development of optimal grinding and polishing tools for aspheric surfaces marty valente jim burge,...
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Development of optimal grinding and polishing tools for aspheric surfaces
Marty Valente
Jim Burge, Bill Anderson, Scott Benjamin,
Myung Cho, Koby SmithOptical Sciences Center
University of Arizona
Fabrication of spherical surfaces
• Spheres are natural and easy, as long as you use– large stiff tools– good supports– smart polishing strokes,
• The tool and the part tend to wear to form mating spheres– The tool always fits the surface, giving rapid convergence,
excellent surface
• Measurement is easy - interferometer, spherometer
The process itself results in a spherical surface
The largest lens (in the world?)
• 1.8-m diameter test plate for measuring the MMT wide field secondary mirror
• Both sides spherical, concave side requires high accuracy• Polished at OSC to achieve slope spec of 0.01 waves/cm • Now has computer generated hologram on concave surface
polishing handling Final figure
Grinding and polishing aspheric surfaces
• The process by itself does not converge to make the correct shape
• It is necessary to set up an accurate test, and work the surface based on the measurement
• The laps generally do not fit the aspheric surface so– there is no tendency towards the correct shape– special attention must be paid to the surface finish
General lap misfit for aspheres
•Circular lap radius a•off center by bAspheric departure is
dominated by lowest modes, with P-V deviation from vertex fit of
The grinding and polishing tool must always accommodate the misfit, as the tool is rotated and stroked over the part
Mechanisms for working aspheric surfaces
• Lapping relies on two mechanisms for correcting shape errors:– Directed figuring : rubbing more, or pressing harder on the
high spots– Natural smoothing : Using a stiff lap, small scales bumps
are naturally worn down
• Optimal tooling will take natural smoothing as far as possible to maximize efficiency
Control of small scales by smoothing
Stiffness of lap
Grinding and polishing of aspheres, always fighting between two issues:
#1) Desire to use large, rigid laps for passive smoothing#2) Requirement that the lap conform to the asphere
– usually leads to small tools or flexible tools at the expense of #1– for small parts, it can be economic to use small tools under computer
control
Optimal lap, controlled to fit the asphere, and very stiff to figure errors
Next best thing, lap is compliant in modes necessary to fit the asphere, yet remains stiff to figure errors
Large tool for aspheres - stressed lap
• Used at Steward Observatory Mirror Lab for f/1 mirrors• 1.2-m, 60 cm, and 30 cm stressed laps are in operation• bent by actuators as the lap is moved, • NC shape changes every msec so it always fits desired asphere • bends up to 1 mm 6.5-m f/1.25 14 nm rms
Active vs. passive laps
• The actively controlled stressed lap works extremely well, yet requires significant initial investment and maintenance.
• Is it possible to design a lap that is naturally compliant to the modes required to fit the asphere, yet remains stiff enough for natural smoothing?
The magic of rings
Power Coma
Function a2r2 a31r
3cos = a31r
2x
for rings ofconstant r
ring shifts withr2 dependence
ring tilts withr2 dependence
Shape
Cross section
If the lap is shaped like a ring, power and coma terms go away
Bending required for ring tool - Astigmatism
Astigmatic bending
• Rings bend easily in astigmatism if the cross section is compliant in torsion
• Use geometry to make rings stiff locally in one direction
• Analogy, bandsaw blade. – Totally compliant for astigmatism– Very rigid over scales of few inches
• So a lap made from thin rings will fit the asphere!Power and coma are taken up by rigid body motion and astigmatism is easily bent in
An important detail for the rings - coning
Cylindrical rings, pressure aligned for maximum stiffnessfor near-flat surfaces only
For curved surfaces, tilted interface causes torsion, too compliant!
Solution:Tilt the beam, rings then become sections of a cone, rather than a cylinder
Cross-section of ring
Polishing pressure
Grinding or polishing pad
Flexible, incompressible joint
Ring tool design
We need to use nested rings to get sufficient polishing area
The rings can be faced with either grinding or polishing pads
The cross sectional height and width of the rings are chosen using finite element modeling to determine the stiffness.
4.0 m
0.6 m
1.5 m
0.9 m
Calculation of ring geometry
Using finite element modeling, we created an empirical model of ring stiffness as function of cross section geometry
Then, for each ring in the nested set:
The aspheric departure is calculated to determine the amount of astigmatic bending required for each ring, at the end of its stroke.
Choose ring cross section to allow the ring to bend by the required amount, forced by pressure variations small compared to the nominal polishing pressure.
Software for designing ring tools
User enters parameters for asphere and desired tool size and stroke
Software calculates the corresponding ring geometry
Attachments of rings
• Allow vertical motion using guide rods in linear bearings
• Allow rotation using spherical joint• Constrain lateral motion• Lateral force near polishing surface
to minimize moments• Supply drive force in circumferential
direction• Apply force using weights• Designed for fabrication ease
ring
Support frame
weight
Teflon bearing
spring
guide rod
ball joint
Teflon bearing
Grinding interface• Use pads, small enough to always fit
asphere • Stiff attachment to ring• Pivot on ball bearing• Held on by silicone• Grinding surface - metal • Polishing surface - urethane • Design for fabrication ease• Maintenance is important
ring
ball joint
guide rod
Aluminum pad with seat for bearing
RTV
grinding/polishing surface
ball bearing
Prototype ring tool
Working 40 cm f/0.5 asphere
Preliminary results from ring tool
• The tool is basically well-behaved– not problems at edge– no problems with chatter
• Fits the aspheric surface• Good smoothing achieved
Initial Ronchigram, after aspherizing with full size compliant tool
Ronchigram, after 4 hr run with the prototype ring tool
Ring tool frame
• Connects drive pin to rings• Has bearings for guide rods• Frame “floats” on rings using soft
springs• Drive torque and lateral forces
taken at hub• Lifting eyes are used to hoist frame
3-m tool for 4-m f/0.5 paraboloid
Membrane laps
• Smaller laps can achieve a good compromise between desired stiffness for smoothing and compliance to fit the asphere using laps faced with membranes
Pin, connecting to polishing machine
Compliant interface (CC neoprene foam)
Membrane
Grinding or polishing pads
Rigid tool
Membrane stiffness
• Finite element used to establish modal stiffness of membrane• Solve for membrane thickness for a given tool, stroke, and membrane
material• Membrane stiffness goes as t3
• Stiffness to ripples on the surface goes as L-4
– L is the period of the ripple
• Membranes with the correct curves can be made by – direct machining– hot-forming plastic sheets onto surface– casting, layup on surface
Membrane Tool’sAspheric Misfit
Analysis using modal decomposition
Displacement
Displacement
Displacement
Displacement
Pressure Distribution
Pressure Distribution
Pressure Distribution
Pressure Distribution
Required Pressure Distribution
Displacement Pressure
The modal stiffness was calculated using a finite element model
Note that the dominant pressure variations are at the edge of the tool
Software for designing membrane tools
User enters parameters for asphere, desired tool size and stroke
Given membrane, software calculates pressure distribution under lap
or given allowable pressure distribution, software calculates membrane thickness
Experience with membranes
Initial Ronchigram
After 5 hours directed figuring with membrane toolFor f/0.5 convex
asphere
(tested in transmission)
Tool made by hot forming plastic sheet, faced with grinding pads
Conclusion
• There is much activity and interest at the University of Arizona in the area of fabrication of aspheric surfaces.
• Stay tuned! Things develop very quickly