Department of Electrical, Management and
Mechanical Engineering
Doctorate School in Industrial and Information Engineering
XXVI Cycle
-Doctoral Thesis
INTELLIGENT
MANUFACTURING SYSTEMS
Supervisor:
Candidate:
Dr. Ing. SORTINO MARCO
BELFIO SANDRO
then finding a smoother pebble or a prettier shell than ordinary, whilst the great ocean of truth lay all undiscovered before me.”
Introduction 1
1 Fundamentals of turning and milling 5
1.1 Turning process . . . 5
1.1.1 Kinematics of turning . . . 6
1.1.2 Tool geometry and nomenclature . . . 8
1.1.3 Cutting forces . . . 8
1.2 Milling process . . . 9
1.2.1 Kinematics of milling . . . 10
1.2.2 Uncut chip thickness . . . 11
1.2.3 Cutting forces . . . 13
1.3 Experimental determination of cutting forces coefficients . . . 15
2 Machining Simulation 17 2.1 State of the art . . . 17
2.1.1 Modeling of machining process . . . 17
2.1.2 Eulerian machining simulation . . . 22
2.2 Turning simulation . . . 29
2.2.1 Workpiece . . . 29
2.2.2 Tool definition . . . 30
2.2.3 Trajectory interpolation and uncut chip volume calculation 31 2.2.4 Cutting force model . . . 31
2.2.5 Experimental validation of the machining simulator . . . . 32
2.3 Milling simulation . . . 35
2.3.1 Workpiece definition . . . 35
2.3.2 Tools definition . . . 36
2.3.3 Trajectory interpolation . . . 46
2.3.4 Uncut chip volume calculation . . . 47
2.3.5 Cutting force calculation . . . 50
2.3.6 Preliminary cutting simulation test . . . 51
2.4 Conclusions . . . 59
3 Machining Optimization 61 3.1 State of the art . . . 61
3.2 Automatic part program generation and optimization overview . . 66
3.2.1 NC code generation . . . 67
3.2.2 Machining cost function . . . 67
3.3 Case study 1 . . . 69
3.3.1 Preliminary evaluation of cost function . . . 70
3.3.2 Gradient Descend optimization . . . 73
3.4 Case study 2 . . . 79
3.4.1 Preliminary evaluation of the cost function . . . 80
3.4.2 Modified Gradient Descent optimization . . . 84
3.4.3 Particle Swarm Optimization . . . 88
3.4.4 Artificially Bee Colony . . . 93
3.5 Conclusions . . . 99
4 Workpiece error compensation 101 4.1 Introduction . . . 101
4.2 Compensation of workpiece geometrical inaccuracies in machining . . . 102
4.3 New approach for automatic compensation of geometrical inaccu-racies . . . 105
4.3.1 Generation of displacement vectors . . . 106
4.3.2 Elimination of registration errors . . . 109
4.3.3 Compensation of the workpiece model . . . 109
4.3.4 Automatic regeneration of tool trajectories . . . 112
4.4 Experimental validation of the proposed approach . . . 112
4.5 Conclusions . . . 119
5 Experimental techniques for identification, monitoring and con-trol of machining systems 121 5.1 System dynamic identification . . . 121
5.1.1 The impact test analysis . . . 122
5.1.2 Software tool for impact test analysis . . . 124
5.1.3 Conclusions . . . 130
5.2 Chatter detection system . . . 130
5.2.1 Introduction . . . 130
5.2.2 Main architecture of the machining system . . . 134
5.2.3 Monitoring system . . . 136
5.2.4 Preliminary tests . . . 136
5.2.5 Monitoring system implementation . . . 139
5.2.6 Conclusions . . . 141
5.3 Adaptive control implementation in grinding . . . 143
5.3.1 Introduction . . . 143
5.3.2 Silicon wafers grinding adaptive control . . . 144
5.3.3 Main architecture of the system . . . 145
5.3.4 Monitoring and control system overview . . . 148
5.3.5 Adaptive control strategy . . . 151
5.3.6 Monitoring and active control system implementation . . . 152
5.3.7 Experimental tests . . . 156
5.3.8 Conclusions . . . 158
Conclusions 159
Acknowledgments 165
1 Trends in manufacturing . . . 2
2 Proposed optimization loops. . . 4
1.1 Example of turning operations. . . 5
1.2 Example of external turning operations . . . 6
1.3 Example of internal turning operations . . . 6
1.4 Longitudinal turning geometry. . . 7
1.5 Cutting forces in turning. . . 8
1.6 Example of milling operations. . . 9
1.7 Face milling geometry. . . 10
1.8 Example of cutting geometry and uncut chip thickness. . . 13
1.9 Down milling (D) and Up milling (U). . . 13
1.10 Cutting force components in milling. . . 14
1.11 Overview of the experimental approach to determine cutting forces coefficients. . . 15
1.12 Experimental setup for cutting force model coefficients estimation. 16 1.13 Scatter plot of measured cutting forces against input factors . . . . 16
2.1 Two-stage modelling approach adopted for machining processes . . 18
2.2 Universal slip-line model and its transformation from six previous models . . . 20
2.3 3D Lagrangian-FEA simulation of a Milling Process . . . 21
2.4 Data structure of conventional Z map . . . 25
2.5 Relations between resolution of Boolean operation and grid size in conventional Z map model . . . 26
2.6 Concept of discrete vector model . . . 26
2.7 DVM and Z map. (a) DVM model and modeling schema, (b) Z map model and modeling schema . . . 27
2.8 Intersections between cutter surface and workpiece surface using CSG modeler . . . 28
2.9 Raster-quadtree representation of the workpiece and tool-workpiece interaction. . . 30
2.10 Tool definition example. . . 30
2.11 Decomposition of tool in segments and calculation of cutting forces. 31 2.12 a)Experimental setup; b) Tool path for the preliminary test of the machining simulator. . . 33
2.13 Comparison of measured and simulated cutting forces, average un-cut chip thickness, chip width and chip shape alarm. . . 34
2.14 Machining simulator overview. . . 35
2.15 Quadrilateral base pyramid element. . . 36
2.16 Axial tetrahedron element. . . 37
2.17 Straight prism type 1 element. . . 38
2.18 Straight prism type 1 element. . . 39
2.19 Straight prism type 1 element. . . 40
2.20 Chip thickness function calculation example, plane definition. . . . 41
2.21 Chip thickness function calculation example, intersection points. . 41
2.22 Definition of hemispherical end mill. . . 42
2.23 Hemispherical end mill - cylindrical part. . . 42
2.24 Hemispherical end mill - cylindrical part. . . 43
2.25 Hemispherical end mill - hemispherical part. . . 43
2.26 Hemispherical end mill - chordal error definition. . . 44
2.27 Hemispherical end mill - chordal error definition. . . 44
2.28 Discretized hemispherical end mill. . . 45
2.29 Kinematic profiles for jerk-limited feed rate generation . . . 46
2.30 Example of interpolated trajectory. . . 47
2.31 Machining simulation client-server architecture flow chart. . . 49
2.32 Tangential, radial, and axial directions of the unite force vectors along the curvilinear coordinate s (cutting edge) . . . 51
2.33 Experimental set-up. . . 52
2.34 Cutting test geometry definition. . . 54
2.35 Comparison between dynamometer signals and simulated cutting tests during a complex interrupted cutting operation executed on aluminum workpiece with 2-flutes endmill (test n.1 of Table 2.5). . 56
2.36 Comparison between dynamometer signals and simulated cutting tests during a face milling operation executed on C45 workpiece with 4-flutes endmill (test n.15 2.5. . . 57
2.37 Measured and simulated cutting force comparison along x axis. . . 58
2.38 Measured and simulated cutting force comparison along y axis. . . 58
2.39 Measured and simulated cutting force comparison along z axis. . . 59
3.1 Machining production design a) classical approach and b) proposed approach. . . 65
3.2 Proposed integrated system overview. . . 66
3.3 Definition of the workpiece profile for code generation module. . . 67
3.4 Workpiece and selected tools geometry. . . 69
3.5 Unit production cost against depth of cut, feed and cutting speed in roughing. . . 71
3.6 Unit production cost against feed speed and depth of cut in rough-ing, detail of cutting speed level vc,r = 250 m/min. . . 72
3.7 a) Workpiece and trajectory overview, b) detail of uncut chip thick-ness in roughing, c) cutting power in roughing operation d) detail of uncut chip thickness in finishing, e) cutting power in finishing operation. . . 73
3.8 Gradient descent optimization flow chart. . . 75
3.9 Gradient Descent optimization results: unit production cost. . . . 76
3.11 Final workpiece geometry. . . 79
3.12 Comparison of sampling with uniform random points and Ham-mersley point set. Number of points n = 100. . . 82
3.13 Modified Gradient Descent optimization results: unit production cost. . . 85
3.14 PSO optimization results: unit production cost. . . 91
3.15 Results of PSO optimization. . . 92
3.16 ABC optimization results: unit production cost. . . 97
3.17 Scatter plot of optimal unit production cost and elapsed time against number of particles q. . . 98
4.1 Concepts of workpiece dimensional error compensation technolo-gies and proposed approach. . . 102
4.2 Difference between compensation of finishing tool path and com-pensation of finishing and previous tool paths. . . 104
4.3 Main phases of the proposed method. . . 105
4.4 Distance vector calculation: a) selection of point cloud subset and triangles normal set; b) planes interpolation and new STL vertex calculation. . . 106
4.5 Results of the DoE for testing the algorithm for evaluation of dis-placement vectors. . . 108
4.6 Concept of STL compensation by solution of equivalent truss struc-ture with compliant constraints. . . 110
4.7 Example of the difference between the original model, displacement vectors and new model. . . 112
4.8 Example of tool trajectories prior and after CAD model substitu-tion in CAM. . . 113
4.9 Benchmark workpiece: a) Solid Edge CAD model; b) STL model; c) remeshed STL model. . . 113
4.10 a) Tool trajectories in CAM software and b) benchmark workpiece after roughing operations. . . 115
4.11 Benchmark workpiece: a) physical workpiece; b) displacement vec-tor calculation. . . 116
4.12 Comparison between original CAD model and the simulated ma-chined workpieces. . . 117
4.13 Average absolute displacement between the original CAD model and the simulated machined workpieces. . . 118
4.14 Simulated machined workpieces. . . 118
4.15 Example of CMM measurement of the hemispherical part of the workpiece: a) first machined workpiece; b) second machined work-piece after compensation. . . 118
5.1 Experimental set-up for a saw blade impact test analysis. . . 122
5.2 Example of impact test signals: hammer and accelerometer signal against time. . . 123
5.3 Impact test software tool user interface - 1st page. . . 125
5.4 Impact test software tool user interface - 2nd page. . . 126
5.6 Impact test software tool block diagram - initialization procedure. 127 5.7 Impact test software tool block diagram - initialization procedure,
chanel configuration. . . 127
5.8 Impact test software tool block diagram - signal acquisition and hammer impulse detector. . . 128
5.9 Impact test software tool block diagram - signal trimming. . . 129
5.10 Impact test software tool block diagram - elaboration tasks. . . 129
5.11 Impact test software tool block diagram - refresh event handler. . . 130
5.12 Machine tool detail with a raw workpiece mounted. . . 135
5.13 Example of machining operations. . . 135
5.14 Comparison of machined surfaces. . . 135
5.15 Chatter detection system hardware. . . 136
5.16 Data acquisition tool user interface. . . 137
5.17 Example of scatter diagram of the minimum and maximum accel-eration value for a specific opaccel-eration. . . 138
5.18 Example of frequency domain analysis. . . 139
5.19 User interface - Parameters control. . . 140
5.20 User interface - Monitoring window with semaphores. . . 141
5.21 Block diagram. . . 142
5.22 Schematic set-up of adaptive control systems . . . 143
5.23 Productivity improvement by adaptive control in cutting processes 144 5.24 Main architecture of active controlled grinding system. . . 145
5.25 Physical system overview. . . 146
5.26 Sensors application. . . 146
5.27 Pilot light for pyrometer positioning. . . 147
5.28 Measuring chain for the pyrometers sensors. . . 147
5.29 Architecture of monitoring and control system. . . 148
5.30 Pyrometers configuration. . . 149
5.31 Example of signals acquired during grinding tests. . . 150
5.32 User interface . . . 153
5.33 Main flow chart. . . 154
5.34 Main block diagram code. . . 155
5.35 Data Acquisition module. . . 156
5.36 Z position measurement module. . . 156
5.37 Adaptive control module. . . 156
5.38 PID controller. . . 157
1.1 Geometric and kinematic parameters in turning. . . 7
1.2 Cutting forces in turning. . . 8
1.3 Geometric and kinematic parameters in milling. . . 12
1.4 Cutting forces in milling. . . 14
2.1 Capabilities and limitations of modelling approaches . . . 19
2.2 State of the art on simulation of machining operations. . . 22
2.3 Cutting force coefficients for AISI1045 . . . 32
2.4 List of tools used during cutting tests. . . 52
2.5 Design of Experiments for cutting tests. . . 53
2.6 Cutting forces coefficients. . . 54
2.7 Simulated tools specification. . . 55
3.1 State of the art on optimization of turning operations. . . 62
3.2 Tool specification. . . 69
3.3 Preliminary DoE to evaluate the influence of cutting parameters selected for roughing on unit production cost . . . 70
3.4 Parameters of the Gradient Descent optimization test. . . 76
3.5 Normalized average trend and global influence of the cutting pa-rameters during the optimization paths. . . 78
3.6 Comparison of machining time and production cost obtained with cutting parameters derived from tool specification, suggested by machining expert and from automatic optimization. . . 79
3.7 Working cycle description. . . 80
3.8 Tool specification. . . 81
3.9 Preliminary evaluation of the feasible solution’s sub-space. . . 83
3.10 Modified Gradient Descent Results. . . 86
3.11 Normalized average trend and global influence of the cutting pa-rameters during the optimization paths. . . 87
3.12 Fixed PSO parameters. . . 89
3.13 DoE on PSO parameters. . . 90
3.14 PSO Results. . . 91
3.15 PSO Results - Parameters. . . 94
3.16 Fixed ABC parameters. . . 96
3.17 DoE on ABC parameters. . . 97
3.18 ABC Results. . . 98
3.19 ABC Results - Parameters. . . 99
4.1 State of the art of workpiece dimensional error compensation tech-nologies. . . 103 4.2 Working cycle of the benchmark workpiece. . . 114 4.3 List of tools used for machining the benchmark workpiece. . . 115 4.4 Design of experiments to evaluate the effect of kb/kc ratio on STL
model compensation. . . 116 5.1 Summary of chatter identification system research . . . 132 5.2 Accelerometer characteristics. . . 136 5.3 Nomenclature of geometrical and physical quantities of interest. . . 148 5.4 Pyrometers characteristics. . . 149
The primary “value-added” factors that now dominate in the global marketplace are innovation, automation, sophisticated skills, and strategic management, all of which are dependent on intelligent systems [1].
This statement emphasizes the recent need in all disciplines of intelligent systems. Over the past several years, there has been an increasing trend in use and devel-opment of artificial intelligence (AI) in various application areas such as machine learning, planning and robotics, modeling human performance, expert systems. However, there are few sectors that have experienced a push towards this tech-nology as rapid as manufacturing.
In recent years, predecessors of intelligent systems have been widely used in man-ufacturing. Many of these systems, such as advanced manufacturing systems, computer integrated manufacturing, flexible manufacturing systems, manufac-turing resource planning, CAD/CAM and NC/CNC numerical control machines are being developed for production and operation management and present a cross-fertilization of ideas from manufacturing and AI that could be named as intelligent manufacturing [2].
The manufacturing process involves a series of complex interactions among ma-terials, machinery, energy, and people. It encompasses the design of products, various processes to change the geometry of bulk material to produce parts, heat treatment, metrology, inspection, assembly, and necessary planning activities. Marketing, logistics, and support services are relating to the manufacturing ac-tivity. The major goals of manufacturing technology are to improve productivity, increase product quality and uniformity, minimize cycle time, and reduce labor costs. The use of computers has had a significant impact on manufacturing activ-ities covering a broad range of applications, including design of products, control and optimization of manufacturing processes, material handling, assembly and inspection of products. [3]
According to Jawahir [4], an intelligent manufacturing system serves as a means of ensuring machining performance to desired standards. Such systems need to be allied with expansive knowledge-bases and should be capable of making im-portant process planning decisions at critical junctures.
The intelligent manufacturing system is a system capable to design, monitor, con-trol and optimize the whole production process of a manufacturing product.
The past few decades have seen a trend towards the establishment of intelligent
manufacturing systems capable of using advanced knowledge-based and intelli-gence techniques in aiding critical operative procedures on manufacturing shop-floors.
In Figure 1 advances in manufacturing process are illustrated.
Manual Machine
Powered Machine
NC Machine
AC Machine
Intelligent Machine Analog / Mechanical Control
(Mechanism)
Digital Control (NC/Servo) (Actuator) (Sensor)
(Objective Function/Constrain) (Sensors)
(Intelligent Information Processing)
- Efficiency - Speed - Accuracy
- Sophisticated Motion Control - Process Integration
- Systematization
- Sensor Feed-back of Machining Process
- Ambiguous Input
- Utilization of Experiences and Know-how - Accumulation of Knowledge through Learning Machine driven based on Self Decision Making (M ac h in e d ri v en b y p re d et er m in ed c o m m an d )
{
{
{
{
(
)
Figure 1: Trends in manufacturing [5].
Since the development of pure-mechanical powered machine tool aims at increas-ing the efficiency and the process accuracy, several innovation were introduced. The greatest innovation was the introduction of computational logic into a ma-chine tool. The mechanisms became servo-assisted axes controlled by a single central processing unit - the Control Unit. The motion was determined by a NC part program instead of predetermined and fixed cams. The most relevant ad-vantage was the systematization and the manufacturing process integration. The expertise was moved from the manufacturer to the NC high-level programmer. Subsequently, the introduction of sensorized machines [6, 7] allowed the devel-opment of Adaptive Controlled - AC - machines. The feedback controls were applied in order to meet an objective function or constrain [8, 9]. Nevertheless, until now the machine tool was driven by predetermined commands. The most relevant challenge of the next future is the development of unmanned machin-ing systems, capable of autonomously machinmachin-ing the raw workpiece from the three-dimensional model of the final workpiece. Efforts are being made in
or-der to develop subsystems capable to increase the human-independence of these machines. Ideally, they should be able to automatically optimize the machining operation by choosing the proper machining strategies, tools, cutting parameters and the optimum cutting paths to obtain the final product. To reach this condi-tion, the machines must be provided with information on the actual machining condition and they must be endowed with self-learning capabilities.
The next generation of manufacturing systems will be described as new intelligent reconfigurable manufacturing systems which realize a dynamic fusion of human and machine intelligence, manufacturing knowledge and state-of-the-art design techniques. This may lead to low-cost self-optimizing integrated machines. It will include fault-tolerant advanced predictive maintenance facilities for produc-ing high-quality error-free workpieces usproduc-ing conventional and advanced manufac-turing processes [10].
The overview of the conventional manufacturing process is illustrated in Figure 2. Starting from the final workpiece 3D CAD model and the stock dimensions, the engineering phase is carried out using commercial CAM software. The machining expert must select the proper tools and machining strategies to design the ma-chining process. Moreover, the CAM software calculates the tool path trajectories and performs the trajectory post-processing. The NC code has to be transferred to a CNC machine tool that produces the physical workpiece. Trajectories and cutting conditions are specified (and fixed) in the NC code. Finally, the physical workpiece could be measured in order to check if it is in accordance to the CAD model specification.
Ideally an intelligent manufacturing system has to perform this process without the human presence. To reach this condition, the manufacturing process must be automated. Moreover, the overall process must be automatically optimized. This research work focuses on the development of innovative techniques in order to realize an intelligent manufacturing system able to automatically optimize the manufacturing process.
The core concept of the work is illustrated in Figure 2.
The main working areas are focused on the development of systems for:
• automatic generation, testing, optimization and preliminary verification through realistic simulation of NC part programs;
• automatic compensation of geometrical and dimensional inaccuracies based on adaptation of the workpiece 3D model;
Optimization loops C A D En gi n ee ri n g C A M Sh o p f lo o r - M ac h in in g Q u al it y co n tr o l CAD Design
Strategies and tool selection Tool path trajectory
calculation Post processing Control Unit Physical system Cutting process Workpiece measurement Part program optimization Monitoring and adaptive control Machined part dimensional error compensation Conventional manufacturing process
Figure 2: Proposed optimization loops.
The thesis is structured as follows.
In chapter 1 a brief introduction on the machining process is given. All main geometric and kinematic parameters are defined and cutting forces models are introduced.
In chapter 2 the state of the art of machining simulation is presented first. Then, the development of turning and milling simulators is described. Eventually, the machining simulator validation using specific cutting test is given.
In chapter 3 innovative methodologies for automatic NC code optimization through machining simulation are discussed. Different case studies are analyzed and used to test the optimization procedures.
In chapter 4 an innovative approach for automatic compensation of geometrical and dimensional inaccuracies based on adaptation of the workpiece 3D model is presented and validated using a specific benchmark workpiece.
In chapter 5 the development of automatic tools for machine dynamic identifica-tion, chatter detection in milling and adaptive control in grinding are presented. Details about the implementation strategies are given.
Fundamentals of turning and
milling
The aim of this chapter is to establish a reference for the conventional nomencla-ture and symbols used for turning and milling in the following chapters. More-over, laboratory procedures for material testing are presented.
1.1
Turning process
Turning is a flexible machining process used to machine axial symmetrical work-pieces. Basically it generates cylindrical forms with a single point stationary tool.
In Figure 1.1 basic turning operation are shown.
(a) Longitudinal turning. (b) Face turning. Figure 1.1: Example of turning operations.
Turning is the combination of two movements: rotation of the workpiece and feed movement of the tool. The feed movement of the tool can be along the axis of the workpiece, which means the diameter of the part will be turned down to a smaller size. Alternatively, the tool can be fed towards the center, at the end of the part, which means the length of the part will be faced down. Often feeds are combination of these two directions, resulting in tapered or curved surfaces. More
generally, the turning process is mainly subdivided in external turning (Figure 1.2) and internal turning (Figure 1.3).
Figure 1.2: Example of external turning operations [11].
Figure 1.3: Example of internal turning operations [11].
1.1.1 Kinematics of turning
In Figure 1.4 the most important geometric and kinematic parameters of the longitudinal external turning process are shown, in accordance to ISO 3002/1 [12] and ISO 3002/3 [13] standards. The basic geometric and kinematic parameters are listed in Table 1.1
The cutting speed vc is the tangential speed of the workpiece and it can be
expressed as follows
vc=
πDn
100 [m/min] (1.1)
where n is the number of revolutions per minute of the spindle and D is the workpiece diameter in [mm].
The feed f is the distance covered by the tool in the direction of the feed, in one workpiece revolution, as shown in Figure 1.4. It can be expressed in [mm/rev]
1.1 Turning process 7
χ
χ
χ’
r
εχ
χ’
r
εUtensile
Truciolo
Forze 1
γ
α
β
v
fΦ
F=F
aF
cF
γF
γNF
fF
shF
shNForze con
fi=90°
Truciolo con piano Psh
h
0Φ
P
shγ
h
chβ
α
v
fv
cv
eF
c=F
fNF
f=F
cNF
eNF
aF
eη
Forze in tornitura longitudinale
η
P
fe
F
f
F
a
F
F
D
v
f
v
e
v
c
F
p
D
F
e
Superficie di
appoggio
Tagliente
secondario S’
Stelo
Fianco
principale A
αTagliente
principale S
Petto A
γFianco
secondario A
α’Punta utensile
χ
a
pf
b
h
χ’
Truciolo con re
γ
α
β
v
fΦ
F=F
aF
cF
γF
γNF
f=F
cNF
sF
sNγ
τ
τ-γ
Tagliente secondario
attivo
Superficie
lavorata
Avanzamento
Superficie
da lavorare
Punto a
χ
re=0°
Tagliente
principale
attivo
Tagliente
principale
operativo
Tagliente
secondario
operativo
Superficie
transitoria
χ
a
pf
b
h
χ’
r
εn
v
fχ
a
pf
b
h
χ’
r
εFigure 1.4: Longitudinal turning geometry.
Table 1.1: Geometric and kinematic parameters in turning.
Symbol Measure Units Name and description
rϵ [mm] Nose radius
vc [m/min] Cutting speed
vf [mm/min] Feed speed
f [mm/(revolution)] Feed per revolution
Ω [rad/s] Angular speed of the spindle
n [rpm] Spindle speed
ap [mm] Depth of cut
D [mm] Actual workpiece diameter
b [mm] Length of the engaged cutting edge
χ [rad] or [deg] Tool cutting edge angle
h [mm] Instantaneous uncut chip thickness
A [mm] Nominal cross-sectional area of the cut or
undeformed chip section area
Consequently, the feed speed vf is as follows:
vf = f n [mm/min] (1.2)
Depth of cut ap is the distance the tool is set below the unmachined surface as
shown in Figure 1.4.
The uncut chip with b is the length of the main active cutting edge and can be approximated as follows:
b = ap
sin(χ) [mm] (1.3)
where χ is the entering angle of the tool.
The average uncut chip height h can be approximated as
h = f sin(χ) [mm] (1.4)
The uncut chip section A is a very important parameter that influences the cutting forces. For a given cutting depth and feed per revolution, the uncut chip section can be expressed as
8 Fundamentals of turning and milling
1.1.2 Tool geometry and nomenclature
1.1.3 Cutting forces
The resultant cutting force F in turning can be split into its components along the main directions of the reference system, as shown in Figure 1.5, see ISO 3002/4 standard [14]. F = Fc+ Ff+ Fp (1.6) χ χ χ’ rε χ χ’ rε Utensile γ α β vf Φ F=Fa Fc Fγ FγN Ff Fsh FshN Forze con fi=90°
Truciolo con piano Psh
h0 Φ Psh γ hch β α vf vc ve Fc=FfN Ff=FcN FeN Fa Fe η
Forze in tornitura longitudinale
η Pfe Ff Fa F FD vf ve vc Fp D Fe Superficie di appoggio Tagliente secondario S’ Stelo Fianco principale Aα Tagliente principale S Petto Aγ Fianco secondario Aα’ Punta utensile χ ap f b h χ’ γ α β vf Φ F=Fa Fc Fγ FγN Ff=FcN Fs FsN γ τ τ-γ Tagliente secondario attivo Superficie lavorata Avanzamento Superficie da lavorare Punto a χre=0° Tagliente principale attivo Tagliente principale operativo Tagliente secondario operativo Superficie transitoria χ ap f b h χ’ rε n vf χ ap f b h χ’ rε
Figure 1.5: Cutting forces in turning.
The active force Fa is the projection of force F in the plane Pf e, as shown in
Figure 1.5. The orthogonal component is the back force Fp.
The feed force Ff and the orthogonal component Ff N can be obtained through
the F projection along the feed speed f direction.
The cutting force Fcis the F component along the cutting direction as illustrated
in Figure 1.5.
Table 1.2: Cutting forces in turning.
Symbol Measure Units Name and description
Fc [N] Cutting force component
Fp [N] Back force component
Ff [N] Feed force component
The cutting forces can be modelled using the shearing and ploughing model proposed by Altintas [15] as follows
Ff = knsA uf + knpb uf Fp = knsA up+ knpb up Fc= kcsA + kcpb (1.7)
where kns and knp are the normal force shearing and ploughing coefficients, kcs
and kcp are the cutting force shearing and ploughing coefficients, b is the length
of cutting edge, uf and upare the feed and normal components of the unit vector
perpendicular to the cutting edge.
From literature, it is possible to find tables reporting shearing and ploughing coefficients values for several combinations of workpiece material, cutting angles and average uncut chip thickness.
1.2
Milling process
Milling is a machining process that consists in removing material from the work-piece by using a spinning tool composed of several cutting edges. A milling cutter is held in a rotating spindle, while the workpiece clamped on the table is linearly moved toward the cutter. The interaction of these two movements produces the removal of the material from the workpiece.
There is a large variety of possible shapes for cutting tools in milling. These range from very simple ones such as orthogonal cutters applied in face milling to very complex shapes applied in the end milling of contours. It is very difficult to make a precise classification of all the possible milling operations [11].
In research applications on metal cutting in milling, simple geometries such as face and peripheral milling are common practice, as shown in Figure 1.6. These basic configurations allow to easily estimate the uncut chip thickness, which is a fundamental parameter in order to understand the basic principles of metal cutting.
In Figure 1.6 the basic milling geometries, face and peripheral milling, are shown.
(a) Face milling. (b) Peripheral milling. Figure 1.6: Example of milling operations.
The main distinction between face and peripheral milling lies in the relative position between the rotation axis of the tool and the workpiece surface. In face milling the axis is orthogonal to the machined workpiece surface, while in peripheral milling it is parallel.
1.2.1 Kinematics of milling
In Figure 1.7 the most important geometric and kinematic parameters of the face milling process are shown. However, a similar notation can also be applied to describe the perhiperal milling process, see ISO 3002/1 [12] and ISO 3002/3 [13] standards. The main difference is the low radial immersion aL = D in the case
of perhiperal milling, and the fact that the machined surface is parallel to the cutter axis. The basic geometric and kinematic parameters are listed in Table 1.3.
Feed per tooth fz is the maximum radial depth of cut of the tool. As shown in
Figure 1.7, feed per tooth is the distance between the paths of two subsequent edges in the direction of the feed. Feed per tooth is a key parameter in milling. The instantaneous uncut chip thickness hj(φj) is the radial depth of cut of the
tool. It is a function of the feed per tooth fz, of the geometry of the cut and it
may be influenced by vibrations, cutter run-out and tool eccentricity. Depth of cut ap is the distance the tool is set below the unmachined surface. Depth of cut
is a fundamental parameter in milling. Cutting speed vc is the tangential speed
of the mill and it can be expressed as follows:
vc=
πDn
100 [m/min] (1.8)
where n is the spindle speed in [rpm] and D is the cutter diameter in [mm]. Cutting speed vc is the speed at which the tool cuts through the inside of the
workpiece. Feed speed vf is the speed at which the workpiece moves towards the
tool, and it can be expressed as follows:
vc= fzz n [mm/min] (1.9)
where z is the number of teeth. The angular speed Ω of the mill is as follows:
Ω = 2πn
60 (1.10)
The entrance and exit angles are φin and φout respectively, which can be
calcu-lated as follows φin= arccos( 2aL1 D ) (1.11) φout= π − arccos( 2aL2 D ) (1.12)
The angular cutter-workpiece engagement is
φe = φout− φin (1.13)
hence the length of the contact arc is
Le= φe
D
2 (1.14)
1.2.2 Uncut chip thickness
The uncut chip thickness hj is a very important parameter that influences the
cutting forces. It is also known as undeformed chip thickness. In face milling, the uncut chip thickness hj represents the depth of the cut in a radial direction,
see Figure 1.7. Due to the interrupted cut, the uncut chip thickness hj varies
continuously. In order to estimate the uncut chip thickness hj, the distance
between two subsequent paths of the tool along the radial direction must be considered. The path of the tool on the reference system of the workpiece is a cycloid, even if the feed speed vf is very low. Therefore, it is very difficult to
Table 1.3: Geometric and kinematic parameters in milling.
Symbol Measure Units Name and description
φj [rad] or [deg] Feed motion angle of the jth tooth
z [teeth] Number of teeth mounted on the cutter
φin [rad] or [deg] Entrance or start angle
φout [rad] or [deg] Exit angle
vc [m/min] Cutting speed
vf [mm/min] Feed speed
fz [mm/(tooth)(revolution)] Feed per tooth
Ω [rad/s] Angular speed of the spindle
n [rpm] Spindle speed
ap [mm] Depth of cut
aL1 [mm] Entrance position in the workpiece
aL2 [mm] Exit position from the workpiece
aL [mm] Width of cut
D [mm] Cutter diameter
b [mm] Length of the engaged cutting edge
χ [rad] or [deg] Tool cutting edge angle
hj [mm] Instantaneous uncut chip thickness
A [mm] Nominal cross-sectional area of the cut
or undeformed chip section area
From the literature [16], when the feed speed vf is very low, the uncut chip
thickness hj can be approximated as follows:
¨
hj(φ) ∼= fzsin(φ) sin(χ), when φin ≤ φ ≤ φout
hj(φ) = 0, elsewhere.
(1.15)
The uncut chip thickness hj can also be estimated exactly by using milling
sim-ulation software. From simsim-ulations, it emerged that the difference between the approximated uncut chip thickness hj and the simulated uncut chip thickness is
negligible in most cases.
Figure 1.8 shows an example of the characteristic in time of the uncut chip thick-ness hj for the milling operation represented on the left.
The uncut chip thickness hj development in time is important to determine the
stresses induced by the interrupted cut. In general it is possible to distinguish between two conditions commonly known as up and down milling, as shown in Figure 1.9.
In up milling the uncut chip thickness hj has a low value when the tool enters the
workpiece and then it increases to reach the maximum value. In down milling the uncut chip thickness hj is high when the tool enters the workpiece and then
it decreases. A low uncut chip thickness hj during the entrance produces a lower
impact; therefore it is favourable when the feed rate is high such as in roughing. Indeed, the low uncut chip thickness hj produces a slippage effect and the tool
0 0.002 0.004 0.006 0.008 0.01 0.012 0.014 0.016 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 time [min] h [ m m ] aL 1 aL2 Ω vf
Figure 1.8: Example of cutting geometry and uncut chip thickness.
Figure 1.9: Down milling (D) and Up milling (U).
deforms and slips on the chip instead of cutting. When the uncut chip thickness hj
becomes too high, the tool enters the workpiece. This effect produces bad quality surfaces. In down milling, the uncut chip thickness hj is maximum during the
entrance in the workpiece, therefore the impact is hard but the slippage effect does not occur. Down milling can not be used when the uncut chip thickness hj is high otherwise the tool could break. Down milling is mainly applied in
finishing and the quality of the machined surface is good. The shape of the chip in down milling is different from the chip produced in up milling. When the feed rate is high, the shape of the chip in up and down milling changes because the movement of the center of the mill is not negligible related to the rotation speed.
1.2.3 Cutting forces
For the sake of simplicity, let us focus on face milling with inserted cutters. Under this hypothesis it is possible to adopt a lumped representation of both cutting edge profiles and cutting forces. Thus, the force Fj acting on the jth tooth can
be decomposed as described in Figure 1.10.
Fj = Fc,j + FcN,j+ Fz,j (1.16)
where Fc,j is the tangential cutting force component usually known as the (main)
cutting force component, FcN,j is the cutting perpendicular force component and
Fz,j is the axial force component. The resultant cutting force acting on the tool
is F (t) = z j=1 Fj(t) = Ff + Ff N + Fz (1.17)
which is decomposed into the sum of the feed (Ff), feed perpendicular (Ff N) and
Figure 1.10: Cutting force components in milling.
The cutting forces can be roughly expressed as follows Fc,j(t) = kcAj(t) FcN,j(t) = kcNAj(t) Fz,j(t) = kaAj(t) (1.18)
where kc, kcN and ka are the cutting pressures and Aj(t) is the instantaneous
chip cross-section area. The cutting pressures are expressed in [N/mm2] and it is possible to find tables reporting their values for several combinations of workpiece material, cutting angles and average uncut chip thickness [17]. The most important cutting pressure is the tangential cutting pressure kc. From the
literature [18], the value of kcis obtained during turning tests. Values of kcN and
ka are usually expressed as a fraction of the kc.
Table 1.4: Cutting forces in milling.
Symbol Measure Units Name and description
Fc,j [N] cutting force acting on jth tooth
FcN,j [N] cutting perpendicular force acting on jth tooth
Ff [N] feed force
Ff N [N] feed perpendicular force
Fz, Fa or Fp [N] back or axial force component
1.3
Experimental determination of cutting forces
co-efficients
Cutting forces are strongly related to cutting process mechanics, and the appli-cation of dynamometers for their measurement during machining is essential for investigating, monitoring and optimizing the turning process [19].
Generally, dynamometers tend to reduce the machining system stiffness. There-fore, a trade-off between sensitivity and stiffness has to be accepted. Also, the frequency bandwidth of the dynamometer should be as wide as possible in or-der to get accurate measurements of rapidly changing cutting forces, since chip formation, interrupted cutting conditions, chatter and tool breakage may cause sudden signal variations that have to be readily detected.
In the last decades, different types of dynamometers have been used in industry and research laboratories for understanding the principles of chip formation [20], for developing cutting force models [21], as well as for cutting process control [22], tool geometry optimization [23], Tool Condition Monitoring - TCM [6,24,25] and for detection and suppression of chatter vibrations [26, 27].
The dynamometers can be used also to calibrate the cutting forces coefficients for a specific workpiece-tool pair. In particular a Design of Experiments - DoE of the main cutting parameters has to be performed. The overview of the experimental approach to determine cutting forces coefficients is given in Figure 1.11
Laboratory test
Input data Analysis
Material to test Machine tool with
dynamometer Design of experiments (vc, f, ap rε) Machining tests and data acqisition Data Analysis (filtering and feature extraction) Linear regression of cutting force model Output Cutting force coefficients
Figure 1.11: Overview of the experimental approach to determine cutting forces coefficients.
Taking as a reference a turning operation, the cutting force coefficients (kcs, kcp,
kns, knp) of the Shearing e Ploughing cutting force model described in Equation
1.7 can be evaluated using specific cutting test. Usually, a DoE on vc, f , ap and rϵ
is performed. The machine tool has to be equipped with a turning dynamometer as show in Figure 1.12.
The acquired signals must be filtered and converted to force measurement units. The extraction of the mean cutting force along the main axis have to be carried out. At the end of this phase, a scatter plot of the cutting forces along the three principal directions against the cutting parameters can be obtained, see Figure 1.13 as example.
Afterwards, the cutting force coefficients are then derived by linear regression of the model given in Equation 1.7 on the cutting forces values. Eventually, square correlation coefficient R2, the root mean square error RM SE and the root mean square relative error RM SE can be calculated in order to provide a measure of how well the cutting force measurements are replicated by the model.
WORKPIECE 0$&+,1( 722/ HEAD TURNING DYNAMOMETER CUTTING INSERT
Figure 1.12: Experimental setup for cutting force model coefficients estimation.
Cutting speed vc[m/min] Nose radius rε[mm]
Feed f [mm/rev] Depth of cut ap[mm]
Main cutting force
Fc =F y [N] Back force Fp =F x [N] Feed force F=f ‒F z [N] 0.2 0.4 0.6 0.8 250 300 350 400 450 0.08 0.1 0.12 0.14 0.16 0.4 0.6 0.8 1 1.2 100 200 300 400 500 40 60 80 100 120 100 200 300 rε=0.2 rε=0.4 rε=0.8
Machining Simulation
An intelligent manufacturing system has to perform the machining process ide-ally without the human presence. Therefore it has to pre-emptively verify the machining conditions in order to avoid any kind of problems during the cutting. Realistic machining simulators can be applied in order to evaluate the feasibil-ity of the NC part program. In this chapter a study on machining simulator is presented. Furthermore, the implementation details of 2D and 3D machining simulator are illustrated. Finally, the results of laboratory validation is given.
2.1
State of the art
2.1.1 Modeling of machining process
Conventional machining processes continue to occupy a dominant fraction of all manufacturing operations. New advances in machine tool and cutting tool technologies, along with advanced material development, all aimed at improving manufacturing productivity, product quality and cost reduction, require predic-tive performance models for use in process planning systems for machining pro-cesses [29].
Predictive models with simulation can be integrated into process planning sys-tems to improve productivity and enhance product quality. Predictive perfor-mance models could also be effectively used in adaptive control for machining processes, reducing and/or eliminating trial and error approaches. Industry is interested in process performance measures such as tool-life, surface finish, sub-surface integrity, chip-form/chip breakability, burr formation, part accuracy, etc. Figure 2.1 summarizes the state of the art of predictive modelling efforts. Quanti-tative input is used to predict output parameters in two distinct stages. Physics-based models are used to predict fundamental process variables, which are used to predict industry-relevant outcomes. Predictive models span numerous methods. Analytical models, including slip-line models, can directly predict cutting forces, friction in the local cutting zones, stresses, strains, strain-rates and temperatures. However, the complexity of industrial processes still makes it difficult to predict all industry relevant outcomes analytically. Analytical models also provide useful input for optimising numerical models. These numerical computational models can then offer realistic prediction of industry-relevant outcomes. This hybrid an-alytical/numerical approach has not been fully implemented, but is likely to be
a major goal of future research.
T able 2.1: Capabilities and limitations of mo delling app roac hes [29]. Analytical Numerical Empirical Hybrid Principle Slip-line theory or min-im um energy principle Con tin uum mec hanics using FEM, FDM & meshless FE M Curv e fitting of exp eri-men tal dat a Com bines the strengths of other appr oac hes Capabilities Predicts cutting forces, chip geometry , to ol -chip con tact length, a v-erage stresses, strains, strain-rates and tem-p eratures Predicts forces, chip ge -ometry , stresses, strain, strain-rates and tem -p eratures Applicable to most mac hining op erations for measurable pro cess v ariables only Pro vides meta-mo dels for a family of mo dels to b e in tegrated Limitations Usually limited to 2-D analysis with single and m ultiple cutting edge, but some 3-D mo dels exist Material mo del, friction as input, computational limitations: e.g., mesh-ing V alid only for the range of exp erimen tation Limited to the strength of the base mo del: i.e., analytical, n umerical, empirical, etc. Adv an tages Abilit y to dev elop fast practical to ols Opp ortunities to connect to industry-relev an t parameters Practical, fast and direct estimation of industry-relev an t p a-rameters Impro v es the capabili-ties an d accuracies of the base mo dels Disadv an tages Unique to eac h mac hin-ing problem Long computation time Extensiv e exp erimen-tation, time-consuming and costly Need for extensiv e data from exp erimen ts and/or sim u lations
Analytical models Slip-line field analysis has been an established analytical modeling method for investigating the chip formation process, typically under plane-strain, rigid-plastic conditions. Merchant’s early shear plane model [30] was based on a single shear-plane with the velocity discontinuity across this plane being expressed by a velocity diagram (also known as hodograph). Subsequent work by Lee and Shaffer [31], and the mathematical foundations for constructing slip-lines have been utilized by researchers from the 1950s through 1990s. Most notable among these include: centred-fan slip-line model for machining with re-stricted contact tools by Johnson [32] and Usui and Hoshi [33]; Kudo’s admissible and inadmissible slip-line models for machining [34]; Dewhurst’s slip-line solutions for non-unique machining with curled chip formation [35]; and the subsequent ex-tended curled chip formation model by Shi and Ramalingam [36]. More recently, Fang et al. [37] developed a universal slip-line model that incorporates all six previously presented slip-line models (Figure. 2.2).
Figure 2.2: Universal slip-line model and its transformation from six previous models [29].
Empirical models Among the modelling approaches, empirical modelling is the simplest approach, and is widely used in the absence of other meaningful mod-els. Empirical models often utilize statistical methods and they are only valid for the ranges of the experiments conducted, and not based on physics of the pro-cess. This technique is based on designing experiments for varying process inputs (e.g., cutting conditions, tool geometry, etc.) and measuring process performance such as cutting forces, surface roughness, tool-life, etc., and correlating them to the input conditions [38, 39]. For this reason, this method utilizes heavy experi-mentation at different cutting conditions, cutting tools, and coolant/lubrication applications [29].
Numerical models Virtual machining is a simulation technology of mechani-cal machining that simulates the actual machining process with high reality and integrates the aspects of geometrical simulation and physical simulation [40]. The geometrical simulation can generate necessary data for the prediction of process parameters in physical simulation.
Three main methods of mechanical formulation are commonly used in Finite-Element-Modelling of metal cutting [41]:
• Eulerian formulation, where the grid is not attached to the material, is computationally efficient but needs the updating of the free chip geometry; • Lagrangian formulation, where the grid is attached to the material, requires updating of the mesh (remeshing algorithm) or the use of a chip separation criterion to form a chip from the workpiece;
• Arbitrary Lagrangian Eulerian (ALE) formulation, where the grid is not attached to the material and it can move to avoid distortion and update the free chip geometry.
• Lagrangian formulation, where the grid is attached to the material, requires updating of the mesh (remesh-ing algorithm) or the use of a chip separation criterion to form a chip from the workpiece [97].
• Arbitrary Lagrangian Eulerian (ALE) formulation, where the grid is not attached to the material and it can move to avoid distortion and update the free chip geometry [67].
A 3D FEA-Simulation of a Milling Process [85], [122] is presented in Figure 29.
3D CAD-Model FEA-Model
3D Simulation of a Milling Process
Figure 29: 3D FEA simulation of a Milling Process.
A successful simulation is dependent on the accurate knowledge of the boundary conditions and the material-behaviour which is different from simple metal models obtained from tensile tests due to the influence of large strain, strain rate, and temperature. In order to achieve an accurate prediction of chip flow, stress and temperature distribution within the chip and tool, an accurate model of flow stress of the material and friction between the rake face of the tool and chip is absolutely necessary. The validity of all numerical models is proven experimentally by comparing predicted forces, average shear angles and shear stresses in metal cutting tests.
5 INTEGRATED SIMULATION OF MACHINE AND PROCESS
Current NC tool path and machining simulation systems consider only the rigid body kinematics of the machine tool, and do not take the physics of the machining proc-ess into consideration. The magnitude of cutting forces, torque, power and thermal energy produced during ma-chining depends on the tool geometry, structural dynam-ics between the workpiece and the tool, work material properties, and cutting conditions such as feed, speed and depth of cut. Currently, the cutting conditions are selected from either tool manufacturers’ handbooks or experience, which may or may not lead to productive and accurate production of parts.
The objective of next generation CAM systems is to in-clude the physics of manufacturing processes in order to produce the first part accurately and optimally. A sample architecture for Virtual Machining Process simulation was proposed by Altintas et al. [2] as shown in Figure 30.
The geometric model of the part, blank and NC tool path in the form of a standard CL file are imported from current CAD/CAM systems using IGES or STEP NC standards. The cutter – part intersection along the tool path is evalu-ated at feed rate increments using solid modelling tech-niques. The intersection geometry is required to solve machining process simulation algorithms [93]. The ma-chining process simulation engine is based on the laws of metal cutting mechanics and dynamics, it pulls the re-quired machine tool and work material parameters from the data base and predicts the cutting forces, torque, power, static and dynamic deformations of the machine tool-part-fixture along the tool path. For a given set of constraints, such as maximum power-torque-dynamic stiffness of the machine and chip thickness limit of the cutting edge, the speed and feed can be optimised to maximise the material removal rate.
CAD MODEL NC Tool Path Cutter Geometry FINAL PROCESS PLAN Optimized Speed, Feed, Depth, Width, Error Compensation PATH PLANNER CL File Path Strategy Analysis MONITORING AND CONTROL DATA Peak force, torque, power, tracking error, modal frequencies Cutter-part intersection calculations Virtual Machining process simulation Tool, Material, Machine-Tool Data Base CAD MODEL NC Tool Path Cutter Geometry CAD MODEL NC Tool Path Cutter Geometry FINAL PROCESS PLAN Optimized Speed, Feed, Depth, Width, Error Compensation FINAL PROCESS PLAN Optimized Speed, Feed, Depth, Width, Error Compensation PATH PLANNER CL File PATH PLANNER CL File Path Strategy Analysis M A C H I N E T O O L M A C H I N E T O O L MONITORING AND CONTROL DATA Peak force, torque, power, tracking error, modal frequencies Cutter-part intersection calculations Virtual Machining process simulation Cutter-part intersection calculations Virtual Machining process simulation Tool, Material, Machine-Tool Data Base
Figure 30: Virtual machining process simulation and opti-misation architecture.
Although intensive research efforts are under way at present, there are several key requirements, that have to be met before a virtual simulation of the machining proc-ess can be realised. The cutter-part intersection along the feed increments requires intensive computational time since the part geometry must be updated as the material is removed at feed increments [45].
Researchers used Constructive Solid Geometry – CSG [93], Boundary Representation – Brep [51], and z- buffer techniques to model material removal [15]. The computa-tional time is rather unaffordable and long at the present time, and considerable research efforts are directed to-wards developing efficient computational models and parallel processing of algorithms at multiple central proc-essing units (CPUs).
Although some commercial NC Simulation systems pro-vide feed optimisation, their algorithms are not based on the laws of cutting mechanics, hence they do not repre-sent the true process. However, considerable effort has been undertaken to integrate the true process physics into NC program optimisation.
Altintas and Spence presented a 2 ½ axis end milling process simulation system [94].
Altan et al. [15], Spence et al.[95], Weinart et al. [118], [121] and Lazoglu et al. [26] presented a process simula-tion and optimisasimula-tion strategy for dies and molds. They illustrated that the machining cycle time can be decreased significantly by scheduling feed rates along the tool path while respecting tool deflection, tool breakage, torque and power limits of the machine tool. Altintas et al. [7] pre-sented algorithms which can handle arbitrary cutter shapes in predicting the forces, torque, power and chatter vibrations during milling.
Figure 2.3: 3D Lagrangian-FEA simulation of a Milling Process [41].
A successful simulation is dependent on the accurate knowledge of the boundary conditions and the material behavior which is different from simple metal mod-els obtained from tensile tests due to the influence of large strain, strain rate, and temperature. In order to achieve an accurate prediction of chip flow, stress and temperature distribution within the chip and tool, an accurate model of flow stress of the material and friction between the rake face of the tool and chip is absolutely necessary. The validity of all numerical models is proven experimen-tally by comparing predicted forces, average shear angles and shear stresses in metal cutting tests [41].
2.1.2 Eulerian machining simulation
Productivity and quality of machined parts highly depend on the NC program used in machining.
Because of the need for unattended machining and higher productivity, it is becoming more critical to simulate more precisely machining process for the op-timization of cutting condition including chip load and material removal volume, prior to actual cutting operation. The main requirement for industry application is that the simulation must be relatively quite fast. The best way to achieve that result is to simulate the machining process through Eulerian FEM simulators.
The geometrical simulation is used to simulate the material removal process so that the material removal rate (MRR), cutting depth, cutting width, etc. can be predicted. This is realized via a Boolean subtraction operation between the workpiece model and tool swept volumes [42] as the NC program is verified and simulated block by block.
The representation of workpiece is one of the key issues in virtual machining, which affects the simulation precision and speed greatly. Up to now, methods to represent the workpiece can be classified into three categories: the discrete vector based method (i.e. Z-Map) [43], the decomposition based method (i.e., voxel, octree) [44], and the solid modeling based method (i.e. B-Rep, CSG) [45]. The benefits of the discrete vector based method include relatively simple and ro-bust algorithms for modeling the machining process, particularly for sculptured surface machining. The decomposition based method is also an approximate method to represent a solid object with a set of cubes with different sizes. The algorithm is so simple that the model represented with it can be modified locally via set operations. The solid modeling based method can directly represent a solid object and its geometrical information. It is of high precision, but the com-putation is quite complex and time-consuming.
Many researches have been done during the last decades focusing on Eulerian machining simulation, as illustrated in Table 2.2.
Table 2.2: State of the art on simulation of machining operations.
Ref. Year Title
Discrete v ector mo del metho d Solid mo deling based metho d Decomp osition based metho d
[46] 1983 Programming for Machining Based on Workpiece Models in Computer
x [47] 1986 Real-time shaded NC milling display x [48] 1987 Switching Functions Based Geometric Modeling
Language and its Application to Numerical Con-trol Program Verification
x
Table 2.2 – continued from previous page
Ref. Year Title
Discrete v ector mo del metho d Solid mo deling based metho d Decomp osition based metho d
[49] 1989 Approximate methods for simulation and verifi-cation of numerically controlled machining pro-grams
x
[50] 1989 A Cutting Simulation System for Machinability Evaluation Using a Workpiece Model
x [51] 1989 Development of a Personal CAD/CAM System
for Mold Manufacture Based on Solid Modeling Techniques
x
[52] 1996 Dimensional verification of NC machining profiles using extended quadtrees
x [53] 1997 The sweep-envelope differential equation
algo-rithm and its application to NC machining veri-fication
x
[54] 1997 C-space approach to tool-path generation for die and mould machining
x [55] 1998 3-D object decomposition with extended octree
model and its application in geometric simulation of NC machining
x
[56] 1999 Computation of a geometric model of a machined part from its NC machining programs
x [44] 2000 Voxel-Based Virtual Multi-Axis Machining x [57] 2000 Cutting force prediction of sculptured surface
ball-end milling using Z-map
x [58] 2000 Integrated solid modeller based solutions for
ma-chining
x [59] 2002 Development of simulation system for machining
process using enhanced Z map model
x [60] 2002 VMMC: a test-bed for machining
[61] 2002 Development of a virtual machining system, part 2: prediction and analysis of a machined surface error
x
[62] 2003 Determination of the chip geometry, cutting force and roughness in free form surfaces finishing milling, with ball end tools
x
[63] 2003 Modeling of cutting geometry and forces for 5-axis sculptured surface machining
x [64] 2003 Estimation of cutter deflection and form error in
ball-end milling processes
x [45] 2003 A solid model-based milling process simulation
and optimization system integrated with CAD/-CAM
x
Table 2.2 – continued from previous page
Ref. Year Title
Discrete v ector mo del metho d Solid mo deling based metho d Decomp osition based metho d
[65] 2003 A Z-map update method for linearly moving tools x
[66] 2003 3D simulation of tool machining x
[67] 2004 Undo facilities for the extended z-buffer in NC machining simulation
x [68] 2004 Mean cutting force prediction in ball-end milling
using force map method
x [69] 2004 Enhanced virtual machining for sculptured
sur-faces by integrating machine tool error models into NC machining simulation
x
[70] 2004 CAD approach for simulation of generation ma-chining and identification of contact lines
x [71] 2005 Simulation of flank milling processes x [43] 2005 Hybrid cutting simulation via discrete vector
model
x [72] 2006 Chip volume prediction using a numerical control
verification model
x [73] 2007 Off line simulation system of machining processes x [74] 2007 Octree-to-BRep conversion for volumetric NC
simulation
x [75] 2007 Incomplete mesh offset for NC machining x
[76] 2008 Feedrate scheduling for free-form surface using an NC verification model
x
[40] 2008 Extended octree for cutting force prediction x [77] 2008 Virtual cutting and optimization of three-axis
milling processes
x [78] 2009 Modeling and simulation of 5-axis milling
pro-cesses
x
Discrete vector method
The vector-based method [43, 49, 79] or discrete vector model (DVM) represents the workpiece as a set of position and direction vectors. The simplest method for representing the workpiece is the Z mapping.
Z mapping Geometric simulation of milling process using Z map method is based on Z buffer algorithm which is developed for making shaded images of solid models in computer graphics. Anderson [80] introduced Z map method to display final shape of sculptured surfaces. Subsequent investigations were con-ducted by Hook [47] and Hsu and Yang [81] to enhance capability and simulation efficiency of Z map method. To verify NC program as well as to optimize the cutting condition using Z map model, estimation of cutting force and
establish-ment of machining data base has been suggested by several researches [50, 82]. Because of its simple data structure and fast computation time of conventional Z map model, it is considered that Z map can be used to predict cutting force in ball end milling and generate tool path planning [54, 57].
The conventional Z map is a special form of decomposition model in which the heights at the grid center are stored in 2D arrays [59]. The process of obtaining Z map data can be regarded as a “virtual” digitizing process. The Z map sampling process is carried out as follows. Let (x0, y0) be the corner point (bottom-left
corner) of a rectangular nonparametric domain on which the regular grid is to be defined in xy plane as Figure 2.4.
Figure 2.4: Data structure of conventional Z map [59].
When r is the grid size, the grid point (xi, yi) is determined by
¨
xi= x0+ ri
yi = y0+ rj
(2.1)
The update of workpiece geometry, i.e. the simulation of cutting process, merely consists of checking calculated height value at a grid (xi, yi). If stored value is
higher than the surface of the tool movement swept volume, then Z map model is updated to the surface generated by the cutter. The distance between the initial (before cutting) and the final (after cutting) Z value can be used for describing the actual chip removal volume.
Due to the discrete nature of the data structure in conventional Z map model, Boolean subtraction is executed only at the center of each pixel. In conventional Z map, part model or cutter immersion geometry is detected at regular grid point as Figure 2.5. As a tool envelope moves downward continuously, removed volume is acquired by Boolean subtraction operation.
The accuracy of point sampling process in conventional Z map model is deter-mined only by the grid size as Figure 2.5. As a tool envelope moves downward continuously, removal volume in conventional Z map is detected only at each grid center, as shown in solid line in Figure 2.5 (a), though exact removal volume is increased linearly as dotted line in Figure 2.5 (a). Smaller grid size can increase the accuracy of simulation, but cannot eliminate it. When the grid size of Z map is decreased by half as shown in Figure 2.5 (b) and (c), the resolution of Boolean operation is increased twice. And, consequently, computation time and memory usage is quadrupled. By this excessive cost in improving accuracy, it is hard to eliminate simulation error in conventional Z map. With the representation of
Figure 2.5: Relations between resolution of Boolean operation and grid size in conventional Z map model [59].
final surface with relatively flat geometry, the accuracy of conventional Z map is sufficient. But it is insufficient to detect material removal volume with relatively small tool diameter or narrowly aligned tool path where fine Boolean subtraction is required.
An enhanced Z-map model has been presented by Lee et al. [59]. The enhanced Z-map model is based on the principle of over-sampling. For every element of the grid more than one sample is considered. Then, all the samples for an element are integrated to obtain the final value for the element. The surfaces obtained with conventional Z-map model and enhanced Z-map model have been compared and the enhanced method proved to produce results 2-5 times more accurate than conventional Z-map with the same computation time.
Discrete vector model method A different workpiece representation could be given by the Discrete normal vector (DNV) model [43, 63]. It consists of discrete vectors whose direction vectors are surface normal vectors, where all directions are not necessarily identical, see Figure 2.6. The z-map can be thought of as a special type of DVM, where all discrete direction vectors are unidirectional along the z-axis of a Cartesian coordinate frame.
As shown in Figure 2.7, this method compared to the conventional Z mapping method has the capability to represent more complex shapes with vertical walls, sharp edges, and overhangs. On the other hand, significant geometry changes in the workpiece during cutting simulation are not handled due to the fixed direction of the unit vectors. For this reason, the method is only suitable for finishing machining of complex shapes. However, as highlighted in Z mapping method, this method is very simple and requires low consumption of computer memory.
Figure 2.7: DVM and Z map. (a) DVM model and modeling schema, (b) Z map model and modeling schema [43].
Solid modeling based method
Nowadays, standard CAD environments can be roughly subdivided into two cat-egories depending on the object representation: solid modeling by constructive solid geometry (CSG) modelers and boundary representation (B-Rep) modelers. These modelers are known as solid modelers or volume modelers and they give unambiguous representation of a wide range of objects. The objects modeled by these solid modelers are used for FEM analysis, contact geometry analysis, mass property calculation, interference checking, production of realistic images and generation of different views of 2D and 3D drawing .
In CSG modeling, an object is built with simpler solid primitives. The modeler uses a set of Boolean operators such as union, intersection and subtraction to build and edit the model. These modelers are limited to simpler objects [70].
Many works have been done using CSG modellers. As an example, Spence et al. [58] proposed milling process simulation combined with online monitoring and control for a 2-1/2 D pocket milling application using ACIS solid modeller kernel.
