DESIGN, OPTIMIZATION AND APPLICATION OF NOVEL PLANAR BENDING ESMAAs

Electrica, Jan 2012

DESIGN, OPTIMIZATION AND APPLICATION OF NOVEL PLANAR BENDING ESMAAs

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DESIGN, OPTIMIZATION AND APPLICATION OF NOVEL PLANAR BENDING ESMAAs

ISTANBUL UNIVERSITY - JOURNAL OF ELECTRICAL & ELECTRONICS ENGINEERING DESIGN, OPTIMIZATION AND APPLICATION OF NOVEL PLANAR BENDING ESMAAs YANG Kai 0 GU Cheng-lin 0 0 Huazhong University of Science and Technology , Wuhan 430074, Hubei Province , China To overcome low response speed and low control precision in the existing traditional shape memory alloy actuators, the new type of structure named planar bending embedded shape memory alloy actuator was developed. Two SMA wires were embedded in parallel with the axis of the elastic rod. The actuating wire, which was superposed along rod's axis, was set to obtain ?U? memory shape and the restoring wire, which was placed off-axially, got straight memory shape. The differential stain gauges were located at suitable position in corresponding to the actuator's bending direction in order to measure the signal of displacement. By making use of continuity, common origin and common limit conditions and adjusting martensite fraction coefficients appropriately, the analytical model was deduced to adequately account for the presence of major and minor hysteresis loops. The structural parameters of 60mm long actuator, such as rod's radius, wire's radius, wire's recoverable curvature and offset distance, were optimized by combining analytical model with experimental results. The experimental results prove the merits in optimal prototype. I. INTRODUCTION Actuators play a critical role in robotic system design and typically rely on electric, hydraulic or pneumatic technology. Unfortunately, there is a drastic reduction in the power that these forms of actuation can deliver as they are scaled down in size and weight. This restriction has opened up investigation of several novel actuator technologies such as those relying on piezoelectrics, polymer gels, magnetostrictive effects, electrostatics and SMA[2, 3]. Due to an SMA?s capability of exerting high force and tolerating high strain, the use of SMAs in actuators is quite intriguing. The actuation of these devices is relatively simple since resistive heating from an electrical current can directly drive the SMA [4,5]. In 1984, Honma demonstrated that it is possible to control the amount of actuation by electric heating, thus opening their use in robotic application[6]. A skeleton muscle type robot was presented that consisted of a 5 degree of freedom (DOF) arm constructed of an aluminium-pipe skeleton operated with thin SMA fibres (0.2 mm) and bias springs. The end-effector of the robot was a gripper driven by a pair of antagonistic fibres. This is the earliest attempt of using SMA in an actuated robot arm. In the recent decade, several researchers have implemented shape memory technology for use in articulated hands. Hitachi produced a four-fingered robotic hand that incorporated 12 groups of 0.2mm fibres that closed the hand when activated. Dario proposed an articulated finger unit using antagonistic coils and a heat pump[7]. Gharaybeh and Burdea fitted several SMA springs to the Exos Dextrous Hand Master for use as a force feedback controller[8]. Considering the applications, there are several disadvantages in the robot hands consisting of SMA actuators mentioned above. Firstly, the separation between actuating elements and executing elements is common in most configurations, which resulted in a complex structure and hampered their use in miniature systems. Secondly, their cartoon motions made grasping and fine manipulation very difficult. Thirdly, the response speed of SMA actuators is low due to the uncontrollable cooling process. To solve these problems, a new type of SMA actuator so called ?Planar Bending ESMAA? is proposed as follows. II. STRUCTURE designed. As shown in Fig.1, the two strain gauges are arranged in complemental configuration. With the dimension 3mm in width and 5mm in length, the gauges stick to the center of rod?s outside surface making use of 502 glue. When the actuator is actuated, the resistance varieties of two gauges have the same values. The final curvature?s signal can be derived by a half measuring bridge in cooperating with the resistance varieties. III. ANALYSIS MODEL A. Index of phase thansformation As we known, shape memory effect depends on the reversible transformation between two crystalline phases known as austenite (at high temperature) and martensite. The transformation is observed by noting the volume fraction of martensite Rm, which can vary between 0(all austenite) and 1(all martensite). Accordingly, Rm=1 indicates the alloy is in 100% martensite and Rm ? 0 represents the alloy is in 100% austenite. The nonlinearity arises in the martensite fraction-temperature characteristic, Rm(T), which is similar to the curvature-temperature characteristic, including the presence of major and minor hysteresis loops, which come from partial heating cycles. So, the determination of Rm is the key point of analysis model. In our design, we adopt the exponential model, which relates the SMA martensite volume fraction to the temperature T and time t. ? ? RmH (T ; t ) = ? ? ? RC (T ; t ) = ? m ? RmHa (t ) [1 + ek H (T ?? H ) ] RmCa (t ) [1 + ekC (T ?? C ) ] + RmHb (t ) + RmCb (t ) (1) For convenience, let the superscript C denote ?cooling? and the superscript H denote ?heating?. Since it is assumed that natural convection is used to cool the wire, the wire temperature cannot fall below the ambient temperature. Also, define two ?temperature constants? k C and k H . In any physical SMA material both k C and k H are positive. The piecewise-constant functions of time, Rma(t) and Rmb(t) are available for different hysteresis loops. As long as the wire is just being heated or just being cooled, the functions RmCa (t) ? RmCb (t) ? RmHa (t) and RmHb (t) remain constant. It is only when the wire goes from heating to cooling, or vice-versa, that these functions change. B. shape change model for rod As shown in fig.2, the vector form of the equations of equilibrium of a flexible rod acted upon by a distributed force, f, acting at a distance d from the centoid, is(Love 1994, Tadjbakhsh and Lagoudas 1993)[9,10] (2) (3) (4) (5) ( 6 ) (7) (8) (9) (10) (11) (12) equilibrium for the wire is dF a dz + f ' = 0 dF a dz + f n = 0 ? k 2 F a + f t = 0 From the operation principle of the actuator, it is obvious that only one wire, w1 or w2, is actuated at one time. Consequently, the movement of the actuator upon w2 being heated is examined in the detail. Since the process for the rod from ?U? shape to straight has the entirely reverse behavior with the process from straight to ?U? shape, the characteristics for rod?s bending upon w2 being heated are investigated as follows. Equation (5) has in general the following resolution in the osculating plane ddFza n + F a ddnz + f t t + f n n = 0 where t is the tangent unit vector and n is the principal normal vector. If the trihedral basis is used to resolve the vector form of the equations of equilibrium into components, the following set of two equations obtains by equation ( 6 ) The distributed forces acting on the rod are given by f1 = ? f n ? f 3 = ? f t and m2 = ?d1 f3 . Appling equations (7)-(8) to equations (2)-(3), then dF1 + k F + dF a dS 2 3 dz = 0 ddFS3 ? k2 F1 ? k2 F a = 0 ddMS 2 + (1 + e) F1 + d1k 2 F a = 0 If the elongation of rod is negligible, and the direction of wire?s actuating force is along the principal normal vector that F3 is approximatively taken as zero, the equations (9)-(11) reduce to k ' = F a = qx qL2 8E a I a dM 2 ? (1 ? d1k 2 )F a = 0 dS Combining with the experimental results, the distributed forces from ?U? shape actuating wire can be regarded as the force of uniformly distributed load. So, according to beam theory, the wire?s recoverable curvature and actuating force have the expressions where Ea , Ia are Young?s moduli and moment of inertia of the cross-section of the wire. q, L are load density and wire length respectively. The distance from calculation point to reference point is denoted by x. The moment M2 obtains making use of equations (13)-(15) M 2 = (1 ? d1k 2 )k ' E a I a Since the following constitutive assumption is made using beam theory M 2 = EIk 2 where E, I are Young?s moduli and moment of the cross-section of the rod respectively. Then, the recovering curvature of wire is derived using equations (16)-(17) k2 = k ' E a I a EI + d1k ' E a I a Defining a constant ? = EI a a E I Then the equation (18) can be rewritten as k 2 = k ' ? + d1k ' w2 serves as restoring wire with remembered straight shape, and the bending curvature is calculated as k2 ' = Rmk m'ax 2 (20) where k m'ax 2 is the maximum, which keeps the following relation with the actuator?s maximum curvature kmax kmax = ' kmax2 ? + d1k m'ax 2 k 2 = ' Rm kmax 2 ? + d1Rm k m'ax 2 The actuators? curvature upon heating wire w2 obtains by equations (19)-(21) When wire w1 is heated: d1=0 and m2=0. The equations (9)-(11) can be rewritten as The relationship between actuator?s curvature and martensite fraction Rm can be calculated by the following formula ? (1 - Rm )k m'ax ?? ? k2 = ????? +Rdm1kRm'maxk2m'ax2 w1 is heated w2 is heated IV OPTIMAI DESIGN OF STRUCTURE It is explicit that the maximum curvature of actuator greatly depends on the rod?s radius, wire?s radius, wire?s recoverable curvature and restoring wire?s offset distance. Neglecting the temperature disturbance and bending resistance of restoring wire when the actuating wire is heated, the simulated relations between actuator?s maximum curvature and rod?s radius, wire?s radius, wire?s recoverable curvature and offset distance obtain from the model mentioned above. All results will provide powerful instructions for the design of prototypes. Fig.3 is the relation between actuator?s maximum curvature kmax and the rod?s radius Rr. It is obvious that maximum curvature, kmax, is decreasing with increasing of the rod?s radius, Rr. Since the load ability depress greatly along with decreasing of Rr, there should be an optimal value. Considering that the actuator is used for anthropopathic robot hand, Rr is choosed as 5mm, which is comparative with the hand of human being. The rod?s radius and wire?s recoverable curvature are set as 5m and 57m-1 respectively. The relation between kmax and the wire?s radius rs as shown in fig.4. In the figure, kmax is increasing with the decreasing of rs exponentially. When rs is less than 0.25mm, the increase of rs has great influence on kmax. On the contrast, after rs is above 0.25mm, the effect weakens rapidly. Although kmax can be increased obviously through increasing rs, the response speed slows down and actuator?s remnants curvature after the temperature of actuator falls below room temperature is biggish. Therefore, to find an optimal value for wire?s radius, an index is defined as ?=kmax/kleft where kleft is remnants curvature. Fig.5 is the simulated result of the index versus wire?s radius rs. It is interesting to see that the optimal radius is around 0.3mm. So, the 0.25mm in radius wire is choosed as the actuation wire from the materials we can get.If rs=0.25 and Rr=5mm, from the model, the relation of kmax versus the wire?s recoverable curvature kr is nearly linear. So, it is explicit that increasing kr is the most effective way to increase kmax. In order to meet the requirement of displacement range and boundary condition of wire?s prestrain, the wire?s recoverable curvature, kr, is set as 57m-1 at last. 35 30 20 15 -1 /m25 xa m k 1 m /xa 15 m k 35 30 25 20 10 5 0 3 4 7 8 5 6 Rr /mm 0.0 0.1 0.4 0.5 0.2 0.3 In the planar bending ESMAA, there are two embedded wires, i.e., w1 and w2. Since wire w2 serves as restoring wire with memorial beenline shape, it is also important to determine the off-axial distance, d, of the wire away from rod?s centerline. Choose rs=0.25mm, Rr=5mm, kr=57m-1 and straighten w2 carefully before embedding it into the rod, the relaition of kmax versus d is shown in fig.6. From the figure, it is explicit that when the off-axial distance, d, is small, wire w2 return the rod to straight line quickly. On the other hand, too small distance will result in heat disturbance between w1 and w2. Considering restrictions mentioned above synthetically, d=3mm is appropriate. Finally, the material and geometrical parameters of designed prototype are summarized below and in table.1. V. EXPERIMENTAL RESEARCH A. Response Speed The bending of ESMAAs attributes to the phase transformation of SMA wires, w1 and w2, which is caused by heating and cooling cycle. The phase transformation of SMA wires from martensite to austenite is induced by electrical heating. The cooling experiments were carried out on the ESMAA prototype with 0.25mm in wire?s radius and 5mm in rod?s radius. The actuator experienced different cooling conditions, i.e. air cooling, wind cooling and water cooling after its curvature reached the maximum 28.5m-1. Besides experiments mentioned above, the time, within that the actuator restored to line by heating wire w2 from maximum bending state, was measured. All tested restoring time were summarized in table.2. From the above table, the former three values were similar since wire w1 was embedded in the rod and the cooling conditions could not influence it directly. So, it is not a perfect 0 1 2 3 d /mm 4 control measure to increase the response speed of ESMAA through external cooling condition. Fortunately, the restoring time fell down drastically when wire w2 was heated. It is no doubt that the designed ESMAA has enhanced performance in rapid response speed. B. Step Response Most actuator applications require displacing an object against an opposing force, such as moving an actuator limb coupled to a load. So accurate and rapid position control has to be implemented. The actuator?s curvature and current duty ratio respectively when a ?proportional-diode? controller is added to the system are simulated in fig.7 and fig.8. Proportional gain, Kp=0.05, and sampling period, Ts, of 15.4 milliseconds, are used. The model exactly provides reasonable agreement with the corresponding experimental results in fig.9 and fig.10. Note in particular that the model predicts a similar steady-state error. Reducing the heat transfer coefficient, an important parameter in the temperature-current relation of actuating wire, may improve the correlation between the simulated and experimental results, since such a reduction in the parameter would mean that heat, in the model, would be lost to the air less readily. Hence, small duty ration of current would be required to maintain the same wire temperature. 10 Time /s 15 20 Measured curve Target value 10 Time /s 15 20 18 16 14 1 /m 12 e r u trva 10 u C 8 6 4 0 5 10 Time /s 15 20 0.8 0.7 o it rya 0.6 t u D 0.5 0.4 0.3 0 5 15 10 Time /s To verity the basic performance of this ESMAA, the anthropopathic robot hand consisting of six ESMAAs was built. The driving experiment was conducted on a sphere weight of 3N with a 15mm radius of the sphere, as shown in fig.11. The novel hand?s finger tip was shown to make a pliable motion with about 115 degree/second up to a designed maximum angle (75 degrees) at the responding speed high enough for the purpose. By controlling the bending of each finger, the hand could accomplish fine manipulation like that of a human being. VI. CONCLUSION The new type of structure named planar bending ESMAA was developed. Two SMA wires were embedded in parallel with the axis of the elastic rod. The actuating wire, which was superposed along rod?s axis, was set to obtain ?U? memory shape and the restoring wire, which was placed off-axially, got straight memory shape. The differential stain gauges were located at suitable position in corresponding to the actuator?s bending direction in order to measure the signal of displacement. By making use of continuity, common origin and common limit co20nditions and adjusting martensite fraction coefficients appropriately, the analytical model was deduced to adequately account for the presence of major and minor hysteresis loops. The structural parameters of the actuator, such as rod?s radius, wire?s radius, wire?s recoverable curvature and offset distance, were optimized by combining analytical model with experimental results. An actuator prototype has been constructed with the following properties: Light weight - 2.5 grams Compact - 10 mm cylinder?60 mm long Big curvature -18m-1 Direct drive actuator Smooth movements The response speed and step experiments were carried out to prove the merits of model. Using the actuators, a three-fingered anthropopathic robot hand was designed to accomplish anthropomorphic grasping and fine manipulations. The maximum bending angle of one finger tip was about 75o when the duty ratio was 70 percent. The prototype can grasp a sphere 15mm in radius. The motions are flexible and lifelike. A clear picture of the grasping experiment shows that the fingertip could reach the set point fast and precisely. VII REFERENCES [1] Elahinia M H, Ashrafiuon H, Ahmadian M et al. A temperature-based controller for a shape memory alloy actuator[J]. Journal of Vibration and Acoustics, 2005, 127(3):285-291 [2] Liu Jianfang, Yang Zhigang, Cheng Guangming et al. A study of precison PZT line setp motor[J]. Proceedings of the CSEE, 2004 , 24 ( 4 ): 102 - 106 [3] Han L H , Lu T J , Evans A G . Optimal design Structures , 2005 , 12 ( 3 ): 217 - 227 [4] Singh K , Sirohi J , Chopra I. An improved Systems and Structures, 2003 , 14 ( 12 ): 767 - 786 [5] Kumagai A , Hozian P , Kirkland M. USA , Mar.6-9 2000 (5): 291 - 299 [6] Hirose S , Ikuta K , Umetani Y . New design MA USA, MIT Press, 1985 [7] Menciassi A , Pernorio G. , Dario P. A SMA Automation , 2004 (4): 3282 - 3287 [8] M. A Gharaybeh and G.C. Burdea . Advanced robotics , 1995 (3): 317 - 329 [9] Dimitris C Lagoudas and Tradj G 1992 (1): 162 - 167 [10] Brett De Blonk , Andrew J. Kurdila , Dmitris C flexible rods: SPIE , 1995 ( 2443 ): 335 - 34


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YANG KAI, GU CHENG-LIN. DESIGN, OPTIMIZATION AND APPLICATION OF NOVEL PLANAR BENDING ESMAAs, Electrica, 2012, 519-527,