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A novel multi-component strain-gauge external balance for wind tunnel tests: Simulation and experiment
Sensors and Actuators A 247 (2016) 172–186
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Sensors and Actuators A: Physical journal homepage: www.elsevier.com/locate/sna
A novel multi-component strain-gauge external balance for wind tunnel tests: Simulation and experiment A.R. Tavakolpour-Saleh ∗ , A.R. Setoodeh, M. Gholamzadeh Department of Mechanical and Aerospace Engineering, Shiraz University of Technology, Shiraz, Iran
a r t i c l e
i n f o
Article history: Received 13 March 2016 Received in revised form 4 May 2016 Accepted 30 May 2016 Available online 1 June 2016 Keywords: Multi-component external balance Wind tunnel Strain gauge
a b s t r a c t This paper presents a novel multi-component strain-gauge external balance to measure lift and drag forces as well as pitching moment in wind tunnel experiments. First, an innovative structure is proposed and its geometry is determined through a tedious trial and error scheme using finite element (FE) simulation. The sensor dimensions are thus chosen so as to acquire acceptable sensitivity and negligible interference error among the components considering maximum loading capacities. Appropriate locations of the strain gauges on the structure are determined via simulation. Then, sensitivities of the balance components are found using the FE analysis. Finally, the designed external balance is constructed and calibrated. It is found that the interference error among the balance components is less than 2.01%. Furthermore, the measured sensitivities of the sensor components are in a good agreement with the simulation results through which the design procedure is validated. © 2016 Elsevier B.V. All rights reserved.
1. Introduction Load cells are known as the most commonly used transducers employed in the wind tunnel balances to measure aerodynamic forces and moments affecting the model of a flying object. Nowadays, industrial load cells are manufactured in different forms and capacities. However, the majority of the load cells available in the market are single-component. On the other hand, single component load cells are not solely sufficient to measure multi-directional aerodynamic loads in the wind tunnel tests. As a solution to this latest problem, several single-component load cells may be installed within a mechanical framework so that each single-component load cell is responsive to a specific direction. Such transducers are usually called multi pieces external balances in the wind tunnel applications [1]. Although the mentioned technique is widely used in the wind tunnel experiments, the accuracy of such balances is significantly dependent on the accuracy of the machining process in constructing the mechanical framework of the balance system. Besides, the multi pieces external balances require more space in the wind tunnel. Another alternative for measurement of the multi-directional loads in the wind tunnel tests is known as the multi-component load cells. The multi-component
∗ Corresponding author. E-mail addresses: [email protected], [email protected] (A.R. Tavakolpour-Saleh). http://dx.doi.org/10.1016/j.sna.2016.05.035 0924-4247/© 2016 Elsevier B.V. All rights reserved.
load cells are usually referred to as one-piece external balances in the wind tunnel applications which are constructed from one single piece of material and are equipped with strain gauges [1]. Unfortunately, the multi-component load cells are rarely found in the market. It can be attributed to the fact that the users usually require different loading capacities in different directions. Consequently, the load cell manufacturers cannot commercially provide the multi-component load cells with very versatile combinations of loading capacities. Thus, such multi-component load cells are usually designed and manufactured based on the user requirements. The most challenging problem in designing such multi-component load cells is known as the interference error among the components. Hence, the designers attempt to reduce this error as best as possible. Different geometries and dimensions have been reported in the literature for such multi-component load cells each of which contains some advantages and drawbacks. Many researchers proposed various multi-component load cells for different applications i.e. wind tunnel, water channel, robotics etc. Dubois [2] investigated the design, equipment, thermal effects compensation, and calibration of various multi-component straingauge balances used in large subsonic and supersonic wind tunnels. Molland [3] presented a five-component strain gauge load cell for wind tunnel tests. A shear-type aluminum sensing structure along with full bridge strain gauge circuitry was employed for each component. The bridge circuits including 120 strain gauges were excited by a 7 V potential difference. The accuracy of the dynamometer was found to be ±1.2% of full scale (FS) for torque and
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Fig. 1. Proposed sensing structure of the multi-component strain gauge external balance.
Fig. 2. Location of the strain gauges in the corresponding Wheatstone bridge circuit.
±0.4% FS for the remaining components. An acceptable repeatability characteristic, as well as relatively small interaction, was reported in this work. Almeida et al. [4] proposed a ring-type strain gauge-based sensing structure for wind-tunnel experiments. This balance was used to measure the lift and drag forces and the pitching moment. High-quality results with acceptable dynamic characteristics (up to 25 Hz) were reported. The first natural frequency of the structure was 250 Hz which was ten times the maximum used frequency in the calibration stage. Tavakolpour-Saleh and Sadeghzadeh [5] designed and developed a three-component force/moment load cell for underwater hydrodynamic tests. Finite element method (FEM) was used to design the sensing structure and to determine the suitable locations of strain gages as well. Experimental evaluation of the proposed three-component load cell revealed an interference error less than 2.25%. A six-axis wrist force/moment sensor for robotic arms was designed by Kim [6] using FEM. An interference error less than 2.85% was reported from the experimental measurements. Sun et al. [7] designed and optimized a novel six-axis force/torque sensor for a space robot. They proposed a novel sensing structure with
the through-hole beam. The presented sensor dimensions were optimized via response surface methodology (RSM). Finally, the experimental results revealed a good performance of the proposed multi-component force/torque sensor. Kang et al. [8] proposed an intentional stress concentration approach based on the application of binocular sensing structure to increase the sensitivity of a sixcomponent load cell. The dimensions of the sensing structure were thus optimized using FE analysis. In addition, the influence of different structural dimensions on the strain distribution of critical points was investigated. Finally, the interference error was reported less than 2.5% FS. Kim et al. [9] designed and fabricated a column type multi-component force/moment transducer. The structural dimensions were first found analytically and later, verified by finite element analysis. A decoupling method based on addition and subtraction processes of signals of the strain gauges were proposed to reduce the interference error. As a result, the interference errors were found to be 7.3% FS for Fx component and 5% FS for the rest of components. Liu and Tzo [10] presented a novel six-component force sensor. They utilized four identical T-shaped bars as force sensing structure of the mentioned transducer. They applied FE
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Fig. 3. Installation method of the external balance in the wind tunnel.
Fig. 4. Meshing method of the sensing structure.
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Fig. 5. Finite element simulation of the sensing structure under lift force (a) strain along x-direction (b) strin along y-direction.
Table 1 Loading capacities of the balance components. Component
Lift (N)
Drag (N)
Pitching moment (Nm)
loading capacity
300
50
60
optimization to obtain maximum sensitivity. However, a significant interference error was reported for their design. In this paper, a three-component strain-gauge one-piece external balance with a novel sensing structure is designed and developed for wind tunnel measurements so that a negligible interference error among the balance components is found. First, a suitable sensing structure is proposed and its dimensions are optimized using FE analysis based on the design requirements. Different mechanical analyses are carried out in designing the sensing structure. Then, suitable locations for installation of the strain gauges on the sensing structure are determined. Finally, the proposed multi-component external balance is developed and the obtained simulation results are verified. 2. Design requirements The multi-component external balance was to be capable of measuring three components such as lift and drag forces as well as pitching moment in the subsonic open wind tunnel of the Shiraz University of Technology. To meet the experimental requirements, the following maximum design loads were considered: Lift, 300 N; Drag, 50 N; Pitching moment, 60 Nm. The dynamic loadings were to be measured effectively up to 10 Hz and hence, the first natural frequency of the load cell structure was considered 10 times the
mentioned frequency as it was reported in Ref. [4]. The required accuracy was 0.2% FS that was similar to that of the commercial single component load cells and the maximum allowable weight of the model was 30 kg. The projectile area of the one-piece external balance should be chosen small to reduce the drag effect on the sensing structure. Table 1 summarizes the loading capacities of the load cell components which must be considered in the design scheme. 3. Proposed sensing structure and bridge circuits The multi-component balance must be designed such that the interference error among the components is reduced as best as possible. Moreover, in order to achieve the required accuracy presented in Section 2, the external balance should be sensitive enough. The sensitivity issue is even more significant for dynamic measurements which are essential for calculation of stability derivatives of a flying object for control applications. Besides, in order to study the flutter of the gas turbine blades, dynamic loadings need to be measured. Consequently, the design scheme was aimed at minimizing the interference error among the balance components as well as increasing the balance sensitivity taking into account the structure strength. It is obvious that increasing the sensitivity results in a more flexibility of the sensing structure, which may eventually lead to structural failure. Following the previous works on multi-component load cell structures [5,8], an innovative binocular-like sensing structure was proposed in this investigation. The proposed structure was achieved through a rigorous trial and error scheme based on the evaluation and integration of different flexible structures presented in the literature [5,8]. Fig. 1 demon-
Table 2 Summary of the simulation results obtained from FE analysis. Lift
ε11 536
ε6 536
ε7 −427
ε8 −427
11 + 6 − 7 − 8 1926
Sensitivity 1.01 mV/V
Drag
ε12 501
ε5 479
ε10 −479
ε9 −501
ε12 + ε5 − ε10 − ε9 1960
Sensitivity 1.08 mV/V
Moment
ε1 582
ε3 421
ε2 −582
ε4 −421
ε1 + ε3 − ε2 − ε4 2006
Sensitivity 0.96 mV/V
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Fig. 6. Strain distribution on the bottom-hand surface (along x-direction).
strates the proposed sensing structure of the multi-component external balance considered in this investigation. The sensing structure thickness was considered as 30 mm. Besides, the locations of the strain gauges are also depicted in the figure. Each strain gauge is denoted by a number in this figure. As can be seen in this figure, the intentional stress concentration technique was used to increase the sensitivity. The sensing structure was designed so that the locations of the strain gauges were on the outside surface of the structure, which resulted in an easier installation process of the strain gauges. Eight design parameters denoted by t1 , t2 , t3 , w1 , w2 , w3 , h1 and h2 were considered as shown in Fig. 1. Thus, the design parameters were chosen so as to achieve the design requirements. It will be discussed with more details in the next section. Three Whetstone full-bridge circuits corresponding to each balance component were considered in this work. Fig. 2 demonstrates the position of each strain gauge in the Whetstone bridge circuits. According to the whetstone bridge of the moment component (see Fig. 2), the output voltage of the bridge circuit can be expressed as [11]:
R3 and R4 . The change of output voltage (Vo ) can be written as: Vo =
(R1 + R1 )(R3 + R3 ) − (R2 + R2 )(R4 + R4 ) V (R1 + R1 + R2 + R2 )(R3 + R3 + R4 + R4 ) i
If the resistance changes of the strain-gauges are assumed too small, then the terms Ri Ri in the numerator and the terms Ri Ri and Ri Ri in the denominator can be ignored, Consequently, Eq. (2) can be simplified as follows: Vo = Vi
R1 R2 (R1 + R2 )2
(
R1 R2 R3 R4 − + − ) R1 R2 R3 R4
(1)
where Vo is the output voltage of Wheatstone bridge, Vi is the input voltage of Wheatstone bridge and R1 –R4 are the initial resistances of the strain gauges in each arm. It is clear that the output voltage of the bridge is zero (i.e., the bridge is balanced) when R1 R3 = R2 R4 . Consider an initially balanced bridge, so that Vo = 0 and then resistances R1 , R2 , R3 , and R4 are changed by the amounts R1 , R2 ,
(3)
The gauge factor of a strain gauge is defined as [11]: GF =
R/R ε
(4)
where GF is the gauge factor, R is the initial resistance of the strain gauge, R denotes the resistance change of the strain gauge and ε is the axial strain. Consequently, Eq. (3) can be rewritten based on the concept of Gauge factor (as defined by Eq. (4)) as, Vo = 0.25GF Vi (ε1 + ε3 − ε2 − ε4 )
R1 R3 − R2 R4 Vo = V (R1 + R2 )(R3 + R4 ) i
(2)
(5)
where 1 and 3 are the strains of the gauges under tension while 2 and 4 are the strains of the gauges under compression. Eq. (5) is the constitutive equation of the strain gauge bridge circuits in the commercial load cells. According to Eq. (5), the change of output voltage of a bridge circuit is proportional to the combination of strains as (1 + 3 − 2 − 4 ). Thus, in order to have the maximum sensitivity, two strain gauges must be in tension state while the rest of them must be in the compression state. Besides, if the strain gauges are placed at high-stress positions on the structure, a higher sensitivity can be expected. Taking into account the outlined considerations,
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Fig. 7. Strain distribution on the left-hand surface (along y-direction).
Table 3 First five natural frequencies of the sensing structure. Mode
1
2
3
4
5
Frequency (Hz)
98
242
363
438
451
the structure of the proposed three-component external balance is designed in the next section using FE analysis. Fig. 3 demonstrates the installation method of the proposed external balance in the wind tunnel. It can be seen that the proposed external balance is constrained from the top side while it is free to deflect from the bottom side where it is attached to the model. 4. Strain analysis of the balance structure using FEM In this study, ANSYS software was used to design and analyze the sensing structure based on FEM. Different element types were previously employed to mesh such a sensing structure [5,12]. In this work, element type Solid 186 was proposed. Solid 186 is a higher order 3D 20-node solid element that exhibits quadratic displacement behavior, which increases the accuracy of the analysis. This element type possesses three degrees of freedom (DOF) per node and is suitable for large deflections. Fig. 4 depicts the mapped meshing of the sensing structure using element type solid 186 in ANSYS software. The number of elements was selected such that the convergence of the results was obtained. Moreover, the number of elements was increased around the regions possessing stress concentration in order to have more accurate results. Different material can be used to construct the sensing structure taking into account the working conditions [13]. Although the standard aeronautical steel can be effectively used to develop
the sensing structure, the 7075 aluminum alloy was utilized in this research because of its lower initial cost and machining time. Besides, successful application of this material was previously reported in Refs. [5,10]. The Young’s modulus and Poisson’s ratio of this aluminum alloy were 72 GPa and 0.33 respectively which were applied to the FE software. In designing the commercial single component load cells the strain value of 1000 (resulting in the rated sensitivity of 2 mV/V) is commonly considered at the gauge positions [14]. However, a lower rated sensitivity of about 1 mV/V at maximum capacity was used in this work to provide acceptable sensitivity and reduce the interference errors as well as the possibility of yielding by stress concentration [6,10]. As mentioned earlier, the most important challenging problem in designing the multi-component force/moment sensors is to minimize the interference errors among the components as best as possible. Hence, the sensing structure dimensions and the suitable positions of the strain gauges were investigated using FE analysis so that negligible interference errors were achieved. As it was shown in Figs. 1 and 2, the points 6, 11, 7 and 8 were considered for mounting the strain gauges of lift component. The FE analysis was thus employed to find the optimum values of the corresponding design variables t1 , t2 , h1 , and w1 so that the desirable rated strain was obtained at the gauge locations under maximum capacity of the lift component (see Table 1). The values of parameters t1 , t2 , h1 , and w1 were respectively found as 0.006 m, 0.0022 m, 0.038 m and 0.080 m. Similar to conventional binocular load cells the diameters of arches were considered as 0.012 m through which a suitable strain distribution was found for strain gauges with the gauge length of 3 mm. Fig. 5a and b respectively represent the strain distribution along x and y directions of the sensing structure under 300 N lift force. It can be seen that the points 6 and 11 experienced
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Fig. 8. Strain distribution on the right-hand surface (along y-direction).
tension state while the points 7 and 8 were under compression. The corresponding strain variations on the bottom, left and right surfaces of the sensing structure were plotted in Figs. 6–8 . It is obvious that the points 6, 11, 7 and 8 were more sensitive to the applied lift force. Thus, the strain values of 536 , 536 , −427 , and −427 were respectively found for the points 6, 11, 7, and 8. The middle part of the sensing structure was designed to measure the drag force and four locations denoted by points 12, 5, 9 and 10 were considered for installing the strain gauges (see Fig. 1). Fig. 9 demonstrates the strain distribution of the sensing structure under a 50 N drag force obtained from FEM simulation. As it can be observed, two strain gauges are in tension while other ones are in compression. The loading capacity of the drag component can be adjusted by changing the design parameters t2 , w2 , and h2 . For instance, by decreasing the parameter w2 and increasing the parameter t2 it is possible to increase the loading capacity of the drag component. Using the FEM analysis, the values of design parameters t2 , h2 and w2 were respectively obtained as 0.0022 m, 0.032 m, and 0.068 m considering the maximum loading capacity of the drag component. Figs. 10 and 11 respectively demonstrate the strain distribution along y-direction on the left and right surfaces of the external balance. The rated strain values of points 12, 5, 9 and 10 were found 501 , 479 , −501 and −479 respectively. The parameters affecting the moment capacity of the proposed wind tunnel balance were t1 , t3 , w3 , and h1 . Thus, the values of the mentioned parameters were found using the FE analysis considering the maximum moment capacity of 60 Nm and rated sensitivity of 1 mV/V. Consequently, the corresponding values of t1 , t3 , w3 and h1 were respectively found as 0.006 m, 0.00935 m, 0.124 m and 0.038 m. The simulated sensing structure under the effect of a 60 Nm moment was shown in Fig. 12. The points 1, 2, 3, and 4 were
considered for installing the strain gauges of moment component. It is clear that the points 1 and 3 are in tension state and the points 2 and 4 are in the compression state. Figs. 13 and 14 demonstrate the strain values along x-direction on the bottom and top surfaces of the external balance respectively. According to Fig. 13, higher strain values were found at the points 8 and 7, however, the points 3 and 4 were selected for the moment component. It was because of a lower interference error between the moment and lift components that could be achieved by this configuration. Finally, the strain values at the points 1, 2, 3, and 4 were respectively obtained as 421 , −421 , 582 , and −582 respectively. Table 2 summarizes the obtained results of the structure design using the FEM simulation. It can be seen that the final sensitivities of the lift, drag, and moment components were found 1.01 mV/V, 1.08 mV/V, and 0.96 mV/V respectively taking into account a gauge factor of 2.13. 5. Interference errors, natural frequencies, and structural strength As mentioned earlier, in designing the multi-axis wind tunnel balances it is too important to minimize the interference errors among the components. Hence, the proposed sensing structure was subjected to single-axis loading and its influence on other components was investigated using FEM simulation. The simulation results revealed that the interference error was 0% for all components and it is one of the main benefits of the proposed sensing structure. Another important consideration affecting the multi-axis external balances was on the dominant natural frequencies of the sensing structure. This latest issue was even more significant when dynamic loadings need to be measured. Therefore, the modal analy-
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Fig. 9. Finite element simulation of the sensing structure under drag force (a) strain along y-direction (b) strain along x-direction.
Fig. 10. Strain distribution on the left-hand surface (along y-direction).
sis was carried out within the FEM simulation platform and the first five natural frequencies of the sensing element were investigated. Figs. 15–19 respectively represent the first five resonant modes of the sensing structure obtained from the FEM simulation. As can be seen, the first, third and fourth modes belong to the drag, lift and moment components respectively. The values of dominant natural
frequencies are given in Table 3. Since the first natural frequency corresponding to the drag component occurred at 98 Hz, the external balance could be used to measure dynamic loads up to 10 Hz as discussed in Section 2. Consequently, the designed sensing structure possessed a suitable dynamic characteristic which fulfilled the design requirements.
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Fig. 11. Strain distribution on the right-hand surface (along y-direction).
Fig. 12. Finite element simulation of the sensing structure under pitching moment.
Another important consideration, which must be taken into account, was on the strength of the structure under full-loadings. Consequently, the pitching moment together with the lift and drag forces were applied simultaneously to the balance structure and
von Mises stress analysis was implemented under full loadings as shown in Fig. 20. The maximum von Mises stress was found 138 MPa which was much smaller than the yield stress of 7075 aluminum alloy (which was about 500 MPa). As a result, a safety
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Fig. 13. Strain distribution on the bottom surface under a moment of 60 Nm (along x-direction).
Fig. 14. Strain distribution on the top surface under a moment of 60 Nm (along x-direction).
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Fig. 15. First resonance mode of the sensing structure.
Fig. 16. Second resonance mode of the sensing structure.
Fig. 17. Third resonance mode of the sensing structure.
Fig. 18. Fourth resonance mode of the sensing structure.
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Fig. 19. Fifth resonance mode of the sensing structure.
Fig. 20. von Mises stress analysis under full loadings.
factor of 3.6 was obtained through FE analysis. Besides, it was safe to carry 30 kg weight considering a safety factor of 3.0. 6. Experimental study The structure of the external balance was made of 7075 aluminum alloy using a wire-cutting machine considering a tolerance of ±0.01 mm. The strain gauge FLA-3-350-23 from Tokyo Sokki Kenkyujo Company was adopted to use in this work. The gauge factor and the gauge resistance were 2.13 ± 1% and 350 ± 1.0 respectively. Such high-resistance strain gauges were intentionally used to increase the bridge circuit sensitivity which is an important requirement to measure the dynamic loads. The gauge length was 3 mm that was similar to that of the conventional strain gauges used in commercial load cells. The strain gauges were bonded to the flexures using polyester adhesive (P-2) to provide a long term of use. The manufacturer’s recommendations for preparing the surface before bonding the strain gauges as well as clamping pressure and curing time of adhesive were all followed. Fig. 21 demonstrates the strain gauge bridge circuit incorporating an instrument amplifier employed in this investigation. Three similar circuits were thus used for the three components of the external balance. Each bridge circuit was excited by a 5 V stabilized D.C. potential difference. The output voltage of each bridge circuit was amplified using an instrument amplifier. The amplifier gain K was considered 501. A balancing potentiometer as shown in Fig. 21 was used to balance
the bridge circuit in order to eliminate the offset voltage due to the initial weight of the sensing structure. Fig. 22 depicts the final developed multi-component one-piece external balance. The locations of strain gauges on the hosted structure can be clearly seen in this photograph. A digital voltmeter with accuracy of ±0.1 mV was utilized to measure the output voltage of the amplifier circuit. Fig. 23 illustrates the calibration scheme considered in this investigation in which forces and moment of known magnitudes and directions were individually applied to the developed balance system. Fig. 23a demonstrates the calibration test of the drag component in which unidirectional known forces are applied to the balance structure so as to excite the drag component individually. Similar calibration schemes were repeated for the lift and moment components of the external balance system as shown in Fig. 23b and c. Such calibration tests are very conventional in multi-component load cells calibration (see Refs. [3–5,14]). The calibration masses were checked relative to certified standards. Two objectives were followed in the calibration experiment. First, it was essential to measure the sensitivity of each component (or the calibration slope) and second, it was important to investigate the interference errors among the balance components. Figs. 24–26 respectively show the calibration curves for the lift, drag and moment components. The calibration slope of lift component was measured 0.0077 V/N which resulted in a sensitivity of 0.924 mV/V (see Fig. 24). The calibration slope and the corresponding sensitivity of the drag component were mea-
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Fig. 21. Strain gauge bridge circuit incorporating instrument amplifier.
Fig. 22. Photograph of the developed multi-component external balance.
sured 0.0546 V/N and 1.09 mV/V respectively (see Fig. 25). Finally, the calibration results for moment component revealed the calibration slope of 0.038 V/Nm and the corresponding sensitivity of 0.938 mV/V for the moment component (see Fig. 26).
Finally, the accuracy of the external balance components was estimated about 0.14% FS by applying the known certified calibration masses to the balance system and comparing this mathematically with the transducer output signal to calculate the an average error as a percentage of the full-scale output using several tests. It is found that the estimated accuracy was close to the value reported by Molland [3]. One should keep in mind that the accuracy is usually defined as the value of uncertainty existing in the sensor output which is expressed as a percentage of full-scale output. However, in wind tunnel applications, the accuracy of a balance is influenced by many factors such as wall and sting interactions, the precision of the model geometry, flow quality, the angle of attach and balance uncertainty. Since there are so many potential errors, it becomes difficult to specify the accuracy for a wind tunnel test. Thus, the balance uncertainty alone must be taken into account through balance calibration [1] as it was done in the paper. As mentioned earlier, the most challenging problem in designing the multi-component balance is to minimize the interference errors as best as possible and it is a key issue considered in many investigations as outlined in the introduction section. In this research, an attempt was made to measure the interference errors among the balance components. Hence, the calibration scheme described in Fig. 23 was repeated to find the interference errors. The final results are given in Table 4. It can be observed all interference errors are less than 2.01%. Furthermore, the highest interactions were due to the effect of the moment on the lift and drag components.
Fig. 23. Photographs of calibration scheme, (a) drag, (b) lift, (c) moment.
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Fig. 24. Calibration curve for lift component (the output voltage of the bridge circuit has been amplified up to 501 times).
Fig. 25. Calibration curve for drag component (the output voltage of the bridge circuit has been amplified up to 501 times).
Table 4 Measured interference errors among the balance components. Interference error (%)
Drag = 50 N Lift = 300 N Pitching moment = 60 Nm
Drag
Lift
Moment
– 0.6 1.86
1.17 – 2.01
0.55 0.3 –
7. Conclusion A multi-component strain-gauge one-piece external balance with a novel sensing structure was presented in this article for wind tunnel experiments. The sensing structure geometry was acquired through a tedious trial and error scheme. An optimization scheme was conducted to find the suitable dimensions of the sensing structure using FEM simulations and taking into account the design requirements. Using the converged results of the FEM sim-
ulation, the sensitivities of the balance components were found to be 1.01 mV/V, 1.08 mV/V and 0.96 mV/V for lift, drag and moment components respectively. The simulation outcomes were further verified through experiment. The sensitivities of the sensor components were respectively measured 0.924 mV/V, 1.09 mV/V and 0.938 mV/V for lift, drag and moment components through calibration tests. Consequently, the calibration results revealed a good agreement with the simulation outcomes through which the validity of the design procedure was affirmed. The interference errors among the balance components were less than 2.01%. Thus, the proposed sensing structure provided a smaller interference errors compared to the previous work presented in Ref. [5]. The accuracy of the balance components was found about 0.14% FS which was close to the value reported in Ref. [3]. Finally, the first resonant frequency of the sensing structure was at 98 Hz for drag component which fulfilled the design requirements.
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Fig. 26. Calibration curve for moment component (the output voltage of the bridge circuit has been amplified up to 501 times).
Acknowledgement The authors would like to acknowledge the Shiraz University of Technology (SU Tech) for providing research facilities and funding. References [1] C. Tropea, A.L. Yarin, J.F. Foss, Springer Handbook of Experimental Fluid Mechanics, Springer, 2007. [2] M. Dubois, Six-component strain-gauge balances for large wind tunnels, J. Exp. Mech. (1981) 401–407. [3] A.F. Molland, A five-component strain gauge wind tunnel dynamometer, J. Strain 12 (1) (1978) 7–13. [4] R.A.B. Almeida, D.C. Vaz, A.P.V. Urgueira, A.R. Janeiro Borges, Using ring strain sensors to measure dynamic forces in wind-tunnel testing, J. Sens. Actuators A 185 (2012) 44–52. [5] A.R. Tavakolpour-Saleh, M.R. Sadeghzadeh, Design and development of a three-component force/moment sensor for underwater hydrodynamic tests, J. Sens. Actuators A 216 (2014) 84–91. [6] G.S. Kim, Design of a six-axis wrist force/moment sensor using FEM and its fabrication for an intelligent robot, J. Sens. Actuators Phys. 133 (2007) 27–34. [7] Y. Sun, Y. Liu, T. Zou, M. Jin, H. Liu, Designa and optimization of a novel six-axis force/torque sensor for space robot, J. Meas. 65 (2015) 135–148. [8] D.I. Kang, G.S. Kim, S.Y. Jeoung, J.W. Joo, Design and evaluation of binocular type six-component load cell by using experimental technique, Trans. Korean Soc. Mech. Eng. 21 (11) (1997) 1921–1930. [9] J.H. Kim, D.I. Kang, H.H. Shin, Y.K. Park, Design and analysis of a column type multi-component force/moment sensor, J. Meas. 33 (2003) 213–219. [10] S.A. Liu, H.L. Tzo, A novel six-component force sensor of good measurement isotropy and sensitivities, J. Sens. Actuators A 100 (2002) 223–230. [11] T.G. Beckwith, R.D. Marangoni, J.H. Lienhard, Mechanical Measurements, 6th edition, Prentice Hall, 2006. [12] V.A. Kamble, P.N. Gore, Use of FEM and photo elasticity for shape optimization of S type load cell, Indian J. Sci. Technol. 5 (3) (2012) 2384–2389. [13] E. Doebelin, Measurement Systems, Application and Design, 5th edition, McGraw Hill, 2004, pp. 438–446. [14] J.W. Joo, K.S. Na, D.I. Kang, Design and evaluation of a six-component load cell, J. Meas. 32 (2002) 125–133.
Biographies
A.R. Tavakolpour-Saleh is an Assistant Professor in the Department of Mechanical and Aerospace Engineering, Shiraz University of Technology, Iran. He acquired his BSc and MSc degrees from the Shiraz University, Iran in 2002 and 2005 respectively and later, his Ph.D. in Mechanical and Mechatronics Engineering from the Universiti Teknologi Malaysia in 2010. His current research interests are Mechatronics, Instrumentation and Measurement, Adaptive and Intelligent Control, Active Vibration/Force Control, Robotics and Automation, System Identification and Energetic Systems. A.R. Setoodeh is an Associate Professor in the Department of Mechanical and Aerospace Engineering, Shiraz University of Technology, Iran. He obtained his BSc, MSc and Ph.D. in Mechanical Engineering, from the Shiraz University, Iran. His research interests are Finite Elements Method (FEM), Computational Mechanics, Nano-Mechanics, Nano-Composite Material and Machine Design.
M. Gholamzadeh is a graduate student of Mechanical Engineering in the Department of Mechanical and Aerospace Engineering, Shiraz University of Technology, Iran. His current research interests are Multi-Component Force/Moment Sensors, Finite Element Optimization, Computational and Solid Mechanics.
Contents lists available at ScienceDirect
Sensors and Actuators A: Physical journal homepage: www.elsevier.com/locate/sna
A novel multi-component strain-gauge external balance for wind tunnel tests: Simulation and experiment A.R. Tavakolpour-Saleh ∗ , A.R. Setoodeh, M. Gholamzadeh Department of Mechanical and Aerospace Engineering, Shiraz University of Technology, Shiraz, Iran
a r t i c l e
i n f o
Article history: Received 13 March 2016 Received in revised form 4 May 2016 Accepted 30 May 2016 Available online 1 June 2016 Keywords: Multi-component external balance Wind tunnel Strain gauge
a b s t r a c t This paper presents a novel multi-component strain-gauge external balance to measure lift and drag forces as well as pitching moment in wind tunnel experiments. First, an innovative structure is proposed and its geometry is determined through a tedious trial and error scheme using finite element (FE) simulation. The sensor dimensions are thus chosen so as to acquire acceptable sensitivity and negligible interference error among the components considering maximum loading capacities. Appropriate locations of the strain gauges on the structure are determined via simulation. Then, sensitivities of the balance components are found using the FE analysis. Finally, the designed external balance is constructed and calibrated. It is found that the interference error among the balance components is less than 2.01%. Furthermore, the measured sensitivities of the sensor components are in a good agreement with the simulation results through which the design procedure is validated. © 2016 Elsevier B.V. All rights reserved.
1. Introduction Load cells are known as the most commonly used transducers employed in the wind tunnel balances to measure aerodynamic forces and moments affecting the model of a flying object. Nowadays, industrial load cells are manufactured in different forms and capacities. However, the majority of the load cells available in the market are single-component. On the other hand, single component load cells are not solely sufficient to measure multi-directional aerodynamic loads in the wind tunnel tests. As a solution to this latest problem, several single-component load cells may be installed within a mechanical framework so that each single-component load cell is responsive to a specific direction. Such transducers are usually called multi pieces external balances in the wind tunnel applications [1]. Although the mentioned technique is widely used in the wind tunnel experiments, the accuracy of such balances is significantly dependent on the accuracy of the machining process in constructing the mechanical framework of the balance system. Besides, the multi pieces external balances require more space in the wind tunnel. Another alternative for measurement of the multi-directional loads in the wind tunnel tests is known as the multi-component load cells. The multi-component
∗ Corresponding author. E-mail addresses: [email protected], [email protected] (A.R. Tavakolpour-Saleh). http://dx.doi.org/10.1016/j.sna.2016.05.035 0924-4247/© 2016 Elsevier B.V. All rights reserved.
load cells are usually referred to as one-piece external balances in the wind tunnel applications which are constructed from one single piece of material and are equipped with strain gauges [1]. Unfortunately, the multi-component load cells are rarely found in the market. It can be attributed to the fact that the users usually require different loading capacities in different directions. Consequently, the load cell manufacturers cannot commercially provide the multi-component load cells with very versatile combinations of loading capacities. Thus, such multi-component load cells are usually designed and manufactured based on the user requirements. The most challenging problem in designing such multi-component load cells is known as the interference error among the components. Hence, the designers attempt to reduce this error as best as possible. Different geometries and dimensions have been reported in the literature for such multi-component load cells each of which contains some advantages and drawbacks. Many researchers proposed various multi-component load cells for different applications i.e. wind tunnel, water channel, robotics etc. Dubois [2] investigated the design, equipment, thermal effects compensation, and calibration of various multi-component straingauge balances used in large subsonic and supersonic wind tunnels. Molland [3] presented a five-component strain gauge load cell for wind tunnel tests. A shear-type aluminum sensing structure along with full bridge strain gauge circuitry was employed for each component. The bridge circuits including 120 strain gauges were excited by a 7 V potential difference. The accuracy of the dynamometer was found to be ±1.2% of full scale (FS) for torque and
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Fig. 1. Proposed sensing structure of the multi-component strain gauge external balance.
Fig. 2. Location of the strain gauges in the corresponding Wheatstone bridge circuit.
±0.4% FS for the remaining components. An acceptable repeatability characteristic, as well as relatively small interaction, was reported in this work. Almeida et al. [4] proposed a ring-type strain gauge-based sensing structure for wind-tunnel experiments. This balance was used to measure the lift and drag forces and the pitching moment. High-quality results with acceptable dynamic characteristics (up to 25 Hz) were reported. The first natural frequency of the structure was 250 Hz which was ten times the maximum used frequency in the calibration stage. Tavakolpour-Saleh and Sadeghzadeh [5] designed and developed a three-component force/moment load cell for underwater hydrodynamic tests. Finite element method (FEM) was used to design the sensing structure and to determine the suitable locations of strain gages as well. Experimental evaluation of the proposed three-component load cell revealed an interference error less than 2.25%. A six-axis wrist force/moment sensor for robotic arms was designed by Kim [6] using FEM. An interference error less than 2.85% was reported from the experimental measurements. Sun et al. [7] designed and optimized a novel six-axis force/torque sensor for a space robot. They proposed a novel sensing structure with
the through-hole beam. The presented sensor dimensions were optimized via response surface methodology (RSM). Finally, the experimental results revealed a good performance of the proposed multi-component force/torque sensor. Kang et al. [8] proposed an intentional stress concentration approach based on the application of binocular sensing structure to increase the sensitivity of a sixcomponent load cell. The dimensions of the sensing structure were thus optimized using FE analysis. In addition, the influence of different structural dimensions on the strain distribution of critical points was investigated. Finally, the interference error was reported less than 2.5% FS. Kim et al. [9] designed and fabricated a column type multi-component force/moment transducer. The structural dimensions were first found analytically and later, verified by finite element analysis. A decoupling method based on addition and subtraction processes of signals of the strain gauges were proposed to reduce the interference error. As a result, the interference errors were found to be 7.3% FS for Fx component and 5% FS for the rest of components. Liu and Tzo [10] presented a novel six-component force sensor. They utilized four identical T-shaped bars as force sensing structure of the mentioned transducer. They applied FE
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Fig. 3. Installation method of the external balance in the wind tunnel.
Fig. 4. Meshing method of the sensing structure.
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Fig. 5. Finite element simulation of the sensing structure under lift force (a) strain along x-direction (b) strin along y-direction.
Table 1 Loading capacities of the balance components. Component
Lift (N)
Drag (N)
Pitching moment (Nm)
loading capacity
300
50
60
optimization to obtain maximum sensitivity. However, a significant interference error was reported for their design. In this paper, a three-component strain-gauge one-piece external balance with a novel sensing structure is designed and developed for wind tunnel measurements so that a negligible interference error among the balance components is found. First, a suitable sensing structure is proposed and its dimensions are optimized using FE analysis based on the design requirements. Different mechanical analyses are carried out in designing the sensing structure. Then, suitable locations for installation of the strain gauges on the sensing structure are determined. Finally, the proposed multi-component external balance is developed and the obtained simulation results are verified. 2. Design requirements The multi-component external balance was to be capable of measuring three components such as lift and drag forces as well as pitching moment in the subsonic open wind tunnel of the Shiraz University of Technology. To meet the experimental requirements, the following maximum design loads were considered: Lift, 300 N; Drag, 50 N; Pitching moment, 60 Nm. The dynamic loadings were to be measured effectively up to 10 Hz and hence, the first natural frequency of the load cell structure was considered 10 times the
mentioned frequency as it was reported in Ref. [4]. The required accuracy was 0.2% FS that was similar to that of the commercial single component load cells and the maximum allowable weight of the model was 30 kg. The projectile area of the one-piece external balance should be chosen small to reduce the drag effect on the sensing structure. Table 1 summarizes the loading capacities of the load cell components which must be considered in the design scheme. 3. Proposed sensing structure and bridge circuits The multi-component balance must be designed such that the interference error among the components is reduced as best as possible. Moreover, in order to achieve the required accuracy presented in Section 2, the external balance should be sensitive enough. The sensitivity issue is even more significant for dynamic measurements which are essential for calculation of stability derivatives of a flying object for control applications. Besides, in order to study the flutter of the gas turbine blades, dynamic loadings need to be measured. Consequently, the design scheme was aimed at minimizing the interference error among the balance components as well as increasing the balance sensitivity taking into account the structure strength. It is obvious that increasing the sensitivity results in a more flexibility of the sensing structure, which may eventually lead to structural failure. Following the previous works on multi-component load cell structures [5,8], an innovative binocular-like sensing structure was proposed in this investigation. The proposed structure was achieved through a rigorous trial and error scheme based on the evaluation and integration of different flexible structures presented in the literature [5,8]. Fig. 1 demon-
Table 2 Summary of the simulation results obtained from FE analysis. Lift
ε11 536
ε6 536
ε7 −427
ε8 −427
11 + 6 − 7 − 8 1926
Sensitivity 1.01 mV/V
Drag
ε12 501
ε5 479
ε10 −479
ε9 −501
ε12 + ε5 − ε10 − ε9 1960
Sensitivity 1.08 mV/V
Moment
ε1 582
ε3 421
ε2 −582
ε4 −421
ε1 + ε3 − ε2 − ε4 2006
Sensitivity 0.96 mV/V
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Fig. 6. Strain distribution on the bottom-hand surface (along x-direction).
strates the proposed sensing structure of the multi-component external balance considered in this investigation. The sensing structure thickness was considered as 30 mm. Besides, the locations of the strain gauges are also depicted in the figure. Each strain gauge is denoted by a number in this figure. As can be seen in this figure, the intentional stress concentration technique was used to increase the sensitivity. The sensing structure was designed so that the locations of the strain gauges were on the outside surface of the structure, which resulted in an easier installation process of the strain gauges. Eight design parameters denoted by t1 , t2 , t3 , w1 , w2 , w3 , h1 and h2 were considered as shown in Fig. 1. Thus, the design parameters were chosen so as to achieve the design requirements. It will be discussed with more details in the next section. Three Whetstone full-bridge circuits corresponding to each balance component were considered in this work. Fig. 2 demonstrates the position of each strain gauge in the Whetstone bridge circuits. According to the whetstone bridge of the moment component (see Fig. 2), the output voltage of the bridge circuit can be expressed as [11]:
R3 and R4 . The change of output voltage (Vo ) can be written as: Vo =
(R1 + R1 )(R3 + R3 ) − (R2 + R2 )(R4 + R4 ) V (R1 + R1 + R2 + R2 )(R3 + R3 + R4 + R4 ) i
If the resistance changes of the strain-gauges are assumed too small, then the terms Ri Ri in the numerator and the terms Ri Ri and Ri Ri in the denominator can be ignored, Consequently, Eq. (2) can be simplified as follows: Vo = Vi
R1 R2 (R1 + R2 )2
(
R1 R2 R3 R4 − + − ) R1 R2 R3 R4
(1)
where Vo is the output voltage of Wheatstone bridge, Vi is the input voltage of Wheatstone bridge and R1 –R4 are the initial resistances of the strain gauges in each arm. It is clear that the output voltage of the bridge is zero (i.e., the bridge is balanced) when R1 R3 = R2 R4 . Consider an initially balanced bridge, so that Vo = 0 and then resistances R1 , R2 , R3 , and R4 are changed by the amounts R1 , R2 ,
(3)
The gauge factor of a strain gauge is defined as [11]: GF =
R/R ε
(4)
where GF is the gauge factor, R is the initial resistance of the strain gauge, R denotes the resistance change of the strain gauge and ε is the axial strain. Consequently, Eq. (3) can be rewritten based on the concept of Gauge factor (as defined by Eq. (4)) as, Vo = 0.25GF Vi (ε1 + ε3 − ε2 − ε4 )
R1 R3 − R2 R4 Vo = V (R1 + R2 )(R3 + R4 ) i
(2)
(5)
where 1 and 3 are the strains of the gauges under tension while 2 and 4 are the strains of the gauges under compression. Eq. (5) is the constitutive equation of the strain gauge bridge circuits in the commercial load cells. According to Eq. (5), the change of output voltage of a bridge circuit is proportional to the combination of strains as (1 + 3 − 2 − 4 ). Thus, in order to have the maximum sensitivity, two strain gauges must be in tension state while the rest of them must be in the compression state. Besides, if the strain gauges are placed at high-stress positions on the structure, a higher sensitivity can be expected. Taking into account the outlined considerations,
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Fig. 7. Strain distribution on the left-hand surface (along y-direction).
Table 3 First five natural frequencies of the sensing structure. Mode
1
2
3
4
5
Frequency (Hz)
98
242
363
438
451
the structure of the proposed three-component external balance is designed in the next section using FE analysis. Fig. 3 demonstrates the installation method of the proposed external balance in the wind tunnel. It can be seen that the proposed external balance is constrained from the top side while it is free to deflect from the bottom side where it is attached to the model. 4. Strain analysis of the balance structure using FEM In this study, ANSYS software was used to design and analyze the sensing structure based on FEM. Different element types were previously employed to mesh such a sensing structure [5,12]. In this work, element type Solid 186 was proposed. Solid 186 is a higher order 3D 20-node solid element that exhibits quadratic displacement behavior, which increases the accuracy of the analysis. This element type possesses three degrees of freedom (DOF) per node and is suitable for large deflections. Fig. 4 depicts the mapped meshing of the sensing structure using element type solid 186 in ANSYS software. The number of elements was selected such that the convergence of the results was obtained. Moreover, the number of elements was increased around the regions possessing stress concentration in order to have more accurate results. Different material can be used to construct the sensing structure taking into account the working conditions [13]. Although the standard aeronautical steel can be effectively used to develop
the sensing structure, the 7075 aluminum alloy was utilized in this research because of its lower initial cost and machining time. Besides, successful application of this material was previously reported in Refs. [5,10]. The Young’s modulus and Poisson’s ratio of this aluminum alloy were 72 GPa and 0.33 respectively which were applied to the FE software. In designing the commercial single component load cells the strain value of 1000 (resulting in the rated sensitivity of 2 mV/V) is commonly considered at the gauge positions [14]. However, a lower rated sensitivity of about 1 mV/V at maximum capacity was used in this work to provide acceptable sensitivity and reduce the interference errors as well as the possibility of yielding by stress concentration [6,10]. As mentioned earlier, the most important challenging problem in designing the multi-component force/moment sensors is to minimize the interference errors among the components as best as possible. Hence, the sensing structure dimensions and the suitable positions of the strain gauges were investigated using FE analysis so that negligible interference errors were achieved. As it was shown in Figs. 1 and 2, the points 6, 11, 7 and 8 were considered for mounting the strain gauges of lift component. The FE analysis was thus employed to find the optimum values of the corresponding design variables t1 , t2 , h1 , and w1 so that the desirable rated strain was obtained at the gauge locations under maximum capacity of the lift component (see Table 1). The values of parameters t1 , t2 , h1 , and w1 were respectively found as 0.006 m, 0.0022 m, 0.038 m and 0.080 m. Similar to conventional binocular load cells the diameters of arches were considered as 0.012 m through which a suitable strain distribution was found for strain gauges with the gauge length of 3 mm. Fig. 5a and b respectively represent the strain distribution along x and y directions of the sensing structure under 300 N lift force. It can be seen that the points 6 and 11 experienced
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Fig. 8. Strain distribution on the right-hand surface (along y-direction).
tension state while the points 7 and 8 were under compression. The corresponding strain variations on the bottom, left and right surfaces of the sensing structure were plotted in Figs. 6–8 . It is obvious that the points 6, 11, 7 and 8 were more sensitive to the applied lift force. Thus, the strain values of 536 , 536 , −427 , and −427 were respectively found for the points 6, 11, 7, and 8. The middle part of the sensing structure was designed to measure the drag force and four locations denoted by points 12, 5, 9 and 10 were considered for installing the strain gauges (see Fig. 1). Fig. 9 demonstrates the strain distribution of the sensing structure under a 50 N drag force obtained from FEM simulation. As it can be observed, two strain gauges are in tension while other ones are in compression. The loading capacity of the drag component can be adjusted by changing the design parameters t2 , w2 , and h2 . For instance, by decreasing the parameter w2 and increasing the parameter t2 it is possible to increase the loading capacity of the drag component. Using the FEM analysis, the values of design parameters t2 , h2 and w2 were respectively obtained as 0.0022 m, 0.032 m, and 0.068 m considering the maximum loading capacity of the drag component. Figs. 10 and 11 respectively demonstrate the strain distribution along y-direction on the left and right surfaces of the external balance. The rated strain values of points 12, 5, 9 and 10 were found 501 , 479 , −501 and −479 respectively. The parameters affecting the moment capacity of the proposed wind tunnel balance were t1 , t3 , w3 , and h1 . Thus, the values of the mentioned parameters were found using the FE analysis considering the maximum moment capacity of 60 Nm and rated sensitivity of 1 mV/V. Consequently, the corresponding values of t1 , t3 , w3 and h1 were respectively found as 0.006 m, 0.00935 m, 0.124 m and 0.038 m. The simulated sensing structure under the effect of a 60 Nm moment was shown in Fig. 12. The points 1, 2, 3, and 4 were
considered for installing the strain gauges of moment component. It is clear that the points 1 and 3 are in tension state and the points 2 and 4 are in the compression state. Figs. 13 and 14 demonstrate the strain values along x-direction on the bottom and top surfaces of the external balance respectively. According to Fig. 13, higher strain values were found at the points 8 and 7, however, the points 3 and 4 were selected for the moment component. It was because of a lower interference error between the moment and lift components that could be achieved by this configuration. Finally, the strain values at the points 1, 2, 3, and 4 were respectively obtained as 421 , −421 , 582 , and −582 respectively. Table 2 summarizes the obtained results of the structure design using the FEM simulation. It can be seen that the final sensitivities of the lift, drag, and moment components were found 1.01 mV/V, 1.08 mV/V, and 0.96 mV/V respectively taking into account a gauge factor of 2.13. 5. Interference errors, natural frequencies, and structural strength As mentioned earlier, in designing the multi-axis wind tunnel balances it is too important to minimize the interference errors among the components. Hence, the proposed sensing structure was subjected to single-axis loading and its influence on other components was investigated using FEM simulation. The simulation results revealed that the interference error was 0% for all components and it is one of the main benefits of the proposed sensing structure. Another important consideration affecting the multi-axis external balances was on the dominant natural frequencies of the sensing structure. This latest issue was even more significant when dynamic loadings need to be measured. Therefore, the modal analy-
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Fig. 9. Finite element simulation of the sensing structure under drag force (a) strain along y-direction (b) strain along x-direction.
Fig. 10. Strain distribution on the left-hand surface (along y-direction).
sis was carried out within the FEM simulation platform and the first five natural frequencies of the sensing element were investigated. Figs. 15–19 respectively represent the first five resonant modes of the sensing structure obtained from the FEM simulation. As can be seen, the first, third and fourth modes belong to the drag, lift and moment components respectively. The values of dominant natural
frequencies are given in Table 3. Since the first natural frequency corresponding to the drag component occurred at 98 Hz, the external balance could be used to measure dynamic loads up to 10 Hz as discussed in Section 2. Consequently, the designed sensing structure possessed a suitable dynamic characteristic which fulfilled the design requirements.
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Fig. 11. Strain distribution on the right-hand surface (along y-direction).
Fig. 12. Finite element simulation of the sensing structure under pitching moment.
Another important consideration, which must be taken into account, was on the strength of the structure under full-loadings. Consequently, the pitching moment together with the lift and drag forces were applied simultaneously to the balance structure and
von Mises stress analysis was implemented under full loadings as shown in Fig. 20. The maximum von Mises stress was found 138 MPa which was much smaller than the yield stress of 7075 aluminum alloy (which was about 500 MPa). As a result, a safety
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Fig. 13. Strain distribution on the bottom surface under a moment of 60 Nm (along x-direction).
Fig. 14. Strain distribution on the top surface under a moment of 60 Nm (along x-direction).
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Fig. 15. First resonance mode of the sensing structure.
Fig. 16. Second resonance mode of the sensing structure.
Fig. 17. Third resonance mode of the sensing structure.
Fig. 18. Fourth resonance mode of the sensing structure.
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Fig. 19. Fifth resonance mode of the sensing structure.
Fig. 20. von Mises stress analysis under full loadings.
factor of 3.6 was obtained through FE analysis. Besides, it was safe to carry 30 kg weight considering a safety factor of 3.0. 6. Experimental study The structure of the external balance was made of 7075 aluminum alloy using a wire-cutting machine considering a tolerance of ±0.01 mm. The strain gauge FLA-3-350-23 from Tokyo Sokki Kenkyujo Company was adopted to use in this work. The gauge factor and the gauge resistance were 2.13 ± 1% and 350 ± 1.0 respectively. Such high-resistance strain gauges were intentionally used to increase the bridge circuit sensitivity which is an important requirement to measure the dynamic loads. The gauge length was 3 mm that was similar to that of the conventional strain gauges used in commercial load cells. The strain gauges were bonded to the flexures using polyester adhesive (P-2) to provide a long term of use. The manufacturer’s recommendations for preparing the surface before bonding the strain gauges as well as clamping pressure and curing time of adhesive were all followed. Fig. 21 demonstrates the strain gauge bridge circuit incorporating an instrument amplifier employed in this investigation. Three similar circuits were thus used for the three components of the external balance. Each bridge circuit was excited by a 5 V stabilized D.C. potential difference. The output voltage of each bridge circuit was amplified using an instrument amplifier. The amplifier gain K was considered 501. A balancing potentiometer as shown in Fig. 21 was used to balance
the bridge circuit in order to eliminate the offset voltage due to the initial weight of the sensing structure. Fig. 22 depicts the final developed multi-component one-piece external balance. The locations of strain gauges on the hosted structure can be clearly seen in this photograph. A digital voltmeter with accuracy of ±0.1 mV was utilized to measure the output voltage of the amplifier circuit. Fig. 23 illustrates the calibration scheme considered in this investigation in which forces and moment of known magnitudes and directions were individually applied to the developed balance system. Fig. 23a demonstrates the calibration test of the drag component in which unidirectional known forces are applied to the balance structure so as to excite the drag component individually. Similar calibration schemes were repeated for the lift and moment components of the external balance system as shown in Fig. 23b and c. Such calibration tests are very conventional in multi-component load cells calibration (see Refs. [3–5,14]). The calibration masses were checked relative to certified standards. Two objectives were followed in the calibration experiment. First, it was essential to measure the sensitivity of each component (or the calibration slope) and second, it was important to investigate the interference errors among the balance components. Figs. 24–26 respectively show the calibration curves for the lift, drag and moment components. The calibration slope of lift component was measured 0.0077 V/N which resulted in a sensitivity of 0.924 mV/V (see Fig. 24). The calibration slope and the corresponding sensitivity of the drag component were mea-
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Fig. 21. Strain gauge bridge circuit incorporating instrument amplifier.
Fig. 22. Photograph of the developed multi-component external balance.
sured 0.0546 V/N and 1.09 mV/V respectively (see Fig. 25). Finally, the calibration results for moment component revealed the calibration slope of 0.038 V/Nm and the corresponding sensitivity of 0.938 mV/V for the moment component (see Fig. 26).
Finally, the accuracy of the external balance components was estimated about 0.14% FS by applying the known certified calibration masses to the balance system and comparing this mathematically with the transducer output signal to calculate the an average error as a percentage of the full-scale output using several tests. It is found that the estimated accuracy was close to the value reported by Molland [3]. One should keep in mind that the accuracy is usually defined as the value of uncertainty existing in the sensor output which is expressed as a percentage of full-scale output. However, in wind tunnel applications, the accuracy of a balance is influenced by many factors such as wall and sting interactions, the precision of the model geometry, flow quality, the angle of attach and balance uncertainty. Since there are so many potential errors, it becomes difficult to specify the accuracy for a wind tunnel test. Thus, the balance uncertainty alone must be taken into account through balance calibration [1] as it was done in the paper. As mentioned earlier, the most challenging problem in designing the multi-component balance is to minimize the interference errors as best as possible and it is a key issue considered in many investigations as outlined in the introduction section. In this research, an attempt was made to measure the interference errors among the balance components. Hence, the calibration scheme described in Fig. 23 was repeated to find the interference errors. The final results are given in Table 4. It can be observed all interference errors are less than 2.01%. Furthermore, the highest interactions were due to the effect of the moment on the lift and drag components.
Fig. 23. Photographs of calibration scheme, (a) drag, (b) lift, (c) moment.
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Fig. 24. Calibration curve for lift component (the output voltage of the bridge circuit has been amplified up to 501 times).
Fig. 25. Calibration curve for drag component (the output voltage of the bridge circuit has been amplified up to 501 times).
Table 4 Measured interference errors among the balance components. Interference error (%)
Drag = 50 N Lift = 300 N Pitching moment = 60 Nm
Drag
Lift
Moment
– 0.6 1.86
1.17 – 2.01
0.55 0.3 –
7. Conclusion A multi-component strain-gauge one-piece external balance with a novel sensing structure was presented in this article for wind tunnel experiments. The sensing structure geometry was acquired through a tedious trial and error scheme. An optimization scheme was conducted to find the suitable dimensions of the sensing structure using FEM simulations and taking into account the design requirements. Using the converged results of the FEM sim-
ulation, the sensitivities of the balance components were found to be 1.01 mV/V, 1.08 mV/V and 0.96 mV/V for lift, drag and moment components respectively. The simulation outcomes were further verified through experiment. The sensitivities of the sensor components were respectively measured 0.924 mV/V, 1.09 mV/V and 0.938 mV/V for lift, drag and moment components through calibration tests. Consequently, the calibration results revealed a good agreement with the simulation outcomes through which the validity of the design procedure was affirmed. The interference errors among the balance components were less than 2.01%. Thus, the proposed sensing structure provided a smaller interference errors compared to the previous work presented in Ref. [5]. The accuracy of the balance components was found about 0.14% FS which was close to the value reported in Ref. [3]. Finally, the first resonant frequency of the sensing structure was at 98 Hz for drag component which fulfilled the design requirements.
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Fig. 26. Calibration curve for moment component (the output voltage of the bridge circuit has been amplified up to 501 times).
Acknowledgement The authors would like to acknowledge the Shiraz University of Technology (SU Tech) for providing research facilities and funding. References [1] C. Tropea, A.L. Yarin, J.F. Foss, Springer Handbook of Experimental Fluid Mechanics, Springer, 2007. [2] M. Dubois, Six-component strain-gauge balances for large wind tunnels, J. Exp. Mech. (1981) 401–407. [3] A.F. Molland, A five-component strain gauge wind tunnel dynamometer, J. Strain 12 (1) (1978) 7–13. [4] R.A.B. Almeida, D.C. Vaz, A.P.V. Urgueira, A.R. Janeiro Borges, Using ring strain sensors to measure dynamic forces in wind-tunnel testing, J. Sens. Actuators A 185 (2012) 44–52. [5] A.R. Tavakolpour-Saleh, M.R. Sadeghzadeh, Design and development of a three-component force/moment sensor for underwater hydrodynamic tests, J. Sens. Actuators A 216 (2014) 84–91. [6] G.S. Kim, Design of a six-axis wrist force/moment sensor using FEM and its fabrication for an intelligent robot, J. Sens. Actuators Phys. 133 (2007) 27–34. [7] Y. Sun, Y. Liu, T. Zou, M. Jin, H. Liu, Designa and optimization of a novel six-axis force/torque sensor for space robot, J. Meas. 65 (2015) 135–148. [8] D.I. Kang, G.S. Kim, S.Y. Jeoung, J.W. Joo, Design and evaluation of binocular type six-component load cell by using experimental technique, Trans. Korean Soc. Mech. Eng. 21 (11) (1997) 1921–1930. [9] J.H. Kim, D.I. Kang, H.H. Shin, Y.K. Park, Design and analysis of a column type multi-component force/moment sensor, J. Meas. 33 (2003) 213–219. [10] S.A. Liu, H.L. Tzo, A novel six-component force sensor of good measurement isotropy and sensitivities, J. Sens. Actuators A 100 (2002) 223–230. [11] T.G. Beckwith, R.D. Marangoni, J.H. Lienhard, Mechanical Measurements, 6th edition, Prentice Hall, 2006. [12] V.A. Kamble, P.N. Gore, Use of FEM and photo elasticity for shape optimization of S type load cell, Indian J. Sci. Technol. 5 (3) (2012) 2384–2389. [13] E. Doebelin, Measurement Systems, Application and Design, 5th edition, McGraw Hill, 2004, pp. 438–446. [14] J.W. Joo, K.S. Na, D.I. Kang, Design and evaluation of a six-component load cell, J. Meas. 32 (2002) 125–133.
Biographies
A.R. Tavakolpour-Saleh is an Assistant Professor in the Department of Mechanical and Aerospace Engineering, Shiraz University of Technology, Iran. He acquired his BSc and MSc degrees from the Shiraz University, Iran in 2002 and 2005 respectively and later, his Ph.D. in Mechanical and Mechatronics Engineering from the Universiti Teknologi Malaysia in 2010. His current research interests are Mechatronics, Instrumentation and Measurement, Adaptive and Intelligent Control, Active Vibration/Force Control, Robotics and Automation, System Identification and Energetic Systems. A.R. Setoodeh is an Associate Professor in the Department of Mechanical and Aerospace Engineering, Shiraz University of Technology, Iran. He obtained his BSc, MSc and Ph.D. in Mechanical Engineering, from the Shiraz University, Iran. His research interests are Finite Elements Method (FEM), Computational Mechanics, Nano-Mechanics, Nano-Composite Material and Machine Design.
M. Gholamzadeh is a graduate student of Mechanical Engineering in the Department of Mechanical and Aerospace Engineering, Shiraz University of Technology, Iran. His current research interests are Multi-Component Force/Moment Sensors, Finite Element Optimization, Computational and Solid Mechanics.