RESEARCH ON PIEZOELECTRIC QUARTZ UNDER MULTIDIMENSIONAL FORCES

Transcription

1 aterials Phsics and echanics (015) eceived: October 31, 014 ESEACH ON PIEZOELECTIC QUATZ UNDE ULTIDIENSIONAL OCES ei Wang *, uji Wang, Zongjin en, Zhenuan Jia, Liqi Zhao, Dong Li Ke Laborator for Precision & Nontraditional achining of inistr of Education, Dalian Universit of Technolog, Dalian 11604, China * Abstract. Considering that the traditional sensors can t work well in the field with spacial requirements, such as wind tunnel eperiment, a research of small sensor to measure multidimensional aerodnamic load is carried out. Based on anisotropic elastic theor, the polariation field inside the square Y0-cut quart wafer under multidimensional/si dimensional (6-D) forces is studied. With the method of splitting electrode, the mapping relationships between forces and the induced charges on each area are deduced. And then b using the pieoelectric effect models of ANSYS, simulation analsis about the quart wafer under 6-D forces is made, obtaining the distribution of electric potential and electric field. The results of the theoretical and simulated analsis show that it eists a quantitative and mathematical relationship between the densit of induced charges on each area and the tangential force and torque.the other stresses can be acquired b overlaing the wafer group. The stud provides a new ideal for the production of small-sie pieoelectric sstem to measure multidimensional forces. 1. Introduction In some fields, essential information is often acquired b measuring the force applied on the object. And with the improvement of propert requirements for products, the demand of force measurement changes from static to dnamic and from macro to micro. But the traditional sensor for multidimensional forces has a large sie, which limits the application in some narrow spaces, such as 6-D forces dnamic measurement of the micro robot joint and some hpersonic wind tunnel eperiments. At present, the multidimensional forces sensor usuall consists of three-component sensors or single-component sensors. Professor akoto, Kushu Universit of Technolog in Japan, designed the 6-D forces sensor through the ingenious combination of the two three-component sensors; Kistler, a compan of Switerland, built the 6-D forces platform b using multiple pieoelectric sensors; Professor Yongsheng Zhao in Yanshan Universit presented the overall preloaded sensor to measure 6-D forces based on the Stewart platform structure; eferences [1] and [] realied the measurement of 6-D forces b optimiing the 015, Institute of Problems of echanical Engineering

2 esearch on pieoelectric quart under multidimensional forces Stewart platform structure of sensor. eference [3] proposed a parallel structure model of 6-D forces sensors with the method of laing out quart wafer in space. In the fields with special space requirements, the above traditional sensors have too large sies to work well. In the paper, the stress model of square Y0-cut quart wafer under 6-D forces is established. Based on anisotropic elastic theor and awell s electromagnetic theor, the distribution of polariation field is acquired. And the man-to-man mapping relationships between multidimensional forces and coupling induced charges are deduced. B using ANSYS, the simulation analsis of quart wafer is conducted with ideal results, providing a new thought of overlaing the wafer group to measure multidimensional forces.. The stress analsis of quart wafer This paper regards a square with a hole Y0-cut α-detrorotation quart wafer as the stud object. The inner hole radius is =.5 mm, length of side is a=8 mm, and thickness is t=1 mm. i one end face and the other end face is acted on 6-D forces. or the convenience of calculation, crstal coordinate O is transformed to calculation coordinate O [4], as shown in ig ig. 1. Crstal coordinate and calculation coordinate. The stress model of quart wafer under 6-D forces. The elastic smmetr plane in the quart wafer is perpendicular to the ais of crstal coordinate, so the plane does not overlap with the cross section under 6-D forces. Namel this is a case of special bending-torsion of the anisotropic elastic bod. And the corresponding stress components [5] can be obtained from equation (1). U, U, s34 s35 1 ( ) s s s s s, s33 I s33 I1 s3 3 A,,, (1)

3 96 ei Wang, uji Wang, Zongjin en, Zhenuan Jia, Liqi Zhao, Dong Li where U represents the eternal force (volume and surface force); s ij represents elastic compliance coefficient. I 1 and I are the principal moments of inertia of wafer for the and ais respectivel;,, are three normal forces;, are the torques for and ais respectivel; is the torque for ais. Stress results under 6-D forces. When three moments are acted on the wafer, no other surface or volume forces eist on the plane, U 0. So in the numerical analsis of electric potential, it s enough to appl onl the three moments on the wafer according to anisotropic elastic theor [6]. Then based on the independence and the superposition of stresses, the final stress mathematical model of quart wafer under 6-D forces is acquired. The wafer acted on three moments is anisotropic elastic s space rotation and satisfies the differential equation () and the boundar condition equation (3) [7]. L4 L3 0, s34 s 35 s35 s34 L3 L, s33 I I1 I1 I () 0, 0, Γ 0. (3) Eventuall the torsion stress function of the wafer under three moments is obtained [8]. After determining the stress of the wafer under three moments, the stress under 6-D forces is calculated on the basis of the the independence and the superposition of stresses, as the equation (4). 0 0 s 34 s34 s33 I I1 s33 a -.5m ch 1 m ( a) cos.5m sh 7 1 m a ( a) sin m1,3,5m ch1.5m a a a m1,3,5m ch1.5m a a - (4) As can be seen from the above result, for the square wafer with a hole under 6-D forces,

4 esearch on pieoelectric quart under multidimensional forces onl the three stress components are eisted Bound charge calculation The eperiment indicates that when the stress of pieoelectric quart material is less, the value of the polariing effect of each dipole is proportional to the local stress ij [9]. B appling coordinate transformation method, the new pieoelectric coefficient d in O is calculated from the pieoelectric coefficient d ' in O, as the equation (5). P d11 0 d11 d P P d35 d 14, (5) where d m / N, d m / N, d m / N. When etra electric field and mechanical load are applied, the densit of bound charge on equivalent surface produced b bending torsional, (the densit of induced charge on the top + and bottom - of the wafer in the -direction respectivel) is listed as the equation (6) and (7)..5m sh 1 m ( a) 7 P d3 5( a sin ) m1,3,5m ch1.5m a a - P n e, (6).5m sh 1 m ( a) 7 P n P e 35( a d sin ) m1,3, 5m ch1.5m a a -, (7) where unit vector of outer normal direction is n e, and e is the unit normal vector. 0, 0, According to the equation (5), P 0 is acquired. It means that the wafer has not the phenomenon of polariation in the direction. Two densities of the charge on the upper cross-section (perpendicular to the ais) etracting charge are smmetr distribution based on the ais, equal and opposite polarit. If the split electrode method is used, two electrode slices are bounded b the ais, and the quantit of electric charge Q and 1 Q are respectivel etracted from area 1 and area, as shown in ig..

5 98 ei Wang, uji Wang, Zongjin en, Zhenuan Jia, Liqi Zhao, Dong Li ig.. ethod of split electrode to etract the charge. Q Q N m ( 1 ) 10 ( ), Q Q N ( 1 ) 10 ( ). (8) Observing the theoretical results above, it is clear that the quantit of Q and 1 Q respectivel has a significant linear correlation with and. The man-to-man mapping relationships are built between multidimensional forces and induced charges on two areas. In the same wa, the other stresses can be acquired through placing the rotated X0-cut or Y0-cut quart wafer (such as being rotated 90 degrees). So the 6-D forces are obtained b overlaing the wafer group to realie small sie and real-time measurement. 4. Simulation research on the quart wafer b ANSYS In this paper, the Y0-cut α-detrorotation quart wafer with certain sie under 6-D forces is analed, acquiring the corresponding electric potential and electric field intensit. irst of all, the model of the wafer is built in calculation coordinate O. The element tpe Solid5 should be chosen. The meshing is mapped b using the combination of manual control and free mesh [10]. Then, the loading step and solving step are followed. When setting constraints, node degrees of freedom on the end face of the wafer are all 0. To simulate the ideal load of concentrated force/torque, the load is applied b establishing ke points on another end face of wafer and on ais. So the ke points and the upper surface form a rigid one on the wafer. rom the above theoretical analsis, onl appling tangential force and torque on the wafer is allowed in simulation. 30kN and 300 N mm are respectivel imposed on the wafer, getting the distribution of electric potential and electric field intensit, as shown in ig. 3 and ig. 4. It is obvious that when onl appling on the wafer, potential values are equal and the same direction on area 1 and area. When onl, potential values are equal but in the opposite direction on area 1 and area.

6 esearch on pieoelectric quart under multidimensional forces 99 ig. 3. Electric potential and electric field intensit ( = 30 kn). ig. 4. Electric potential and electric field intensit ( = 300 N mm). inall, the specific process of loading is: appl and on the quart wafer. The numerical values of the tangential force are 10, 15, 0, 5 kn in sequence and that of torque is 100, 150, 00, 50 N mm in sequence. When appling and, theoretical potential value at node 1 (0, 0.003, 0.001) and node (0, 0.003, 0.003) of plane of the wafer is calculated b using the above equations. At the same time, the simulation analsis value of potential is acquired. Comparison between theoretical calculation and simulation analsis is shown as ig. 5 and ig. 6. ig. 5. Potential contrast figure at node 1. ig. 6. Potential contrast figure at node.

7 100 ei Wang, uji Wang, Zongjin en, Zhenuan Jia, Liqi Zhao, Dong Li As is shown in ig. 5 and ig. 6, it is obvious that for ever node, when tangential force and torque act on the quart wafer separatel, the potential value is equal to the sum of value when acting tangential force and torque at the same time. Potential value has a linear correlation with the load, which is consistent with the result of theoretical analsis. 4. Conclusion The polariation field of the Y0-cut wafer under 6-D forces is acquired b the building and the solution of stress model. At the same time, the mapping relationships between multidimensional forces and induced charges on each area are deduced. Then b using ANSYS, the quart wafer is analed to get the distribution of electric potential and electric field under 6-D forces. The results of the theoretical analsis and simulation show that it eists a quantitative and mathematical relationship between the densit of induced charges on the surface of the wafer and the tangential force and torque, making possibilit design the quart wafer for the integrated measurement of tangential force and torque. The other stresses can be acquired through placing the rotated X0-cut or Y0-cut quart wafer (such as being rotated 90 degrees). The stud provides theor basis to the application of pieoelectric measurement sstem of multidimensional forces in some narrow space and greatl epands its application fields. Acknowledgements The authors gratefull acknowledge the financial supports of the National Natural Science ound of China (No ) and the undamental esearch unds for the Central Universities (DUT14ZD(G)01). eferences [1] Chul-Goo Kang // Sensors and Actuators A: Phsical 90 (001) 31. [] Wang Hong-rui, Gao eng, Huang Zhen // Chinese Journal of echanical Engineering (English Edition) 11 (1998) 17. [3] Li Ying-jun, Sun Bao-uan, Zhang Jun // easurement 4 (009) 730. [4] Zhu ing-i, Wu Xiao-ling, Gao Chang-in// China echanical Engineering (011) [5] Han Li-li, Sun Bao-uan, Qian in // Journal of Dalian Universit of Technolog 40 (004) 150. [6] S.G. Lekhnitskii, Theor of Elasticit of an Anisotropic Bod (ir Publisher, oscow, 1981). [7] Gao Chang-in, Sun Bao-uan // Chinese Journal of echanical Engineering 40 (004) 150. [8] Hirofumi Kawashima, Kenji Sunaga // IEEE Transactions on Ultrasonics, erroelectrics, and requenc Control 43 (1996) 83. [9] Jan Söderkvist // IEEE Transactions on Ultrasonics erroelectrics and requenc Control 38 (1991) 71. [10] Li Bei-hi, Huang Hao, Wang Sheng-li // Journal of Donghua Universit (English Edition) 33 (007) 87.