Development of a three-component dynamometer to measure turning force

Abstract

This work is focused on the design, construction and testing of a strain gauge dynamometer devised to measure the three components of the turning force. For this purpose, an elastic element sensitive to torsion and flexion was developed. The effect of the cutting parameters (cutting speed, feed rate and depth of cut) on the force components was investigated. Additionally, the performance of the dynamometer was compared with a commercial piezoelectric device. The results indicated that the three components of the turning force decrease slightly as cutting speed was elevated and increase linearly with feed rate and depth of cut. Furthermore, the analysis of variance indicated that the three components are not significantly affected by cutting speed; however, they are significantly affected by feed rate and depth of cut. The comparative tests indicated that the strain gauge dynamometer presented a satisfactory performance, providing closer values to the piezoelectric dynamometer at higher depth of cut values.

Full text

ORIGINAL ARTICLE
Development of a three-component dynamometer to measure
turning force
Tulio Hallak Panzera &Paulo Roberto Souza &
Juan Carlos Campos Rubio &
Alexandre Mendes Abrão &Tanius Rodrigues Mansur
Received: 27 April 2011 /Accepted: 14 December 2011
#Springer-Verlag London Limited 2011
Abstract This work is focused on the design, construction
and testing of a strain gauge dynamometer devised to measure
the three components of the turning force. For this purpose, an
elastic element sensitive to torsion and flexion was developed.
The effect of the cutting parameters (cutting speed, feed rate
and depth of cut) on the force components was investigated.
Additionally, the performance of the dynamometer was com-
pared with a commercial piezoelectric device. The results
indicated that the three components of the turning force de-
crease slightly as cutting speed was elevated and increase
linearly with feed rate and depth of cut. Furthermore, the
analysis of variance indicated that the three components are
not significantly affected by cutting speed; however, they are
significantly affected by feed rate and depth of cut. The
comparative tests indicated that the strain gauge dynamometer
presented a satisfactory performance, providing closer values
to the piezoelectric dynamometer at higher depth of cut
values.
Keywords Dynamometer .Strain gauge .Data acquisition .
Engineering design .Turning
1 Introduction
The current trend observed in the modern industry points
out to the increasing need for automation and integration of
manufacture; in this way, much research has focused on the
optimization of manufacturing processes using advanced
methods for online controlling and monitoring of critical
parameters involved. Ezugwu [1] reported that approximately
10% of all metal worldwide produced is converted into swarf;
therefore, the proper selection of the most adequate machine
tool, cutting tool and machining condition associated to the
online process monitoring is crucial for the production of
goods with ever increasing quality and for the reduction of
machining costs. Within this scenario, the implementation of
reliable monitoring systems can provide usefulinformation on
the process condition that could be used to set up an automatic
control system [2]. According to Kim and Kim [3], the main
purpose to use dynamometry in machining processes is
assessing aspects such as cutting mechanism, effect of the
cutting parameters on force components, materials perfor-
mance, chip formation, chatter and tool wear progression.
Among the numerous tool condition monitoring systems
available to monitor machining operations, Byrne et al. [4]
reported that the most commonly sensors employed in the
industrial environment are force, power and acoustic emis-
sion sensors which are mainly employed to monitor tool
wear and to prevent collision and breakage. Turning and
drilling are the principal machining operations which em-
ploy tool condition monitoring systems, followed to a lesser
extent by milling and grinding. Nevertheless, a survey on
the monitoring systems implemented by Mercedes Benz AG
T. H. Panzera (*)
Department of Mechanical Engineering,
Federal University of São João del Rei—UFSJ,
São João del Rei, Brazil
e-mail: panzera@ufsj.edu.br
P. R. Souza
Centre for Education in Technology of Minas Gerais—CEFET,
Belo Horizonte, Brazil
J. C. C. Rubio :A. M. Abrão
Department of Mechanical Engineering,
Federal University of Minas Gerais—UFMG,
Belo Horizonte, Brazil
T. R. Mansur
Centre of Nuclear Technology Development—CDTN,
Belo Horizonte, Brazil
Int J Adv Manuf Technol
DOI 10.1007/s00170-011-3866-5

in their production line indicated that only 46% were fully
operational, while 25% were non-functional for technical
reasons and 16% had limited functionality.
The knowledge on the behaviour of the machining forces
is relevant not only for the design of the machine tool
components, such as motors, guide ways and bearings, but
also for the quality of the finished component. The higher
the machining forces, the poorer the surface finishing and
the wider the dimensional and geometric tolerances. Fur-
thermore, vibration during cutting may lead to accelerated
tool wear rates.
In addition to vibrations caused by forces applied periodi-
cally, such as those caused by tool engagement or machine
misalignment, chatter may take place as a result of the inter-
action between periodic force variations and the dynamic
stiffness characteristics of the machine tool, particularly in
the case where discontinuous chips are generated or the depth
of cut varies causing fluctuations in the machining force. A
detailed account on chatter vibrations during machining was
given by Altintas [5].
During the machining of metallic alloys, Strafford and
Audy [6] noticed that the amplitude characteristics of the
force components are dependent on the grain sizes of the
ferrite and pearlite phases, as well as on the proportions of
these phases. Moreover, the presence of inclusions, oxides
and sulphides in the work materials resulted in wider scatter
in the force amplitude.
This work is focused on the design, construction and
testing of a strain gauge dynamometer devised to measure
the three components of the turning force. Additionally to
sensitivity, stiffness and accuracy, the proposed dynamometer
must present low cost and construction simplicity.
2 Background
Machining forces can be measured directly or indirectly; the
former requires the mounting of a dynamometer on the
machine tool which will correlate elastic deflection (within
the range of micrometres) to electrical signals [7]. Indirect
measuring relies on detecting the power consumed by the
spindle or feed drive motors and using these data to calcu-
late, respectively, the principal and feed forces. According to
Childs et al. [7], the indirect measuring is less accurate than
direct methods; however, it is quite suitable for monitoring
numerical controlled machine tools, which possess motors
with high sensitivity and response.
The principal requirements for a dynamometer are high
stiffness, sensitivity and accuracy [8]. The stiffness of the
dynamometer should be high enough to ensure that deflec-
tions will not affect the operation (static stiffness of approx-
imately 108 N/m). As far as the sensitivity and accuracy are
concerned, the above-mentioned author states that these
parameters should range within ±1%. Furthermore, the
natural frequency of the dynamometer must be at least four
times the value of the frequency of the exciting vibration in
order to ensure that the recorded force values are not affected
by vibration [9].
Strain gauge dynamometers rely on the elastic strain
caused by machining forces to promote alterations on the
electrical resistance of gauges bonded on the tool holder or
work table. Typically, a Wheatstone bridge connected to an
amplifier is employed to simultaneously measure alterations
induced by compression and tension, which will promote
changes in the resistance lower than 0.5%. In spite of its
simplicity, strain gauges bonded directly on the tool holder
present the following limitations, they cannot detect the
radial force, the principal and feed forces depend on the
distance between the load and the gauges and compensation
due to temperature elevation (when a single gauge is
employed) may be necessary. Three-component force and
torque can be measured by using devices such as a strain
ring. A number of strain gauge dynamometer configurations
suitable for a variety of machining operations were presented
by Karabay [9]. Special attention is paid to the design of the
elastic components, which are the most critical elements of a
strain gauge dynamometer.
A three-component force dynamometer based on a strain
gauge ring was designed, built and tested by Yaldiz and
Ünsaçar [10,11]. The equipment possesses four octagonal
rings with four strain gauges each. The strain gauges were
conveniently connected to form Wheatsone bridges. Cali-
bration of the device indicated a maximum error of 1.4% in
the linearity test, cross sensitivity ranging from 0.17 to
0.92% and sensitivity of ±5 N (maximum force of 3,500 N).
On the other hand, piezoelectric dynamometers use sin-
gle crystals, especially quartz, to induce a separation of
charge when subjected to machining forces. When these
crystals are piled up, the three components of the machining
force and torque can be measured independently. Table 1
compares piezoelectric and strain gauge force sensors, and
the former are constituted of quartz piled stack and the latter
of platinum [12,13]. It can be noticed that piezoelectric
sensor possesses higher resonant frequency and stiffness
(which also depends on the tool holder used) and
Table 1 Properties of piezoelectric and strain gauge force sensor
[12,13]
Characteristics Piezoelectric Strain gauge
Resonant frequency (kHz) 102 3.5
Stiffness (N/μm) 24× 10
3
3.3× 10
3
Repeatability (%) 0.03 0.5
Maximum temperature 150°C 426°C
Displacement rate 1.6 μm/m/V 0.9 μm/mm
Int J Adv Manuf Technol

considerably lower repeatability. In contrast, strain gauge
sensors present higher depolarization temperature and there-
fore can withstand higher temperatures. Finally, the strain
gauge cost per component force is drastically lower than that
of a piezoelectric sensor.
Alternatively, Jin et al. [14] present a dynamometer based
on tool deflection measurement using an optical fibre trans-
ducer. The device operates similarly to a split tool, i.e. when
the tool tip is subjected to deflection; in this case, the
corresponding displacement can be measured by a sensor
which detects the difference of light intensity emitted from a
source and reflected on a sensor. The main advantages of the
above-described dynamometer are related to the fact that
additional room is not required for mounting the equipment
and the stiffness of the machine tool system is not reduced
by the incorporation of the device, which presents a natural
frequency of 950 Hz. Nevertheless, the main drawbacks
associated with this dynamometer are related to the prepa-
ration of the tool holders and difficulty to measure the radial
force.
The ratio of feed force and cutting force was used by
Choudhury and Kishore [15] to monitor tool wear. Accord-
ing to the authors, this ratio can be successfully used to
predict tool wear, presenting a correlation coefficient
between experimental and predicted values nearly 0.99.
Nevertheless, Dimla Sr. [16] reported that the dynamic force
and vibration signals are more applicable for tool wear
monitoring, considering that the tool condition (sharp, worn
Tool holde
r
Elastic
element
13π
Strain-gauges
Fig. 1 Schematic diagram of the elastic element of the dynamometer
(a) (b)
Fig. 2 Dynamometer design: (a) tool post and (b) elastic element
Fig. 3 Strain gauge dynamometer
Int J Adv Manuf Technol

or chipped edge) can be more easily detected compared to
the individual static force signals.
Gunay et al. [17] devised a dynamometer using two beam
type load cells in order to investigate the effect of the tool
rake angle on the cutting forces when turning AISI 1040
steel. The findings indicated that the cutting forces de-
creased when the rake angle was increased.
A dynamometer for triaxial cutting force measurement in
turning endowed with indexable tool heads or with rotating
turrets was developed by Totis and Sortino [18]. The sensor
was able to follow rapid signal variations in actual production
conditions; however, the authors emphasized the interest to
improve the geometry of the device in order to increase the
force measuring range and to investigate new frequency
bandwidth.
In the particular case of turning steels with hardness
above 55 HRC, Scheffer et al. [19] stated that turning forces
coupled to an artificial intelligence method (static and dy-
namic neural network) are the most suitable tool wear mon-
itoring system. Additionally, crater wear must be taken into
account together with flank wear; besides, the identification
and isolation (using digital filters) of disturbances on tool
wear are critical in order to obtain an accurate force model.
Finally, the authors reported that while the static force
components are widely used to monitor tool wear due to
the fact that their signal values increase with friction be-
tween the tool and workpiece, the dynamic component of
the machining force contains relevant information due to the
increase in vibration amplitudes for determined frequency
ranges as tool wear progresses.
Fig. 4 Experimental setup
Table 2 Experimental data used in calibration curves
F
c
F
f
F
p
Load
(N)
Voltage
(mV)
Load
(N)
Voltage
(mV)
Load
(N)
Voltage
(mV)
3.76 5 8.4 0 9.76 5
13.13 15 28.01 20 19.66 10
13.52 35 37.38 30 29.42 15
23.37 40 47.67 40 39.28 20
33.18 48 57.43 50 49.03 25
42.99 60 66.38 60 58.01 30
52.79 75 76.26 70 67.91 35
61.77 95 86.02 80 77.67 40
71.67 110 106.51 90 87.52 45
81.43 120 125.78 100 97.28 50
91.28 135 154.37 120 145.97 75
101.48 150 203.01 160 194.61 100
149.73 215 251.26 180 242.86 125
198.37 285 300.64 200 291.89 150
286.19 400
383.91 500
500.91 660
558.91 750
Table 3 Experimental conditions
Cutting speed Feed rate Depth of cut
C1 100 0.1 0.5
C2 100 0.1 1.0
C3 100 0.1 1.5
C4 100 0.2 0.5
C5 100 0.2 1.0
C6 100 0.2 1.5
C7 100 0.3 0.5
C8 100 0.3 1.0
C9 100 0.3 1.5
C10 200 0.1 0.5
C11 200 0.1 1.0
C12 200 0.1 1.5
C13 200 0.2 0.5
C14 200 0.2 1.0
C15 200 0.2 1.5
C16 200 0.3 0.5
C17 200 0.3 1.0
C18 200 0.3 1.5
C19 250 0.1 0.5
C20 250 0.1 1.0
C21 250 0.1 1.5
C22 250 0.2 0.5
C23 250 0.2 1.0
C24 250 0.2 1.5
C25 250 0.3 0.5
C26 250 0.3 1.0
C27 250 0.3 1.5
Int J Adv Manuf Technol

The power spectrum density of the cutting force was
employed by Tangjitsitcharoen [20] to monitor and identify
chip forms and chatter of turning process in order to achieve
intelligent machining, irrespectively of the cutting condition
used. Therefore, an algorithm was proposed to avoid both
chatter and breaking continuous chips by changing the
cutting conditions during the operation. In a similar work
concerned with milling, Huang et al. [21] used cutting force
values to feed an uncertain linear model aiming to monitor
tool wear. As a result, threshold values were computed for
detecting machine tool fault. Nevertheless, the authors state
that a new model is required if the milling cutter and work
material are changed.
3 Dynamometer design and construction
The elastic element is a circular hollow bar made of AISI
4340 steel. The tool holder is fixed inside a square cross-
section bar which is welded on the elastic element. The
forces acting on the tool tip are measured by means of
bending and torsion of the elastic element, as indicated
schematically in Fig. 1. The strain gauges are cemented on
the elastic element in order to independently measure de-
flection caused by the three components of the turning force:
cutting or tangential force (F
c
), feed or axial force (F
f
) and
thrust or radial force (F
p
). The strain gauges were connected
as a full Wheatstone bridge in order to compensate the
influence of temperature on strain measurement. A metallic
cover was attached to protect the strain gauges from the
swarf.
In order to calculate the dimensions of the elastic ele-
ment, a maximum resulting force of 1,500 N and a maxi-
mum torque of 7,500 Nmm were established. In practical
terms, it means that the dynamometer can be used for
turning a normalized medium carbon steel with maximum
feed rate and depth of cut values of 0.4 mm/rot and 2 mm,
respectively.
Figure 2shows the principal dimensions of the designed
dynamometer. The remaining dimensions were defined
taking into account the dimensions of the compound rest
of the lathe where the equipment was mounted. A photo-
graph of the finished dynamometer is presented in Fig. 3.
The following strain gauges manufactured by Tokyo Sokki
Kenkuyujo Co. were used: QFLT-1-350B-002LE (cutting
force), QFLT-1-350A-002LE (feed force) and QFLA-2-
350A-002LE (thrust force).
The voltage applied to the Wheatstone bridge is 2 V.
Consequently, the output voltage has to be amplified 1,000
times using an operating amplifier with passive filtering
(low pass). An analogical/digital data acquisition system
Fig. 5 Effect of cutting speed and feed rate on cutting force
Fig. 6 Effect of feed rate and depth of cut on cutting force
Fig. 7 Effect of cutting speed and feed rate on feed force
Fig. 8 Effect of feed rate and depth of cut on feed force
Int J Adv Manuf Technol

(Quatech DAQ 800) connected to a computer was used to
convert, record and plot force values at a sampling rate of
120 Hz using the software package Quatech DAQSuite
provided by the manufacturer of the data acquisition system.
Figure 4shows the experimental setup.
4 Calibration and testing
Static calibration for each force component was undertaken
using a cantilever beam with loads ranging from 3.7 to
558.9 N. As a consequence, the following linear regression
models and corresponding correlation coefficients (R
2
) were
obtained:
Fc¼0:7587V7:6306 R2¼0:9985 ð1Þ
Ff¼1:4268V11:647 R2¼0:9784 ð2Þ
Fp¼1:9439Vþ0:111 R2¼0:9989 ð3Þ
where Vis the output voltage (millivolts), F
c
is the cutting
force (Newton), F
f
is the feed force (Newton) and F
p
is the
thrust (radial) force (Newton). It can be noticed that the
linear regression models fit the calibration points quite
satisfactorily, as indicated by the R
2
values. Table 2
presents the experimental data used in the calibration
procedure.
Continuous dry turning tests were conducted on a computer
numerical control lathe (5.5 kW power and 3,500 rpm maxi-
mum rotational speed) using AISI 1045 medium carbon steel
as work material (average hardness of 290 HV) and ISO P01-
P30 coated carbide inserts (geometry code SMNG 120406)
mounted on a tool holder coded DCLNR 2020 K12. The
following cutting conditions were employed, cutting speeds
(v
c
) of 100, 200 and 250 m/min; feed rates (f) of 0.1, 0.2 and
0.3 mm/rev and depths of cut (a
p
) of 0.5, 1 and 1.5 mm, thus
resulting in 27 runs (see Table 3).
Figures 5,6,7,8,9and 10 show the effect of cutting
speed, feed rate and depth of cut on the force components.
The parameter which variation is not shown in the graphs
was kept at its intermediate value. It can be seen in Figs. 5
and 6that the cutting force (F
c
) is not drastically affected by
Fig. 9 Effect of cutting speed and feed rate on thrust force
Fig. 10 Effect of feed rate and depth of cut on thrust force
0
100
200
300
400
500
600
F
p
FfFc
Force value (N)
Fc (N) Ff (N) Fp (N)
Average 455.1 299 235.07
St. dev. 30.97 17.86 19.85
Fig. 11 Turning forces obtained for the centralpoint using four replicates
(v
c
0200 m/min, f00.2 mm/rev and a
p
01mm)
0
100
200
300
400
500
0.1 0.2 0.3
Feed rate (mm/rev)
Cutting force (N)
Kienzle
Strain gauge
Piezoelectric
Fig. 12 Effect of feed rate on cutting force (v
c
0200 m/min and
a
p
00.5 mm)
Int J Adv Manuf Technol

cutting speed, despite a slight reduction in the former is
verified when the latter is elevated. In contrast, the increase
of feed rate and depth of cut resulted in a linear increase of
F
c
. The reduction of F
c
while cutting speed is increased is
probably caused by the reduction of the shear strength of the
work material owing to the elevation of temperature in the
cutting zone. On the other hand, increasing feed rate and
depth of cut means that the shear area is elevated, thus
requiring higher cutting forces.
Figures 7and 8show the same trend observed for F
c
recorded for the feed force (F
f
), i.e. this force component
decreased slightly as cutting speed was elevated and in-
creased with feed rate and depth of cut due to the same
reasons previously discussed. The effect of cutting speed,
feed rate and depth of cut on thrust force can be seen in
Figs. 9and 10. Similarly to F
c
and F
f
, thrust force decreases
as cutting speed is elevated and increases with feed rate and
depth of cut.
The experimental data used to plot Figs. 5,6,7,8,9and
10 were analysed by analysis of variance, which indicated
that the three components of the turning force are not
statistically affected by cutting speed within a significance
level of 5%; nevertheless, they are significantly affected by
feed rate and depth of cut.
The cutting condition representing the central point
(v
c
0200 m/min, f00.2mm/revanda
p
01mm)was
replicated four times in order to estimate the scatter
associated with the force measuring system developed
in the present work. Figure 11 shows the individual
force values and corresponding average and standard
200
300
400
500
600
700
800
0.1 0.2 0.3
Feed rate (mm/rev)
Cutting force (N)
Kienzle
Strain gauge
Piezoelectric
Fig. 13 Effect of feed rate on cutting force (v
c
0200 m/min and
a
p
01 mm)
200
400
600
800
1000
1200
0.1 0.2 0.3
Feed rate (mm/rev)
Cutting force (N)
Kienzle
Strain gauge
Piezoelectric
Fig. 14 Effect of feed rate on cutting force (v
c
0200 m/min and
a
p
01.5 mm)
0
50
100
150
200
0.1 0.2 0.3
Feed rate (mm/rev)
Feed force (N)
Strain gauge
Piezoelectric
Fig. 15 Effect of feed rate on feed force (v
c
0200 m/min and
a
p
00.5 mm)
0
100
200
300
400
0.1 0.2 0.3
Feed rate (mm/rev)
Feed force (N)
Strain gauge
Piezoelectric
Fig. 16 Effect of feed rate on feed force (v
c
0200 m/min and
a
p
01mm)
Int J Adv Manuf Technol

deviation obtained. The standard deviation of the cutting
force (F
c
) represented 6.8% of the average value, whereas for
the feed force (F
f
) and thrust force (F
p
), the standard deviation
corresponded, respectively, to 5.9% and 8.4% of the average
force values.
5 Comparative tests
Finally, the performance of the strain gauge dynamometer
was compared with a commercial piezoelectric dynamome-
ter (Kistler model 9257BA) when continuous dry turning
AISI 1045 steel using the cutting tool previously described.
Additionally, the cutting force obtained experimentally was
compared with the value calculated using Kienzle model
equation as follows:
Fc¼ks1bh1zð4Þ
The selected parameters (1 −z)andk
s
were, respectively, 0.83
and 2,069.20 N/mm
2
, according to Koenig and Klocke [22]
The comparative tests were carried out at a constant
cutting speed (v
c
0200 m/min) and feed rates of 0.1, 0.2
and 0.3 mm/rev and depths of cut of 0.5, 1 and 1.5 mm.
Figures 12,13 and 14 show the effect of feed rate on cutting
force obtained experimentally and using Kienzle model for
depths of cut of 0.5, 1 and 1.5 mm, respectively.
Figures 12,13 and 14 show that F
c
increases with both
feed rate and depth of cut, and the cutting force obtained
200
300
400
500
600
0.1 0.2 0.3
Feed rate (mm/rev)
Feed force (N)
Strain gauge
Piezoelectric
Fig. 17 Effect of feed rate on feed force (v
c
0200 m/min and
a
p
01.5 mm)
0
100
200
300
400
0.1 0.2 0.3
Feed rate (mm/rev)
Thrust force (N)
Strain gauge
Piezoelectric
Fig. 18 Effect of feed rate on thrust force (v
c
0200 m/min and
a
p
00.5 mm)
0
100
200
300
400
0.1 0.2 0.3
Feed rate (mm/rev)
Thrust force (N)
Strain gauge
Piezoelectric
Fig. 19 Effect of feed rate on thrust force (v
c
0200 m/min and
a
p
01 mm)
0
100
200
300
400
0.1 0.2 0.3
Feed rate (mm/rev)
Thrust force (N)
Strain gauge
Piezoelectric
Fig. 20 Effect of feed rate on thrust force (v
c
0200 m/min and
a
p
01.5 mm)
Int J Adv Manuf Technol

through Kienzle model presents the highest values, thus
suggesting that the values given by the above-mentioned
equation are overestimated. Furthermore, the values
recorded by the strain gauge dynamometer at a depth of
cut of a
p
00.5 mm (Fig. 12) were considerably lower com-
pared with those obtained using the piezoelectric device.
However, as depth of cut is elevated to a
p
01 and 1.5 mm
(Figs. 13 and 14, respectively), similar values are recorded
using both dynamometers. These findings indicate that the
sensitivity of the strain gauge dynamometer increases with
depth of cut.
The influence of feed rate on the feed force values
obtained experimentally using both the strain gauge and
piezoelectric dynamometers is given in Figs. 15,16 and 17
when turning at a constant cutting speed (v
c
0200 m/min)
and depths of cut of 0.5, 1 and 1.5 mm, respectively. As
expected, the feed force increased with feed rate and depth
of cut, and the difference between the values recorded by
both dynamometers was minimal (maximum difference of
10.7% for a feed rate of 0.1 mm/rev and depth of cut of
0.5 mm, see Fig. 15).
Finally, Figs. 18,19 and 20 present the influence of feed
rate on thrust force values obtained experimentally when
turning at a constant cutting speed of 200 m/min and depths
of cut ranging from 0.5 to 1.5 mm, respectively. These
findings indicate that the strain gauge and piezoelectric
dynamometers offer closest values for the thrust component
of the turning force, with a maximum difference of 7.8% at a
feed rate of 0.3 mm/rev and depth of cut of 0.5 mm, as
indicated in Fig. 18.
Based on the results of Figs. 15 and 18, it can be noticed
that when a depth of cut of 0.5 mm is used, the value of the
thrust force becomes higher than the feed force. This behav-
iour can be explained by the fact that the cutting tool nose
radius (r
ε
00.8 mm) is higher than the depth of cut
employed. As a consequence, the effective side cutting edge
angle is reduced from χ
r
045-to χ
r
034-, thus promoting the
elevation of thrust force.
6 Conclusions
The following conclusions can be drawn from this work:
1. The performance of the strain gauge dynamometer de-
veloped for measuring the three components of the
turning force was considered satisfactory, especially
when taken into account simplicity and low cost as
requirements for the design and construction of the
device, additionally to accuracy, stiffness and sensitivity.
Similarly, the data acquisition system was found to be
simple and reliable.
2. The elevation of cutting speed promoted a slight reduc-
tion in the components of the turning force; neverthe-
less, the analysis of variance indicated that this effect
was not statistically significant for a 5% significance
level. In contrast, an increase in both feed rate and depth
of cut resulted in significant elevation of the turning
force components.
3. The replicate tests showed that the repeatability of strain
gauge dynamometer was satisfactory, exhibiting the
following results: 6.8% for the cutting force, 5.9% for
the feed force and 8.4% for the thrust force.
4. The comparative tests with a commercial piezoelectric
dynamometer demonstrated the accuracy and the poten-
tial use of the developed dynamometer, exhibiting closer
values when turning at higher depth of cut values. In
addition, closer values were recorded for the thrust
component.
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