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 before the operation to avoid such accidents. The following section will explore the principles behind overcutting. 1. Overcutting Detection in Straight Line Machining Figure 1 illustrates how overcutting occurs during straight line machining. The contour being machined consists of straight segments. If the tool radius is too large, it can cause overcutting, leading to damaged workpieces. In Figure 1, the programmed path is ABCD, and B' represents the intersection point of the tool center path corresponding to AB and BC. When the system reads the CD segment, it adjusts the tool center path from B' to C'. As shown in the figure, this adjustment results in overcutting at this point.

Figure 1

During straight line processing, the sign of the scalar product between the correction vector and the original programming vector can be used to determine overcutting. In the figure, BC is the programming vector, and B'C' is the corrected vector. The angle α between them determines whether overcutting occurs. The scalar product formula is:

If the scalar product is negative (i.e., 90° < α < 270°), the tool moves away from the intended path, resulting in overcutting. In the FLASH animation, α = 180°, which definitely leads to overcutting. 2. Overcutting Detection During Arc Machining

In inner contour arc machining (using G41G03 or G42G02 commands), if the selected tool radius rD is larger than the arc radius R, overcutting will occur. This situation is illustrated in Figure 2. It’s important to note that overcutting only happens with specific command combinations like G41G03 or G42G02. If the command is G41G02 or G42G03, overcutting won’t occur when machining the outer contour. By analyzing these scenarios, we can develop a detection flow for overcutting when the tool radius exceeds the required arc radius, as shown in Figure 3.

Figure 4

Figure 4 shows an example of overcutting that occurs during arc machining. In real-world applications, there are many types of overcutting conditions, but due to time constraints, they cannot all be listed here. However, based on the analysis above, it's clear that overcutting typically occurs when the transition involves a shortened path. Using this principle, it is possible to design an overcutting detection program that identifies and prevents such issues effectively.

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