an attempt to evaluate accuracy of diameter of shallow

CMST 21(1) 29-43 (2015) DOI:10.12921/cmst.2015.21.01.004

An Attempt to Evaluate Accuracy of Diameter of Shallow BlindHoles Drilled in Solid Wood

Bolesław Porankiewicz

Poznan University of TechnologyPiotrowo 3, 60-965 Poznan, Poland

E-mail: [email protected]

Received: 07 July 2014; revised: 13 March 2015; accepted: 13 March 2015; published online: 23 March 2015

Abstract: The paper examines accuracy of low depth, blind holes drilled in a solid wood. Evaluated were statistical de-pendencies of the exponential form with several double interactions, between shift of average hole diameter series dN anddispersion of holes diameter DH and parameters of Machine-Tool-Working element (M-T-W) set by drilling solid wood.Significant, nonlinear dependencies of the shift of average hole diameter series dN and dispersion of holes diameter DH

from height of centering spike hCS , drill lateral stiffness EL, drill bit diameter DD , radial run out of main cutting edge RR

were found.Key words: drill bit, hole diameter shift, dispersion of holes diameter, drilling parameters, solid wood, drilling machine

I. INTRODUCTION

Increasing demand on high quality products in wood in-dustry has also forced an increase of dimensional accuracyof wood machining. Dimensional accuracy of drilling pro-cesses, described by the shift of average hole diameter seriesdN and the dispersion of holes diameter DH is one of crite-ria of machining quality. In the literature, however, no quan-titative relationship between the dN and the DH and param-eters of M-T-W set by drilling wood has been developedyet. Instead of dimensional accuracy, edge quality of holesdrilled in wood and wood-based materials was recently thesubject of interest [1]. Because of limited stiffness of bothtool (typically smaller for closed cutting, in direction per-pendicular to tools side surfaces) and work piece, changes inside forces dependent from actual cutting conditions, gen-erate deviations of their mutual position, which results incutting inaccuracies [4]. This is the reason that parametersdescribing the M-T-W set influence dimensional accuracyof the drilling process. Dimensional accuracy is importantin case of fitted dimensions, especially for mixed and fixedglued connections. Studies in this field were contributory, ac-cording to an assumption about the existence of machiningtolerances. Parameters describing actual drilling conditions

were not taken into consideration. Machining accuracy wasevaluated as an average value of hole diameter and standarddeviation for undefined cutting conditions. This assumptionwas employed in works aimed at creation of a limits andfits system for wood industry [3,5,6]. It should be noted thatwidespread scarcity in the works on woodworking is not de-termining cutting parameters.

The present study attempts to evaluate quantitative de-pendencies of shallow blind holes diameter accuracy, definedby the shift of average hole diameter from nominal dimen-sion dN and the dispersion of holes diameter DH , upon pa-rameters describing M-T-W set during drilling solid wood.

II. EXPERIMENTAL

The holes were drilled in wood of Scotch pine (Pinus sylves-rtis), with the use of a multi-spindle drilling machine (typeDCWGW), and a horizontal milling and drilling machine(type DWJA). Experiments were done by vertical position ofthe DCWGW 19 working unit. The horizontal oscillations ofthe DWJA working unit was blocked.

30 B. Porankiewicz

Fig. 1. Scheme of the multi-spindle drilling machine DCWGW 19;1 – working unit, 2 – drill bit, 3 – working element, 4 – workingtable, 5 – air cylinders, 6 – electrical motor, 7 – working unit feedair cylinder, 8 – latch mechanism, 9 – snail gear box, 10 – screw

mechanism, 11 – end switch

For drilling experiments a random level of independentvariables was assumed. New drill bits as well as ones aftermultiples sharpening were used:

• with and without a centering spike,• with and without side edges,• short and long bits, having high and low stiffness EL,• small and large diameter DD,• with and without main cutting edge bevel angle BA,• with a different flute lead angle (maximum rake angle

GF ),• with different tangential STT and axial SRT side sur-

faces taper angle,• with a spiral and straight flute,• with a cylindrical grip as well as a centering spike to-

gether with mounting thread.

The holes were drilled perpendicularly to wide surfaceof wood specimen, in transversal direction towards woodgrains. The following parameters, typical for such drillingoperation, were applied. Minimum, average and maximumvalues were given.Machining parameters:

• spindle rotational speed n〈2880; 6268; 10000〉min−1,• feed per revolution fR=0.6 mm,• depth of drilled hole HO=12 mm.

Fig. 2. Scheme of the milling – drilling machine DWJA; 1 – drilling bit, 2 – tool spindle, 3 – working element, 4 – working table, 5 –electrical motor, 6 – belt transmission, 7 – hydraulic – pneumatic cylinder, 8 – throttle valve, 9 – hydraulic – pneumatic reservoir, 10– air, 11 – oil, 12 – end switch, 13 – adjustable cam, 14 – adjustable back stop, 15 – bumper, 16 – back stop switch, 17 – reversiblevalve, 18 – horizontal working table support, 19 – single acting fixing air cylinder, 20 – horizontal adjusting and fixing mechanism, 20– vertical adjusting and fixing mechanism, 22 – table turn mechanism, 23 – vertical working table support, 24 – screw mechanism, 25 –

latch mechanism, 26 – electrical motor friction brake

An Attempt to Evaluate Accuracy of Diameter of Shallow Blind Holes Drilled in Solid Wood 31

Parameters of the drill bits (Fig. 3):• drill bit diameter DD〈6.02; 11.54; 40.13〉 mm,• main edge contour rake angle GF 〈0◦; 12.52◦; 29◦〉,• main edge contour clearance angle AF 〈2◦; 15.81◦;43◦〉,• main cutting edge bevel angle in base (frontal) plainBA〈0◦; 10.83◦; 62◦〉,• side edge height hSE〈0; 0.15; 0.8〉 mm,• side surface arc length lSS〈0; 4.43; 49.4〉 mm,• height of centering spike hCS〈0; 2.27; 6.15〉 mm,• drill bits working part side surface tangential taperSTT 〈0◦; 2.46◦; 31◦〉

• drill bit working part side surface axial taper SAT

〈0; 5.11′; 87′〉 (arc minute),• lateral stiffness of drill bits mounted in a spindleEL〈8; 72.78; 1000〉N · mm−1,

• number of cutting edges z = 2.

Fig. 3. Stereometrical parameters of the drill bit; 1 – main (face)cutting edge, 2 – side edge, 3 – centering spike, hCS – centeringspike height, hSE – side edge height, lSS – side surface arc length,PF – Working plain, GF – rake angle of main cutting edge, AF –clearance of main cutting edge, BA – bevel angle of main cuttingedge, BCS – angle of centering spike, PR – tool reference plain,

PP – back plain

Parameters of accuracy of the drill bits (Fig. 3)• radial play of main cutting edge RP 〈0.01 0.02;0.07〉 mm,• radial run out of main cutting edge RR〈0; 0.44;1.8〉 mm,• axial run out of main cutting edge AR〈0; 0.12;0.9〉 mm,• radial run out of centering spike RRCS〈0; 0.08;0.55〉 mm,• axial run out of side edge ARSE〈0; 0.04; 0.19〉 mm,• rake angle difference dGF 〈0◦; 0.6◦; 1.8◦〉,• clearance angle differences dAF 〈0◦; 2.68◦; 23◦〉

• main cutting edge bevel angle in base (frontal) plaindifference dBA〈0◦; 3.48◦; 12◦〉

• side surface arc length difference dlSS〈0; 0.24; 3〉mm.• centering spike maximum asymmetry angle

dBCS〈0◦; 1.87◦; 11◦〉.Physical properties of solid wood specimens:

• Brinell hardness HB 〈0.845; 1.84; 4.025〉MPa,• moisture content 12-15 %.

Dependent variable was an average hole diameter shiftfrom nominal dimension dN〈0; 0.31; 1.42〉 mm and dis-persion of holes diameter DH〈0.04; 0.46; 2.75〉 mm.Experiments were performed for sharp drill bits.Diameter dH of 10 shallow, blind holes, drilled for one setof parameters, were measured near the edge in two perpen-dicular directions, with the use of internal micrometer withaccuracy of 0.01 mm, and an average value was taken as aresult of the measurement. The hole diameter shift dN wasthe difference between the average hole diameter dH and thedrill bit diameter DD. Dispersion of the hole diameter DH

was a standard deviation.In order to eliminate sorption or desorption dimensional

changes of machined wood specimen on holes diameter,measurements were performed just after drilling. The diam-eter of drill bits DD was measured with the use of externalmicrometer with accuracy of 0.01 mm.

The radial run out RR and axial run out AR and the ra-dial play RP of drill bits mounted in the tool spindle weremeasured with a dial gauge with accuracy of 0.01 mm, fixedwith the use of a universal magnetic stand. The lateral stiff-ness EL of drill bits mounted in the tool spindle was mea-sured with the use of a dial gauge fixed on a machine tableby magnetic stand and hand spring dynamometer.

The other linear and angular parameters of drill bits, like:hCS , hSE , lSS , SAT , STT , dGF , BA, dBA, ARSE weremeasured with the use of a tool microscope type BMI, usinga prism for drill bits fixing.

The differences dAF , dGF , dlSS and dBA were evalu-ated for left and right edges.

During the evaluation process of statistical formulas de-termining quantitative dependencies dN = f(RRCS , SAT ,ARSE , hSE , n, GF , DD, hCS , AR, RR, EL, RP , AF , dGF ,STT , HB, dBCS) and DH = f(hCS , EL, HB, RR, AR,RP , SAT , STT , RRCS , n, hSE , GF , dGF , AF , dAF , BA,lSS), linear functions, second order multinomial formulas, aswell as power type and exponential functions, with and with-out possible interactions, were analyzed in preliminary cal-culations. These relations should fit the experimental matrixby the lowest summation of residuals square SK , by the low-est SD, and by the highest correlation coefficient R betweenpredicted and observed values. It is also very important toget the proper influence of variables analyzed, especially inthe case of an incomplete experimental matrix. Usually theuse of a simpler model results in decreasing approximationquality (larger SK and SD, and lower R) and may also re-

32 B. Porankiewicz

verse the impact of lower importance variables. It should bepointed out that the statistical relationship is valid only forranges of independent variables chosen in the experimen-tal matrix. For some functions, points lying outside the an-alyzed range of independent variables, especially evaluatedfor an incomplete experimental matrix, are usually chargedby a significant error.

The most adequate models, according to the madeassumptions, appeared to be the exponential equation(1) and (2).

dN =a28 · exp (A1 +A2 +A3 +A4 +A5 +A6)

+a29 (0 < dN < 1.42) (mm)(1)

A1 =a1 · dBCS + a2 · SAT + a3 ·ARSE + a4 · hSE

A2 =a5 · n+ a6 ·GF + a7 ·DD + a8 · hCS + a9 ·AR

A3 =a10 ·RR + a11 · EL+a12 ·RP + a14 ·AF

A4 =a16 · dGF · EL + a17 · STT + a19 ·RR ·RP

+a20 ·HB + a13 · EL · hCS

A5 =a15 · hCS ·RRCS + a18 · hCS ·HB

+a21 ·RR · EL + a22 ·RRCS ·RP + a23 · dBCS ·RP

A6 =a24 · dBA ·RP + a25 · dBCS · EL

+a26 · hSE ·RP + a27 ·ARSE · hSE

DH =b34 · exp (B1 +B2 +B3 +B4 +B5 +B6)

+b35 (0.04 < DH < 2.75) (mm)(2)

B1 =b1 · dBCS · Ea28L + b2 · SAT + b3 ·ARSE · Ea29

L

+b4 · hSE

B2 =b5 · n+ b6 ·GF + b7 ·DD + b8 · hCS

B3 =b9 ·AR + b10 ·Rb24R · hb30

CS + b11 · Eb31L

+b12 ·RP · Eb33L

B4 =b13 ·RRCS + b14 ·AF + b15 · dAF + b16 · dGF

+b17 · STT

B5 =b19 ·BA + b20 ·HB · hb32CS + b18 · hb22

CS · Eb23L

B6 =b21 · hCS · lSS + b25 · hb26CS ·Rb27

P ,

where: exp(x) = ex and e = 2.7182818.Estimators, also called coefficients of regression equa-

tion, were evaluated from an incomplete experimental ma-trix having 145 data points. During the evaluation processof chosen mathematical models, unimportant or low impor-tant estimators were eliminatedusing coefficient of relative

importance CRI , defined by equation (3), by assumptionCRI > 0.1

CRI = (SK + SKOk) · S−1K · 100 (%) (3)

In equation (3) the new terms are:• SK0k – summation of square of residuals, by estimator

ak = 0,• ak – estimator of the number k in empirical formula

evaluated.Summation of square of residuals SK , standard deviation

of residuals SR, correlation coefficient R and the square ofcorrelation coefficient R2, between predicted and observedvalues were used for characterization of approximation qual-ity [2].

Calculation was performed at Poznan Supercomputingand Networking Center (PCSS) on a SGI Altix 3700 ma-chine, using an optimization program, prepared by the au-thor, based on the least square method. For the defined math-ematical formula and initial approximation, this program(Fig. 4) is searching, in an iterative manner, for a solutionwith minimum summation of square of residuals SK . Pre-ferred values of initial estimators can be any small numbers.For linear (LF), polinominal (PNF) as well as trygonomet-rical functions (TF) it can be just 1.0. For power (PF) andexponential functions (EF) can be respectively 0.1 and 0.001or smaller, depending on the value of independent variables.Corrected estimators for every loop are determined from adefined range of searches, using gradient and Monte Carlomethods as well as several combinations of them. Construc-tion of the program allows adding new parts to the statisti-cal formula. It is efficient to start calculation from a simpleequation and stepwise add new parts. It is also possible to re-move parts of the formula due to the lack of importance. Incase of reaching the local minimum or out of range instance,calculation needs interference. Depending on the size of anexperimental matrix, for LF, PNF and TF cases, a final solu-tion can be found after less than 108 iterations. For cases PFand EF, especially for a large number of independent vari-ables, interactions and number of tests, as well as in case ofpresence of local minimums, the necessary number of itera-tions can be much higher (1013).

III. RESULTS AND DISCUSSION

Appendix contains a collection of estimators and coeffi-cients of relative importance for equations (1) and (2).

Approximation quality of the fit of the equation (1) canbe characterized by the quantifiers: SK = 2.06, R =0.89; R2 = 0.80; SR = 0.12 mm, and was also illus-trated in Fig. 5. The final solution was obtained after thenumber of iteration of 5.8108. In formula (1) twelve inter-actions were found: −dGF · EL, −RR · RP , EL · hCS ,


Fig. 4. Flowing chart of the optimization program; variants: MC – Monte Carlo, G – gradient, MCG – combined MC and G, SK –summation of square of residuals, R – correlation coefficient, SR – standard deviation of residuals

hCS ·RRCS ,−hCS ·HB, RR·EL,−hCS ·RRCS , dBCS ·RP ,−dBA ·RP , dBCS ·EL, −hSE ·RP and ARSE · hSE . Themost involved independent variables in the interactions are:transversal stiffness EL, height of the centering spike hCS

and – radial play RP .The approximation quality of the fit of the equation (2)

can be characterized by quantifiers: SK = 4.83, R = 0.92,R2 = 0.84, SD = 0.18 mm, and was also illustrated in Fig.6. The final result was obtained after the number of iterationof 2.2109.

In the formula (2) eight interactions can be seen: dBCS ·EL,−ARSE ·EL, RR ·hCS , RP ·EL,−HB ·hCS , hCS ·EL,hCS · lSS , hCS · RP . The most involved independent vari-ables in the interactions are: transversal stiffness of the drillbit EL, height of the centering spike hCS , radial run out RR

and radial play RP .Figs. 5 and 6 show asymmetric distribution of measuring

points of the dN and DH . More than 60% of the dN arelower than 0.25 mm. Differences between the observed andpredicted values are low, for several ranges of the dN andDH . For some measuring points these differences are muchlarger. Uncontrolled variation of the dN and DH . (Figs. 5and 6) may have a source in random, unsymmetrical dis-tribution of wood properties in the cutting region. It is alsopossible an influence of not taken into account independentvariables or interactions. The analyzed problem looks very

complex. However, most of variation of the dN and DH ,considered in the past as machining tolerances [3,5,6] wastaken into account in the formulas (1) and (2).

Fig. 5. Plot of observed hole diameter shift dNO against predicteddNP value

Fig. 7 shows that the hole diameter shift dN strongly,non-linearly depends upon the SAT and the dBCS . With

34 B. Porankiewicz

a reduction of the SAT and the dBCS the dN significantlyincreased. The dependence of the dN from both variables bythe SAT > 40′ (where: ′ means angle minute) was negligiblysmall.

Fig. 8 shows the dN dependency from the ARSE and thehSE . An increase of the hSE , together with an decrease ofthe ARSE , significantly increased the dN , by strong increas-ing tendency.

Fig. 9 reveals slight, positive dependency of the dN fromincreasing of the n and the GF .

Fig. 10 shows hole diameter shift dN strong, non-lineardependency from the hCS and the DD. A decrease of thehCS and an increase of the DD increased the average holediameter shift dN . Reduction of the hCS caused signifi-cant enlargement of the dN , more intensive with increasingof the DD.

Fig. 6. The plot of observed hole diameter shift DHO against pre-

dicted DHP value

Fig. 11 shows influence of the RR and the AR on the dN .It can be seen that the dN strongly, nonlinearly increasedwith an enlargement of the RR for the whole range of varia-tion of the AR. However, for low values of the RR the influ-ence of the AR on the dN was negligibly small.

Fig. 12 shows dependency of the dN upon the EL andthe RP . It can be seen that the dN strongly, nonlinearly in-creased with an increase of the EL, for the whole range ofvariation of the RP . The influence of the RP on the dN , forlow values of the EL was negligibly small.

Fig. 13 shows dependency of the dN from the AF andRRCS . With increasing tendency, an enlargement of theRRCS , and decreasing of the AF the dN increased. The in-fluence of the AF was lower and disappeared starting fromRRCS < 0.1 mm.

Fig. 14 depicts influence of the dBA and the STT on thedN . An increase of the dBA results in slight decreasing ofthe dN . An increase of the STT slightly increased the dN .

Fig. 15 shows dependence of the dN upon the HB andthe dGF . An enlargement of the HB decreased the dN . Therelation dN = f(dGF ) was much smaller. An increase ofthe dGF results in slight decreasing of the dN .

Because of a large number of interactions: −dGF · EL,−RR ·RP , EL · hCS , hCS ·RRCS , −hCS ·HB, RR · EL,−hCS · RRCS , dBCS · RP , −dBA · RP , dBCS · EL,−hSE · RP and ARSE · hSE , dependencies shown in Figs.7-15 may differ for another set of independent variables.

No correlation between the dN and following indepen-dent variables: dAF , BA, lSS , dlSS was found.

Fig. 16 shows that the DH was strongly depended uponthe hSE . With an increase of the hSE and the ARSE the DH

significantly decreased. The side edge seems to have a stabi-lization effect on the a drill during work.

The hole diameter shift DH was strongly, non-linearlydependent upon the n and the GF , which can be seen inFig. 17. An increase of the n and the GF decreased the av-erage hole diameter dispersion DH . With an increase of then the DH slightly dropped down. Increasing accuracy of thedrilling process with increase of the n and GF can be as-sociated with shortening of cutting (larger n) and loweringcutting forces (lower GF ).

The hole diameter shift DH was strongly, non-linearlydependent upon the hCS and the DD, which can be seenin Fig. 18. An increase of the hCS and the DD increasedthe dispersion of hole diameter DH . With an decrease of thehCS the DH slightly dropped down. This relation was moreintensive for large DD and hCS . For low hCS the relationDH = f(DD) was negligibly small.

The hole diameter shift DH was strongly, non-linearlydepend upon the RR, which can be seen in Fig. 19. An in-crease of the RR increased the dispersion of hole diameterDH . This influence of the relation AR was negligibly smallfor low values of the RR.

Fig. 20 shows dependency of the RP upon the EL. It canbe seen that the DH strongly, nonlinearly decreased with anincrease of the RP , especially for larger values of the EL.For low EL the relation DH = f(RP ) was negligibly small.

Fig. 21 shows dependency of the DH upon the AF andthe RRCS . It can be seen that the DH nonlinearly decreasedwith an increase of the AF . The influence of the RRCS onthe Dh was very small.

Fig. 22 shows the DH dependency on the dGF and thedAF . With an increase of the dGF the DH decreased. Theinfluence of the dAF was opposite and lower, especially forthe highest dGF .

Fig. 23 depicts the influence of the STT and the BA onthe DH . An increase of the STT and of the BA results inslightly increasing of the DH .

Fig. 24 shows the influence of the HB and the hCS

on the DH . An increase of the hCS slightly decreased theDH for large values of the HB. For small values of theHB, increasing value of the hCS rapidly increasing of theDH can be seen. For high hCS and the HB the relationDH = f(hCS , HB) was negligibly small.


Fig.

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9.Pl

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betw

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36 B. Porankiewicz

Fig.

10.

Plot

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nbe

twee

nth

eho

ledi

am-

eter

shif

tdN

and

the

drill

bit

diam

eter

DD

and

the

heig

htof

cent

erin

gsp

ikehCS

;cen

teri

ngsp

ike

max

imum

asym

met

ryan

gledB

CS=

1.9

mm

;dri

llbi

twor

king

part

side

surf

ace

axia

ltap

erSAT=

5′ ;

axia

lrun

outo

fsi

deed

geA

RSE

=0.4

mm

;sid

eed

gehe

ight

hSE

=0.8

mm

;sp

indl

ero

tatio

nal

spee

dn

=2880

min−1;

mai

ned

geco

ntou

rra

kean

gleG

F=

12◦;

axia

lru

nou

tof

mai

ncu

tting

edge

AR

=0.1

mm

;ra

dial

run

out

ofm

ain

cut-

ting

edge

RR

=0.4

mm

;la

tera

lst

iffne

ssof

drill

bits

mou

nted

ina

spin

dleE

L=

140

Nm

m−1;r

a-di

alpl

ayof

mai

ncu

tting

edge

RP=

0.02

mm

;ra-

dial

run

outo

fce

nter

ing

spik

eR

RCS=

0.08

mm

;m

ain

edge

cont

ourc

lear

ance

angl

eA

F=

15◦;r

ake

angl

edi

ffer

ence

sdG

F=

0.6◦;

drill

bits

wor

king

part

side

surf

ace

tang

entia

ltap

erSTT

=2◦;m

ain

cutti

nged

gebe

vel

angl

ein

base

plai

ndi

ffer

ence

dB

A=

3◦;B

rine

llha

rdne

ssHB

=4

MPa

Fig.

11.

Plot

ofre

latio

nbe

twee

nth

eho

ledi

am-

eter

shif

tdN

and

the

axia

lru

nou

tof

mai

ncu

t-tin

ged

geA

Ran

dth

era

dial

run

out

ofm

ain

cut-

ting

edge

RR

;cen

teri

ngsp

ike

max

imum

asym

me-

try

angl

edB

CS

=1.9

mm

;dri

llbi

twor

king

part

side

surf

ace

axia

lta

perSAT

=5′ ;

axia

lru

nou

tof

side

edge

ARSE

=0

mm

;si

deed

gehe

ight

hSE

=0

mm

;spi

ndle

rota

tiona

lspe

edn=

2880

min−1;m

ain

edge

cont

our

rake

angl

eG

F=

29◦;

heig

htof

cent

erin

gsp

ikehCS

=6

mm

;dr

illbi

tdi

amet

erD

D=

11

mm

;la

tera

lst

iffne

ssof

drill

bits

mou

nted

ina

spin

dleE

L=

42

Nm

m−1;

ra-

dial

play

ofm

ain

cutti

nged

geR

P=

0.01

mm

;ra-

dial

run

outo

fce

nter

ing

spik

eR

RCS=

0.08

mm

;m

ain

edge

cont

ourc

lear

ance

angl

eA

F=

15◦;r

ake

angl

edi

ffer

ence

sdG

F=

0.6◦;

drill

bits

wor

king

part

side

surf

ace

tang

entia

ltap

erSTT

=2◦;m

ain

cutti

nged

gebe

vel

angl

ein

base

plai

ndi

ffer

ence

dB

A=

3◦;B

rine

llha

rdne

ssHB

=4

MPa

Fig.

12.

Plot

ofre

latio

nbe

twee

nth

eho

ledi

ame-

ter

shif

tdN

and

the

late

ral

stiff

ness

ofdr

illbi

tsm

ount

edin

asp

indl

eE

Lan

dth

era

dial

play

ofm

ain

cutti

nged

geR

P;

cent

erin

gsp

ike

max

imum

asym

met

ryan

gledB

CS=

1.9

mm

;dri

llbi

twor

k-in

gpa

rtsi

desu

rfac

eax

ial

tape

rSAT

=5′ ;

axia

lru

nou

tof

side

edge

ARSE

=0.1

mm

;sid

eed

gehe

ight

hSE

=0.1

mm

;sp

indl

ero

tatio

nal

spee

dn

=2880

min−1;

mai

ned

geco

ntou

rra

kean

gle

mai

ned

geco

ntou

rra

kean

gleG

F=

0◦;h

eigh

tof

cent

erin

gsp

ikehCS

=1.5

mm

;dr

illbi

tdi

ame-

terD

D=

11

mm

;ax

ial

run

out

ofm

ain

cutti

nged

geA

R=

0.1

mm

;ra

dial

run

out

ofm

ain

cut-

ting

edge

RR

=0.6

mm

;rad

ialr

unou

tof

cent

er-

ing

spik

eR

RCS

=0.08

mm

;m

ain

edge

cont

our

clea

ranc

ean

gleA

F=

15◦;r

ake

angl

edi

ffer

ence

sdG

F=

0.6◦;

drill

bits

wor

king

part

side

surf

ace

tang

entia

ltap

erSTT=

2◦;m

ain

cutti

nged

gebe

vel

angl

ein

base

plai

ndi

ffer

ence

dB

A=

3◦;

Bri

nell

hard

ness

HB

=4

MPa


Fig.

13.

Plot

ofre

latio

nbe

twee

nth

eho

ledi

am-

eter

shif

tdN

and

the

radi

alru

nou

tof

cent

erin

gsp

ikeR

RCS

and

the

mai

ned

geco

ntou

rcl

eara

nce

angl

eA

F;

cent

erin

gsp

ike

max

imum

asym

met

ryan

gledB

CS

=1.9

mm

;dr

illbi

tw

orki

ngpa

rtsi

desu

rfac

eax

ial

tape

rSAT

=5′ ;

axia

lru

nou

tof

side

edge

ARSE

=0.04

mm

;si

deed

gehe

ight

hSE=

0.8

mm

;spi

ndle

rota

tiona

lspe

edn=

2880

min−1;m

ain

edge

cont

our

rake

angl

eG

F=

12◦;

heig

htof

cent

erin

gsp

ikehCS

=6

mm

;dr

illbi

tdi

amet

erD

D=

11

mm

;axi

alru

nou

tofm

ain

cut-

ting

edge

AR

=0.1

mm

;ra

dial

run

out

ofm

ain

cutti

nged

geR

R=

0.4

mm

;la

tera

lst

iffne

ssof

drill

bits

mou

nted

ina

spin

dleE

L=

8N

mm−1;

radi

alpl

ayof

mai

ncu

tting

edge

RP

=0.02

mm

;ra

kean

gle

diff

eren

cesd

GF=

0.6◦;d

rill

bits

wor

k-in

gpa

rtsi

desu

rfac

eta

ngen

tial

tape

rSTT

=2◦;

mai

ncu

tting

edge

beve

lang

lein

base

plai

ndi

ffer

-en

cedB

A=

3◦;B

rine

llha

rdne

ssHB

=4

MPa

Fig.

14.P

loto

fre

latio

nbe

twee

nth

eho

ledi

amet

ersh

iftdN

and

the

drill

bits

wor

king

part

side

sur-

face

tang

entia

ltap

erSTT

and

the

mai

ncu

tting

edge

beve

lan

gle

inba

sepl

ain

diff

eren

cedB

A;

cent

er-

ing

spik

em

axim

umas

ymm

etry

angl

edB

CS

=1.9

mm

;dri

llbi

twor

king

part

side

surf

ace

axia

ltap

erSAT=

5′ ;

axia

lrun

outo

fsid

eed

geA

RSE=

0.04

mm

;sid

eed

gehe

ighthSE=

0.8

mm

;spi

ndle

rota

-tio

nals

peed

n=

2880

min−1;m

ain

edge

cont

our

rake

angl

eG

F=

12◦;

heig

htof

cent

erin

gsp

ike

hCS

=1

mm

;dr

illbi

tdi

amet

erD

D=

11

mm

;ax

ialr

unou

tof

mai

ncu

tting

edge

AR

=0.1

mm

;ra

dial

run

outo

fmai

ncu

tting

edge

RR=

0.4

mm

;la

tera

lst

iffne

ssof

drill

bits

mou

nted

ina

spin

dle

EL

=72

Nm

m−1;

radi

alpl

ayof

mai

ncu

tting

edge

RP

=0.02

mm

;ra

dial

run

out

ofce

nter

-in

gsp

ikeR

RCS

=0.08

mm

;m

ain

edge

cont

our

clea

ranc

ean

gleA

F=

15◦;r

ake

angl

edi

ffer

ence

sdG

F=

0.6◦;B

rine

llha

rdne

ssHB

=4

MPa

Fig.

15.P

loto

fre

latio

nbe

twee

nth

eho

ledi

amet

ersh

iftd

Nan

dth

eB

rine

llha

rdne

ssHB

and

the

rake

angl

edi

ffer

ence

sdG

F,a

ccor

ding

toeq

uatio

n(3

);dB

CS

=1.9

mm

;dr

illbi

tw

orki

ngpa

rtsi

desu

r-fa

ceax

ial

tape

rSAT

=5′ ;

axia

lru

nou

tof

side

edge

ARSE

=0.04

mm

;sid

eed

gehe

ight

hSE

=0.8

mm

;spi

ndle

rota

tiona

lspe

edn=

2880

min−1;

mai

ned

geco

ntou

rra

kean

gleG

F=

0◦;h

eigh

tof

cent

erin

gsp

ikehCS

=1.5

mm

;dr

illbi

tdi

ame-

terD

D=

6m

m;

axia

lru

nou

tof

mai

ncu

tting

edge

AR=

0.2

mm

;rad

ialr

unou

tofm

ain

cutti

nged

geR

R=

0.2

mm

;la

tera

lst

iffne

ssof

drill

bits

mou

nted

ina

spin

dleE

L=

8N

mm−1;r

adia

lpla

yof

mai

ncu

tting

edge

RP

=0.01

mm

;ra

dial

run

outo

fce

nter

ing

spik

eR

RCS=

0m

m;m

ain

edge

cont

our

clea

ranc

ean

gleA

F=◦;

drill

bits

wor

k-in

gpa

rtsi

desu

rfac

eta

ngen

tial

tape

rSTT

=0◦;

mai

ncu

tting

edge

beve

lang

lein

base

plai

ndi

ffer

-en

cedB

A=

0◦

38 B. Porankiewicz

Fig.

16.

The

plot

ofre

latio

nbe

twee

nth

edi

sper

-si

onof

hole

diam

eter

DH

and

the

axia

lrun

outo

fsi

deed

geA

RSE

and

the

side

edge

heig

hthSE

;cen

-te

ring

spik

em

axim

umas

ymm

etry

angl

edB

CS

=11

mm

;dr

illbi

tw

orki

ngpa

rtsi

desu

rfac

eax

ial

ta-

perSAT

=5’;

spin

dle

rota

tiona

lsp

eedn

=2880

min−1;

mai

ned

geco

ntou

rra

kean

gleG

F=

0◦;

heig

htof

cent

erin

gsp

ikehCS=

0.2

mm

;dri

llbi

tdi

amet

erD

D=

11

mm

;axi

alru

nou

tofm

ain

cut-

ting

edge

AR

=0.4

mm

;ra

dial

run

out

ofm

ain

cutti

nged

geR

R=

0.6

mm

;lat

eral

stiff

ness

ofdr

illbi

tsm

ount

edin

asp

indl

eE

L=

72

Nm

m−1;

ra-

dial

play

ofm

ain

cutti

nged

geR

P=

0.02

mm

;ra-

dial

run

outo

fce

nter

ing

spik

eR

RCS=

0.08

mm

;m

ain

edge

cont

our

clea

ranc

ean

gleA

F=

15◦;

clea

ranc

ean

gle

diff

eren

cesdA

F=

2◦;

rake

an-

gle

diff

eren

cesdG

F=

0.6◦;

drill

bits

wor

king

part

side

surf

ace

tang

entia

ltap

erSTT

=2◦;m

ain

cutti

nged

gebe

vel

angl

ein

base

plai

ndi

ffer

ence

dB

A=

3◦;m

ain

cutti

nged

gebe

vela

ngle

inba

sepl

ainB

A=

10◦;B

rine

llha

rdne

ssHB

=4

MPa

Fig.

17.

The

plot

ofre

latio

nbe

twee

nth

edi

sper

-si

onof

hole

diam

eter

DH

and

the

spin

dle

rota

-tio

nals

peed

nan

dth

em

ain

edge

cont

ourr

ake

angl

eG

F;

cent

erin

gsp

ike

max

imum

asym

met

ryan

gle

dB

CS=

0m

m;d

rill

bitw

orki

ngpa

rtsi

desu

rfac

eax

ialt

aper

SAT

=87′ ;

axia

lrun

outo

fsi

deed

geA

RSE

=0

mm

;si

deed

gehe

ight

hSE

=0

mm

;he

ight

ofce

nter

ing

spik

ehCS

=0.01

mm

;dr

illbi

tdi

amet

erD

D=

8m

m;

axia

lru

nou

tof

mai

ncu

tting

edge

AR=

0.9

mm

;rad

ialr

unou

tofm

ain

cutti

nged

geR

R=

1.8

mm

;lat

eral

stiff

ness

ofdr

illbi

tsm

ount

edin

asp

indl

eE

L=

90

Nm

m−1;

ra-

dial

play

ofm

ain

cutti

nged

geR

P=

0.07

mm

;ra

dial

run

out

ofce

nter

ing

spik

eR

RCS

=0

mm

;m

ain

edge

cont

our

clea

ranc

ean

gleA

F=

43◦;

clea

ranc

ean

gle

diff

eren

cesdA

F=

23◦;

rake

an-

gle

diff

eren

cesdG

F=

1.8◦;

drill

bits

wor

king

part

side

surf

ace

tang

entia

ltap

erSTT=

31◦;m

ain

cutti

nged

gebe

vel

angl

ein

base

plai

ndi

ffer

ence

dB

A=

3◦;m

ain

cutti

nged

gebe

vela

ngle

inba

sepl

ainB

A=

0◦;B

rine

llha

rdne

ssHB

=4

MPa

Fig.

18.T

hepl

otof

rela

tion

betw

een

the

disp

ersi

onof

hole

diam

eter

DH

and

the

drill

bitd

iam

eter

DD

and

the

heig

htof

cent

erin

gsp

ikehCS

,ac

cord

ing

toeq

uatio

n(3

);dB

CS=

11

mm

;dri

llbi

twor

king

part

side

surf

ace

axia

ltap

erSAT=

5′ ;

axia

lrun

out

ofsi

deed

geA

RSE

=0.04

mm

;sid

eed

gehe

ight

hSE=

0.2

mm

;spi

ndle

rota

tiona

lspe

edn=

2880

min−1;m

ain

edge

cont

our

rake

angl

eG

F=

12◦;

axia

lrun

outo

fm

ain

cutti

nged

geA

R=

0.4

mm

;ra

dial

run

outo

fmai

ncu

tting

edge

RR=

0.6

mm

;la

tera

lst

iffne

ssof

drill

bits

mou

nted

ina

spin

dle

EL=

8N

mm−1;r

adia

lpla

yof

mai

ncu

tting

edge

RP

=0.02

mm

;rad

ialr

unou

tof

cent

erin

gsp

ike

RRCS=

0.08

mm

;AF

=15◦;d

AF

=2◦;r

ake

angl

edi

ffer

ence

sdG

F=

0.6◦;

drill

bits

wor

king

part

side

surf

ace

tang

entia

ltap

erSTT

=2◦;m

ain

cutti

nged

gebe

vel

angl

ein

base

plai

ndi

ffer

ence

dB

A=

3◦;m

ain

cutti

nged

gebe

vela

ngle

inba

sepl

ainB

A=

10◦;B

rine

llha

rdne

ssHB

=1

MPa


Fig.

19.T

hepl

otof

rela

tion

betw

een

the

disp

ersi

onof

hole

diam

eter

DH

and

the

radi

alru

nou

tofm

ain

cutti

nged

geR

Ran

dth

eax

ialr

unou

tof

mai

ncu

t-tin

ged

geA

R;c

ente

ring

spik

em

axim

umas

ymm

e-tr

yan

gledB

CS

=11

mm

;dr

illbi

tw

orki

ngpa

rtsi

desu

rfac

eax

ial

tape

rSAT

=5′ ;

axia

lru

nou

tof

side

edge

ARSE

=0.04

mm

;sid

eed

gehe

ight

hSE=

0.8

mm

;spi

ndle

rota

tiona

lspe

edn=

2880

min−1;m

ain

edge

cont

our

rake

angl

eG

F=

12◦;

heig

htof

cent

erin

gsp

ikehCS=

0.1

mm

;dri

llbi

tdi

amet

erD

D=

12

mm

;lat

eral

stiff

ness

ofdr

illbi

tsm

ount

edin

asp

indl

eE

L=

150

Nm

m−1;

radi

alpl

ayof

mai

ncu

tting

edge

RP

=0.02

mm

;rad

ial

run

outo

fcen

teri

ngsp

ikeR

RCS=

0.08

mm

;mai

ned

geco

ntou

rcl

eara

nce

angl

eA

F=

15◦;

clea

r-an

cean

gle

diff

eren

cesdA

F=

2◦;dG

F=

0.6◦;

drill

bits

wor

king

part

side

surf

ace

tang

entia

lta

-pe

rSTT

=2◦;

mai

ncu

tting

edge

beve

lan

gle

inba

sepl

ain

diff

eren

cedB

A=

3◦;m

ain

cutti

nged

gebe

vela

ngle

inba

sepl

ainB

A=

10◦;B

rine

llha

rd-

ness

HB

=0.85

MPa

Fig.

20.T

hepl

otof

rela

tion

betw

een

the

disp

ersi

onof

hole

diam

-et

erD

Han

dth

era

dial

play

ofm

ain

cutti

nged

geR

Pan

dth

ela

t-er

alst

iffne

ssof

drill

bits

mou

nted

ina

spin

dleE

L;c

ente

ring

spik

em

axim

umas

ymm

etry

angl

edB

CS

=11

mm

;dr

illbi

tw

orki

ngpa

rtsi

desu

rfac

eax

ialt

aper

SAT=

5′ ;

axia

lrun

outo

fsi

deed

geA

RSE

=0.04

mm

;si

deed

gehe

ight

hSE

=0.1

mm

;sp

indl

ero

tatio

nal

spee

dn=

2880

min−1;

mai

ned

geco

ntou

rra

kean

gle

GF

=12◦

;dri

llbi

tdia

met

erD

D=

11

mm

;hCS=

1.5

mm

;ax-

ial

run

out

ofm

ain

cutti

nged

geA

R=

0.1

mm

;ra

dial

run

out

ofm

ain

cutti

nged

geR

R=

0.4

mm

;ra

dial

run

out

ofce

nter

-in

gsp

ikeR

RCS=

0.08

mm

;mai

ned

geco

ntou

rcl

eara

nce

angl

eA

F=1

5◦;c

lear

ance

angl

edi

ffer

ence

sdA

F=

2◦;r

ake

angl

edi

f-fe

renc

esdG

F=

0.6◦;d

rill

bits

wor

king

part

side

surf

ace

tang

en-

tialt

aper

STT

=2◦;m

ain

cutti

nged

gebe

vela

ngle

inba

sepl

ain

diff

eren

cedB

A=

3◦;m

ain

cutti

nged

gebe

vela

ngle

inba

sepl

ain

BA

=10◦;

Bri

nell

hard

ness

HB

=0.85

MPa

cent

erin

gsp

ike

max

imum

asym

met

ryan

gledB

CS

=11

mm

;dr

illbi

tw

orki

ngpa

rtsi

desu

rfac

eax

ial

tape

rSAT

=87′ ;

axia

lru

nou

tof

side

edge

ARSE

=0

mm

;si

deed

gehe

ight

hSE

=0

mm

;sp

indl

ero

tatio

nals

peed

n=

2880

min−1;m

ain

edge

cont

our

rake

angl

eG

F=0◦;h

eigh

tofc

ente

ring

spik

ehCS

;dri

llbi

tdia

met

erD

D=

6m

m;

axia

lru

nou

tof

mai

ncu

tting

edge

AR

=0.2

mm

;ra

dial

run

out

ofm

ain

cutti

nged

geR

R=

0.4

mm

;la

tera

lst

iffne

ssof

drill

bits

mou

nted

ina

spin

dleE

L=

72

Nm

m−1;

radi

alpl

ayof

mai

ncu

tting

edge

RP

=0.05

mm

;ra

dial

run

out

ofce

nter

-in

gsp

ikeR

RCS=

0.55

mm

;mai

ned

geco

ntou

rcl

eara

nce

angl

eA

F=

43◦;c

lear

ance

angl

edi

ffer

ence

sdA

F=

23◦;r

ake

angl

edi

ffer

ence

sdG

F=

1.8◦;d

rill

bits

wor

king

part

side

surf

ace

tan-

gent

ial

tape

rSTT

=0◦;

mai

ncu

tting

edge

beve

lan

gle

inba

sepl

ain

diff

eren

cedB

A=

12◦;

mai

ncu

tting

edge

beve

lan

gle

inba

sepl

ainB

A=

31◦;B

rine

llha

rdne

ssHB

Fig.

21.T

hepl

otof

rela

tion

betw

een

the

disp

ersi

onof

hole

diam

eter

DH

and

the

radi

alru

nou

tofc

en-

teri

ngsp

ikeR

RCS

and

the

mai

ned

geco

ntou

rcle

ar-

ance

angl

eA

F;c

ente

ring

spik

em

axim

umas

ymm

e-tr

yan

gledB

CS

=11

mm

;dr

illbi

tw

orki

ngpa

rtsi

desu

rfac

eax

ial

tape

rSAT

=5′ ;

axia

lru

nou

tof

side

edge

ARSE

=0.04

mm

;sid

eed

gehe

ight

hSE=

0.2

mm

;spi

ndle

rota

tiona

lspe

edn=

2880

min−1;m

ain

edge

cont

our

rake

angl

eG

F=

12◦;

drill

bitd

iam

eterD

D=

11

mm

;hei

ghto

fcen

teri

ngsp

ikehCS=

4m

m;a

xial

run

outo

fm

ain

cutti

nged

geA

R=

0.1

mm

;ra

dial

run

out

ofm

ain

cut-

ting

edge

RR

=0.4

mm

;la

tera

lst

iffne

ssof

drill

bits

mou

nted

ina

spin

dleE

L=

72

Nm

m−1;

ra-

dial

play

ofm

ain

cutti

nged

geR

P=

0.02

mm

;cl

eara

nce

angl

edi

ffer

ence

sdA

F=

2◦;

rake

an-

gle

diff

eren

cesdG

F=

0.6◦;

drill

bits

wor

king

part

side

surf

ace

tang

entia

ltap

erSTT

=2◦;m

ain

cutti

nged

gebe

vel

angl

ein

base

plai

ndi

ffer

ence

dB

A=

3◦;m

ain

cutti

nged

gebe

vela

ngle

inba

sepl

ainB

A=

10◦;

Bri

nell

hard

ness

HB

=0.85

MPa

40 B. Porankiewicz

Fig.

22.

The

plot

ofre

latio

nbe

twee

nth

edi

sper

-si

onof

hole

diam

eter

DH

and

the

clea

ranc

ean

-gl

edi

ffer

ence

sdA

Fan

dth

era

kean

gle

diff

eren

ces

dG

F;

cent

erin

gsp

ike

max

imum

asym

met

ryan

gle

dB

CS

=11

mm

;dr

illbi

tw

orki

ngpa

rtsi

desu

rfac

eax

ial

tape

rSAT

=5′ ;

axia

lru

nou

tof

side

edge

ARSE

=0.19

mm

;si

deed

gehe

ight

hSE

=0.8

mm

;sp

indl

ero

tatio

nal

spee

dn

=2880

min−1;

mai

ned

geco

ntou

rra

kean

gleG

F=

12◦;

drill

bit

diam

eter

DD

=11

mm

;he

ight

ofce

nter

ing

spik

ehCS=

5m

m;a

xial

run

outo

fm

ain

cutti

nged

geA

R=

0.2

mm

;ra

dial

run

out

ofm

ain

cut-

ting

edge

RR

=0.6

mm

;la

tera

lst

iffne

ssof

drill

bits

mou

nted

ina

spin

dleE

L=

72

Nm

m−1;

ra-

dial

play

ofm

ain

cutti

nged

geR

P=

0.02

mm

;ra-

dial

run

outo

fce

nter

ing

spik

eR

RCS=

0.08

mm

;m

ain

edge

cont

our

clea

ranc

ean

gleA

F=

15◦;

drill

bits

wor

king

part

side

surf

ace

tang

entia

lta

-pe

rSTT

=2◦;

mai

ncu

tting

edge

beve

lan

gle

inba

sepl

ain

diff

eren

cedB

A=

3◦;m

ain

cutti

nged

gebe

vela

ngle

inba

sepl

ainB

A=

10◦;B

rine

llha

rd-

ness

HB

=0.85

MPa

Fig.

23.

The

plot

ofre

latio

nbe

twee

nth

edi

sper

-si

onD

Hof

hole

diam

eter

and

the

drill

bits

wor

king

part

side

surf

ace

tang

entia

ltap

erSTT

and

the

mai

ncu

tting

edge

beve

lang

lein

base

plai

nB

A;c

ente

r-in

gsp

ike

max

imum

asym

met

ryan

gledB

CS=

11

mm

;dri

llbi

twor

king

part

side

surf

ace

axia

ltap

erSAT=

5′ ;

axia

lrun

outo

fsid

eed

geA

RSE=

0.19

mm

;sid

eed

gehe

ighthSE=

0.8

mm

;spi

ndle

rota

-tio

nals

peed

n=

2880

min−1;m

ain

edge

cont

our

rake

angl

eG

F=

12◦;d

rill

bitd

iam

eter

DD

=11

mm

;hei

ghto

fcen

teri

ngsp

ikehCS=

5.1

mm

;ax-

ial

run

out

ofm

ain

cutti

nged

geA

R=

0.2

mm

;ra

dial

run

outo

fmai

ncu

tting

edge

RR=

0.6

mm

;la

tera

lst

iffne

ssof

drill

bits

mou

nted

ina

spin

dle

EL

=72

Nm

m−1;

radi

alpl

ayof

mai

ncu

tting

edge

RP

=0.05

mm

;ra

dial

run

out

ofce

nter

ing

spik

eR

RCS=

0.55

mm

;mai

ned

geco

ntou

rcle

ar-

ance

angl

eA

F=

15◦;c

lear

ance

angl

edi

ffer

ence

sdA

F=

2◦;

rake

angl

edi

ffer

ence

sdG

F=

0.6◦;

mai

ncu

tting

edge

beve

lang

lein

base

plai

ndi

ffer

-en

cedB

A=

3◦;

Bri

nell

hard

ness

HB

=0.85

MPa

Fig.

24.

The

plot

ofre

latio

nbe

twee

nth

edi

sper

-si

onof

hole

diam

eterD

Han

dB

rine

llha

rdne

ssHB

and

the

heig

htof

cent

erin

gsp

ikehCS;

cent

erin

gsp

ike

max

imum

asym

met

ryan

gledB

CS

=11

mm

;dri

llbi

twor

king

part

side

surf

ace

axia

ltap

erSAT=

87′ ;

axia

lrun

outo

fsi

deed

geA

RSE

=0

mm

;sid

eed

gehe

ight

hSE

=0

mm

;spi

ndle

rota

-tio

nals

peed

n=

2880

min−1;m

ain

edge

cont

our

rake

angl

eG

F=

0◦;

drill

bit

diam

eter

DD

=6

mm

;axi

alru

nou

tof

mai

ncu

tting

edge

AR

=0.2

mm

;rad

ialr

unou

tofm

ain

cutti

nged

geR

R=

0.4

mm

;lat

eral

stiff

ness

ofdr

illbi

tsm

ount

edin

asp

in-

dleE

L=

72

Nm

m−1;r

adia

lpla

yof

mai

ncu

tting

edge

RP

=0.05

mm

;ra

dial

run

out

ofce

nter

ing

spik

eR

RCS=

0.55

mm

;mai

ned

geco

ntou

rcle

ar-

ance

angl

eA

F=

43◦;c

lear

ance

angl

edi

ffer

ence

sdA

F=

23◦;r

ake

angl

edi

ffer

ence

sdG

F=

1.8◦;

drill

bits

wor

king

part

side

surf

ace

tang

entia

ltap

erSTT

=0◦;m

ain

cutti

nged

gebe

vela

ngle

inba

sepl

ain

diff

eren

cedB

A=

12◦;

mai

ncu

tting

edge

beve

lang

lein

base

plai

nB

A=

31◦


Because of interactions: dBCS · EL, −ARSE · EL,RR · hCS , RP · EL, −HB · hCS , hCS · EL, hCS · lSS ,hCS · RP , the dependency of the DH upon analyzed vari-ables may differ from those presented in Figs. from 16 to 24for another set of independent variables.

No correlation between the DH and following indepen-dent variables: dBA, BA, dlSS was found.

Acceptable hole diameter dispersion DH can be obtainedby low value of: RR, AR and high values of ARSE , hSE , n,GF . In case of high values of the HB, despite of some drillbit inaccuracies, acceptable DH can be obtained by largevalues of the hCS . This observation is not valid for low val-ues of the HB (Fig. 24). It should be noted that formulas (1)and (2) are not valid for combinations of independent vari-ables, not present in the examined incomplete experimen-tal matrix, and, giving values (0 > dN > 1.48) mm and(0.04 > DH > 2.75) mm.

The performed experiments show that it is possible tocontrol, up to a certain level (standard deviation of residualsSR), the drilling holes accuracy what condition is to identifyall machining parameters.

IV. CONCLUSIONS

Experiments and analysis of the performed results allowstating that:

1. When drilling solid wood of the Scotch pine, the de-pendency of the shift of hole diameter dN from sev-eral machining parameters dN = f(RRCS , SAT ,ARSE , hSE , n, GF , DD, hCS , AR, RR, EL, RP ,AF , dGF , STT , HB, dBCS), can be described byformula (2), by: SK = 2.06, R = 0.89; R2 = 0.80;SD = 0.12 mm.

2. The height of centering spike hCS , lateral stiffness ofdrill bits mounted in a spindle EL and radial run out ofmain cutting edge RR, independent variables had thelargest influence on the shift of hole diameter dN .

3. The largest values of the shift of hole diameter dN wasobserved by a minimum value of the height of center-ing spike hCS .

4. The largest values of the shift of hole diameter dN wasobserved by a maximum value of the lateral stiffnessof drill bits mounted in a spindle EL and radial run outof main cutting edge RR.

5. A decrease of the shift of hole diameter dN was ob-served by an increase of the: height of centering spikehCS , Brinell hardness HB, drill bits working part sidesurface tangential taper STT and an decrease of the:lateral stiffness of drill bits mounted in a spindle EL,drill bit diameter DD, radial run out of main cuttingedge RR, as well as axial run out of main cutting edgeRR.

6. When drilling solid wood of Scotch pine, the depen-dency of the dispersion of hole diameter DH from

several machining parameters DH = f(RRCS , EL,SAT , ARSE , hSE , n, GF , DD, hCS , AR, RR, RP ,AF , dAF , dGF , STT , BA, HB), can be described byformula (2), by: SK = 2.06, R = 0.89; R2 = 0.80;SD = 0.12 mm.

7. The height of centering spike hCS , the lateral stiffnessof drill bits mounted in a spindle EL and the radialrun out of main cutting edge RR independent variableshad the largest influence on the dispersion of hole di-ameter DH .

8. The largest values of the dispersion of hole diameterDH was observed by a minimum value of the heightof centering spike hCS .

9. The largest values of the dispersion of hole diameterDH was observed by a maximum value of the lateralstiffness of drill bits mounted in a spindle EL and theradial run out of main cutting edge RR.

10. A decrease of the dispersion of hole diameter DH

was observed by a decrease of the following inde-pendent variables: height of centering spike hCS , byHB < 1.3, lateral stiffness of drill bits mounted in aspindle EL, radial run out of main cutting edge RR,drill bit diameter DD, drill bits working part side sur-face tangential taper STT , main cutting edge bevel an-gle in base (frontal) plain BA, main edge contour rakeangle GF , clearance angle differences dAF .

Acknowledgements

The author is grateful for the support of the Poznan Su-percomputing and Networking Center (PCSS) calculationgrant.

References

[1] K. Banshoya, Y. Kitani, Differences in burr formation in ma-chine through-hole boring of woo-based materials by boringtools, Proc. of 16th International Wood Machining Seminar,Matsue, Japan: 515-523, 2003.

[2] N.R. Draper, H. Smith, Analiza regresji stosowana (in Pol-ish), PWN, Warszawa, 1973.

[3] W. Marzymski, Badanie dokładnosci maszynowej obróbkiskrawaniem drewna i wynikajace przesłanki do ustale-nia jednostki tolerancji, Zeszyty Naukowe PolitechnikiSzczecinskiej 83 (1966).

[4] T. Ohuchi, N. Suzuki, W. Murase, Axial deviation of holein deep machine-boring of wood. Proc. of 16th InternationalWood Machining Seminar, Matsue, Japan: 524-531, 2003.

[5] B. Porankiewicz, Problem tolerancji i pasowan dla prze-mysłu drzewnego (in Polish), Rocz. AR Poznan, Prace ha-bilitacyjne 183, 70 (1989).

[6] TGL 24421 (1972) Masstoleranzen und Passungen für dieMöbelindustrie, p. 1-35, 1972.

42 B. Porankiewicz

Appendix

Following estimators for equation (1), describing the depen-dence dN = f(RRCS , SAT , ARSE , hSE , n, GF , DD, hCS ,AR, RR, EL, RP , AF , dGF , STT , HB, dBCS) were eval-uated:• a1 = −0.80121,• a2 = −0.06955,• a3 = −31.54445,• a4 = 5.04548,• a5 = 1.4082610−4,• a6 = 0.02625,• a7 = 0.11193,• a8 = −1.00176,• a9 = 1.80529,• a10 = 0.41386,• a11 = −0.0967,• a12 = 28.88261,• a13 = 3.7948810−3,• a14 = −0.05196,• a15 = 5.66612,• a16 = −0.01345,• a17 = 0.03073,• a18 = −0.18505,• a19 = −26.6443,• a20 = −0.15406,• a21 = 0.1583,• a22 = −139.6572,• a23 = 15.3268,• a24 = −3.44529,• a25 = 5.8214510−3,• a26 = −53.33068,• a27 = 30.0126,• a28 = 0.16888,• a29 = 0.1467.Rounding of the values of estimators estimators for equa-

tion (2) to a number decimal digits of 5 caused acceptabledeterioration of the fit less than 0.1%. Reducing number ofrounding of decimal digits to 4, 3 and 2 causes unacceptabledeterioration of the fit as much as: 3%, 9%, 1216% respec-tively.

The coefficients of relatively importance CRI for estima-tors of equation (1) took following values:• CRI1 = 4107,• CRI2 = 9.7106,• CRI3 = 1.6106,• CRI4 = 98,• CRI5 = 233,• CRI6 = 42,• CRI7 = 293,• CRI8 = 2.4106,• CRI9 = 49,• CRI10 = 41,• CRI11 = 4.91016,• CRI12 = 150,

• CRI13 = 12,• CRI14 = 3925,• CRI15 = 68,• CRI16 = 101,• CRI17 = 46,• CRI18 = 2194,• CRI19 = 7750,• CRI20 = 71,• CRI21 = 385,• CRI22 = 476,• CRI23 = 49,• CRI24 = 137,• CRI25 = 15,• CRI26 = 341,• CRI27 = 40,• CRI28 = 595• CRI29 = 152.

The following estimators for equation (2), describing thedependence DH = f(hCS , EL, HB,RR, AR, RP , SAT ,STT , RRCS , n, hSE , GF , dGF , AF , dAF , BA, lSS) wereevaluated:

• b1 = 4.30602,• b2 = −0.15875,• b3 = −41632.23976,• b4 = −246.62085,• b5 = −1.4886310−5,• b6 = −0.05401,• b7 = 0.04447,• b8 = −8.50122,• b9 = −0.17005,• b10 = 8.0416,• b11 = −0.02198,• b12 = 0.83519,• b13 = −63.65569,• b14 = −0.03694,• b15 = −0.14687,• b16 = 1.70285,• b17 = 0.03377,• b18 = 8.12981,• b19 = 0.07385,• b20 = −1.08859,• b21 = 0.17004,• b22 = 0.28044,• b23 = 0.25544,• b24 = 0.02633,• b25 = 21.96488,• b26 = 5.45599,• b27 = 2.99612,• b28 = −0.6339,• b29 = −0.41513,• b30 = 0.01096,• b31 = 1.21944,• b32 = 0.72199,• b33 = 1.34811,


• b34 = 9.34110−4,• b35 = 0.22733.The number of decimal digits of 5, after rounding estima-

tors for equation (2), causes acceptable deterioration of thefit as much as 0.4%. Reducing number of decimal digits to 4and 3, due to rounding, causes unacceptable deterioration ofthe fit as much as: 22 %, 1547 % respectively.

Coefficients of relatively importance CRI for estimatorsof equation (2) took following values:• CRI1 = 39,• CRI2 = 5119,• CRI3 = 7275,• CRI4 = 0.4,• CRI5 = 7,• CRI6 = 679,• CRI7 = 92,• CRI8 = 2.071016,• CRI9 = 2,• CRI10 = 692,• CRI11 = 2.071016,• CRI12 = 317,• CRI13 = 3.451014,

• CRI14 = 2364,• CRI15 = 23863,• CRI16 = 269,• CRI17 = 119,• CRI18 = 429,• CRI19 = 194,• CRI20 = 11663.8,• CRI21 = 27,• CRI22 = 2.11016,• CRI23 = 271,• CRI24 = 26,• CRI25 = 26,• CRI26 = 26,• CRI27 = 2.11016,• CRI28 = 2.11016,• CRI29 = 609,• CRI30 = 702,• CRI31 = 2.11016,• CRI32 = 1833,• CRI33 = 310,• CRI34 = 693,• CRI34 = 155.

Bolesław Porankiewicz, habilitated in 2005 year at the Agricultural University of Poznan, Faculty of WoodTechnology, where he also received his Doctor of Technical Science and the MSc degrees, respectively inyears 1973 and 1968. In the years 2008-2011 he was employed as the contract professor at the Universityof Zielona Góra, Faculty of Mechanical Engineering. Since 2013 guest at Poznan University of Technology,Faculty of Machines and Transportation. Research interest: wood cutting forces, cutting accuracy, wearing ofwood cutting tools, construction and exploitation of wood cutting tools and woodworking machinery.

CMST 21(1) 29-43 (2015) DOI:10.12921/cmst.2015.21.01.004

an attempt to evaluate accuracy of diameter of shallow

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