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What Does the Mathematical Processing of CNC Turning Lathe Include?

The mathematical processing of CNC turning lathe part drawing is mainly to calculate the size of part machining path, that is, to calculate the coordinates of base point and node of part machining appearance, or the coordinates of base point and node of tool center appearance, so as to compile machining program.

Ⅰ. Calculation of base point coordinates of CNC turning lathe

Generally, the CNC turning machine has only linear and circular interpolation performance. As for the plane appearance composed of straight lines and arcs, the key point of numerical calculation during programming is to find the coordinates of each base point.

1. The meaning of CNC turning lathe base point

The intersection or tangent point of the differential geometric lines that make up the appearance of the part is called the base point. The base point of the CNC turning lathe can be directly used as the starting point or endpoint of its activity track.

2. The content of the direct calculation

According to the requirements of filling in the processing program sheet, the direct calculation of the base point of the CNC turning lathe includes the coordinates of the starting point and endpoint of each moving track in the selected coordinate system, and the center coordinate value of the circular arc moving track.

The direct calculation of the base point of the CNC turning lathe is relatively simple, which can usually be completed manually according to the known conditions given by the part drawing. That is, according to the dimensions given in the part drawing, the values are directly calculated by applying the relevant knowledge of algebra, trigonometry, geometry, or analytical geometry. During calculation, pay attention to the number of digits after the decimal point to ensure sufficient accuracy.

Ⅱ. Calculation of node coordinates of CNC turning lathe

As for the composition of some plane appearance right and wrong circle equation curves Y=F(X), such as involute and Archimedean spiral, they can only be approximated by Machinable straight lines and arcs. At this time, the mission of numerical calculation is to calculate the coordinates of nodes.

1. Definition of CNC turning machine node

When the CNC turning machine without non-circular curve interpolation performance is selected to process the CNC machining parts with Non-circular Curve appearance, in the preparation of machining program, multiple straight lines or arcs are often used to approximately replace the non-circular curve, which is called fitting processing. The intersection or tangent point of the fitting line segment is called a node.

2. Calculation of node coordinates of CNC turning machine

The calculation of node coordinates of the CNC turning machine is difficult and the workload is large, so it is often completed by computer. If necessary, it can also be calculated manually. The commonly used methods are the straight-line approximation method (equal spacing method, equal step method, and equal deviation method) and arc approximation method.

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