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    This study enhances the linear equation dwell time model for subaperture polishing by using Tikhonov regularization and constrained least squares QR decomposition (LSQR). These methods improve accuracy and efficiency for large-scale surface error correction in precision engineering.

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    Area of Science:

    • Precision Engineering
    • Manufacturing Processes
    • Computational Mechanics

    Background:

    • The linear equation dwell time model simplifies material removal in subaperture polishing.
    • Solving this model accurately is challenging due to its ill-posed nature, limiting practical applications for large surface errors.

    Purpose of the Study:

    • To improve the accuracy and efficiency of the linear equation dwell time model for subaperture polishing.
    • To address the limitations of traditional methods in handling large-scale surface error matrices.

    Main Methods:

    • Tikhonov regularization and the least square QR decomposition (LSQR) method were employed to solve the ill-posed dwell time equation.
    • A constrained LSQR method was developed to enhance the robustness of the regularization parameter.
    • A matrix segmentation and stitching approach was implemented for large-scale surface error matrices.

    Main Results:

    • An automated method for determining the optimal regularization parameter interval and value was established, linked to tool influence function peak removal rates.
    • The constrained LSQR method yielded more consistent dwell time maps compared to traditional LSQR.
    • The matrix segmentation and stitching method effectively managed large-scale surface error data.

    Conclusions:

    • The proposed enhancements make the linear equation dwell time model more reliable and efficient for practical engineering applications.
    • This work advances computational approaches for precision surface manufacturing and error correction.