Materials

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Materials and Design 27 (2006) 839–846

& Design

Design, development and testing of a turningdynamometer for cutting force measurement

Suleyman Yaldız *, Faruk Unsacar

Mechanical Department, Technical Science College, Selcuk University, 42031 Konya, Turkey

Received 19 November 2004; accepted 4 April 2005Available online 9 June 2005

Abstract

In this study, a turning dynamometer that can measure static and dynamic cutting forces by using strain gauge and piezo-electricaccelerometer, respectively, has been designed and developed. The orientation of octagonal rings and strain gauge locations has beendetermined to maximize sensitivity and to minimize cross-sensitivity. The developed dynamometer is connected to a data acquisitionsystem. Cutting force signals were captured and transformed into numerical form and processed using a data acquisition systemconsisting of necessary hardware and software running on MS-Windows based personal computer. The obtained results of machin-ing tests performed at different cutting parameters showed that the dynamometer could be used reliably to measure cutting forces.Although the dynamometer was developed primarily for turning operations, it can be used to measure cutting forces during nearlyall machining operations (milling, drilling, etc.).� 2005 Elsevier Ltd. All rights reserved.

Keywords: C-dynamometer; G-strain gauge; G-data acquisition; Engineering design

1. Introduction

The importance of monitoring the cutting force inturning has been well recognized in machine toolcommunities. In particular, Sukvittayawong and Inasaki[1], Tlusty and Andrews [2], and Weck [3] pointed outthat on-line and real-time information of the normalcutting force is closely related to the tool wear predic-tion, breakage detection or other malfunctioninspections.

A considerable amount of investigations has been di-rected towards the prediction and measurement of cut-ting forces. That is because the cutting forcesgenerated during metal cutting have a direct influence

0261-3069/$ - see front matter � 2005 Elsevier Ltd. All rights reserved.doi:10.1016/j.matdes.2005.04.001

* Corresponding author. Tel.: +90 332 223 2347; fax: +90 332 2410185.

E-mail addresses: syaldiz@selcuk.edu.tr, suleymanyaldiz@hotmail.com (S. Yaldız).

on the generation of heat, and thus tool wear, qualityof machined surface and accuracy of the workpiece.Due to the complex tool configurations/cutting condi-tions of metal cutting operations and some unknownfactors and stresses, theoretical cutting force calcula-tions failed to produce accurate results. Therefore,experimental measurement of the cutting forces becameunavoidable. For this purpose, many dynamometershave been developed [4]. In these dynamometers, cuttingforce measurement is mainly based on elastic deforma-tion of the materials.

Various studies concerning dynamometer design andconstruction can be found in [5,6]. Force components inturning are often measured using either an octagonal-ringdynamometer type or a tool shank type. The tool-shanktype is always characterized by its inaccuracy and insen-sitivity in measuring either one or two components [7].

This study outlines a strain gauge based octagonal-ringtype analogue dynamometer design and prototyping.

Ff

840 S. Yaldız, F. Unsacar / Materials and Design 27 (2006) 839–846

This dynamometer is capable of measuring three-forcecomponents. As the reading of analogue values manuallyis a difficult and tedious job, a computer connection fordata acquisition has been realized.

F

F

F

t

c

Fig. 2. Cutting force components which occurs during metal cutting inturning.

2. Materials and methods

2.1. Dynamometer

A three-force component analogue dynamometercapable of measuring cutting forces during turningwas designed, developed and tested. A computer con-nection for data acquisition was also made andcalibrated. The analogue data can be evaluated numer-ically on a computer and when required can be con-verted back to analogue. The schematic representationof the cutting force measurement system is shown inFig. 1.

The dynamometer is capable of measuring feed force(Ff), thrust force (Ft) and main cutting force (Fc) whichoccurs during turning operations as seen in Fig. 2.

This dynamometer consist of four elastic octagonalrings on which strain gauges were mounted and neces-sary connection were made to form measuring theWheatstone bridges.

2.2. Data acquisition

On-line and real-time information of the cutting forcedata are automatically read and stored by a system dur-ing metal cutting. Since the output from Wheatstonebridge circuits is very low due to the high stiffnessrequirement of the dynamometer, the analogue signalscoming from dynamometer amplified by strain gauge in-put modules (Advantech ADAM 3016) are then con-verted to digital signals and captured by PCL-818Hdata acquisition card installed in MS-Windows basedPC. The stored data can be retrieved and used for anal-ysis when required. The data acquisition software iscapable of averaging and graphical simulation of forcesignals in process.

Fig. 1. Schematic representatio

3. Design and construction of a strain gauge based

dynamometer for lathe

3.1. Design criterions and material of dynamometer

Sensitivity, rigidity, elasticity, accuracy, easy calibra-tion, cost and reliability in the harsh cutting environ-ment have been taken into account in designing thedynamometer. Dimensions, shape and material of dyna-mometer are considered to be effective factors on dy-namic properties of the dynamometer.

A dynamometer essentially consists of an importantring element. The rigidity, high natural frequency, cor-rosion resistance and high heat conductivity factorswere taken into consideration while selecting the ringmaterials. Also, deformation under the load should con-form to that of strain gauges [2].

In this study, AISI 4140 steel, which meets aboverequirements, was selected as the ring material. Theproperties of this material are given in Table 1.

3.2. Determination of dimensions of the octagonal rings

The thickness t, radius r, and width of the circularstrain ring b are the three basic controllable parametersthat affect the rigidity and sensitivity. Since there is no

n of experimental set-up.

(a) (b) (c)

39.6˚

M cFFt

AA

A

A

A

B

B

r

t

cF

Ft

A

Fig. 3. The deformation of circular strain ring under: (a) combined,(b) thrust Ft, (c) main cutting Fc forces.

b

t

r

Fig. 4. Octagonal dynamometer ring dimensions.

Table 1Properties of AISI 4140 steel

Yield strength(N/mm2)

Modulus ofelasticity (N/mm2)

Poissonratio

Hardness

550–900 210,000 0.3 217 HB

S. Yaldız, F. Unsacar / Materials and Design 27 (2006) 839–846 841

effect of ring width b and modulus of elasticity (E) onthe strain per unit deflection, bmin can be taken as20 mm to set up the rings securely [8].

The deformation of circular ring under the effect ofthrust force Ft and main cutting force Fc separately isshown in Fig. 3(b) and (c), respectively. As long as strainon A and B where the strain gauges are going to be fixed(Fig. 3(a)) are within the elastic limits of the ring mate-rial, the strain and deflection due to the main cuttingforce should be considered for the purpose of the ringdesign for maximization of sensitivity (ec/Fc) and stiff-ness (Fc/dc).

The strain gauges should be placed where the stressconcentration has maximum value. The experimentshave shown that good results are obtained for octagonalrings when the inclined gauges are at points 45� from thevertical instead of 39.6� required by the circular ring the-ory. The strain per unit deflection can be expressed as [8]

et

dt=r¼ 1.09t

1.8rffi 0.61

tr; ð1Þ

where dt is the deflection in a radial direction and et isthe strain due to thrust force Ft. It is clear that for max-imum sensitivity and rigidity et/dt should be as large aspossible. This requires that r should be as small as pos-sible and t as large as possible. But small r brings somedifficulties in mounting the internal strain gauges accu-rately. Therefore, for a given size of r and b, t shouldbe large enough to be consistent with the desired sensi-tivity. Ito et al. [9] performed a finite element analysisfor the elastic behaviour of octagonal rings. They ex-pressed that the octagonal ring is substantially stifferthan the circular ring when t/r equals 0.05 or less, thedifference in displacement of circular ring and octagonalring is less than 10% if t/r equals 0.25 or greater. Inorder to be consistent with this expression, the ringthickness and ring radius were taken as 4 and 16 mm,

respectively. Thus, the rate of t/r (4/16 = 0.25) providescorresponding sensitivity to stiffness ratio e/(d/r) foroctagonal ring.

3.3. Verifying the dimensions of octagonal rings

The maximum expected force, which the rings mayface in each direction, is assumed as 3500 N. If thecross-sectional dimensions of a curved bar is smallerthan the radius of the centre line, it is considered to bethin ring [10]. Taking into account dimensions as seenin Fig. 4. (b = 20 mm; r = 16 mm; t = 4 mm), elasticstrains et and ec due to forces Ft and Fc are calculatedaccording to ring theory by using the following equa-tions [7,8]:

et ¼ �1.09F tr

Ebt2¼ 9.1� 10�4; ð2Þ

ec ¼ �2.18F cr

Ebt2¼ 1.82� 10�3. ð3Þ

The stress occurring on rings caused by thrust and maincutting forces can be calculated by placing elastic strainratio values in Eq. (4) and (5) as follows:

rt ¼ Eet ¼ 190.8 N=mm2; ð4Þrc ¼ Eec ¼ 381.5 N=mm2. ð5Þ

As AISI 4140 steel was used for manufacturing the ringand its yield strength is 550–900 N/mm2, the calculatedstress values (rt and rc) occurring on the rings are withinsafety limits for this material.

3.4. Dynamic properties of dynamometer

Vibration frequency of the machine tool, to which thedynamometer is mounted for cutting force measure-ment, should conform to the natural frequency of thedynamometer. A dynamometer�s natural frequencyshould be as high as possible. Vibration frequency ofthe machine tool is related to the spindle speed of themachine tool. The dynamometer should have naturalfrequency of at least four times the vibration frequencyof the machine tool [8].

842 S. Yaldız, F. Unsacar / Materials and Design 27 (2006) 839–846

The dynamometer is considered to be a small masssupported by ring elements for analytical purpose. In or-der to determine the natural frequency of the dynamom-eter, the ring constant of dynamometer should bedetermined first. The stiffness value for a thin circularring is given as in the following equation [8]:

K t ¼F t

dt

¼ Ebt3

1.8r3. ð6Þ

As placing the related values in Eq. (6), the ring constantof the dynamometer is computed as; Kt = 36,458 N/mm.

The natural frequency of dynamometer, which is as-sumed to be a small mass supported by ring elements,can be obtained from the following relation [8]:

fd ¼1

2p

ffiffiffiffiffiffiffiffiffiffiK=m

p; ð7Þ

where K is the dynamometer ring constant (N/mm), m

the dynamometer mass (kg), fd the dynamometer natu-ral frequency (rev/s).

The ring mass is 36.43 kg. As placing the related val-ues in Eq. (7), the natural frequency of dynamometer iscomputed as fd = 159.2 rev/s. To fulfil the requirementas stated above fd > 4fm, the maximum spindle speedof the lathe should be 200 rev/s or 12,000 rpm.

3.5. The orientation of the strain gauges and the rings on

the dynamometer

The proper selection of the points where the straingauges are mounted is essential for achieving high accu-racy in the Wheatstone bridge circuits. The orientationof the strain gauges on the rings and the position ofthe rings on the dynamometer are given in Fig. 5.

Section L-

12

3 4

5 6

78

W

B C

DF

F

Y

X

W

A

L

F

A C

f

c

t

Fig. 5. The strain gauges and ring or

The thrust force Ft are supported by A, B, C and Drings of the dynamometer as shown in Fig. 5. The straingauges 3, 4, 7, 8, 11, 12, 15 and 16 are affected by thethrust force Ft. Among these strain gauges, 3, 7, 11and 15 are subject to tensile stress while 4, 8, 12 and16 are subject to compressive stress.

The feed force Ff is supported by A and C rings of thedynamometer as shown in Fig. 5. The strain gauges tomeasure the feed force Ff should be mounted on the out-er surfaces of A and C rings with 45� inclination angle.As shown in Fig. 5, the strain gauges 1, 2, 5 and 6 areaffected by the feed force Ff. Among these strain gauges,1 and 5 are subject to tensile stress while 2 and 6 are sub-ject to compressive stress.

The main cutting force Fc is supported by B and Drings as seen in Fig. 5. The strain gauges for measuringthe main cutting force Fc are mounted on rings B and Dwith 45� inclination angle with respect to the verticalplane. As shown in Fig. 5, the strain gauges 9, 10, 13and 14 are affected by the main cutting force Fc.

3.6. Setting the Wheatstone bridges used in the

dynamometer

One full eight active arms bridge arrangement can bearranged for thrust force measurement and two full fouractive arms bridge can be arranged for feed force andmain cutting force. Thus, if four active arms are usedin one bridge, the bridge output becomes four timesgreater than the single arm bridge. Also, full bridge cir-cuit is fully compensated for any change in resistancedue to the temperature.

The strain gauges used have 5% elongation limit on a6 mm. length. So the maximum allowed elongation

L

Strain guages

Section W-W

9 10

11 12

13 14

1516

L

B D

ientation on the dynamometer.

Fig. 6. Wheatstone bridge connections (a) for Ff, (b) for Ft and (c) forFc.

A

A

Section A-A

M6

5 10

Ø3

40

32

Fig. 7. Manufactured octagonal dynamometer rings.

S. Yaldız, F. Unsacar / Materials and Design 27 (2006) 839–846 843

should be less than 6 · 5% = 0.3 mm. The possible elon-gation could occur by 3500 N maximum permissibleforce (F) on a dynamometer and it has 36,458 N/mmrigidity (K) can be calculated as follows:

K t ¼ F t=dt;

dt ¼ F t=K t ¼ 0.096 mm.ð8Þ

Thus, the obtained possible elongation value 0.096 mmis lower than 0.3 mm allowable elongation limits.

The strain occurring in the strain gauges can be statedby the following relation [7,11]:

DRR¼ k

DLL0

; ð9Þ

where DR is the differential resistance due to the voltage(X), R the resistance of the strain gauge prior to applica-tion to voltage (X), K the gauge factor (ratio) of straingauge, DL the elongation due to the stress (mm), andL0 the initial length (mm).

Elongation percent of the strain gauge is stated byDL/L0 = e. Therefore, the above formula can be rewrit-ten as DR/R = ke. The bridge unbalance V is the ratio ofoutput voltage UA to input voltage UE of the bridgecircuit is given by the following relation [11–14]:

V ¼ UA

UE¼ 1

4

DR1

R1

� DR2

R2

þ DR3

R3

� DR4

R4

� �. ð10Þ

If R1 = R2 and R3 = R4 the bridge is balanced or, in theother words, the bridge unbalance is zero. SubstitutingDR/R =keV is found as

V ¼ UA

UE¼ 1

4kðe1 � e2 þ e3 � e4Þ; ð11Þ

where as e1 = �e2 = e3 = �e4 = e/UA/UE = (1/4)(k ·4e) and strain gauge ratio factor is taken k = 2, the outputvoltage can be reduced to the following definition:

UA ¼ 2eUE. ð12ÞIf the Eq. (12) giving the output voltage of Wheatstonebridge circuit is applied to thrust force Ft, bridgecircuit

UA

UE¼ 1

4k

DR3

R3

þ DR11

R11

� �� DR4

R4

þ DR12

R12

� ��

þ DR7

R7

þ DR15

R15

� �� DR8

R8

þ DR16

R16

� ��ð13Þ

is obtained.As

UA

UE¼ 1

4k½ðe3þ e11Þ � ðe4þ e12Þ

þ ðe7þ e15Þ � ðe8þ e16Þ�; ð14Þe3 ¼ e11 ¼�e4 ¼�e12 ¼ e7 ¼ e15 ¼�e8 ¼�e16 ¼ e ð15Þ

for UA/UE = (1/4)(k · 8e) and k = 2

UA ¼ 4eUE ð16Þ

relation is obtained. Or, this relation can be rearrangedas

UA ¼ 4UE � 10�6. ð17ÞThe principles applied to the thrust force Ft are also va-lid for the feed force Ff. By using the principles of thrustforce Ft, the feed force Ff equation can be formed.Again, from Eq. (12)

UA ¼ 2eUE

or can also be written as

UA ¼ 2UE � 10�6. ð18ÞSimilarly, the principles applied for feed force Ff andthrust force Ft are also valid for the main cutting forceFc. See Fig. 6.

3.7. Dynamometer construction

3.7.1. Mounting of strain gauges on the rings

The rings of dynamometer were manufactured atCNC machine tools by using AISI 4140 steel as seenin Fig. 7. The surfaces of the rings were ground for bet-ter strain gauge application.

Prior to the mounting of the strain gauges, the ringsurfaces on which strain gauges were mounted had beenground and then these surfaces were cleaned by cleaningset ‘‘HBM: FC1’’. Around 30 min after the cleaning of

844 S. Yaldız, F. Unsacar / Materials and Design 27 (2006) 839–846

the surfaces, the strain gauges were mounted using coldcuring rapid adhesive ‘‘HBM: Z70’’ and were left fordrying for 10 min. After curing time, the surfaces ofthe strain gauges were covered by nitrile rubber HBM:NG150 to protect against the influence of cutting fluid.

Totally 16, strain gauges were mounted on fouroctagonal rings. Two strain gauges were mounted hori-zontally on to outsides of each ring at 45� angles. Twomore strain gauges, one inside and the other outsidewere also mounted vertically. See Fig. 5.

HBM: LY11 6/120 type strain gauges recommendedfor steel specimens and for static or dynamic loadingwere utilised. To achieve low energy dissipation andhence a stable zero setting for a long time, excitationvoltage must be selected carefully. The range of excita-tion voltage for a thick steel mounting surface may beobtained from the relation [15]

V in ¼ 2ffiffiffiffiffiffiffiffiffiffiffiffiffiRP 0gAg

q

in which R is the gauge resistance in ohms, P 0g is thepower density in the gauge grid (between 2 and 5 kW/m2), and Ag is the active grid area (6 · 2.8 for HBMfor LY11 6/120). For convenience, an excitation voltageof 10 V (calculated between 8 and 12.7 V) wasemployed.

3.7.2. Mounting of the dynamometer

The rings of dynamometer were mounted betweentwo plates by using (B4 mm) pins and M5 screws. Pinswere used in order to prevent the motion of plates due toclearance, which may cause the cross-sensitivity duringmeasurements. The dimensions of plates were100 · 100 · 12 mm. The cutter was placed tightly intothe hole of the front plate and tightened with M8 screwsto upper plate in order to sustain the perpendicularity tothe ring plane (see Fig. 8). The sides of front and rear

Fig. 8. Designed and developed dynamometer.

plates were covered with 5 mm thick transparent plasticmaterial in order to prevent the strain gauges from hotchips and from cutting fluid during turning.

The dynamometer was fixed on to the saddle of lathein a position where the nose of the cutter tips was on thesame line with chuck centre.

3.8. Dynamometer calibration

3.8.1. Static calibration of the dynamometer

In order to determine the elastic deflection of ringcomponents and consequently the output voltage understatic load, the dynamometer was calibrated. The cali-bration was made in three directions for Ff, Ft, Fc andthe output voltages of millivolt were averaged for eachdirection. The loads up to 2000 N · 50 N intervals wereapplied and the strain values were recorded for eachload intervals. Thus, calibration curves were obtainedto convert the output readings into cutting force values.Figs. 9–11 show the calibration curves for feed force,thrust force and main cutting force, respectively. In or-der to verify the consistency, the measurements were re-peated three times and very close values were obtainedas seen in Figs. 9–11. The effect of loading in one direc-tion on the other force components was also examinedand minor fluctuations were observed. These effects were

Fig. 9. Calibration curve and cross-sensitivity for feed force Ff.

Fig. 10. Calibration curve and cross-sensitivity for thrust force Ft.

Fig. 11. Calibration curve and cross-sensitivity for main cutting forceFc.

S. Yaldız, F. Unsacar / Materials and Design 27 (2006) 839–846 845

small enough to be ignored. The dynamometer was runidle for 5 min before each calibration tests as it wasready for measurement in order to determine theconsistency.

3.8.2. Dynamic calibration of the dynamometer

The natural frequency of the dynamometer deter-mines its general dynamic stiffness. In order that the re-corded force is not influenced by the dynamic responseof the dynamometer, its natural frequency must be high-er than the frequency of exciting vibration [16]. The nat-ural frequency of the dynamometer is determinedaccurately by setting the dynamometer into vibrationand by measuring its response using accelerometer and

Fig. 12. Dynamic cutting force within the

oscilloscope. So, the developed dynamometer, the dy-namic cutting force within the time domain and fre-quency domain were recorded while the machine wasrunning as idle and during the cutting operation asshown in Fig. 12.

3.9. The dynamometer testing

3.9.1. Cross-sensitivity test

The cross-sensitivity can be expressed as the strainmeasured on axes which is normal to the main axes. Itis desired that dynamometers must not be completelyinsensitive to the cross-strain. It is possible to measurethe cutting forces independently and accurately as longas the cross-sensitivity is small. The strain errors willbe less if this effect is within an acceptable range. Theseerrors can arise because the strain gauges are not fittedsymmetrically to the ring axes and if the strain ringsare not mounted in the direction of measured force axes.When the dynamometer tested X-direction, the cross-sensitivity for Y- and Z-direction was calculated as0.18% and 0.7%. While the tests were being carriedout on Y- and Z-direction, the cross-sensitivity was cal-culated as 0.33% and 0.5%, and 0.92% and 0.17%,respectively, as shown in Table 2(a).

3.9.2. Eccentricity test

In a three-component dynamometer, the applied loadwithin the square outlined by axes of rings must always

time domain and frequency domain.

Table 2The results of tests performed on the dynamometer

Axes Load (N) Output e (digital) Average error (%)

X Y Z X Y Z

The results of cross-sensitivity test

Ff 2000 278 5 2 0.18 0.7Ft 2000 8 239 1.3 0.33 0.5Fc 2000 16 3 173 0.92 0.17

Axes Load (N) e = 0 mm (mV) e = 50 mm (mV) Output error (%)

The results of eccentricity test

Ff 1000 119 118 �0.8Ft 1000 122 120 �0.16Fc 1000 82 81 �0.12

846 S. Yaldız, F. Unsacar / Materials and Design 27 (2006) 839–846

give same output value. To test this condition, the dyna-mometer was subject to eccentricity test. In order to testthe dependence of outputs of gauges affected by applica-tion point of Ff, Ft and Fc forces, the force (1000 N) wasapplied to the dynamometer at centre and at e = 50 mmdistance from the calibration point. The percentage ofoutput errors for Ff, Ft and Fc were found as �0.8%,�0.16% and �0.12% as shown in Table 2(b).

4. Conclusion

In this study, strain gauge based dynamometer hasbeen designed and developed. It has been devised andconnected with necessary data acquisition system con-sisting of hardware and software. Dynamometer canmeasure three perpendicular cutting force componentssimultaneously during turning and the measured numer-ical values can be stored in computer by data acquisitionsystem. This dynamometer was designed to measure upto 3500 N maximum force and the sensitivity of systemis ±5 N. In order to determine accuracy, the dynamom-eter was calibrated statically and dynamically and sub-jected to cross-sensitivity test and eccentricity test. Thevalues of cross-sensitivity of the dynamometer for thethree directions were calculated in the range of 0.17–0.92%. Dynamometer can be assumed as reliable as thissmall value can be neglected. In turning operations,appropriate results were obtained in cutting force mea-surements. The obtained results of machining tests per-formed at different cutting parameters show that thedynamometer can be used reliably to measure cuttingforces. Although it was designed primarily for turning,it can be used for milling, drilling, etc.

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