Straight line equation:
When the equidistant line is above the original line, take the "+" sign, otherwise the "-" sign.
Round equidistance line equation:
When the equidistant line is an outer equidistant line, the "+" sign is taken, and the "-" sign is taken.
Solving the coordinates of the base points on the equidistant line, you only need to solve the related equidistant line equations in parallel. For example, the coordinates of the 3' point, the coordinates of 2 points (40, 85), and the coordinates of 3 points (70, 105).
A=y2-y3=-20
B=x3-x2=30
C=x3y2-ybx2=1750
Find the coordinates of the center of the circle as (85,105).
Two equidistant line equations are connected:
-20x+30y=1750+144.222
(x-85)+(y-105)=(15+4)
Solve x=66.134y=107.231
That is, the coordinates of the 3' point are (66.34, 107.231), and the coordinates of other base points or nodes on the tool center trajectory can be obtained by the same method, and then programmed according to this.
2. Offset calculation of imaginary tool tip point of CNC lathe
In the CNC turning process, in order to facilitate the tool, the knives are often pointed at the imaginary tool point P point. If there is no tool nose radius compensation, undercut will occur when turning the cone or arc. When the precision of the part is high and there is a cone or arc, the solution is: calculate the center track size of the tool nose arc, and then perform the local compensation calculation according to this compilation.
Figure 3 shows the amount of tool position compensation due to the radius r of the tool nose during turning. When the tool position compensation is performed simultaneously in the Z direction and the X direction, the actual blade edge and the workpiece contact point A are moved to the tool nose setting point P during programming, and the compensation amount of r can be calculated as follows:
When programming the workpiece taper surface program, the base point coordinates are the workpiece contour base point coordinates (Z and X) plus the tool nose arc diameter r compensation amount (Dz and DX), thus solving the radius without the tool nose radius The problem of compensation.
Fourth, the conclusion
In CNC machining, since the tool tip has a circular arc, the workpiece contour is formed by the tool motion envelope, so the motion path of the tool point does not coincide with the contour of the workpiece. In the full-function CNC system, the tool compensation command can be applied, and the machining process can be conveniently performed according to the workpiece contour size. In the economical numerical control system, the movement trajectory of the tool point can be calculated according to the workpiece contour size, the tool, etc. According to this programming, it can also be solved according to the local compensation method.
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