This representative case demonstrates deterministic magnetorheological finishing of a Ø170 mm steep spherical optic on the PKC300-Q. The workpiece had a spherical radius of R = 158 mm and an edge-normal angle of 32.55°. According to the published measurement record, the figure error was reduced from 17.136 nm RMS before processing to approximately 2 nm RMS after MRF. The result illustrates the use of the PKC300-Q for final correction of small- to medium-aperture spherical surfaces and steep edge regions after workpiece, fixture, and polishing-head reachability have been verified.
Item | Published Record |
Workpiece | Ø170 mm spherical optic; spherical radius R = 158 mm; edge-normal angle 32.55°. |
Initial Condition | Published initial figure error: 17.136 nm RMS. Effective aperture and analysis settings were not disclosed. |
Spherical radius | R = 158 mm |
Edge-normal angle | 32.55° |
Initial figure error | RMS 17.136 nm |
Calculated RMS reduction | Approximately 88% |
Machine Used | PKC300-Q magnetorheological finishing machine. |
Manufacturing Challenge | Steep-edge access, interference clearance, stable ribbon/removal function, edge behavior and comparable before/after data processing. |
Measurement | The record reports RMS values but does not disclose material, effective aperture, instrument, wavelength, fit, removed terms, filtering, wheel/fluid, time or uncertainty. The interface shows 1.655 nm RMS; annotations also reference about 2.2 nm and 1.6 nm after astigmatism removal. |
Steep spherical optics exhibit large changes in local surface normal, particularly near the edge. This increases the importance of polishing-head orientation, path reachability, fixture clearance, and stable ribbon formation. Instead of relying on uniform polishing or operator judgment, MRF converts a measured error map into a deterministic material-removal plan through removal-function calibration, dwell-time calculation, and coordinated multi-axis motion.
• Steep-edge accessibility: The 32.55° edge-normal angle requires interference-free motion of the workpiece, fixture, and polishing head while maintaining a stable process zone.
• Deterministic convergence: Local removal must be calculated from the measured error distribution rather than applied uniformly across the surface.
• Consistent metrology processing: The effective aperture, best-fit reference, removed terms, and filtering rules must remain consistent for a valid before-and-after RMS comparison.
The PKC300-Q uses an X/Y/Z/B/C five-axis architecture with a lower-mounted MRF head and an inverted-workpiece layout for compact access to steep optical geometries. Within the deterministic process chain, figure data are processed and used for removal-function calibration, dwell-time solution, and path generation. The surface is then remeasured, and the remaining error determines whether another correction iteration is required.
1. Initial figure measurement: Measure the deviation from the target sphere and lock the data aperture and processing rules.
2. Data preparation: Map coordinates, apply the agreed mask and fit, and remove only the specified terms.
3. Removal-function calibration: Characterize the localized removal function for the selected wheel, MRF fluid, and process settings.
4. Dwell-time solution: Calculate local dwell time from the target removal map and verify steep-edge reachability.
5. Five-axis polishing: Coordinate the machine axes to maintain the required process geometry while performing deterministic micro-removal.
6. Remeasurement and verification: Use the same data-processing convention to confirm convergence from 17.136 nm RMS to approximately 2 nm RMS.
The published record reports 17.136 nm RMS before processing and a final result in the approximately 2 nm RMS range. Using 2.0 nm as the rounded final value, the RMS reduction is approximately 88%, or an improvement factor of about 8.6. The engineering significance is not that one number can be applied to every optic, but that a steep spherical surface can be managed within a measurement–calculation–polishing–remeasurement loop and show substantial convergence at a 32.55° edge-normal angle.
Publish as approximately 2 nm RMS after MRF. Using 2.0 nm as a rounded value, the calculated RMS reduction is approximately 88%. Do not publish 1.655 nm as an unqualified universal value.
RMS decreased from 17.136 nm to approximately 2 nm.
Machining setup for the steep spherical workpiece.
• Multi-axis access to steep spherical surfaces and edge regions in the 300 mm class.
• Deterministic figure correction based on a calibrated removal function and dwell-time solution.
• Representative convergence from the tens-of-nanometers RMS range to approximately 2 nm RMS.
• Suitability for high-mix, low-volume optical production and process development.
• Steep spherical mirrors
• Short-radius convex or concave optics
• Final correction of infrared and laser optics
• Precision optics requiring controlled edge performance
Data and Metrology Note: The published measurement interface shows 1.655 nm RMS after processing, while a figure annotation reports approximately 2.2 nm and also references 1.6 nm after astigmatism removal. These values may reflect different apertures or removed-term settings; this page therefore reports the final result as “approximately 2 nm RMS.” The material, effective test aperture, metrology instrument and wavelength, removed terms, filtering, polishing wheel and fluid, processing time, and measurement uncertainty were not disclosed. The result applies only to the recorded workpiece, setup, process, and data-processing conditions.
Case boundary Final performance is application-specific and depends on workpiece material, geometry, initial condition, fixturing, process parameters, environmental control and metrology. Numerical results apply only to this cited record and its disclosed conditions.
