重力对超静定结构受力的影响

摘要/Abstract

摘要： 目前有关超静定结构的受力分析中几乎均未考虑分支重力的影响，针对此，提出了一种考虑分支重力情况下超静定结构受力分析的方法。首先基于分支的力矩平衡方程直接求解出在分支重力作用下产生的施加给动平台的垂直分支轴线方向的约束力分量，并将其视作施加给结构的广义外力;然后基于结构变形协调关系和受力平衡方程，获得超静定结构各分支沿其轴线方向的约束力分量的完整解析表达式以及存在制造误差时装配内力的解析表达式;最后讨论了分支重力对超静定结构受力的影响机理。以平面超静定结构3-RR和空间超静定结构7-SS为例进行了实例分析，并建立对应的刚柔混合模型,进行了仿真验证。

关键词: 重力, 超静定结构, 3-RR结构, 7-SS并联机构, 受力分析, 装配内力

Abstract: In view of the facts that the literatures about force analyses of the statically indeterminate structures almost had not considered limb's gravity at present, a method was proposed, which took it into account. Firstly, the constraint force components perpendicular to the axis of each limb which were caused by the corresponding limbs' gravity were solved based on single limb's torque equilibrium equations, and it was regarded as the generalized force imposed on the whole structure. Then, according to the force equilibrium equations and deformation compatibility conditions of the whole structure, the analytical expressions were derived including the limbs' axial constraint force components and the assembly internal forces brought by manufacturing errors. Finally, the influences of limbs' gravity on the force analysis of the statically indeterminate structures were discussed. Taking the planar mechanism 3-RR and the spatial mechanism 7-SS as examples, the constraint forces were analyzed and the rigid-flexible mixed models of the two mechanisms were established. Based on the models the theoretical results were verified.

Key words: gravity, statically indeterminate structure, 3-RR structure, 7-SS parallel mechanism, force analysis, assembly force

中图分类号:

TH112

刘文兰, 许允斗, 闫文楠, 姚建涛, 赵永生, . 重力对超静定结构受力的影响[J]. 中国机械工程.

LIU Wenlan, XU Yundou, YAN Wennan, YAO Jiantao, ZHAO Yongsheng, . Influences of Limbs' Gravity on Force Analyses of Statically Indeterminate Structures[J]. China Mechanical Engineering.

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