圆弧投影法在圆柱立铣刀容屑槽刃磨中的应用

Application of Circular Arc Projection Method in Flute Grinding of Cylindrical End-mills

将圆弧投影法应用于圆柱立铣刀容屑槽刃磨,提出了砂轮安装位姿、砂轮最大允许圆角半径、砂轮最大允许斜角的确定方法。采用刀刃曲线、槽宽曲线和芯厚回转面三项几何要素定义容屑槽几何模型,利用砂轮曲面与容屑槽刀刃曲线之间的共轭条件约束砂轮的安装位姿,保证前角精度;将容屑槽的芯厚回转面和槽宽曲线在砂轮轴截面内作圆弧投影,提出圆弧投影面内芯厚半径和槽宽等效加工误差的概念,以等效加工误差的平方和最小为目标建立砂轮安装位姿优化模型,用于确定砂轮安装位姿,保证芯厚半径和槽宽的加工精度;在圆弧投影面内定义砂轮的切触圆角半径和切触斜角,分别以切触圆角半径最大和切触斜角最大为目标建立砂轮的圆角半径优化模型和斜角优化模型,用于计算砂轮的最大允许圆角半径和最大允许斜角,为砂轮几何参数的选择提供依据。圆弧投影法借助于等效加工误差对芯厚半径和槽宽的加工误差进行定量评价,无需求解容屑槽的端截面廓形,因此所建模型适用于多种类型的砂轮,而且具有较高的精度和运算效率。

Applying circular-arc-projection method in flute grinding of cylindrical end-mills,methods of determining the position,the maximum allowable fillet radius,and the maximum allowable oblique angle of the grinding wheel are presented.The flute geometry is defined by cutting-edge curve,flute-width curve,and surface of revolution corresponding to core radius.The accuracy of rake angle is ensured by restraining the wheel position by conjugating the wheel surface with the cutting-edge curve.The surface of revolution corresponding to core radius and the flute-width curve are projected into the axial section of the wheel by using circular-arc-projection method.Equivalent machining errors of core radius and flute width are presented,and an optimization model for wheel-position determination is constructed to minimize the sum of squares of the equivalent machining errors and to ensure the accuracy of core radius and flute width.Contact fillet radius and contact oblique angle of the wheel are defined in the circular-arc-projection plane.Optimization models of fillet radius and oblique angle are constructed to maximize the contact fllet radius and contact oblique angle and to obtain the maximum allowable fillet radius and the maximum allowable oblique angle,which can provide a reference for selection of the geometric parameters of the wheel.The circular-arc-projection method adopt the equivalent machining errors to quantitatively evaluate the machining errors of core radius and flute width without determination of the cross-sectional profile of the flute in each iteration.Thus,the constructed models can be applied to various types of wheels and have high accuracy and short time consumption.