- Email: [email protected]
Principles and validation of strain gauge shunt design for large dynamic strain measurement
Sensors and Actuators A 241 (2016) 124–134
Contents lists available at ScienceDirect
Sensors and Actuators A: Physical journal homepage: www.elsevier.com/locate/sna
Principles and validation of strain gauge shunt design for large dynamic strain measurement Qingfeng Xia a,b,∗ , Francis Quail a a b
School of Engineering, University of Glasgow, Glasgow G12 8QQ, United Kingdom Osney Thermo-Fluids Laboratory, Department of Engineering Science, University of Oxford, Oxford OX2 0ES, United Kingdom
a r t i c l e
i n f o
Article history: Received 3 August 2015 Received in revised form 26 January 2016 Accepted 2 February 2016 Available online 4 February 2016 Keywords: Strain gauge Large strain Fatigue failure Dynamic strain Structural health monitoring
a b s t r a c t In order to eliminate the fatigue failure of metallic thin film strain gauges under large alternating strain condition, a mechanical structure reducing the large strain on the target surface proportionally to a safe level is proposed as strain shunt in this study. The working principles of the strain shunt structure are illustrated and the shunt ratio of strain reduction is derived theoretically from a simplified one dimensional model. The prototype strain shunt is validated by tensile load test experiments which confirm the repeatability and linearity. Moreover, the usability of the strain shunt structure under alternating loads, the stability of shunt ratio under the combined stress conditions, and the dynamic response of the strain shunt structure are investigated by finite element analysis. © 2016 Elsevier B.V. All rights reserved.
1. Introduction Current challenges in large scale off-shore wind turbine condition monitoring systems require robust sensors that can operate continuously for a long period of time on rotating and shielded components. Condition monitoring of critical components in a wind turbine system is vital for health assessment of the asset [1], minimising down time and reducing significant maintenance and operational impact [2,3]. Considering the inconvenience of strain sensor replacement for off-shore wind turbine systems, this paper highlights the potential of developing novel strain sensors that can survive large dynamic strain conditions over a long period of time. Metallic thin-film strain gauges have the advantages of excellent linearity, stable electrical signal output, compactness, low cost, etc. However, it is challenging to measure extremely large static strain or large dynamic strain found on structure of multi-megawatt offshore wind turbines. High strength material for modern megastructures, e.g. towers for off-shore wind turbine, must survive large dynamic strain induced by vibration or other transient loads. For example, the yield strength for high strength Maraging steel is in the range of 1030–2420 MPa [4] with a Young’s modulus of 190–210 GPa; it means the maximum permitted strain without plastic deformation will be more than 5000 . Although metal-
∗ Corresponding author. E-mail addresses: [email protected], [email protected] (Q. Xia). http://dx.doi.org/10.1016/j.sna.2016.02.007 0924-4247/© 2016 Elsevier B.V. All rights reserved.
lic foil strain gauges can measure the static strain up to 5%, the maximum dynamic strain can be measured is lower than 2000 for 106 alternating loading cycles [5]. Metallic thin-film gauges are likely to break as a result of limited fatigue life under dynamic loads, before the failure of the monitored structure can be identified. Research on the metallic thin-film strain gauges has improved their performance at higher temperature [6] or under large strain conditions [7], however achievement in large dynamic strain measurement is limited. For example, a patent on strain gauge pattern can reduce the stress concentration on the metal tap connecting gauge pattern and wire terminals, thus the claimed measurement range for static strain is extended to 15% [7]. However, the fatigue failure of thin-film gauges under the long-term alternating loads has not been solved; an achievable range for dynamic strain measurement is 1600 for 106 alternating loading cycles [5]. Meanwhile, optical fibre strain gauges have been extensively investigated in the last decades, and they have the potential to measure large dynamic strain [8]. The strain gauges based on fibre Bragg grating (FBG) have the advantages of immunity to electromagnetic interference (EMI), intrinsic safety in highly explosive atmospheres, and good resistance to large strain and alternating loads, etc. [9]. In addition, optical strain gauges offer a more stable measurement in respect of zero-drifting after loading [10]. The resistance of optical strain gages to alternating load has been tested for an alternating strain of ±1000 ; no change in measurement characteristics or the reflection peak wavelength is observed after 107 loading cycles, i.e. sensitivity and base wavelength are unchanged [10].
Q. Xia, F. Quail / Sensors and Actuators A 241 (2016) 124–134
Nomenclature Symbol A D E F f G H I L M t x,y,z r ␦
Cross-section area, m2 Diameter of column, m Normal elastic modulus, GPa Force on joint of shunt sheet and columns, N Frequency, Hz Shearing elastic modulus, GPa Height of column, m Second moment of area, m4 Spanning of shunt sheet, m Moment acting on joint of shunt sheet and columns, N·m Time, s; Thickness of thunt sheet, m Coordination, m Ratio Density of material, kg/m3 Deflection angle Deformation of material under stress, m Stress of material under load, Pa Poisson ratio
Subscripts supporting columns c input from the target surface i s shunt sheet wrapping effect of the shunt sheet w bending beam bending upper upper surface of the shunt sheet lower surface of the shunt sheet lower
Despite those advantages, FBG strain sensors have not significantly extended the measurement range for dynamic strain, compared with traditional metal thin-film strain gauges [10]. Nevertheless, FBG sensors require expensive optical equipment to detect wavelength shifting precisely [11]. Although using low power LED light sources and photo-detectors may reduce the power consumption for the fibre optical sensor nodes [12], the prohibiting power consumption is not acceptable for battery-powered wireless sensor networks. Recent innovations in strain-sensitive material have the potential to measure large strain, surpassing the intrinsic maximum strain level (approximately 4%) of silicon fibre optical FBG sensors limited by the failure strain of silica [13]. A novel fluidic strain sensor has been validated for the large deformation measurement up to 40% [14]. This design utilises the piezoresistive effect of the tube elastomer filled with Glycerin and aqueous sodium chloride. Moreover, plastic optical fibres (POF) interwoven into geotextile sheets have been tested to measure large strain up to 40% and dynamic strain under submerged circumstances. Instead of the wave-length displacement detection as in FBG sensors, the correlation between strain and the intensity of light transmitting within POF offers a cost-effective way for strain measurement. In addition, carbon nanotube material has been applied into piezoresistive strain sensors for structural health monitoring applications [15] and human motion sensors [16]. However, repeatability and material specific calibrations need further investigation on these innovative methods [17]. Other optical methods developed for the large strain measurement are based on the high resolution digital camera technology. For example, Vishay Micro-Measurement has developed PhotoStress® technology using reflection polariscope [9]; it is a full-field strain measurement solution ideal for the mea-
125
surement of large deformations. Similarly, Polytec laser-based vibrometer is capable of strain measurement in laboratory environment [18]. However, these optical solutions may be restricted by non-vibratory condition, as well as high power consumption and equipment cost. Thereby, they are excluded from massive deployment in industrial scenarios, in particular, off-shore wind turbine condition monitoring and structural health monitoring. Currently, commercial optical or resistive strain measurement techniques are not yet available for large and dynamic strain measurement which is required by the long-term structural health monitoring (SHM) and condition monitoring systems, e.g. wireless force sensing on rotating machines. The main technical challenges are sensor fatigue failure due to large dynamic strain and sustainable power supply for wireless sensor nodes. Metallic thin film strain gauges are subject to fatigue failure at heavy alternating loads, while the high power consumption for the FBG signal acquisition system is prohibiting for battery-powered wireless sensor networks. To address such challenges, this paper presents a novel strain shunt structure which reduces the large strain proportionally to a manageable range for the metallic thin film strain gauges. The strain shunt structure, together with metallic thin film strain gauges, is bonded onto the target surface. Combined with the advantages of metallic resistive strain gauges, this strain shunt design offers an attractive solution for large and dynamic strain measurement in challenging environments, such as off-shore wind turbine up-tower condition monitoring and structural health monitoring system for supporting structures. In this paper, the working principles of strain shunt design are illustrated and shunt ratio is derived theoretically base on the simplified one-dimensional model. The prototype of the strain shunt is experimentally tested by the tensile load test. Moreover, the impact of complex loads or dynamic loads on the shunt structure is investigated by finite element analysis (FEA).
2. Strain shunt design 2.1. Principles of strain shunt The concept of electrical ammeter shunt, which assists the measurement of electrical current too large to be measured directly by a particular ammeter, has been well established [19]. The strain shunt structure, in a similar manner, enables the measurement of large strain using commercial metal foil strain gauges without fatigue failure. The ammeter shunt has a small fixed-value resistor in series and the current is derived from the measured voltage across the resistor. While, a parallel configuration is proposed for the strain shunt which can be conveniently bonded to the target surface with large strain. One possible strain shunt design is a mechanical structure consists of one elastic shunt sheet bridging two supporting columns fixed onto the target surface, see Fig. 1, If both supporting columns and the shunt sheet are made of elastic material, the supporting columns will bend when the target surface is under tensile or compressive load, due to the binding effect of the shunt sheet on top. Consequently, the deformation on the shunt sheet will be less than the target surface underneath. Fig. 1 illustrates the working principles of the strain shunt structure subjected to compressive or tensile load in y axis direction, compared with the structure without load. The supporting column can be modelled as a cantilever with one end fixed onto the target surface and the other end under bending load at the joint with the shunt sheet. Due to the fixed connection of the shunt structure on the target surface, y axis strain on the target surface leads to deformation on the shunt sheet and supporting columns. The supporting
126
Q. Xia, F. Quail / Sensors and Actuators A 241 (2016) 124–134
Fig. 1. Schematic of strain gauge shunt on the target surface.
columns’ deflection relieves the strain on the shunt sheet, resulting in less deformation on the shunt sheet than that of the target surface between two supporting columns. For the target structure under purely compressive or tensile loading, the deformation on the loading direction (y axis) is proposed as,
εs is averaged from the measured strain on the upper and lower surfaces of the shunt sheet, see gauge position in Fig. 1.
ıi = Lεi = L − L = 2ıc + ıs
A formula for shunt ratio can be derived from the simplified structure of supporting columns and shunt sheet, based on Eq. (1). It is assumed that the cross sections of the shunt sheet and supporting columns are homogenous; the target surface is under the purely tensile or compressive load in parallel with the shunt sheet. The shunt structure’s dimension is much smaller than the target surface so that it does not alter the strain to be measured on the target surface. The deflection deformation the columnsıc , is expressed by Euler beam theory for slender beams [20],
(1)
where ıi is y axis deformation of the target surface between the supporting columnsL; εi is the average y axis normal strain on the target surface beneath the shunt structure; ıc is the y axis deflection of each supporting column; ıs = L − Ls is y axis deformation of the shunt sheet. Since the supporting columns are subject to elastic deformation (ıc > 0), the average y axis strain on the shunt sheet εs should be less than that on the target surface εi . The ratio of strain is defined as shunt ratio rs. rs (Shunt ratio) =
ıs Lεs = Lεi ıi
(2)
where, εs is the average normal strain on shunt sheet along the loading direction. In particular, the strain on the upper and the lower surface of the shunt sheet is different, due to the warping effect of the shunt sheet. As a result of the bending moment introduced at the joint of the shunt sheet and the supporting columns, the shunt sheet warps with the deflection of supporting columns. Therefore,
2.2. Theoretical derivation of shunt ratio
ıEular = c
FH 3 3Ec Ic
(3)
where Ec is the elastic modulus of the supporting column; F is the tensile or compressive force acting on the shunt sheet from the supporting column; H is the height of the supporting columns; I c is the second moment of area for the support column with respect to x axis. It should be noted that the bending displacement derived from Euler beam theory is under-estimated for short columns. According to Timoshenko’ beam theory, the shearing parallel to the
Q. Xia, F. Quail / Sensors and Actuators A 241 (2016) 124–134
127
central plane should not be neglected. To estimate the displacement for short rectangular cantilever beam [21], the following equation applies, ıc =
F 6EI
3vz 2 (H − z) + (4 + 5v)
zW 2 + (3H − z) z 2 4
(4)
where E and I are the elastic modulus and the second moment of area for the x-axis of the beam, W is thickness, is Poisson ratio. Since F is applied at the end of the cantilever, the displacement at the loading end on the top of circular column (z = H) can be simplified as: ıc = (1 + rc ) ıEular wherer c = c
(4 + 5) W 2 8H 2
(5)
where rc is the ratio to correct the under-estimated displacement. This ratio depends on the Poisson ratio of the material and H/W (slenderness of column). If H/W > >1, the beam can be regarded as Euler beam without any correction. The y-axis deformation of the shunt sheet (Lεs ) is primarily caused by the tensile or compressive force F. In addition, the warping effect of the shunt sheet may lead to deformation in y axis direction, and this is denoted as ıw . Thereby, the deformation of shunt sheet on y axis can be expressed as, ıs = Lεs + ıw εs =
Fig. 2. (a) strain gauge positioning for loading test; (b) close-up of strain shunt structure.
(6)
F As Es
(7)
where As is cross-section area for the shunt sheet; Es is the elastic modulus for the sheet. Since the materials of column can be different from the shunt sheet, the material properties like elastic modulus are distinguished by different subscript. The shunt ratio rs can also be represented by the ratio of the averaged strain on the shunt sheet εs and that on the target surface under the shunt sheet εi : rs =
εs εi
(8)
Neglecting the warping effect of the shunt sheet (discussed in Section 2.3), Eq. (1) can be rewritten into, 2 (1 + rc ) (
LF FH 3 )+ = ıi = Lεi 3Ec Ic As Es
(9) Fig. 3. Strain shunt validation for the incremental tensile loads.
According to Eq. (8) and Eq. (9),
2 (1 + rc )
FH 3 3Ec Ic
+
LF 1 LF = As Es rs As Es
(10)
L
rs = 2 (1 + rc )
As Es H3 3Ec Ic
(11) +
L As Es
This theoretical derivation suggests that the shunt ratio is independent of the target surface material properties and loading force on the shunt sheet, assuming rigid connection between the supporting columns and the target surface. In practice, the material of shunt sheet should have the similar thermal expansion coefficient with the target surface material, thus the impact of thermal variation target surface can be minimised. 2.3. Warping effect The strain on upper and lower surface is not equal, due to the warping of the shunt sheet. Since the joint of columns and shunt sheet is not hinged, the deflection of the supporting columns will bend the shunt sheet connecting them. Consequently, measurement of averaged strain on the shunt sheet needs two strain gauges on both the upper and lower surfaces, as shown in Fig. 1.
As the moment acted on the shunt sheet is unknown, the warping angle s can be derived from the flexural angle of the upper surface of the columnc . It is assumed that angle between the column top surface and shunt sheet angle remains constant during deformation and the warping shunt sheet has neglectable effect on the supporting columns’ deflection (deformation in y axis), given the thickness of shunt sheet is much thinner than the cross-section supporting columns. According to this geometrical relationship, the warping angle of the shunt sheet is equal to that of deflection angle of column and sheet joint: c = s
(12)
Furthermore, the deflection angle on the top of the column c can be derived from Euler cantilever beam theory, c =
FH 2 2Ec Ic
(13)
The extra strain on the shunt sheet can be calculated, assuming the simply supported beam at both ends for the shunt sheet. Given the large ratio of shunt sheet length to thickness, classic Euler
128
Q. Xia, F. Quail / Sensors and Actuators A 241 (2016) 124–134
beam theory can calculate the shunt sheet warping angle due to the bending moment Ms . s =
Ms 2L
(14)
Es Is
where I s is the second moment of area of the support column with respect to y axis. In addition to the tensile or compressive force, the shunt sheet is considered under bending moment Ms at both ends. Ms =
Es Is FH 2 Ec Ic L
(15)
The deflected supporting column leads to significant warping of the thin shunt sheet, but the reaction moment acting on the supporting column Mc is not considered in the simplified 1D analysis. This moment-induced deflection can be neglected, compared with the force-induced one in Eq. (3), since the second moment of area of the shunt sheet is an order of magnitude smaller than that of the support columns, Ic > >Is . The additional strain εw on both the lower and upper surfaces of the shunt sheet, induced by Ms , can be estimated as, εw =
Fig. 4. (a) boundary condition for load test simulation; (b) mesh with a medium cell density for the finite element model.
Hs Ms 2
Is Es
=
Hs FH 2 2LIc Ec
(16)
where H s is the thickness of the shunt sheet. The bending moment Ms does not change the strain at the neutral position of the beam [22]; and the strain on the upper and lower surface has the identical magnitude but the opposite sign. The shunt sheet is deformed into an arc shape of elastic curve with angle s to the horizontal on both ends. Once the warping
Fig. 5. Contour of y-axis normal strain on the top surface of shunt sheet for purely compressive loading on test bar.
Fig. 6. Y-axis normal stress contour to illustrate the stress concentration (unit: Pa).
Q. Xia, F. Quail / Sensors and Actuators A 241 (2016) 124–134
angle s is calculated, the y-axis deformation of the shunt sheet ıw incurred by the warping effect can be estimated.
ıw =
tan s − sin s s
2
L=
s L 2
(17)
where ıw is one order infinitesimal of ıc , therefore, the impact of the shunt sheet warping on the shunt ratio is neglected. The shunt ratio rs refers to the averaged of both upper and lower surfaces through this theoretical analysis, which is independent of the warping effect. However, the warping of the shunt sheet leads to the different strain level on the upper and lower surfaces of the shunt sheet. rs
rs
upper
= rs −
εw = rs εi
lower
= rs +
εw = rs εi
1−
As Es Hs H 2 2LIc Ec
1+
As Es Hs H 2 2LIc Ec
(18)
(19)
Similarly, the strain ratio for the upper or lower surface strain is independent from the loading force on the target surface. In the field testing, only one strain shunt ratio is necessary to represent the strain level on the target surface. The bottom surface is preferred, since the shunt sheet served as a physical shelter for the shunt strain gauge, protecting the gauge from weathering and other kind of physical damage. 2.4. Buckling of the shunt sheet Buckling of the shunt sheet should be inspected for the heavy compressive loading cases. The buckling safety criterion needs to be satisfied during shunt sheet design, y > s + buckling
(20)
where y is the yielding strength for the shunt sheet material. Careful selection of shunt sheet thickness will reduce the risk of buckling failure. According to Euler beam buckling stability criterion [22], the following applies, buckling =
2 Es Is (Le )
2
(21)
where the effective beam length Le is selected as L for a beam with both ends fixed. 3. Experimental validation 3.1. Load test setup The prototype of strain shunt structure (see Fig. 2(a)) is experimentally validated on the Tinus Olsen MOM35 tensile load testing facility whose maximum tensile load is 900 kN. The dimension of the ASTM 1045 carbonate steel bar under the non-destructive test is 19.7 × 70.0 × 1000 mm. The calculated strain on the bar surface is limited to 1800 with an elastic modulus of 207 GPa; corresponding to a peak stress of strength 360 MPa less than the material’s yield stress of 450 MPa [23]. The tested strain shunt structure is welded onto the target steel bar, shown in Fig. 2(b). The steel strain shunt structure under load testing comprises of two circular supporting columns and a shunt sheet bridging on the top. The dimension of the shunt sheet is 1.9 × 13 × 60 mm; the spanning distance between the centres of two columns is L = 40 mm. The supporting columns (D = 9.6 mm) are welded onto the target bar surface at the bottom, and the shunt sheet is screwed at a height of 15 mm. The supporting columns are threaded on the top for fixing the shunt sheet by M5 nuts. The effective height of the shunt structure is selected as the distance of the shunt sheet’s central plane to the target bar
129
surface (H = 15.95). In order to enhance the fastening of the supporting columns with the shunt sheet’s lower surface, a thin layer of Vishay M200 strain gauge adhesive is applied to the contact surface. Instead of a single piece of supporting columns and shunt sheet, this assembly design aims to minimise the stress introduced during welding. Metallic thin film strain gauges are utilised to measure the strain on different positions of the steel bar surface and the shunt sheet, marked in Fig. 2(a). C2A-06-125LW-350 (SA0) and WK-06-125AD350 (SW0) strain gauges, supplied by Vishay MicroMeasurement, are used as cross-validation of strain measurement on the bar surface. The dimension of the effective gauge grid is 1 × 2 mm for both gauge types. As the strain levels on the upper and lower surfaces of the shunt sheet are different under loads due to warping effect, two C2A-06-125LW-350 gauges are bonded onto the centres of the upper (SA1) and the lower (SA2) surfaces of the shunt sheet respectively. The voltage signal from the strain gauges is amplified and digitalised by the wireless sensor network strain gauge module NI-WSN 3214 supplied by National Instrument, which has a high analogue to digital conversion resolution of 20 bit. Quarter-bridge is regarded as sufficient for the strain gauges in the constant temperature laboratory environment. Finally, the digitalised voltage signal is gathered by the Ethernet gateway NI-WSN 9791 for further data processing. Both incremental and decremental loads are tested for the shunt sheet structure on the bar. Ten points of tensile load are selected from zero to 500 kN, with a step of 50 kN approximately. The maximum load force of 500 kN is maintained precisely for the purpose of strain gauges calibration. At least 200 samples of strain readings have been recorded for each load step, at a sampling rate of 10 samples per second. For the tensile load of 500 kN, the theoretical stress level on the bar is 1751 , while the gauge measurement gives a value of 1759 (SW0) and 1748 (SA0) respectively according to the nominal gauge factor of 2.01 mV/V. Measurements by both types of strain gauges agree with the theoretical derivation with error less than 1%.
3.2. Result analysis The relationship of the strain readings on the shunt sheet surfaces and the strain on target bar surface is presented in Fig. 3, for the incremental tensile load. The x axis of Fig. 3 is obtained from strain measurement of strain gauge SA0; standard deviation of the strain gauge readings is insignificant as 3 . The strain readings measured on the top centre (SA1) and the bottom centre (SA2) of the shunt sheet surfaces are obviously smaller than strain level on the target bar surface (SW0). Moreover, the strain at the centre of the shunt sheet is proportional to the increasing load in a linear manner; hence the reduced strain on the shunt structure proportional to the strain on the target surface is confirmed. Furthermore, the linearity of shunt ratio is confirmed by the incremental load test result in Table 1. The first row of Table 1 records the zero-adjusting readings without any tensile loading; it is not applicable (N.A.) to calculate the shunt ratio. The biggest discretion is found at the second row, which is the first loading case at the tensile force 50 kN approximately. This significant error may be attributed to the small readings compared with strain gauge measurement standard deviation. The magnitude of error is reduced with the increased loading force. Therefore, the case of 50 kN should be excluded to calculate the averaged shunt ratio. After excluding the first two rows in Table 1, the averaged shunt ratio is 0.126. This shunt ratio is calculated from the average of strain on the upper and lower surface centres of the shunt sheet. The shunt ratios based on the shunt strain SA1 and SA2 are 0.051 and 0.201 respectively in the experiment.
130
Q. Xia, F. Quail / Sensors and Actuators A 241 (2016) 124–134
Table 1 Averaged strain for the incremental load test for strain shunt. Loading force Approx. (kN)
Strain on bar SA0 ()
Shunt strain SA1 ()
Shunt strain SA2 ()
Strain on bar SW0 ()
Averaged shunt ratio
0.0 50 100 150 200 250 300 350 400 450 500
0.08 133 316 456 682 854 1030 1210 1380 1550 1748
−0.9 2.8 10.8 21.0 35.5 45.6 55.4 64.4 73.6 82.1 107
1.3 21.4 58.9 91.5 142 179 213 243 273 302 350
−0.8 134 323 467 700 874 1050 1220 1390 1570 1759
N.A. 0.091 0.110 0.123 0.130 0.131 0.130 0.127 0.126 0.124 0.129
Table 2 Averaged strain for the decremental load test for strain shunt. Loading force Approx. (kN)
Strain on bar SA0 ()
Shunt strain SA1 ()
Shunt strain SA2 ()
Strain on bar SW0 ()
Averaged shunt ratio
500 450 400 350 300 250 200 150 100 50 0
1748 1601 1425 1237 1063 883 699 518 348 171 −0.9
107 98.7 85.9 72.8 61.6 50.4 39.1 28.6 18.7 8.7 −0.5
350 320 282 242 207 171 134 98.6 65.2 31.5 −0.6
1759 1603 1429 1243 1072 895 713 530 356 177 0.6
0.129 0.131 0.129 0.127 0.126 0.125 0.124 0.123 0.121 0.118 N.A.
The result of step-down load test confirms the constancy of shunt ratio, as the experimental data are illustrated in Table 2. The decremental load test is conducted immediately after the incremental load reaches the design peak of 500 kN. For the loading force of 450 kN, a noticeable difference in shunt ratio is found when the loading direction is reversed. Similarly, the maximum error happens at the lowest loading force of 50 kN. The averaged shunt ratio is 0.126, excluding the cases of 0 and 50 kN loading force. Moreover, the incremental and immediately decremental load test is repeated after 24 h, and no difference in shunt ratio is observed. The tensile load tests also confirm the theoretical analysis. According to the theoretical analysis, the averaged shunt ratio estimated by Eq. (11) is 0.140 for the current shunt structure (column height is selected as the distance between the target bar surface and the central plane of the shunt sheet; and the deflection of the short supporting columns is corrected by Timoshenko beam theory with a correction factor of rc = 0.24). The experiment shows the averaged shunt ratio is 11.5% over-predicted by the simplified 1D model. Despite the complexity of the three dimensional structure of the strain shunt assembly, the theoretical derivation is still useful to estimate the range of shunt ratio. Furthermore, the shunt ratios based on the shunt strain SA1 and SA2 are predicted theoretically as 0.08 and 0.20. Compared with the experimental result of 0.051 and 0.201, the estimation of the strain difference induced by the bending moment at both ends of the shunt sheet is acceptable.
4. Numerical analysis Due to the limitation of the tensile load test facility, some complicate cases can not be validated via experiment, for example, the response to compressive load, stress concentration, sensitivity to complex load. Therefore, a numerical study is conducted using the finite element analysis software, Ansys Mechanical version 14.0.
4.1. Model simplification and validation Boundary conditions for the finite element analysis are modelled from the tensile load test experiment; see Fig. 4(a). Firstly, fixed constraint is selected at one end for the target bar, and uniform surface force loading is applied on the other end. Secondly, all the contact faces are modelled as “bonded” type to simulate the nonseparate and non-sliding joint boundary conditions for the shunt structure assembly. Thirdly, welding fillet is treated as homogenous part of the solid. The welding fillet radius R is estimated as 2 mm, averaged from welding fillet measurement. Finally, the adhesive layer with a thickness 0.1 mm between the supporting columns and the shunt sheet is modelled as bonded material with an elastic modulus of 10 GPa. Mesh independence is checked on three meshes of different density; the mesh sizes are shown as row 2–4 in Table 3. The coarse mesh can predict the strain distribution for the strain shunt structure, but the strain values (see Table 3) on the shunt sheet is 1% higher than the medium mesh (see Fig. 4(b)) with 1323527 nodes or the finest mesh. As the difference in calculated strains is less than 0.1% for the medium and the finest meshes, the mesh with medium cell density is regarded as sufficient for the numerical analysis. The current numerical model has been validated by the strain gauge measurement on the loading bar surface. For the tensile loading force of 500 kN, the simulation obtains a strain value of 1768 at bar surface at SA0 position. Meanwhile, the experimental measurement indicates the strain on bar is 1748 by strain gauge SA0 and 1759 for SW0. The disagreement between the numerical analysis and experimental results is less than 1.2% for SA0 measurement, and the disagreement is reduced to 0.6% based on the SW0’s measurement. In particular, the strain at SA4 position, marked out in Fig. 4(b), is the strain value that the strain shunt aims to derive. The numerical study shows the strain at SA0 position is 1755 , and it is 0.9% less than other place of the bar surface, like SW0. The surface strain beneath the shunt sheet is relieved for the rigidity of strain shunt structure. However, this intrusion effect on the strain measurement can be reduced by decreasing cross-section of strain
Q. Xia, F. Quail / Sensors and Actuators A 241 (2016) 124–134
131
Table 3 FEA result based on welding fillet 2 mm with tensile loading of 500 kN. Case
Model description
Strain on bar SA0 ()
Strain on the upper surface of shunt sheet SA1 ()
Strain on the lower surface of shunt sheet SA2 ()
Averaged shunt ratio
1 2 3 4 5 6
Experimental result Coarse mesh, 763977 nodes Medium mesh, 1323527 nodes Finest mesh, 3187121 nodes Medium mesh R = 1 mm Medium mesh for single piece model, R = 1 mm
1748 1768 1768 1768 1768 1768
107 106.6 106.2 106.1 106.6 107.3
350 360.9 357.6 358.7 371.6 376.8
0.131 0.132 0.131 0.131 0.135 0.137
Note: An adhesive layer thickness of R = 2 mm and shearing elastic modulus of 10 GPa, and a welding fillet radius of 2 mm are selected for case 2, 3 and 4. Case 5 and 6 are based on the medium mesh; a welding fillet radius of R = 1 mm are selected for both cases. Single piece model means the test bar, shunt sheet and columns are modelled as one solid geometry.
shunt structure, e.g. the diameter of supporting columns and the thickness of the shunt sheet. Regarding to the shunt ratio, there is a noticeable difference between experimental result and FEA simulation, due to the specific welding and fastening condition of the strain shunt structure. The shunt ratio based on strain gauge measurement is 0.131 for the experimental case of loading force of 500 kN, as an average of the strain 350 for the lower surface and 107 for the upper surface of the shunt sheet. On the other hand, the shunt ratio averaged from strain on the centre of the upper and lower surfaces of the shunt sheet is 0.132 in numerical analysis (case 3 of Table 3), which is close to the average experimental result of 0.126. Although the exact modulus and thickness of the adhesive layer, the fillet radius of welding and the assembly contact boundary conditions are challenging to measure precisely, impact of parameter variation, such as the fillet radius of welding, the adhesive layer thickness and elastic modulus is evaluated numerically. The existence of the welding fillet can significantly increases the shunt ratio, and it is not modelled by the 1D theoretical analysis. Given an elastic modulus for 10 GPa for the adhesive layer, and a fillet diameter of 1.0 mm, the shunt ratio averaged from both lower and upper surfaces increases to 0.135. Due to the smaller modulus of the polymer adhesive layer, a significant deformation of this thin layer is possible if the shunt structure is under loading. Modelling the assembly as single-body steel (case 6 in Table 3) gives a shunt ratio of 0.137; it suggests the variance in thickness and elastic modulus of the adhesive layer has a limited impact on the strain distribution on the strain shunt. Therefore, this numerical model can provide reliable prediction on the shunt structure under complex load conditions.
4.2. Stress distribution and concentration The stress distribution on the shunt sheet top surface is evaluated numerically. For the purely compressive load of 500 kN, the y-axis normal strain is homogenous at the centre of shunt sheet where strain gauge is installed, indicated in Fig. 5. The strain distribution changes dramatically at the joint of the shunt sheet and the supporting columns, as the position of the supporting column is blanked out as circles in Fig. 5. Noticeably, the strain is almost zero at the end of the shunt sheet for the free hanging boundary conditions. On the other hand, the stress distribution is smooth at the centre of the shunt sheet. Strain at 4 points near the top surface centre is shown in contour, only 1% deviation is observed for 5 mm displacement. It suggests that shunt ratio is not sensitive to the positional error of strain gauge installation. The maximum stress occurs at the root of the supporting column, shown in Fig. 6. The stress concentration factor, the ratio of the maximum stress to the stress on the bar surface, is about 2.0 at the root of the supporting columns. Such a high level of stress concentration may incur fatigue failure of welding joint, leading to detachment of supporting columns. The stress concentration can
be relieved by increasing the transition fillet radius for welding, which provides smooth transition from the target surfaced to shunt structure. For example, the numerical analysis indicates the stress centration factor is reduced to 1.9 if the fillet radius is 3 mm. Alternatively, decreasing the shunt sheet thickness or diameter of the supporting columns can reduce the force on the shunt structure, then the stress concentration near the column root is controlled. For example, the numerical analysis suggests the stress centration factor is reduced to 1.9 if the shunt sheet thickness is reduced from 1.9 mm to 1.1 mm. However, dimension reduction of the shunt sheet is insufficient to solve the challenge of the stress concentration, redesign of the connection of supporting columns and target surface is demanded.
4.3. Linearity and sensibility Experimental loading test has demonstrated the linear response of the strain shunt structure to the tensile loading, while the constancy of shunt ratio under the compressive loading is essential for the application of alternating loading. Although the compressive loading test is not supported by the current experimental loading test equipment, it is conducted by the FEA model via simply reversing the loading direction. Thereby, the compressive loading of 500 kN is applied to the loading bar by reversing the loading force direction in the previous numerical model of tensile loading. The constancy of shunt ratio is confirmed by the cases with purely tensile or compressive loading of 500 kN and 250 kN, listed in Table 4. Exempted from experimental errors such as digitalization error, gauge factor deviation, loading test control error, the linear response of the strain shunt can be validated by the numerical study. Case 1–4 in Table 4 confirms the stability of the shunt ratio, regardless of loading direction or magnitude. However, the strain shunt ratio under the purely bending load is found constant but different from that of purely compressive or tensile load. Case 5–8 in Table 4 shows the shunt ratio for the bending loads is stable as 0.3494, regardless of the bending loads direction and magnitude. The purely bending force results in not only strain but also deflection on the bar surface where strain shunt is installed. According to Fig. 7, the purely bending force does not change the length of the neutral plane of the beam, and beam surface strain is proportional to the distance to the neutral plane and the local deflection angle .
ıi = Lεi =
h 2
(22)
The purely bending load leads to a larger deformation of the strain shunt between the supporting columns at the height of the shunt sheet h2 + H. Therefore, a bigger shunt ratio is expected, due
132
Q. Xia, F. Quail / Sensors and Actuators A 241 (2016) 124–134
Table 4 Y-axis normal strain FEA result based on welding fillet 2 mm. Case number Tensile loading ft (kN) Bending loading fb (kN) Strain on bar SA4 () Shunt strain upper SA1 () Shunt strain lower SA2 () Average shunt ratio 1 2 3 4 5 6 7 8 9 10
500 250 −250 −500 0 0 0 0 250 250
0 0 0 0 1.0 2.0 −1.0 −2.0 1.0 −1.0
1755 877.8 −877.8 −1755 518 1036 −518 −1036 1404 362.8
106.2 53.24 −53.24 −106.2 141.7 282.5 −141.7 −282.5 −88.12 194.6
357.6 178.9 −178.9 −357.5 220.3 440.6 −220.3 −440.6 −41.45 399.7
0.1321 0.1321 0.1321 0.1321 0.3494 0.3494 0.3494 0.3494 N.A. N.A.
Fig. 7. Schematic of deformation of strain shunt structure under purely bending load.
Fig. 8. Y axis normal strain on the bottom surface of shunt sheet, actuated by 10 Hz triangle wave load.
to the additional deformation on the shunt sheet induced by the bending deformation of the target surface, see Eq. (22)–(23).
ıi
shunt
=
h 2
+H
(23)
Thereby, the deformation on the bar surface ␦i between the supporting column is less than the potential deformation of the shunt
Q. Xia, F. Quail / Sensors and Actuators A 241 (2016) 124–134
sheet and supporting cantilever, ıi Eq. (24). ıi
shunt
=
h 2
+H
=2
shunt ,
FH 3 LF + 3Ec Ic As Es
and Eq. (1) is rewritten as
(24)
Accordingly, the extra deformation of H resutlts in a larger shunt ratio, and it is approximately (2H/h + 1) times of rs . For the current design of strain shunt (2H/h + 1) = 2.6, a bigger shunt ratio for the bending load is confirmed by the numerical study. Table 4 shows a multiple of 2.6 for the averaged shunt ratio; it is suggested the shunt ratio for the purely bending load can also be estimated. This error could be explained by the deflection of the supporting columns which reduce the extra deformation H. Compared with conventional metal thin film strain gauges, the strain shunt structure has a drawback that the bending and tensile/compressive loads result in different shunt ratios if the shunt height H is not neglectable with respect to the target structure, i.e. h/2 > >H. However, installing two strain shunt structures on both sides of target bar can address this inconvenience. Similarly, it is necessary to install two strain gauges on both side of a beam to distinguish the tensile-compressive force and the bending force. This strategy can be applied to the strain shunt, once the tensile and bending strain shunt ratios are identified. For example, adding the case 9 of ft = 250 kN and fb = 1 kN with the case 10 of ft = 250 kN and fb = −1 kN results in the strain values equal to those of case 1 (purely tensile loading ft = 500 kN) on both lower and upper surfaces of the shunt sheet. Meanwhile, subtracting case 10 from case 9 in Table 4 results in strain values of the purely bending case, as shown in case 6. Thereby, the bending force and tensile/compressive force can be derived, if multiple strain shunts are properly configured. 4.4. Dynamic response The dynamic response of the shunt structure is crucial for the measurement of large dynamic strain. For the beam structure fixed at the both ends under the tensile/compressive perturbation, the model response of the beam can be predict theoretically [24]. 2i − 1 fi = 4Lb
E (i = 1, 2. . .n) l
(25)
where fi is the characteristic frequencies and E is the elastic modulus and Lb is the length of the beam, l is the line density of the beam under compression. Eq. (25) also applies to the shunt sheet whose both ends are constrained by the supporting columns. For the steel bar under loading tests Lb = 1 m, the first characteristic frequency f1 is about 49 Hz, secondary frequency f2 is 146 Hz. Meanwhile, the first characteristic frequency f1 is 162 Hz for the shunt sheet length Lb = 0.04 m, which is higher than that of the target structure. Since the shunt sheet normally has a smaller cross-section thus lower line density than the target structure, the resonance of strain shunt is less concerned. In addition, considering the smaller dimension of the strain shunt structure, the dynamic response characteristics of the target structure is not likely to be altered by the strain shunt installation. Furthermore, the matched phase and amplitude of forced dynamic response between the shunt sheet and the target surface is confirmed by the numerical study. Temporal variation of Y-axis tensile and compressive loading as a triangle wave function is applied to the one end of the bar while the other end is fixed. A dynamic tensile loading of 10 Hz, which is sufficient for the applications such as the structural health monitoring of wind turbine tower, is investigated numerically. Fig. 8 shows neither phase delay nor waveform distortion between the strain probed at the centre of the lower surface of the shunt sheet (SA2) and that of the target bar surface beneath (SA4). The strain peaks coincide at t = 0.025s, matching the
133
peak of tensile loading force on the bar. Double Y-axis is used to correlate the temporal variation of the strain on the target surface and that of the lower surface of the shunt sheet. The Y-axis on the left is scaled down by the shunt ratio 0.204, thus the dot line and the solid line coincides in Fig. 8. The excellent agreement indicates the strain shunt has a good frequency response to the dynamic loading up to 10 Hz.
5. Conclusion In this paper, the concept of the strain shunt is proposed to address the challenge of measuring large dynamic strain over a long period. The working principles are illustrated by theoretical analysis of the simplified one dimensional model. The prototype of strain shunt structure consisting of one shunt sheet and two supporting columns has been experimentally studied, and the linearity and stability of shunt ratio is confirmed by the tensile load experiments. Moreover, the response of strain shunt to compressive and bending force is evaluated by finite element analysis. It is found purely bending loads result in another shunt ratio and at least two strain shunts are required to distinguish the tensile and bending loads. Nevertheless, this prototype design of strain shunt invites further improvement to solve the stress concentration and inconvenient installation.
References [1] M.D.C. Segovia Garcia, M.J.T. Revie, F. Quail, Condition monitoring data in the study of offshore wind turbines’ risk of failure, in: Proceedings of the 19th AR2TS Advances in Risk, Reliability and Technology Symposium, ASME, 2013. [2] C.C. Ciang, J.-R. Lee, H.-J. Bang, Structural health monitoring for a wind turbine system: a review of damage detection methods, Meas. Sci. Technol. 19 (2008) 122001. [3] A. Hamilton, F.J. Quail, Detailed state of the art review for the different on-line/in-line oil analysis techniques in context of wind turbine gearboxes, J. Tribol. 133 (2011). [4] ASM International, ASM Handbook Volume 1, Properties and Selection: Irons, Steels, and High-Performance Alloys, USA, 1990, pp. 793-800800. [5] Vishay Micro-Measurements, Strain Gage Selection: Criteria, Procedures, Recommendations, Tech Note TN-5052007. [6] P. Kayser, J. Godefroy, L. Leca, High-temperature thin-film strain gauges, Sens. Actuators A: Phys. 37 (1993) 328–332. [7] T. Sugimoto, H. Furukawa, Y. Uchino, Strain gauge for measuring large strains, Google Patents 2010. [8] J.M. López-Higuera, L. Rodriguez Cobo, A. Quintela Incera, A. Cobo, Fiber optic sensors in structural health monitoring, Lightwave Technol. J. 29 (2011) 587–608. [9] Vishay Micro-Measurements, Introduction to Stress Analysis by the PhotoStress® Method, Vishay Tech Note TN-702-22005. [10] T.K.B. Günther, Optical Versus Electrical Strain Aages: A Comparison, HBM Measurements, Germany, 2007. [11] J. Roths, A. Wilfert, P. Kratzer, F. Jülich, R. Kuttler, Strain calibration of optical FBG-based strain sensors, (EWOFS’10) fourth European workshop on optical fibre sensors, Int. Soc. Opt. Photonics (2010), 76530F-F-4. [12] S. Yang, B. Zhou, T. Sun, K.T. Grattan, A novel optical sensor platform designed for wireless sensor networks, J. Phys. Conf. Ser. (2013) 012007, IOP Publishing. [13] M. Komachiya, R. Minamitani, T. Fumino, T. Sakaguchi, S. Watanabe, Proof-testing and probabilistic lifetime estimation of glass fibers for sensor applications, Appl. Opt. 38 (1999) 2767–2774. [14] Y.-N. Cheung, Y. Zhu, C.-H. Cheng, C. Chao, W.W.-F. Leung, A novel fluidic strain sensor for large strain measurement, Sens. Actuators A: Phys. 147 (2008) 401–408. [15] I. Kang, M.J. Schulz, J.H. Kim, V. Shanov, D. Shi, A carbon nanotube strain sensor for structural health monitoring, Smart Mater. Struct. 15 (2006) 737. [16] T. Yamada, Y. Hayamizu, Y. Yamamoto, Y. Yomogida, A. Izadi-Najafabadi, D.N. Futaba, et al., A stretchable carbon nanotube strain sensor for human-motion detection, Nat. Nanotechnol. 6 (2011) 296–301. [17] K. Peters, Polymer optical fiber sensors—a review, Smart Mater. Struct. 20 (2011) 013002. [18] C. Rembe, R. Kant, R.S. Muller, Optical measurement methods to study dynamic behavior in MEMS, lasers in metrology and art conservation, Int. Soc. Opt. Photonics (2001) 127–137. [19] L. Matthaei, Microwave Filters, Impedance-matching Networks, and Coupling Structures, McGraw-Hill, New York, 1964. [20] O. Bauchau, J. Craig, Euler-Bernoulli beam theory, Structural Analysis, Springer, 2009, pp. 173–221.
134
Q. Xia, F. Quail / Sensors and Actuators A 241 (2016) 124–134
[21] C.E. Augarde, A.J. Deeks, The use of Timoshenko’s exact solution for a cantilever beam in adaptive analysis, Finite Elem. Anal. Des. 44 (2008) 595–601. [22] R.C. Juvinall, K.M. Marshek, Fundamentals of Machine Component Design, 4th ed., J. Wiley, New York, 2006. [23] W.J. Wright, Steel Bridge Design Handbook: Bridge Steels and Their Mechanical Properties, 2012. [24] S.G. Kelly, Mechanical Vibrations: Theory and Applications, Cengage Publishing, 2012.
Biographies Dr Qingfeng Xia obtained his Ph.D. degree from Manchester University in March 2012. Currently, he is a researcher in the Osney Thermo-fluid Lab, Oxford University. His research interests include fluid visualization, condition monitoring of turbomachines, and sensor and instrumentations.
Prof. Francis Quail (CEng, FIMechE, FCMI, FIES) was director of turbomachine group, School of Engineering Science, University of Glasgow.
Contents lists available at ScienceDirect
Sensors and Actuators A: Physical journal homepage: www.elsevier.com/locate/sna
Principles and validation of strain gauge shunt design for large dynamic strain measurement Qingfeng Xia a,b,∗ , Francis Quail a a b
School of Engineering, University of Glasgow, Glasgow G12 8QQ, United Kingdom Osney Thermo-Fluids Laboratory, Department of Engineering Science, University of Oxford, Oxford OX2 0ES, United Kingdom
a r t i c l e
i n f o
Article history: Received 3 August 2015 Received in revised form 26 January 2016 Accepted 2 February 2016 Available online 4 February 2016 Keywords: Strain gauge Large strain Fatigue failure Dynamic strain Structural health monitoring
a b s t r a c t In order to eliminate the fatigue failure of metallic thin film strain gauges under large alternating strain condition, a mechanical structure reducing the large strain on the target surface proportionally to a safe level is proposed as strain shunt in this study. The working principles of the strain shunt structure are illustrated and the shunt ratio of strain reduction is derived theoretically from a simplified one dimensional model. The prototype strain shunt is validated by tensile load test experiments which confirm the repeatability and linearity. Moreover, the usability of the strain shunt structure under alternating loads, the stability of shunt ratio under the combined stress conditions, and the dynamic response of the strain shunt structure are investigated by finite element analysis. © 2016 Elsevier B.V. All rights reserved.
1. Introduction Current challenges in large scale off-shore wind turbine condition monitoring systems require robust sensors that can operate continuously for a long period of time on rotating and shielded components. Condition monitoring of critical components in a wind turbine system is vital for health assessment of the asset [1], minimising down time and reducing significant maintenance and operational impact [2,3]. Considering the inconvenience of strain sensor replacement for off-shore wind turbine systems, this paper highlights the potential of developing novel strain sensors that can survive large dynamic strain conditions over a long period of time. Metallic thin-film strain gauges have the advantages of excellent linearity, stable electrical signal output, compactness, low cost, etc. However, it is challenging to measure extremely large static strain or large dynamic strain found on structure of multi-megawatt offshore wind turbines. High strength material for modern megastructures, e.g. towers for off-shore wind turbine, must survive large dynamic strain induced by vibration or other transient loads. For example, the yield strength for high strength Maraging steel is in the range of 1030–2420 MPa [4] with a Young’s modulus of 190–210 GPa; it means the maximum permitted strain without plastic deformation will be more than 5000 . Although metal-
∗ Corresponding author. E-mail addresses: [email protected], [email protected] (Q. Xia). http://dx.doi.org/10.1016/j.sna.2016.02.007 0924-4247/© 2016 Elsevier B.V. All rights reserved.
lic foil strain gauges can measure the static strain up to 5%, the maximum dynamic strain can be measured is lower than 2000 for 106 alternating loading cycles [5]. Metallic thin-film gauges are likely to break as a result of limited fatigue life under dynamic loads, before the failure of the monitored structure can be identified. Research on the metallic thin-film strain gauges has improved their performance at higher temperature [6] or under large strain conditions [7], however achievement in large dynamic strain measurement is limited. For example, a patent on strain gauge pattern can reduce the stress concentration on the metal tap connecting gauge pattern and wire terminals, thus the claimed measurement range for static strain is extended to 15% [7]. However, the fatigue failure of thin-film gauges under the long-term alternating loads has not been solved; an achievable range for dynamic strain measurement is 1600 for 106 alternating loading cycles [5]. Meanwhile, optical fibre strain gauges have been extensively investigated in the last decades, and they have the potential to measure large dynamic strain [8]. The strain gauges based on fibre Bragg grating (FBG) have the advantages of immunity to electromagnetic interference (EMI), intrinsic safety in highly explosive atmospheres, and good resistance to large strain and alternating loads, etc. [9]. In addition, optical strain gauges offer a more stable measurement in respect of zero-drifting after loading [10]. The resistance of optical strain gages to alternating load has been tested for an alternating strain of ±1000 ; no change in measurement characteristics or the reflection peak wavelength is observed after 107 loading cycles, i.e. sensitivity and base wavelength are unchanged [10].
Q. Xia, F. Quail / Sensors and Actuators A 241 (2016) 124–134
Nomenclature Symbol A D E F f G H I L M t x,y,z r ␦
Cross-section area, m2 Diameter of column, m Normal elastic modulus, GPa Force on joint of shunt sheet and columns, N Frequency, Hz Shearing elastic modulus, GPa Height of column, m Second moment of area, m4 Spanning of shunt sheet, m Moment acting on joint of shunt sheet and columns, N·m Time, s; Thickness of thunt sheet, m Coordination, m Ratio Density of material, kg/m3 Deflection angle Deformation of material under stress, m Stress of material under load, Pa Poisson ratio
Subscripts supporting columns c input from the target surface i s shunt sheet wrapping effect of the shunt sheet w bending beam bending upper upper surface of the shunt sheet lower surface of the shunt sheet lower
Despite those advantages, FBG strain sensors have not significantly extended the measurement range for dynamic strain, compared with traditional metal thin-film strain gauges [10]. Nevertheless, FBG sensors require expensive optical equipment to detect wavelength shifting precisely [11]. Although using low power LED light sources and photo-detectors may reduce the power consumption for the fibre optical sensor nodes [12], the prohibiting power consumption is not acceptable for battery-powered wireless sensor networks. Recent innovations in strain-sensitive material have the potential to measure large strain, surpassing the intrinsic maximum strain level (approximately 4%) of silicon fibre optical FBG sensors limited by the failure strain of silica [13]. A novel fluidic strain sensor has been validated for the large deformation measurement up to 40% [14]. This design utilises the piezoresistive effect of the tube elastomer filled with Glycerin and aqueous sodium chloride. Moreover, plastic optical fibres (POF) interwoven into geotextile sheets have been tested to measure large strain up to 40% and dynamic strain under submerged circumstances. Instead of the wave-length displacement detection as in FBG sensors, the correlation between strain and the intensity of light transmitting within POF offers a cost-effective way for strain measurement. In addition, carbon nanotube material has been applied into piezoresistive strain sensors for structural health monitoring applications [15] and human motion sensors [16]. However, repeatability and material specific calibrations need further investigation on these innovative methods [17]. Other optical methods developed for the large strain measurement are based on the high resolution digital camera technology. For example, Vishay Micro-Measurement has developed PhotoStress® technology using reflection polariscope [9]; it is a full-field strain measurement solution ideal for the mea-
125
surement of large deformations. Similarly, Polytec laser-based vibrometer is capable of strain measurement in laboratory environment [18]. However, these optical solutions may be restricted by non-vibratory condition, as well as high power consumption and equipment cost. Thereby, they are excluded from massive deployment in industrial scenarios, in particular, off-shore wind turbine condition monitoring and structural health monitoring. Currently, commercial optical or resistive strain measurement techniques are not yet available for large and dynamic strain measurement which is required by the long-term structural health monitoring (SHM) and condition monitoring systems, e.g. wireless force sensing on rotating machines. The main technical challenges are sensor fatigue failure due to large dynamic strain and sustainable power supply for wireless sensor nodes. Metallic thin film strain gauges are subject to fatigue failure at heavy alternating loads, while the high power consumption for the FBG signal acquisition system is prohibiting for battery-powered wireless sensor networks. To address such challenges, this paper presents a novel strain shunt structure which reduces the large strain proportionally to a manageable range for the metallic thin film strain gauges. The strain shunt structure, together with metallic thin film strain gauges, is bonded onto the target surface. Combined with the advantages of metallic resistive strain gauges, this strain shunt design offers an attractive solution for large and dynamic strain measurement in challenging environments, such as off-shore wind turbine up-tower condition monitoring and structural health monitoring system for supporting structures. In this paper, the working principles of strain shunt design are illustrated and shunt ratio is derived theoretically base on the simplified one-dimensional model. The prototype of the strain shunt is experimentally tested by the tensile load test. Moreover, the impact of complex loads or dynamic loads on the shunt structure is investigated by finite element analysis (FEA).
2. Strain shunt design 2.1. Principles of strain shunt The concept of electrical ammeter shunt, which assists the measurement of electrical current too large to be measured directly by a particular ammeter, has been well established [19]. The strain shunt structure, in a similar manner, enables the measurement of large strain using commercial metal foil strain gauges without fatigue failure. The ammeter shunt has a small fixed-value resistor in series and the current is derived from the measured voltage across the resistor. While, a parallel configuration is proposed for the strain shunt which can be conveniently bonded to the target surface with large strain. One possible strain shunt design is a mechanical structure consists of one elastic shunt sheet bridging two supporting columns fixed onto the target surface, see Fig. 1, If both supporting columns and the shunt sheet are made of elastic material, the supporting columns will bend when the target surface is under tensile or compressive load, due to the binding effect of the shunt sheet on top. Consequently, the deformation on the shunt sheet will be less than the target surface underneath. Fig. 1 illustrates the working principles of the strain shunt structure subjected to compressive or tensile load in y axis direction, compared with the structure without load. The supporting column can be modelled as a cantilever with one end fixed onto the target surface and the other end under bending load at the joint with the shunt sheet. Due to the fixed connection of the shunt structure on the target surface, y axis strain on the target surface leads to deformation on the shunt sheet and supporting columns. The supporting
126
Q. Xia, F. Quail / Sensors and Actuators A 241 (2016) 124–134
Fig. 1. Schematic of strain gauge shunt on the target surface.
columns’ deflection relieves the strain on the shunt sheet, resulting in less deformation on the shunt sheet than that of the target surface between two supporting columns. For the target structure under purely compressive or tensile loading, the deformation on the loading direction (y axis) is proposed as,
εs is averaged from the measured strain on the upper and lower surfaces of the shunt sheet, see gauge position in Fig. 1.
ıi = Lεi = L − L = 2ıc + ıs
A formula for shunt ratio can be derived from the simplified structure of supporting columns and shunt sheet, based on Eq. (1). It is assumed that the cross sections of the shunt sheet and supporting columns are homogenous; the target surface is under the purely tensile or compressive load in parallel with the shunt sheet. The shunt structure’s dimension is much smaller than the target surface so that it does not alter the strain to be measured on the target surface. The deflection deformation the columnsıc , is expressed by Euler beam theory for slender beams [20],
(1)
where ıi is y axis deformation of the target surface between the supporting columnsL; εi is the average y axis normal strain on the target surface beneath the shunt structure; ıc is the y axis deflection of each supporting column; ıs = L − Ls is y axis deformation of the shunt sheet. Since the supporting columns are subject to elastic deformation (ıc > 0), the average y axis strain on the shunt sheet εs should be less than that on the target surface εi . The ratio of strain is defined as shunt ratio rs. rs (Shunt ratio) =
ıs Lεs = Lεi ıi
(2)
where, εs is the average normal strain on shunt sheet along the loading direction. In particular, the strain on the upper and the lower surface of the shunt sheet is different, due to the warping effect of the shunt sheet. As a result of the bending moment introduced at the joint of the shunt sheet and the supporting columns, the shunt sheet warps with the deflection of supporting columns. Therefore,
2.2. Theoretical derivation of shunt ratio
ıEular = c
FH 3 3Ec Ic
(3)
where Ec is the elastic modulus of the supporting column; F is the tensile or compressive force acting on the shunt sheet from the supporting column; H is the height of the supporting columns; I c is the second moment of area for the support column with respect to x axis. It should be noted that the bending displacement derived from Euler beam theory is under-estimated for short columns. According to Timoshenko’ beam theory, the shearing parallel to the
Q. Xia, F. Quail / Sensors and Actuators A 241 (2016) 124–134
127
central plane should not be neglected. To estimate the displacement for short rectangular cantilever beam [21], the following equation applies, ıc =
F 6EI
3vz 2 (H − z) + (4 + 5v)
zW 2 + (3H − z) z 2 4
(4)
where E and I are the elastic modulus and the second moment of area for the x-axis of the beam, W is thickness, is Poisson ratio. Since F is applied at the end of the cantilever, the displacement at the loading end on the top of circular column (z = H) can be simplified as: ıc = (1 + rc ) ıEular wherer c = c
(4 + 5) W 2 8H 2
(5)
where rc is the ratio to correct the under-estimated displacement. This ratio depends on the Poisson ratio of the material and H/W (slenderness of column). If H/W > >1, the beam can be regarded as Euler beam without any correction. The y-axis deformation of the shunt sheet (Lεs ) is primarily caused by the tensile or compressive force F. In addition, the warping effect of the shunt sheet may lead to deformation in y axis direction, and this is denoted as ıw . Thereby, the deformation of shunt sheet on y axis can be expressed as, ıs = Lεs + ıw εs =
Fig. 2. (a) strain gauge positioning for loading test; (b) close-up of strain shunt structure.
(6)
F As Es
(7)
where As is cross-section area for the shunt sheet; Es is the elastic modulus for the sheet. Since the materials of column can be different from the shunt sheet, the material properties like elastic modulus are distinguished by different subscript. The shunt ratio rs can also be represented by the ratio of the averaged strain on the shunt sheet εs and that on the target surface under the shunt sheet εi : rs =
εs εi
(8)
Neglecting the warping effect of the shunt sheet (discussed in Section 2.3), Eq. (1) can be rewritten into, 2 (1 + rc ) (
LF FH 3 )+ = ıi = Lεi 3Ec Ic As Es
(9) Fig. 3. Strain shunt validation for the incremental tensile loads.
According to Eq. (8) and Eq. (9),
2 (1 + rc )
FH 3 3Ec Ic
+
LF 1 LF = As Es rs As Es
(10)
L
rs = 2 (1 + rc )
As Es H3 3Ec Ic
(11) +
L As Es
This theoretical derivation suggests that the shunt ratio is independent of the target surface material properties and loading force on the shunt sheet, assuming rigid connection between the supporting columns and the target surface. In practice, the material of shunt sheet should have the similar thermal expansion coefficient with the target surface material, thus the impact of thermal variation target surface can be minimised. 2.3. Warping effect The strain on upper and lower surface is not equal, due to the warping of the shunt sheet. Since the joint of columns and shunt sheet is not hinged, the deflection of the supporting columns will bend the shunt sheet connecting them. Consequently, measurement of averaged strain on the shunt sheet needs two strain gauges on both the upper and lower surfaces, as shown in Fig. 1.
As the moment acted on the shunt sheet is unknown, the warping angle s can be derived from the flexural angle of the upper surface of the columnc . It is assumed that angle between the column top surface and shunt sheet angle remains constant during deformation and the warping shunt sheet has neglectable effect on the supporting columns’ deflection (deformation in y axis), given the thickness of shunt sheet is much thinner than the cross-section supporting columns. According to this geometrical relationship, the warping angle of the shunt sheet is equal to that of deflection angle of column and sheet joint: c = s
(12)
Furthermore, the deflection angle on the top of the column c can be derived from Euler cantilever beam theory, c =
FH 2 2Ec Ic
(13)
The extra strain on the shunt sheet can be calculated, assuming the simply supported beam at both ends for the shunt sheet. Given the large ratio of shunt sheet length to thickness, classic Euler
128
Q. Xia, F. Quail / Sensors and Actuators A 241 (2016) 124–134
beam theory can calculate the shunt sheet warping angle due to the bending moment Ms . s =
Ms 2L
(14)
Es Is
where I s is the second moment of area of the support column with respect to y axis. In addition to the tensile or compressive force, the shunt sheet is considered under bending moment Ms at both ends. Ms =
Es Is FH 2 Ec Ic L
(15)
The deflected supporting column leads to significant warping of the thin shunt sheet, but the reaction moment acting on the supporting column Mc is not considered in the simplified 1D analysis. This moment-induced deflection can be neglected, compared with the force-induced one in Eq. (3), since the second moment of area of the shunt sheet is an order of magnitude smaller than that of the support columns, Ic > >Is . The additional strain εw on both the lower and upper surfaces of the shunt sheet, induced by Ms , can be estimated as, εw =
Fig. 4. (a) boundary condition for load test simulation; (b) mesh with a medium cell density for the finite element model.
Hs Ms 2
Is Es
=
Hs FH 2 2LIc Ec
(16)
where H s is the thickness of the shunt sheet. The bending moment Ms does not change the strain at the neutral position of the beam [22]; and the strain on the upper and lower surface has the identical magnitude but the opposite sign. The shunt sheet is deformed into an arc shape of elastic curve with angle s to the horizontal on both ends. Once the warping
Fig. 5. Contour of y-axis normal strain on the top surface of shunt sheet for purely compressive loading on test bar.
Fig. 6. Y-axis normal stress contour to illustrate the stress concentration (unit: Pa).
Q. Xia, F. Quail / Sensors and Actuators A 241 (2016) 124–134
angle s is calculated, the y-axis deformation of the shunt sheet ıw incurred by the warping effect can be estimated.
ıw =
tan s − sin s s
2
L=
s L 2
(17)
where ıw is one order infinitesimal of ıc , therefore, the impact of the shunt sheet warping on the shunt ratio is neglected. The shunt ratio rs refers to the averaged of both upper and lower surfaces through this theoretical analysis, which is independent of the warping effect. However, the warping of the shunt sheet leads to the different strain level on the upper and lower surfaces of the shunt sheet. rs
rs
upper
= rs −
εw = rs εi
lower
= rs +
εw = rs εi
1−
As Es Hs H 2 2LIc Ec
1+
As Es Hs H 2 2LIc Ec
(18)
(19)
Similarly, the strain ratio for the upper or lower surface strain is independent from the loading force on the target surface. In the field testing, only one strain shunt ratio is necessary to represent the strain level on the target surface. The bottom surface is preferred, since the shunt sheet served as a physical shelter for the shunt strain gauge, protecting the gauge from weathering and other kind of physical damage. 2.4. Buckling of the shunt sheet Buckling of the shunt sheet should be inspected for the heavy compressive loading cases. The buckling safety criterion needs to be satisfied during shunt sheet design, y > s + buckling
(20)
where y is the yielding strength for the shunt sheet material. Careful selection of shunt sheet thickness will reduce the risk of buckling failure. According to Euler beam buckling stability criterion [22], the following applies, buckling =
2 Es Is (Le )
2
(21)
where the effective beam length Le is selected as L for a beam with both ends fixed. 3. Experimental validation 3.1. Load test setup The prototype of strain shunt structure (see Fig. 2(a)) is experimentally validated on the Tinus Olsen MOM35 tensile load testing facility whose maximum tensile load is 900 kN. The dimension of the ASTM 1045 carbonate steel bar under the non-destructive test is 19.7 × 70.0 × 1000 mm. The calculated strain on the bar surface is limited to 1800 with an elastic modulus of 207 GPa; corresponding to a peak stress of strength 360 MPa less than the material’s yield stress of 450 MPa [23]. The tested strain shunt structure is welded onto the target steel bar, shown in Fig. 2(b). The steel strain shunt structure under load testing comprises of two circular supporting columns and a shunt sheet bridging on the top. The dimension of the shunt sheet is 1.9 × 13 × 60 mm; the spanning distance between the centres of two columns is L = 40 mm. The supporting columns (D = 9.6 mm) are welded onto the target bar surface at the bottom, and the shunt sheet is screwed at a height of 15 mm. The supporting columns are threaded on the top for fixing the shunt sheet by M5 nuts. The effective height of the shunt structure is selected as the distance of the shunt sheet’s central plane to the target bar
129
surface (H = 15.95). In order to enhance the fastening of the supporting columns with the shunt sheet’s lower surface, a thin layer of Vishay M200 strain gauge adhesive is applied to the contact surface. Instead of a single piece of supporting columns and shunt sheet, this assembly design aims to minimise the stress introduced during welding. Metallic thin film strain gauges are utilised to measure the strain on different positions of the steel bar surface and the shunt sheet, marked in Fig. 2(a). C2A-06-125LW-350 (SA0) and WK-06-125AD350 (SW0) strain gauges, supplied by Vishay MicroMeasurement, are used as cross-validation of strain measurement on the bar surface. The dimension of the effective gauge grid is 1 × 2 mm for both gauge types. As the strain levels on the upper and lower surfaces of the shunt sheet are different under loads due to warping effect, two C2A-06-125LW-350 gauges are bonded onto the centres of the upper (SA1) and the lower (SA2) surfaces of the shunt sheet respectively. The voltage signal from the strain gauges is amplified and digitalised by the wireless sensor network strain gauge module NI-WSN 3214 supplied by National Instrument, which has a high analogue to digital conversion resolution of 20 bit. Quarter-bridge is regarded as sufficient for the strain gauges in the constant temperature laboratory environment. Finally, the digitalised voltage signal is gathered by the Ethernet gateway NI-WSN 9791 for further data processing. Both incremental and decremental loads are tested for the shunt sheet structure on the bar. Ten points of tensile load are selected from zero to 500 kN, with a step of 50 kN approximately. The maximum load force of 500 kN is maintained precisely for the purpose of strain gauges calibration. At least 200 samples of strain readings have been recorded for each load step, at a sampling rate of 10 samples per second. For the tensile load of 500 kN, the theoretical stress level on the bar is 1751 , while the gauge measurement gives a value of 1759 (SW0) and 1748 (SA0) respectively according to the nominal gauge factor of 2.01 mV/V. Measurements by both types of strain gauges agree with the theoretical derivation with error less than 1%.
3.2. Result analysis The relationship of the strain readings on the shunt sheet surfaces and the strain on target bar surface is presented in Fig. 3, for the incremental tensile load. The x axis of Fig. 3 is obtained from strain measurement of strain gauge SA0; standard deviation of the strain gauge readings is insignificant as 3 . The strain readings measured on the top centre (SA1) and the bottom centre (SA2) of the shunt sheet surfaces are obviously smaller than strain level on the target bar surface (SW0). Moreover, the strain at the centre of the shunt sheet is proportional to the increasing load in a linear manner; hence the reduced strain on the shunt structure proportional to the strain on the target surface is confirmed. Furthermore, the linearity of shunt ratio is confirmed by the incremental load test result in Table 1. The first row of Table 1 records the zero-adjusting readings without any tensile loading; it is not applicable (N.A.) to calculate the shunt ratio. The biggest discretion is found at the second row, which is the first loading case at the tensile force 50 kN approximately. This significant error may be attributed to the small readings compared with strain gauge measurement standard deviation. The magnitude of error is reduced with the increased loading force. Therefore, the case of 50 kN should be excluded to calculate the averaged shunt ratio. After excluding the first two rows in Table 1, the averaged shunt ratio is 0.126. This shunt ratio is calculated from the average of strain on the upper and lower surface centres of the shunt sheet. The shunt ratios based on the shunt strain SA1 and SA2 are 0.051 and 0.201 respectively in the experiment.
130
Q. Xia, F. Quail / Sensors and Actuators A 241 (2016) 124–134
Table 1 Averaged strain for the incremental load test for strain shunt. Loading force Approx. (kN)
Strain on bar SA0 ()
Shunt strain SA1 ()
Shunt strain SA2 ()
Strain on bar SW0 ()
Averaged shunt ratio
0.0 50 100 150 200 250 300 350 400 450 500
0.08 133 316 456 682 854 1030 1210 1380 1550 1748
−0.9 2.8 10.8 21.0 35.5 45.6 55.4 64.4 73.6 82.1 107
1.3 21.4 58.9 91.5 142 179 213 243 273 302 350
−0.8 134 323 467 700 874 1050 1220 1390 1570 1759
N.A. 0.091 0.110 0.123 0.130 0.131 0.130 0.127 0.126 0.124 0.129
Table 2 Averaged strain for the decremental load test for strain shunt. Loading force Approx. (kN)
Strain on bar SA0 ()
Shunt strain SA1 ()
Shunt strain SA2 ()
Strain on bar SW0 ()
Averaged shunt ratio
500 450 400 350 300 250 200 150 100 50 0
1748 1601 1425 1237 1063 883 699 518 348 171 −0.9
107 98.7 85.9 72.8 61.6 50.4 39.1 28.6 18.7 8.7 −0.5
350 320 282 242 207 171 134 98.6 65.2 31.5 −0.6
1759 1603 1429 1243 1072 895 713 530 356 177 0.6
0.129 0.131 0.129 0.127 0.126 0.125 0.124 0.123 0.121 0.118 N.A.
The result of step-down load test confirms the constancy of shunt ratio, as the experimental data are illustrated in Table 2. The decremental load test is conducted immediately after the incremental load reaches the design peak of 500 kN. For the loading force of 450 kN, a noticeable difference in shunt ratio is found when the loading direction is reversed. Similarly, the maximum error happens at the lowest loading force of 50 kN. The averaged shunt ratio is 0.126, excluding the cases of 0 and 50 kN loading force. Moreover, the incremental and immediately decremental load test is repeated after 24 h, and no difference in shunt ratio is observed. The tensile load tests also confirm the theoretical analysis. According to the theoretical analysis, the averaged shunt ratio estimated by Eq. (11) is 0.140 for the current shunt structure (column height is selected as the distance between the target bar surface and the central plane of the shunt sheet; and the deflection of the short supporting columns is corrected by Timoshenko beam theory with a correction factor of rc = 0.24). The experiment shows the averaged shunt ratio is 11.5% over-predicted by the simplified 1D model. Despite the complexity of the three dimensional structure of the strain shunt assembly, the theoretical derivation is still useful to estimate the range of shunt ratio. Furthermore, the shunt ratios based on the shunt strain SA1 and SA2 are predicted theoretically as 0.08 and 0.20. Compared with the experimental result of 0.051 and 0.201, the estimation of the strain difference induced by the bending moment at both ends of the shunt sheet is acceptable.
4. Numerical analysis Due to the limitation of the tensile load test facility, some complicate cases can not be validated via experiment, for example, the response to compressive load, stress concentration, sensitivity to complex load. Therefore, a numerical study is conducted using the finite element analysis software, Ansys Mechanical version 14.0.
4.1. Model simplification and validation Boundary conditions for the finite element analysis are modelled from the tensile load test experiment; see Fig. 4(a). Firstly, fixed constraint is selected at one end for the target bar, and uniform surface force loading is applied on the other end. Secondly, all the contact faces are modelled as “bonded” type to simulate the nonseparate and non-sliding joint boundary conditions for the shunt structure assembly. Thirdly, welding fillet is treated as homogenous part of the solid. The welding fillet radius R is estimated as 2 mm, averaged from welding fillet measurement. Finally, the adhesive layer with a thickness 0.1 mm between the supporting columns and the shunt sheet is modelled as bonded material with an elastic modulus of 10 GPa. Mesh independence is checked on three meshes of different density; the mesh sizes are shown as row 2–4 in Table 3. The coarse mesh can predict the strain distribution for the strain shunt structure, but the strain values (see Table 3) on the shunt sheet is 1% higher than the medium mesh (see Fig. 4(b)) with 1323527 nodes or the finest mesh. As the difference in calculated strains is less than 0.1% for the medium and the finest meshes, the mesh with medium cell density is regarded as sufficient for the numerical analysis. The current numerical model has been validated by the strain gauge measurement on the loading bar surface. For the tensile loading force of 500 kN, the simulation obtains a strain value of 1768 at bar surface at SA0 position. Meanwhile, the experimental measurement indicates the strain on bar is 1748 by strain gauge SA0 and 1759 for SW0. The disagreement between the numerical analysis and experimental results is less than 1.2% for SA0 measurement, and the disagreement is reduced to 0.6% based on the SW0’s measurement. In particular, the strain at SA4 position, marked out in Fig. 4(b), is the strain value that the strain shunt aims to derive. The numerical study shows the strain at SA0 position is 1755 , and it is 0.9% less than other place of the bar surface, like SW0. The surface strain beneath the shunt sheet is relieved for the rigidity of strain shunt structure. However, this intrusion effect on the strain measurement can be reduced by decreasing cross-section of strain
Q. Xia, F. Quail / Sensors and Actuators A 241 (2016) 124–134
131
Table 3 FEA result based on welding fillet 2 mm with tensile loading of 500 kN. Case
Model description
Strain on bar SA0 ()
Strain on the upper surface of shunt sheet SA1 ()
Strain on the lower surface of shunt sheet SA2 ()
Averaged shunt ratio
1 2 3 4 5 6
Experimental result Coarse mesh, 763977 nodes Medium mesh, 1323527 nodes Finest mesh, 3187121 nodes Medium mesh R = 1 mm Medium mesh for single piece model, R = 1 mm
1748 1768 1768 1768 1768 1768
107 106.6 106.2 106.1 106.6 107.3
350 360.9 357.6 358.7 371.6 376.8
0.131 0.132 0.131 0.131 0.135 0.137
Note: An adhesive layer thickness of R = 2 mm and shearing elastic modulus of 10 GPa, and a welding fillet radius of 2 mm are selected for case 2, 3 and 4. Case 5 and 6 are based on the medium mesh; a welding fillet radius of R = 1 mm are selected for both cases. Single piece model means the test bar, shunt sheet and columns are modelled as one solid geometry.
shunt structure, e.g. the diameter of supporting columns and the thickness of the shunt sheet. Regarding to the shunt ratio, there is a noticeable difference between experimental result and FEA simulation, due to the specific welding and fastening condition of the strain shunt structure. The shunt ratio based on strain gauge measurement is 0.131 for the experimental case of loading force of 500 kN, as an average of the strain 350 for the lower surface and 107 for the upper surface of the shunt sheet. On the other hand, the shunt ratio averaged from strain on the centre of the upper and lower surfaces of the shunt sheet is 0.132 in numerical analysis (case 3 of Table 3), which is close to the average experimental result of 0.126. Although the exact modulus and thickness of the adhesive layer, the fillet radius of welding and the assembly contact boundary conditions are challenging to measure precisely, impact of parameter variation, such as the fillet radius of welding, the adhesive layer thickness and elastic modulus is evaluated numerically. The existence of the welding fillet can significantly increases the shunt ratio, and it is not modelled by the 1D theoretical analysis. Given an elastic modulus for 10 GPa for the adhesive layer, and a fillet diameter of 1.0 mm, the shunt ratio averaged from both lower and upper surfaces increases to 0.135. Due to the smaller modulus of the polymer adhesive layer, a significant deformation of this thin layer is possible if the shunt structure is under loading. Modelling the assembly as single-body steel (case 6 in Table 3) gives a shunt ratio of 0.137; it suggests the variance in thickness and elastic modulus of the adhesive layer has a limited impact on the strain distribution on the strain shunt. Therefore, this numerical model can provide reliable prediction on the shunt structure under complex load conditions.
4.2. Stress distribution and concentration The stress distribution on the shunt sheet top surface is evaluated numerically. For the purely compressive load of 500 kN, the y-axis normal strain is homogenous at the centre of shunt sheet where strain gauge is installed, indicated in Fig. 5. The strain distribution changes dramatically at the joint of the shunt sheet and the supporting columns, as the position of the supporting column is blanked out as circles in Fig. 5. Noticeably, the strain is almost zero at the end of the shunt sheet for the free hanging boundary conditions. On the other hand, the stress distribution is smooth at the centre of the shunt sheet. Strain at 4 points near the top surface centre is shown in contour, only 1% deviation is observed for 5 mm displacement. It suggests that shunt ratio is not sensitive to the positional error of strain gauge installation. The maximum stress occurs at the root of the supporting column, shown in Fig. 6. The stress concentration factor, the ratio of the maximum stress to the stress on the bar surface, is about 2.0 at the root of the supporting columns. Such a high level of stress concentration may incur fatigue failure of welding joint, leading to detachment of supporting columns. The stress concentration can
be relieved by increasing the transition fillet radius for welding, which provides smooth transition from the target surfaced to shunt structure. For example, the numerical analysis indicates the stress centration factor is reduced to 1.9 if the fillet radius is 3 mm. Alternatively, decreasing the shunt sheet thickness or diameter of the supporting columns can reduce the force on the shunt structure, then the stress concentration near the column root is controlled. For example, the numerical analysis suggests the stress centration factor is reduced to 1.9 if the shunt sheet thickness is reduced from 1.9 mm to 1.1 mm. However, dimension reduction of the shunt sheet is insufficient to solve the challenge of the stress concentration, redesign of the connection of supporting columns and target surface is demanded.
4.3. Linearity and sensibility Experimental loading test has demonstrated the linear response of the strain shunt structure to the tensile loading, while the constancy of shunt ratio under the compressive loading is essential for the application of alternating loading. Although the compressive loading test is not supported by the current experimental loading test equipment, it is conducted by the FEA model via simply reversing the loading direction. Thereby, the compressive loading of 500 kN is applied to the loading bar by reversing the loading force direction in the previous numerical model of tensile loading. The constancy of shunt ratio is confirmed by the cases with purely tensile or compressive loading of 500 kN and 250 kN, listed in Table 4. Exempted from experimental errors such as digitalization error, gauge factor deviation, loading test control error, the linear response of the strain shunt can be validated by the numerical study. Case 1–4 in Table 4 confirms the stability of the shunt ratio, regardless of loading direction or magnitude. However, the strain shunt ratio under the purely bending load is found constant but different from that of purely compressive or tensile load. Case 5–8 in Table 4 shows the shunt ratio for the bending loads is stable as 0.3494, regardless of the bending loads direction and magnitude. The purely bending force results in not only strain but also deflection on the bar surface where strain shunt is installed. According to Fig. 7, the purely bending force does not change the length of the neutral plane of the beam, and beam surface strain is proportional to the distance to the neutral plane and the local deflection angle .
ıi = Lεi =
h 2
(22)
The purely bending load leads to a larger deformation of the strain shunt between the supporting columns at the height of the shunt sheet h2 + H. Therefore, a bigger shunt ratio is expected, due
132
Q. Xia, F. Quail / Sensors and Actuators A 241 (2016) 124–134
Table 4 Y-axis normal strain FEA result based on welding fillet 2 mm. Case number Tensile loading ft (kN) Bending loading fb (kN) Strain on bar SA4 () Shunt strain upper SA1 () Shunt strain lower SA2 () Average shunt ratio 1 2 3 4 5 6 7 8 9 10
500 250 −250 −500 0 0 0 0 250 250
0 0 0 0 1.0 2.0 −1.0 −2.0 1.0 −1.0
1755 877.8 −877.8 −1755 518 1036 −518 −1036 1404 362.8
106.2 53.24 −53.24 −106.2 141.7 282.5 −141.7 −282.5 −88.12 194.6
357.6 178.9 −178.9 −357.5 220.3 440.6 −220.3 −440.6 −41.45 399.7
0.1321 0.1321 0.1321 0.1321 0.3494 0.3494 0.3494 0.3494 N.A. N.A.
Fig. 7. Schematic of deformation of strain shunt structure under purely bending load.
Fig. 8. Y axis normal strain on the bottom surface of shunt sheet, actuated by 10 Hz triangle wave load.
to the additional deformation on the shunt sheet induced by the bending deformation of the target surface, see Eq. (22)–(23).
ıi
shunt
=
h 2
+H
(23)
Thereby, the deformation on the bar surface ␦i between the supporting column is less than the potential deformation of the shunt
Q. Xia, F. Quail / Sensors and Actuators A 241 (2016) 124–134
sheet and supporting cantilever, ıi Eq. (24). ıi
shunt
=
h 2
+H
=2
shunt ,
FH 3 LF + 3Ec Ic As Es
and Eq. (1) is rewritten as
(24)
Accordingly, the extra deformation of H resutlts in a larger shunt ratio, and it is approximately (2H/h + 1) times of rs . For the current design of strain shunt (2H/h + 1) = 2.6, a bigger shunt ratio for the bending load is confirmed by the numerical study. Table 4 shows a multiple of 2.6 for the averaged shunt ratio; it is suggested the shunt ratio for the purely bending load can also be estimated. This error could be explained by the deflection of the supporting columns which reduce the extra deformation H. Compared with conventional metal thin film strain gauges, the strain shunt structure has a drawback that the bending and tensile/compressive loads result in different shunt ratios if the shunt height H is not neglectable with respect to the target structure, i.e. h/2 > >H. However, installing two strain shunt structures on both sides of target bar can address this inconvenience. Similarly, it is necessary to install two strain gauges on both side of a beam to distinguish the tensile-compressive force and the bending force. This strategy can be applied to the strain shunt, once the tensile and bending strain shunt ratios are identified. For example, adding the case 9 of ft = 250 kN and fb = 1 kN with the case 10 of ft = 250 kN and fb = −1 kN results in the strain values equal to those of case 1 (purely tensile loading ft = 500 kN) on both lower and upper surfaces of the shunt sheet. Meanwhile, subtracting case 10 from case 9 in Table 4 results in strain values of the purely bending case, as shown in case 6. Thereby, the bending force and tensile/compressive force can be derived, if multiple strain shunts are properly configured. 4.4. Dynamic response The dynamic response of the shunt structure is crucial for the measurement of large dynamic strain. For the beam structure fixed at the both ends under the tensile/compressive perturbation, the model response of the beam can be predict theoretically [24]. 2i − 1 fi = 4Lb
E (i = 1, 2. . .n) l
(25)
where fi is the characteristic frequencies and E is the elastic modulus and Lb is the length of the beam, l is the line density of the beam under compression. Eq. (25) also applies to the shunt sheet whose both ends are constrained by the supporting columns. For the steel bar under loading tests Lb = 1 m, the first characteristic frequency f1 is about 49 Hz, secondary frequency f2 is 146 Hz. Meanwhile, the first characteristic frequency f1 is 162 Hz for the shunt sheet length Lb = 0.04 m, which is higher than that of the target structure. Since the shunt sheet normally has a smaller cross-section thus lower line density than the target structure, the resonance of strain shunt is less concerned. In addition, considering the smaller dimension of the strain shunt structure, the dynamic response characteristics of the target structure is not likely to be altered by the strain shunt installation. Furthermore, the matched phase and amplitude of forced dynamic response between the shunt sheet and the target surface is confirmed by the numerical study. Temporal variation of Y-axis tensile and compressive loading as a triangle wave function is applied to the one end of the bar while the other end is fixed. A dynamic tensile loading of 10 Hz, which is sufficient for the applications such as the structural health monitoring of wind turbine tower, is investigated numerically. Fig. 8 shows neither phase delay nor waveform distortion between the strain probed at the centre of the lower surface of the shunt sheet (SA2) and that of the target bar surface beneath (SA4). The strain peaks coincide at t = 0.025s, matching the
133
peak of tensile loading force on the bar. Double Y-axis is used to correlate the temporal variation of the strain on the target surface and that of the lower surface of the shunt sheet. The Y-axis on the left is scaled down by the shunt ratio 0.204, thus the dot line and the solid line coincides in Fig. 8. The excellent agreement indicates the strain shunt has a good frequency response to the dynamic loading up to 10 Hz.
5. Conclusion In this paper, the concept of the strain shunt is proposed to address the challenge of measuring large dynamic strain over a long period. The working principles are illustrated by theoretical analysis of the simplified one dimensional model. The prototype of strain shunt structure consisting of one shunt sheet and two supporting columns has been experimentally studied, and the linearity and stability of shunt ratio is confirmed by the tensile load experiments. Moreover, the response of strain shunt to compressive and bending force is evaluated by finite element analysis. It is found purely bending loads result in another shunt ratio and at least two strain shunts are required to distinguish the tensile and bending loads. Nevertheless, this prototype design of strain shunt invites further improvement to solve the stress concentration and inconvenient installation.
References [1] M.D.C. Segovia Garcia, M.J.T. Revie, F. Quail, Condition monitoring data in the study of offshore wind turbines’ risk of failure, in: Proceedings of the 19th AR2TS Advances in Risk, Reliability and Technology Symposium, ASME, 2013. [2] C.C. Ciang, J.-R. Lee, H.-J. Bang, Structural health monitoring for a wind turbine system: a review of damage detection methods, Meas. Sci. Technol. 19 (2008) 122001. [3] A. Hamilton, F.J. Quail, Detailed state of the art review for the different on-line/in-line oil analysis techniques in context of wind turbine gearboxes, J. Tribol. 133 (2011). [4] ASM International, ASM Handbook Volume 1, Properties and Selection: Irons, Steels, and High-Performance Alloys, USA, 1990, pp. 793-800800. [5] Vishay Micro-Measurements, Strain Gage Selection: Criteria, Procedures, Recommendations, Tech Note TN-5052007. [6] P. Kayser, J. Godefroy, L. Leca, High-temperature thin-film strain gauges, Sens. Actuators A: Phys. 37 (1993) 328–332. [7] T. Sugimoto, H. Furukawa, Y. Uchino, Strain gauge for measuring large strains, Google Patents 2010. [8] J.M. López-Higuera, L. Rodriguez Cobo, A. Quintela Incera, A. Cobo, Fiber optic sensors in structural health monitoring, Lightwave Technol. J. 29 (2011) 587–608. [9] Vishay Micro-Measurements, Introduction to Stress Analysis by the PhotoStress® Method, Vishay Tech Note TN-702-22005. [10] T.K.B. Günther, Optical Versus Electrical Strain Aages: A Comparison, HBM Measurements, Germany, 2007. [11] J. Roths, A. Wilfert, P. Kratzer, F. Jülich, R. Kuttler, Strain calibration of optical FBG-based strain sensors, (EWOFS’10) fourth European workshop on optical fibre sensors, Int. Soc. Opt. Photonics (2010), 76530F-F-4. [12] S. Yang, B. Zhou, T. Sun, K.T. Grattan, A novel optical sensor platform designed for wireless sensor networks, J. Phys. Conf. Ser. (2013) 012007, IOP Publishing. [13] M. Komachiya, R. Minamitani, T. Fumino, T. Sakaguchi, S. Watanabe, Proof-testing and probabilistic lifetime estimation of glass fibers for sensor applications, Appl. Opt. 38 (1999) 2767–2774. [14] Y.-N. Cheung, Y. Zhu, C.-H. Cheng, C. Chao, W.W.-F. Leung, A novel fluidic strain sensor for large strain measurement, Sens. Actuators A: Phys. 147 (2008) 401–408. [15] I. Kang, M.J. Schulz, J.H. Kim, V. Shanov, D. Shi, A carbon nanotube strain sensor for structural health monitoring, Smart Mater. Struct. 15 (2006) 737. [16] T. Yamada, Y. Hayamizu, Y. Yamamoto, Y. Yomogida, A. Izadi-Najafabadi, D.N. Futaba, et al., A stretchable carbon nanotube strain sensor for human-motion detection, Nat. Nanotechnol. 6 (2011) 296–301. [17] K. Peters, Polymer optical fiber sensors—a review, Smart Mater. Struct. 20 (2011) 013002. [18] C. Rembe, R. Kant, R.S. Muller, Optical measurement methods to study dynamic behavior in MEMS, lasers in metrology and art conservation, Int. Soc. Opt. Photonics (2001) 127–137. [19] L. Matthaei, Microwave Filters, Impedance-matching Networks, and Coupling Structures, McGraw-Hill, New York, 1964. [20] O. Bauchau, J. Craig, Euler-Bernoulli beam theory, Structural Analysis, Springer, 2009, pp. 173–221.
134
Q. Xia, F. Quail / Sensors and Actuators A 241 (2016) 124–134
[21] C.E. Augarde, A.J. Deeks, The use of Timoshenko’s exact solution for a cantilever beam in adaptive analysis, Finite Elem. Anal. Des. 44 (2008) 595–601. [22] R.C. Juvinall, K.M. Marshek, Fundamentals of Machine Component Design, 4th ed., J. Wiley, New York, 2006. [23] W.J. Wright, Steel Bridge Design Handbook: Bridge Steels and Their Mechanical Properties, 2012. [24] S.G. Kelly, Mechanical Vibrations: Theory and Applications, Cengage Publishing, 2012.
Biographies Dr Qingfeng Xia obtained his Ph.D. degree from Manchester University in March 2012. Currently, he is a researcher in the Osney Thermo-fluid Lab, Oxford University. His research interests include fluid visualization, condition monitoring of turbomachines, and sensor and instrumentations.
Prof. Francis Quail (CEng, FIMechE, FCMI, FIES) was director of turbomachine group, School of Engineering Science, University of Glasgow.