مقالات مهندسی مکانیک - ساخت و تولید

1. Introduction
Force measurement in metal cutting is an essential requirement as it is related to machine part design, tool design, power consumptions, vibrations, part accuracy, etc. It is the purpose of the measurement of cutting force to be able to understand the cutting mechanism such as the effects of cutting variables on the cutting force, the machinability of the work piece, the process of chip formation, chatter and tool wear [1]. For over 100 years, metal-cutting researches attempting to understand the cutting behaviour better have investigated the cutting forces in metal cutting. It has been observed that the force values obtained by engineering calculations contain some errors compared to experimental measurements. Since the undeformed chip thickness and the direction of cutting speed vary at every moment, cutting process in milling is geometrically complex. Owing to such complexity, the cutting forces even in steady-state conditions is affected by many parameters and the variation of cutting force with time has a peculiar characteristic [2]. The need for measurement of all cutting force component arises from many factors, but probably the most important is the need for correlation with the progress of tool wear [3]. If this can be obtained, it will be possible to achieve tool wear monitoring in milling based on force variation. Another reason for the cutting forces measurement is that it is a good indicator in detecting tool wear. It is well known that during the cutting process, the cutting parameters such as cutting speed, feed rate and depth of cut often present a deviation from the calculated values. In a three-dimensional cutting operation, three force components are necessary, whereas while drilling or tapping, only a torque and thrust drill are required [4].

The strain gauge produces a clear relation between the measured quantity and the strain on a suitable spot on the spring element [5]. In most cases, the static force is obtained by a strain gauge type sensor which produces an output voltage proportional to elastic deformation.

The cutting force dynamometers must be manufactured at sufficient accuracy and high rigidity, and particularly suitable for dynamic loads [6]. Ito et al. [7] designed some strain gauge-based dynamometers that can be adapted to some machine tools and defined the criterions of their rigidity and sensitivity. In designing the dynamometer, some principles such as parallel beam type [1] and [8], circular hole [9], [10] and [11], piezo-electric [12] and [13], etc., have been used widely.

This study outlines a strain gauge-based octagonal-ring type analogue dynamometer design and prototyping. This dynamometer is capable of measuring three-force components and can as well be used to read the torque value in drilling, tapping, etc. As the reading of analogue values manually is a difficult and tedious job, a computer connection for data acquisition has been realised.

In comparison of the piezoelectric sensors, semiconductor (silicon) strain gages and strain gages, the desirable features of piezoelectric sensors include their rugged construction, small size, high speed, and self-generated signal. On the other hand, they are sensitive to temperature variations and require special cabling and amplification. They also require special care during installation. Electrostatic pressure transducers provide high-speed responses (30 kHz with peaks to 100 kHz). A piezoelectric force sensor is almost as rigid as a comparably proportioned piece of solid steel. Semiconductor (silicon) strain gages are small in size and mass, low in cost, easily attached, and highly sensitive to strain but insensitive to ambient or process temperature variations. Strain gages require simple construction with a small mass and volume. Unfortunately, the most desirable strain gage materials are also sensitive to temperature variations and tend to change resistance as they age. For tests of short duration, this may not be a serious concern. Although the materials exhibited substantial nonlinearity and temperature sensitivity, they had gage factors more than 50 times, and sensitivity more than a 100 times. The fundamental difference between these piezoelectric crystal sensors and static-force devices such as strain gages is that the electric signal generated by the crystal decays rapidly [14] and [15].

It is well known that the strain gage-based multicomponent sensors were superseded by piezoelctric ones, due to the increased rigidity which has vital function in metal-cutting tests and improved dynamic range. The peizoelectric ones are, however, more expensive, around 20:1. Hence, this paper describes a specific design of a strain gage-based multicomponent sensor due to the reached necessary rigidity and dynamic range, without the need to choose the piezoelectric option.

2. Experimental set-up
2.1. Dynamometer
A three-force component analogue dynamometer capable of measuring cutting forces during milling was designed, developed and tested. A computer connection for data acquisition was also made and calibrated. The analogue data can be evaluated numerically on a computer and when required can be converted back to analogue. The schematic representation of the cutting force measurement system is capable of measuring feed force (Ff), thrust force (Ft) and main cutting force (Fc) which occurs during milling operations as seen in Fig. 1. This dynamometer consists of four elastic octagonal rings on which strain gauges were mounted and necessary connections were made to form measuring the Wheatstone bridges.

 
 (40K)

Fig. 1. Schematic representation of experimental set-up.

2.2. Data acquisition
On-line and real-time information of the cutting force data are automatically read and stored by a system during metal cutting. Since the output from Wheatstone bridge circuits is very low due to the high stiffness requirement of the dynamometer, the analogue signals coming from dynamometer amplified by strain gauge input modules (Advantech ADAM 3016) are then converted to digital signals and captured by PCI-1712 data acquisition card installed in MS-Windows-based PC. The stored data can be retrieved and used for analysis when required. The data acquisition software is capable of averaging and graphical simulation of force signals in process. The lists of the experimental equipments used are shown in Table 1.

 Table 1.

Experimental equipments and their technical properties Machine tool Universal milling: Taksan, FU-315 V/2×1250
Dynamometer Strain gauge-based four-component cutting force dynamometer
Strain gauge HBM: LY 41-10/350; effective gauge length 10 mm; Gauge factor 2.09±1%; gauge resistance 350±0.3% Ω; transverse sensitivity of −0.3%
Strain ring Octagonal in shape; made of AISI 4140 steel; b=30 mm; r=32 mm; t=8 mm
Strain amplifier Advantech: ADAM 3016
Data acquisition card Advantech: A/D converter; PCI 1712, 16 single channels (8 differential), 1–10 MHz
Data recording software Written in C; capable of recording, simulating and data processing.
Vibration analyser package Commtest Instrument vb3000: range 1–20.000 Hz, ISO 2372 and ISO10816 standard. Accelerometer: frequency range 0.5–15 kHz, dynamic range ±50 g
Coupler/power supply Kistler: 5118B2; bandwidth 0.03, 0.006 Hz; gain 1×, 10×, 100×; output voltage ±10 V; operated by internal battery (4×1.5 V) or external voltage 6–28 VDC
Universal testing machine LLOYD instrument T50 K

3. Design and construction of a dynamometer for milling
3.1. The criterions for dynamometer design
The rigidity and sensitivity are two opposing but basic requirements in dynamometer design. In addition, the structure of the dynamometer has to meet more strict requirements concerning the natural frequency and wide frequency response and small cross-sensitivity. The ring elements must be machined identical and symmetrical to prevent cross-sensitivity and they should have certain surface quality and high measurement tolerance. The mechanical properties of strain rings must be determined experimentally [16].

A dynamometer essentially consists of an important ring element. The rigidity, high natural frequency, corrosion resistance and high heat conductivity factors were taken into consideration while selecting the ring materials. Also, deformation under the load should conform to that of strain gauges [17].

In this study, AISI 4140 steel, which meets the above requirements, was selected as the ring material.

3.2. Determination of dimensions of the octagonal rings
The thickness t, radius r, and width of the circular strain ring b are the three basic controllable parameters that affect the rigidity and sensitivity. Since there is no effect of ring width b and modulus of elasticity (E) on the strain per unit deflection, bmin can be taken as 30 mm to set up the rings securely [6].

The deformation of circular ring under the effect of thrust force Ft and main cutting force Fc separately is shown in Fig. 2(b) and (c), respectively. As long as strain on A and B where the strain gauges are going to be fixed (Fig. 2(a)) are within the elastic limits of the ring material, the strain and deflection due to the main cutting force should be considered for the purpose of the ring design for maximisation of sensitivity (εc/Fc) and stiffness (Fc/δc).

 
 (17K)

Fig. 2. The deformation of circular strain ring under (a) combined, (b) thrust Ft, and (c) main cutting Fc forces.

The strain gauges should be placed where the stress concentration has maximum value. The experiments have shown that good results are obtained for octagonal rings when the inclined gauges are at points 45° from the vertical instead of 39.6° required by the circular ring theory. The strain per unit deflection can be expressed as [6]

 (1)

where δt is the deflection in a radial direction and εt is the strain due to thrust force Ft. It is clear that for maximum sensitivity and rigidity εt/δt should be as large as possible. This requires that r should be as small as possible and t as large as possible. But small r brings some difficulties in mounting the internal strain gauges accurately. Therefore, for a given size of r and b, t should be large enough to be consistent with the desired sensitivity. Ito et al. [7] performed a finite element analysis for the elastic behaviour of octagonal rings. They expressed that the octagonal ring is substantially stiffer than the circular ring when t/r less then or equals to 0.05, the difference in displacement of circular ring and octagonal ring is <10% if t/r greater then or equals 0.25. In order to be consistent with this expression, the ring thickness and ring radius were taken as 8 and 32 mm, respectively. Thus, the rate of t/r (8/32=0.25) provides corresponding sensitivity to stiffness ratio ε/(δ/r) for the octagonal ring.
3.3. Verifying the dimensions of octagonal rings
The maximum expected force, which the rings may face in each direction, is assumed as 5000 N. If the cross-sectional dimensions of a curved bar is smaller than the radius of the centre line, it is considered to be thin ring [18]. Taking into account dimensions as width (b)=30 mm; radius (r)=32 mm; thickness (t)=8 mm, elastic strains εt and εc due to forces Ft and Fc are calculated according to ring theory by using the following equations [6] and [9]:

 (2)

 (3)

The stress occurring on rings caused by thrust and main cutting forces can be calculated by placing elastic strain ratio values in Eqs. (4) and (5) as follows:

 (4)

 (5)

As the yield strength of AISI 4140 steel is 550–900 N/mm2, the calculated stress values (σt and σc) occurring on the rings are within safety limits for this material.

3.4. Dynamic properties of dynamometer
Vibration frequency of the machine tool, to which the dynamometer is mounted for cutting force measurement, should conform to the natural frequency of the dynamometer. A dynamometer's natural frequency should be as high as possible. Vibration frequency of the machine tool is related to the spindle speed of the machine tool. The dynamometer should have natural frequency of at least four times the vibration frequency of the machine tool [6]. The dynamometer is considered to be a small mass supported by ring elements for analytical purpose as shown in Fig. 3.

 
 (5K)

Fig. 3. Free-body diagram of the developed dynamometer.

In order to determine the natural frequency of the dynamometer, the ring constant of dynamometer should be determined first. The stiffness value for a thin circular ring is given as in the following equation [6]:

 (6)

By placing the related values in Eq. (6), the ring constant of the dynamometer is computed as Kt=39.375 N/mm.

The natural frequency of dynamometer, which is assumed to be a small mass supported by ring elements, can be obtained from the following relation [6]:

 (7)

where K is the dynamometer ring constant (N/mm); m the dynamometer mass (kg) and fd the dynamometer natural frequency (rev./s).
The ring mass is 52.26 kg. As placing the related values in Eq. (7), the natural frequency of dynamometer is computed as fd=138.1 rev/s. To fulfil the requirement as stated above fd>4 fm, the maximum spindle speed should not exceed 2071 rpm.

3.5. The orientation of the strain gauges and the rings on the dynamometer
The proper selection of the points where the strain gauges are mounted is essential for achieving high accuracy in the Wheatstone bridge circuits. The orientation of the strain gauges on the rings and the position of the rings on the dynamometer are given in Fig. 4.

 
 (9K)

Fig. 4. The strain gauges and ring orientation on the dynamometer.

The thrust force Ft are supported by A–D rings of the dynamometer as shown in Fig. 4. The strain gauges 3, 4, 7, 8, 11, 12, 15 and 16 are affected by the thrust force Ft. Among these strain gauges, 3, 7, 11 and 15 are subject to tensile stress while 4, 8, 12 and 16 are subject to compressive stress.

The feed force Ff is supported by A and C rings of the dynamometer as shown in Fig. 4. The strain gauges to measure the feed force Ff should be mounted on the outer surfaces of A and C rings with 45° inclination angle. As shown in Fig. 4, the strain gauges 1, 2, 5 and 6 are affected by the feed force Ff. Among these strain gauges, 1 and 5 are subject to tensile stress while 2 and 6 are subject to compressive stress.

The main cutting force Fc is supported by B and D rings as seen in Fig. 4. The strain gauges for measuring the main cutting force Fc are mounted on rings B and D with 45° inclination angle with respect to the vertical plane. As shown in Fig. 4, the strain gauges 9, 10, 13 and 14 are affected by the main cutting force Fc.

The strain gauges 17 and 18 mounted on to ring B, 19 and 20 mounted on to ring C, as seen in Fig. 4, are for the torque. These strain gauges are mounted onto the outer surfaces of rings with 45° inclination angle. The reason for using the separate strain gauges on the same location for the torque is to prevent any interference of Wheatson bridge signals in real-time operation dedicated for force and torque. So, the signals of strain gauges 17–20 are used to form the Wheatson bridge to be used for torque in operations like drilling, tapping, etc.

3.6. Dynamometer construction
3.6.1. Mounting of strain gauges on the rings
The rings of dynamometer were manufactured at CNC machine tools as seen in Fig. 5. The surfaces of the rings were ground for better strain gauge application. Totally 20, strain gauges were mounted on four octagonal rings. Two strain gauges were mounted horizontally on to outsides of each ring at 45° angles. Two more strain gauges, one inside and the other outside were also mounted vertically, see Fig. 4.

 
 (5K)

Fig. 5. Manufactured octagonal dynamometer rings.

HBM: LY41 10/350 type strain gauges recommended for steel specimens and for static or dynamic loading were utilised. To achieve low-energy dissipation and hence a stable zero setting for a long time, excitation voltage must be selected carefully. The range of excitation voltage for a thick steel-mounting surface may be obtained from the relation [19]:

in which R is the gauge resistance in Ω,  is the power density in the gauge grid (between 2 and 5 kW/m2), and Ag is the active grid area (10×5). For convenience, an excitation voltage of 15 V (calculated between 11.8 and 18.7 V) was employed.
3.6.2. Mounting of the dynamometer
The rings of dynamometer were mounted between two plates by using (6 mm) pins and M8 screws. Pins were used in order to prevent the motion of plates due to clearance, which may cause the cross-sensitivity during measurements. The dimensions of upper plate were 245×270×25 mm and 245×300×25 mm four the lower plate. The sides of upper and lower plates were covered with 5-mm-thick transparent plastic material in order to prevent the strain gauges from hot chips and from cutting fluid during milling (Fig. 6).

 
 (54K)

Fig. 6. The photo of designed and developed dynamometer.

The dynamometer was fixed on to the table of milling machine.

3.7. Dynamometer calibration
3.7.1. Static calibration of the dynamometer
In order to determine the elastic deflection of ring components and consequently the output voltage under static load, the dynamometer was calibrated. The calibration was made in three directions for Ff, Ft, Fc and also for torque. The output voltages of milivolt were averaged for each direction. The loads up to 5000 by 50 N intervals were applied and the strain values were recorded for each load intervals. Thus calibration curves were obtained to convert the output readings into cutting force and torque values. Fig. 7, Fig. 8, Fig. 9 and Fig. 10 shows the calibration curves for feed force, thrust force, main cutting force and torque, respectively. In order to verify the consistency, the measurements were repeated three times and very close values were obtained as seen in Fig. 7, Fig. 8, Fig. 9 and Fig. 10. The effect of loading in one direction on the other force components was also examined and minor fluctuations were observed. These effects were small enough to be ignored. The dynamometer was run idle for 5 min before each calibration tests as it was ready for measurement in order to determine the consistency.

 
 (6K)

Fig. 7. The dynamometer calibration curve in Ff-direction.

 (6K)
Fig. 8. The dynamometer calibration curve in Fc-direction.

 (6K)
Fig. 9. The dynamometer calibration curve in Ft-direction.

 (5K)
Fig. 10. Torque calibration curve of the dynamometer.

3.7.2. Dynamic calibration of the dynamometer
The natural frequency of the dynamometer determines its general dynamic stiffness. In order to the recorded force is not influenced by the dynamic response of the dynamometer, its natural frequency must be higher than the frequency of exciting vibration [3]. The natural frequencies of the dynamometer were determined by setting the dynamometer into vibration using appropriate hammer blows, and by measuring its response using Vibration Analyser Package (Commtest Instrument vb3000). The natural frequency for X-, Y- and Z-directions were found approximately 1.200, 1.050 and 1.500 Hz, respectively. The frequency–amplitude diagram for each direction has been shown in Fig. 11, Fig. 12 and Fig. 13.

 
 (48K)

Fig. 11. Naturally frequency of dynamometer in X-axis.

 (51K)
Fig. 12. Naturally frequency of dynamometer in Y-axis.

 (54K)
Fig. 13. Naturally frequency of dynamometer in Z-axis.

As seen in Fig. 11, Fig. 12 and Fig. 13, it is believed that the necessary rigidity and dynamic range is obtained by designed strain gauge-based dynamometer.

3.8. The dynamometer testing
3.8.1. Linearity test
In order to test the dynamometer for linearity, approximately 80% of maximum load (5.000 N) was applied on it. The dynamometer outputs and calibration values obtained are shown in Table 2(a). The percentage error of Ff, Fc and Ft were calculated as 1.3%, 1.4% and 1.2%, respectively. These errors seem to be acceptable for the dynamometer that will be used in intermittent cutting operations.

 Table 2.

The results of tests performed on the dynamometer (a) The results of linearity test
Axes Load (N) Output-ε (mV) Calibration value-ε (mV) Error (%)
Ff 2400 128.3 130.0 1.3
Fc 2400 126.8 125.0 1.4
Ft 5000 134.2 135.8 1.2
    
(b) The results of cross sensitivity test
Axes Load (N) Output ε (mV/μm) Average error (%)
  X Y Z X Y Z
Ff 2400 128.3 −0.8 1.3  −0.6 1
Fc 2400 −1.2 126.8 −2.2 −1  −1.7
Ft 5000 1.6 1.2 134.2 −1.2 −1.2 0.9
       
(c) The results of eccentricity test
Axes Load (N) e=0 mm (mV) e=50 mm (mV) (%) Output error
Ff 1000 54.6 54.7 0.18
Fc 1000 53.8 53.9 0.18
Ft 1000 25.86 25.53 0.13
    
(d) The results of performance test
Axes ε (mV) F (N) F (N) % Output error
X 14.45 255  Accuracy=1000/1014.9=0.985
Y 13.50 250 1014.9 N Error=14.9/1000=0.015
Z 32.87 950  Error=0.15%

3.8.2. Cross-sensitivity test
The cross-sensitivity can be expressed as strain measured on axes that is normal to the main axes. It is desired that dynamometers must not be completely insensitive to the cross-strain. It is possible to measure the cutting forces independently and accurately as long as the cross-sensitivity is small. The strain errors will be less if this effect is within an acceptable range. These errors can arise because the strain gauges are not fitted symmetrically to the ring axes and if the strain rings are not mounted in the direction of measured force axes. The average errors for cross-sensitivity in three axes were calculated in range of 0.6–1.7% as shown in Table 2(b).

3.8.3. Eccentricity test
In a three-component dynamometer, the applied load within the square outlined by axes of rings must always give same output value. To test this condition, the dynamometer was subjected to eccentricity test. In order to test the dependence of outputs of gauges effected by application point of Ff, Fc and Ft forces, the force (1000 N) was applied to the dynamometer at centre and at e=50 mm distance from the calibration point. The percentage of output errors for Ff, Fc and Ft were found as 0.18, 0.18 and 0.13 as shown in Table 2(c).

3.8.4. Performance test
For this test, the dynamometer axes were kept neither horizontal nor vertical position, but inclined 5° and 1000 N load was applied from the point of zero eccentricity. The outputs (εf, εc, εt-με) were measured and percentage of output error was calculated as 0.15%. The performance test results are given in Table 2(d). When the working conditions such as intermittent cutting in milling are considered, the force signals are oscillated at high amplitudes. The average values of the signals were taken instead of a force signal in a defined time for evaluation. Therefore, this error can be accepted as negligible.

4. Conclusion
In this study, strain gauge-based dynamometer has been designed and developed. It has been devised and connected with necessary data acquisition system consisting of hardware and software. Dynamometer can measure three perpendicular cutting force components and torque simultaneously during milling and the measured numerical values can be stored in computer by data acquisition system. This dynamometer was designed to measure up to 5000 N maximum force and the sensitivity of system is ±5 N.

The orientation of octagonal rings and strain gauge locations were determined to obtain maximum output of ring minimum cross-sensitivity under deformation. To measure the dynamic cutting force, an accelerometer was attached to the dynamometer in measurement direction and the dynamic cutting force calculation was also given. For data transfer between the dynamometer and PC, a proper experimental set-up was performed and suitable software was written. In order to determine accuracy, the dynamometer was calibrated statically and dynamically and subjected to the linearity test, cross-sensitivity test, eccentricity test and performance test.

The static calibration curves for Ff, Fc and Ft forces have shown that it has very high linearity (in errors 1.3%, 1.4% and 1.2%) and low cross-sensitivity errors (in range of 0.6–1.7%). In face-milling operations, appropriate results were obtained in cutting force measurements. As a result, recorded cutting force data were presented for evaluation. Also the natural frequency of dynamometer in X-, Y- and Z-directions satisfies the necessary rigidity and dynamic range.

The results obtained from the machining tests performed at different cutting parameters showed that the dynamometer could be used reliably to measure cutting forces not only in milling but also in other machining processes as turning, grinding and shaping.

The signal recording and processing unit can be used, for example, to monitor or control processes. This type of measuring chain has proved successful for measuring force and torque.
 

Acknowledgements

This experimental study was supported by the Coordination Office to Scientific Research projects of Selcuk University. The authors would like to thank the Coordination Office to Scientific Research projects of Selcuk University for providing financial support to accomplish the project.
 

References
[1] J.D. Kim and D.S. Kim, Development of a combined-type tool dynamometer with a piezo-film accelerometer for an ultra-precision lathe, Journal of Materials Processing Technology 71 (1997), pp. 360–366. Abstract | Full Text + Links | PDF (1025 K) | Abstract + References in Scopus | Cited By in Scopus

[2] S.K. Birla, Sensors for adaptive control and machine diagnostics, Proceedings of the Machine Tool Task Force Conference 4 (1980), pp. 7–12.

[3] S.E. Oraby, Mathematical modelling and in-process monitoring techniques for cutting tools, Ph.D. Thesis, University of Sheffield, 1989.

[4] E.G. Loewen, E.R. Marshall and M.C. Show, electric strain gauge tool dynamometer, Proc. Soc. Exp. Stress Anal. 8 (1951), p. 1.

[5] K. Hoffmann, The Strain Gauge, a Universal Tool of the Experimental Stress Analysis, vd 73004 e, Hottinger Baldwin Messtechnik, Darmstadt (1973).

[6] M.C. Shaw, Metal Cutting Principles, Clarendon Press, Oxford (1984).

[7] S. Ito, S. Sakai and M. Ishikawa, Bulletin of the Japan Society of Precision Engineering (1980), pp. 14–25. Abstract + References in Scopus | Cited By in Scopus

[8] Y. Tani, Y. Hatamura and T. Nagao, Development of small three-component dynamometer for cutting force measurement, Bulletin of the Japan Society of Mechanical Engineering 26 (1983), pp. 650–658. Abstract-Compendex   | Abstract + References in Scopus | Cited By in Scopus

[9] S.E. Oraby and D.R. Hayhurst, High-capacity compact three-component cutting force dynamometer, International Journal of Machine Tools and Manufacture 30 (1990) (4), pp. 549–559. Abstract | Abstract + References | PDF (633 K) | Abstract + References in Scopus | Cited By in Scopus

[10] I. Korkut, A dynamometer design and its construction for milling operation, Materials Design 24 (2003), pp. 631–637. SummaryPlus | Full Text + Links | PDF (188 K) | Abstract + References in Scopus | Cited By in Scopus

[11] U. Şeker, A. Kurt and İ. Çiftçi, Design and construction of a dynamometer for measurement of cutting forces during machining with linear motion, Materials Design 23 (2002), pp. 355–360. SummaryPlus | Full Text + Links | PDF (153 K) | Abstract + References in Scopus | Cited By in Scopus

[12] Y. Hara, S. Motonish, K. Yoshida and N. Ikawa, A new micro-cutting device with high stiffness and resolution, Annals of CIRP 39 (1990), pp. 375–378.

[13] Kistler Instrument Corp. Force Sensors: High-resolution Measurement of Force, Torque and Strain, US, 2004.

[14] The Pressure, Strain, and Force Handbook, Omega Press LLC, 1996.

[15] B. Liptak, Instrument Engineers’ Handbook, CRC Press LLC, Boca Raton, FL (1995).

[16] S. Yaldız and F. Unsacar, A dynamometer design for measurement the cutting forces on turning, Measurement 39 (2006), pp. 80–89. SummaryPlus | Full Text + Links | PDF (230 K) | Abstract + References in Scopus | Cited By in Scopus

[17] J. Tlusty and G.C. Andrews, A critical review of sensors for unmanned machining, CIRP Annals 32 (1983) (2), pp. 563–572. Abstract-Compendex   | Abstract + References in Scopus | Cited By in Scopus

[18] S. Timoshenko, Strength of Materials, Part II (second ed.), D. Van Nostrand Company Inc., New York (1950).

[19] Measurement Group Tech Note, Selection and optimising strain gauge excitation voltage,