为了构建小型化全张量重力梯度测量系统,提出一种轴向分量与交叉分量同时敏感的基于超导的重力梯度敏感结构。基于螺旋理论分析两分量敏感结构的自由度,利用自由空间的运动螺旋系与互逆原理得到约束螺旋系,进一步得到具有冗余约束的对称约束构型,并选择柔性元件构建并联机构形式的两分量敏感结构,利用柔性虎克铰的横向与竖向柔性铰链实现等效球铰的功能。然后分析转臂质量沿轴移动与绕轴转动时柔性元件的变形,根据几何关系与功能定理得出两分量敏感结构的沿轴移动刚度与绕轴转动刚度。通过实际参数的计算,明确了各参数对结构刚度的影响,仿真结果验证了分析过程的准确性。
In order to measure the whole range of components of a gravity gradient with a miniaturized system, a simultaneous sensing mechanism of both the inline and cross components is presented. Based on the screw theory, the freedoms of the sensing mechanism of the superconductor gravity gradient are analyzed. The wrench of the free space and reciprocity of the screw theory are adopted to obtain the twists to express constraints. One symmetry type mechanism with redundancy constraints is deduced, which can be built by flexible elements according to a parallel mechanism form. Based on the transverse and vertical flexible hinges of flexible Hooke hinge, the function of equivalent spherical hinge can be realized. The deformation of the flexible elements is analyzed when the pivoted arm moves along the axial direction or rotates around the same axis. According to the geometrical relationship and the principle of conservation of energy, the axial rigidity and rotational stiffness are deduced. By means of finite element simulation, it can be concluded that the stiffness of the designed motion is influenced by the parameters of the mechanism. The simulation results verify the analysis process.
[1] Richeson J A. Gravity gradiometer aided inertial navigation within non-GNSS environments. 20th International Technical Meeting of the Satellite Division of The Institute of Navigation. Fort Worth, TX, United States: Institute of Navigation, 2007: 1089-1100.
[2] Rogers M M, Huffman R E, Shearer C M. An investigation into the feasibility of using a modern gravity gradio-meter instrument for passive aircraft navigation and terrain avoidance. Proceedings of the Institute of Navigation, National Technical Meeting. Anaheim, CA, United States: Institute of Navigation, 2009: 49-60.
[3] Wen Z, Liu Y, Yang W J. Experimental analysis on dynamic performance of scale model high temperature superconductor bulk magnetic levitation and propulsion system. Acta Aeronautica et Astronautica Sinica, 2007, 28(s): 19-22. (in Chinese) 温正, 刘宇, 杨文将. 高温超导磁悬浮助推缩比试验系统动态测试分析. 航空学报, 2007, 28(s): 19-22.
[4] Liu L, Wang J S, Deng Z G, et al. Levitation force transition of high-Tc superconducting bulks in varying external magnetic field. IEEE Transactions on Applied Superconductivity, 2010, 20(3): 920-923.
[5] Patitsas S N. Stability analysis for axially-symmetric magnetic field levitation of a superconducting sphere. Physica C: Superconductivity, 2011, 471(1): 12-18.
[6] Nan H L. Foundation of superconducting magnet design. Beijing: National Defense Industry Press, 2007. (in Chinese) 南和礼. 超导磁体设计基础. 北京: 国防工业出版社, 2007.
[7] Chan H A, Paik H J. Superconducting gravity gradiometer for sensitive gravity measurement. I. Theory. Physical Review D: Particles and Fields, 1987, 35(12): 3551-3571.
[8] Yang G L, Liu Y X, Li X P. Analysis and design on control loops of gravity gradiometer accelerometer. Journal of Chinese Inertial Technology, 2009, 17(2): 145-147. (in Chinese) 杨功流, 刘洋希, 李晓平. 重力梯度仪加速度计控制回路分析与设计. 中国惯性技术学报, 2009, 17(2): 145-147.
[9] Lumley J M, White J P, Barnes G, et al. A superconducting gravity gradiometer tool for exploration. Airborne Gravity 2004 Geoscience Australia Record. 2004: 21-40.
[10] Moody M V, Paik H J, Canavan E R. Three-axis superconducting gravity gradiometer for sensitive gravity experiments. Review of Scientific Instruments, 2002, 73(11): 3957-3974.
[11] Jia M, Yang G L. Measurement of inline-component of gravity gradient by three-position method based on superconductor. Journal of Chinese Inertial Technology, 2011, 19(4): 211-214. (in Chinese) 贾明, 杨功流. 基于超导的三位置重力梯度轴向分量测量方法. 中国惯性技术学报, 2011, 19(4): 211-214.
[12] Yu J J, Pei X, Bi S S, et al. State-of-arts of design method for flexure mechanisms. Journal of Mechanical Engineering, 2010, 46(13): 2-13. (in Chinese) 于靖军, 裴旭, 毕树生, 等. 柔性铰链机构设计方法的研究进展. 机械工程学报, 2010, 46(13): 2-13.
[13] Yu J J, Bi S S, Zong G H. Stiffness matrix method for displacement analysis of fully spatial compliant mechanisms. Journal of Beijing University of Aeronautics and Astronautics, 2002, 28(3): 323-326. (in Chinese) 于靖军, 毕树生, 宗光华. 空间全柔性机构位置分析的刚度矩阵法. 北京航空航天大学学报, 2002, 28(3): 323-326.
[14] Zhang P, Zhou L, Qiu T. A new flexible honeycomb structure and its application in structure design of morphing aircraft. Acta Aeronautica et Astronautica Sinica, 2011, 32(1): 156-163. (in Chinese) 张平, 周丽, 邱涛. 一种新的柔性蜂窝结构及其在变体飞机中的应用. 航空学报, 2011, 32(1): 156-163.
[15] Paros J, Weisbord L. How to design flexure hinges. Machine Design, 1965, 37(27): 151-156.
CJA