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    Area of Science:

    • Manufacturing Engineering
    • Optical Metrology
    • Precision Engineering

    Background:

    • Workpiece form error in complex optics grinding is influenced by arc grinding wheel profile accuracy.
    • Existing research lacks a systematic analysis of how different frequency bands of wheel profile errors affect workpiece form errors.

    Purpose of the Study:

    • To elucidate the generation mechanism of workpiece form error during arc-envelope grinding.
    • To analyze the mapping relationship between wheel profile errors and workpiece form errors.
    • To propose a novel compensation method for arc grinding wheels to improve precision.

    Main Methods:

    • Kinematic simulation to model workpiece form error generation considering wheel profile errors across different frequency bands.
    • Analysis of the mapping relationship between profile errors and form errors, considering amplitude and frequency.
    • Development and experimental validation of a novel compensation method for arc grinding wheels.

    Main Results:

    • The mapping coefficient between profile and form errors is dependent on both amplitude and frequency.
    • Conventional compensation methods fail to fully correct errors due to neglecting wheel profile errors.
    • The novel compensation method reduced cylindrical workpiece form error from 8.8 µm PV to 2.1 µm PV in a single iteration.
    • Achieved a 38.2% improvement in compensation accuracy compared to conventional methods after two iterations.

    Conclusions:

    • The proposed method effectively enhances grinding precision for complex optics.
    • The novel compensation strategy significantly reduces iteration cycles in grinding-measurement-compensation processes.
    • This approach addresses limitations of conventional methods by accounting for wheel profile errors across frequency bands.