Development and theoretical analysis of novel center-inlet computer-controlled polishing process for high-efficiency polishing of optical surfaces

Robotics and Computer Integrated Manufacturing 59 (2019) 1–12

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Development and theoretical analysis of novel center-inlet computercontrolled polishing process for high-efficiency polishing of optical surfaces

T

⁎

Lin Bina, Jiang Xiang-Mina, Cao Zhong-Chena,b, , Huang Tianb a b

Key Laboratory of Advanced Ceramics and Machining Technology, Ministry of Education, Tianjin University, 300072, Tianjin, China Key Laboratory of Mechanism Theory and Equipment Design of Ministry of Education, Tianjin University, 300072, Tianjin, China

A R T I C LE I N FO

A B S T R A C T

Keywords: Center-inlet computer-controlled polishing Removal analysis Surface generation Pad wear Optical surface

Although traditional computer-controlled optical surfacing (CCOS) technology has been successfully developed for polishing large aspheric optics, the polishing process continues to pose several challenges, including polishing tool wear and uneven distribution of polishing particles in contact areas. To improve the efficiency and stability of the polishing process, we present a novel center-inlet computer-controlled polishing (CCCP) process and tool for high-efficiency polishing of large-diameter aspheric optics. Compared with traditional CCOS, the most distinctive feature of CCCP is that the polishing slurry is supplied by the central hole of the polishing tool to improve its utilization efficiency. Moreover, a flexible coupling is used to connect the tool and motorized spindle to keep the tool in parallel with the work surface during the polishing process. The experimental apparatus and optimization design of the CCCP tool were first constructed based on CCOS. Then, the material removal mechanisms were explained by a series of theoretical and experimental studies. Results indicated that CCCP can improve the wear resistance of the polishing pad and make fuller and more even abrasive grain supply compared with traditional CCOS. The innovative theoretical model was verified and used for optimizing the epicyclic tool motion in CCCP. The experiments indicated that CCCP can produce a higher material removal rate and a better surface state than can CCOS.

1. Introduction The application of aspheric surfaces can result in fewer component quantity, smaller package size, lower weight, and better imaging performance compared with the application of all-spherical solutions [1]. These advantages promote the use of large aspheric surfaces in astronomical instruments [2]. For example, aspherical segments are universally adopted in ground-based optical telescopes for eliminating central obstructions and improving throughput [3]. Although the diameter of segmented primary mirrors for optical telescopes is approximately tens of meters, the specification for the segment polishing is less than 36 nm for form accuracy and 18 nm for the peak-to-valley value of the surface residual error [4]. Given increased surface requirements for functional enhancement, the processing time of large aspheric components for large-telescope instrumentation has increased to several weeks or months [5]. Therefore, an improved next-generation computer-controlled ultra-precision polishing (CCUP) technique is needed to produce aspherical surfaces with high efficiency and precision. At present, many CCUP processes can be used for polishing large aspheric surfaces and off-axis segments; these processes include

⁎

computer-controlled optical surfacing (CCOS) technique [6], computer numerical control (CNC)-processed bonnet polishing [7], magnetorheological finishing [8], stress lap polishing [9], and ion figuring [10]. Typically, each polishing process has its own advantages and limitations, and each one is correspondingly selected to perform specific functions in the manufacturing process chain. For example, Beaucamp et al. [11] used a fully automated two-step finishing method, namely, fluid jet polishing and continuous-processing bonnet polishing, to fabricate molding dies to super-smooth surface finishes. Kim et al. [2] used a dual-head large polishing machine (LPM) equipped with two polishing tools, a 1.2 m diameter stressed lap, and a variety of rigid conformal polishing tools to fabricate a large-diameter off-axis segment. The proposed method can improve the surface texture down below 1 nm rms surface roughness under appropriate polishing parameters [12]. CCOS technology provides superior optical manufacturing performance for low-cost mass production because of its advantages of high polishing efficiency and shape accuracy [13,14]. Burge et al. [15] successfully fabricated 1.4 m diameter aspheric optical surfaces by CCOS technology, and the final surface roughness of the aspheric

Corresponding author at: Tianjin University, RM.422, Building 37, 135 Yaguan Rd, Jinnan District, 300350, Tianjin, China. E-mail address: [email protected] (Z.-C. Cao).

https://doi.org/10.1016/j.rcim.2019.01.017 Received 23 September 2018; Received in revised form 11 January 2019; Accepted 21 January 2019 0736-5845/ © 2019 Elsevier Ltd. All rights reserved.

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Fig. 1(a) and (b) show a schematic and the experimental setup of a traditional CCOS. In the traditional CCOS process, the soft polishing tool contacts the workpiece with a certain load, and the rotation of the tool drives the abrasive particles to wipe the workpiece surface to remove the material. On the one hand, the produced surface state is affected by slurry concentration, particle property, particle size, and pad surface topography. On the other hand, the polishing slurry is supplied by the surrounding nozzle in traditional CCOS, thereby introducing difficulties in flow into the central part of the polishing area, especially for the large polishing tool. This condition may lead to several defects, including polishing tool wear and uneven distribution of abrasive particles in the contact area. To improve the efficiency and stability of the polishing process, we developed a novel CCCP process for large-diameter aspheric optics. Fig. 1(c) and (d) show a schematic and the experimental setup of the proposed CCCP process. Compared with the traditional CCOS, the most distinctive feature of CCCP is that the polishing slurry is supplied through the central hole of the polishing tool to improve the utilization efficiency. To keep the tool parallel to the work surface during the polishing process, flexible coupling connects the tool and the motorized spindle. An ER connecting rod is designed and locked through the ER nut so that the connecting rod positions and seals at the same time. The flexible coupling is used to compensate the mounting error of the ER connecting rod and disc tool, thereby improving the vibration resistance of the tool, the compatibility with the workpiece, and the uniformity of the contact pressure. The connecting rod and the small polishing disc are hollow structures that guide the polishing slurry. The sealing performance of the two ends of the hose will increase with increasing hydraulic supply strength. A soft sponge sandwich is added between the small polishing disc and the polishing pad, thereby further improving the adhesion between the tool and the pad surface. A cross groove is engraved on the surface of the polishing pad, and the groove intersection point is placed at the center of the polishing disc so that the polishing slurry can be uniformly supplied from the tool center to all sides, and minimal flow supply of the polishing slurry is maintained in the experiment.

surface was approximately 1.2 nm rms. Feng et al. [16] obtained a freeform lens (FFL) with CCOS. The accuracy of FFL reaches 4 μm, and the roughness is under 5 nm. Zhang et al. [17] used the CCOS technique to grind and polish a 600 mm class off-axis aspherical mirror with a figure error less than 13 nm rms. However, the polishing process continues to poses several challenges, including polishing tool wear and uneven distribution of polishing particles in the contact area. A significant improvement in the efficiency and performance of the traditional CCOS is essential for meeting the many critical requirements of next-generation optical systems, which commonly adopt segmented primary mirrors and may have hundreds of aspheric segments [18,19]. To improve the efficiency and stability of the polishing process, a novel center-inlet computer-controlled polishing (CCCP) process is developed for large-diameter aspheric optics. First, the experimental apparatus of CCCP is designed and constructed based on the basic theory of CNC for the polishing method. Then, the material removal mechanisms are explained by a series of theoretical and experimental analyses. Finally, the design of the CCCP tool is optimized for material removal and surface figuring, and comparative analysis is discussed in detail. 2. Design and optimization of CCCP tool 2.1. Principle of CCCP In terms of mechanical behavior, the wear of materials in the polishing process is mainly caused by abrasive wear due to the abrasiveworkpiece and abrasive-pad contact and/or erosion caused by hard particles that strike the surface [20]. Given that the material removal is extremely small (in the order of sub-micrometers or less), mechanisms of abrasive wear or erosion in the polishing process can involve both plastic flow and brittle fracture because of the polishing process parameters, even for brittle materials. In contact polishing, the relatively soft polishing tools impose pressure and relative motion with respect to the target surface and affect slurry and swarf transport by contact [21]. Thus, the control of the pad modulus and surface topography of the polishing tool, and the hydrodynamic conditions in the contact polishing process greatly affect the micro-contact behavior.

Fig. 1. (a) Schematic and (b) experimental setup of traditional CCOS technique; (c) schematic and (d) experimental setup of the novel CCCP process. 2

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Fig. 2. (a) Experimental setup of epicyclic motion module and (b) schematic of epicyclic trajectory of the polishing tool.

concentration, particle property, and workpiece material. The selection of the proper polishing parameters is important for a successful optical finishing process with high machining efficiency. To realize an optimum tool removal profile with a strong central peak, removal analysis is necessary for the proper selection of optimal polishing parameters. Most recent material removal models were developed for the rotary tool configuration without consideration of the effect of the polishing pad surface topography [24–26]. However, the porous structure of the pad surface significantly affects the micro-contacts between the pad and workpiece, thereby influencing the pressure distribution and spatial distribution of active abrasive particles [27]. Therefore, a novel statistical asperity model and a material removal model are developed to predict and optimize the tool removal profile of the epicyclic tool motion, as shown in Fig. 3. First, the surface topography of the polishing pad is simulated by a mathematical statistical method. The data is then used to calculate the equilibrium pad compression depth under the given tool load. Then, the contact pressure on each individual pad asperity can be determined by using the contact mechanics. The next key step is to determine the load on each particle at the interface and the amount of the removed material by each individual particle. Finally, the macroscopic material removal characteristics of the epicyclic tool motion are predicted by the cumulation of individual particle abrasion.

Fig. 3. Flowchart of the theoretical modeling process for CCCP.

2.2. Optimization design of CCCP tool for surface figuring The profile of the influence function is a critical factor that affects the achieved form accuracy, polishing time, and convergence characteristics of the form correction process [22]. The original CCCP rotary motion tends to produce no central removal and results in limited figuring capability. Thus, Jones [23] proposed an epicyclic tool motion to produce a tool removal profile with strong central peaks. The results showed that the Gaussian-shape influence function can produce good surface figuring results with high polishing efficiency. In the present study, a novel actuating element is designed and developed to realize the epicyclic motion of the polishing tool; the element is then used to generate Gaussian-shape tool influence functions for deterministic polishing of optical surfaces. Fig. 2(a) shows the schematic of an epicyclic motion module. It mainly consists of an orbit driving motor, a spin driving motor, a loading cylinder, an eccentric mechanism, and a disc polishing tool. The polishing tool head spins on a spindle axis with angular velocity ω2, and this spindle orbits around the TIF center with orbital radius R0 and angular velocity ω1. The orbit and spin motion motor are in the same horizontal position. The spin motion was driven by a servo motor through the synchronous belt and wheel, and the orbit motion was conducted by a motor-driven eccentric mechanism. Meanwhile, the orbital radius R0 could be adjusted by an eccentric cross slider mechanism. For ultra-precision machining of optical surfaces, the polishing tool needs not only epicyclic motion but also flexible loading on it. The cylinder with a hollow shaft was designed to achieve the flexible loading on the polishing tool. Fig. 2(b) illustrates the epicyclic motion of the disc polishing tool. Based on the motion mechanism of the epicyclic polishing, the eccentric ratio can be defined as the ratio of eccentricity to radius of disc tool R0/R. The angle speed ratio can be defined as ω1/ω2. The epicyclic polishing trajectory of the disc tool on the workpiece varies under different parameters.

3.1. Modeling of the pad surface topography A statistical asperity model that conforms to the probability distribution feature by a randomly generated method has been developed to predict and characterize the polishing pad surface topography. In the model, the factors, including the shape and diameter of the asperity summit, asperity height, and asperity density, are used to characterize the pad surface topography with the following assumptions. (i) All asperities are spherical at their summit with the normally distributed radius β ∼ [μβ, δβ]. (ii) The center of the asperity summit is determined by the variable of point spacing γ, which is distributed normally with mean μγ and variance δγ. (iii) The center is shifted along the z-axis by the normally distributed variable z0 ∼ [μz, δz]. Measurements suggest (μγ, δγ, μβ, δβ, μz, and δz) = (40, 10, 110, 35, 170, and 20 μm). The data of the pad surface topography is then used to calculate the micro-contact behavior between the polishing pad and the workpiece surface. 3.2. Contact between workpiece and pad surface

3. Removal analysis for the epicyclic tool motion in CCCP

The contact between workpiece and pad surface is presumed to be a solid-solid contact, and the effects of the slurry film are neglected to simplify the modeling process [28]. Based on the above pad surface model, the real area of the pad-workpiece contact is discontinuous, and the real contact area is a small part of the apparent area of contact [26].

The material removal characteristics of the epicyclic tool motion are affected by various polishing parameters, such as tool load, rotation speed, orbit speed, eccentric ratio, pad property, particle size, slurry 3

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removal analysis at each rotation angle and track coordinate. Thus, the macroscopic material removal characteristics of the epicyclic tool motion can be calculated by the cumulation of the material removal element as follows:

The applied pressure on the polishing tool is balanced by the sum of the elastic response of those pad asperities with the asperity height greater than the equilibrium pad compression depth as can be expressed by

Ft =

4 Nt E′ 3

∫d

∞

3

1

(z − d ) 2 β 2 ϕ (z ) dz ,

(1)

TIFi =

where Ft is the tool load, Nt is the total number of asperities covered on the pad surface, E′ is the effective Young's modulus, z is the asperity height of the polishing pad, d is the equilibrium pad compression depth, and β is the asperity radius of the polishing pad. Given that the hardness of the workpiece is commonly much higher than that of the polyurethane polishing pad, the effective Young's modulus E′ can be calculated by

E′ =

Ep 1 − νp2

(2)

where Ep and vp are the Young's modulus and Poisson's ratio of the polishing pad, respectively. Thus, the equilibrium pad compression depth d can be determined by Eq. (1) for a given tool load. The contact properties of the spherical asperity i are known from the following Hertz's equations [25,29]:

Fi =

(4)

1

Fi 4E′ ⎛ z i − d ⎞ 2 = ⎜ ⎟ . Ai 3π ⎝ βi ⎠

(5)

3.3. Single particle abrasion mechanism According to Luo and Dornfield [26], the abrasion action of polishing particles is the main means of material removal, which occurs when the particles embedded in the pad asperities rub against the target surface. The force applied on each abrasive particle can be determined by

Fp =

1 πDp2Pi, 4

j=1

MRRi, j, θ (i=1, 2, 3,...,M ),

θ=0

4.1. Comparison of pad wear between CCCP and CCOS In contact polishing, the surface of the polishing pad, typically made of polyurethane or other polymeric materials, is porous and relatively

(6)

where Dp is the diameter of the abrasive particle. The depth of indentation for the abrasive particle δp can be expressed by

δp =

2Fp πDp Hw

,

(8)

In recent years, robots, such as serial and parallel robots, have been widely used in the surface finishing process [32,33]. The combination of robot technology and polishing process is a new research direction that deserves concern. In this study, a series of polishing experiments is conducted on a 5-DOF hybrid robot system developed by Liu et al. [34], as shown in Fig. 4. The robotic polishing system consists of a 5-DOF hybrid robot, polishing slurry circulation system, polishing mechanism, and computer control system. The 5-DOF hybrid mechanism consists of a 3-DOF open-look kinematic chain and a 2-DOF parallel spherical mechanism. The polishing mechanism includes the epicyclic tool motion mechanism and the polishing tool of CCCP. All movement mechanisms are controlled by the computer system. The functions of the slurry circulation system include flow pressure and temperature control and feedback. Polishing slurry with stable pressure and temperature were supplied to the polishing tool.

where Ai is the contact area of the pad asperity i, zi is the asperity height of the pad asperity i, and Fi is the load carried by the pad asperity i. The average contact pressure on the pad asperity i is calculated by

Pi =

2πnr / ne

4. Experiments and discussion

(3)

4 3 1 E′β 2 (z i − d ) 2 , 3 i

N

∑ ∑

where TIFi is the material removal rate of the epicyclic tool motion at the ith sample point, ne is the rotation speed of the orbit motion, M is the sample point number, N is the track point number along the orbit path, nr is the rotation speed of the spinning motion, and MRRi, j, θ is the material removal element of ith sample point when the polishing tool moves to the jth track point at rotation angle θ. The value of MRRi, j, θ depends on the micro-contact behavior between the pad asperities and the workpiece, and the spatial distribution of the abrasive particles.

,

Ai = πβi (z i − d ),

ne 60

(7)

where Hw is the hardness of the workpiece material. The depth of the abrasive particle pressed into the target surface is usually in nanometers; thus, the deformation of the plastic particle-workpiece contact may lead to multiphase transformations without achieving final material removal [30]. Thus, in the present study, the fraction of the material removal η is introduced to describe the actually removed part as wear debris. 3.4. Establishment of the material removal characteristics A previous study found that the surface generation of the polishing process tends to be a relative and cumulative process [31]. Thus, the amount of the material removal by each individual particle, combined as the material removal element based on the multiple Herzian contacts of slurry particles at a moment, forms the basis for modeling the removal profile of the epicyclic tool motion. The track coordinates of the polishing tool are determined in terms of the orbit motion characteristics, whereas the material removal element is calculated by the

Fig. 4. Experimental setup of the robotic polishing system. 4

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Table 1 Measured and analyzed pad surface after polishing.

and improve the transfer of the polishing slurry, thereby enhancing the uniformity of the abrasive particle distribution. This phenomenon infers that with high rotation speed, the wear resistance of the polishing pad in CCCP is much better than that in CCOS. Table 2 shows the measured and analyzed pad surface when using a rotation speed of 800 rpm and tool loads of 42, 52, and 62 N. Agglomerated particles are also circularly stacked at the center in the CCOS process, and the radius of the stacked area is almost unchanged with the variation of the tool load. No particle agglomeration occurs under different tool loads in the CCCP process because the variation of the tool load cannot change the centrifugal force and hence has no effect on the radius of the stacked area. Furthermore, a large tool load tends to increase the agglomeration of abrasive particles in CCOS. The comparison further proves that the wear resistance of the polishing pad in CCCP is better than that in CCOS. Thus, the proposed CCCP has better polishing stability. To verify the superiority of the wear resistance of the polishing pad in CCCP, special conditions with high rotation speed (1000 rpm) and large tool load (160 N) are adopted in the comparative experiments. Fig. 5 shows the results after 5 min of polishing by CCCP and CCOS. Interestingly, the pad surface of CCOS is seriously worn, and the pad surface of CCCP has no obvious change. Given the uneven distribution of polishing slurry in the interface, the actuating element is significantly vibrated and accompanied by harsh frictional sounds during the CCOS process. By contrast, the performance of CCCP is extremely stable and does not have any frictional sound. The results prove that CCCP has much better polishing ability than does CCOS at large tool loads and high rotation speeds.

rough compared with that of the polished surfaces [27]. The porous structure of the pad surface facilitates the transfer of the polishing slurry into the interface to chemically and/or mechanically remove the material from the target surface. The porous structure of the pad surface significantly affects the micro-contacts between the pad and workpiece, thereby influencing the pressure distribution and spatial distribution of active abrasive particles. Thus, the wear of the pad surface tends to reduce the material removal rate, hence causing surface scratches and prolonging the polishing time. Thus, the wear resistance of dressed polishing pad is important for effectively maintaining constant tool influence function and efficiently improving the surface roughness in the ultra-precision polishing process. To compare the pad wear characteristics between CCCP and CCOS, a series of experiments was conducted on fused quartz glass using polyurethane polishing pad, 5 wt.% cerium oxide polishing slurry of 0.4 μm nominal diameter, and polishing time of 20 min. Table 1 shows the measured and analyzed pad surface with use of a tool load of 52 N and rotation speeds of 400, 600, and 800 rpm. Results show that agglomerated particles are circularly stacked in the center in the CCOS process and the radius of the stacked area is increased with increasing rotation speed. Moreover, no particle agglomeration occurs in the CCCP process because the centrifugal force produced by rotation of the polishing tool prevents polishing slurry from entering the central area in CCOS. Thus, abrasive particles in the central area of CCOS are difficult to update and tend to agglomerate. This condition will exacerbate wear in the center of the polishing pad and cause surface scratches on the polished surface. Moreover, the higher the rotation speed, the greater the centrifugal force, thereby increasing the difficulty for the polishing slurry to enter the central area, thereby producing a larger radius in the stacked area in CCOS. The polishing slurry is supplied through the center hole of the polishing tool in CCCP, and the centrifugal force facilitates the uniform and stable transfer of the polishing slurry into the interface. A large rotation speed will increase the centrifugal force

4.2. Comparison of the rotatory material removal characteristics between CCCP and CCOS To compare the rotatory material removal characteristics of CCCP 5

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Table 2 Measured and analyzed pad surface after polishing.

A higher rotation speed produces greater centrifugal force, thereby resulting in greater difficulty for the polishing slurry to enter the center area, and hence larger width of the non-removal area in the central region of the material removal profile in CCOS, as shown in Fig. 6(c). Moreover, the width of the non-removal area is nearly constant in CCCP. Fig. 6(d) shows that the maximum depth of the material removal profile for CCOS is larger than that for CCCP, whereas the volumetric material removal of CCOS is smaller. Although the particle agglomeration of CCOS results in a larger maximum depth of the material removal profile for CCOS than for CCCP, the sufficient supply of polishing slurry in CCCP facilitates the involvement of more polishing particles in the material removal, thereby producing a higher volumetric material removal rate. The particle agglomeration of CCOS may cause surface scratch and hence should be avoided in the ultra-precision polishing process. The results indicate that the material removal characteristics of CCCP tend to be more stable and controllable than that of CCOS.

Fig. 5. Images of pad surface after 5 min of polishing by (a) CCCP and (b) CCOS.

and CCOS, a series of experiments was conducted on fused quartz glass using a polyurethane polishing pad, 5 wt.% cerium oxide polishing slurry of 0.4 μm nominal diameter, and polishing time of 20 min. Fig. 6 shows the measured and calculated results when using the tool load of 52 N at rotation speeds of 400, 600, and 800 rpm. Fig. 6(a) shows that the amount of material removal of CCCP increases linearly with increasing rotation speed because a higher rotation speed results in entrapment of more polishing particles in the interface, thereby producing a higher material removal rate. Given the stable lubrication conditions of polishing slurry, the shape of the material removal profile is stable, and the width of the material removal profile does not change with varying rotation speed in CCCP. Fig. 6(b) shows that the amount and the shape of the material removal profile irregularly change as the rotation speed is varied in CCOS, because the centrifugal force produced by the rotation of the polishing tool prevents the polishing slurry from entering the central area. In addition, the lubrication condition of polishing slurry in the interface is deteriorated by the variation of the rotation speed in CCOS.

4.3. Optimization analysis of the epicyclic tool motion for CCCP To optimize the surface form correction for CCCP, we perform a series of Taguchi design experiments to produce the tool removal profile with strong central peaks. In this study, the approaching factor λ is proposed to describe the degree of concentration at the center of the epicyclic tool motion.

λ =

W1/2 , W

(9)

where W1/2 is the amount of the material removal within the ½ radius range of the polishing center, and W is the total amount of the material removal for the epicyclic tool motion. A larger value of the approaching factor means a more concentrated removal function; thus, a higher signal-to-noise ratio (S/N) is adopted in the present simulation experiments. Table 3 shows six fixed process parameters in the simulation experiments, whereas Table 4 shows three control factors (each with five levels) as arranged in an L25(53) orthogonal array. Give that no 6

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Fig. 6. Comparison of the material removal characteristics between CCCP and CCOS: (a) material removal profile of CCCP, (b) material removal profile of CCOS, (c) width of the non-removal area, and (d) amount of the material removal.

To study the relationship between the approaching factor and the surface shape of the tool removal profile with different polishing parameters, four sets of simulation results with different approaching factors are analyzed and presented in Fig. 8. The material removal characteristics of the epicyclic tool motion become closer to the Gaussian-like shape when the approaching factor is increased. Fig. 8(a) and (b) show that the recessed area appears in the central region of the material removal characteristics when the approaching factor is smaller than 0.5. Fig. 8(c) shows that the maximum depth of the material removal occurs in the center of the tool removal profile when the approaching factor is 0.508. However, the tool profile has a mutational central peak and an obese full width, which is not conducive to the form correction process. Fig. 8(d) shows that the shape of the material removal characteristics becomes more concentrated with the increment of the approaching factor, compared with Fig. 8(c). The results can validate the assumption that a larger value of the approaching factor produces a concentrated removal function and thus tends to be more conducive to subsequent surface finishing. To clarify further the reason why the approaching factor and the surface shape of the tool removal profile vary with use of different polishing parameters, 11 reference points on the polishing tool, as shown in Fig. 2(b), are analyzed with different eccentric ratios and angular speed ratios. Fig. 9 shows the corresponding trajectory of the polishing tool for Fig. 8. Fig. 9(a) shows that the trajectory is extremely sparse at the center when the eccentric ratio and angular speed ratio are 0.4 and 1, respectively. Thus, nearly no material removal occurs at the center in Fig. 8(a). When the eccentric ratio is increased to 0.5, the polishing area increases relatively, as shown in Fig. 9(b) and (c). Given the different angular speed ratios, the polishing trajectory in the polished areas vary. Fig. 9(b) shows the ring region with different sparsities of trajectories, thereby resulting in three different values of peaks

Table 3 Fixed process parameters in Taguchi design of simulation experiments. Fixed factors

Levels

Fixed factors

Levels

Tool radius Polishing cloth Particle type

38 mm × 38 mm square Polyurethane pad CeO2

Polishing time Slurry concentration Particle size

20 min 5 wt.% 0.4 μm

Table 4 Control factors and levels in Taguchi design of simulation experiments. No.

A B C

Control factors

Angular speed ratio Eccentric ratio Tool load

Levels 1

2

3

4

5

0.1 0.2 40 N

0.2 0.4 45 N

0.3 0.6 50 N

0.4 0.8 55 N

0.5 1 60 N

material is removed at the center when the eccentric ratio is larger than 1, the range of the eccentric ratio is set to 0–1. Following the operational range for the safety and stability of a polishing machine, the range of rotatory speed is 600–1200 rpm, and the maximum orbit speed is 300 rpm; thus, the range of the angular speed ratio is set to 0–0.5. Fig. 7(a) and (b) show the plots of the means and S/N for the approaching factor in graphical form, respectively. Both figures indicate that the combination of the optimal factor level for the approaching factor is A1B2C2. Thus, the optimal process parameters for the epicyclic tool motion are angular speed ratio of 0.1, eccentric ratio of 0.4, and tool load of 45 N. Moreover, the eccentric ratio, angular speed ratio, and tool load are critical factors that affect the approaching factor in descending order. 7

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Fig. 7. (a) Mean and (b) S/N ratio factor response graphs for the approaching factor of CCCP.

greater than 0.008 mm and thus better assess the surface roughness. Fig. 11(a) shows that the peak-to-valley (PV) value and the surface roughness Ra of the sample A are 1.25 μm and 8.7 nm, respectively. Many obvious scratches and surface waviness are produced on the surface of sample A mainly because agglomerated particles can be easily stacked at the center of the polishing area in CCOS. This condition can deteriorate the stability of the material removal characteristics and cause surface waviness and surface scratching during the polishing process. The measured results of sample B indicate that the PV value is 0.368 μm and the surface roughness Ra is 4.37 nm, as shown in Fig. 11(b). Although a few small scratches remain on the surface, the surface waviness and surface roughness of the polished surface can be significantly improved for CCCP without epicyclic tool motion compared with CCOS without epicyclic tool motion. This result is because CCCP can improve the wear resistance of the polishing pad and produce fuller and more even abrasive grain supply compared with the traditional CCOS. Interestingly, the PV value and the surface roughness Ra of sample C decrease to 0.1 μm and 1.6 nm, respectively. Moreover, the measured surface topography of sample C shows that almost no scratches are present on the surface. This finding proves that CCCP, with the optimized parameters of the epicyclic tool motion, can produce an ultra-smooth optical surface with high surface convergence efficiency. Thus, CCCP can effectively reduce the surface profile error and avoid surface scratching caused by particle agglomeration in CCOP. Furthermore, CCCP is a promising method of polishing large-diameter aspheric optics with high efficiency and capability. Fig. 12 shows the power spectral density (PSD) analysis of the measured surfaces (original and polished surfaces of samples A, B, and C). The Welch method with rectangle windows function is used to analyze the PSD in the spatial wavelength of the sample surface. Results show that the surface error of sample A is improved in the spatial frequency range of less than 0.1 mm−1 and above 1.1 mm−1 but is rarely improved in the middle-spatial frequency. This difference may be caused by the production of scratches and surface waviness on the polished surface of sample A by CCOS. Moreover, the PSD curve of sample B shows that the surface error is distinctly improved in the whole spatial frequency compared with the original surface. However, CCCP does not show obvious advantages over CCOS in suppressing high-frequency errors when the spatial frequency is greater than 0.3 mm−1. The surface error is restricted obviously in the entire spatial frequency when the sample surface is polished by the CCCP process with the optimized parameters of the epicyclic tool motion. By comparison, the surface improvement of sample C is the most significant in the entire spatial frequency, thereby further proving that the CCCP

of the material removal profile, as shown in Fig. 8(b). Significant differences in trajectory density between the surrounding and the central areas in Fig. 9(c) tend to cause a mutational central peak of material removal at the center, as shown in Fig. 8(c). When the eccentric ratio and angular speed ratio are decreased to 0.2 and 0.2, respectively, the polishing area is decreased, and the uniformity of the polishing trajectory is improved (Fig. 9(d)), thereby producing a concentrated removal profile (Fig. 8(d)). To validate the performance of the proposed theoretical model, simulation and practical experiments are conducted by using the optimal parameters in CCCP. Fig. 10(a) shows the simulated three-dimensional topography of the material removal characteristics of the epicyclic tool motion. The material removal characteristics tend to be in a Gaussianlike shape under the optimized polishing condition, which can be effectively explained by the excellent uniformity of the polishing trajectory in Fig. 10(b). The experimental result measured by a contact-type Form Talysurf profiler system is shown in Fig. 10(c). The predicted result agrees reasonably with the measured data in surface shape. Fig. 10(d) shows the cross-section profile of the simulated and experimental results. The comparison proves that the material removal model can be successfully used for optimizing the polishing process. Moreover, the asymmetry of the experimental result may be caused by the perpendicular error of polishing spindle, which will be improved in future work.

4.4. Comparison of uniform polishing between CCCP and CCOS Uniform polishing experiments are conducted to compare the generated surface of CCOS without the epicyclic tool motion, CCCP without the epicyclic tool motion, and CCCP with the epicyclic tool motion. Three pieces of fused quartz glass are used as test samples (A, B, and C). The samples are preprocessed by a surface grinding machine under the same machining conditions to maintain the same surface state, in which the initial roughness Ra is approximately 0.1 μm. Sample A is polished by CCOS without epicyclic tool motion, and the polishing tool rotates at 600 rpm. Sample B is polished by CCCP without epicyclic tool motion, and the polishing tool rotates at 600 rpm. Sample C is polished by CCCP with the epicyclic tool motion. The eccentric ratio and the angle speed ratio are 0.4 and 0.1, respectively. After uniform polishing for 4 h, the cross-section profile of 10 mm and the surface topography of 2 mm × 2 mm on the polished surface of three samples are measured to evaluate the surface profile error and the surface roughness, respectively, as shown in Fig. 11. The presented 3D surface topography of the measured results uses a Gaussian filter to remove wavelength bands 8

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Fig. 8. Simulated 3D topography and 2D profile of the material removal characteristics of the epicyclic tool motion for approaching factor: (a) 0.407, (b) 0.449, (c) 0.508, and (5) 0.547.

area. A novel material removal model was established, and Taguchi trials were conducted to understand the polishing mechanisms and optimize the tool removal profile of the epicyclic tool motion in CCCP. Simulation and practical experiments showed that agglomerated particles were circularly stacked at the center of the pad surface in CCOS, whereas no particle agglomeration occurred in the CCCP process. CCCP can significantly improve the wear resistance of the polishing pad compared with traditional CCOS. The sufficient supply of polishing slurry in CCCP facilitated the involvement of more polishing particles in the material removal, thereby producing a higher volumetric material

process with epicyclic motion has obvious advantages over the traditional CCOS in terms of improving the middle-spatial frequency error and high-frequency error of optical surfaces. 5. Conclusions In this paper, we present the development of a novel CCCP process and tool for polishing of large-diameter aspheric optics to overcome several challenges in traditional CCOS technology, including polishing tool wear and uneven distribution of polishing particles in the contact 9

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Fig. 9. Trajectory of epicyclic motion for approaching factor: (a) 0.407, (b) 0.449, (c) 0.508, and (d) 0.547.

by particle agglomeration in CCOS. Moreover, CCCP with optimized parameters of the epicyclic tool motion can produce an ultra-smooth optical surface with high surface convergence efficiency. Therefore, CCCP is a promising method of polishing large-diameter aspheric optics with high capability and efficiency.

removal rate than CCOS. Moreover, a comparative analysis suggested that the material removal characteristics of CCCP were more stable and controllable than those of CCOS. Uniform polishing experiments also showed that CCCP can effectively reduce surface profile error and avoid surface scratching caused

Fig. 10. Simulated and experimental results for the optimal process parameters: (a) simulated result, (b) trajectory of epicyclic motion experimental result, (c) experimental result, and (d) comparative result of the material removal profile. 10

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Fig. 11. Surface topography of (a) sample A by CCOS without the epicyclic tool motion, (b) sample B by CCCP without the epicyclic tool motion, and (c) sample C by CCCP with the epicyclic tool motion.

Acknowledgements This work was partly supported by the Key Projects of Tianjin Science and Technology Support Program (No.18JCZDJC38900); National Science and Technology Major Project of the Ministry of Science and Technology of China (Grant No. 2017ZX04022001-206); Research Project of State Key Laboratory of Mechanical System and Vibration MSV201907. References [1] R. Henselmans, L.A. Cacace, G.F.Y. Kramer, P.C.J.N. Rosielle, M. Steinbuch, The NANOMEFOS non-contact measurement machine for freeform optics, Precis. Eng. 35 (2011) 607–624. [2] D.W. Kim, J.H. Burge, J.M. Davis, H.M. Martin, M.T. Tuell, L.R. Graves, S.C. West, New and improved technology for manufacture of GMT primary mirror segments, in: R. Navarro, J.H. Burge (Eds.), Advances in Optical and Mechanical Technologies for Telescopes and Instrumentation Ii, 2016. [3] D.D. Walker, A.T.H. Beaucamp, R.G. Bingham, D. Brooks, R. Freeman, S.W. Kim, A. King, G. McCavana, R. Morton, D. Riley, J. Simms, The precessions process for efficient production of aspheric optics for large telescopes and their instrumentation, Special. Opt. Dev. Astron. 4842 (2003) 73–84. [4] T.E. Andersen, A.L. Ardeberg, J.M. Beckers, A. Goncharov, M. Owner-Petersen, and H. Riewaldt, Euro50 (2004), Vol. 5382, pp. 169–182. [5] Z. Dong, H. Cheng, Study on removal mechanism and removal characters for SiC

Fig. 12. PSD analysis for measurement results.

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