The rotational stiffness characteristics of cross-spring pivot are important consideration for designers, but some of these attributes of the pivots subjected to vertical loads have not been revealed. A simple rotational angle model with high order terms of vertical loads is developed to study the influence of vertical loads on Quasi-constant rotational stiffness of cross-spring pivot used in compliant static balance instrument. Then rotational stiffness and vertical stiffness are analyzed to better characterize the influence of vertical loads on rotational stiffness. The study shows that can rotational stiffness be deemed to be quasi-constant only when the value of vertical load and rotational angle both are small. Otherwise, when vertical load is very large, rotational stiffness is quadratic function of vertical load. While when rotational angle is very large, vertical load will be a driving load, and the nonlinear characteristic of rotational stiffness becomes apparent. Finally, these attributes, analyzed by theoretical model, are verified by finite element analysis (FEA) and experiments.
LI Yongzhen
,
BI Shusheng
,
ZHAO Hongzhe
,
YANG Qizi
,
ZHANG Shuqing
. Influence of Vertical Loads on Quasi-constant Rotational Stiffness of The Cross-spring Flexure Pivot[J]. Journal of Mechanical Engineering, 2018
, 54(3)
: 1
-7
.
DOI: 10.3901/JME.2018.03.001
[1] LOBONTIU N. Compliant mechanisms:Design of flexure hinges[M]. CRC Press,2002.
[2] PAROS J M,WEISBORD L. How to design flexure hinges[J]. Machine Design,1965,37:151-156.
[3] HOWELL L L. Compliant mechanisms[M]. New York:Wiley,2001.
[4] 于靖军,郝广波,陈贵敏,等. 柔性机构及其应用研究进展[J]. 机械工程学报,2015,51(13):53-68. YU Jingjun,HAO Guangbo,CHEN Guimin,et al. State-of-art of compliant mechanisms and their applications[J]. Journal of Mechanical Engineering,2015,13(51):53-68.
[5] 杨其资,刘浪,毕树生,等. 广义三交叉簧片柔性轴承的旋转刚度特性研究[J]. 机械工程学报,2015,51(13):189-195. YANG Qizi,LIU Lang,BI Shusheng,et al. Rotational stiffness characterization of generalized triple-cross-spring flexure pivots[J]. Journal of Mechanical Engineering,2015,51(13):189-195.
[6] BOYNTON R,WIENER K,KENNEDY P. Static balancing a device with two or more degrees of freedom (the key to obtaining high performance on gimbaled missile seekers)[C]// the 62nd Annual Conference of Society of Allied Weight Engineers,Inc. May19-21,2003,New Haven,Connecticut,2003:8-24.
[7] BI Shusheng,ZHANG Shuqing,ZHAO Hongzhe. Quasi-constant rotational stiffness characteristic for cross-spring pivots in high precision easurement of unbalance moment[J]. Precision Engineering,2016,43:328-334.
[8] HUANG Hongbiao,ZENG Taiying,ZHANG Tao,et al. Research on the stability of large aperture mirror mounts using cross-flexure pivots in ICF lasers[J]. Chinese Optics Letters,2007(5):60-63.
[9] AWTAR S,SLOCUM A H,SEVINCER E. Characteristics of beam-based flexure modules[J]. ASME Journal of Mechanical Design,2007,129 (6):625-639.
[10] AWTAR S,SLOCUM A H. Constraint-based design of parallel kinematic xy flexure mechanisms[J]. ASME Journal of Mechanical Design,2007,129 (8):816-830.
[11] WITTRICK W. The properties of crossed flexural pivots and the influence of the point at which the strips cross[J]. The Aeronautical Quarterly,1951,Ⅱ:272-292.
[12] HARINGX J A. The cross-spring pivot as a constructional element[J]. Applied Science Research A1,(1949):313-332.
[13] ZHAO Hongzhe,BI Shusheng. Accuracy characteristics of the generalized cross-spring pivot[J]. Mechanism and Machine Theory,2010,45:1434-1448.
[14] ZHAO Hongzhe,BI Shusheng,YU Jingjun. Nonlinear deformation behavior of a beam-based flexural pivot with monolithic arrangement[J]. Precision Engineering,2011,35:369-382.
[15] ZHAO Hongzhe,BI Shusheng. Stiffness and stress characteristics of the generalized cross-spring pivot[J]. Mechanism and Machine Theory,2010,45:378-391.
[16] JENSEN B.D,HOWELL L.L. The modeling of cross-axis flexural pivots[J]. Mechanisms and Theory,2002,37 (5):461-476.
[17] TREASE B,MOON Y,KOTA S. Design of large-displacement compliant joints[J]. ASME Journal of Mechanical Design,2005,127 (4):788-798.
[18] ZELENIKA S,BONA F D. Analytical and experimental characterisation of high-precision flexural pivots subjected to lateral loads[J]. Precision Engineering,2002,26:381-388.
[19] EIJK J V. On the design of plate spring mechanisms[D]. Delft University,1985.
[20] 张述卿,毕树生,赵宏哲,等. 交叉簧片柔性胡克铰在静平衡仪中的应用及性能测试[J]. 机械工程学报,2015,51(21):1-6. ZHANG Shuqing,BI Shusheng,ZHAO Hongzhe,et al. Application study and performance testing of cross-spring flexible Hooke hinge in static balancing instrument[J]. Journal of Mechanical Engineering,2015,51(21):1-6.
