**How to program and process oblique ellipse in CNC turning?**

I take a part drawing as an example to explain the processing of the oblique ellipse as concisely as possible.

In CNC turning, for the processing of oblique ellipse, you can understand that since there is no rotation command of the coordinate system, then you have to consider what exists between the coordinates of each point on the ellipse after rotation and the coordinates of each point on the unrotated ellipse. The relationship can be, for the part of the ellipse to be processed, it can be programmed according to the unrotated ellipse! This is a way of processing oblique ellipse!

First, let's look at the relationship between the two ellipticals about the point system.

Regardless of how the ellipse rotates, the length of the OA does not change. To understand this, the following is easy, as the X coordinate of point A is X = b × sin a before rotation and X = b × sin (a + b) after rotation. We can formulate the formula X=Z*SIN(b)+X*COS(b), the same is true for the Z coordinate, Z=Z*COS(b)-X*SIN, explain: in order to distinguish the unrotated Before and after the rotation, the bold X and Z are before the rotation.

Usually in CNC turning, we usually use Z as the independent variable, so according to the above formula, we only need to find the starting point and the ending Z coordinate of the ellipse of the machined part. The starting point and the end point coordinate must be in the unrotated elliptical coordinate system. So, according to the angle of rotation, everyone will establish the coordinate system, as shown below

It can be seen from the figure that the arc of ab is to be processed, wherein the Z coordinate of point a is the starting point, and the coordinate of point b is the end point. In the coordinate system XOZ, the Z coordinate is the starting point of 9, which is easier to see, Z The end point of the coordinate needs to be calculated, or it can be directly searched in the software. As shown in the figure below, the end point of the Z coordinate is 2.01.

After understanding the above knowledge, it is very easy to program. First, in the unrotated ellipse, Z[9,2.01] is the independent variable #1, and the dependent variable X is #3=15*SQRT[1-#1*#1/81], and then X, Z Bring them into the parametric equation of the rotated ellipse:

X=#1*SIN(25)+#3*COS(25);

Z=#1*COS(25)-#3*SIN(25),

Finally, you can use G01 interpolation.

In particular, we must also consider the offset problem of the ellipse center. The ellipse of the part drawing is (127.8, 8.16).

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