently with existing solvers in the
problem size relevant in industrial applications. Although this
QCQP is structurally similar to the model presented in [4], a
Fig. 3. Filtering the points assigned to a hole feature. The green surface con-
tains the points originally assigned to the rough hole feature. Black dots are the
projection of those points into the xy plane. The red polygon is their convex
hull. The gray disk is the projection of the machined hole.
4
T. Cserteg et al. /Procedia CIRP 00 (2023) 000–000 5
Minimize X
t
2
N
At(et)−b+
t+b−
t
2
b+
t−b−
t
(1)
subject to et=
Tp(f1)·vM
f1if s1=1
vR
f1if s1=0
−
Tp(f2)·vM
f2if s2=1
vR
f2if s2=0
∀t=(f1,f2,s1,s2) (2)
b−
t≤At(et)≤b+
t∀t(3)
vM
f−T−1
p(f)·vQ
q=dq=
xd
q
yd
q
zd
q
1
∀f∈H∪F,q∈PC f(4)
(xd
q)2+(yd
q)2=(dxy
q)2∀f∈H,q∈PC f(5)
dxy
q−rM
f≥δmin ∀f∈H,q∈PC f(6)
−zd
q≥δmin ∀f∈F,q∈PC f(7)
Fig. 4. QCQP model of the blank localization problem.
Table 1. Notation.
Indices, sets and functions
fFeature index
tTolerance index
qPoint index
sFeature state: rough (s=0) or machined (s=1)
p(f) Part zero index of feature f
At(.)Projected length of a vector along the direction of tolerance t
[mm]
HSet of hole features that are present on the blank (rough state)
and must be machined (machined state)
FSet of face features that are present on the blank (rough state)
and must be machined (machined state)
PC fSet of points from the point cloud assigned to feature f
NNumber of tolerances
Parameters
δmin Minimum machining allowance [mm]
vR
f
Feature point coordinates of rough feature fw.r.t. the work-
piece datum [hv, mm]
vM
f
Feature point coordinates of machined feature fw.r.t. the cor-
responding part zero [hv, mm]
vQ
q
Coordinates of point qof the point cloud w.r.t. the workpiece
datum [hv, mm]
rM
fRadius of hole feature fin the machined state [mm]
b−
t,b+
tLower and upper bounds of tolerance t[mm]
Variables
Tp=
xp
Rpyp
zp
0 0 0 1
Homogeneous transformation matrix of part zero p
w.r.t. the workpiece datum. Rotation matrix Rpis
fixed, whereas translation values xp,yp,zpare deci-
sion variables [mm]
dq
Distance between a point qand the feature point of
its corresponding machined feature [hv, mm]
dxy
qProjected length of dqin the xy plane [mm]
et
Distance of two feature points connected by toler-
ance t[hv, mm]
substantial difference is that here, allowance is computed for
individual points of the cloud, rather than for features.
4. Experimental evaluation
The proposed approach was validated in an industrial case
study involving the machining of the automotive part displayed
in Fig. 1. Departing from a near net shape cast blank, 10 hole
and 10 face features must be machined on a four-axis CNC ma-
chine in 4 operations. The features are connected with 3 rough-
machined and 18 machined-machined tolerances. Most of the
tolerances are defined between the axes of two machined holes
and a typical value is 60 ±0.2 mm.
Point cloud measurements were taken using a Scantech 3D
laser scanner with resolution up to 0.025 mm. The scanner
produced a point cloud with 964630 points. The diameter of
the point cloud was 150.47 mm. Parameters ϵ=0.1 mm and
α=10◦were used for classification, which resulted in 390-
14478 points per feature, whereas the remaining 895244 points
belong to unmachined surfaces, irrelevant for blank localiza-
tion. Filtering for the relevant points led to 43-239 points for
each hole feature, and a single point for each face feature. The
involved optimization problem had to be solved for these alto-
gether 946 relevant points for the 20 features.
The blank localization approach was implemented in Ju-
lia [1], using FICO Xpress 9.0 as a QCQP solver. Solving this
problem to proven optimality required 0.14 seconds of com-
putation time on a laptop computer with Intel i7-1165G7 2.80
GHz CPU and 16 GB RAM under Windows 11.
Experiments investigated the performance of three different
approaches to solve the blank localization problem. The con-
ventional solid approach places the final product in the blank
as a single geometry. The sequential multi-operation method
determines the applicable part zero for each operation one by
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T. Cserteg et al. /Procedia CIRP 00 (2023) 000–000 6
Table 2. Experimental results.
Average tolerance error
Min. allowance Solid Sequential multi-op Integrated multi-op
0.025 mm 3.4% 12.5% 2.1%
0.050 mm 4.6% - 2.3%
0.068 mm 5.7% - 2.5%
0.100 mm - - 16.1%
0.120 mm - - 35.3%
one, considering the tolerances that connect the actual group
of features to previously placed features. Finally, the proposed
integrated multi-operation approach computes the optimal part
zero for every operation in one computational step.
The results are presented in Table 2, where different rows
correspond to different minimum allowance values, while
columns display the tolerance error achieved by the given
approach. A dash ’-’ indicates that the approach could not
find a feasible solution for the given bound on the allowance.
The classical solid approach could solve the problem with
at most 0.068 mm allowance, and led to a tolerance error
of 3.4-5.7%. The heuristic, sequential multi-operation method
achieved rather poor results, with at most 0.025 mm allowance
and a high, 12.5% tolerance error; this was due to fixing the
first part zeros without a proper, holistic view of the conse-
quences on later operations. Finally, the proposed integrated
multi-operation approach could not only improve the tolerance
error for each value of the allowance (2.1-2.5% for values fea-
sible with other approaches), but it could also warrant a sig-
nificantly higher allowance of 0.120 mm. The latter is particu-
larly important, as an allowance of at least 0.1 mm is desired by
the industrial partner. Obviously, better allowance comes with
worse tolerance error, which is consistent with the underlying
idea of trading tolerance for machining allowance.
5. Conclusions and future work
The paper introduced a new blank localization technique
for compensating the inevitable small geometrical deviations of
blanks. The novelty of the proposed approach lies in (1) captur-
ing the actual geometry of the blank via a point cloud represen-
tation, (2) describing the desired final product geometry by us-
ing a feature-based model, and (3) applying different part zero
correction values for groups of features machined in different
operations. It was demonstrated that the proposed approach can
be applied to real industrial problems in an automated and com-
putationally efficient way. In experiments, it resulted in 76%
higher machining allowance compared to classical approaches
that place the entire final product in the blank as a single solid
geometry. Moreover, for a given minimum allowance, the pro-
posed approach achieved 38–56% lower average tolerance error
than classical approaches.
The next step towards practical application is physical veri-
fication via machining multiple lots of the product at the indus-
trial partner. Verification will focus on establishing performance
guarantees by quantifying potential errors introduced during the
different stages of the procedure, including measurement, com-
putations, and actual machining. An important research ques-
tion is assessing the practical applicability of the two alterna-
tive techniques for modeling blank geometry: the feature-based
model that is less sensitive to certain measurement errors but
fails to capture local geometrical errors of individual features,
versus the point cloud representation that captures all fine de-
tails of the blank surfaces but can be more sensitive to noisy
measurement data.
Acknowledgements
This research has been supported by the National Labora-
tory for Autonomous Systems RRF-2.3.1-21-2022-00002 and
the ED 18-2-2018-0006 grants of the NRDIO.
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