Author: Site Editor Publish Time: 2026-09-22 Origin: Site
Peak Removal Rate Footprint Size and Repeatability
Magnetorheological finishing corrects optical surfaces through controlled local material removal. Dwell-time calculation needs a spatial description of that removal, so the magnitude, shape and location of the removal function require a defined measurement basis. A single removal-rate number cannot describe all of them. This article explains what calibration establishes and when its results can be used for subsequent processing. [1,2]
A removal function, also called a tool influence function, describes spatial removal for a specified material, tool and process state, commonly per unit interaction time. In one spot-calibration method, the macroscopic position of the workpiece relative to the tool is held while the wheel or fluid ribbon continues its prescribed motion. If Δh is the measured removal-depth distribution produced during time T, the average depth-removal rate over that interval is:
Here, x and y are surface coordinates of the spot. Depth in nm and time in seconds give an average rate in nm/s. This quotient is an interval average. Applying it to other dwell times requires validation of the time-scaling relationship. If contact entry, flow establishment or motion transients are significant, a very short test may not represent longer-duration steady behavior.
Spot characterization should describe both removal strength and spatial shape. The following measures serve different purposes and are not interchangeable. [2]
Measure | Meaning | Required interpretation |
Peak depth-removal rate | Maximum average depth-removal rate within the spot, for example nm/s | A local peak, not a uniform thinning rate for the whole part. |
Volumetric removal rate | Removed volume divided by interaction time, for example mm³/min | The integration region, depth reference and units must be consistent. |
Footprint width or contour | Spatial extent of the removal action | State the direction, profile and threshold; full width at half maximum is not a universal spot diameter. |
Peak location and shape | Peak coordinates, asymmetry and distribution details | Define registration and tool orientation; one size value cannot describe the full shape. |
For a local spot represented in approximately planar coordinates, volumetric removal rate can be obtained by integrating depth-removal rate over area after converting to consistent length units. Curved surfaces require appropriate treatment of coordinates, area and the direction in which depth is measured.
Figure 1 Two synthetic removal distributions have the same peak but different widths and spatial integrals. Coordinates and amplitudes are normalized and cannot be used to compare equipment performance. Actual removal spots may also be markedly asymmetric.
A reviewable calibration record covers the workpiece, process and metrology. The following points describe an engineering assessment; actual operation follows the applicable equipment and fluid instructions.
· Select representative material, surface condition and local geometry. Validate the transfer relationship when using a specimen of another material to predict workpiece removal. [1]
· Record relevant tool state, relative motion, field setting, gap or immersion condition, and fluid identity, batch, actual condition, flow and temperature, using the equipment’s parameter definitions.
· Define the start and end of interaction time. Produce a measurable spot with sufficient unprocessed reference area, or use another validated depth-reference method.
· Register before-and-after data and apply consistent reference processing. Tilt or curvature fitting must not remove the real removal depth from the result. Surface-height and wavefront data are not directly interchangeable.
· Assess repeated measurements and repeated spots. Consider changes in peak, volume, contour and location together with measurement repeatability and uncertainty.
Normalizing each spot to the same peak helps compare shape but hides changes in rate magnitude. A repeatability assessment should retain unnormalized data as well as appropriate normalized shape comparisons, and examine peak positions before and after registration.
The same fluid grade or command settings do not automatically establish the same removal function. Fluid condition, relative motion and contact conditions can change. Process variables also interact; increasing field strength or abrasive concentration does not necessarily increase removal rate. [3]
Repeatability limits should follow the correction task, measurement capability and validation results. Fluid replacement, replenishment, conditioning, changes in tool state or material, and abnormal monitoring results can trigger a review of applicability. A validated process procedure should determine whether recalibration is needed and how frequently it is performed.
An interior removal function may not apply at the workpiece edge. Published research identifies differences between interior behavior and entry or exit at an edge. Simply clipping an interior footprint at the boundary may therefore fail to represent the actual edge-removal distribution. [4]
Significant changes in local curvature, tool orientation or contact conditions also require a check of applicability. A smaller footprint may help address more localized errors, but correction remains limited by metrology, dwell constraints and process stability. Tool size alone does not determine final accuracy.
Useful questions concern the material and state represented by the removal function, evidence of repeatability, comparison of predicted and measured removal, and treatment of edges and geometry changes. Whole-part cycle time also includes path execution, measurement, cleaning, workholding and any further correction. Neither peak depth-removal rate nor volumetric rate alone determines that cycle time.
APEX supports magnetorheological finishing equipment selection and project coordination. Share the workpiece material, geometry drawing, starting surface data, target requirements and acceptance method to discuss suitable equipment and process evaluation. Configuration and performance requirements are governed by the applicable technical documents and written agreement.
Contact APEX to discuss your magnetorheological finishing equipment project.
[1] Dai, Y., Song, C., Peng, X., and Shi, F. (2010). Calibration and prediction of removal function in magnetorheological finishing. Applied Optics, 49(3), 298–306. Source
[2] Miao, C., Shafrir, S. N., Lambropoulos, J. C., Mici, J., and Jacobs, S. D. (2009). Shear stress in magnetorheological finishing for glasses. Applied Optics, 48(13), 2585–2594. Source
[3] Miao, C., Lambropoulos, J. C., and Jacobs, S. D. (2010). Process parameter effects on material removal in magnetorheological finishing of borosilicate glass. Applied Optics, 49(10), 1951–1963. Source
[4] Hu, H., Dai, Y., Peng, X., and Wang, J. (2011). Research on reducing the edge effect in magnetorheological finishing. Applied Optics, 50(9), 1220–1226. Source
This article provides general technical information and does not replace workpiece-specific process documents, inspection reports or safe operating procedures. Literature findings and illustrations do not establish the performance of APEX-supplied equipment or create an additional warranty. Obligations imposed by applicable law remain unchanged.
