一种应用等效平面的公差分析方法

A tolerance analysis method based on equivalent plan

针对复杂机械系统公差分析问题,提出一种应用等效平面的公差分析方法。首先将零部件安装配合面的实际轮廓抽象为等效平面,用其单位法矢量表示位置和方向,在刚体条件下从设计信息中提取出等效平面的单位法矢量。在各个零件的局部坐标系下对单位法矢量位置和方向叠加,应用齐次转换矩阵计算出末端单位法矢量在基准坐标系中的位置和方向,从而对装配尺寸链进行求解。以某型圆柱磨齿机的砂轮修整器为例进行了公差分析计算,进行了1 000次的模拟计算,结果验证了设计精度指标,证明了该方法在公差分析方面的有效性。

A new tolerance analysis method is proposed for complex mechanical systems by using equivalent plan. Firstly, the mating surfaces of installation parts are abstracted as equivalent plans. The position and orientation of these plans are expressed by the normal unit vectors from the design information in the condition of rigid body. Stack up the normal unit vectors of every part in local coordinate system, the dimensional chain for assembly can be solved, by calculating the normal unit vector of end part using the homogeneous transformation matrix in the foundational coordinate system. Taking a grinding wheel dresser for example, the results of the tolerance analysis and 1 000 times simulations verified the design accuracy index. This method is proved to be effective in tolerance analysis.