Effect of System Dynamics on Surface Topography in Fast Tool Servo-Based Diamond Turning of Microlens Arrays
At a Glance
Section titled âAt a Glanceâ| Metadata | Details |
|---|---|
| Publication Date | 2025-05-12 |
| Journal | Nanomanufacturing and Metrology |
| Authors | Takeshi Hashimoto, Jiwang Yan |
| Citations | 3 |
| Analysis | Full AI Review Included |
Executive Summary
Section titled âExecutive SummaryâThis study investigates and optimizes the ultraprecision diamond turning of microlens arrays using a Fast Tool Servo (FTS) system, focusing on mitigating surface waviness induced by system dynamics.
- Core Problem Solved: Dynamics-induced surface waviness, particularly high Sdq values (slope change) at the lens array edges, was traced directly to the FTS servo response behavior.
- Dynamic Identification: The FTS system exhibited a resonant frequency of 1367 Hz, which correlated strongly with the observed ripple pattern in the tool position error signal.
- Optimization Strategy: A new machining strategy was implemented based on system settling time (identified as 0.001 s). This involved maintaining a constant, low surface speed (5 m/min) across the entire array and applying a 5.0 ”m tool offset in the uncut zone for stabilization.
- Waviness Reduction: The optimized strategy reduced the average Sdq (waviness amount) from 93.3 ”rad to 49.9 ”rad (a 53% improvement).
- Consistency Improvement: The standard deviation of Sdq across all lenslets was drastically reduced from 33.5 ”rad to 3.1 ”rad (a 90% improvement), ensuring uniform form accuracy.
- Surface Quality: Average surface roughness (Sq) improved from 2.8 nm (unoptimized) to 1.6 nm (optimized).
- Contribution: Provides a methodology for optimizing FTS cutting parameters based on real-time system dynamics analysis, crucial for high-productivity manufacturing of advanced optics.
Technical Specifications
Section titled âTechnical Specificationsâ| Parameter | Value | Unit | Context |
|---|---|---|---|
| Workpiece Material | Oxygen-free copper | N/A | Substrate machined |
| Lens Array Layout | 10 x 10 | N/A | Total 100 lenslets |
| Lenslet Diameter | 1.7 | mm | Concave sphere design |
| Lenslet Radius | 20 | mm | Concave |
| Tool Type | Natural diamond | N/A | Tool radius 0.496 mm |
| FTS Acceleration Limit | 25 | G | Hardware constraint |
| Unoptimized Spindle Speed | 125 | rpm | Constant spindle speed test (Max surface speed 17 m/min) |
| Optimized Surface Speed | 5 | m/min | Constant surface speed strategy |
| FTS Resonant Frequency (Ïr) | 1367 | Hz | System dynamics identification |
| FTS Settling Time (Calculated) | 0.001 | s | Within linear system bandwidth |
| Optimized Tool Offset | 5.0 | ”m | Applied in uncut zone for stabilization |
| Unoptimized Avg Sdq (Waviness) | 93.3 ± 33.5 | ”rad | Average ± Standard Deviation |
| Optimized Avg Sdq (Waviness) | 49.9 ± 3.1 | ”rad | Average ± Standard Deviation |
| Optimized Avg Sq (Roughness) | 1.6 | nm | Root mean square height distribution |
Key Methodologies
Section titled âKey Methodologiesâ- Machining Platform: Fabrication was performed on an ultraprecision diamond turning machine (Nanoform X) utilizing an independent Fast Tool Servo (FTS5000) system (W-axis) with a 5 mm full stroke and fully closed feedback control.
- Initial Parameter Selection: Cutting parameters were initially set based on the FTS acceleration limit (25 G), resulting in an unoptimized spindle speed of 125 rpm and a finish feed rate of 0.002 mm/rev.
- Dynamics Data Acquisition: The FTS command signal and actual position signal were captured by a data analyzer at a sampling frequency of 20 kHz during the machining process.
- Position Error Analysis: Servo delay (223.5 ”s) was calculated and canceled from the captured signals. The resulting following error plots revealed a ripple pattern whose cycle time (0.75 ms at 20 m/min surface speed) correlated with the waviness cycle observed on the surface (0.70 ms equivalent).
- System Identification: The FTS control system characteristics were derived using a frequency response plot (resonant frequency 1367 Hz, peak magnitude +1.0 dB) and step response curves, yielding an approximated natural frequency of 2029 Hz and a damping ratio of 0.523.
- Waviness Quantification: Surface topography was measured using a Coherence Scanning Interferometric (CSI) optical profilometer. Waviness was quantified using the Sdq parameter (root mean square of the gradient) after applying a form removal process (4th-order polynomial) and a low-pass Gaussian filter (100 ”m wavelength).
- Optimization Implementation: The cutting strategy was optimized by switching to a constant surface speed of 5 m/min (within the FTS linear system range) and incorporating a calculated tool offset of 5.0 ”m from the uncut zone, ensuring the FTS stabilized (settling time 0.001 s) before engaging the surface.
Commercial Applications
Section titled âCommercial ApplicationsâThe ultraprecision FTS-based diamond turning methodology developed for high-quality microlens arrays is critical for several advanced optics sectors:
- Advanced Sensing Systems: Manufacturing components for autonomous technologies and high-resolution imaging devices where surface waviness is highly detrimental to performance.
- Optical Metrology: Fabrication of high-accuracy lens arrays used in Shack-Hartmann wavefront sensors (SHWSs) for measuring wavefront errors.
- Consumer and Medical Optics: Production of complex structured surfaces, such as chirped microlens arrays for laser beam homogenization, and lens arrays used in ophthalmic devices for myopia control (spectacle lenses).
- Augmented/Virtual Reality (AR/VR): Fabrication of advanced optical components for wearable devices, requiring nanometer-level form accuracy.
- Freeform and Structured Optics: General ultraprecision manufacturing of various advanced optics, freeform surfaces, and structured surfaces where high productivity and form accuracy are simultaneously required.
View Original Abstract
Abstract A lens array is often used for optical components of sensing devices, requiring high surface quality and form accuracy. Fast tool servo (FTS)-based diamond turning is one of the technologies for manufacturing complicated shapes, such as freeform optics, structured surfaces, and microlens arrays, with high machining efficiency. In this study, lens array machining was performed on copper using an FTS on a diamond turning machine. For evaluating the lens array surface topography, the focus was on surface waviness formation. As a dominating factor of surface waviness, the system dynamics behavior was investigated by capturing and analyzing the position signal. It was found that a specific waviness pattern could be formed on the surface due to the servo response. By considering the dynamics of the FTS system from the captured signals, the FTS system behavior was identified, and optimal machining parameters for the lens array were proposed. A machining test under the optimized cutting conditions reduced the average Sdq used to quantify the waviness amount from 93 to 50 ”rad and the standard deviation from 33 to 3 ”rad, which greatly improved the consistency in accuracy for all lens arrays. This study will contribute to the appropriate utilization of FTS systems in the ultraprecision machining of various advanced optics, such as microlens arrays.