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Figure 1.43 Approximation error
The CNC machining error â–³ number is the result of multiple contributing factors such as programming errors â–³ program, machine errors â–³ machine, positioning errors â–³ set, and tool errors â–³ tool. These errors collectively contribute to the overall deviation in the final machined part. Mathematically, this can be expressed as: â–³ number = f (â–³ program + â–³ machine + â–³ set + â–³ tool).Among them:
(1) The programming error △ program consists of two main components: approximation error δ and rounding error. The approximation error δ occurs when a non-circular curve is approximated by straight lines or arc segments during the toolpath generation process, as illustrated in Figure 1.43. This type of error is common in complex geometries that cannot be perfectly represented by linear or circular interpolation. The rounding error, on the other hand, arises from the conversion of coordinate values into integer pulse equivalents during data processing. A pulse equivalent refers to the smallest displacement that the machine axis can move for each pulse signal sent by the CNC controller. For standard precision CNC machines, the typical pulse equivalent is 0.01 mm, while high-precision systems may use 0.005 mm or even 0.001 mm, allowing for more accurate movements.
(2) The machine tool error â–³ machine is influenced by several internal factors, including the accuracy of the numerical control system, the performance of the feed system, and mechanical wear over time. Any misalignment or inconsistency in these components can lead to deviations in the final output. Additionally, thermal expansion and vibration from the machine itself can also introduce small but significant errors during operation.
(3) Positioning error â–³ set occurs when the workpiece is mounted on the fixture and the fixture is placed on the machine. This includes inaccuracies due to improper clamping, misalignment of the fixture, or variations in the mounting surface. Ensuring precise alignment of the workpiece is crucial to minimize this type of error, especially in high-tolerance applications.
(4) Tool setting error â–³ tool is introduced when determining the relative position between the cutting tool and the workpiece. This includes errors from incorrect tool length compensation, improper tool offset settings, or misalignment of the tool holder. Proper calibration and regular maintenance of the tooling system are essential to reduce this source of error and ensure consistent machining results.
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