基于状态向量矩阵传递液压缸抗失稳研究

Anti-unstableness study for hydraulic cylinders based on state vector matrix transfer

液压缸在工程上可视为承受轴向压缩的阶梯细长压杆,其稳定性影响机构可靠性.液压缸由直径不同的缸体和活塞杆构成,把液压缸的每段结构视作1个受压单元,受压单元中的弯矩和剪力分别表示为状态向量,求出单元矩阵,通过各单元传递矩阵相乘,获得活塞杆2端的状态向量关系,根据液压缸不同约束条件,推导液压缸稳定性普遍方程.结合MATLAB优化设计技术,获取体积约束条件下液压缸的合理尺寸,通过和Ritz法计算结果比对,并进行模型实验验证,表明该方程计算结果接近准确值.

In general,the hydraulic cylinder can be treated as a slender bar that is suffered from axial compressions.Meanwhile,the mechanism reliability is significantly impacted by cylinder stability.Due that the hydraulic cylinder is composed of diverse cylindrical cases and piston rods,each cylindrical segment is processed as a compressed unit.In details,the bending torques and shearing forces of these units can be regarded as state vectors to solve the unit matrix.By multiplying unit transfer matrices,the correlation between state vectors at both ends of piston rod is obtained.Based on the constraints of hydraulic cylinder,a generic function is deduced for cylinder stability.With integration of optimization design techniques via MATLABTM,the rationale dimensions of hydraulic cylinder are obtained under volume constraint.Through comparing the results from Rits method and verifying the model from experiments,it is indicated that the calculated functional calculation results are close the prices values.