混凝土湿喷机臂架系统的动力学建模与分析

Dynamics modeling and analysis on boom system of wet spraying machine

针对混凝土湿喷机臂架系统的液压油缸驱动力难以显式计算的问题,采用解析几何法和拉格朗日方程建立混凝土湿喷机臂架系统的动力学模型.将驱动油缸等效为活塞杆沿着套筒运动的二连杆机构,这样臂架成为不完全开链的十连杆机构.采用解析几何法,推导臂架杆件转角与液压油缸行程的函数关系,即臂架系统的运动学方程.在运动学基础上根据拉格朗日动力学方程,建立广义力(液压油缸驱动力)对广义坐标(油缸行程)的数学模型.仿真分析时选择了湿喷机的一个典型工作过程,利用符号运算工具MAPLE求解广义力的解析式,并导入MATLAB进行数值求解.同时,利用PRO/E的机构动力学仿真工具对臂架进行分析.对比可见MATLAB与PRO/E仿真结果相吻合,验证了混凝土湿喷机臂架系统动力学模型的正确性.最后,结合动力学模型分析驱动油缸铰点位置变化对油缸工作过程中最大驱动力的影响,结果表明原湿喷机臂架系统结构有待进一步优化.因此,该动力学模型为油缸选型和油缸受力优化提供了理论依据.

In view of the problem in explicitly calculating the driving force of hydraulic cylinders accurately in the boom system of a wet spraying machine, the dynamics model of the boom system was established by using the method of analytic geometry and Lagrange equation. An equivalent driving cylinder was established as a two-bar linkage mechanism including a cylinder rod and a sleeve which were in rectilinear motion relatively. Thus the boom became a multi-link mechanism that was an incomplete-opened-chain. Using the method of analytic geometry, a functional rela- tion between boom bars＂ rotation angles and hydraulic cylinders＂ stroke was deduced as the kine- matic model of the boom system. On the basis of kinematics and Lagrange＇s dynamical equations, the mathematical model related generalized forces （driving force of hydraulic cylinders） to generalized coordinates （cylinder stroke） was established. A typical working process of the wet spraying machine was selected to analysis. The analytic expressions of the generalized forces were solved by using the software of MAPLE. Then the expressions were imported into MATLAB to carry out numerical solutions. At the same time, the boom system was analyzed by using the tool of Pro/E mechanism dynamics. It contrastively showed that the simulation results of MATLABwere approximately in conformity with the PRO/E＇s, which verified the validity of the dynamics model of the boom system. Finally, the influence on maximum driving force of driving cylinder on a typical condition by change of position of the cylinder pivot point was analyzed and the results showed the original structure of boom system should be optimized. Thus, the dynamical model provides a theoretical basis for selecting the type of cylinders and optimization on the actuator force of driving cylinders.