夹具定位分析模型的统计特征及相对误差分析

Statistical Characteristic and Relative Error among Fixturing Analysis Models

推导基于距离函数三种夹具定位分析模型的期望和方差。试验表明线性方法低估了工件定位误差,而双边二次方法最确切地反映出工件定位误差,因此双边二次模型的精度高但最复杂,而线性方法分析精度低但最简单。为了折中精度和复杂度,进一步推导双边二次模型与单边二次模型、单边二次模型与线性模型的相对误差与源误差之间的关系,提出三种夹具定位分析模型的选择方法。该方法在确定相对误差水平(即保证夹具定位分析的精度)前提下,依据源误差的协方差选择三种夹具定位分析模型,仿真试验验证了该方法的有效性。

The expectation and variances of the three distance function based models is derived, Examples demonstrate that the linear model tends to underestimate the workpiece deviation while the two-sided quadratic model provides the most accurate precision prediction. However this precision gain is at the cost of complex matrix calculation. In comparison, the linear model is the most simple and straightforward one. To strike the right balance between precision gain and model complexity, the linkage between the relative error and the locator error for the three models is built. And this leads to model selection method. Given a relative error level （i.e. to ensure the required precision requirement is met）, the proposed method makes the model selection based on the covariance of locator errors. Several examples verified the validity of the proposed method.