Design, development and testing of a turning dynamometer for cutting force measurement

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    2004;line 9

    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 acquisition

    turning has been well recognized in machine tool tions of metal cutting operations and some unknown

    dynamometer 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.


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

    E-mail addresses:, (S. Yaldz).

    Materials and Design 27 (2

    Materials0261-3069/$ - see front matter 2005 Elsevier Ltd. All rights reservedcommunities. 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 inuence

    factors 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 oftenmeasured using either an octagonal-ringsystem. 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 dierent 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 in

    on the generation of heat, and thus tool wear, qualityof machined surface and accuracy of the workpiece.Due to the complex tool congurations/cutting condi-Design, developmentdynamometer for cut

    Suleyman Yald

    Mechanical Department, Technical Science

    Received 19 NovemberAvailable on

    Abstractdoi:10.1016/j.matdes.2005.04.001d testing of a turningg force measurement

    Faruk Unsacar

    e, Selcuk University, 42031 Konya, Turkey

    accepted 4 April 2005June 2005

    006) 839846


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

    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-

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








    840 S. Yaldz, F. Unsacar / Materials and Design 27 (2006) 839846nection 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 stinessrequirement of the dynamometer, the analogue signalscoming from dynamometer amplied 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 representatio3. 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 eective 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

    Fig. 2. Cutting force components which occurs during metal cutting inturning.n of experimental set-up.

  • respectively. Thus, the rate of t/r (4/16 = 0.25) providescorresponding sensitivity to stiness 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), elastic

    S. Yaldz, F. Unsacar / Materials and Design 27 (2006) 839846 841eect of ring width b and modulus of elasticity (E) onthe strain per unit deection, bmin can be taken as20 mm to set up the rings securely [8].

    The deformation of circular ring under the eect 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 xed(Fig. 3(a)) are within the elastic limits of the ring mate-rial, the strain and deection due to the main cuttingforce should be considered for the purpose of the ringdesign for maximization of sensitivity (ec/Fc) and sti-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-

    (a) (b) (c)


    M cFFt












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

    Table 1Properties of AISI 4140 steel

    Yield strength(N/mm2)

    Modulus ofelasticity (N/mm2)



    550900 210,000 0.3 217 HBory. The strain per unit deection can be expressed as [8]



    0.61 tr; 1

    where dt is the deection 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 somediculties 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 nite element analysisfor the elastic behaviour of octagonal rings. They ex-pressed that the octagonal ring is substantially stierthan the circular ring when t/r equals 0.05 or less, thedierence 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,strains et and ec due to forces Ft and Fc are calculatedaccording to ring theory by using the following equa-tions [7,8]:

    et 1.09F trEbt2

    9.1 104; 2

    ec 2.18F crEbt2

    1.82 103. 3

    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 Eet 190.8 N=mm2; 4rc Eec 381.5 N=mm2. 5As AISI 4140 steel was used for manufacturing the ringand its yield strength is 550900 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 dynamometers 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].



    rFig. 4. Octagonal dynamometer ring dimensions.

  • 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 rst. The stiness value for a thin circularring is given as in the following equation [8]:

    K t F tdt Ebt3

    1.8r3. 6

    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 12p


    p; 7

    where K is the dynamometer ring constant (N/mm), mthe dynamometer mass (kg), fd the dynamometer natu-ral frequency (rev/s).

    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 aected 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 areaected 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 aected by the main cutting force Fc.

    on L-



    842 S. Yaldz, F. Unsacar / Materials and Design 27 (2006) 839846The 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 full 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.


    123 4




    B C









    A C



    tFig. 5. The strain gauges and ring or3.6. Setting the Wheatstone bridges used in the


    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


    Strain guages

    Section W-W

    9 10

    11 12

    13 14



    B Dientation on the dynamometer.

  • relation is obtained. Or, this relation can be rearrangedas

    UA 4UE 106. 17The 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 2eUEor can also be written as

    UA 2UE 106. 18Similarly, 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 cleaning

    S. Yaldz, F. Unsacar / Materials and Design 27 (2006) 839846 843should 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 F t=dt;dt F t=K t 0.096 mm.


    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]:


    k DLL0

    ; 9

    where DR is the dierential 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 vol...


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