VIBRATION ATTENUATION IN OPTICAL PITCH

Mohammad Mainuddin1, and Brigid A. Mullany1 1Department of Mechanical Engineering and Engineering Science

University of North Carolina at Charlotte Charlotte, NC, USA

INTRODUCTION Optical polishing pitch has been used to obtain high quality optical surface finishes with little subsurface damage. A pitch tool consists of a metal platen coated with a layer of polishing pitch whereby pitch is a viscoelastic material naturally derived from tree resin [1]. Synthetic versions are also produced [2]. Polishing with pitch was first introduced by Sir Isaac Newton in the 1700’s and has since been used to produce high quality optical surfaces [3]. Pitch polishing can generate surfaces with roughness and flatness values less than 1 Å RMS and �/20 respectively [4]. As pitch is viscoelastic it has the ability to flow (creep) with time [5], enabling the pitch to deform and make good contact with the work piece. The influence of temperature and preparation methods on its long term response has been described in several published papers [1, 6, and 7]. Until recently, the short term (millisecond domain) dynamic response of pitch has not received much attention. Previous work by this research group utilized an impact frequency response test to evaluate the effect of pitch type and age on the transient responses [8, 9]. These tests demonstrate that each grade (hardness) and type of pitch (natural or synthetic) has unique dynamic properties. Age also affects the response of natural pitches. During polishing the system is more likely to be subjected to steady state than transient vibrations, i.e. consistent machine/process vibrations. Are all vibrations transferred through the pitch to the workpiece surface? Do vibrations have an impact on polishing outcomes such as roughness and material removal rates (MMRs)? Recent work done by the group utilized a shaker table (described later) to impart steady state vibrations into the pitch sample across a wide frequency bandwidth (50 Hz - 16 kHz) [9]. Initial results revealed that all vibrations input into the pitch sample were transmitted through the pitch. The transmitted process vibrations do not undergo any attenuation, but are somewhat amplified as shown in Figure 1 [10]. Vibration transmission through the pitch should be

controllable if their affect on MRRs and surface finishes are to be determined.

FIGURE 1. Transmission of vibrations through pitch (Acculap™VeryFirm) [10]. As early testing indicated all pitches failed to attenuate vibrations a passive damping material is required. Nine different materials (vinyl, gum, neoprene, viton, polyurethane, nitraile (Buna N), rubber, cork, and lead) were evaluated on the shaker table to assess their ability to provide attenuation between 50 Hz and 16 kHz. Completed experiments show that at lower frequencies (50 Hz to 450 Hz) the input vibrations are somewhat amplified as they pass through the passive damping sheets, but at higher frequencies (above 550 Hz) the input vibrations are significantly attenuated. The following sections provide more details on the materials tested, the experimental set up, and the results. SAMPLE PREPARATION In this experimental investigation, two different sample configurations are tested. The first configuration, Type-A, identifies the damping quality of different passive damping materials. It consists of the passive damping material adhered to an aluminum platen (6 mm thick and 50 mm in diameter), see Figure 2(a). An alternative version of Type-A samples has an additional thin sheet of lead attached to the damping material to increase the mass of the sample. The second configuration, Type-B,

0

1

2

3

4

5

6

7

0 4 8 12 16

Tra

nsm

ittan

ce ra

tioFrequency (kHz)

Pitch

Al. Platen

, X/Y X

Y

Input vibration

consists of a Type-A samples with 50g of pitch attached the damping material, see Figure 2 (b). A parameter termed as Inverse Quality Factor, Q-1 [11] is used to identify the damping quality of different materials. Higher Q-1 value means higher damping ability.

FIGURE 2. (a) Type-A, and (b) Type –B Sample. To generate Type-A samples, different damping sheets are cut to size and glued (3M Super 77 Aerosol Spray Adhesive) on to the aluminum platen. Acculap™VeryFirm pitch is used in Type-B samples. A defined mass (50g) of melted pitch is poured into a cylindrical shaped silicon molds which contains the platen and passive damping material as its base. Type-B samples are cooled overnight before removing from the molds. The evaluated Type-A and Type-B samples are listed in Table 1 and Table 2. While more materials than listed in Table 1 were tested, preliminary testing eliminated them from full testing. TABLE 1. Evaluated Type-A foam samples.

Type-A Name Damping material

A1 3.18 mm Vinyl Extra Soft A2 3.18 mm Vinyl Soft A3 3.18 mm Gum Extra Soft A4 3.18 mm Gum Soft A5 3.18 mm Polyurethane Extra Soft A6 3.18 mm Viton Extra Soft A7 3.18 mm Neoprene Extra Soft A8 6.35 mm Gum Extra Soft A9 1.1 mm lead sheet (� 24g) between

3.18 mm Vinyl Extra Soft layers A10 1.6 mm lead sheet (� 35g) between

3.18 mm Vinyl Extra Soft layers A11 9.53 mm Vinyl Soft A12 6.35 mm Vinyl Soft A13 12.7 mm Gum Soft A14 6.35 mm Gum Soft A15 3.18 mm lead sheet (64g) on A12

TABLE 2. Evaluated Type-B samples.

Type-B Name Damping material

B1 Acculap™VeryFirm on A12 B2 Acculap™VeryFirm on A15

Samples A1 – A7 have same thickness and used to identify the damping quality of different materials. Test results will show (Figure 5) that Vinyl Soft and Vinyl Extra Soft foams have the best damping quality among the tested materials. Samples A8 – A15 evaluated different thicknesses of the Vinyl and Gum foams to determine if the Q-1 could be further improved. Samples with added lead sheeting are also evaluated. EXPERIMENTAL SETUP AND TEST PROCEDURE The test setup consists of a shaker table (BK Vibration Exciter Type 4809) driven by a HP35639A dynamic signal analyzer (DSA). The shaker table can vibrate up to 20 kHz with a maximum displacement of 8 mm. The sample under investigation is screwed onto the shaker table. The vibrations entering and exiting the sample are monitored by two accelerometers (PCB 352B10) that operate up to 17 kHz. See figure 3 for a schematic of the set-up, figure 4 illustrates photos of the shaker table and mounted sample.

FIGURE 3. Block diagram of the test setup.

FIGURE 4. Close up of sample mounted on shaker table.

a

Aluminum platen

Vinyl foam

20 mm

b

Pitch

Vinyl foam20 mm

Digital Signal Analyzer (DSA)

Amplif ier

Shaker Table

Signal Conditioner Sample

A2

A1

A1 & A2 = Accelerometer

Signal Conditioner

Swept Sine-wave

X

Y

A2

A1

DSASample, see inert

Pitch

Vinyl foam

Shaker table

20mm

In this investigation the samples were subjected to a swept sine wave input (50 Hz to 5 kHz, preliminary tests shown that above 5 kHz all input vibrations are damped out). Step increments were 12.375 Hz. Typical vibration amplitudes range from 30 µm to 2.5 nm. The resulting accelerometer readings are monitored by the DSA, and the ratio of the top accelerometer (A2) output (X) to the bottom accelerometer (A1) output (Y), i.e. the vibration transmittance (X/Y) is plotted versus the input frequency. The results from testing all samples listed in Table 1 and Table 2 are given in the following section. RESULTS AND ANALYSIS In most cases multiple samples of each material were evaluated. Each curve in the graphs represents a samples’ typical response. Note for the sake of clarity the full frequency response (up to 5 kHz) is not illustrated in the graphs. In all cases with increased frequency (above 1450 Hz) the transmittance continued to decay to less than 0.02. Samples were evaluated with respect to the Q-1 factor, maximum vibration amplification, and the frequency at which X/Y < 0.5 (50% attenuation). Results for Type-A samples Figure 5 depicts the response curves for samples A1 to A7.

FIGURE 5. Vibration transmission for different damping materials. Calculation of the Q-1 factor from the experimental data revealed that sample A1 (Vinyl Extra Soft) has the highest Q-1 value (1.45), and 50% attenuation was attained at the lowest input frequency (540 Hz). While the Q-1

value for A2 (Vinyl Soft) was not as high (0.52), it did provided 50% attenuation at a similar frequency to A1 and thus is considered for further evaluation. From an application point of view A2 is preferred over A1 as it is considered more mechanically robust and not as compressive as A1 suggesting it would be better suited for use on an actual polishing tool. Sample A6 has a high Q-1 factor but is not considered further at this point for two reasons, firstly, 50% attenuation doesn’t occur until 925 Hz and secondly, like Vinyl Extra Soft it is also considered too soft to withstand the cyclic loading and unloading of an actual polishing process. The frequency response curves for different thickness soft foams and samples with added lead sheeting are given in Figure 6. Samples A11, A12, A15 are of most interest. The shapes of the frequency responses for both Vinyl Soft samples (A11 and A12) are very similar, as are their Q-1 values (0.81 and 0.82 respectively). The only difference between the samples is their thickness. From a practical standpoint the thinner A12 (6.35 mm) is preferred over the thicker A11 (9.53 mm) sample. The thinner sample is expected to be easier implement on actual tooling. The thinner sample is also cheaper.

FIGURE 6. Vibration transmission curves for different thicknesses and variations of samples. Sample A12 has a natural frequency at 149 Hz with a peak amplification value of 1.97 and 50% attenuation observed at 315 Hz. Sample A15 is the same as A12 but will an additional lead disk (3.18 mm thick, 64g) adhered to the top surface. As expected the additional mass reduced the

0

1

2

3

4

5

6

50 250 450 650 850 1050 1250 1450

Tran

smitt

ance

ratio

, X/Y

Frequency (Hz)

A1

A2

A3

A4

A5

A6

A7

(Q-1= 1.45)

(Q-1= 0.52)

(Q-1= 0.19)

(Q-1= 0.19)

(Q-1= 0.23)

(Q-1= 1.39)

(Q-1= 0.47)

0

1

2

3

4

5

6

7

8

50 250 450 650 850 1050 1250 1450

Tran

smitt

ance

ratio

, X/Y

Frequency (Hz)

A8

A9

A10

A11

A12

A13

A14

A15

(Q-1= 0.32)

(Q-1= 0.33)

(Q-1= 0.59)

(Q-1= 0.81)

(Q-1= 0.82)

(Q-1= 0.15)

(Q-1= 0.18)

(Q-1= 0.50)

samples’ natural frequency from 315 Hz to 99.5 Hz, with a maximum amplification value of 4.35. While this value is significantly higher than that obtained with A12, the sample is remains of interest as 50% attenuation is observed at the lower frequency of 212 Hz. Both A12 and A15 were chosen for testing with pitch. Results for sample Type-B Figure 7 compares the dynamic responses of samples A12 to B1, and A15 to B2. Addition of the pitch onto the sample does alter the responses some-what, however the overall trends remain the same. Pitch samples without an intermediate damping sheet showed no vibration attenuation below 10 kHz [10], refer back to figure 1. In addition to providing attenuation the damping materials reduce the maximum vibration amplification, the maximum X/Y for sample B1 and the sample in figure 1 are approximately 3 and 6 respectively. This shows the ability of this approach to control vibration transmission through the pitch to the work piece.

FIGURE 7. Comparison between Type-A and Type-B samples. SUMMARY AND FUTURE WORK Passive damping materials can be used between the pitch and the metal platen to reduce vibration transmission. Vinyl foam is the best damping material among those tested. Increasing the overall sample mass through the addition of lead sheeting, further reduced vibration amplification (sample B2 versus B1). Experimental work is underway to test the damping materials on actual pitch tools and to determine if the process vibrations have a significant influence on the polishing outcomes (roughness and MMRs).

ACKNOWLEDGEMENTS This material is based upon the work supported by the National Science Foundation under Grant No. 0747637. Any opinions, findings, and conclusions or recommendations expressed in this material are those of the authors and do not necessarily reflect the views of the National Science Foundation. REFERENCES [1] Gillman B, Tinker F. Fun facts about pitch

and the pitfalls of ignorance. Proceedings of SPIE. 1999; 3782: 72-79.

[2] Sutton S. Development of new synthetic optical polishing pitches. In: Optical Society of America. 2004.

[3] Newton I. Opticks. Reprint of the 4th edition. 1931; 104.

[4] Leistner A. J. Fabrication and testing of precision spheres. Metrologia. 1992; 28: 503-506.

[5] Findley W. N, Lai J. S, K Onaran. Creep and relaxation of nonlinear viscoelastic materials. Introduction to linear viscoelasticity. North-Holland Publishing Company. New York: 1976.

[6] Brown N.J. Optical polishing pitch. Preprint of a paper prepared for submission to the Optical Society of America workshop on Optical Fabrication and Testing. Nov. 10-12, 1977; San Mateo, CA.

[7] DeGroote J.E, Jacobs S.D, Gregg L, Marino A, Hayes J. Quantitative characterization of optical polishing pitch. Proceedings of SPIE. 2001; 4451: 209–221.

[8] Mullany B, Corcoran E. An innovative look at precision polishing tools. Proceedings of 3rd CIRP International Conference on High Performance Cutting, Dublin, Ireland: June 12-13, 2008; 589-598.

[9] Mullany B, Turner S. Optical polishing pitches: Impact frequency responses and indentation depths. Applied Optics. 2010; 49-3: 442–449.

[10] Mullany B, Beaman J. The Response of Pitch to Higher Frequency Vibrations. Topical Meeting of the Optical Fabrication & Testing (OF&T). Jackson Hole, WY, OThB5, June 2010.

[11] Graesser E. J, Wong C. R. The Relation of Traditional Damping Measure for Materials with High Damping Capacity: A Review. ASTM Special Technical Publication. 1992; 1169: 316-343.

0

0.5

1

1.5

2

2.5

3

3.5

4

4.5

50 250 450 650 850 1050 1250 1450

Tran

smitt

ance

ratio

, X/Y

Frequency (Hz)

A12

A15

B1

B2

(Q-1= 0.82)

(Q-1= 0.50)

(Q-1= 0.51)

(Q-1= 0.54)