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Optics Express

Optics Express

  • Editor: Andrew M. Weiner
  • Vol. 22, Iss. 9 — May. 5, 2014
  • pp: 10761–10774
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Edge effect modeling and experiments on active lap processing

Haitao Liu, Fan Wu, Zhige Zeng, Bin Fan, and Yongjian Wan  »View Author Affiliations


Optics Express, Vol. 22, Issue 9, pp. 10761-10774 (2014)
http://dx.doi.org/10.1364/OE.22.010761


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Abstract

Edge effect is regarded as one of the most difficult technical issues for fabricating large primary mirrors, especially for large polishing tools. Computer controlled active lap (CCAL) uses a large size pad (e.g., 1/3 to 1/5 workpiece diameters) to grind and polish the primary mirror. Edge effect also exists in the CCAL process in our previous fabrication. In this paper the material removal rules when edge effects happen (i.e. edge tool influence functions (TIFs)) are obtained through experiments, which are carried out on a Φ1090-mm circular flat mirror with a 375-mm-diameter lap. Two methods are proposed to model the edge TIFs for CCAL. One is adopting the pressure distribution which is calculated based on the finite element analysis method. The other is building up a parametric equivalent pressure model to fit the removed material curve directly. Experimental results show that these two methods both effectively model the edge TIF of CCAL.

© 2014 Optical Society of America

1. Introduction

Edge effects are very common in many contact optical fabricating methods and are regarded as one of the most difficult technical issues, which can dominate the performance of segmented-mirror telescopes such as GMT [1

1. M. Johns, “The Giant Magellan Telescope (GMT),” Proc. SPIE 6986, 698603 (2008). [CrossRef]

], E-ELT [2

2. M. Cayrel, “E-ELT optomechanics: Overview,” Proc. SPIE 8444, 84441X (2012). [CrossRef]

], and JWST [3

3. M. Clampin, “Status of the James Webb Space Telescope (JWST),” Proc. SPIE 7010, 70100L (2008). [CrossRef]

]. On the other hand, the edge effects will make the mirror edge “roll down” (except the magnetorheological finishing); to rectify this, more material needs to be removed over the bulk surface, and much more time will be consumed. To satisfied the demand of large mosaic primary mirror telescopes, fine edge figure controlling and a high-efficiency fabricating process are both needed urgently.

There are many studies that have been done regarding the edge effects based on computer controlled optical surfacing (CCOS) technology. The early studies tried to build a simplified pressure model to describe the pressure distribution when the tool overhangs the edge of the mirror. Jones [4

4. R. A. Jones, “Computer-controlled optical surfacing with orbital tool motion,” Opt. Eng. 25(6), 785–790 (1986). [CrossRef]

] suggested a linear pressure model in 1986. The skin model, which was proposed by Luna-Aguilar et al. [5

5. E. Luna-Aguilar, A. Cordero-Davila, J. Gonzalez Garcia, M. Nunez-Alfonso, V. H. Cabrera-Pelaez, C. Robledo-Sanchez, J. Cuautle-Cortez, and M. H. Pedrayes-Lopez, “Edge effects with Preston equation,” Proc. SPIE 4840, 598–603 (2003). [CrossRef]

] and Cordero-Davila et al. [6

6. A. Cordero-Dávila, J. González-García, M. Pedrayes-López, L. A. Aguilar-Chiu, J. Cuautle-Cortés, and C. Robledo-Sánchez, “Edge effects with the Preston equation for a circular tool and workpiece,” Appl. Opt. 43(6), 1250–1254 (2004). [CrossRef] [PubMed]

], supposes that there are two different pressure regions: high- and low-pressure regions on the contact area. Combining these two models, a constant-linear (C-L) model was proposed by Han et al. [7

7. Y. Han, F. Wu, and Y. J. Wan, “Pressure distribution model in edge effect,” Proc. SPIE 7282, 72822Q (2009). [CrossRef]

], which divides the contact region into two parts: constant pressure region C and linear region L. Kim et al. [8

8. D. W. Kim, W. H. Park, S. W. Kim, and J. H. Burge, “Parametric modeling of edge effects for polishing tool influence functions,” Opt. Express 17(7), 5656–5665 (2009). [CrossRef] [PubMed]

] provided a new idea which defines a parametric model based on measured data, rather than assigning the edge effects to a certain type of analytical pressure model, which matches the experimental data very well. Hu et al. [9

9. H. Hu, Y. Dai, X. Peng, and J. Wang, “Research on reducing the edge effect in magnetorheological finishing,” Appl. Opt. 50(9), 1220–1226 (2011). [CrossRef] [PubMed]

] researched reducing the edge effect in magnetorheological finishing by using small size removal function and utilizing the removal function compensation. Walker et al. [10

10. D. D. Walker, G. Yu, H. Li, W. Messelink, R. Evans, and A. Beaucamp, “Edges in CNC polishing: from mirror-segments towards semiconductors, paper 1: edges on processing the global surface,” Opt. Express 20(18), 19787–19798 (2012). [CrossRef] [PubMed]

] developed the edge-control technology on hexagonal parts for bonnet polishing by utilizing variable size influence functions through tool-lift method. Li et al. [11

11. H. Li, G. Yu, D. Walker, and R. Evans, “Modelling and measurement of polishing tool influence functions for edge control,” J. Eur. Opt. Soc. Rap. Publ. 6, 110480 (2011).

,12

12. H. Li, D. Walker, G. Yu, A. Sayle, W. Messelink, R. Evans, and A. Beaucamp, “Edge control in CNC polishing, paper 2: simulation and validation of tool influence functions on edges,” Opt. Express 21(1), 370–381 (2013). [CrossRef] [PubMed]

] reported the edge tool influence functions (TIFs) modeling for the tool-lift method based on measured TIF data [11

11. H. Li, G. Yu, D. Walker, and R. Evans, “Modelling and measurement of polishing tool influence functions for edge control,” J. Eur. Opt. Soc. Rap. Publ. 6, 110480 (2011).

], theoretic pressure, and velocity analysis [12

12. H. Li, D. Walker, G. Yu, A. Sayle, W. Messelink, R. Evans, and A. Beaucamp, “Edge control in CNC polishing, paper 2: simulation and validation of tool influence functions on edges,” Opt. Express 21(1), 370–381 (2013). [CrossRef] [PubMed]

] and got good results on a 200-mm across-corners hexagonal witness part. All these studies were based on CCOS technology.

In order to improve the efficiency of active lap processing and obtain the fine controlled edge figure on a large primary mirror, the edge effect of active lap first must be eliminated. To accomplish that, first, the edge ring TIFs, which mean the material removal rules of active lap when it overhangs the mirror edge, must be known. Precise and stable edge ring TIF modeling is also important. Second, the ability of active lap in edge figure control must be studied, and a good edge control strategy also must be developed. In this paper, we primarily focus on the former problem.

The theoretical background of the edge ring TIF modeling for active lap is shown in Section 2. Two methods are presented in Section 3 to model the edge ring TIFs. The experiments are carried out on a Φ1090 circular flat mirror. A 375-mm-diameter flat lap is used in the experiments. The experiment results and the comparisons between model TIFs and measured TIFs are reported in Section 4. The improvement of these two models and the discussions are presented in Section 5.

2. Theoretical background

2.1 The Preston equation

In active lap grinding or polishing processes, the material removal on the mirror surface can be calculated based on the Preston equation, which was presented by Preston [14

14. F. Preston, “The theory and design of plate glass polishing machines,” J. Soc. Glass Technol. 9, 214–256 (1927).

] in 1927.
dz(x,y)=kP(x,y)V(x,y)dt,
(1)
where dz is the integrated removal material during dt time, k is the Preston coefficient, P is the pressure on the lap–mirror contact region, and V is the magnitude of relative speed between the lap and mirror.

2.2 Methods to calculate the ring TIF

In rotational symmetric fabricating process, the workpiece will rotate about its symmetrical axis with speed ω1, and the active lap will dwell at different radial positions with rotate speed ω2. The values of ω1 and ω2 are at the same level, so the workpiece motion cannot be ignored when someone tries to calculate the TIFs for the active lap [13

13. L. Haitao, Z. Zhige, W. Fan, F. Bin, and W. Yongjian, “Study on active lap tool influence function in grinding 1.8 m primary mirror,” Appl. Opt. 52(31), 7504–7511 (2013). [CrossRef] [PubMed]

]. The ring TIF was proposed to describe the material removal rule in this situation [15

15. D. W. Kim, S. W. Kim, and J. H. Burge, “Non-sequential optimization technique for a computer controlled optical surfacing process using multiple tool influence functions,” Opt. Express 17(24), 21850–21866 (2009). [CrossRef] [PubMed]

]. The ring TIF is the rotational symmetric removal profile and looks like a ring on the workpiece. The ring TIF can be represented by a 1D profile, its x axis is the radial position on the workpiece, and its y axis is the removal depth after one unit time.

TIFA(e)=k2πPE(ρ,e)ϕϕVdθ.
(5)

There are two ways to get the edge ring TIF. One is to find out the pressure distribution, P(ρ,θ,e), and the other is to construct an equivalent pressure curve, PE(ρ,e). The linearity model, skin model, and C-L model belong to the first method, and they all hypothesize a simple pressure distribution model to calculate the removal material. Instead of assuming a simple pressure distribution model, one can use the finite element analysis (FEA) to solve the pressure distribution for the first way, and this will be reported in Section 3. The parametric model proposed by Kim et al. [8

8. D. W. Kim, W. H. Park, S. W. Kim, and J. H. Burge, “Parametric modeling of edge effects for polishing tool influence functions,” Opt. Express 17(7), 5656–5665 (2009). [CrossRef] [PubMed]

] does not aim to model the pressure distribution but to fit a parametric Preston coefficient map, κ(x,y), based on the linearity pressure model. Based on this idea and Eq. (5), we can build up a parametric pressure model PE(ρ,e) for the active lap, and this will be discussed in Section 3.

2.3 The lap overhang ratio

The lap overhang ratio, Slap, is a dimensional irrelevant parameter that is used to describe the lap position status in edge figuring, as shown in Fig. 3.
Fig. 3 Definition of lap overhang ratio, Slap.

3. Edge effect modeling

3.1 Parametric pressure model for edge ring TIFs

The parametric model proposed by Kim et al. [8

8. D. W. Kim, W. H. Park, S. W. Kim, and J. H. Burge, “Parametric modeling of edge effects for polishing tool influence functions,” Opt. Express 17(7), 5656–5665 (2009). [CrossRef] [PubMed]

] suggests that the Preston coefficient, κ, is a function of the distance from the mirror edge, x, and the lap overhang ratio, Slap. It is a five-parameter function, as follows:
κmap(x,α,β,γ,δ,ε)=κ0{1+Slapε[f1(x,α,β)+f2(x,γ,δ)]},
(6)
where κ0 is the Preston coefficient when there is no overhang, f1 is the edge-side correction, and f2 is the workpiece-center-side correction.

Based on this idea, we build up a parametric equivalent pressure curve, PE(ρ,e), and put it into Eq. (5) to calculate the edge ring TIF. Considering that the active lap is working like the spin tool motion, the workpiece-center-side correction, f2, is not necessary. So, when we build up PE(ρ,e), only the edge-side correction, f1, is considered. Also, the variables ρ and e were replaced by x and Slap in PE(ρ,e) for convenience. The basic form of the parametric equivalent pressure curve is
PE(x,α,β,ε)=ps[1+Slapεf(x,α,β)],
(7)
where ps is the pressure scale factor, which scales the whole pressure to a reasonable level. The parameter ε represents how fast the pressure increases in edge area. The basic idea of the parametric equivalent pressure curve is shown in Fig. 4.
Fig. 4 Sketch of parametric equivalent pressure curve model.

The function f in Eq. (7) is used to describe the nonlinear pressure distribution in edge effects. It is a second-order function of variable x, and its influence width is equal to Wlap·α. The maximum value of this function can be controlled by the parameter β.
f(x,a,β)=β(x+Wlapα)2(Wlapα)2Θ(x+Wlapα),
(8)
where Θ(x) is the step function: 1 for x ≥ 0 and 0 for x < 0. Consider that the width of edge effects may be different at each overhang ratio, so the parameter α is a function of Slap, α=g(Slap). The parameters (i.e., α, β, and ε) are determined by using the measured edge ring TIF data to fit Eq. (5), and the least square method is used to solve this problem. This will be discussed in Section 4.

Example curves of the parametric pressure model for a 300-mm-diameter lap are plotted in Fig. 5.
Fig. 5 Parametric pressure curves for various overhang ratio, Slap (α = –2Slap + 0.8, β = 3, and ε = 0.2).
An arbitrary parameter set was used in the example, where α = –2Slap + 0.8, β = 3, and ε = 0.2. The example shows that both width and slope of the nonlinear pressure curve are different at each overhang ratio in this model.

3.2 FEA model considering a soft layer for pressure analysis

The finite element method can be used to analyze the contact status between bodies and calculate the pressure distribution. The material of the active lap base plate and grind layer is aluminum alloy, and the material of the mirror is K4 glass. The material characteristics for modeling are listed in Table 1.

Table 1. Material properties for FEA

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The workpiece is a circular flat mirror with 1090-mm diameter. To simplify, only part of the mirror is considered in the FEA model, which is a 375-mm-wide and 18-mm-thick block. Only the base plate and the grinding layer of the active lap are included in the model. The diameter is 375 mm for the base plate and 300 mm for the grinding layer. The thickness is 18 mm for the base plate and 2.5 mm for the grinding layer.

It is difficult to simulate the mechanical behavior of abrasives or slurry in FEA. So we add a thin soft layer between the lap and mirror in our model to approximate it. The Young’s modulus of the soft layer, Es, is much smaller than that of the mirror, Em. The soft layer is about 2 mm thick and with 1-mm mesh size in our model. The deformable to deformable separable surface contact is used in the model. Two symmetric contact pairs are created for lap–soft layer and soft layer–mirror contact. The FEA model is shown in Fig. 6.
Fig. 6 FEA model for pressure analysis when active lap overhang mirror edge (Slap = 0.3).
Fixed constraint is applied on the workpiece bottom, and only the gravity load is considered. The mesh size is 6 mm for the workpiece part and the lap and 1.25 mm for the grinding layer. The FEA modeling and analyzing are carried out on ANSYS Workbench 14.5.

The Young’s modulus of the soft layer, Es, is essential to this model. Different Es will produce different pressure distribution on the workpiece surface, as shown in Fig. 7.
Fig. 7 Center pressure curves for different rigidity soft layer (Slap = 0.3, and Em is Young’s modulus of the workpiece).
The width of the nonlinear pressure area is narrow, and the slope of the pressure along the radial line is high when Es is close to Em; otherwise, the width and slope are wide and low when Es is smaller than Em.

A best Es which satisfies the condition that theoretical edge ring TIFs coincide with the measured TIFs may exist. But the proper Es is hard to find out. Our approach to solve this is to use one group of measured TIF data with the same overhang ratio to fit the Es and then use this Es to analyze the pressure distribution for different overhang ratios. After that, put the pressure in Eq. (3) to calculate the edge ring TIFs for those overhang ratios. Finally, we compared these TIFs with the measured data from experiments to verify Es. This will be presented in Section 4.

4. Edge ring TIF experiments and model fitting

4.1 Experiment setup and measured TIFs

The active lap edge ring TIF experiments are carried out on a 1090-mm-diameter circular flat mirror. The lap is a 375-mm-diameter flat lap with a 300-mm-diameter grinding layer, as shown in Fig. 8(a).
Fig. 8 Active lap edge ring TIF experimental setup (a) and measuring method (b).
The W40 grit emery was used in the experiments, and the ratio between the emery and water is about 1–5 in volume. The pH of the slurry is about 7, and the temperature of the experimental environment is about 25 °C. The mirror rotate speed is 2.7 rpm, and the lap rotate speed is –6 rpm. The positive/negative indicates the rotation direction. The LEITZ PMM30-20-10 CMM is used to measure the mirror surface shape along four radial lines [see Fig. 8(b)]. The surface profile was measured with 1-μm height accuracy and 1-mm spatial sample space. The edge ring TIF is calculated by subtracting the measured data after grind from the data before grind.

Five group experiments are carried out to verify the models. The parameters for each group are shown in Table 2.

Table 2. Parameters for edge ring TIF experiments

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Groups 1, 2, and 4 have same dwell time but different overhang ratios, and groups 3, 4, and 5 have same overhang ratio but different dwell times.

The edge ring TIFs from the experiments are shown in Fig. 9.
Fig. 9 Edge ring TIFs from the experiments.
The unit of the TIF value is μm/min. The shape of the edge ring TIF is changed with the overhang ratio but relatively stable with the dwell time. This is very important to the dwell time-based deterministic fabrication.

4.2 Parametric pressure model fitting

Measured edge ring TIFs are used to fit the parametric pressure model, PE [see Eq. (7)]. There are five parameters that need to be fitted: parameter α for each overhang ratio (i.e., for Slap = 0.1, 0.2, and 0.3), β, and ε. We use the least square method to solve this problem. The target curves are the edge ring TIFs for Slap = 0.1 and 0.2 and the average edge ring TIF for Slap = 0.3. The fitted results are α0.1 = 1.559, α0.2 = 1.101, α0.3 = 0.540, β = 18.511, and ε = 0.642, where α0.1 represents α for Slap = 0.1 and so on. The fitted parametric pressure curves are shown in Fig. 10.
Fig. 10 Fitted parametric pressure curves. Normalized by the pressure when active lap inside the mirror. The zero position on the x axis is the mirror edge, and the negative direction of the x axis is toward the mirror center (α0.1 = 1.559, α0.2 = 1.101, α0.3 = 0.540, β = 18.511, and ε = 0.642).
The curves are normalized by the pressure when the active lap is inside the mirror. Edge ring TIFs predicted by the fitted parametric pressure model are shown in Fig. 11, where the solid lines represent the predicted TIFs and the dashed lines represent the experimental TIFs.
Fig. 11 Comparison between predicted TIFs and measured TIFs.
The unit of the TIFs is μm/min.

To improve the model accuracy, more edge ring TIF experiments with different overhang ratios are needed. Once the model is built up, it can be used in the entire fabricating process.

4.3 FEA model fitting

Another way is analyzing the pressure distribution directly based on the FEA model which was proposed in Section 3.2. A series of finite element analyses are carried out in order to find the best fitting Young’s modulus of the soft layer, Es, in Fig. 6. The average experimental edge ring TIFs with 0.3 overhang ratio are used as the target in the searching. Figure 13 shows the comparison between the experimental TIF and theoretical TIFs with different scale Es.
Fig. 13 Comparison between the experimental TIF and theoretic TIFs with different Es, Slap = 0.3.
From the figure we can find out (1) the theoretical TIF when Es equal or close to Em is far away from the experimental TIF and (2) the best fitting Es exists between 0.0001Em and 0.001Em. Through the searching we found that the best fitting modulus for this case is about 20.78 MPa, which is approximately 0.0003Em. More FEA models are built up with this Young’s modulus soft layer, and the pressure distributions are analyzed. The results are shown in Fig. 14.
Fig. 14 Pressure distribution FEA results for different overhang ratios: (a) Slap = 0.05, (b) Slap = 0.1, (c) Slap = 0.15, (d) Slap = 0.2, (e) Slap = 0.25, (f) Slap = 0.3, (g) Slap = 0.35, and (h) Slap = 0.4 (Es = 20.78 MPa).
The overhang ratio varies from 0.05 to 0.4 at regular intervals of 0.05.

Center pressure curves are calculated from the FEA results and shown in Fig. 15(a).
Fig. 15 Center pressure curves from FEA results (a) and edge ring TIF family calculated based on these pressure curves (b).
We noticed that the pressure on the inner side area is close to zero when the lap overhang ratio is up to 0.4. Based on the analyzed pressure distribution, the edge ring TIF family is calculated and plotted in Fig. 15(b). The TIFs are normalized because the Preston coefficient is unknown. These TIF curves are similar to those from the fitted parametric pressure model [see Fig. 12(b)]. Due to the pressure, the material removal rate on the inner side area is also close to zero when the lap overhang ratio is up to 0.4. This may be the reason why the edge is rolling down deeply but the near-edge part remains relatively high in Fig. 1.

A comparison between FEA modeling TIFs and experimental TIFs is shown in Fig. 16.
Fig. 16 Comparison between predicted TIFs from FEA results and measured TIFs.
The model-predicted TIFs match well with the measured TIFs in our experiments. This means that the FEA model is working, and adding the soft layer can help us to get more accurate pressure distribution.

5. Model comparison and application

5.1 Comparison and discussion

The parametric pressure model and the FEA model are two different methods. Both of them are trying to achieve more accurate edge ring TIF modeling. In order to compare these two methods, we define the normalized model fit error, Err, as follows:

Err=|TIFModelTIFMeasure|TIFMeasure100(%).
(9)

It represents the ratio of fit residual material to total removed material. The ideal model fit error is zero based on Eq. (9). So the volume convergent efficiency of the edge effect model can be expressed as 1 – Err. The fit errors for both models are all below 16%, which means these two models have more than 84% volume convergent efficiency. The parametric model can achieve 6.9% fit error at 0.3 overhang ratio, better than the FEA model (10.7%). There is nearly no difference between uncompensated TIF and model TIF when the overhang ratio is small because the overhang effects can be ignored [8

8. D. W. Kim, W. H. Park, S. W. Kim, and J. H. Burge, “Parametric modeling of edge effects for polishing tool influence functions,” Opt. Express 17(7), 5656–5665 (2009). [CrossRef] [PubMed]

]. The model fit errors (15.8% for the parametric model and 14.1% for the FEA model) are slightly larger than uncompensated fit error (10.8%) at 0.1 overhang ratio in Fig. 17, and this difference may be caused by heterogeneity of the slurry during grinding.
Fig. 17 Normalized fit error, Err, for the parametric and FEA model at different overhang ratios.
As the overhang ratio increases, obvious improvement can be observed for both models.

The parametric model is simple and direct but needs a series of edge ring TIFs to fit it before using. The FEA model reveals the pressure distribution on the workpiece surface. It allows us to calculate more edge TIFs, especially for uncircular tools and uncircular workpieces.

5.2 Application in simulation process

Two groups of virtual fabrication are carried out to study the error profile fit capability for different edge pressure models. The first one considers the piston target removing process, which means to remove material equally at each position, and the second one considers an arbitrary error profile removing process. The fabricating parameters for the two groups are the same: workpiece rotating at 2.1 rpm and active lap starting at 200 mm, stopping at 830 mm, and rotating at 3.3 rpm when its position is less than 600 mm and –3.3 rpm when its position is beyond 600 mm. The effective radius of the active lap is 175 mm, the radius of the workpiece is 892 mm, and the radius of the workpiece center hole is 145 mm. Two hundred lap dwell positions and 200 error profile sample points are used in the simulation. The nonnegative least square method is used to fit the target removal profile and get the lap dwell time distribution. In FEA modeling, 16 group FEA results are used, and the overhang ratio varies from 0.025 to 0.4 at regular intervals of 0.025.

The results from the first group of simulations are shown in Fig. 18.
Fig. 18 Simulation results for CCAL piston target removal process. Curves are normalized by the target removal profile.
Curves are normalized by the target removal profile. The target removal profile is a horizontal line in which the y axis value is equal to 1. The parametric pressure model can fit the target profile very well, and the maximum fit residual error is only 0.4%. Because the number of FEA results is limited, FEA modeling results are not as smooth as the parametric modeling results, but they also fit the target profile reasonable well, and the maximum fit residual error is 2.6%. The skin model cannot fit well at the edge area (i.e., the right side), and the maximum fit residual error is 12%.

The results of the second group of simulations are shown in Fig. 19.
Fig. 19 Simulation results for CCAL arbitrary target removal process.
The target removal profile is the error profile of a 1.8-m primary mirror during grinding. The parametric model and the FEA model fit the target removal profile better than the skin model at the edge area. The maximum fit residual error is 6.2 μm for the parametric model, 5.6 μm for the FEA model, and 10 μm for the skin model.

Simulation results indicate that one adopting parametric pressure model or FEA pressure model could achieve more accurate fabrication and reduce the edge effect. Both of these two models are better than the skin pressure model.

6. Concluding remarks

We presented a way to calculate the edge ring TIF for active lap processes and two methods (the parametric model and the FEA model) to describe the edge effects when lap overhangs the workpiece edge. Parametric model builds up a parametric equivalent pressure curve in order to calculate the edge ring TIF and uses the measured TIFs to fit this curve. The FEA model simulates the pressure distribution on the workpiece surface using the finite element method. A thin soft layer with a special Young’s modulus is considered in our model between the lap and the workpiece in order to simulate the effect of abrasives or slurry in the process. The Young’s modulus of this soft layer is determined by fitting the model-predicted TIFs to the measured TIFs.

Experimental results show that both of these methods are effective in edge effect modeling for the CCAL process. The normalized fit error was proposed to evaluate the fit ability of edge effect models. About 10% fit error can be achieved in these two models. This means about 90% of the materials in the edge ring TIF can be modeled by these models and makes engineering use possible. Further fabricating simulations indicate that both the parametric model and the FEA model are better than the skin model in error profile fitting, especially at the edge area. This may be helpful in edge effects controlling and compensating.

Acknowledgments

This work was supported by the National Natural Science Foundation of China (61178043). We thank Yong Zhang, Kai Fang and Linhan Xian for help in the grinding process and Changqing Lin for support of CMM measurement.

References and links

1.

M. Johns, “The Giant Magellan Telescope (GMT),” Proc. SPIE 6986, 698603 (2008). [CrossRef]

2.

M. Cayrel, “E-ELT optomechanics: Overview,” Proc. SPIE 8444, 84441X (2012). [CrossRef]

3.

M. Clampin, “Status of the James Webb Space Telescope (JWST),” Proc. SPIE 7010, 70100L (2008). [CrossRef]

4.

R. A. Jones, “Computer-controlled optical surfacing with orbital tool motion,” Opt. Eng. 25(6), 785–790 (1986). [CrossRef]

5.

E. Luna-Aguilar, A. Cordero-Davila, J. Gonzalez Garcia, M. Nunez-Alfonso, V. H. Cabrera-Pelaez, C. Robledo-Sanchez, J. Cuautle-Cortez, and M. H. Pedrayes-Lopez, “Edge effects with Preston equation,” Proc. SPIE 4840, 598–603 (2003). [CrossRef]

6.

A. Cordero-Dávila, J. González-García, M. Pedrayes-López, L. A. Aguilar-Chiu, J. Cuautle-Cortés, and C. Robledo-Sánchez, “Edge effects with the Preston equation for a circular tool and workpiece,” Appl. Opt. 43(6), 1250–1254 (2004). [CrossRef] [PubMed]

7.

Y. Han, F. Wu, and Y. J. Wan, “Pressure distribution model in edge effect,” Proc. SPIE 7282, 72822Q (2009). [CrossRef]

8.

D. W. Kim, W. H. Park, S. W. Kim, and J. H. Burge, “Parametric modeling of edge effects for polishing tool influence functions,” Opt. Express 17(7), 5656–5665 (2009). [CrossRef] [PubMed]

9.

H. Hu, Y. Dai, X. Peng, and J. Wang, “Research on reducing the edge effect in magnetorheological finishing,” Appl. Opt. 50(9), 1220–1226 (2011). [CrossRef] [PubMed]

10.

D. D. Walker, G. Yu, H. Li, W. Messelink, R. Evans, and A. Beaucamp, “Edges in CNC polishing: from mirror-segments towards semiconductors, paper 1: edges on processing the global surface,” Opt. Express 20(18), 19787–19798 (2012). [CrossRef] [PubMed]

11.

H. Li, G. Yu, D. Walker, and R. Evans, “Modelling and measurement of polishing tool influence functions for edge control,” J. Eur. Opt. Soc. Rap. Publ. 6, 110480 (2011).

12.

H. Li, D. Walker, G. Yu, A. Sayle, W. Messelink, R. Evans, and A. Beaucamp, “Edge control in CNC polishing, paper 2: simulation and validation of tool influence functions on edges,” Opt. Express 21(1), 370–381 (2013). [CrossRef] [PubMed]

13.

L. Haitao, Z. Zhige, W. Fan, F. Bin, and W. Yongjian, “Study on active lap tool influence function in grinding 1.8 m primary mirror,” Appl. Opt. 52(31), 7504–7511 (2013). [CrossRef] [PubMed]

14.

F. Preston, “The theory and design of plate glass polishing machines,” J. Soc. Glass Technol. 9, 214–256 (1927).

15.

D. W. Kim, S. W. Kim, and J. H. Burge, “Non-sequential optimization technique for a computer controlled optical surfacing process using multiple tool influence functions,” Opt. Express 17(24), 21850–21866 (2009). [CrossRef] [PubMed]

16.

H. Liu, Z. Zeng, F. Wu, B. Fan, and Y. Wan, “Improvement of active lap in the grinding of a 1.8m honeycomb primary mirror,” AOMMAT, in press.

OCIS Codes
(220.0220) Optical design and fabrication : Optical design and fabrication
(220.4610) Optical design and fabrication : Optical fabrication
(220.5450) Optical design and fabrication : Polishing

ToC Category:
Geometric Optics

History
Original Manuscript: January 6, 2014
Revised Manuscript: March 27, 2014
Manuscript Accepted: April 3, 2014
Published: April 28, 2014

Citation
Haitao Liu, Fan Wu, Zhige Zeng, Bin Fan, and Yongjian Wan, "Edge effect modeling and experiments on active lap processing," Opt. Express 22, 10761-10774 (2014)
http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-22-9-10761


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References

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  16. H. Liu, Z. Zeng, F. Wu, B. Fan, Y. Wan, “Improvement of active lap in the grinding of a 1.8m honeycomb primary mirror,” AOMMAT, in press.

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