Paper

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doi:10.1016/j.ijmachtools.200

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r # 2004 Elsevier Ltd. All rights reserved.

4.04.018

International Journal of Machine Tools & Manufacture 44 (2004) 1261–1269

www.elsevier.com/locate/ijmactool

Tool life determination based on the measurement of wear and toolforce ratio variation

S.E. Oraby a,1, D.R. Hayhurst b,�

a Department of Production Engineering, Faculty of Engineering and Technology, Suez-Canal University, Port Said, Egyptb Department of Mechanical, Aerospace and Manufacturing Engineering, UMIST, P.O. Box 88, Sackville Street, Manchester M60 1QD, UK

Received 19 April 2004; accepted 29 April 2004

Abstract

Non-linear regression analysis techniques are used to establish models for wear and tool life determination in terms of the vari-ation of a ratio of force components acting at the tool tip. The ratio of the thrust component of force to the power, or vertical,force component has been used to develop models for (i) its initial value as a function of feed, (ii) wear, and (iii) tool lifetimes.Predictions of the latter model have been compared with the results of experiments, and with predictions of an extended Taylormodel. In all cases, good predictive capability of the model has been demonstrated. It is argued that the models are suitable foruse in adaptive control strategies for centre lathe turning.# 2004 Elsevier Ltd. All rights reserved.

Keywords: Tool life; Tool wear; Tool force ratio

1. Introduction

In the manufacture of metallic components usingconventional machine tools, cutter tool wear, its effectson surface finish, and cutter tool failure provide majorlimitations to the achievement of economic production[1,2]. Techniques for describing tool wear and failureare based either on the use of databases with inter-polative and extrapolative techniques, or on the use ofexplicit mathematical relationships. In both cases, thestochastic nature of tool wear provides an obstacle tothe achievement of optimal production conditions. Thissituation can be improved by using adaptive control(AC) techniques [3,4], which create the possibility tomeasure and to control the process in situ, and soavoid the need to relate the current machine, workpieceand tool conditions to those conditions under whichthe existing databases and mathematical equationshave been generated.

Instead of using complex tool databases, it is pro-

posed that models be employed which describe wear;

which determine tool life in terms of measurements ofin-process variables; and which can, if necessary, be

recalibrated during metal cutting. Ideally, the form ofthe models should be such that the workpiece–tool var-

iations, and the variations from machine tool tomachine tool, are sufficiently small not to provide

obstacles to their effective use in industry. Some poss-

ible approaches are now discussed.It is possible to use a range of process variables to

indirectly measure the effects of tool wear. Measure-

ments have been made by many investigators [5–8].Theses included the use of on-line electronic equip-

ment/transducers to measure: motor power, spindletorque or even the current drawn by a.c. feed drive ser-

vomotors [4,9,10]. Another technique which has gained

wide acceptance in sensing wear is the dynamic behav-iour of the tooling system [1,11–15]. However, one of

the most promising techniques for sensing tool wearand breakage involves the measurement and obser-

vation of the components of static/dynamic force act-

ing at the tool tip during machining [5,16–23]. In aprevious study reported by the authors [24] for centre

lathe turning, force variation during cutting was found

1262 S.E. Oraby, D.R. Hayhurst / International Journal of Machine Tools & Manufacture 44 (2004) 1261–1269

to correlate well with tool wear and breakage. Both thefeed component of force Fx, Fig. 1, and the radialcomponent of force Fz were found to be more affectedby tool wear than by the vertical component of forceFy. This suggests that force variation during real-timecutting may provide an accurate and reliable techniqueto monitor tool wear and breakage. However, one ofthe drawbacks of such an approach is its non-lineardependence on the control variables, and the influenceof the current tool–workpiece interface conditions. Areformulation of the approach has therefore been pro-posed [25,26] which seeks to eliminate as many of theseaspects as possible. The proposed approach is now out-lined.

2. Outline of investigation

Mackinnon et al. [26] expressed a component offorce Fi acting at the tool tip by

Fi ¼ j1jmjti fai dbiVcið1þ giWÞ; ð1Þ

where f (mm/rev) is the cutting feed, d (mm) is thedepth of cut, V (m/min) is the cutting speed, W (mm)is an average measure of wear, gi is a wear constant, j1is a lubrication constant, jm is the workpiece materialhardness, and jti relates to the tool geometry associa-ted with the force component Fi.In order to reduce the dependency of the relationship

between Fi and W upon process conditions, Eq. (1) isnormalised with respect to another force measure Fj toyield:

FiFj

¼ jtið1þ giWÞjtj ð1þ gjWÞ f

ðai�ajÞdðbi�bjÞV ðci�cjÞ: ð2Þ

In this paper, two new equations are proposed;firstly, a simplified equation for force ratio:

FiFj

¼ UðV ;f ;d;t;WÞ; ð3Þ

where U is a function of the process variable, t (min) isthe accrued cutting time; and secondly, an equation fortool life T:

T ¼ HinitðV ;f ;dÞ þ WðFi=FjÞ; ð4Þ

where Hinit is a function of the initial cutting con-ditions, and W is a function of the current and initialforce ratios. The form and validity of Eqs. (3) and (4)are experimentally investigated in this paper.

3. Components of force and wear at the tool tip

In a previous study [24], the variations of the compo-nents of force were found to correlate, to differingdegrees, with tool wear and breakage. These results arenow discussed. Both the feed component of force Fxand the radial component of force Fz were found to bemore strongly affected by tool wear than the verticalcomponent of force Fy. This is because Fx and Fz(Fig. 1) are closely related to the sliding and frictionalconditions between the tool and workpiece; and, Fyreflects the combined effects of Fx and Fz, and theirrespective friction conditions, in terms of the torqueand power required to drive the lathe.At the start of cutting with a virgin tool both of the

force components Fx and Fz were found to be almostequal [24]. Subsequently, as wear developed at the cut-ting edge, the values of Fx and Fz differed and becamedependent on how the wear scars were distributed onthe cutting edge.Wear scars are usually not evenly distributed on the

tool flank and three regions of wear can be dis-tinguished, Fig. 2(a): nose wear NW, over region C;flank wear FW, over region B; and notch wear NCWover region N. The radial component of force Fz hasbeen shown [24] to be most affected by nose wear, NW,while the feed component of force Fx is most influencedby wear scars in the flank, FW, and notch, NCW, areas.In general, if the wear in one area dominates, then theassociated force component is most influenced. Hence,if an average value of flank wear is used to correlatewith the behaviour of Fx and Fz, then an erroneouseffect on the individual force components will be pre-dicted. To overcome this and to permit the use of anaverage value of flank wear, the individual force compo-nents are replaced by their resultant or thrust force:Fxz ¼ Fxsinv þ Fzcosv, as shown is Fig. 2(b).The vertical component of force acting at the tool

tip, Fy, will be used as the normalising force Fj inEq. (3). It has been selected for three reasons:

(i)
I t reflects the overall torque and power input tothe lathe, and hence provides a global measure.
(ii)
I t is the force component which is least sensitive totool wear.
Fig. 1. Cutting force components in turning operations.

S.E. Oraby, D.R. Hayhurst / International Journal of Machine Tools & Manufacture 44 (2004) 1261–1269 1263

(iii)
I ts magnitude is most sensitive to the workpiecematerial and to the workpiece–tool interface con-ditions; and, hence its measurement should reflectthose factors in Eq. (1) which one is seeking toremove through normalisation.
Following Colwell [27,28], who first introduced theforce ratio concept, Goforth and Kulkarni [29] and,Choudhury and Kishore [19] have used the sameapproach to develop models for cutter tool wear andlife. They used the ratio of the power, or verticalcomponent of force, Fy, and the feed component offorce, Fx, given by Fy=Fx. The novel approach adoptedhere is to use the ratio of the thrust components offorce, Fxz, and the power component of force, Fy, givenby Fxz=Fy.

The next section outlines the experimental facilityused in this research to asses the validity of the pro-posed models.

4. Experimental procedures and set-up

Triple coated (1 lm TiN, 3 lm Al2O3, 5 lm TiC) car-bide inserts [Sandvik GC345] were clamped to a three-component strain gauge dynamometer [30]. Theseinserts were used to machine an alloy steel 709M40

(En 19), under dry cutting conditions, using a Colche-ster Mascot centre lathe. The range of operating para-meters used were: cutting speed (V) 50–200 m/min, feed(f) 0.06–0.6 mm/rev; and depth of cut (d) 1.3–3 mm.Three mutually perpendicular components of the forcewere measured, Fx, Fy and Fz, as shown in Fig. 1.Tests were periodically interrupted and wear scars

were measured at the three different locations on thetool flank as shown in Fig. 2(a), namely: nose wear, atthe point of maximum projection of the tool into theworkpiece; flank wear, at the maximum wear land onthe flank; and, notch wear at the point of intersectionof the depth of cut, d, with the tool flank. The measureof tool wear used in the paper is the average of thethree values measured at the three locations. The selec-tion of the average value of wear at failure Wf ¼0:25 mm has been carefully made to reflect the behav-iour over the entire domain of conditions, in whichwear at any one of the three zones may predominate.In this way, better correlations have been achievedbetween model predictions and experimental resultsthan if the ISO recommended value of Wf ¼ 0:30 mmhad been used.Since the experimental results are to be used to

identify explicit mathematical equations, and to fitthem to the data obtained for subsequent use over the

rce system and wear distribution on the cutting edge. (a) Flank wear elements and (b) for
Fig. 2. Fo ce system.


selected domain of operating parameters, the planning

of the 24 experiments has been carried out using the

central composite design (CCD) technique.

5. Mathematical model for the initial force ratio

Initial values of the force components, denoted by

Fx0, Fy0 and Fz0 for the feed, radial and vertical com-

ponents, respectively, are determined, using a virgin

tool, by the intercept of the force–time history at zero

cutting time. The initial force ratios Fi0=Fj0 may thenbe formed using Eq. (2). Since the geometry factors jtiand jtj are constants, and the wear W is zero, then

Eq. (2) becomes

Fi0=Fj0 ¼ jf ðai�ajÞdðbi�bjÞV ðci�cjÞ; ð5Þ

where j is a constant. The cutting force, both initially

and in the stable cutting region, where no built-up-edgehas formed, is principally dependent on the cross-

sectional area of the material cut; and, is relatively

independent of cutting speed [3]. Similar observations

have been made by Oraby [31] particularly with regardto the vertical, Fy, and radial, Fz, components of force.

In their investigation, the index c of the velocity was

found to be relatively constant in the range 0.06–0.10,

the term in Eq. (5) V ðci�cj Þ ffi 1, since ci ffi cj, and hence

it was neglected to a good order of approximation.

They also observed a similar effect with regard to the

depth of cut d, where bi ffi bj, and hence the term

dðbi�bj Þ in Eq. (5) was also neglected to a good order of

approximation. The validity of using Eq. (5) without

the terms in V and d is now examined in this paper

using an experimental test programme.From each of the 24 experiments, the initial values

of the force components, normalised with respect to

Fy0, have been determined and used as input, together

with the values of d, f and V, into a numerical

regression analysis technique to determine the terms j,ðai�ajÞ, ðbi�bjÞ and ðci�cjÞ in Eq. (5).

The technique makes use of both forward and back-

ward elimination methods to remove and to insert

terms in Eq. (5) according to their statistical signifi-

cance in describing the input data. The procedures lead

to the elimination of the terms d and V (i.e. ðbi � bjÞ ¼ðci � cjÞ ¼ 0Þ and the following equations result:

Fx0=Fy0 ¼ 0:193f ð�0:400Þ;Fz0=Fy0 ¼ 0:186f ð�0:370Þ; andFxz0=Fy0 ¼ 0:253f ð�0:405Þ:

ð6Þ

These results are shown graphically in Fig. 3. The

feed Fx0=Fy0, and the radial Fz0=Fy0 ratios of the force

components are similar in magnitude, whilst the nor-

malised thrust force component Fxz0=Fy0 is elevated

approximately according to the vector addition of Fx0and Fz0 shown diagrammatically in Fig. 2(b).Since the results of Eq. (6) have been obtained with a

greater than 85% factor of determination R2, which

corresponds to a 92% correlation factor R, it may be

concluded that the normalised force ratios are strongly

Fig. 3. Relationship between initial force ratio and feed.


ally determined variation of force ratios and wear with cutting time for (a) test 5 with V ¼ 104 m=
Fig. 4. (a) Experiment min, f ¼ 0:2 mm=rev,
and d ¼ 2:25 mm, (b) test 3 with V ¼ 145 m=min, f ¼ 0:12 mm=rev, and d ¼ 2:5 mm, and (c) test 2 with V ¼ 145 m=min, f ¼ 0:3 mm=rev, and

d ¼ 2:0 mm.


independent of both speed V and depth of cut d. Theresult demonstrates the significance of using the forceratio to eliminate the parameters that reflect the tool–workpiece interfacial conditions.

6. Effect of tool wear on force ratio

From the 24 experiments carried out, the results ofthree have been selected for presentation here. Theyrepresent a wide range of cutting conditions and thetime variation of wear and of the force ratios Fx=Fy,Fz=Fy and Fxz=Fy are presented in Fig. 4(a)–(c). Each is

now discussed in turn with a view to identifying thelink between the respective forms of wear and the com-ponents of force measured.

6.1. Feed dependence

In general, Fig. 4 shows that, as cutting proceeds,wear increases causing an increase in the values of thedifferent force ratios. The rate of increase of a forceratio depends on the severity of the cutting conditionsused. More severe conditions produce a wider wearland and consequently an increase in the force, and inthe force component ratios. Fig. 4(a)–(c) shows thatthe difference between the normalised feed Fx=Fy andthe radial Fz=Fy force components decreases as the

magnitude of the feed increases. For example, compari-son of Fig. 4(b), f ¼ 0:12, with Fig. 4(c), f ¼ 0:3,shows that as feed is increased, for V ¼ 145 and simi-lar values of d ¼ 2� 2:5, the radial and feed compo-nents of force become closer. The same trend is bornout by Fig. 4(a), although it is less easy to identify dueto difference in speed.

6.2. Interrelationship between wear and force ratios

It was observed in the tests that the wear scars werenot uniformly distributed over the three locationsshown in Fig. 2. Certain trends have been observed:elevated nose wear affects the radial force componentratio Fz=Fy more than it does the feed force componentratio Fx=Fy. For example, in Fig. 4(a), for Test 5, with

V ¼ 104, f ¼ 0:2, and d ¼ 2:25, the radial force ratioFz=Fy is initially larger than the feed force ratio Fx=Fy,

but this situation is reversed after 2.5 min of cutting.Thereafter Fx=Fy > Fz=Fy and wear develops uniformly

in the nose and flank areas. For the first 18 min of cut-ting, wear scars were observed, using optical examin-ation techniques [31], to be uniformly distributed in thenose and flank regions. After 18 min of cutting, wear inboth the flank and nose regions increased, but thegrowth in flank wear predominated, hence causing alarger increase in Fx=Fy than in Fz=Fy. As cutting con-

tinued nose wear was observed to increase at a higher

rate than notch wear, causing the Fz=Fy to increase, on

average, at a higher rate than Fx=Fy. The overall effect

was that Fz=Fy gradually increased to a value at the

end of the test almost equal to that of Fx=Fy.

In Fig. 4(b), test results are presented for a higher

speed V ¼ 145 and a depth of cut d ¼ 2:5, but for a

lower value of feed, f ¼ 0:12. Experimental observa-

tions of the wear-time behaviour [31] indicated that

notch wear was dominant during the early part of the

test resulting in the radial force Fx=Fy being the highest

force component throughout the test. After approxi-

mately 20 min of cutting, a rapid increase in wear took

place in the nose and flank regions, which caused both

Fz=Fy and Fx=Fy to increase non-linearly with time.

The average wear level shown in the figure closely fol-

lows the same behaviour.In Fig. 4(c) test results are presented with V ¼ 145,

f ¼ 0:3 and d ¼ 2:0; here, the higher value of feed

reduces the difference between Fx=Fy and Fz=Fy. A uni-

form distribution of wear observed over the nose

region, and over the flank and notch regions, has

ensured an approximately equal balance between Fx=Fyand Fz=Fy.

It is clear from the foregoing discussion of Fig. 4

that the observations of wear [31] can be linked to the

changes in the force component ratios Fx=Fy and

Fz=Fy. Examination of all three figures clearly shows

that the time variations of both Fx=Fy and Fz=Fy are

clearly mirrored in the time variations of wear. In

addition, the need is also clear to include both the nor-

malised radial component of force Fz=Fy, and the nor-

malised feed component of force Fx=Fy to obtain an

accurate wear-time description. In the next section, the

significance is discussed of the experimental observa-

tions of the normalised thrust force component.

6.3. The thrust force component ratio Fxz=Fy and wear

In Section 5, it was proposed that the normalised

thrust force component Fxz=Fy, cf. Fig. 2(b), be used to

describe wear. The normalised thrust force component

(Fxz=Fy) has been plotted in Fig. 4(a)–(c) and in all

cases is shown to correlate well with wear. Hence, the

evidence presented in Fig. 4 clearly supports the use of

the normalised thrust force component (Fxz=Fy) to

model wear growth.In the next section, the development of mathematical

models is outlined, which describe: (i) the variation of

Fxz=Fy as defined by Eq. (3); and (ii) the tool life as

defined by Eq. (4).


7. Mathematical models of tool wear

7.1. Cutter life as a function of wear

The discussion in Section 5 regarding experimentalobservations clearly vindicates the dependency on V, f,d, t and W, where t is the cutting time in minutes,expressed by Eq. (3). To investigate the form of themathematical relationship which couples these vari-ables with Fxz=Fy, a non-linear multiple regressionanalysis has been carried out using the 669 data pointsobtained from the 24 experiments, which has led to thedetermination of the parameters in Eq. (3):

Rxz¼Fxz=Fy¼ 10:79V�0:306f �0:393d�0:188t�0:160W 0:944;

ð7Þ

with a greater than 81% factor of determination R2,which corresponds to a 90% correlation factor R.This equation is of a form that may be used in an

AC strategy for centre lathe turning. When used underthese conditions, the force ratio Rxz and the time of cutt may be continuously monitored and, by inversion ofEq. (7), the wear W can be determined using embeddedcomputer processing from the input parameters V, fand d. When the calculated value of W exceeds thevalue at failure Wf ¼ 0:25, then the tool is replaced.It is not always convenient, or expedient, to express

cutter life in terms of wear. Very often the time of cut-ting as expressed in Eq. (4) is a more convenient mea-

sure. In the next section, the mathematical form ofEq. (4) is investigated.

7.2. Cutter life as a function of time

A mathematical model which expresses the forceratio (Fxz=Fy) has been achieved using non-linearregression analysis techniques, similar to thosedescribed in Sections 5 and 7, to select those combina-tions of simple functions which describe the input datato the highest degree of statistical significance achiev-able. The model for the cutter tool life of T min wasfound to be:

T ¼ 78573:35V�1:712f �0:714d�1:107

þ 249:49e�78:571ðRf�RoÞ; ð8Þ

where Ro ¼ Fxz0=Fy and Rf ¼ Fxz=Fy denote, respect-

ively, the original value and the experimental value atfailure when W ¼ 0:25 mm. Eq. (8) holds for a factorof determination R2 of 0.95, which corresponds to a98% correlation factor R. The high correlation factorhas been achieved since only (24� 5) input data pointshave been made use of out of the 669 data points usedto develop Eq. (7). This was achieved by selection ofthe original condition Ro, and of a single data set fromeach test, namely, the experimental value of Rf, whenthe time t is equal to the cutter life T; this occurs whenW reaches the failure value Wf ¼ 0:25 mm. The value

Table 1

Comparison of experimental and predicted tool lifetime values made using both conventional, Eq. (9), and force ratio models, Eq. (8)

Test no. C
onditions Tool life values (min) (Wf ¼ 0:25 mm)
V (m/min) f
(mm/rev) d (mm) Experimental value C onventional model Eq. (9) F orce ratio model Eq. (8)
1
72 0 .12 2 .00 119 1 26 1 10
2 1
45 0 .30 2 .00 13 10 17
3 1
45 0 .12 2 .50 20 21 25
4
72 0 .30 2 .50 30 46 44
5 1
04 0 .20 2 .25 36 39 35
6 1
04 0 .20 2 .25 65 39 46
7 1
45 0 .12 2 .00 37 28 33
8
72 0 .30 2 .00 79 62 57
9
72 0 .12 2 .50 79 94 86
10 1
45 0 .30 2 .50 7 8 13
11 1
04 0 .20 2 .25 50 39 59
12 1
04 0 .20 2 .25 35 39 36
13 2
06 0 .20 2 .25 4 4.5 13
14
50 0 .20 2 .25 140 1 22 1 27
15 1
04 0 .60 2 .25 9 8.5 18
16 1
04 0 .06 2 .25 96 74 84
17 1
04 0 .20 3 .00 24 25 26
18 1
04 0 .20 1 .50 55 58 56
19 2
06 0 .20 2 .25 4.5 4.5 11
20
50 0 .20 2 .25 119 1 22 1 26
21 1
04 0 .60 2 .25 8 8.5 16
22 1
04 0 .06 2 .25 65 74 84
23 1
04 0 .20 3 .00 31 25 26
24 1
04 0 .20 1 .50 48 58 56


of Rf ¼ Rxz being determined from Eq. (7). The first

term on the right-hand side of Eq. (8) gives the tool lifeas expressed by the cutting conditions, and the secondterm reflects the decrease in life due to the evolution ofwear.An advantage of using this approach for adaptive

tool life control is that a two-stage approach can beused. In the first stage, prior to machining, the mostappropriate combination of cutting conditions for agiven life T can be determined from the first term on theright-hand side of Eq. (8). In the second stage, oncemachining has commenced, the entire Eq. (8) isemployed, in conjunction with Eq. (7), and the tool isdiscarded when the right-hand side becomes equal to T.To assess the effectiveness of this approach relative

to the well-established second-order tool life model, thefollowing previously calibrated [31], and widelyaccepted, equation will be used:

T ¼ expf�7:953þ 7:257lnV � 1:121ðlnVÞ2

� 0:371ðlnf Þ2 � 0:810ðlndÞ2 � 0:469lnV lnf g ð9ÞThis model depends only on the cutting parameters;

and has the form of the ‘‘extended Taylor equation’’. Acomparison of the tool lifetimes predicted by Eqs. (8)and (9) is made in Table 1 with the experimental dataused to establish them. The table lists 24 CCD experi-ments, together with their respective cutting para-meters. Results are graphically illustrated by Fig. 5. Itmay be seen that in particular tests, the predictions ofEq. (8) are superior for reasons which are now dis-cussed. Firstly, better predictions of the experimentaltool lifetimes are made using the force ratio model.This can be observed for test numbers: 4, 5, 6, 7, 8, 9,11, 12, 14, 16, 18, 23 and 24. Secondly, in situations

where a test has been repeated with the same nominaltest parameters, e.g. test numbers: 5, 6, 11 and 12Eq. (9) predicts a constant tool life of 39 min, whereasEq. (8) predicts tool lifetimes of 35, 46, 59 and 36 min,respectively, due to the different experimental values ofRf at failure; which in all cases are closer to the experi-mental results.However, in the tests numbered 2, 3, 17, 20 and 22,

for which the tool lifetimes T � 13 min, the predictionsmade using the force ratio method are in excess ofthose determined experimentally (non-conservative).The average error being less than 12%. For the remain-ing tests numbered 10, 13, 15, 19 and 21, for which thetool lifetime T � 10 min, the average errors are non-conservative by 130%. For the latter conditions, it isexpected that the first term of Eq. (8) will contributestrongly to the predictive accuracy; and, that if second-order functions were to be admitted in this term thenthe corresponding predictions for small T wouldimprove significantly.It would appear, therefore, that provided the low

tool lifetimes behaviour is neglected then the forceratio method Eq. (8) provides a continuous monitoringof tool wear/life from the initial to the final conditions.Its aspect that provides the flexibility necessary for theuse of a model in a machine tool AC facility.

8. Conclusions

Non-linear regression analysis techniques have beenused to establish models for wear, tool life, and initialcutting conditions in terms of force ratios rather thanabsolute values of force. It has been shown that the

between experimental lifetimes and values determined using the conventional model (Eq. (9)) and force ra
Fig. 5. Comparison tio model (Eq. (8)).


thrust component of force, when normalised withrespect to the power, or vertical, component of forceacting on the tool, provides a sensitive measure ofnose, flank and notch wear.A model has been developed which describes the

initial force ratios as functions of the feed component,other cutting parameters have been shown to be of sec-ondary importance.A model has been developed Eq. (7) which relates an

average measure of wear to the cutting parameters,time, and thrust force ratio. A further model has alsobeen established which relates the tool life, to cuttingparameters, and to initial and final/failure thrust forceratios, Eq. (8). Good predictive capability of themodel, has been shown by comparison with the predic-tions of an extended Taylor model, and with the resultsof experiments.Eq. (8) has the potential for use, with force ratio Rxz

measurement, in an AC facility for centre lathe toolmanagement.

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