基于全微分和CAD模型的公差分析方法

A Tolerance Analysis Method Based on Total Derivative and CAD Model

运用全微分进行公差分析时,需要先求得封闭环与各组成环之间的传递函数。由于零件的结构一般比较复杂,尺寸之间的相互影响呈三维非线性,所以传递函数及其偏导数一般也比较复杂,难以求得,这限制了全微分在公差分析中的应用。针对这一问题,通过推导证明,封闭环对组成环的偏微分等于封闭环增量对组成环增量的偏微分。运用这一结论,结合零件的CAD模型,使全微分在公差分析中的应用大为简化、实用。最后,推导了笔者工作中两类常见模型的偏微分公式,这些公式可在实际应用中直接调用。

In the process of tolerance analysis with the total derivative, it is necessary to get the transfer function of the closed loop relative to each component loop. The structure of actual parts is usually three-dimensional and the relationship of dimen- sions is usually non-linear, therefore the transfer function is usually complicated and difficult to get, which limits the use of total derivative in tolerance analysis. To counter this problem, it is proved in this paper that the partial derivative of the clos- edloop relative to the component loop is equal to the partial derivative of the increment of the closedloop relative to the incre- ment of the component loop. By using this conclusion and combining the CAD mode] of parts, it becomes greatly simplified and practical to use the total derivative in tolerance analysis. In the end, the partial derivative formulae of two types of models which are frequently met in the authors work are derived, and these formulae can be applied directly in actual work.