Toward the complete practicability for the linear-equation dwell time model in subaperture polishing

Area of Science:

• Manufacturing Engineering
• Computational Science

Background:

• Deterministic subaperture polishing is crucial for high-precision surface finishing.
• The linear equation dwell time model (LEDTM) faces challenges in memory and time efficiency for large datasets.

Purpose of the Study:

• To improve the practicability of the LEDTM for deterministic subaperture polishing.
• To address limitations in memory cost, time cost, and arbitrary boundary/tool path handling.

Main Methods:

• Implementation of sparse matrix operations for building and storing the coefficient matrix.
• Development of a method to handle arbitrary surface error boundaries and tool paths.

Main Results:

• Reduced memory and time costs by tens to hundreds of times compared to traditional methods.
• Achieved processing times of approximately 1-6 seconds for 300x300 to 600x600 surface error matrices.
• Demonstrated compatibility with arbitrary boundaries and tool paths.

Conclusions:

• The proposed sparse matrix method makes LEDTM fully practical for engineering applications.
• Efficient handling of large-scale surface error matrices is now feasible on common personal computers.