Dynamic compensation method for conformal channels in fused quartz abrasive flow polishing

Quartz glass is indispensable for high-end optical and resonant components because of its extreme hardness, low thermal expansion, and outstanding optical transparency. Yet its inherent brittleness often triggers fracture during polishing, so attaining simultaneously high surface quality and sub-micron form fidelity remains a formidable challenge. To overcome this, we introduce a parameter-regulated abrasive-flow process. By linking the medium's rheological fingerprint to the Preston equation within a White-Metzner framework, we derive a conformal-flow control law that explicitly incorporates clearance-induced rigidification. A correction term, scaled by the base-circle radius, is then embedded to counter local rheology shifts. Validation experiments show that the optimized process yields a surface roughness of Ra < 10 nm (RMS ∼ 7-12 nm) while maintaining a form accuracy variation RMS of less than 1 μm, providing a reliable route to ultra-precision finishing of quartz optics.