钢球全表面展开机构模型建立及其运动分析

Modeling of the whole surface unfolding mechanism of a steel ball and its motion analysis

针对镜面钢球缺陷检测装置中的球体全表面展开问题,建立展开机构接触模型并对球体运动进行分析,证明展开机构结构合理可行。首先由坐标变换建立数学模型,基于Matlab对模型空间接触位置进行计算,将展开运动合理简化,得到钢球和展开轮之间转动的同步关系;其次,对展开运动过程进行等效变换,寻找传动过程中能使钢球稳定展开的最优参数关系;最后,依据迭代法对球面上点的运动轨迹进行数值仿真,获得其具体规律为偏角固定的螺旋线。最终结果表明展开机构能够实现球体的全表面展开。

For the whole surface unfolding problem in the defect detection device of a mirror steel ball, the rationality and reliability of the whole surface unfolding mechanism are proven through the contact modeling and motion analysis. First, establish the mathematical model through coordinate transformation, and calculate the contact points in the space of the model based on Matlab, reasonably simplify the movement to get the synchronous relationship of turning between the steel ball and unfolding wheel; second, conduct an equivalent transformation of the relative motion and look for the optimal parameter relationship which can make steel ball unfold steadily during the transmission process; at last, conduct numerical simulation on the movement track of the point on the ball by iterative method, deriving the spiral line with fixed deflection angle. The final result proves that this unfolding mechanism can complete full extension of the sphere.