Ultra-Precision Optics & Freeform Micro-Machining

Fast Tool Servo (FTS) Freeform Optics Diamond Turning Calculator

Precision dynamic toolpath kinematic solver for single-point diamond turning (SPDT) of freeform optical surfaces, micro-optics, and HUD mirrors.

1. Input Parameters

Spindle Speed (N, RPM)

Ultra-precision air-bearing spindle rotational velocity

Part Outer Radius (R_max, mm)

Maximum freeform optical clear aperture radius

Azimuthal Symmetry / Waves per Rev (m)

Peak-to-Valley Z-Sagitta Stroke (Z_pv, µm)

Total dynamic travel of Piezo / Voice-Coil FTS actuator

Diamond Tool Nose Radius (r_tool, mm)

Single-crystal natural diamond tool nose radius

Target Surface Roughness (Ra, nm)

Target optical specular finish (typical 1 - 5 nm Ra)

2. Calculation Results

FTS Operating Frequency (f_FTS)

50.0 Hz

Max Tool Acceleration (a_max)

19.7 m/s² (2.0 G)

Max Spiral Feed per Rev (f_rev)

3.46 µm/rev

Total Spiral Arc Length

2,267 m

Estimated Machining Time

9.6 min

FTS Actuator Feasibility

Optimal (Piezo Range)

3. Dynamic Visualizer & CAM Preview

4. Engineering Notes & Physics Specifications

Fast Tool Servo (FTS) diamond turning enables ultra-precision single-point diamond machining of non-rotationally symmetric optical surfaces (freeforms, Alvarez lenses, toric intraocular optics, HUD mirrors) by modulating tool position at high bandwidth synchronized with spindle encoder angle $\theta$.

Dynamic Tool Kinematics: Operating frequency $f_{\text{FTS}} = m \cdot \frac{N}{60}$. Peak dynamic acceleration: $a_{\text{max}} = \pi^2 f_{\text{FTS}}^2 Z_{\text{pv}}$.
Theoretical Surface Finish (Cusp Height): In the radial direction, surface roughness follows $Ra = \frac{f_{\text{rev}}^2}{32 r_{\text{tool}}}$. The maximum spiral feedrate per revolution is $f_{\text{rev}} = \sqrt{32 r_{\text{tool}} Ra}$.
3D Tool Nose Vector Compensation: CAM post-processors must compensate for diamond tool nose curvature ($r_{\text{tool}}$) in 3D polar coordinates $(r, \theta, z)$ with sub-nanometer interpolated spline trajectory points.

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