sensors Article
Development and Testing of an Integrated Rotating Dynamometer Based on Fiber Bragg Grating for Four-Component Cutting Force Measurement Mingyao Liu 1 , Junjun Bing 1 , Li Xiao 2 , Kang Yun 1, * and Liang Wan 1 1 2
*
School of Mechanical and Electronic Engineering, Wuhan University of Technology, Wuhan 430070, Hubei, China;
[email protected] (M.L.);
[email protected] (J.B.);
[email protected] (L.W.) Jianghan Machinery Research Institute Co., Ltd., CNPC, Jingzhou 430024, Hubei, China;
[email protected] Correspondence:
[email protected]
Received: 19 March 2018; Accepted: 16 April 2018; Published: 18 April 2018
Abstract: Cutting force measurement is of great importance in machining processes. Hence, various methods of measuring the cutting force have been proposed by many researchers. In this work, a novel integrated rotating dynamometer based on fiber Bragg grating (FBG) was designed, constructed, and tested to measure four-component cutting force. The dynamometer consists of FBGs that are pasted on the newly designed elastic structure which is then mounted on the rotating spindle. The elastic structure is designed as two mutual-perpendicular semi-octagonal rings. The signals of the FBGs are transmitted to FBG interrogator via fiber optic rotary joints and optical fiber, and the wavelength values are displayed on a computer. In order to determine the static and dynamic characteristics, many tests have been done. The results show that it is suitable for measuring cutting force. Keywords: cutting force; rotating dynamometer; fiber Bragg grating (FBG); arcuate beam
1. Introduction Nowadays, real-time on-line monitoring of cutting force is an essential requirement in the machining processes. As one of the most significant machining process variables, cutting force can be used to optimize cutting parameters, improve cutting conditions, investigate cutting tools performance, predict the surface roughness, monitor tool wear or failure, and others. Commonly, studies about cutting force measurement mainly focus on direct measurement and indirect measurement of cutting force. Indirect measurement always detects the power or current of the spindle motor or the driving motor to reflect the cutting force [1–4]. Besides, some researchers work on measuring the displacement of the machining tool spindle [5,6]. The indirect measurement has the advantages of simple structures and easy installation. However, the signals from electrical transducers are susceptible to forces of temperature, transmission, mechanical structure, and so on, so it is difficult to measure the cutting force precisely. Direct measurement of cutting force can be divided into two parts according to the installation, which are clamped on the table and mounted on the spindle. No matter what the dynamometer is, it usually utilizes an elastic structure to convert cutting force into strain, and then detects the strain by sensing elements. In table dynamometers, elastic structures include the octagonal ring [7,8], the oval octagonal ring [9], the ring [10], and so on. For rotating dynamometers mounted on the spindle, elastic structures consist of a cylindrical deformation beam [11], Γ beam-type [12,13], E-type diaphragm [14,15] and others. In contrast to table dynamometers, rotating dynamometers have several advantages, such as less intermediate force transmission components, allowing for various cutting tools sizes and force configurations. From the sensing elements, there are capacitive [11], strain gauge [13–16], piezoelectric [17–19], fiber Bragg grating (FBG) [10,20,21], and so
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dynamometers, rotating dynamometers have several advantages, such as less intermediate force transmission components, allowing for various cutting tools sizes and force configurations. From the sensing elements, Sensors 2018, 18, 1254 there are capacitive [11], strain gauge [13–15], piezoelectric [17–19], fiber Bragg 2 of 11 grating (FBG) [10,[20,21], and so on. Capacitors and strain gauges are susceptible to electromagnetic interference and their processing circuits are complex. Piezoelectric materials have high demand for on. Capacitors and strain are susceptible interference and their processing ambient temperature andgauges humidity. However, to theelectromagnetic cutting force test environment is filled with circuits are complex. Piezoelectric materials have high demand for ambient temperature and humidity and magnetic fields, in which capacitors, strain gauges, and piezoelectric materialshumidity. are not However, theiscutting force test environment is filled with humidity and magnetic fields, in which suitable. FBG not sensitive to humidity and magnetic fields, and is resistant to corrosion, small in capacitors, strain gauges, and piezoelectric materials are not suitable. FBG is not sensitive to humidity volume, and can measure multiple points in one optical fiber. Therefore, FBG is more applicable for and magnetic fields, and is resistant to[12,22] corrosion, small ainspindle-integrated volume, and can measure points cutting force measurement. Reference designed methodmultiple for cutting forcein one optical fiber. Therefore, is more for cutting force measurement. [12,22] measurement based on FBG,FBG realizing theapplicable measurement of three-axis forces, but notReference measuring the designed a spindle-integrated method for cutting force measurement based on FBG, realizing the torque. measurement of three-axis forces, but rotating not measuring the torque. In this paper, a novel integrated dynamometer based on fiber Bragg grating for fourIn this paper, a novel integrated rotating dynamometer on fiber Braggused grating for component cutting force measurement has been proposed. Firstly,based the elastic structure in this four-component cutting force measurement has been proposed. Firstly, the elastic structure used in system is introduced as two mutual-perpendicular semi-octagonal rings which are convenient for this system is introduced as two mutual-perpendicular semi-octagonal which are convenient for pasting FBGs. Secondly, the layout of the FBGs is specially selectedrings under the analysis of finite pasting FBGs. Secondly, the layout of the FBGs is specially selected under the analysis of finite element element method (FEM) simulation results and can realize the decoupling of four-component cutting method results and realize the decouplingwere of four-component force force in (FEM) theory.simulation Static calibration andcan dynamic experiments undertaken tocutting evaluate thein theory. Staticofcalibration and dynamic experiments were to evaluate the performance performance the dynamometer. Test results indicate thatundertaken the developed dynamometer is qualifiedof the dynamometer. Test results indicate that the developed dynamometer is qualified to measure the to measure the four-axis loads in milling or drilling processes. four-axis loads in milling or drilling processes. 2. Experimental Section 2. Experimental Section 2.1. Design Principle 2.1. Design Principle The purpose of this study aimed at developing an integrated rotating dynamometer to measure The purpose of this study aimed at developing an integrated rotating dynamometer to measure four-axis loads (viz. Fx , Fy , Fz , T ) for milling or drilling processes. A novel elastic structure of two four-axis loads (viz. Fx , Fy , Fz , T) for milling or drilling processes. A novel elastic structure of mutual-perpendicular semi-octagonal rings rings has been as depicted in Figure 1. The1. two mutual-perpendicular semi-octagonal has put beenforward, put forward, as depicted in Figure measurement structure consists of the spindle, elastic structure, and connector. The spindle The measurement structure consists of the spindle, elastic structure, and connector. Theconnects spindle with the machine head and the connector joins the tools. But, this connector is designed to be applied connects with the machine head and the connector joins the tools. But, this connector is designed to be to the multi-dimensional force device. The elasticThe structure made upisof the intermediate shaft, the applied to the multi-dimensional force device. elastic is structure made up of the intermediate arcuate beam, and beam, the flange. Theflange. arcuateThe beam is used to convert force into strain. the shaft, the arcuate and the arcuate beam is usedcutting to convert cutting force When into strain. four-axis loads act on the end of the connector, the four arcuate beams produce deformation and When the four-axis loads act on the end of the connector, the four arcuate beams produce deformation stress. and stress. Intermediate shaft Arcuate beam Spindle Elastic structure Connector Flange
Figure Figure1.1.The Themeasurement measurementstructure. structure.
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In order to to obtain range of the measurement, we 40CrNiMoA choose 40CrNiMoA steel as the In order obtainaa larger larger range of the measurement, we choose steel as the material material of the elastic structure; its elastic modulus, poisson ratio, and yield strength are 210 of the elastic structure; its elastic modulus, poisson ratio, and yield strength are 210 GPa, 0.3, andGPa, 835 0.3, and 835 MPa, respectively. The material the spindle the connector is steel stainless steelsize 304. MPa, respectively. The material of the of spindle and theand connector is stainless 304. The of The the size is shown in Figure 2. 2. of theelastic elasticstructure structure is shown in Figure
φ30
14
33.14
r32 40
86.57
. 33
15
8
Figure 2.2.The elasticstructure. structure. Figure Thesize size of of the elastic 2.2. Sensor Design 2.2. Sensor Design When a broad-band light enters the fiber Bragg grating through the optical fiber, the narrow-
When a broad-band light enters the fiber Bragg grating through the optical fiber, the narrow-band band light of a particular wavelength is reflected back. The reflected light satisfies the Bragg light scattering of a particular wavelength is reflected back. The reflected light satisfies the Bragg scattering conditions. It is expressed by the following equation. conditions. It is expressed by the following equation. B 2neff
(1)
λ Beffective = 2ne f refractive fΛ where λB is the Bragg wavelength, neff is the index of the fiber core, and Λ is the (1) grating period. The wavelength of a FBG is influenced by strain and temperature simultaneously. whereSince λB isthethe Bragg wavelength, is theout effective index the fiber core, and Λ experiment of the study n iseffcarried at roomrefractive temperature, thisof paper doesn’t consider theis the grating period. The wavelengthThe of equation a FBG iscan influenced by strain and temperature simultaneously. impact on the dynamometer. be given by Since the experiment of the study is carried out Bat room temperature, this paper doesn’t consider the (1 pe ) by (2) impact on the dynamometer. The equation can be given B
∆λ B where Pe is the effective photo-elastic coefficient; generally, the value of Pe is 0.22; △λB is the change = (1 − p e ) ε (2) of wavelength; ε is the strain. λB As it is difficult to get the theoretical formula to calculate the surface stress of the elastic wherestructure, Pe is the the effective photo-elastic coefficient; generally, the value of Pedistribution is 0.22; ∆λBofisthe theelastic change of finite element method (FEM) was used to investigate the wavelength; ε is the strain. structure and select the layout of FBGs. In order to achieve a larger sensitivity and decrease the crossinterference influence, of the FBGs on the force sensing element is shown in Figure 3. As it is difficult to get the the location theoretical formula to calculate the surface stress of the elastic structure, FBGselement 1–12 aremethod pasted on the surfaces of the structure modified acrylic Different and the finite (FEM) was used toelastic investigate theby distribution of theadhesive. elastic structure can beofconnected optical fiber. When four-component cuttingthe force acts on the selectFBGs the layout FBGs. Inwith orderone to achieve a larger sensitivity and decrease cross-interference dynamometer, the surfaces of the elastic structure produce strains. Besides, the wavelengths FBGs 1–12 influence, the location of the FBGs on the force sensing element is shown in Figure 3. ofFBGs change along with the surface strains of the elastic structure. And then, the information of are pasted on the surfaces of the elastic structure by modified acrylic adhesive. Different FBGs can wavelengths is transmitted to the FBG interrogator through optical fiber. The wavelengths of FBGs be connected with one optical fiber. When four-component cutting force acts on the dynamometer, are demodulated by the interrogator and are displayed on the computer. At last, the relationship the surfaces the elastic structure strains. Besides, the wavelengths of FBGs change along betweenofthe wavelength changesproduce of the FBGs and the four-component cutting forces is established. with the surface strains of the elastic structure. And then, the information of wavelengths is transmitted The X-direction force Fx is detected by FBG1 and FBG3; the Y-direction force F y is supported by to theFBG2 FBGand interrogator through optical The wavelengths of FBGs are demodulated by the FBG4; the Z-direction force Ffiber. z is described by FBG5-8; the torque T is represented by interrogator and are displayed on the computer. last, the FBG9-12. The self-decoupling relation is shown in At Equation (3).relationship between the wavelength changes of the FBGs and the four-component cutting forces is established. The X-direction force Fx is detected by FBG1 and FBG3; the Y-direction force Fy is supported by FBG2 and FBG4; the Z-direction force Fz is described by FBG5-8; the torque T is represented by FBG9-12. The self-decoupling relation is shown in Equation (3).
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Y
X
X
C
FBG4
FBG3
FBG1 FBG10 FBG5
FBG2
D FBG6
A FBG11 FBG7
C
B A
FBG9 FBG1 FBG10
FBG12 FBG3 FBG11
D FBG2
Figure 3. 3. The The layout layout of Bragg gratings gratings (FBGs). (FBGs). Figure of fiber fiber Bragg
When the force Fx acts on the tool holder, the wavelengths changes of FBG1 and FBG3, FBG5 When the force Fx acts on the tool holder, the wavelengths changes of FBG1 and FBG3, FBG5 and FBG7 are equal in magnitude and opposite in direction; the wavelengths changes of FBG9 and and FBG7 are equal in magnitude and opposite in direction; the wavelengths changes of FBG9 and FBG10, FBG11 and FBG12 are equal in magnitude and direction. The wavelengths of FBG2, FBG4, FBG10, FBG11 and FBG12 are equal in magnitude and direction. The wavelengths of FBG2, FBG4, FBG6, and FBG8 are almost unchanged because of their locating in the neutral layer. So, under the FBG6, and FBG8 are almost unchanged because of their locating in the neutral layer. So, under the force F , the strains of FBG2 and FBG4, the strains of FBG5–8, and the strains of FBG9–12 cancel force Fx ,x the strains of FBG2 and FBG4, the strains of FBG5–8, and the strains of FBG9–12 cancel each other other out is applied applied to to the the tool tool holder, holder, the the effect effect is is each out through through Equation Equation (3). (3). When Whenthe theforce force FFyy is When the the force FF loaded,the thewavelength wavelengthchanges changesof ofFBG1–FBG4 FBG1–FBG4 are are equal equal similar to force force FFxx. .When loaded, z zis is in magnitude magnitude and anddirection directiontotoFBG5–8 FBG5–8 and FBG9–12. So, under the force F , the strains of FBG1 and FBG9–12. So, under the force Fz , the z strains of FBG1 and and FBG3, the strains of FBG2 FBG4, and strainsofofFBG9–12 FBG9–12cancel canceleach each other other out out through FBG3, the strains of FBG2 andand FBG4, and thethe strains through Equation (3). When the torque T acts on the tool holder, the wavelengths of FBG1–4 and Equation (3). When the torque T acts on the tool holder, the wavelengths of FBG1–4 and FBG5–8 FBG5–8 are almost unchanged unchangedbecause becauseofoftheir their location in the neutral layer. The wavelengths changes of are almost location in the neutral layer. The wavelengths changes of FBG9 FBG9 and FBG10 are equal in magnitude and direction to FBG11 and FBG12. So, under the torque and FBG10 are equal in magnitude and direction to FBG11 and FBG12. So, under the torque T , the T, the strains of and FBG1 and FBG3, the strains of and FBG2 and FBG4, and the strains of FBG5-8 each strains of FBG1 FBG3, the strains of FBG2 FBG4, and the strains of FBG5-8 cancelcancel each other other out through Equation (3). Therefore, every force andattorque at any can be measured by out through Equation (3). Therefore, every force and torque any time can time be measured by Equation Equation (3) due to the structure’s symmetry. (3) due to the structure’s symmetry. F = k ε 1−ε3 = k ε x Fx 1kε12 −21ε 4 3 1k1FxFx Fy = k2 2 2 = k2 ε Fy (3) Fz = k3 (ε 5 2+ε64 + ε 7 + ε 8 ) = k3 ε Fz F k k y ε 92−ε 10 +ε 11 −ε 122 Fy 24 = k4 ε T T= k4 (3) Fz k3 ( 5 6 7 8 ) k3 F z Although the experiment of the study temperature compensation is conducted at room temperature, 9 10 11environment. 12 must be discussed considering the actual processing Since the heat conducts from the k 4 T T k4 4 tool, it has the same effect on FBG1–4, as on FBG5–8 and FBG9–12. Therefore, temperature effects can be offset bythe subtraction in the through Equation (3). Although experiment of X-direction, the study isY-direction, conductedand at T-direction room temperature, temperature As for the Z-direction, FBG is considering located near FBG5–8 as aprocessing reference for eliminating the interference compensation must bea free discussed the actual environment. Since the heat of temperature. Besides, TCFBGs can be used for temperature compensation [23]. conducts from the tool, it has the same effect on FBG1–4, as on FBG5–8 and FBG9–12. Therefore, temperature effects can be offset by subtraction in the X-direction, Y-direction, and T-direction 2.3. Theoretical Analysis of Static Properties through Equation (3). As for the Z-direction, a free FBG is located near FBG5–8 as a reference for ANSYS the Workbench (ANSYS Inc., Pittsburgh, PA, America) determine the strain eliminating interference of temperature. Besides, TCFBGswas canused be to used for temperature distributions of the arcuate beams subjected to each load. The measurement structure used in this compensation [23]. simulation is “Hex Dominant”; the volume mesh size of the elastic structure is 1 mm and the volume mesh sizes of Analysis the spindle andProperties the connector are 2 mm. According to analysis of the structural 2.3. Theoretical of Static strength of the dynamometer by ANSYS Workbench, the dynamometer is designed to measure cutting ANSYS Workbench (ANSYS Inc., Pittsburgh, PA, America) was used to determine the strain force up to 1400 N in X-direction and Y-direction, 3000 N in Z-direction, and torque up to 30 Nm. distributions of the arcuate beams subjected to each load. The measurement structure used in this When the dynamometer is under the maximum of Fx , Fy , Fz , and T simultaneously, the result shows simulation is “Hex Dominant”; the volume mesh size of the elastic structure is 1 mm and the volume the maximum equivalent (Von-Mises) stress is 573.15 MPa, which is less than the yield strength of the mesh sizes of the spindle and the connector are 2 mm. According to analysis of the structural strength 40CrNiMoA material of 835 MPa. Considering the real constraint and load conditions, the spindle of the dynamometer by ANSYS Workbench, the dynamometer is designed to measure cutting force up to 1400 N in X-direction and Y-direction, 3000 N in Z-direction, and torque up to 30 Nm. When the dynamometer is under the maximum of Fx , F y , Fz , and T simultaneously, the result shows
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the maximum equivalent (Von-Mises) stress is 573.15 MPa, which is less than the yield strength of the 40CrNiMoA material of 835 MPa. Considering the real constraint and load conditions, the spindle dynamometer to and the connector was designed to endure the X-direction was selected to fix the dynamometer , the Y-direction forceFy ,Fthe , the Z-direction force andtorque the torque The T individually. Fz , the force FF , the Y-direction force Z-direction force Fz , and T individually. The static xx y calibration loads loads of simulation are based on fullon scale (FSO) (FSO) with an incremental step ofstep 200 of N static calibration of simulation are based fulloutput scale output with an incremental in X, Y-direction force, 300 N in Z-direction force, and 3 Nm torque. The strains of FBGs through the 200 N in X, Y-direction force, 300 N in Z-direction force, and 3 Nm torque. The strains of FBGs through simulation are recombined by Equation (3), and theand calibration curves of four-axis loads were achieved, the simulation are recombined by Equation (3), the calibration curves of four-axis loads were as shown in achieved, as Figure shown4a–d. in Figure 4a–d. 0
0 Z
-200 -400 X-direction Y-direction Z-direction T-direction
-600 -800
-1000
Y
-200
X
Micro-strain(με)
Micro-strain(με)
Z
Y
X
-400 X-direction Y-direction Z-direction T-direction
-600 -800
F -0.95834 Fy
-1000
F -0.95832 Fx - 0.0028
y
x
-1200
-1200
-1400
-1400 200
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1000
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Fx (N)
a) The strains under Fx 500
800
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30
b) The strains under Fy
Z Y
X
0 Z
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Y X
Micro-strain(με)
-50
Micro-strain(με)
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Fy (N)
300
F 0.15393Fz
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z
X-direction Y-direction Z-direction T-direction
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X-direction Y-direction Z-direction T-direction
-100 -150
T -8.2024T - 0.0001
-200
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1000
1500
2000
2500
0
3000
5
10
15
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T (Nm)
Fz (N)
c) The strains under Fz
d) The strains under T
Figure 4. The strains under the four-axis loads.
It is is known known from from the the fitting fittingline lineof ofFigure Figure44that thatthe theforce forcesensing sensingelement elementcan canbebeconsidered consideredasas It a a linear system. So, the relationship can be described as Equation (4) (Figure 4). linear system. So, the relationship can be described as Equation (4) (Figure 4). Fx
958.32
0.01
1.16
0.51 Fx 0.00245
F 3 0.02 958.34 0 0.15 Fy 0.00015 + Fx ε Fx 958.32 0.01 1.16 − 0.51 − 0.00245 (4) − =10 0.05 153.93 0.18 Fz 0.00023 ε F 0.02 0.04 Fy −0.00015 − 958.34 0 − 0.15 Fy −3 0.04 0 8202.4 T 0.01145 1.41 (4) = 10 · T + ε Fz −0.04 −0.05 153.93 0.18 Fz −0.00023 −1.41 −0.04 0 −8202.4 T −0.01145 εT 2.4. Experimental Device Introduction 2.4. Experimental Device Introduction A static calibration test was performed to determine the static properties of the dynamometer in static calibration the static properties of the5.dynamometer in T determine four A directions, namely test , F y performed , Fz , and to , respectively, as shown in Figure The calibration Fx was four directions, namely Fx , Fy , Fz , and T, respectively, as shown in Figure 5. The calibration tests of tests of the X-direction and Y-direction are operated on the spindle rotation experimental platform the X-direction and Y-direction are operated on the spindle rotation experimental platform which was which was designed by ourselves. Before the X-direction calibration test, the arcuate beam A was designed by ourselves. Before the X-direction calibration test, the arcuate beam A was adjusted to be adjusted to be horizontal using a Vernier caliper. After that, the force Fx is loaded by the hand horizontal using a Vernier caliper. After that, the force Fx is loaded by the hand wheel of the radial wheel of the radial force device. When calibrating the Y-direction, we rotated the dynamometer 90
y
z
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2018,When 18, 1254calibrating the Y-direction, we rotated the dynamometer 90 degrees and 6 ofused 11 the forceSensors device. sameSensors calibration method as for the X-direction. The Z-direction calibration test was carried out 2018, 18, 1254 6 of 11on an degrees and used the same calibration method as for the X-direction. The Z-direction calibration test MTS (Eden Prairie, MN, USA) static universal material testing machine. The T-direction calibration was carried out on an MTS (Eden Prairie, MN, USA) static universal material testing machine. The Tand used the same calibration method as for the X-direction. The Z-direction calibration test test isdegrees done by the microcomputer-controlled material torsion test machine. The output wavelengths direction calibration test is done by the microcomputer-controlled material torsion test machine. The wasunder carriedcutting out on an MTSare (Eden Prairie, MN, USA) staticinterrogator. universal material testing machine. The Tof FBGs forces all recorded by the FBG output wavelengths of FBGs under cutting forces are all recorded by the FBG interrogator.
direction calibration test is done by the microcomputer-controlled material torsion test machine. The output wavelengths of FBGs under cutting forces are all recorded by the FBG interrogator. X and Y-direction calibration X and Y-direction Computer calibration
Computer Network cable Z-direction FBG Inerrogator Network cable calibration Z-direction The dynamometer FBG Inerrogator calibration The dynamometer Optical fiber Optical fiber
T-direction calibration T-direction calibration Figure calibrationdevice. device. Figure5. 5. Static Static calibration Figure 5. Static calibration device.
Considering the fact that cutting force is not static during the cutting process, the impacting
Considering the fact that cutting force is not static during the cutting process, the impacting modal test and the dynamic test should be performed to identify the dynamic performance of the Considering the fact that forceperformed is not staticto during the the cutting process, the impactingof the modal test and theThe dynamic test cutting should dynamic performance dynamometer. dynamometer wasbeexcited by usingidentify a modal impact hammer, and an modal test and the dynamic test should be performed to identify the dynamic performance of the dynamometer. Thewas dynamometer excitedbeam by using modal impactinhammer, and an accelerometer accelerometer connected to was the arcuate of thea dynamometer the impacting modal test. dynamometer. The dynamometer was excited by using a modal impact hammer, and an was connected to the beam of by the simulating dynamometer in the impacting The rotation dynamic test The dynamic testarcuate was completed loading cutting forces modal on thetest. spindle accelerometer was connected to the arcuate beam of the dynamometer in the impacting modal test. was experimental completed by simulating loading cutting6. forces on the spindle rotation experimental platform platform as depicted in Figure The experimental platform consists of the headstock The dynamic test was completed by simulating loading cutting forces on the spindle rotation and the force device.6.The headstock is madeplatform up of the servo motor and the spindle housing. The force as depicted in Figure The experimental consists of the headstock and the force device. experimental platform as depicted in Figure 6. The experimental platform consists of the headstock device is composed of the radial forcemotor deviceand and the the axial force device. The force device is is used to The headstock is made up of the servo spindle housing. The force device composed and the force device. The headstock is made up of the servo motor and the spindle housing. The force simulate actual loading cutting force. The cutting forces , F y areisloaded by simulate the radial force Fx device of the radialisthe force device andof the axial used to thetoactual device composed of the radial force force devicedevice. and theThe axialforce force device. The force device is used device and the cutting force is loaded by the axial force device. F z loading of cutting force. The cutting forces , Fycutting are loaded radial force device and the cutting simulate the actual loading of cutting force.FxThe forcesbyFthe , are loaded by the radial force F x y force device Fz is loaded the axial device. and theby cutting forceforce loaded by the axial force device. Fz is
The dynamometer The dynamometer The headstock The headstock The radial force device The radial force device
The axial force device The axial force device
Figure 6. The dynamic experimental device. Figure 6. The dynamic experimental device.
Figure 6. The dynamic experimental device.
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3. Results Results and and Discussion Discussion 3. 3.1. Static Static Calibration Calibration 3.1. The calibration test toto determine thethe relationship between the input and output data. The testisisaaprocess process determine relationship between the input and output The output wavelengths of the dynamometer were recombined and calculated using Equation (2) data. The output wavelengths of the dynamometer were recombined and by calculated by using and Equation (3), (3), andand the calibration curves of theofX-direction force force forceforce Fx , the Fy , Equations (2) and the calibration curves the X-direction Fx , Y-direction the Y-direction Fthe Z-direction force andthe thetorque torque TT were y , the Z-direction force were achieved, achieved, as as shown shown in in Figure Figure 7a–d. 7a–d. FzF,z ,and 200
0
0
-200
-200
-600
Micro-strain(με)
X-direction Y-directon Z-direction T-direction
-400
-800
-1000
F 1.06789 Fx 35.9518
-1200
-800 -1000
F 1.08034 Fy 20.2992 y
-1400 -1600
-1600 0
200 400 600 800 1000 1200 1400 Fx (N)
-200 0
50
X-direction Y-direction Z-direction T-direction
400
0
300 200
200 400 600 800 1000 1200 1400 1600 Fy (N) b) The strains under Fy
a) The strains under Fx
500
Micro-strain(με)
-600
-1200
x
-1400
F 0.14896 Fz 6.8802 z
100 0 -100
X-direction Y-direction Z-direction T-direction
-400
Micro-strain(με)
Micro-strain(με)
200
X-direction Y-direction Z-direction T-direction
-50 -100 -150
T 7.8611T 2.1170
-200
0
500
1000
1500 2000 2500 Fz (N)
3000
-250
0
c) The strains under Fz
5
10
15 T (Nm)
20
25
30
d) The strains under T
Figure 7. 7. The The strains strains under under the the four-axis four-axis loads. loads. Figure
According to the calibration lines, it is obvious that the dynamometer’s sensitivities were about According to the calibration lines, it is obvious that the dynamometer’s sensitivities were about −1.06789 με/N, −1.08034 με/N, 0.14896 με/N, and −7.8611 με/Nm. The differences of sensitivities are −1.06789 µε/N, −1.08034 µε/N, 0.14896 µε/N, and −7.8611 µε/Nm. The differences of sensitivities 11.43%, 12.73%, −3.23%, and −4.16%, in contrast to the sensitivities of simulation analysis. The are 11.43%, 12.73%, −3.23%, and −4.16%, in contrast to the sensitivities of simulation analysis. sensitivity differences of the X-direction and the Y-direction are relatively large. The sensitivity differences of the X-direction and the Y-direction are relatively large. Besides, the coefficient of determination for the calibration lines is basically above 0.9. The matrix Besides, the coefficient of determination for the calibration lines is basically above 0.9. The matrix of the static calibration can be achieved by the least square method. Equation (5) shows the of the static calibration can be achieved by the least square method. Equation (5) shows the relationship relationship between loads and strains. between loads and strains. Fx 30.55 16.18 1067.89 81.68 1080.34 7.12 Fy 3 − =10 1067.89 16.18 96.08 30.55 59.47 −148.90 F z 81.68 − 1080.34 − 40.27 7.12 0.57 107.51 10−3 · T
188.35 Fx 31.86 10.65 376.56 Fy + F 188.35 x 154.73 Fz 11.80 F 376.56 y 7861.1 T 6.19 +
(5) ε Fx 31.86 ε 10.65 Fy (5) = ε Fz −96.08 −59.47 148.90 154.73 Fz 11.80 Cross-interference, defined as the − ratio of sensor in lateral directions to6.19 the one when 107.51 40.27 −0.57output −7861.1 T − εT force in primary direction, is an important factor for precise applications requiring high accuracy. To Cross-interference, defined as the ratio of sensor output in lateral directions to theloads one when assess the cross-interference in four directions, some tests were done. Some maximum were force in primary direction, is an important factor for precise applications requiring high accuracy. applied to the dynamometer in the four directions, and the outputs of the FBGs were obtained and To assess the cross-interference in four directions, testsBywere done. Some loads were then substituted to Equation (5) to calculate thesome forces. comparing the maximum force values between
applied and calculated, the decoupling errors can be calculated, as shown in Table 1. The results
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applied to the dynamometer in the four directions, and the outputs of the FBGs were obtained and then substituted to Equation (5) to calculate the forces. By comparing the force values between applied and calculated, the decoupling errors can be calculated, as shown in Table 1. The results showed the Sensors 2018, 18, 1254 8 of 11 measurement errors were small with a maximum of −2.10%. The maximum cross-interference error was −showed 5.35%, which occurred for the Y-direction to torque of all the did not exceed the measurement errors were small force with aFymaximum −2.10%. Theothers maximum crossT , and 4%. Itinterference means thaterror the dynamometer is acceptable forthe useY-direction in cuttingforce forceFmeasurement. was −5.35%, which occurred for to torque T , and all the y others did not exceed 4%. It means that the dynamometer is acceptable for use in cutting force Table 1. The results of cross-interference. measurement.
Output after Decoupling Table 1. The results of cross-interference. Axes
Load
Fx (N) Fy (N) after Fz Decoupling (N) T (Nm) Output Axes Load Fx (N)33.05 Fy (N) −9.31 Fz (N) −T (Nm) Fx (N) 1400 1403.7 0.88 Fy (N) Fx (N)1400140050.871403.71389.0 33.05 −62.18 −9.31 −1.57 −0.88 Fz (N) Fy (N)3000140026.8250.87 9.431389.0 2975.0 −62.18 −0.21 −1.57 T (Nm) Fz (N) 30 300031.9326.82 31.989.43 −43.06 2975.0 29.37 −0.21 T (Nm) 30 31.93 31.98 −43.06 29.37
Fx Fx 0.26 3.62 0.26 1.91 3.62 2.27 1.91 2.27
Error (%) Fy (%) Fz T Error Fy2.38 Fz−0.31 T −3.00 −0.79 −0.31 −2.09 −3.00 −5.35 2.38 0.68 −2.09 −0.83 −5.35 −0.72 −0.79 2.30 −0.83 −1.45 −0.72 −2.10 0.68 2.30
−1.45
−2.10
3.2. Natural Frequency Identification 3.2. Natural Frequency Identification
In order to ensure the stability of the machining process, the natural frequency of a sensor should In order to ensure the stability of the machining process, the natural frequency of a sensor should be four times larger than the frequency of the machine tool’s exciting vibration [24]. The first-order be four times larger than the frequency of the machine tool’s exciting vibration [24]. The first-order natural frequency was 320 Hz, as shown in Figure 8. Hence, the dynamometer can fulfill real-time natural frequency was 320 Hz, as shown in Figure 8. Hence, the dynamometer can fulfill real-time cutting forceforce measurement when thethe spindle than320 320×× 0.25 ×=60 = 4800 r/min. cutting measurement when spindlespeed speedis is less less than 0.25 × 60 4800 r/min.
Amplitude
320
Frequency (Hz) Figure 8. First-order frequency of impacting modal test. Figure 8. First-order frequency of impacting modal test.
3.3. Dynamic Characteristic Analysis
3.3. Dynamic Characteristic Analysis
In order to simulate the actual processing conditions, dynamic experiments were carried out.
In order simulate actual processing conditions, dynamic experiments were carried Since the to spindle was the in the process of rotation, 12 FBGs were divided into three groups, namely out. Since FBG1–4, the spindle wasand in FBG9–12. the process of experiment, rotation, 12the FBGs were divided intor/min, three200 groups, namely FBG5–8, In this spindle speeds were 100 r/min, and 300 FBG5–8, r/min, respectively. The applied in the radial directionspeeds (X and Y directions) were 200 400 N, FBG1–4, and FBG9–12. In thisforces experiment, the spindle were 100 r/min, r/min, 800r/min, N, and respectively. 1200 N, respectively, and the applied forces in Zdirection direction (X were 500 1000 N, and 1500 and 300 The applied forces in the radial and Y N, directions) were 400 N, N, respectively. The obtained wavelengths were fitted with sinusoidal functions over time. The 800 N, and 1200 N, respectively, and the applied forces in Z direction were 500 N, 1000 N, and 1500 N, quality of the fitted curves was described by the “coefficient of determination”. The closer the respectively. The obtained wavelengths were fitted with sinusoidal functions over time. The quality of coefficient is to 1, the stronger the explanatory power of the equation’s variable to y is, and the better the fitted curves was described by the “coefficient of determination”. The closer the coefficient is to the fitting of the model to the data is. Moreover, the characteristics of the fitting curves were 1, therepresented stronger the ofvelocity, the equation’s variable to y is, and the better the fitting of byexplanatory the amplitude,power angular and intercept. the modelWhen to thecarrying data is.out Moreover, the characteristics of fittingwas curves wereWhen represented by the radial loading tests, the first group the (FBG1–4) analyzed. the spindle amplitude, angular velocity, andloading intercept. speed was 100 r/min and the forces were 400 N, 800 N, and 1200 N, respectively, taking FBG3 and FBG4 as an example, the amplitude and angular velocity were expressed as illustrated by Figure
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When carrying out radial loading tests, the first group (FBG1–4) was analyzed. When the spindle speed was 100 r/min and the loading forces were 400 N, 800 N, and 1200 N, respectively, taking FBG3 and FBG4 as an example, the amplitude and angular velocity were expressed as illustrated by Figure 9. Sensors 2018, 18, 1254 9 of 11 As theSensors fitting coefficients were above 0.98, we could see that the fitting effect was good. The amplitude 2018, 18, 1254 9 of 11 and angular velocity of FBG3 and FBG4 have little forces. Therefore, 9. As the fitting coefficients were above 0.98, wedifference could see under that thedifferent fitting effect was good. TheFBG3 9. As can the fitting coefficients were 0.98, thatFBG4 the fitting effect was good. The to and FBG4 be regarded as the same class. Inwe thecould same way, can be used as an example amplitude and angular velocity ofabove FBG3 and FBG4 havesee little difference under different forces. amplitude and angular velocity of FBG3 and FBG4 have little difference under different forces. Therefore, FBG3 and FBG4 can be regarded as the same class. In the same FBG4 be used as analyze the relationship between the amplitude and angular velocity ofway, FBG1–4 atcan different speeds Therefore, FBG3 and FBG4 can be regarded as the same class. In the same way, FBG4 can be used as an example to analyze the relationship between the amplitude and angular velocity of FBG1–4 and different forces. As illustrated in Figure 10, the amplitude of fitting curves at 100 r/min, 200 at r/min, an example to analyze the relationship between the amplitude and angular velocity of FBG1–4 at different speeds and different As illustrated in Figure the amplitude of fitting curves atbasically 100 and 300r/min were basically the forces. same under the same radial 10, force, and the angular velocities different illustrated in Figure 10,the thesame amplitude of fitting at 100 200speeds r/min,and anddifferent 300r/minforces. were As basically the same radial force, andcurves the angular meet r/min, the 1 times, 2 times, and 3 times relationship; theunder angular velocities of the fitting curves were r/min, 200basically r/min, and 300r/min were basically the same under the same radial force, and the angular velocities meet the 1 times, 2 times, and 3 times relationship; the angular velocities of the basically the same under the same rotational speed and different radial forces, and the amplitudes velocities basically the 1the times, times, the andsame 3 times relationship; velocities of the fitting curves were meet basically same2 under rotational speedthe andangular different radial forces, basically satisfy the relations of 1 times, 2 times, and 3 times. The features of the second group (FBG5–8) fitting were basically same the of same rotational speed different radial forces, and thecurves amplitudes basically the satisfy theunder relations 1 times, 2 times, and and 3 times. The features of the and the third group (FBG9–12) were similar to those of the first group (FBG1–4) at different speeds and thegroup amplitudes basically satisfy relations of 1 times, 2 times,toand 3 times. of the second (FBG5–8) and the thirdthe group (FBG9–12) were similar those of the The firstfeatures group (FBG1– and different sizes(FBG5–8) of radial forces. second group and the third group (FBG9–12) were similar to those of the first group (FBG1– 4) at different speeds and different sizes of radial forces. 1.6
11.5
1.6 1.4
11.5 FBG3 FBG4 FBG3 FBG3 FBG4 FBG4 FBG3
(nm) Amplitude (nm) Amplitude
1.4 1.2 1.2 1.0
11.0 11.0
FBG4
1.0 0.8
10.5
0.8 0.6
10.5
0.6 0.4
10.0
0.4 0.2
10.0
(rad/s) speed Angular (rad/s) speed Angular
4) at different speeds and different sizes of radial forces.
0.2 0.0 0.0
0
400
800
1200
Radial 400
9.5 9.5
force(N) 800 1200 Radial force(N) Figure 9. The characteristicsof of FBG3 FBG3 and Figure 9. The characteristics and44atat100 100r/min. r/min. 0
Figure 9. The characteristics of FBG3 and 4 at 100 r/min. 1.6 100r/min 200r/min 100r/min 300r/min 200r/min 100r/min 300r/min 200r/min 100r/min 300r/min 200r/min 300r/min
1.4 1.2 1.2 1.0 1.0 0.8
30 30
25 25
20
0.8 0.6
20
0.6 0.4
15
0.4 0.2
15
0.2 0.0 0.0
(rad/s) velocity Angular (rad/s) velocity Angular
(nm) Amplitude (nm) Amplitude
1.6 1.4
0
400
0
Radial force (N) 400 800 Radial force (N)
800
1200 1200
10 10
Figure 10. The characteristics of FBG4 at different spindle speeds. Figure 10. The characteristics of FBG4 at different spindle speeds.
Figure 10. The characteristics of FBG4 at different spindle speeds. When carrying out the axial loading test, the second group (FBG5–8) was analyzed. When the When carrying outr/min the axial test, forces the second was1500 analyzed. When the spindle speed was 100 and loading the loading were group 500 N,(FBG5–8) 1000 N, and N, respectively, When the axial loading the second group (FBG5–8) When spindle speedaswas 100 r/min the loading forces were 500 N, N, andwas 1500analyzed. N, velocity, respectively, taking carrying FBG6 anout example to and analyze thetest, relationship between the1000 amplitude, angular and the taking FBG6 as an to analyze the relationship between and spindle speed 100example r/min and the loading forces forces, were 500 N,amplitude, 1000 N, and 1500velocity, N,Figure respectively, intercept ofwas FBG5–8 at different speeds and different thethe results were asangular shown in 11. intercept of FBG5–8 at different speeds andexcept different forces, the results were asaxial shown in Figure 11. AsFBG6 the fitting coefficients were above 0.99, when there was nothe external force, the fitting taking as an example to analyze the relationship between amplitude, angular velocity, As thewas fitting coefficients were above except when there was external axial effect Theat intercepts ofspeeds the0.99, fitting curves at 100 r/min, 200 r/min, or 300 r/minthe basically and intercept ofgood. FBG5–8 different and different forces, theno results were as force, shown infitting Figure 11. effect was good. The intercepts of the fitting curves atwith 100 the r/min, 200 r/min, or forces. 300 r/min basically showed an increasing tendency, which was consistent increasing of the The angular As the fitting coefficients were above 0.99, except when there was no external axial force, the fitting showed increasing tendency, was consistent with under the increasing of the forces. The angular velocitiesanof the fitting curves which were basically the same the same rotational speed. The velocities of the fitting curves were basically the same under the same rotational speed. The
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effect was good. The intercepts of the fitting curves at 100 r/min, 200 r/min, or 300 r/min basically showed an2018, increasing Sensors 18, 1254 tendency, which was consistent with the increasing of the forces. The 10 ofangular 11 velocities of the fitting curves were basically the same under the same rotational speed. The amplitude of the fitting curves basically showed an increasing trend. The reason was that the loading of theamplitude fitting curves basically showed an increasing trend. The reason was that the loading axis didn’t axis didn’t coincide with the axis of the main shaft. The features of the first group (FB1–4) and the coincide with the axis of the main shaft. The features of the first group (FB1–4) and the third group third group (FBG9–12) were similar to those of the second group (FBG5–8) at different speeds and (FBG9–12) were similar to those of the second group (FBG5–8) at different speeds and different forces. different forces. 100r/min 200r/min 300r/min
0.07
100r/min 200r/min 300r/min
100r/min 200r/min 300r/min
1549.80 30
0.05
1549.75
25 0.04
1549.70
20
0.03 0.02
15
Intercept (nm)
Angular velocity (rad/s)
Ampltiude (nm)
0.06
1549.65
0.01 0.00
10 0
500
1000
1549.60
1500
Axial force (N) Figure 11. The characteristics of FBG4 under different spindle speeds. Figure 11. The characteristics of FBG4 under different spindle speeds.
4. Conclusions
4. Conclusions
A novel integrated rotating dynamometer based on fiber Bragg grating for four-component
A novel integrated rotating dynamometer based on fiber Bragg grating for four-component cutting force measurement has been developed and tested. The corresponding theoretical analysis cutting has been developed andand tested. The corresponding analysis hasforce been measurement completed to support structural design the layout of FBGs. Statictheoretical and dynamic tests has were done in order to evaluate the performance of the developed rotating dynamometer. The results been completed to support structural design and the layout of FBGs. Static and dynamic tests were sensitivities were 1.06789ofμε/N, 1.08034 με/N, 0.14896 με/N, and The 7.8611 με/Nm, doneshowed in orderthat to evaluate the performance the developed rotating dynamometer. results showed respectively, with low cross-sensitivity errors below 5.35%. The results of dynamic analysis showed that sensitivities were 1.06789 µε/N, 1.08034 µε/N, 0.14896 µε/N, and 7.8611 µε/Nm, respectively, that the first-order natural frequency was approximately 320 Hz. The simulation processing with low cross-sensitivity errors below 5.35%. The results of dynamic analysis showed that the experiment indicated that the dynamometer could operate at the actual processing conditions. first-order natural frequency was approximately 320 Hz. The simulation processing experiment indicated that the dynamometer could operate actualNatural processing conditions. Acknowledgments: This work was supported by at thethe National Science Fund of Chinese (General Program, Grant No. 51375359)
Acknowledgments: This work was supported by the National Natural Science Fund of Chinese (General Program, Contributions: Mingyao Liu and Junjun Bing designed the research; Liang Wan and Li Xiao helped with GrantAuthor No. 51375359). the implement of experiment; Junjun Bing and Kang Yun conceived and performed the experiment; Mingyao
Liumanuscript. and Junjun Bing designed the research; Liang Wan and Li Xiao helped with Author LiuContributions: and Junjun Bing Mingyao co-wrote the the implement of experiment; Junjun Bing and Kang Yun conceived and performed the experiment; Mingyao Liu Conflicts of co-wrote Interest: The declare no conflict of interest. and Junjun Bing theauthors manuscript. Conflicts of Interest: The authors declare no conflict of interest. Reference 1. Sevilla-Camacho, P.Y.; Herrera-Ruiz, G.; Robles-Ocampo, J.B.; Jáuregui-Correa, J.C. Tool breakage References
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