In the previous discussion, we explained that C cutter compensation helps prevent overcutting. This means that if a programmer accidentally creates a machining program that could result in overcuts, the system can issue an alarm in advance during operation, thus avoiding potential damage or scrapped parts. The following sections will delve into the principles behind overcutting. 1. **Overcutting Detection in Straight Line Machining** Figure 1 illustrates how overcutting occurs during straight line machining. The contour to be machined consists of straight segments. If the tool radius is too large, it may cause the tool to cut beyond the intended path, resulting in damaged workpieces. In the figure, the programmed path is ABCD, and B' represents the intersection point of the tool center path corresponding to AB and BC. When processing CD, the corrected tool center path from B' to C' is determined. As shown in Figure 1, this situation inevitably leads to overcutting.

Figure 1

During straight line machining, the scalar product between the correction vector and the original programming vector can help determine whether overcutting will occur. In the example, BC is the programming vector, and B'C' is its corresponding correction vector. The angle α between them plays a key role. The scalar product is calculated as follows:

If the angle α is between 90° and 270°, the tool moves away from the programmed path, leading to overcutting. In the FLASH animation example, α is 180°, which clearly results in overcutting. 2. **Overcutting Detection During Arc Machining**

When machining inner contours using arc commands such as G41G03 or G42G02, if the selected tool radius rD is larger than the arc radius R, overcutting occurs. This is illustrated in Figure 2. It's important to note that overcutting only happens with specific combinations like G41G03 or G42G02. If the command is G41G02 or G42G03, no overcutting occurs during outer contour machining. By analyzing these scenarios, an overcutting detection algorithm can be developed for cases where the tool radius exceeds the required arc radius, as shown in Figure 3.

Figure 4

In real-world machining, there are numerous conditions that can lead to overcutting. While it’s impossible to list all of them due to time constraints, the key takeaway is that overcutting typically occurs when the transition is of a "shortened" type. Based on this principle, an overcutting detection program can be designed to identify and prevent such situations effectively.

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