Effect of Fillet on the Resolution of a Four-Axis Force/Torque Sensor

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1 Effect of Fillet on the Resolution of a Four-Axis Force/Torque Sensor Mohammad Hosein Tashakori Heravi, Alireza Akbarzadeh, Amin Valizadeh Center of Excellence on Soft Computing and Intelligent Information Processing (SCIIP), Mechanical Engineering Department Ferdowsi University of Mashhad Mashhad, Iran mohamad.tashakori@gmail.com, ali_akbarzadeh_t@yahoo.com, amin.valizadeh.66@gmail.com Abstract The wrist force/torque sensors has been increasinly used in variety of robotic fields which the most important one is human-computer interactions. Applied features of the force/torque sensors have motivated scientists to investigate novel techniques with regard to save machining costs and time before fabricating them. This paper represents the effect of fillet as a practical manufacturing method to decrease the costs and time and icrease the resolution of a four axis force/torque sensor, simultaneously. In adition, a kind of face machining technique is performed to aim the proposed goals. Using finite element analysis by commercial finite element software, ABAQUS, is then implemented to validate the proposed model. The results proof the efficiency of the methods. Keywords force and torque sensor; human-computer interaction, cross-beams; fillet; finite element analysis I. INTRODUCTION. The cross-beams force and torque sensors are typically multi axis sensors used in various fileds of engineering for their beneficial prperties such as simplicity, compactness, good machinability and precise measurements. The elastic crossbeams are the key elements of the F/T sensors. Several types of cross-beams force sensors were considered and developed in the 198s and in the 199s the studies aim the industrial areas to fulfill various tasks. [1, 2, 3]. Cross-beams six-axis F/T sensors mainly categorized into two types according to the relationship between the applied force and the output signal: mechanically coupled sensors which the output signal must be calibrated with a relatively complicated calibration matrix, and mechanically decoupled sensors which the output signal of a bridge selectively responds to a specific force or moment component [4, 5]. If the strain output matrix is a diagonal matrix with all zero off-diagonal values, then the sensor is considered completely decoupled. However, when one bridge circuit responds to more than one load component, non-zero off-diagonal values appear and they sacrifice some portion of output range of the i-th bridge circuit which causes a decrease of the measurement resolution of load component i [6]. Thus, designing the decoupled F/T sensor with high resolution is main purpose of the studies. The maximum error causes by cross coupling interference should be minimized to achieve the high resolution matrices. The procedures for making the multi component F/T sensors are implemented as follows. First, the equations to predict the bending strains on the surfaces of the plate beams under the forces or the moments are carried out. Next, the size of the sensing element of the F/T sensor is investigated using the derived equations. Finally, the attaching locations of the strain gauges for each sensor are selected. Then the multi axis F/T sensor is fabricated. Moreover, a characteristic test of the F/T sensor could be performed usnig FEM softwares [7, 8]. In this study, with regard to a preliminary design of a four axis F/T sensor, two manufacturing techniques to decrease the costs of machining and increase the measurement resloution is considered and analyzed. The model is created and analyzed in a commercial FEM software, ABAQUS, numerically. In each methods, the maximum error in each is calculated and compared to the original model of the F/T sensor and the acceptance of the model is discussed. II. MECHANICAL STRUCTURE OF THE FORCE/TORQUE SENSOR A four-axis force/torque sensor is commonly designed as shown in Fig. 1. As it is shown, the model basically consists of four cross elastic beams which are symmetric horizontal beams and compliant vertical beams. The vertical compliant beams connect the corresponding horizontal beams to the base, respectively. Fig. 1. Structure of a four-axis force/torque sensor

2 The whole model is manufactured monolithic and symmetric and hence all the parts have same material properties. As illustrated in Fig. 1, b, t, l are width, thickness and length of the horizontal elastic beams, and d and h are thickness and height of the vertical compliant beams, respectively. Commonly the basic relation between the design parameters are b=t and d 1/3 b [9]. Before designing the F/T sensor, konwledge of the force and torque bandwidth is of prime importance for identifynig the design parameters values. For instance, in Haptic based human-computer interaction (HapHCI) systems, the speed and stiffness of human hand is much more lower than other applications such as industrial areas. So, designing the parrameters to be appropriate for the high bandwidth is not essential in fileds like HapHCI systems. As a result, the four DOF1 F/T sensor which measures three axis forces Fx, Fy, Fz and one axis torque Mz is adequate for low bandwidth applications like HapHCI controls. III. STRAIN GAUGES DISTRIBUTION In the four-axis force/torque sensor, 16 linear strain gauges measure the applied Fx, Fy, Fz and Mz. Fig. 2 shows the distribution of the 16 axial strain gauges where the positive ones are tensile strains and the negative ones are compressive strains. Four Wheatsone bridge circuit is required to determine the applied load results from the 16 strains measurments. The relationship between these axial 16 strain gauges and the output strains can be expressed as: S fx K1 ( S6 S8 S16 S14 ) S K (S S S S ) fy 2 4 S fz K 3 ( S1 S3 S9 S11 ) S mz K 4 ( S7 S5 S15 S13 ) S11 S12 S13 S14 S15 S16 S S 22 S 23 S 24 S 25 S S [ Sij ] S31 S32 S33 S34 S35 S36 S 41 S 42 S 43 S 44 S 45 S 46 (3) The strain output matrix, S, is approximately a diagonal matrix, which idnicates the sensor is self-decoupled. Under each load applied to the sensor, the cross sensitivity caused by coupled interference from other axes is defined as maximum error, Er, and is evaluated by (4). Er ( Fx ) ( S12 S13 Er ( F ) ( S S 23 y Er 21 Er ( Fz ) ( S31 S32 Er ( M z ) ( S 41 S 42 S14 S15 S16 ) / S11 S 24 S 25 S 26 ) / S 22 S34 S35 S36 ) / S33 (4) S 43 S 45 S 46 ) / S 44 From the Er matrix, the maximum coupled error is determined which the lower error values cause the lower coupled interference and higher efficiency of the F/T sensor. In the design of a mechanically decoupled F/T sensor, the maximum error should be minimized, as the larger cross coupling error causes a decrease of resolution [9]. (1) Where Ki is the coefficient of the strain gauges configuration and is determined when the force sensor is designed. Under a certain load applied to the six-axis sensor with the F =[Fx Fy Fz Mx My Mz]T components, the strain output vector in a four Wheatsone bridge circuit configuration, is expressed by (2). Where [C] is a 4 6 strain compliance whose element Cij represents the strain contribution at bridge circuit i due to a unit pure load j. S 4 1 [C ]4 6 F6 1 (2) Under the 6 maximum pure load T components as F [ Fx Fy Fz M z M x M y ], the strain matrix, [Sij], can be defined by combining six S column vectors as follows: 1 Degrees of freedom Fig. 2. Strain gauges disrtirbution of the six-axis force/torque sensor IV. FINITE ELEMENT MODELING Using a commercial FEM software, ABAQUS, to numerically test the experiments is a key factor before fabricating the mechanical elastic sensor. Fig. 3 shows the FEA model designed in ABAQUS by meshing all the regions into finite number of nodal elements with the size of.5 mm for each node. The model is fixed at the ring shape base, and the force and torque component is applied at the center of the qubic support center along the neutral axis of the elastic horizontal cross-beams. Material and the preliminary parameters of the elastic body used in this study are expressed in Table I and Table II, respectively.

3 TABLE I. THE MATERIAL PROPERTIES OF THE TYPICAL FOUR DOF F/T SENSOR (I) AL775-T6 unit value Young s Modulus GPa 72 Poisson Ratio -.33 Density Kg/m Yield Strength MPa 51 TABLE II. THE PRELIMINARY PARAMETRS OF THE TYPICAL FOUR DOF F/T SENSOR Factors Horizontal elastic beams Vertical compliant beams Qubic center support Length (mm) l= 21 h= 7 14 Width (mm) b= 4.5 b= Thickness (mm) t= 4.5 d= (II) The rated capacity of the forces Fx, Fy, Fz and Mz are 2 N and 2 4.5=9 N.mm, respectively. The attaching locations for each 16 strain gauges was determined in consideration of the results of FEM analysis where the attachment location for measuring the force and torque components are 3 mm and 6 mm from the start point of the elastic beams, respectively. As a summary, the deformation of the F/T sensor under each single force and torque calculated by the FEM software are shown in Fig. 4 and the Wheatsone brdidge circuts outputs are seen in Table. III. (III) (IV) Fig. 3. The FEM model of the four DOF F/T sensor TABLE III. THE THE WHEATSONE BRIDGE STRAIN OUTPUTS UNDER EACH SINGLE FORCE AND TORQUE Strain (μm/m) Applied Forces: Fx= Fy= Fz= 2 N Applied Torques: Mx= My= Mz=.9 N.m Fx Fy Fz Mz Mx My Sfx K K1 Sfy K K2 Sfz K3 Smz K4 Fig. 4. Deformation of the FEM model under each single force/torque: Fx=2N II) Fz=2N II) Mz=.9 N.m IV) Mz=.9 N.m I)

4 V. RESULTS AND DISCUSSION In order to decrease the cost of fabricating and increase the resolution of the F/T sensor, two manufacturing methods is considered in this section. In the first case, the face machining process is considered to be applied to the bottom of the qubic center support. This process makes the bottom surface of the qubic center support flat with the elastic cross-beams. As illustrated in Fig. 5, this process reduces the costs of machining since the sensor could be fabricated simply by a three axis CNC machine. A FEM model of the F/T sensor whith fillet is also created using ABAQUS. From (4) and numerical results, the maximum error of the F/T sensor reducess when the sensor is modeled with fillet connections as shown in Table V. In other words, the strain gauges measurements have more values with fillet feature and hence the resolution of the sensor would increase while the coupling interference decreases. In addition, the max von Misses stress is also reduced from 1.47 to 1.89 Mpa. Thus, the fillet feature developes the safety factor of the F/T sensor as the strength of the structure becomes more strength. TABLE V. COPMARE THE MAX CROSS COUPLING ERROR FOR THE CREATING FILLET PROCESS Applied Forces: Fx= Fy= Fz= 2 N Max Error (cross coupling) Fig. 5. Face machining the qubic center support of the four DOF F/T sensor This feature is designed and analysed on the F/T sensor in ABAQUS and the results are expressed in Table IV. As it is shown, the maximum error calculated from (4) is similar in both models which represented the efficiency of the method. TABLE IV. COPMARE THE MAX CROSS COUPLING ERROR FOR THE FACE MACHINING PROCESS Applied Forces: Fx= Fy= Fz= 2 N Max Error (cross coupling) Applied Torques: Mx= My= Mz=.9 N.m Typical Model Face machined Model Er(fx) 1.28 % 1.31 % Er(fy) 1.67 % 1.68 % Er(fz).35 %.37 % Er(Mz).9 %.12 % Max Er In the second case, the fillet is created on the edge of the elastic beams where they connect to the qubic center support. Fig. 6 depicts the four edge fillets which are on the horizontal cross-beams. Applied Torques: Mx= My= Mz=.9 N.m Typical Model Fillet Created Model Er(fx) 1.28 %.72 % Er(fy) 1.67 %.73 % Er(fz).35 %.14 % Er(Mz).9 %.1 % Max Er.7 % von Misses S 1.89 MPa 1.47 MPa VI. CONCLUSION The application of F/T sensors has been interestingly increased in various fields and hence decreasing the costs of manufacturing it and increasing the resolution of the measurements plays prominent role in studies. Two manufacturing techniques are considered in this paper. Firstly, a face machining process in order to reduce the machining time and cost was considered. With his technique the F/T sensor is conviniently fabricated using a simple three axis CNC machine since the maximum error has no changed and remains equal to the typical model. Secondly, four edge fillets on the connections between elastic horizontal beams and the qubic center support are created. Numerical results shows the efficiency of the method while the maximum cross coupling error decreases and the resolution of the sensor increases, simalteanously. This method similarly reduces the cost and time of machinig as it does not required precise prependicular edge finishing on the connections. The von Misses stress of the sensor also decreases since the fillet developes the strength of the structure. REFERENCES [1] [2] Fig. 6. Create fillet on the edge of the four DOF F/T sensor s cross beams M. Perry, Multi-axis force and torque sensing, Sensor Rev., vol. 17, 1997, pp Zy. Nakamuro, T. Yoshikawa, Futamata, Design and singal processing of six-axis force sensor, 4th International Symposium of Robotics Research, Cambridge, MA, USA, pp , 1987.

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