基于张量理论的数控机床误差补偿模型

为了进一步提高数控机床多体运动学误差模型的精度,提出了基于张量理论的机床误差补偿模型。首先面向数控系统列表插值补偿方式,提出了应用张量理论设定基础阶、扩展阶和误差阶来建立机床误差张量模型。然后,提出了采用设定机床信息、建立张量模型及设定检测参数3个流程实施误差补偿,并通过多元回归分析提出了采用4阶多项式拟合机床空间误差。最后,以某重型车铣复合机床实验为例,提出了分轴步进对角线法下的张量误差模型,采用球杆仪进行了圆度误差检测实验,结果表明该方法能够有效地提高机床精度,比多体运动学误差模型的补偿效果更优。

The Study on Motion of a Rigid Body Carrying a Rotating Mass

The free motion of a rigid body carrying a rotating mass without change of the centroid (this system may be called one-rotor gyrostat) is discussed. Equations of motion are derived: first integrals as a vectorial equation which contained the right vector of an angular velocity of the given rotor with respect to the carrier body and the turn-tensor of this body;a scalar relation between rotation angle of the given rotor with respect to the carrier body and the angular velocity of the carrier body. Only two of these parameters are independent variables. To get equations and to exclude the singular points in the solutions, it is necessary to determine the turn-tensor of the carrier body in the most suitable form. To this end the representation theorem of the turn-tensor and some additional arguments are used. As a final result, we enabled to get two complicated differential equations of the first order. In particular case, the exact solution is represented. Excluding the singular points numerical solutions are determined.

化学位移张量的测量

对于刚性晶格中的分子 ,化学位移是与外加磁场空间取向相关的张量 ,这个张量有 6个独立的分量 .化学位移张量也可以利用其主轴分量及主轴与晶体坐标系的方向余弦来表示 .很显然 ,知道了固体分子中各不等价位置处的化学位移张量 ,就可以推测出分子中电子分布的图象 ,具有重要意义 .本文首先描述了化学位移张量测量的理论 ,对测量化学位移各向异性的各种方法作了介绍和比较 ,并详细论述了一些常用的方法 ,如二维魔角跳旋转(MagicAngleHopping ,MAH)、二维魔角慢旋转 (MagicAngleTurning ,MAT)和二维变相旋转边带分离 ( 2Dphase adjustedspinningsidebands,2D PASS)技术等 .最后 ,还介绍了单晶化学位移张量的常规测量方法 .