Abbreviations |
APT | Automatically programmed tool |
CAM | Computer-aided manufacturing |
CNC | Computer numerical control |
MCS | Machine coordinate system |
NC | Numerical control |
RCCS | Rotation center coordinate system |
RCS | Reference coordinate system |
RTCP | Rotating tool center point |
TCS | Tool coordinate system |
WCS | Workpiece coordinate system |
Variables |
a | Projection value of the vector w′ on the X-axis |
A | Angle of the tool rotating around the X-axis |
A_{1}, A_{2} | First and second solutions of angle A, respectively |
A_{u} | Ultrasonic amplitude |
b | Projection of the vector ${\mathit{w}}^{\prime}$ on the Y-axis |
c | Projection of the vector ${\mathit{w}}^{\prime}$ on the Z-axis |
C | Angle of the tool rotating around the Z-axis |
C_{1}, C_{2}, C_{3}, C_{4} | First, second, third, and fourth solutions of angle C, respectively |
d | Half-length of the bottom edge of the straight blade |
d | Unit direction vector along the bottom edge to tool location point O |
D | Tool location point vector of the flat end mill |
e | Radius along the tool face vector w from point D |
E | Intersection vector between the flat end mill and the workpiece surface |
f | Vibration frequency |
F | Cross product of tool face vectors 3 and 4 |
F_{Z} | z-coordinate value of the vector F |
G | Direction vector of the bottom edge of the straight blade |
G′ | Unit vector of G |
H | Machine tool spindle rotation angle value |
i | Projection of the tool axis vector Q_{W} on the X-axis |
i′ | Projection of the flat end mill axis vector t on the X-axis |
i″ | Projection of the straight blade axis vector T on the X-axis |
j | Projection of the tool axis vector Q_{W} on the Y-axis |
j′ | Projection of the flat end mill axis vector t on the Y-axis |
j″ | Projection of the straight blade axis vector T on the Y-axis |
k | Projection of the tool axis vector Q_{W} on the Z-axis |
k′ | Projection of the flat end mill axis vector t on the Z-axis |
k″ | Projection of the straight blade axis vector T on the Z-axis |
L | Tool swing length |
O | Tool location point vector of the straight blade |
P_{1}, P_{2}, P_{3}, P_{4} | First, second, third, and fourth feature points of Feature 1, respectively |
P | Tool location point vector in the RCS |
P_{W} | Tool location point vector in the WCS |
Q | Tool axis vector in the RCS |
Q_{W} | Tool axis vector in the WCS |
Q_{1}, Q_{2}, Q_{3}, Q_{4} | First, second, third, and fourth feature points of Feature 2, respectively |
r = [r_{1}, r_{2}] | Tangent vector of the adjacent two tool location point lines |
R | Rotation matrix of the flat end mill axis vector t rotating around w |
R_{A} | Rotation matrix for tool rotation around the X-axis |
R_{C} | Rotation matrix for tool rotation around the Z-axis |
t = [t_{1}, t_{2}, t_{3}] | Tool axis vector of the flat end mill in each position |
T | Tool axis vector of the straight blade |
T_{S} | Homogeneous coordinate matrix of the translation axis of the machine tool |
T_{L} | Homogeneous coordinate matrix of tool pendulum length |
v_{f} | Feed speed |
w | Flat end mill neutral surface vector |
w′ | Unit vector of w |
w_{1} | Tool face vector in the initial state |
w_{3} | Tool face vector after the tool rotation angles A and C |
x | Projection of the tool location point vector P_{W} on the X-axis |
X | Coordinate of the machine tool in the X direction |
y | Projection of the tool location point vector P_{W} on the Y-axis |
Y | Coordinate of the machine tool in the Y direction |
z | Projection of the tool location point vector P_{W} on the Z-axis |
Z | Coordinate of the machine tool in the Z direction |
θ | Half of the angle between the two sides of the cutting edge |