The Ceramic Samurai

1. Room 3-470 77 Massachusetts Ave. Cambridge, MA 02139 Phone: (617) 253-1953 Fax: (703) 991-5353 http://pergatory.mit.edu/ The Ceramic Samurai Alex Ceramic Lathe Concept by Roger Cortesi Roger rcortesi@alum.mit.edu http://pergatory.mit.edu/rcortesi/ Precision Engineering Research Group Massachusetts Institute of Technology, Mechanical Engineering Department

2. Basic Machine Requirements • Turn Ceramic Parts of up to 15” diameter and 12” long • Target Part Accuracy of 1 micron (0.00004”) • Provide a “Dry” option for turning green parts • Robust with respect to Ceramic Swarf • Minimal Assembly

3. Early Machine Concepts • Simplest to Manufacture • More complicated to manufacture • Swarf can fall away from bearing surfaces • A possible design if it is not practical to move the spindle & work piece A few more variations on these concepts were considered in the 1st pass sketch models

4. The Dry Machine and Wet Machine have sufficiently different requirements, that they have developed into separate machine concepts. • Dry Machine • Much lower accuracy since it will be rough turning parts while they are still green. • No liquid coolants or lubricants to trap swarf and cause problems in firing the green part. Roger in the desert and very dry (just like the dry machine) • Wet Machine • A much higher stiffness and cooling requirement since it will turning finish parts to their 1 micron target accuracy. • Liquid coolants and lubricants are not a problem since the part has already been fired. Roger underwater and wet (just like the wet machine)

5. The Dry Machine and the Axtrusion The Axtrusion is a linear motion concept developed and implemented by Prof. Slocum and Roger Cortesi. It uses porous air bearings and linear motors to make an easy to assemble, non-contact linear motion system. Because it is a non-contact air system it will should be very robust with respect to the ceramic swarf

6. 2nd Generation Sketch of Dry Machine Rough Error Abbe Errors were calculated for this design with the following assumptions: • Average errors in Prototype Axtrusion used for the work piece and grinder carriage’s pitch, yaw, and roll errors. • No MAPPING CASE: Error magnitude is the actual error in prototype, 10 mradians (2 arc sec) • PERFECT MAPPING CASE: Error magnitude is the repeatability of prototype 2.5 mradians (0.5 arc sec) • No errors in spindles • Rough machine size based on a 15” dia. by 12” long work piece • All Magnitude Abbe errors are added for a worst case • Maximum Total Abbe Error • With NO Error Mapping • Radial 13 mm (0.0005”) • Axial 10 mm (0.0004”) • Maximum Total Abbe Error • With PEFECT Error Mapping • Radial 3.2 mm (0.00013”) • Axial 2.5 mm (0.0001”)

7. Notes on the Dry Machine Concept The previous error estimates are for an Axtrusion with a permanent magnet linear motor. A coreless linear motor would dramatically reduces these error motions further. • Total RMS Abbe Error • With NO Error Mapping • Radial 6.6 mm • Axial 5.0 mm • Total RMS Abbe Error • With PEFECT Error Mapping • Radial 1.6 mm • Axial 1.2 mm • Estimated Total Abbe Error • With NO Error Mapping • Radial 9.8 mm • Axial 7.4 mm • Estimated Total Abbe Error • With PEFECT Error Mapping • Radial 2.4 mm • Axial 1.8 mm

8. The Wet Machine Hydrobushing Rail Ballnut and Drive Motor Assembly Ballscrew Hydrobushing

9. The Wet Machine • This machine was designed to maximize accuracy at a minimum of cost • The motive force could come from either a coreless linear motor or a ballscrew. • The linear guides could be either traditional ballrails or a Hydrobushing • It should be very easy to assemble and error map

10. Wet Machine Concept Better dynamic stability due to heavy (and varying) workpiece mass mounted between rails It is easier to integrate wheel “dressing” station, since grinder is moving orthogonal to its axis. Better Access to Work Piece

11. Minimizing the Abbe Errors The machine was designed to bring the Center of Motion (COM) of the two axes as close the contact point as possible. If the COM for an axis can be brought inline with the axis of the spindle (either the grinder or work piece), then all the errors associated with either roll, pitch, or yaw of that carriage will vanish It is preferred to use the above technique to eliminate error due to carriage roll, since mapping the carriage roll over the length of travel is much more difficult. The Abbe errors in the X direction for the wet machine are estimated to be about half than the dry machine. The Abbe errors in the Z direction for the wet machine are about one third that those for the Dry Machine

12. Minimizing Motion Errors • The motive force for the two axis can be applied through the COM for each axis. This minimizes errors as the carriages are accelerated. • The Ballscrew and Ballnut/Drive Motor Assembly is designed to be removed straight of the end of the machine, making it very easy to replace when the swarf kills it. • A similar implementation could also be used for a coreless linear motor in place of the Ballscrew (eliminating the wear problem) Ballscrew acting on spindle carriage COM

13. The Wet Machine Structure The wet machine is base on a very simple structure. The two main pieces are shown below. These could be aluminum extrusions, a casing (polymer concrete, cast iron, etc) or pressed aluminum oxide. A third piece not shown will be needed to join the structure.

14. Load Fully Round Hydrobushing Partially Round Hydrobushing Sides flex outward, under load conditions, Fluid gap widens, stiffness lost Fully round End Support Hydrobushing Rail Completely Bottom Supported Hydrobushing Rail Hydrobushing Rails Because the axis only require a short range of motion the Hydrobushing rails can be completely round. This means that fully round Hydrobushing can be used. This eliminates the compliance due to a partially round Hydrobushing.

15. Load L Stiffness of an end clamped round beam Hydrobushing Stiffness Estimate

16. Questions Still Remaining • Where does one get the workpiece spindle? (This component will heavily affect the design.) • Are there suitable, infinite stiffness, and infinite life spindles available? • Should we build our own with the Hydrobushing. • Is there a standard grinding spindle that you like to use? • What the tradeoffs between a linear motor and an easily replaceable ballscrew? • What is the manufacturing cost goal?

17. Hydrobushing Supplemental Information

18. Hydrobushing™ Modular Bearings Concepts • Aesop Inc.’s self-compensating water hydrostatic bearing technology can be used to enable machines where: • Bellows can be eliminated • Bearing maintenance and wear can be virtually eliminated • Bushings can run on standard hard ground 2” diameter Stainless Steel shafting • Self-cleaning action can enable a friction drive to be used, thereby also eliminating the ballscrew • Modular: all features injection moldable or lost-wax castable (using rapid prototyping) Compensator-to-pocket connection grooves on OD Upper compensator for lower pocket “Picture frame” upper pockets for greater damping Supply groove Lower compensator for upper pocket

19. RodWay™ Self-Aligning Hydrostatic Ways • The RodWay system minimizes the need for precision alignment of bearing ways • Accommodates change in way parallelism if machine foundation changes • Machine accuracy is not affected by self-aligning function • Enables low-cost use of water hydrostatic bearings in rugged industrial environment • Old US Patent (4,637,738) OMAX can improve on with damping materials and rod-end bushing to create RodWay design and trademark • Operating principle: • One hard ground stainless steel round shaft (the fixed shaft) is mounted in a normal manner using supports that can be replicated to structural steel so the shaft remains straight • The second round shaft (the pivot shaft) is mounted as parallel as is reasonable to the first • One hydrostatic bearing carriage rides on the fixed shaft, and it is bolted to the machine structure (e.g., bridge structure risers) • One hydrostatic bearing carriage rides on the pivot shaft, and it is connected to the machine structure (e.g., bridge structure risers) by a spherical bearing • A steel hemisphere stud mounted in the machine structure and resting in a replicated spherical seat in the bearing carriage, where the center of the hemisphere is a distance H above the round shaft center • Alignment errors (pitch and yaw) between the round shafts are accommodated by the spherical bearing • Center distance errors (d) between the round shafts are accommodated by roll (q) of the bearing carriage. • Vertical error motion (D) of the hemisphere is a second order effect • Example: d = 0.1”, H = 4”, q = 1.4 degrees, and D = 0.0012”

20. Axtrusion Supplemental Information The slides that follow contain: • Background information on the Axtrusion • Performance Data on the Prototype Axtrusion

21. Axtrusion Components Not Shown: Position Encoder and Position Encoder Scale

22. How the Axtrusion™ Works The attractive force between the motor coil and magnets preload the air bearings. Changing the values of q, ym, and zm the values for Fside, Ftop1, and Ftop2 can all be set independently

23. The Bench Level Prototype Magnet Adjustment Screw Magnet 2 Rollers (side surface) Way side surface Way top surfaces 3 Rollers (top surface) The first Axtrusion ever built! It uses 5 CAM rollers as bearings

24. Load Applied Here Vertical Displacement Measured Here The Pitch, Yaw, Position Accuracy,Vertical Straightness, and Vertical Stiffness Setup. The basic setup for the pitch, yaw, and accuracy measurements. A laser and a variety of optics was used to make each measurement. The basic setup for the vertical straightness measurement. The probe is suspended above the straight edge on the carriage. The basic setup for the vertical stiffness measurements The load is applied in the center of the carriage and measurements made above each of the top bearing pads.

25. Raw Accuracy: 2.44 arc sec Raw Repeatability: 0.50 arc sec The Pitch Data Period of Variation 29.9 mm This period is the distance between alternating poles on the magnet track! Measurements every 10 mm Carriage Speed of 10 mm/sec 6 passes (3 in each direction) The way also appears to be slightly curved (from –0.5 arc seconds to +0.5 arc seconds). Pitch data was also taken at a carriage speed of 40 mm/s, after incremental movements, and as a function of time. There were no major differences. Please see the appendix for the complete data.

26. Raw Accuracy: 1.59 arc sec Raw Repeatability: 0.56 arc sec The Yaw Data Raw Yaw Data Yaw Data with Linear Slope Removed Measurements every 10 mm Carriage Speed of 10 mm/sec 6 passes (3 in each direction) Period of Variation 30.1 mm Pitch data was also taken at a carriage speed of 40 mm/s, after incremental movements, and as a function of time. There were no major differences. Please see the appendix for the complete data.

27. Raw Accuracy: 1.34 micron Raw Repeatability: 0.33 micron The Linear Accuracy Data Raw Linear Accuracy Data Linear Accuracy with Linear Slope Removed This is the difference between the actual carriage position and the position that the controller thinks it is in.

28. Carriage Carriage errors in pure translation Abbe error Carriage Carriage errors in pitch translation The Vertical Straightness Data An Abbe error of 1.2 microns vertical displacement at both edges of the carriage. Data for displacement of carriage center Period of Variation is 28.6 mm Notice that the hourglass shape of the data is due to pitch errors measured away from the center of pitch rotation. To get better data, the test must be rerun with the probe mounted in the middle of the carriage and the mirror suspended above it. The data from the center of the carriage shows the pure translation of the carriage to be about 0.3 microns. Data for displacement of carriage edges. Two passes are shown for a carriage speed of 10 mm/s Because the plane mirror could not be leveled perfectly, any linear slope in the data was removed.

29. Load Applied Here Vertical Displacement Measured Here The Vertical Stiffness Data Masses were place on the top center of the carriage and the displacement above the four (4) top air bearings was measured.