A New and Accurate Mathematical Model for Computer Numerically Controlled Programming of 4Y1 Wheels in 2½-Axis Flute Grinding of Cylindrical End-Mills

Abstract

Solid carbide cylindrical end-mills are widely used in machining, and their helical flutes are crucial to their cutting peiformance. In industry, the flute is simply defined with four key parameters: the helical angle, the radial rake angle, the fluting angle, and the core radius, which are specified in an end-mill design. The flute shape is not fully defined, while it is ofien generated by a lAl or IV1 diamond wheel in 2^l2-axis computer numerically controlled (CNC) grinding. Unfortunately, the two simple wheels cannot make largely different flute shapes, preventing further improvement of the end-mills. Although no research result on how the flute geometry affects the end-mill cutting attribute has come into public yet, it is now necessary to employ more complicated wheels to grind flutes with the specified parameter values but much different flute shapes. For this purpose, the 4YI diamond wheel is employed in this work. However, the commercial tool grinding software cannot determine the dimensions and the set-up angle for the 4Y1 wheel. To address this problem, a new mathematical model of the flute parameters in terms of the dimensions and the setup angle of the 4Y1 wheel is formulated, thus, the 4Y1 wheel can be used in flute grinding. This work lays a foundation of using complex wheels to grind flutes with more shapes in order to improve the end-mill's cutting ability.

Modeling and analysis of variable-core groove for integral cutting tools

“…The helical cutting edge curve formula could be easily established by substituting the point into equation (5). Substituting t ¼ ts into the formula, the target point p c0_ts (x pc0_ts , y pc0_ts , z pc0_ts ) was then obtained and the corresponding tangent vector could be represented in the form According to equations (5) and (6), the point of intersection between the normal section plane at p c0_ts and the helical curve corresponding to p ci should obey the equation Then, the intersection p ni could be obtained by substituting p ci and t, which was solved from equation (7), into equation (5). Repeating the above procedures until all the points on the groove cross section line were calculated, the normal section line of the groove could be described by a series of point p ni .…”

“…The calculation results was t ¼ 1.026 by solving the equation by ''fzero()'' function in Matlab. By substituting t ¼ 1.026 into equation (5), the corresponding point on the normal section line of the groove was calculated as p n1 ¼ (À8.48, À1.43,10.26). Then, some other points could be derived by replacing p c1 with p ci .…”

“…The intersection of the helical curve and the normal section plane, p ni , could be identified by the method mentioned in Mathematical model of variable-core groove in normal section section. Considering that p 0 ci and p ni were on the same helical curve, it could be calculated by equation (5) and M z ¼ z pc0_ts . Thus, the maximum distance, which was called the departure distance, between the cross and normal section lines of the variable groove was obtained.…”

“…Kang et al 2 studied the fundamental analytical conditions and pointed out that the common normal vector at the contact point between the groove and wheel surface should intersect the axis of the wheel. Accordingly, Hsieh, 3 Wang and Chen, 4 Xiao et al 5 established the contact line equation and deduced the groove formula. Additionally, Nguyen and Ko 6 discussed the wheel with singular points.…”

“…Accordingly, Hsieh, 3 Wang and Chen, 4 Xiao et al. 5 established the contact line equation and deduced the groove formula. Additionally, Nguyen and Ko 6 discussed the wheel with singular points.…”