Design of a compact six-component force and moment sensor for aerodynamic testing Marin SANDU*, Adriana SANDU*, Georgeta IONAŞCU* *Corresponding author POLITEHNICA University of Bucharest, Splaiul Independenţei 313, 060042, Bucharest, Romania marin_sandu@yahoo.com DOI: 10.13111/2066-8201.2011.3.1.13 Abstract: The measurement of steady and fluctuating forces acting on a body in a flow is one of the main tasks in wind-tunnel experiments. Usually, a multi-component strain gauge force and moment sensor (also known as balance) is used to generate signals which are processed by means of an adequate instrumentation. To design a wind-tunnel balance, the specifications of the load ranges and the available space (for the placement of the balance inside or outside the model) are required. The main challenge is to conceive the elastic element of the sensor as a monolithic part with a relative simple geometry and to identify the adequate placement of strain gauges to maximize the measuring sensitivities and to diminish the inter-influence of the components. This paper describes the design of a six-component force/moment sensor which is compact, has high measuring sensitivities, and can be used either as internal or as external balance in the aerodynamic testing. Key Words: six-component sensor, wind-tunnel balance, design procedure 1. INTRODUCTION The force and moment strain gauge transducers have important applications in Aeromechanics, Robotics, Automatic Control and Monitoring Systems, and also in Biomechanics. Since the force and moment are vectorial physical quantities, their magnitudes and directions are used to define them. As is well known, a mechanical load can be divided into six components: three force components and three moment components. Consequently, to define completely the load, it is necessary to know the values of all six components. A multi-component force/moment sensor is a device that enables forces and moments to be measured simultaneously. If they are placed inside of the model they are referred to as internal balances and if they are located outside of the model or the wind tunnel, they are referred to as external balances. There is limited space inside of the model itself, so internal balances have to be relatively small in comparison to external balances. There are two main types of internal balances. The monolithic type, in which the balance body consists of a single piece, properly designed such that certain areas are primarily stressed by the applied loads. The other internal balance type uses six small transducers which are oriented with their sensing axes in the direction of the applied loads. Such a balance is combined into a solid structure. A balance measures the total load acting on the model and therefore is placed at the center of gravity of the model. The six different components of aerodynamic loads (three forces in the directions of the coordinate axes and the moments around these axes themselves), are measured in a certain coordinate system which can be either fixed to the model or to the wind tunnel., pp. 95 100 ISSN 2066 8201
Marin SANDU, Adriana SANDU, Georgeta IONAŞCU 96 The basic metrological features of multi-component strain gauge sensors are determined to a great extent by the shapes and sizes of elastic elements on which the strain gauges are bonded [1]-[8]. The geometry of the elastic element of the sensor must comply with several metrological requirements concerning parameters as: nominal loads, allowed overload, measuring sensitivities, rigidities, linearity, hysteretic effects, interaction between the measured components, eigenfrequencies, fatigue life. 2. DESIGN DATA AND GEOMETRY OF THE ELASTIC ELEMENT The components which act on the model and are required to be measured are the following: axial force Fxm, side force Fym, normal force Fzm, rolling moment M xm, pitching moment, yawing moment M. According to the standard ISO 1151 their positive directions M ym zm are considered as in figure 1. A balance which stays fixed in the tunnel, being related to the wind-tunnel axis system, always gives the pure aerodynamic loads on the model. In the case of the axis system attached on model, the balance does not measure the aerodynamic loads directly. The loads acting on the model are given by the balance and the pure aerodynamic loads must then be calculated from these components using the correct yaw and pitch angles. Fig. 1 Definition of model-fixed axis system according to standard ISO 1151 To choose the configuration of an elastic element, some general recommendations are taken in consideration such as: symmetric structures are preferred because it is possible to eliminate the cross influences of the load components by an adequate positioning of strain gauges, the signals can be amplified connecting in Wheatstone bridges pairs of stretched and compressed strain gauges, the elastic element will be designed as a monolithic structure in order to reduce the nonlinearities and the hysteretic effects which can be induced if assembled parts with clearance are used. The elastic element of the sensor that will be discussed in this paper is a relative simple beam structure (Fig. 2), made from an alloyed steel (34MoCrNi15) that has the following characteristics: ultimate strength R 1300 MPa, yield limit R 1000 MPa, Young s modulus 5 E 2 10 MPa and Poisson s ratio m 0.3. p 0,2
97 Design of a compact six-component force and moment sensor for aerodynamic testing The values of nominal loads which will be considered in the origin of the global system 4 OXYZ are: F = F = 500 N, F = 1000 N, M = M = 5 10 N mm. xm ym zm Other design requirements were the following: - external sizes of the sensor (mm): Φ80 120, - measuring sensitivities greater than 0.5 mv/v (for a supply voltage of 10 V), - cross influences between the measured components: max. 8%. In order to design an elastic element with convenient external sizes, the lengths of the beams were taken as: l 50 mm, l 35 mm, l 20 mm. 1 2 xm 3 ym M zm Fig. 2 The calculus model of the sensor elastic structure All the beams have the same square cross section a a. Using the well known method of the forces [7], an analytic pre-dimensioning calculus, that will not be presented here, was performed for the case when the components F xm, F zm and M ym act simultaneously and the allowed maximum stress in the structure is a R p 0,2 / 2 =500 MPa. As a result it was established that the convenient dimension is a 8 mm. The combined loading case that was taken into account in the pre-dimensioning stage is corresponding, at the model level, to the aircraft take-off. 3. FINITE ELEMENT ANALYSES, PLACEMENT OF STRAIN GAUGES AND EVALUATION OF MEASURING SENSITIVITIES Six cases, corresponding to successive loading with the nominal values of forces and moments were considered, i.e the load applied in the origin of global reference system OXYZ (Fig. 2) was: 1) Fxm, 2) Fym, 3) Fzm, 4) M xm, 5) M ym, 6) M zm. The hypothetic case 7 when all the loads which are applied in cases 1 to 6 act simultaneously will be obtained by superposing the effects. The point O is placed on the middle of a fictive and more rigid beam that materialize the joint between the model and the sensor. At the opposite end, the elastic structure is fixed in the tail sting which sustains the aircraft model in the wind tunnel.
Marin SANDU, Adriana SANDU, Georgeta IONAŞCU 98 The main results of finite element analyses are the bending moment diagrams (fig. 3) which are reported to the local reference systems proposed for each component beam (Fig. 2). Because the beams have a massive section, the effect of bending moments is dominant and the contributions of axial and shear forces can be neglected. Load case 1 Load case 2 Load case 3 Load case 4 Load case 5 Load case 6 Fig. 3 The bending moments diagrams (values in N mm)
99 Design of a compact six-component force and moment sensor for aerodynamic testing Also, because the strain gauges will be bonded in longitudinal direction on the beams, their indications will be not influenced by the torques. However, the effect of the torques was taken into account in the evaluation of maximum equivalent stress ( ) in the structure. The strength condition ( eq, max eq, max a ) was accomplished in all loading cases 1 to 6. Consequently, the dimensions of elastic element are convenient, although in the practically improbable case 7, the maximum equivalent stress is of about 800 MPa. Taking into account the symmetry/antisymmetry of the diagrams from figure 3 and the presence of some cross sections with zero or very little values of bending moments, the adequate positioning of strain gauges was identified as in figure 4. Fig. 4 Placement of strain gauges on the elastic element and the measuring Wheatstone bridges The shape of elastic elements for multi-component sensors is conceived in order to ensure the independence of the signals which are proportional /to the measured components. In the ideal situation when the influence between effects is totally eliminated, a significant signal is obtained for the measured component while the signals for the other components are zero. When the effect are coupled, a coupling matrix [ C ij ] is experimentally established by calibrating the sensor. For a six component sensor, the following relation can be written { Si} [ Cij ]{ L j}, ( i, j 1,2,...,6), (1) where [ C ij ] is a 6 6 matrix, { S i } is the output signal vector for the six measuring bridges and { L j } is the load vector ( L, L F, L F, L M, L M L M ) 1 F x 2 y 3 z 4 x 5 y, 6 z. 1 [ C ij ] The relation obtained from (1) after multiplication to the left by { L } [ C j 1 ij ] { S }, ( i, j 1,2,...,6), (2) i
Marin SANDU, Adriana SANDU, Georgeta IONAŞCU 100 will be used to determine the unknown loads that act on the model, based on the signals recorded during its testing in the wind-tunnel. In the particular case of total independence of the six signals, [ C ij ] is a diagonal matrix. Usually, because of manufacturing imperfections and of strain gauges positioning errors, the matrix will have most of its elements different from zero, but the elements of the main diagonal will be larger than the others. The signal provided by a full Wheatstone bridge (Fig. 4), corresponding to any component can be evaluated by the relation U e ( kt / 4)( 1 2 3 4) U a, (3) where kt is the constant of strain gauge (usually kt =2), i (i=1, 2, 3, 4) are the strains captured by the strain gauges T 1, T 2, T 3, T 4 and U a is the measuring bridge supply voltage. The measuring sensitivity of each Wheatstone bridge can be determined by the formula S m U e / Ua. (4) Based on the bending moments diagrams (Fig. 3) and taking into account the strain gauges positions (Fig. 4), measuring sensitivities ranging from 0.7 mv/v to 2.9 mv/v were estimated for the six components. The maximum coupling error was identified between the components F y and M z, being of about 5%. 4. CONCLUSIONS The six-axes force/moment sensor that was analysed in this paper has a compact configuration and it can be used either as internal or as external balance in the aerodynamic testing of aircraft models in the wind-tunnel. Also, since the shape of elastic element is simple, an accurate manufacturing with a low cost price is possible. The estimated metrological characteristics of the sensor are convenient for usual measurements. REFERENCES [1] I. Constantinescu, D. M. Ştefǎnescu, M. Sandu, Mǎsurarea mǎrimilor mecanice cu ajutorul tensometriei, Bucureşti, Editura Tehnicǎ, 1989 [2] J. W. Dally, W. F. Riley, K. G. McConnell, Instrumentation for engineering measurements, New York, USA, John Wiley & Sons, 2 nd ed., 1984 [3] G. S. Kim, Development of a six-axis force/moment sensor with rectangular taper beams for an intelligent robot, International Journal of Control, Automation, and Systems, vol. 5, no. 4, pp. 419-428, 2007 [4] A. Marinescu, Metode, aparate şi instalaţii de măsură în aeromecanică, Editura Academiei Române, Bucureşti, 1970 [5] Y. K. Rark, R. Kumme, D. Roeske, D. I. Kang, Column-type multi-component force transducers and their evaluation for dynamic measurement, Measurement Science and Technology, vol. 19, pp. 1-10, 2008 [6] A. Sandu, M. Sandu, C. Atanasiu, A low-profile sensor for six force/torque components, pp. 67-69, Proceedings of the 18 th DANUBIA-ADRIA Symposium on Experimental Methods in Solid Mechanics, Steyr, Austria, September 26-29, 2001 [7] M. Sandu, A. Sandu, Analytic-numerical approach in a multicomponent strain gauge transducer design, Scientific Bulletin of University POLITEHNICA of Bucharest, vol 67, no. 3, pp. 37-44, 2005 [8] M. Sandu, A. Sandu, M. Gǎvan, Consideraţii privind proiectarea balanţelor tensometrice de suflerie, Aerospace International Symposium Carafoli 2001, pag. 169-174, Bucharest, 2001 [9] * * * COSMOS/M Finite Element System, User Guide, Structural Research & Analysis Co.,USA, 1998