“K形图”的变异空间及教学要点——变异理论视域下

变异理论认为,以相似性为基础的差异性是学习迁移的关键。因此,教学中,要对一个学习对象的各个维度进行多种变异,从而获得更多的差异对象,扩大变异空间,进而进行审辩学习。“K形图”是平面几何问题中常见的基本图形,可以通过旋转直角三角形、旋转直线一侧的直角、改变角度大小、改变长度关系、隐藏部分图形等方式不断扩大其变异空间。相应的教学要点为:感悟变化过程中的数学思维,把握“变中不变”的数学本质,体会“学以致用”的模型价值。

齿轮齿形和齿向修形的设计

主要介绍齿轮齿形和齿向修形的设计,并根据齿轮可连续传动的条件,进行齿形检测框图的设计。通过齿轮的修形,可以弥补制造误差、安装误差等因素的影响,降低齿轮的动载荷,改善齿轮的受力不均匀现象,提高齿轮寿命。

Comparative study on forming limit prediction of AA7075-T6 sheet with M−K model and Lou−Huh criterion

In order to effectively predict the fracture of AA7075-T6 sheet, the forming limit curves of AA7075-T6 high-strength sheet were drawn according to Morciniak Kuczyski (M K) model and Lou Huh criterion, respectively. The errors between the predicted values of the two theoretical prediction models and experimental values were calculated by error analysis. The forming limit curves were verified by the punch stretch test to evaluate the prediction accuracy of M K model and Lou Huh criterion. The error analysis results show that the mean error of Lou Huh criterion with the optimal parameters for all tensile specimens is 25.04%, while the mean error of M K model for all tensile specimens is 74.24%. The prediction accuracy of Lou Huh criterion in predicting the fracture of AA7075-T6 sheet is higher. The punch stretch test results show that the forming limit curve drawn by Lou Huh criterion can effectively predict the fracture of AA7075-T6 sheet, but the prediction accuracy of M K model is relatively poor.