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MODELING OF VIBRATION IN SINGLE-POINT DIAMOND TURNING

Alex Sohn, Lucas Lamonds and Ken GarrardPrecision Engineering Center

North Carolina State University

Raleigh, North Carolina, USA.

INTRODUCTION

The objective of this work is to develop a modelto simulate the effects of vibration on the surfacefinish of single-point diamond turned parts. Thismodel can be used to optimize cutting conditionsfor best surface finish and to predict geometriccharacteristics of the surface beyond theconventional rules of thumb. These

characteristics can also have a significantimpact on optical surfaces that operate in thevisible range by introducing coherent scatter thatproduces the familiar rainbow appearance ofdiamond turned surfaces in white light.

Surface finish in single-point diamond turning isprimarily influenced by four factors: Geometry,vibration, material properties, and tool edgequality. The first-order geometric model usingthe parabolic approximation gives the peak-to-valley roughness which is determined solely bythe crossfeed (f), and the tool radius (R).

RfPV8

2

= (1)

This approximation is often used as the soledeterminer for choosing radius and feedrateeven though at large radii and small feeds, thepredicted finish is not achievable.

VIBRATION

Assuming suitable materials are selected andthe tool edge quality is high, vibration is typicallythe next largest factor in determining surfacefinish. The origin of this vibration can be from anumber of sources, although the axes of the

machine or the spindle are the most likelycandidates. The ASG 2500 Diamond TurningMachine at the Precision Engineering Centersuffers mainly from a 65 Hz vibration of the Z-axis which has a magnitude of about 30 nm.This amplitude can vary slightly depending onspindle rpm and balance. Either of these canincrease this vibration. For the purposes of thefollowing discussions and examples, thevibration of the ASG 2500 Z-slide will be used as

the source of the vibration, though the techniquecan be applied to any source.

The impact of vibration on a diamond-turnedsurface is generally to degrade the surfacefinish. In its simplest form, a sinusoidal vibrationin the normal direction would leave an RMSsurface finish of 0.707 times the amplitude of the

vibration. It would seem that the surface finishcould never be improved beyond this value andthere would be no point in slowing the feedrateor using a larger radius tool. This assumption is,however, incorrect due to interaction betweenneighboring grooves at small feedrates. Bymodeling the surface produced by a vibratingtool, it can be shown that the surface finish is nolonger limited by the vibration amplitude but canbe improved by moving to finer feedrates.

THE SURFACE FINISH MODEL

A number of points along the edge of the toolare calculated for each x-position in incrementsof the crossfeed. The depth of cut changesaround the periphery of the part with thevibration environment.

=

f

xAdepth

sin (2)

where A is the vibration amplitude, is thevibration frequency of the tool, x is the radialposition of the tool and is the vibrationfrequency of the spindle.

As shown in Figure 1, after multiple profiles aregenerated, redundant points in the overlapping

regions are eliminated and only the point withthe largest depth at each x-coordinate isretained. Individual cross-traces at differentrotational positions of the spindle can then alsobe assembled into 3D profiles as shown inFigure 2.

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FIGURE 1. Points along multiple tool profiles, atvarying depths due to vibration, produce afinished surface contour.

FIGURE 2. Multiple simulated surface profilesassembled into a 3-D surface.

It is at lower feedrates that the effects of toolvibration on a diamond-turned surface becomeinteresting as illustrated in Figure 3. Theillustration shows the surface left at smallfeedrates where the crossmarks show the toollocation at each pass in the profile. A number ofpasses are not represented at all in the finishedsurface, leaving only the most extreme passesand, hence, a smoother surface than would beexpected if all cuts were represented.

FIGURE 3. At fine feedrates, some passes ofthe tool (+) are not represented in the finishedsurface. This produces a better finish than

would be expected from the RMS of thevibration alone.

EXPERIMENT

To verify the simulations, a plated coppersample was machined with the same feedratesused in the simulations. Machining experimentswere performed on an ASG 2500 DTM using a505 rpm spindle speed and a 0.5 mm radius,zero rake natural diamond tool. The laboratorytemperature was controlled to 20 0.05C.Petroleum oil cutting fluid (Mobilmet Omicron)was used for lubrication and chip removal.

Eight 2 mm wide bands were machined on the50 mm diameter sample with crossfeeds of 0.6,0.9, 1.9, 2.7, 6.1, 8.6 and 19.1 m/rev. Thesurface was ultrasonically cleaned and thenmeasured on a Zygo NewView 5000 ScanningWhite-Light Interferometer (SWLI) using 50Xmagnification. The measurement area is 108m X 144 m. Figures 4 and 5 show the typicalprofile measurement result. The effects ofvibration on groove depth can clearly be seen inthe profile at this large feedrate. The depthvaries seemingly randomly as the tool traversesthe part. Note a small chip is visible in the tool

edge as a repeatable defect from each pass. Atfiner feedrates, this portion of the tool does not,however, have an effect.

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FIGURE 4. Typical surface profile measurementillustrating the depth change as a result ofvibration with large feed rate of 12 m/rev.

FIGURE 5. A typical measurement result inoblique plot form. This is the same machinedsurface shown in Figure 4.

Feedrate (m/rev)

FIGURE 6. Triangles show the simulated finish with vibration and the squares show the machiningresults. Variation in roughness around the periphery is shown in both model and experiment.

Figure 6 shows the results for a series ofsimulations and cuts performed to verify themodel. The plot also shows the line thatrepresents the theoretical finish approximationfor a parabolic surface.

R

fRMS

6.26

2

= (3)

Clearly, the surface finish can improvesignificantly beyond the RMS 7.7 nm limit of asimple sinusoidal vibration. The finish alsocontinues to improve with finer feedratesbetween 2 and 5 m, when they already deviatesignificantly from the theoretical approximation.

ENVIRONMENT

As the results displayed in Figure 6 show, attheoretical finishes below 2 nm RMS, the modeldoes not predict the surface finish. At theseextremely fine finishes, other factors begin to

take effect such as environmental effects andmaterial anisotropies. While the temperature inthe laboratory is controlled to less than 0.1C,even such small temperature fluctuation canhave an impact. At small feedrates, the long-period fluctuations of the temperature over 1-8min can have an impact on finish, as shown inFigure 7.

The Z-axis deadpath on the ASG 2500interferometer was approximately 250 mm at theposition where the sample was machined.

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Given a maximum temperature variation of 0.1C, the calculated resultant deadpath error usingthe Edln equation[1] is 25 nm. This limitationreflects the need to reduce deadpath,compensate for environmental fluctuations witha refractometer, operate in a vacuum, or useanother means of position feedback such as alinear encoder. While linear encoders do noteliminate errors due to thermal fluctuations,expansion of the scale due to temperaturechanges tends to have a much longer period, soerrors move into the figure error regime ratherthan roughness.

FIGURE 7. Temperature fluctuations at lowfeedrates can produce surface finishdegradation due to deadpath error in the DTMlaser interferometer.

MATERIALS

Material effects, such as inclusions or grainboundaries have a much larger impact in

materials such as 6061 Aluminum[2], thoughapparently there are still defects even in theplated copper used as shown in Figure 8.

FIGURE 8. 3D surface profile of a plated coppersurface machined at fine feedrates showing pitsin the surface due to material defects.

The final contribution to a degraded surfacefinish is from errors in the control of the axes. Inthe case of the ASG, tests of the custom, DSP-based, controller showed tracking errors of less

than 10 nm Peak-to-Valley [3]. While of somesignificance, the effects of this tracking error arestill not as significant as those due totemperature variations and material defects.

CONCLUSION

Understanding what determines surface finishenhances the ability to improve surface finish inthe most efficient manner. It also allows us toexploit all of the capabilities of a diamond turningmachine to achieve the best possible finish forthat machine. The conventional wisdom thatthere is little point in machining at lowerfeedrates beyond the point where the measuredsurface finish is worse than the theoretical finish(obtained from the parabolic approximation)simply does not hold. Ever finer feedratescontinue to reduce the impact of vibration to apoint where it does not impact the surface finishany more and material or environmental effects

take over. In the particular case of the PECsASG 2500 DTM, lower feedrates than 2 musing a 0.5 mm radius tool do not improve thesurface finish. Factors other than vibrationdominate below this feedrate. Until these theimpact of these factors is reduced, smallerfeedrates simply add time to the machining effortwith little gain.

FUTURE WORK

In another application, the model can be used toperform the same analysis with the tool vibratingparallel to the surface. The advantage of this

action is that the normally regularly spacedgrooves formed in diamond turning that turn thesurface into a diffraction grating can berandomized. This could reduce coherentscattering that produces undesirable structure inthe optical output that often makes diamond-turned optics unsuitable for visible applications.

REFERENCES

[1] Alexander H. Slocum, Precision MachineDesign 1994 John Wiley, New York.[2] John P. Schaefer, Progress in Precision Single Point Diamond Turning (SPDT) of Optical

Components ASPE Proceedings 2001 SpringTopical Meeting Presentations DVD.[3] T.A. Dow, L. Lamonds, Fabrication of OpticalSurfaces and Fiducials, 2005 PEC AnnualReport, pg 81.