Doc. Ing. Miroslav Píška, CSc.

MACHINING TODAY: FROM THEORY TO APPLICATIONS

OBRÁBĚNÍ DNES: OD TEORIE K APLIKACÍM

BRNO 2008

A THESIS OF A TALK FOR THE PROFESSIORIAL APPOINTIVE PROCEDURE IN THE STUDY FIELD

OF MANUFACTURNG TECHNOLOGY

BRNO UNIVERSITY OF TECHNOLOGY FACULTY OF MECHANICAL ENGINEERING

Key words machining, cutting, drilling, milling, tool, wear, force, specific cutting force, specific energy of cutting, coating Klíčová slova obrábění, řezání, vrtání, frézování, nástroj, opotřebení, síla, měrná řezná síla, měrná energie obrábění, povlakování

Miroslav Píška, 2008 ISBN 978-80-214-3777-7 ISSN 1213-418X

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CONTENTS

Author´s Introduction ....................................................................................................... 4

Background .................................................................................................................. 6

1 INTRODUCTION .............................................................................................. 7

2 THEORETICAL AND EXPERIMENTAL ANALYSIS OF SHOULDER MILLING............................................................................................................

2.1 Analysis of chip cross-section and tool loading .................................................

2.2 Geometrical model of the cutting tool ................................................................

2.3 CALCULATIONS OF THE TOOL DEFORMATIONS...................................

2.3.1 Analytical solution .........................................................................................

2.3.2 Analysis with the FEA (Finite Element Method) ..........................................

2.4 EXPERIMENTAL .............................................................................................

2.5 RESULTS ...........................................................................................................

2.5.1 FEA stress-strain analysis ..............................................................................

2.5.2 Application of the results in the CNC machining – advanced tool deflection compensations ..............................................................................

2.6 OTHER TECHNOLOGICAL MEASURES FOR A BATCH PRODUCTION - EFFECT OF COOLING AND PVD COATING, SOLID CARBIDE CUTTERS .........................................................................................................

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12

12

13

13

13

13

15

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3 THEORETICAL AND EXPERIMENTAL ANALYSIS OF DRILLING FOR TRANSOSSEOUS EXTERNAL FIXATION ..................................................

3.1 K-WIRE tip design .............................................................................................

3.2 Mechanical work and heat inserted when drilling .............................................

3.3 Mechanical loading of the K-WIRE, its performance ........................................

3.4 A new K-wire fixation ........................................................................................

3.5 Other bio-mechanical in vitro tests for implant insertion ..................................

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17

19

20

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224 CONCLUSIONS .............................................................................. 23

References ....................................................................................................................

24

Czech Abstract (Shrnutí) .............................................................................................

30

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Author’s Introduction

Name: Miroslav Píška Born: July 8, 1961 Uherské Hradiště, Czech Republic

Education and degrees 1984, Ing. (MSc.) Brno University of Technology, Faculty of Mechanical

Engineering, specialization Manufacturing Technology 1989, CSc. (Ph.D.) Brno University of Technology, Faculty of Mechanical

Engineering, specialization Manufacturing Technology 2001, Doc. (Assoc. Prof.) Brno University of Technology, Faculty of Mechanical

Engineering, specialization Manufacturing Technology Profesional experience

1980-1983 Slovácké strojírny Uherský Brod, machinist 1985-1989 Brno University of Technology, Faculty of Mechanical Engineering,

specialization Manufacturing Technology, doctoral study 1989-1997 Brno University of Technology, Faculty of Mechanical Engineering,

specialization Manufacturing Technology, senior lecturer 1997-1997 The University of Sheffield, Clinical Science Centre, Senior research worker 1998-2001 Brno University of Technology, Faculty of Mechanical Engineering,

specialization Manufacturing Technology, senior lecturer 2001-2003 Brno University of Technology, Faculty of Mechanical Engineering,

specialization Manufacturing Technology, Assoc. Prof. 2003-2008 Brno University of Technology, Faculty of Mechanical Engineering,

specialization Manufacturing Technology, Assoc. Prof., Director/Vice Director/ Head of Department of Machining

Research activities

Analyses of new a cutting tool performance and PVD/CVD coatings. Mechanism of chip formation. Machinability of materials. CNC, CAD/CAM machining. Design of cutting tools for machining. Technological aspects of surgery, orthopaedics and stomatology. Optimization of machining.

Publication activities

Author or co-author of 34 papers in journals, 67 papers in conferences, 2 Czech patents, 1 pattern, 46 research works, 3 multimedial e-learning textbooks, 5 movies, 5 study supports, 1 learning textbook 12 references abroad, 36 home references

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Scientific acknowledgement

Member of 9 international scientific conference committees, member of 6 organizing conference committees. Reviewer of the scientific journals: Surface & Coating Technology - ELSEVIER, Great Britain, ISSN 0257-8972 (IF 1.678), MM Science - Czech Republic, ISSN 1212-2572, Member of the evaluation committee for The Gold Medal of Brno Grandfair (2003-08).

Teaching

BSc. and MSc. lectures: Manufacturing Technology, CNC Machining, Diploma Project, Semester Project, Experimental Methods in Machining. Ph.D. lectures: Applications of CAD/CAM in Technology of Machining, CNC Technologies in Machining. Supervisor of 78 diplomma works, 3 foreign students (ENSAM - Bordeaux, Paris, Cluny), 2 Czech students at DTU Lyngby, Denmark. Supervisor of 14 doctorand students (4 of them have defended Ph.D. thesis successfully).

Collaboration with industry (a selection)

1985-1989 VUNAR, Nové Zámky, VÚOSO Praha, LET Kunovice (High speed machining, ceramics for high speed cutting, surface integrity)

1987-1989 Bytex Brno (Cutting of textile threads) OSS Prostějov (Production of bridge parts)

1989-1992 Královopolská strojírna (Optimisation of milling technology) 1993-1994 FICEP-METORA (Optimisation of sawing) 1995-2008 LASAK Praha, MEDIN Nové Město (Optimisation of dental drill design) 1996-1997 Zbrojovka Vsetín (Optimisation of dental drill design)

(The effect of cooling on drilling) SAFINA Praha (Machining of platinum, gold and silver products)

1998-2000 FAB Rychnov (Cutting performance of end mills for Skoda Car locks) 1997-2008 JKZ Bučovice, BLASER Brno, CIMCOOL Jihlava (The effect of cooling

on machining) 1990-2008 SHM Šumperk, LISS-Platit, Czech Coating, Zbrojovka Vsetín, ZPS-FN, Zlín,

HVM Praha, Pramet Tools, Šumperk (Cutting performance of PVD coatings) 2001-2008 ZPS-FN, Zlín, K-TOOLS, Zlín, Pramet Tools, Šumperk, Vrtáky CZ, Kyjov

(Cutting performance of new cutting tools) 2000-2008 SIEMENS, Praha (Effective use of Sinumerik 810/840D for industrial CNC

use and programming)

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Background Machining today is concerned with understanding the behaviour and performance of cutting tools, machines, equipment, and manufacturing of new products. A wide range of mathematical, physical, material and mechanical disciplines is included in the field with many applications across industries, and also in surgery and orthopaedics. This works deals with the selection of applied cutting theory, wear, stress-strain analysis and CNC programming and with some engineering and technical problems in general. The author started his research of machining as a student under the supervision of Prof. Ing. L. Ptacek, CSc. at the Department of Material Science FME BUT in the years 1980-1990. His research was focused on the application of light and electron microscopy on plastic deformation as a process of dislocation mechanisms, chip separation (including fracture mechanics), surface quality (including X-ray analyses of phases and stress state) and wear. This experience was used in many applications of machining theory in the following years and also in the machining of bio-materials. The author was introduced to the art of machine control and productive manufacturing by Ing. J. Rosenfeld, CSc. (Slovacke Strojirny, Uhersky Brod) at the age of 15, and has since devoted his whole life to NC/CNC machining. Following this experience, the first part of the work describes monitoring and analyses of wear when cutting, based on time-series force measurement and statistical assessment. Special emphasis is put on specific variables evaluations as physical phenomena for cutting technology. The second part applies the measurements to cutting tool deformations and to CNC compensations for effective and precise machining. The third part deals with one of the Kirschner wire bone drilling problems and an FME BUT patented solution for external transosseal fixation. Furthermore, the author acknowledges colleagues at FME BUT, namely Prof. Ing. P. Janicek, DrSc., Assoc. Prof. RNDr. F. Knoflicek, CSc. and Assoc. Prof. RNDr. B. Maros, CSc. for their education and ethical personal examples as university teachers.

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1 INTRODUCTION A theory is something nobody believes, except the person who made it.

An experiment is something everybody believes, except the person who made it.

(Albert Einstein)

Generally, the machining processes milling, turning, drilling and grinding represent the most frequently used cutting processes. According to the theoretical fundamentals, the productivity and economic efficiency of the manufacturing processes can be substantially increased by an increase of cutting speed and feed today [1-3]. End mills with spiral flutes belong to the most frequently used for grooving and shoulder milling. The best progress is presented by the whole-carbide cutters today, but high speed steel (HSS) cutters can not be substituted in all applications [4-6]. However, bigger deflections and higher stresses can be expected for the HSS cutters due to their lower Young´s modulus in general [5-7]. This deflection affects geometry, dimensions and quality of the machined surfaces [8,9]. A rising loading of the tools can be expected due to wear development and increase of the passive and cutting forces. Calculations can be based on analytical method or the Finite Element Analysis (FEA) [10,11]. A precise geometrical model of the cutting tool, time series of the loading and material constants are needed for these computations which result in advanced CNC machining as very precise and economical technology.

2 THEORETICAL AND EXPERIMENTAL ANALYSIS OF SHOULDER MILLING 2.1 ANALYSIS OF CHIP CROSS-SECTION AND TOOL LOADING

A total differential of the cutting force Fcj and the normal component FcNj for a cutting tool with spiral flutes depends on machined material and chip cross-section, that is furthermore function of engagement angle φ, tool radius R, average chip thickness h and angle of the spiral inclination λS [12-14] – Fig. 1: ( ) dz).z,(h.Kz,dF jtcj ϕ=ϕ ( ) )z,(dFc.Kz,dF cjrcNj ϕ=ϕ , (1) where Kt, Kr are material and cutting empirical constants. For practical use the cutting force can be expressed in an integrated form [15]

,.sin..sin..2

..2

1

2

1

2

1

2

1

1112

211 ∫ ∫∫ ∫ −−− =⎟

⎠⎞

⎜⎝⎛+===

ϕ

ϕ

ϕ

ϕ

ϕ

ϕ

ϕ

ϕ

ϕϕϕϕπ

dcdfzpRkdAkdFF mco

mcmcscrcDccc (2)

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where pscr is the pitch of the screw helix, fz feed per teeth, kc1 is the specific cutting force, Ad chip cross section and mc expresses the effect of chip thickness on the specific cutting force.

F

Fz1M = F

F

Vc

F1M

Fy1M fN1= Fp1

cN1c1

x1MFf1

= F

Vf

Fig. 1 A physical model of a milling cutter force loading when machining (simplified).

The time series of the orthogonal forces downloaded from Kistler dynomometer (Fig. 2) can be defined as in Carthesian coordinate system as Fxmi, Fymi, Fzmi, where i={1,...,n} for a series of n data. Supposing, that the magnitude of the resultant force is invariant to the Kistler coordinate system and the system according to the technological nomenclature CSN ISO 3002 [16]

2p

2f

2c

2z

2y

2x1 i1i1i1Mi1Mi1Mi1i

FFFFFFF ++=++= . (3)

Fig. 2 Kistler dynometer apparatus for data acquisition. As the time synchronization of the real cutting edge angular position and time data acquisition is difficult to measure, a statistical analyses and numerical programming for the individual time intervals with p values can be used to find the maxima of the force F1, acting on one cutting edge and corresponding to the expected maximal chip-cross section in the form

{ } p/n;1j,p;1iFFFmaxF 2z

2y

2xj1 Mi1Mi1Mi1

∈∈++= . (4)

For testing of normal distribution of the variable tests χ2 and was used. Those values can be averaged for individual time series for all n data (see Fig. 3-5)

∑=

=p/n

1jj11 F

p/n1F . (5)

Anyway, the cutting forces when machining change and the change have a static and dynamic influence on tool behaviour including vibrations, tool life, quality of surface, machining rate,

F

x1M

Fz1M

F

y1M

V

aω ea p

F 1 f

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shape of chip and its flow. The force loading and its changes can be expressed as function of cutting time t

2fr

2v

2h

2p

2f

2c dt

tFdt

tFdt

tFdt

tF

dtt

Fdtt

FdF ⎟⎠⎞

⎜⎝⎛ ⋅∂∂

+⎟⎠⎞

⎜⎝⎛ ⋅∂∂

+⎟⎠⎞

⎜⎝⎛ ⋅∂∂

=⎟⎟⎠

⎞⎜⎜⎝

⎛⋅

∂∂

+⎟⎠⎞

⎜⎝⎛ ⋅∂∂

+⎟⎠⎞

⎜⎝⎛ ⋅∂∂

= (6)

or in the form regarding the significant components – cutting force Fc, feed force Ff, or transformed components – horizontal force Fh, vertical force Fv (resp. transversal force Ftr – Fig. 3)

Fig. 3 A schematic view of the force decomposition for milling and drilling [18-20].

2v

2h

2f

2c dt

tFdt

tFdt

tFdt

tFdF ⎟

⎠⎞

⎜⎝⎛ ⋅∂∂

+⎟⎠⎞

⎜⎝⎛ ⋅∂∂

=⎟⎠⎞

⎜⎝⎛ ⋅∂∂

+⎟⎠⎞

⎜⎝⎛ ⋅∂∂

= && . (7)

According to [17], these force components reflect the wear of the cutting tool in the differential equations for horizontal and vertical components of the total force

rara

hvn

n

h0

0

hhh dR

RFdF.dr

rFdFdt

tFdF ⋅

∂∂

+μ+⋅∂∂

+γ⋅γ∂∂

=⋅∂∂

= (8)

nn

vvvv dr

rF

dVBVBF

dtt

FdF ⋅

∂∂

+⋅∂∂

=⋅∂∂

= , (9)

where γo is orthogonal rake angle, VB is width of flank wear, rn is normal radius of cutting edge, Rar is roughness average on the rake plane and μ is Newton-Coulomb coefficient of friction between tool and workpiece (in the first approximation).

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Fig. 4 Example of the time series of the total force.

Fig. 5 Statistical assessment of the selected total force time series.

A stabilised machining can be determined by the equations

0tF2h

2

=∂∂

& , respectively 0tF2v

2

=∂∂

& . (10)

Fig. 6. Time series of forces Fc, FcN, Fp a F. Some typical changes of the loading forces in magnitude (up to 300 %) and orientation

can be expected as result of wear. At the beginning of machining, the cutting tip is pulled into cutting and place of chip formation. In the end of tool life, the totally worn out cutting edge is pushed out from the contact area – Fig. 6 (see Fp). Very useful variables (analogical to some physical and mechanical properties of materials) as specific cutting energy for milling is then defined as the function of total work for cutting A and volume of removed material V, cutting power Pc and removal rate Q

QP

VAe c

c == (11)

or for drilling in the form of diameter of the drill d, measured variables and cutting conditions

11

2fc

2

4fc

c d1F0012732,0

fM8

l4d

fn60l

106fnF

55,9nM

VAe ⋅⎟

⎠⎞

⎜⎝⎛ ⋅+

⋅≅

⋅⋅π

⋅⋅

⋅⎟⎠

⎞⎜⎝

⎛⋅

⋅⋅+

⋅

== . (12)

Some examples of the time series can be seen in the Fig. 7,8.

Fig. 7 Time series of specific energy for milling [21].

Fig. 8 Time series of specific cutting force and cutting power for milling [22].

2.2 GEOMETRICAL MODEL OF THE CUTTING TOOL

The short end milling HSSE PM cutters, CODE 120517m, φ10x72, with 4 flutes and straight cylindrical shanks (producer ZPS FN, share company, Zlín) were used. Three advanced geometrical models of the tools have been worked-out : • a geometry designed by SolidWorks 2007, using simplified drawing parameters – Fig. 9a; • a STL mesh, generated with the scanner ATOS II SO and use of the software ANSYS ICEM CFD (MCAE Systems) for acquisition of finite element mesh– Fig. 9b. Nevertheless, some problems have been observed with precision and distinction of fine facets of cutting tools; • a model generated by reconstructions of the STL file onto plane model by the program Tebis (MCAE Systems) – Fig. 9c. This plane model was reworked to volume model with programs Catia and Solidworks 2007. A very low discrepancy (below 0.05 mm compared to the origin STL grid) was achieved [23].

Fig. 9a-c. Three geometrical models of the tool - CAD, STL and a reconstructed model.

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2.3 CALCULATIONS OF THE TOOL DEFORMATIONS

An end mill cutter with spiraled teeth undergoes combined loading, that is composed from a torque, bending and shear under rotation. Regarding the standard claims for perpendicularity of the workpiece walls, the bending is a crucial loading. 2.3.1 Analytical solution

The cutting tool in conditions of high loading deflects from its axis of rotation and the resultant surface is not geometrically smooth and of poor quality. A perpendicular projection of cutting force onto rake of milling cutter has been used in the calculations. The cutting tool was loaded with instantaneous forces proportional to the chip cross section. The tool deflection can be calculated analytically as a deformation of fixed-end beam derived from a general active force F. The clamping end is regarded as built-in, and the flutes are considered to be made by a normal cross-section, following the spirals. Any technological deviations of the real shapes are neglected. The beam is defined by one or two cross-section characteristics J1/J2. The cutting part is defined by the inertia moment J1 of length L1, cylindrical shank with circular inertia moment J2 and length L2. Beam deformation wf can be calculated by the relation in general (E means Young’s modulus of elasticity):

∫∫∫ ∂∂

+∂

∂β+

∂∂

=∂∂

=)l(

k

p

k

)l(

zz

)l(

y

y

yF dx.

F)x(M.

)x(J)x(M.

G1dx.

F)x(T.

)x(G)x(T.

6dx.

F)x(M

.)x(J)x(M

.E1

FWw (13)

or angle of twist of the beam torsion deformation as follows:

∫ ∫∫ ∂∂

+∂∂β

+∂

∂⋅=

∂∂

=ϕ)l( )l(

k

p

k

)l(

zzy

y

yM dx.

M)x(M.

)x(J)x(M.

G1dx.

M)x(T.

)x(G)x(T

6dx.

M)x(M

.)x(J)x(M

E1

MW

(14)

where W is total stored elastic energy of the cantilever, E is Young´s modulus of elasticity, F is a loading force, M, Myx and Mk are bending and torque moments, Tz is a shearing force, Jy and Jp are inertia and polar inertia moments, G is a shear modulus of elasticity, β is a geometrical constant (1.66 for cylindrical shape of a beam with l in length). The deformations

Fig. 10 Calculated values of the beam central line deformations (simplified model). in the x distance (from the free end of the beam) can be derived in the general forms

(15) ( ) ( )323 xxl3l2

JE6Fxy +⋅⋅−⋅⋅⋅⋅

= ( ) ( )22 xlJE2

Fx −⋅⋅⋅

−=ϕ

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and the recalculated values can be seen in Fig. 10. 2.3.2 Analysis with the FEA (Finite Element Method)

The exerted total force was divided on the acting surface of this model evenly; for the STL model was the force applied directly into nodes of the loaded rake surface – Fig. 11. The calculation consisted of several periods according to the wear and load development. A change of the loaded surface geometry due to wear was not taken into consideration for stress and deformation analyses. The mesh of finite elements was made by tetrahaedrons of the size 0.5 mm, but a refinement to 0.3 mm was made for the loaded edge areas. ANSYS program/Ansys Workbench were used for the following analyses. Static loading was used as the first loading approximation.

2.4 EXPERIMENTAL

Cutting speed for down milling with the cutting tools was vc=35 m/min, feed per tooth fz=0.05 mm, axial depth of cut ap=4.0 mm, radial depth of cut ae=2.0 mm, cooling with CIMSTAR HD 650 - 5% emulsion, rate of flow 2 l/min. Statistical assessment of the data was done by Statgraphics v.5 (Statistical Graphics Corp., U.S.A.). As workpiece the steel blank 40x90-300 mm (the Czech standard ČSN 41 5241.9) with the tensile strength Rm = 1 100 MPa was used. The force measurement was checked by the pieso-electrical dynamometer Kistler 9257B, equipped with the charge amplifiers Kistler 9011A, fully controlled by a PC. A long time constant was set up. The frequency spectrum was checked by the FFT and only one (teeth frequency and their multiplications) were found. None significant influences from outer sources of vibrations or instabilities of cutting process were observed [24]. 2.5 RESULTS 2.5.1 FEA STRESS-STRAIN ANALYSIS

Static state of stress was found different with respect to the three models due to the differences in the geometries and generated meshes. Nevertheless, all three models confirmed three significant places of stress concentration (Fig. 12,13), identical for sharp and worn mill tooth:

• a root of the tooth - Fig. 12a, which is loaded from the whole tool the most. To get a good cutting performance and sufficient space for chip transport the cutting edge is pointed, but this intersection makes a stress riser where local stress is high; • a grinding run out of the flute – Fig. 12b – at the flank part of the tooth, close to the shank. The stress state comes from the bending, change of dimensions and sharp corner;

Fig. 11. Calculated mesh of the end mill for FEA.

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• a place of clamping - Fig. 12c, but an influence of this place can be expected lower in reality due to an elasticity of the holder, so the stress peaks would be lower.

Fig. 12a Stress in the teeth root. Fig. 12b Stress in the end of a flute. Fig. 12c Stress at the holder.

However, the maximum calculated values of the stresses were lower being compared to the limit strength of HSS. The reduced stresses according to HMH theory reached at the root and for a sharp edge in the beginning of cutting 380 MPa (100%), the run out 230 MPa (60%), and place at tool holder about 270 MPa (70%), approximately.

The same worn out edge (after 40 minutes of machining) and the same places of loading reached the following values 590 MPa, 350 MPa and 410 MPa, respectively. However, it was a static calculation anyway, so for dynamic impacts the total stress can be regarded as higher. The places of stress acting would not change significantly, however.

These areas correspond to the most typical places of crack initiation and fractures of end milling cutters when machining. The STL model and model reconstructed from STL are identical nearly. For CAD model the calculations confirm bigger values, but it was due to simplified geometry, having lower load-bearing cross section of the cutting part – Fig. 14. STL geometry of a real cutting tool can be used for stress and deformation relatively easily. Time consumption for the design and calculations is

shorter compared to the reconstructed model and approximately the same calculating accuracy acquired (20 minutes compared to several hours at powerful workstation HP9300). The three critical places for an end mill cutter are very typical and common for similar tools and it is very valuable to carry on further research for their advanced solutions.

Fig. 13 Critical places of tool loading.

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Fig. 14 Total deformation as function of loading force (for constant tool overhang 50 mm). 2.5.2 APPLICATION OF THE RESULTS IN THE CNC MACHINING – ADVANCED TOOL DEFLECTION COMPENSATIONS

As the name of the work declares, all these theoretical calculations should be reflected in a practical use. For example, a simple application can be seen in 4-axes shoulder milling. Normally, the mechanical loading makes a deflection of the tool and affects perpendicularity of the shoulder against the basement [25-28]. Another cutter pass should machine the non-cut chip cross-section, but due to the non-uniform chip cross section a similar new surface can be made, with additional machining time and costs.

Fig. 15 Variants of advanced tool compensations for CNC machining.

A convenient solution can be seen in the Fig. 15 and in Table 1: a continuous rotational axes or table can effectively solve the problem.

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Table 1 Example of a CNC programme for table rotation and a compensation of milling cutter (simplified and truncated). %_N_HLAVNI_MPF ;$PATH=/_N_WKS_DIR/_N_RT_WPDDEF INT J DEF INT I DEF INT PK DEF REAL AP DEF REAL UH DEF REAL ZI DEF REAL XI G17 G57 G90 G94 M06 H1 T1 D1; milling cutter G0 X-20 Y0 Z0 ... M1 G42 G94 UH=.612; total correction of the angle PK=15; number pcs for T R1=UH/PK; AP=10; axial depth of cut G0 X-10 Z=-AP M3 S2000 M08 G4 F2

...

... FOR J=1 to PK FOR I=0 to 3000 XI=I/10 AI=J*R1+I*R1/3000 YI=-AP*TAN(AI) G01 X=XI Y=YI Z=-AP A=AI F100 ENDFOR G0 Z200 M5 M9 X-10AP Z=-AP M1 ENDFOR ENDFOR X62 G0 X-10140 Z300 M30

2.6 OTHER TECHNOLOGICAL MEASURES FOR A BATCH PRODUCTION - EFFECT OF COOLING AND PVD COATING, SOLID CARBIDE CUTTERS Apart of the change of the tool substrate, an effective cooling and hard resistant PVD coating [29,30] can reduce the mechanical loading due to lower wear rate and extend the tool life – Fig. 16 – more than three times with another reduction of chattering, etc.

Fig. 16 Effect of cooling and PVD coating on the tool loading.

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3 THEORETICAL AND EXPERIMENTAL ANALYSIS OF DRILLING FOR TRANSOSSEOUS EXTERNAL FIXATION

Fig. 17 Illustrative picture of the external Ilizarov’ s fixator with the K-wires.

This part deals with a new Kirschner wire (K-wire) design and its experimental testing in laboratory conditions and clinics. This instrument (Fig. 17) is widely used in orthopaedics, surgery, traumatology and clinics for many applications of Ilizarov external transosseous long bone fixation and osteosynthesis, bone drilling and pin implant insertion [38-46]. As indications, the K-wires are used for temporary fixation during some operations as standard parts of external fixators. They can be used for definitive fixation if the fracture fragments are small (eg. wrist fractures and hand injuries). In some settings they can be used for intramedullary fixation of bones such as the ulna (lengthening of long bones). Tension band wiring is a technique in which the bone fragments are transfixed by K-wires which are then also used as an anchor for a loop of flexible wire. As the loop is tightened the bone fragments are compressed together. Fractures of the kneecap and the olecranon process of the elbow are commonly treated by this method, especially for children patients. In skeletal traction a wire is passed through the skin then transversely through the bone and out the other side of the limb. The wire is then attached to some form of traction so that the pull is applied directly to bone. K-wires can be used for temporary immobilization of a joint. After definitive fixation they are then removed. Some mechanical engineering methods for the external skeletal implant insertion have been used, mainly based on insertion into polymethylmetacrylate, wood, pig and goat bones (tibias) [47-58].

3.1 K-WIRE TIP DESIGN

For the K-wire tip production, a "V" shaped grinding wheel with low tip radius (below 0.3 mm) was prepared. The top angle of the grinding wheel and its geometrical orientation to the workpiece had been calculated, verified and optimised.

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The mathematical calculations were focused on the intersection of a general cone and two planes mostly – Fig. 18. A general hyperbolic cone intersection has been found which tends asymptotically to a straight line according to the angles a, b. For engineering calculations two intersection boundary points were taken into consideration of a straight line substitution and concave surplus material was ground away.

Fig. 18 Analytical and technological solution of the cutting geometry of the rake plane. The planes make orthogonal edge angle β0, that can be defined as

sin βo = │(a1.a2 + b1.b2 + c1.c2)/ ((a12 + b1

2 + c12). (a2

2 + b22 + c2

2))-1/2)│, (16) where a1, b1, c1 a a2, b2, c2 are components of normal vectors of rake and flank planes expressed as

ai .x + bi .y + ci .z + d = 0. (17)

To solve the flank plane orientation another condition should be defined, e.g. scalar product of he normal vector of the flank and direction vector of the intersection straight line which gives zero

s1 . n2 = 0, (18)

and to define a unit magnitude of the normal vector of the flank plane in the general form

(a22

+ b22 + c2

2)1/2 = 1. (19)

The solution results in calculation of system of three equations with three variables (substitute method is not convenient because results in the algebraic equation of the fourth order). Nevertheless, a conventional solution of the drill edge diagram can also be used effectively - Fig. 14. Final solution was optimised (Cauchy’s method) for the diameter of K-wire φ 2.5 mm, top angle 70°, diameter of core (resp. cross-lip edge) φ 0.5 mm, feed rake angle γf = 5° and rake angle γp = 5°).

In general, twelve time period can be observed when inserting K-wire into femoral diaphyseal bone with the help of thrust force measurement – Fig. 19: I run-in of the drill, passing through soft tissues and periosteum, II drilling of the first cortex (circumferential lamellae), III stabilized drilling,

19

IV reduction of the loading due to change of Haversian osteons orientation, V reduced chip flow, clogging of the K-wire with bone debris, VI first peak of the loading, VII run-out of the K-wire, finishing of the first cortex drilling, VIII passing through the medulla, IX starting of the second cortex drilling, X stabilized drilling of the second cortex, XI second peak drilling of the second cortex (circumferential lamellae), XII run-out of the drill from the second cortex.

Fig. 19 Haversian cortical bone - a structure and twelve time phases of its drilling. 3.2 MECHANICAL WORK AND HEAT INSERTED WHEN DRILLING

Mechanical work for the bone removal covers elastic and plastic deformation of the collagen fibers and the hydroxyapatite crystals mainly, including their fracture.

Considering approximately whole transformation of exerted mechanical work into heat during bone drilling and K-wire insertion, the total value within the time interval t0-t1 (with a partial participation of the cutting moment and the thrust force) can be expressed by the formula

( )dt.55.9/n).t(Mf.n).t(FQ c

t

tf

1

0

+= ∫ . (20)

For numerical data acquisition and limited data frequency approximate a summary relations were used for translation and rotary motions in the form

ii Asc

4if

k

1i

.t)).55.9/n.M()10.6/f.n.F((Q Δ+=∑

=

, (21)

where Ff(t), Ff(i) mean instantaneous thrust or feed forces, Mc(t), Mc(i) instantaneous cutting moments, n is a number of K-wire rotations, f is a feed per rotation, k is a total number of measurements and the last term ΔtAsi means the instantaneous time of drilling.

Numerous tests of the K-wire performance (and other drills) tested in vitro and in vivo have been done [59-82]. The novel type of K-wire can be characterised by its superior position

20

and statistically significant (Scheffé multiple range test, confidence level 95%) lowest effort needed for its insertion, expressed in terms of thrust force (35.23±1.43N, torque moment 0.064±0.007Nm, work needed for its insertion 32.6±2.5J - Fig 20,21, and the lowest elevation of temperature (63±3°C) measured in the place of insertion compared to the current types of K-wires (trochar, diamond) under the same cutting conditions. Two methods for optimisation of drilling conditions concluded in the lowest insertion energy for the lowest feeds and speeds, with no significant anomaly due to e.g. specific cutting force for drilling of such tissues. Scanning electron microscopy was used for morphology of drilled bone surfaces that confirmed a lower crack initiation and propagation in the drilled surface [82].

Fig. 20 A schematic view of K-wires. Fig. 21 Inserted work of the K-wires.

3.3 MECHANICAL LOADING OF THE K-WIRE, ITS PERFORMANCE

Finite element analysis confirmed an excellent drilling performance and endurance of the new drilling tips – Fig. 22-23 as had been predicted on the base of tool life testing (more than 35 holes in a hard cortical bone) – Fig. 24. A study of threaded variants of K-wires to improve anchoring performance of the implant in the bone was included also. The range of pull-out forces reached the intervals 1 792±341N (proximal part), 2 385±200N (medial part) and 1 312±322N (distal part) of pig tibia, but a reduction of 20 % of tensile strength due to thread

Fig. 22 Stress analysis of the torque loading.

Fig. 23 Stress analysis of the axial loading.

21

Fig. 24 Effect of wear due to drilling on the loading of the innovated K-wire.

cold rolling should be taken into consideration. No significant evidences have been found for cyclical dynamic loading of K-wire-bone interface, coursed by mechanical phenomena (stress, wear). Partially threaded olive K-wires were compared to a standard tension band wire fixation (AO) as well, with favouring results. A study of residual torque moments for K-wires and the Orthofix screw pins when clinically extracting in the end of healing was done. 3.4 A NEW K-WIRE FIXATION A typical problem of K-wire failure is skidding of the screw on the surface, accompanied with

Fig. 25 Pull-out test of various units with friction-gripping mechanism.

Fig. 26 Dynamic loading of the new unit with plastic deformation of the K-wire (as stopper).

22

plastic deformation and weakening of the wire. The problem is in the force composition – Fig. 25 - and possibly no high tightening moment can suppress this phenomenon. A simple, but very effective solution was invented by the author: a little dent of the K-wire in a recess makes a very effective stopper and prevents the skidding without any K-wire weakening – Fig. 26. 3.5 OTHER BIO-MECHANICAL IN VITRO TESTS FOR IMPLANT INSERTION

A general problem of the pin and screw performance consist in keeping of the pin and machine axes alignment. Normally, there is no unit for insertion and pull-out tests. A solution has been found by the author that presents a use of a CNC milling machine and the standard Kistler apparatus, with a special device for the bone holding – Fig. 27-32.

Fig. 27-32 New device for drilling end testing of the cutting loading and pull-out forces for screws, pins and other implants, an example of some tests.

The device and all laboratory arrangement confirmed a very good repeatability and consistency of the measured data so this technique is used for testing of pins, screws and other anchoring implants today in our university and the joint stock company MEDIN, Nove Mesto, nowadays.

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4 CONCLUSIONS

The measurement equipment, as well as all the procedures and analyses have been using by BUT FME and many EU companies - ZPS-FN (Zlín), Pramet Tools (Šumperk), SHM (Šumperk), LISS PLATIT (Rožnov pod Radhoštěm), Czech Coating (Rožnov pod Radhoštěm), Zbrojovka Vsetín, PIVOT (Šumperk), LASAK (Praha), PVD Pro (Kopidlno), Vrtáky CZ (Kyjov), CIMCOOL BV (Vlaardingen), K-TOOLS (Zlín), Blaser CZ (Brno), FUCHS OIL (Praha), Gühring (Albstadt), HAM-FINAL (Brno), JKZ Bučovice, SAFINA (Prague), PREFA (Brno), ROTANA (Velké Meziříčí), for more than 15 years for testing of cutting tools, technological routines, technological allowances, PVD/CVD/MTCVD coatings, cooling fluids, etc. A wide range of applications, references [31-37] and other research works have been published. Up today, 4 doctoral students succeeded in the defending their thesis based on the research and use of the hardware and software.

The new K-wire design has been patented as the Czech patent and licenced to MEDIN joint stock company MEDIN, Nove Mesto and to the company Orthofix, Buzulengo, Italy. Up today, about 200,000 pieces has been sold without any complaints or objections. In general, it may present about 50,000-100,000 human patients. The author hopes that he contributed to a alleviation of human pain, safer operations and to the advanced general health care in EU. Some references regarding the subject of the research work can be found in the works [83-95].

24

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Shrnutí

Technologie obrábění dnes zahrnuje znalosti aplikace řezných nástrojů, obráběcích strojů, příslušenství a výrobu nových součástí. Tato oblast zahrnuje aplikaci matematiky, fyziky, mechaniky a materiálových disciplín, které nalézt v řadě průmyslových odvětví, ale také v chirurgii a ortopedii. Tato práce se zabývá výběrem aplikací teorie obrábění, opotřebení, napjatostně-deformačních analýz a CNC obrábění na praktické inženýrské a technické problémy. Autor začal s výzkumem obrábění již v době studia vysoké školy pod vedením Prof. Ing. L. Ptáčka, CSc. na Katedře nauky o materiálu FS VUT v Brně v letech 1980-1990. Tento výzkum byl zaměřen na aplikaci světelné a elektronové mikroskopie při studiu plastické deformace jako procesů dislokačních mechanismů, oddělování třísek formou lomového porušování, studium kvality obrobených povrchů (včetně aplikace rentgenové analýzy fází a zbytkové napjatosti) a fyzikálně-mechanických mechanismů opotřebení. Autor tyto poznatky využil v následujících letech v řadě aplikací teorie obrábění a také při obrábění biomateriálů. Nicméně, NC a CNC obrábění věnoval prakticky celý život od svých patnácti let, kdy ho Ing. J. Rosenfeld, CSc. zasvětil do umění řízení obráběcích strojů a produktivního obrábění. V souladu s těmito zkušenostmi popisuje první část této práce monitorování a analýzu opotřebení při obrábění na základě silových měření a statistického zpracování dat v digitálním tvaru. Zvláštní důraz je kladen na měrné veličiny jako významné fyzikální veličiny technologie obrábění. Zkušenosti z této oblasti využívá více než 20 výrobních společností v České republice i ze zahraničí.V druhé části práce jsou tato měření a analýzy aplikována na deformaci řezných nástrojů a CNC korekce pro efektivní přesné obrábění s aplikací na řídicí systém Sinumerik 810/840D. Třetí část práce je věnována problémům vrtání kostí pomocí tzv. Kirschnerova drátu a vlastnímu patentovanému řešení FSI VUT v Brně, které se využívá zejména při zevní transoseální skeletální fixaci v rámci prakticky celé Evropské unie.