CNC Knowledge: Calculation method of the CNC machine-tool arc

The part between two points of a circle is called an arc

The process of derivating the calculation formula L = the length of the arc:

Because the length of the arc in front of the central angle of 360 ° is the circumference C = 2πr (r is the radius of the circle)

Therefore, the length of the arc at which the central angle of 1 ° is 2πr / 360, that is to say.

The calculation formula for the arc length of the central angle of n ° is l = n * 2πr / 360

For example:

We know that the distance between the two arc points is 5285 mm, the radius of the circle R = 3359 mm, find the length of the arc?

The line between two points is 5285 in length, half is 2642.5

Take the median point of the line, the center of the circle and every final point forms a right triangle.

The angle to which the center of the circle is half the diagonal of the arc.

The value of the sin of this angle is 2642.5 / 3359 = 0.7867

The number of angle is arcsin0,7867 = 51.88 degrees

Consequently, the diagonal angle of the arc is 51.87 * 2 = 103.76 degrees

Arc length = 2 sieve R × 103.76 / 360

= 2 * 3.14 * 103.76 / 360

= 6083 mm

R is the value of the radius on the drawing.

Instruction format: G02 / G03 x (U) ___ Z (w) _____k______;

G02 / G03 x (u) ___ z (w) ___ r___f___ ；

1. Judgment of the arc forward and reversed

The investigation of interpolation of the arc is divided into an investigation of interpolation of arc in the hourly direction G02 and the instruction of interpolation of arc in the antihorarous sense G03.

The Lathes CNC are machine tools with two coordinates, with only the X axis and the Z axis. The observer allows the positive direction of the y axis to point to itself (that is to say to look in the negative direction of the Y axis), and stand in such a position, you can judge Correctly the direction in the anti -oh direction of the arc on the XZ aircraft.

The arc judgment forward and vice versa

① When using absolute value programming, the coordinates of the final point are the coordinate values ​​of the final point of the arc in the coordinate system of the part, which are represented by x and z . When using incremental value programming, the COP coordinate is the incremental value of the Arc point with regard to the starting point of the Arc, represented by U and W.

② The central coordinates I and K are the divided vectors of the vectors manufactured from the starting point of the arc in the center of the arc in the X and Z coordinate axes (the vector direction points to the center of the circle). This system I and K are incremental values ​​and have a sign “±”.

③ When you use the radius to specify the central position, because there is only one possibility of two arcs from the starting point of the arc at the end of the arc, to distinguish the two, if the angle Central is ≤ 180 °, use ” + R” means. If the central angle of the bow is> 180 °, it is represented by “-r”.

④ When you use the radius to specify only the central position, the whole circle cannot be described.