Open Access
Add to BibSonomy
Abstract
In recent years, extensive research and development have been conducted on an active fluid jet (AFJ) polishing-based post-polishing process aimed at removing periodic marks from diamond-turned surfaces. This cost-effective method demonstrates its machining capability across a wide range of materials. Notably, it excels in preserving the form accuracy during the post-polishing process for traditional optics, allowing for the attainment of high-precision shape and an ultra-smooth texture. However, the challenge arises when attempting to maintain form preservation on diamond-cut surfaces located on the side-walls of structures due to non-uniform material removal. This limitation significantly restricts its application in advanced opto-mechanical systems, including monolithic multi-surface workpieces. Therefore, this paper systematically investigates the form-preserving capability of AFJ polishing for side-wall surfaces through multi-scale analysis. The micromachining characteristics of the diamond-cut surface are elaborated upon using elastic-plastic theory, and the impact of polishing parameters on form preservation is studied at the microscopic scale. Furthermore, at the macroscopic scale, a simulation model of the AFJ polishing process is established based on fluid-structure interaction (FSI) analysis and rigid dynamic analysis. To validate the proposed theory, a series of tests are conducted. Theoretical and experimental results indicate that non-uniform material removal occurs in the contact area between the tool and the workpiece due to the influence of gravity, thereby hindering the form-preservation polishing process. Building upon the simulation model, a new AFJ tool is designed and optimized to enhance the form-preserving capability of AFJ post-polishing for side-wall surfaces. Experimental results confirm that the innovative AFJ tool uniformly eliminates the periodic marks on diamond-cut surfaces. The theory and methodology presented in this work have broad applicability to various form-preservation post-polishing processes on diamond-cut surfaces.
© 2024 Optica Publishing Group under the terms of the Optica Open Access Publishing Agreement
1. Introduction
Modern optomechanical systems have greatly benefited from advancements in the fabrication and metrology of monolithic multi-surface workpieces (MMSWs). These MMSWs have a wide range of applications in aerospace, remote sensing, and high-performance optical imaging systems [1–3]. Typically, MMSWs consist of multiple surfaces with different positions and orientations on a single monolith, effectively reducing the number of optical elements and the assembly complexity of the system [4]. Compared to traditional optics, MMSWs offer advantages such as compactness, reduced weight, and superior imaging performance. Often, the optical components of MMSWs are spatially distributed within a semi-closed cavity [1,5], with optical surfaces located on the side-walls of the structure, posing significant manufacturing challenges.
With the rapid development of ultra-precision CNC machining technology, single-point diamond turning (SPDT) has become a common method for producing MMSWs [3,6]. It enables the direct production of optical surfaces with sub-micrometer form accuracy and nanometric roughness, while ensuring precise position and orientation for each optical surface. However, the residual tool marks (RTMs) that remain after SPDT adversely affect the optical performance, leading to undesirable diffraction and stray light [7]. The expanding applications of MMSWs in advanced optical instruments require smoother surfaces with high accuracy. Therefore, there is a strong need for an effective post-treatment method that can remove RTMs without compromising form accuracy.
To date, various post-polishing technologies have been developed for SPDT surfaces, including ion beam figuring (IBF) [8,9], magnetorheological finishing (MRF) [10,11], micro-dissolution polishing (MDP) [12,13], abrasive jet polishing (AJP) [14], and bonnet polishing [15]. These methods have significantly improved optical performance, thanks to the efforts of numerous researchers. As the application scope of ultra-precision optics continues to diversify and the demand for post-polishing technology grows, there is an increasing need for low-cost and widely applicable solutions. Unfortunately, these methods have some limitations. Firstly, the escalating demand for high-quality optics has spurred significant interest in reducing production costs. The high cost of an SPDT machine results from its intricate components, such as precise feedback systems, high-precision bearing systems, tooling drivers, and other sophisticated mechanisms [16]. Typically, achieving the desired optical performance requires a slow feed rate to minimize surface roughness, thereby prolonging the process duration. Consequently, the utilization rate of these expensive devices is notably higher in ultra-precision optical manufacturing. Therefore, there is a dire need for a cost-effective and efficient post-polishing technique that can surpass the surface quality achieved by the SPDT machine. In essence, the optical surface is initially created on the SPDT machine at a relatively high feed rate and further refined through the post-polishing method. Nevertheless, the exorbitant cost of MRF hinders its widespread adoption in mass production. Secondly, owing to the rapid advancements in non-conventional machining techniques, the modern SPDT is capable of machining a diverse range of materials [17]. Hence, it is imperative to consider the compatibility of post-polishing techniques. Previous studies indicate that both IBF and MDP exhibit pronounced material selectivity. Commonly used SPDT materials, including nonferrous metals and plastics, are unsuitable for IBF [14]. Similarly, the MDP method relies on the solubility of potassium dihydrogen phosphate (KDP) in water [12]. Currently, there is no definitive solution to address the abrasive embedding phenomenon in AJP [18]. Thirdly, bonnet polishing technology, renowned for its versatility in handling a broad spectrum of materials, is deemed an effective approach for eliminating turning marks. This process involves the use of an inflated spherical membrane tool to smoothen the surface texture. Past research reveals that the material removal rate is substantially influenced by various factors such as process parameters, mechanical errors, the rigidity of the bonnet tool, tool clamping errors, and numerous others [19,20]. However, it is worth noting that the residual tool marks are typically confined to a depth of merely a few dozen nanometers. Given this minuscule scale, the challenge lies in eliminating these marks without compromising form accuracy during the post-polishing process. Nevertheless, the inevitable mechanical errors associated with the bonnet polishing process complicate the demonstration of its form-preserving capabilities.
Recently, an active fluid jet (AFJ) polishing technology has been developed and investigated for the removal of diamond turning marks. In this process, a small sub-aperture polishing pin is pressed against the workpiece surface using polishing fluid, while the pin is rotated eccentrically. Material removal occurs due to the relative velocity and pressure between the tool and workpiece, following Preston's law. Initially developed for correcting aspherical and freeform optics, AFJ polishing has gained interest due to its affordability and applicability to a wide range of materials. Many scholars have conducted theoretical analyses, experimental research, and proposed improved methods for AFJ polishing. Vipender Singh Negi et al. analyzed the contact pressure distribution, relative velocity, and tool influence function (TIF) of AFJ polishing [21]. They experimentally presented the smoothing effect of the optical surface with respect to tool path spacing. Bi et al. designed a new polishing pin with a helical blade to optimize the TIF, resulting in higher removal efficiency and improved TIF [22]. Zhang et al. applied AFJ polishing to remove diamond turning marks, investigating the effect of polishing parameters on the material removal rate. They demonstrated the effectiveness and superior form-preserving capability of AFJ polishing on diamond-turned surfaces, showing that it enables deterministic post-treatment while preserving the surface form [23].
A literature review indicates that the AFJ polishing method is affordable and can be used for a wide range of materials. However, previous studies have mainly focused on ordinary optics (the tool is positioned vertically), and there have been few studies on optical components with complex spatial structures. As mentioned above, optical surfaces in MMSWs are often found on the side-walls of semi-closed structures. As a result, during the AFJ polishing process, the tool is positioned horizontally, leading to non-constant contact pressure on the workpiece due to the influence of gravity. This results in non-uniform material removal in the contact area between the tool and the workpiece. In other words, RTMs may still be evident in some areas, while the substrate has already been damaged in other areas within the same polishing region. The non-uniform material removal poses a challenge in demonstrating form-preserving performance in AFJ polishing for diamond-cut surfaces located on the side-walls of the structure.
In this research paper, the principle of the AFJ technology was applied and a comprehensive study was conducted to investigate the post-polishing process for side-wall surfaces through multi-scale analysis. Based on the analysis, a method was proposed to enhance the form-preserving capability during the polishing process. The research framework is presented in Fig. 1. Firstly, the micromachining characteristics of the diamond-cut surface were explored based on elastic-plastic theory. The impact of polishing parameters on the form-preserving ability was studied at the microscopic scale. Secondly, the contact pressure between the AFJ tool and the side-wall surface was calculated through fluid-structure interaction (FSI) analysis. Additionally, the motion of the polishing pin was simulated to gain a better understanding of the polishing process. Based on the simulation model of AFJ polishing, the influence of processing parameters on the RTMs removal can be analyzed at the macroscopic scale so that the uniformity of RTMs removal in the polishing area can be evaluated. Finally, a series of experiments were conducted to validate the proposed theoretical analysis. To improve the uniformity of RTMs removal, an innovative AFJ tool was designed and optimized based on the simulation model. The experimental results demonstrated the effectiveness of the new AFJ polishing method in uniformly removing RTMs.
Fig. 1. The research framework: the influence factors of RTMs removal were theoretically studied at the microscopic and macroscopic scale; a series of experiments was conducted to verify the theoretical model and a new AFJ tool was designed to improve the form-preserving ability.
2. Theoretical analysis
The diamond-cut surface comprises a turning mark layer and a substrate, collectively defining the overall microtopography. At the microscopic level, the turning mark layer exhibits anisotropic properties due to its periodic structure in the high spatial frequency domain. Unlike isotropic surfaces, the presence of the ripple structure within the turning mark layer impacts the distribution of active abrasives and the micromachining state of a single abrasive. Consequently, the material removal process within the rippled layer varies significantly depending on the direction of abrasive movement and the position of contact. The primary objective of form-preserved post-polishing is to eliminate the ripple structure while preserving the integrity of the substrate. To gain a better understanding of its form-preserving capability, it is imperative to study the characteristics of material removal during this process. This involves analyzing the distribution of active abrasives and studying the contact mechanics of a single abrasive on the ripple structure using a theoretical model. Through such investigations, researchers can gain insights into how material removal occurs during the form-preserved post-polishing process, which is essential for achieving the desired surface quality without compromising the substrate's integrity.
2.1 Material removal characteristics of RTMs
2.1.1 Modelling of active abrasive particles
Previous research has shown that a gap forms between the polishing pad and the workpiece surface near larger abrasives during polishing [24]. Only abrasives larger than the gap can remove material, and they are called active abrasives. The distribution of abrasive particle sizes (diameters) in the polishing slurry affects the number of active abrasives. In most cases, this distribution follows a normal probability density function, which is expressed as
As shown in Fig. 2, a coordinate system x'Oz’ is established, with the origin point O located at the apex of the turning mark. The z’ axis is defined in the vertical direction, while the x’ axis is defined in the horizontal direction. This allows for the determination of the number of active abrasive particles at a specific point P.
where g is the distance between the workpiece and the polishing pad at the peak of the turning mark. Eq. (3) means only abrasives larger than g + z’ can participate in the material removal. According to the previous study [23], where Dmax is the diameter of the largest particle, δwmax and δpmax are the penetration depth of the largest abrasive particle into the workpiece and the polishing pad respectively. Attributed to the contact between pad and grain, the normal force acted on the single grain (see Fig. 2) can be expressed below based on plastic contact theory, where Hw and Hp are the hardness of the workpiece and the pad, respectively; aw and ap are the radius of the projected circle of contact on the workpiece and the pad, respectively. Usually, the penetration depth is much smaller than the diameter of the abrasive, therefore, an approximate relation can be obtained asAccording to the above analysis, the number of active abrasive particles at point P can be given by
Fig. 2. Distribution of active abrasives exhibits periodic variations on the rippled surface due to the height deviation between the peaks and valleys.
It can be found from Eq. (8) that the number of active abrasives N decreases as z’ increases. This implies that the distribution of active abrasives exhibits periodic variations on the rippled surface due to the height deviation between the peaks and valleys. In particular, at the peak of the turning marks, a greater number of abrasive particles can participate in the material removal process compared to the valley regions.
2.1.2 Contact of single grain
During the polishing process, the grain is positioned between the pad and the turning mark, as illustrated in Fig. 3. The geometry of the single grain can be simplified as a sphere, particularly when considering silica as the material, which is commonly used in such applications. To analyze the forces and contact, a new coordinate system xPz, is introduced. In this system, the contact point P serves as the origin, while the z-axis is defined as perpendicular to the surface of the ripple, and the x-axis is tangent to the surface. Stresses are of great importance in the polishing process as they contribute to dislocation, micro-crack formation, and material removal. The stress field generated by a single grain can be viewed as a combination of the Boussinesq field and Cerruti field. The Boussinesq field arises from the normal polishing force, denoted as Fawn, and it can be calculated using Eq. (9), which is derived from the theory of elasticity.
Here, υ is the Poisson’s ratio of the workpiece. Similarly, the Cerruti field arises due to the tangential polishing force Fawt can be evaluated using the following equations.
Fig. 3. Calculation model of the Boussinesq stress and Cerruti stress of an arbitrary point in the workpiece when an active abrasive is positioned between the pad and the turning mark.
According to the superposition principle, the state of stress generated by the grain at an arbitrary point is
Correspondingly, the first stress invariant ${\mathrm{\Theta }_1}$ and the second tress invariant ${\mathrm{\Theta }_2}$ is
Thus, von Mises stress [25] can be expressed as
According to Eqs. (9)-(13), the von Mises stress rapidly decreases as the distance R increases. This indicates that high stress is primarily concentrated near the contact point. Therefore, the stress field has minimal impact on the substrate when the abrasive particle interacts with the turning mark. Additionally, it is suggested in Eq. (8) that reducing the load Fpan can decrease the number of active abrasives in the entire polishing area. Ideally, if Fpan is small enough, only a few active abrasives will be present in the valleys, while several active abrasives will be distributed at the peaks. Consequently, it becomes highly unlikely to cause damage to the substrate of the workpiece when removing the turning marks. Therefore, achieving form-preserved polishing is feasible by minimizing the load Fpan as much as possible.
Considering the forces in the contact region depicted in Fig. 3, the reaction forces of Fawn and Fawt are defined as Fwan and Fwat, respectively. Hence, a mechanical equilibrium equation can be constructed along the z’ axis, which is expressed as
Hence,
In the provided equation, the friction coefficient is denoted as μ, and the contact angle is represented by θ. It is important to note that the angle θ decreases as the contact point approaches the apex of the turning mark. According to Eq. (15), the normal force Fawn exerted on the ripple decreases as θ decreases, while the applied force Fpan remains constant. Consequently, it can be inferred from Eq. (13) that the corresponding von Mises stress also decreases. This indicates that abrasives on the substrate or hillside generate a larger high-value stress zone and exhibit more pronounced micro-cutting or ploughing, while abrasives at the apex have little impact on material removal. Based on this understanding, attempting to achieve form-preserved post-polishing by reducing the polishing pressure to decrease the ratio of active abrasives at the valleys, as previously mentioned, may not yield meaningful results.
The above analysis is focused on the effect of the contact position on the micro-cutting forces in the vertical direction, resulting from the anisotropic nature of the ripple structure. Similarly, the micro-cutting areas vary based on the movement direction of the abrasives due to microscopic anisotropy in the horizontal plane. To better demonstrate the analysis, the abrasive's movement direction is divided into two components: one perpendicular to the turning mark ripples and the other parallel to the turning marks.
When the abrasive moving direction is parallel to the turning mark (with a velocity denoted as vpara), as depicted in Fig. 4, the micro-cutting area approximately forms an isosceles triangle. The base and height of the triangle are represented as MN = 2a, and the penetration depth δ, respectively. So, the area can be calculated by
Usually, the penetration depth is much smaller than the diameter of the abrasive D; therefore, an approximate relation can be obtained as
Equation (16) can be rewritten as
When the abrasive moving direction is perpendicular to the turning mark (the velocity is vperp), the micro-cutting area is an isosceles triangle approximately with base length 2a and height h, so the area is
Considering Eq. (17) while solving the triangle ΔNJK in Fig. 4, the height can be given as
Namely,
Fig. 4. Schematic diagram of micro-cutting areas when an active abrasive moving direction is parallel or perpendicular to turning marks.
Equations (18) and (21) describe the impact of the abrasive's movement direction on the micro-cutting area. When the abrasive moves perpendicular to the ripples, it typically collides with the turning mark. As a result, the micro-cutting area (Sperp) is significantly larger since it encompasses both the front and underneath portions of the abrasive. On the other hand, when the abrasive's movement direction is parallel to the ripples, the micro-cutting area (Spara) is smaller as the abrasive primarily affects the material underneath it. This means that there will be no obvious ploughing or cutting phenomenon. In extreme cases where the abrasives are located at the apex of the turning mark, the contact angle θ becomes zero, and the height of the isosceles triangle (represented as h in Eq. (20)) becomes equal to δ. This implies that the differences in micro-cutting area caused by the abrasives’ motion direction can be neglected when the abrasives act on the apex of the turning mark.
Ultimately, the von Mises stress induced by abrasives contributes to material removal on the surface. In most cases, it is primarily distributed in the turning mark layer and rapidly decreases away from the contact point. The anisotropy in the horizontal dimension results in larger von Mises stress and remarkable deformation when the abrasive's motion direction is perpendicular to the ripples. However, when the motion direction is parallel to the ripples, there is little impact on material removal. In the vertical direction, abrasives acting on the apex generate relatively small von Mises stress and deformation, mainly concentrated near the contact position, with minimal influence on material removal. In addition, the contact position and motion of polishing abrasives lead to the strain of the sub-surface in different directions. This suggests that fatigue loads can be generated when many polishing abrasives slide on the rippled surface in various directions. Hence, corresponding fatigue stress may trigger micro-cracks or material removal in the substrate, which can compromise the form-preserving polishing process.
The above analysis provides information on the material removal characteristics of diamond-cut surfaces at the microscopic level. This information is crucial in understanding the fundamental processes that govern material removal and dimensional accuracy of the machined parts. As is known, the purpose of post-polishing is to eliminate the RTMs efficiently without destroying the substrate. However, the depth of the RTMs is about dozens of nanometers in general. Because of the small scale, the dimensional accuracy of the machined parts is a key issue in the post-polishing process. Thus, the above analysis is required. Additionally, the micromachining analysis can contribute to simulation-based predictions and the evaluation of various post-polishing technologies for diamond-cut surfaces. It is valuable in selecting appropriate methods or optimizing the processing parameters.
According to the analysis, the micro-cutting process of the rippled structure is influenced by polishing pressure and the movement of the abrasives. During the AFJ post-polishing process, the load applied to the grains and their movements are influenced by factors such as the fluid flow field, the motion of the pin, and gravity, particularly for side-wall surfaces where contact pressure varies significantly. To enhance the form-preserving ability, it is necessary to systematically investigate the contact pressure and motion of the pin in the AFJ post-polishing process for side-wall surfaces.
2.2 Dynamic analysis of the AFJ polishing process
The schematic diagram of the AFJ polishing tool for side-wall surfaces is shown in Fig. 5. The tool consists of an aluminum alloy nozzle (grey part) with an eccentric hole that holds a polishing pin. The diameter of the pin is slightly smaller than that of the hole. The tool is mounted on a machine spindle, allowing it to rotate around its axis during the polishing process. The AFJ tool is moved by the machine to the desired location on the workpiece. Simultaneously, a constant flow of polishing slurry is maintained to exert pressure on the pin against the workpiece. The fluid serves the dual purpose of generating the polishing pressure and flowing through the gap to support the polishing area. Similar to other sub-aperture polishing methods, a piece of polishing pad, e.g. polyurethane (PU) or polishing cloth, is attached to the end surface of the pin, which is typically made of polyethylene or rubber.
Fig. 5. Schematic diagram of AFJ polishing for side-wall surface: an AFJ tool features a nozzle (grey part) with an eccentric hole for a polishing pin, slightly smaller in diameter. Mounted on a machine spindle, it rotates during polishing. The AFJ tool is precisely positioned by a machine while polishing slurry flows constantly, pressing the pin against the workpiece.
During the polishing process for side-wall surfaces, the AFJ tool is maintained in a horizontal position. However, the material removal mechanism becomes more complex due to the influence of gravity on the flow hydrodynamic characteristics of the polishing slurry and the motion of the pin. In this study, the FSI method is employed to calculate the contact pressure between the workpiece and the polishing pad. Meanwhile, the forces exerted on the pin by the fluid pressure can be determined. Then, the motion of the pin is simulated using a rigid dynamic method to analyze the distribution of the relative velocity in the contact area.
2.2.1 FSI model of AFJ polishing tool
In the AFJ polishing process for side-wall surfaces, the polishing pin is in contact with the workpiece surface through a continuous flow of polishing slurry. At the beginning, due to gravity, the pin contacts the inner wall of the nozzle, and the slurry flows out from the top (as shown in Fig. 6. (a)). The pressure distribution on the workpiece is determined by the hydrodynamic flow within the nozzle and the elastic deformation of the pin. This situation poses a complex multi-physics problem that requires FSI analysis to solve the nonlinear hydrodynamic elastic problem. It is worth noting that the deformation of the pin does not significantly affect the flow of the polishing slurry. Therefore, a one-way FSI analysis is employed in this model. The interaction between the two analyses takes place at the boundary, where the results obtained from the computational fluid dynamics (CFD) analysis are transferred to the structural analysis as a load. This approach allows for considering the coupling effects between the flow of the slurry and the deformation of the pin, enabling a more accurate simulation of the polishing process.
Fig. 6. Simulation of the AFJ polishing for side-wall surface: (a) FSI model, (b) CFD model of the slurry flow, (c) simulation results of the fluid flow field, (d) simulation results of the pressure distribution on the workpiece.
This study simulated the AFJ polishing process using the ANSYS-Fluent software to analyze the pressure field. The simulation involved separate fluid and structure models that were coupled through FSI to accurately capture their interaction. Both models were aligned in the same geometric position. The fluid model represented the central pipe through which the slurry was delivered. To balance computational accuracy and cost, a basic element size of 0.5 mm was selected near the coupling surface. The element size gradually increased to 5 mm with increasing distance from the coupling surface, as illustrated in Fig. 6(b). The parameters used in the CFD analysis are listed in Table 1. Since the pin is composed of rubber and exhibits hyper-elastic behavior, the nonlinear Mooney-Rivlin material model was chosen to predict its mechanical response.
Table 1. Parameters used in the CFD simulation.
The relationship between the strain energy W and the material constants is expressed as
where, C10 = 1.5 × 105 Pa and C01 = 1.5 × 104 Pa are Mooney-Rivlin material constants, I1 and I2 are strain invariants. The material parameters of the workpiece, which is made of aluminum alloy, are listed in Table 2. In the simulation process, the FSI analysis is performed sequentially. First, the CFD analysis is conducted to determine the fluid pressure generated by the flow of the polishing slurry. Then, the computed fluid pressure is applied as a load on the pin in the subsequent structure analysis. A no-slip boundary condition is defined on the contact surface between the pin and the workpiece. The results obtained from the CFD analysis include the fluid flow field, as depicted in Fig. 6(c), and the corresponding pressure distribution, as illustrated in Fig. 6(d). It can be observed that due to the influence of gravity, the fluid flow field exhibits uneven distribution at the outlet. Consequently, the contact pressure on the workpiece is non-uniform, with the maximum value shifting in the direction of gravity (namely + X direction).Table 2. Properties of the aluminum alloy.
2.2.2 Motion of the pin
The motion of the pin in the AFJ polishing process for the side-wall surface was simulated using the ANSYS Workbench software. The initial condition of the model is depicted in Fig. 7(a) and (b). Initially, the pin is in a state of static equilibrium, with the combined effect of gravity (G), the supporting force applied by the inner wall of the tool (Ftn), the reaction force of the workpiece (Fwn), and the fluid pressure on the pin, as shown in Fig. 7(b). Figure 7(a) represents the left view of Fig. 7(b), illustrating that the symmetric axis of the tool and the pin project to points N and P, respectively, on the XOZ plane. During the polishing process, the AFJ tool rotates around axis O at a speed of 200 revolutions per minute (RPM).
Fig. 7. Forces acted on the pin at initial state (ω=0): (a) left view; (b) front view; (c) fluid pressure on the pin.
The positions of point P and point Q along the Z-coordinate and X-coordinate are shown in Fig. 8, it can be seen that the positions of P and Q undergo sinusoidal-like oscillations in the polishing spatial area based on the simulation results. Figure 9 presents the position of the pin and the velocity distribution in the contact area during the rotation of the AFJ tool. It can be observed that the relative position between the pin and the tool remains constant, with the pin consistently located at the bottom of the nozzle. Consequently, the contact pressure on the workpiece remains stable since the boundary conditions of the flow field remain unchanged. Furthermore, the trajectory coordinates of point P and point Q exhibit sinusoidal functions with the same period. This indicates that the motion of the pin during the process involves eccentric rotation, with the center of rotation being M at coordinates ((xmax + xmin)/2, (zmax + zmin)/2). This is confirmed by the velocity field distribution and trajectory. Point P revolves around point M, and the contact area for one rotation cycle (represented by dashed lines) is the superposition of all the instantaneous contact areas.
3. Experimental study
3.1 Experimental setup
The AFJ polishing experiments were conducted using an industrial robot (Nachi-Fujikoshi Corp.). The AFJ tool was equipped with a pin featuring a moderately hard polishing cloth, as depicted in Fig. 10(a). The pin had a hemisphere nose with a radius of 5 mm. The polishing slurry utilized in the experiments consisted of SiO2 abrasives with an average size of 0.4 μm, suspended in deionized water at a concentration of 20 vol%. Prior to polishing, planar Al6061 aluminum mirrors measuring 50 mm × 50 mm were prepared by cutting them using an SPDT lathe, ensuring the ripple structure was oriented in the same direction.
Fig. 10. Experimental setup: (a) AFJ polishing equipment for side-wall surface; (b) measurement points; (c) initial surface; (d) PSD analysis.
The surface roughness of the mirrors was measured using a white light interferometer (Zygo Newview) with a scanning size of 0.5 mm × 0.5 mm adopting vertical scanning interference (VSI) mode, the direction of the tool markings can be determined and marked on the surface of the sample. After that, the aluminum mirror was mounted vertically, and two types of tests were conducted in this study. In Test A, the direction of the ripple was set to be parallel to the Z-axis by adjusting the orientation of the sample initially, as indicated by the green arrow in Fig. 10(b). The experimental parameters are presented in Table 3. Three sets of fixed spot polishing experiments were carried out, with polishing times of 2 minutes, 4 minutes, and 6 minutes, respectively. The surface texture of point B1 was measured using a white light interferometer (Zygo Newview) after each polishing session. Subsequently, the sample was rotated by 90 degrees so that the direction of the ripple became perpendicular to the Z-axis, as illustrated by the brown arrow. Three identical sets of polishing experiments and measurements were conducted for comparison. It should be noted that the motion direction of the abrasives remained unchanged, allowing for observation of the influence of the abrasives’ movement direction. In Test B, the fixed spot polishing time was extended to 15 minutes while keeping other parameters the same as in Test A. This was done to observe the uniformity of material removal in the polishing area. The surface topographic textures of four measurement points B1 to B4 were measured. The material removal distribution in the entire region was extracted using a laser interferometer (Zygo GPI).
Table 3. Experimental parameters.
The distribution of roughness measurement points within the polishing area is shown in Fig. 10(b). The measurement results from four points (B1 to B4) were found to be quite similar after diamond turning. Therefore, the results obtained at point B1 were taken as an example, as shown in Fig. 10(c). A contour line perpendicular to the turning marks was extracted, and power spectrum density (PSD) analysis was performed to visualize the spatial frequency, as depicted in Fig. 10(d). Due to the presence of periodic turning marks, a prominent peak appeared at a spatial frequency of 1.397 mm-1 (logarithm of spatial frequency) in the PSD curve. The objective of the post-polishing process was to reduce the PSD value at 1.397 mm-1 without compromising the surface accuracy.
3.2 Results and discussions
Figure 11 illustrates the surface texture obtained in Test A when the motion direction of the abrasive is perpendicular to and parallel to the turning mark ripples, respectively. A comparison of the two figures reveals that the decline in PSD amplitude at 1.397 mm-1 is more pronounced when the motion of the abrasive is perpendicular to the turning mark ripples.
Fig. 11. Surface texture in Test A. (a) motion direction of the abrasive is perpendicular to the turning mark ripples; (b) motion direction of the abrasive is parallel to the turning mark ripples
In Fig. 11(a), the periodic tool marks are noticeably deteriorated due to the occurrence of micro-breaches and deformation in the peak. On the other hand, when the motion of the abrasive is parallel to the turning mark ripples (Fig. 11 (b)), the ripple structure remains largely intact, although there is a slight decrease in the height of the RTMs and the PSD amplitude. Additionally, no significant deformation can be observed on the rippled layer. This phenomenon can be explained by the differences in von Mises stress and micro-cutting area resulting from the anisotropic properties of rippled surfaces, as presented in Section 2.1.
Furthermore, the logarithm of PSD value at the spatial frequency of the turning marks, after a polishing duration of i minutes, is denoted as ΔPSDTMi. The change in ΔPSDTMi in Test A is demonstrated in Fig. 12. The ordinate, ΔPSDTMi is calculated by
It is worth noting that ΔPSDTMi decreases as the polishing time increases, indicating a decline in the efficiency of the post-polishing process. This phenomenon can be attributed to the microscopic characteristics of the rippled surfaces, as explained in the theoretical model presented in Section 2.1. Diamond-cut surfaces exhibit periodic properties in their microtopography. Previous studies have indicated that the period of the ripple structure is determined by the parameters of the diamond-cutting process and material properties [26], and it remains stable during the post-polishing process. However, the height of the ripple structure gradually decreases over time due to the action of polishing abrasives. This results in a decrease in the contact angle θ (as mentioned in Fig. 3). According to Eq. (15), this reduction in height leads to a decrease in the force Fawn applied to the workpiece, thereby reducing the material removal efficiency. Additionally, as the height deviation between the peak and valley decreases, the number of active abrasives at the peak becomes comparable to that at the valley during the polishing process. Consequently, the material removal rate of the ripple structure is gradually reduced. Overall, these factors contribute to the observed decrease in ΔPSDTMi and the decline in the efficiency of material removal during the post-polishing process. In practical applications, the influence of anisotropy of the diamond-cut surface on the overall polishing process is mainly manifested in two directions. In the horizontal direction, the direction of motion of the abrasives relative to the periodic ripple structure changes with the rotation and feed of the polishing tool. From theoretical models and experimental results of Test A, it can be seen that abrasive abrasives with different motion directions have significant differences in the removal rate of RTMs. It can be inferred that the removal rate of tool marks can be further controlled by controlling the tool trajectory. In the vertical direction, the anisotropy of the diamond-cut surface is mainly manifested in that the removal rate of RTMs gradually decreases with increasing polishing time, as mentioned above.
Figure 13 presents the measurement results of Test B. It can be observed that the shape of TIF resembles a crescent due to the influence of gravity. The material removal amount is significantly lower at the center and top of the polishing area. The surface textures of the four measurement points in Test B are depicted as well.
At point B1, the turning marks have been eliminated, and at point B2, they are barely visible. However, at measurement points B3 and B4, the ripple structure is still clearly visible despite the presence of numerous micro-breaches. Therefore, the RTMs removal rate is much higher at the bottom of the polishing area. Considering the TIF, it can be observed that the substrate has been significantly altered at the bottom (point B1), indicating a noticeable change in the surface form. However, at the top of the same polishing area (point B4), the ripple structure is still observable. These experimental results demonstrate the non-uniform removal of RTMs at both the macroscopic and microscopic scales during the AFJ polishing process for side-wall surfaces. This phenomenon poses challenges for achieving a form-preserving post-polishing process.
3.3 Improvements of the polishing tool
According to the analysis conducted, it is evident that the relative position between the pin and the tool remains constant throughout the AFJ polishing process for side-wall surfaces. The pin consistently stays at the bottom of the nozzle because of gravity, while the fluid flow field always exits from the top. This stable but uneven flow field contributes to the non-uniform distribution of polishing pressure and RTMs removal, as supported by both the simulation in Section 2.2 and the observations from Test B.
To address this issue and enhance the form-preserving capability, a method for rotating the nozzle outlet of the AFJ tool is proposed in this study. Four new designs, depicted in Fig. 14(a)-(d), were developed with specific structures and sizes. These designs feature miniature semicylinder blocks and grooves on the outer cylindrical surface of the pin and the inner wall of the AFJ tool, respectively. The gap between the two semicylindrical surfaces was set to 0.2 mm. This structural arrangement enables the outlet of the flow field and the polishing pressure field to rotate along with the AFJ tool during the polishing process for side-wall optical surfaces, thereby improving the uniformity of RTMs removal. According to the theoretical analysis in Section 2, the RTMs removal at an arbitrary point in the polishing area depends on the local pressure and abrasives’ velocity. Hence, the degree of RTMs removal in one processing cycle can be evaluated by an accumulation of instantaneous polishing pressure and relative velocity. In the polishing process, the pin rotates along with the AFJ tool driven by the “keyway structure” so the velocity fields of the four new designs are identical in condition of the same spindle speed and eccentric distance. The distinction among them is mainly determined by the polishing pressure field. To compare the uniformity of RTMs removal of the four new designs (as shown in Fig. 14), discussions of the polishing pressure were conducted based on the simulation methods proposed in Section 2.2.
Fig. 14. Improved AFJ tools with (a) one groove; (b) two grooves; (c) three grooves; and (d) four grooves.
Taking the improved AFJ tool with one groove as an example, a fixed coordinate system XOZ connected with the workpiece surface and a moving coordinate system X'PZ’ which represents the orientation of the instantaneous pressure field is defined, as depicted in Fig. 15(a). It is assumed that the system XOZ and the system X'PZ’ are coincident at the initial moment. The cycle time of the AFJ tool can be discretized into several time segments. As shown in Fig. 15(b), at the moment ti (i = 1, 2, …, n, where n is the number of discrete moments), the position of an arbitrary point A(x, z) in the moving coordinate system X'PZ’ can be determined as
Fig. 15. Illustration of the motion of polishing pressure field: (a) coordinate systems at the initial time; (b) instantaneous pressure field at the moment ti.
It should be noted that p(xi’, zi’) which represents the pressure at point A(x, z) at the moment ti can be extracted by the FSI model proposed in Section 2.2.1. By calculating the accumulation of instantaneous pressure at all the points on the workpiece surface for one cycle, the pressure distribution in the polishing area can be acquired.
Figure 16 demonstrates the simulation results of Γ before and after improvement. Apparently, the polishing pressure distribution becomes symmetric and uniform in the new designs. To describe the non-uniformity of the pressure distribution, an evaluation index NUMR is defined as the optimization objective, which can be denoted as
where ${\hat{\Gamma }_j}$ is the normalized accumulated pressure at point j, while $\bar{\Gamma }$ is the average of the normalized accumulated pressure on the polished surface and m is the number of discrete points. A lower NUMR indicates a more uniform pressure distribution. The values of NUMR of the four designs are shown in Fig. 17. The results indicate that the AFJ tool with three grooves yields the optimal performance which is deemed the most suitable option for improving the uniformity of RTMs removal in the AFJ polishing process for side-wall surfaces. Utilizing this tool design, a form-preserved post-polishing process can be realized.Fig. 16. Simulation results of Γ: (a) traditional AFJ tool; (b) improved tool with one groove; (c) improved tool with two grooves; (d) improved tool with three grooves; (e) improved tool with four grooves.
3.4 Verification
A comparative experiment was conducted to demonstrate the form-preserving capability of the improved AFJ tool. A planar Al6061 aluminum mirror was vertically mounted after diamond cutting. In this test, both the traditional AFJ tool and the improved AFJ tool traveled 10 mm along straight lines, as depicted in Fig. 18. The AFJ polishing parameters are specified in Table 4. The polishing slurry comprised SiO2 abrasives with an average size of 0.4 μm in deionized water, with a concentration of 20 vol%.
Table 4. Polishing parameters for verification
The surface roughness of six points (C1, C2, C3, D1, D2, D3) was measured using a white light interferometer (Zygo Newview) with a scan size of 0.5 mm × 0.5 mm. Figure 19(a) and (c) demonstrate the non-uniform RTMs removal achieved using the traditional AFJ tool. The ripple structure is faint at point C3, while it remains evident at point C1. PSD analysis was performed to visualize the spatial frequency, revealing that the protruding peak in the PSD curve of point C3 is smaller than the others. This implies a higher RTMs removal rate at the bottom of the polishing area. This observation has profound implications for the removal distribution of RTMs using traditional AFJ tools. The non-uniform RTMs removal could be attributed to several factors, including non-uniformity in the flow dynamics of the fluid jet, differences in the applied pressure, and the motion of the pin. Moreover, this phenomenon also raises concerns about potential damage to the substrate. It can be inferred that the substrate at point C3 may be damaged with increasing polishing time, while the RTMs are not removed at point C1 or point C2. Such non-uniform RTMs removal hampers the achievement of a form-preserved post-polishing process. Of course, to address this issue, the polishing parameters or the dwell-time can be adjusted to lower the material removal rate, ensuring that only RTMs at the bottom are removed. Meanwhile, complex adaptive tool paths are necessary to guarantee uniformity across the entire polished surface. Nevertheless, these methods can lead to a decrease in efficiency and increased complexity in the form-preserving post-polishing process. Improvement can be observed in Fig. 19(b) and (c), respectively. The outlet of the flow field and the polishing pressure field rotate along with the AFJ tool during the process, overcoming the influence of gravity. It can be found that the use of the new AFJ tool results in identical RTMs removal at the three points (D1, D2, D3). The protruding peaks in the three PSD curves are similar, indicating uniform material removal within one polishing area. This suggests that the periodic marks can be eliminated without compromising the surface form by simply adjusting the dwell time in practical applications, eliminating the need for complex tool paths. These results demonstrate that the improved AFJ tool enables the achievement of a form-preserved AFJ post-polishing process for side-wall surfaces.
Fig. 19. Comparison of the uniformity of RTMs removal in AFJ polishing for side-wall surface: (a) PSD analysis of the surface polished by traditional AFJ tool; (b) PSD analysis of the surface polished by improved AFJ tool; (c) surface texture of the six measurement points.
4. Conclusions
The paper investigates the form-preserving capability of AFJ post-polishing for side-wall surfaces through theoretical and experimental approaches. The contributions of the study can be summarized as follows.
- (1) Micromachining characteristics of anisotropic diamond-cut surfaces are discussed using elastic-plastic theory. The effects of the periodic structure on active abrasives and micromachining state are analyzed theoretically, providing insights into the removal characteristics at the microscopic scale.
- (2) Theoretical and experimental results demonstrate that the von Mises stress is larger and RTMs removal is more pronounced when the motion direction of the polishing abrasive is perpendicular to the ripples. This is attributed to the anisotropy in the horizontal dimension of the rippled surface.
- (3) The dynamic analysis of AFJ polishing for side-wall surfaces is proposed. The simulations and experiments reveal that the uneven distribution of contact pressure on the workpiece, influenced by gravity, results in a crescent-shaped TIF, which is detrimental to the form-preserving polishing process.
- (4) Based on the simulation method, a new AFJ tool is designed and optimized to improve the uniformity of RTMs removal. Experimental results demonstrate the effectiveness of the new tool in achieving a more uniform material removal.
In conclusion, the study provides comprehensive insights into the material removal characteristics on rippled surfaces through theoretical analysis and simulation modeling. The uniformity of AFJ post-polishing for side-wall surfaces is analyzed and optimized, and the newly designed tool expands the application of AFJ polishing technology to various integrated optomechanical systems with special spatial distributions of optical components, such as MMSWs. The research presented in this paper holds significant research value and potential in the fields of freeform optics and advanced optical systems.
Funding
National Key Research and Development Program of China (2017YFA0701200); National Natural Science Foundation of China (52275460); National Natural Science Foundation of China (62373274).
Acknowledgments
The authors would like to express their sincere thanks to Hongshun Zhang for the preparation of the experiments.
Disclosures
The authors declare no conflicts of interest.
Data availability
Data underlying the results presented in this paper are not publicly available at this time but may be obtained from the authors upon reasonable request.
References
1. X. L. Li, M. Xu, X. D. Ren, et al., “An optical design of off-axis four-mirror-anastigmatic telescope for remote sensing,” J. Opt. Soc. Korea 16(3), 243–246 (2012). [CrossRef]
2. E. Muslimov, E. Hugot, W. Jahn, et al., “Combining freeform optics and curved detectors for wide field imaging: a polynomial approach over squared aperture,” Opt. Express 25(13), 14598–14610 (2017). [CrossRef]
3. Y. Xiong, T. Luo, Y. Dai, et al., “In situ measurement and error compensation of monolithic multisurface optics,” Opt. Commun. 484, 126665 (2021). [CrossRef]
4. Z. Li, L. Liu, C. Li, et al., “Complete topographic measurement of the monolithic multi-surface workpiece on a cylindrical cavity,” Opt. Laser Technol. 161, 109222 (2023). [CrossRef]
5. T. Yang, G. F. Jin, and J. Zhu, “Automated design of freeform imaging systems,” Light: Sci. Appl. 6(10), e17081 (2017). [CrossRef]
6. Z. Li, X. Liu, F. Fang, et al., “Integrated manufacture of a freeform off-axis multi-reflective imaging system without optical alignment,” Opt. Express 26(6), 7625–7637 (2018). [CrossRef]
7. Z. Zhu, S. To, and S. Zhang, “Active control of residual tool marks for freeform optics functionalization by novel biaxial servo assisted fly cutting,” Appl. Opt. 54(25), 7656–7662 (2015). [CrossRef]
8. C. Du, Y. Dai, C. Guan, et al., “High efficiency removal of single point diamond turning marks on aluminum surface by combination of ion beam sputtering and smoothing polishing,” Opt. Express 29(3), 3738 (2021). [CrossRef]
9. Y. Huang, B. Fan, Y. Wan, et al., “Improving the performance of single point diamond turning surface with ion beam figuring,” Optik 172, 540–544 (2018). [CrossRef]
10. Y. Bai, Z. Zhang, D. Xue, et al., “Ultra-precision fabrication of a nickel-phosphorus layer on aluminum substrate by SPDT and MRF,” Appl. Opt. 57(34), F62–F67 (2018). [CrossRef]
11. M. Jeona, S. Hyuna, B. Jeonga, et al., “Removal of diamond turning marks with magneto-rheological finishing,” in SPIE Optical Engineering Applications, (SPIE, 2017), 32.
12. X. Wang, H. Gao, and J. Yuan, “Experimental investigation and analytical modelling of the tool influence function of the ultra-precision numerical control polishing method based on the water dissolution principle for KDP crystals,” Precis. Eng. 65, 185–196 (2020). [CrossRef]
13. X. Wang, H. Gao, Y. Chen, et al., “A water dissolution method for removing micro-waviness caused by SPDT process on KDP crystals,” Int. J. Adv. Manuf. Technol. 85(5-8), 1347–1360 (2016). [CrossRef]
14. Z. Z. Li, J. M. Wang, X. Q. Peng, et al., “Removal of single point diamond-turning marks by abrasive jet polishing,” Appl. Opt. 50(16), 2458–2463 (2011). [CrossRef]
15. A. Beaucamp and Y. Namba, “Super-smooth finishing of diamond turned hard X-ray molding dies by combined fluid jet and bonnet polishing,” CIRP Annals - Manufacturing Technology 62(1), 315–318 (2013). [CrossRef]
16. S. Hatefi and K. Abou-El-Hossein, “Review of single-point diamond turning process in terms of ultra-precision optical surface roughness,” The International Journal of Advanced Manufacturing Technology 106(5-6), 2167–2187 (2020). [CrossRef]
17. S. Hatefi and K. Abou-El-Hossein, “Review of non-conventional technologies for assisting ultra-precision single-point diamond turning,” The International Journal of Advanced Manufacturing Technology 111(9-10), 2667–2685 (2020). [CrossRef]
18. Y. Zhu, W. Lu, D. Zuo, et al., “Development of abrasive jet polishing by using amino thermosetting plastic abrasive for aluminum alloy,” J. Manuf. Process. 43, 218–228 (2019). [CrossRef]
19. S. Zeng and L. Blunt, “Experimental investigation and analytical modelling of the effects of process parameters on material removal rate for bonnet polishing of cobalt chrome alloy,” Precis. Eng. 38(2), 348–355 (2014). [CrossRef]
20. X. Yang, Z. Wang, C. Wang, et al., “Analysis of effects of precession mechanism error on polishing spot for bonnet polishing,” Proc. Inst. Mech. Eng., Part B 232(2), 350–357 (2018). [CrossRef]
21. V. S. Negi, H. Garg, R. R. Shravan Kumar, et al., “Smoothing effect analysis for active fluid jet polishing,” in Optical Fabrication and Testing, (2021).
22. C. Bi, H. Zhang, and Y. Li, “Research on active fluid jet polishing process with revolution and rotation pin,” in 10th International Symposium on Advanced Optical Manufacturing and Testing Technologies, (Chengdu, China, 2021). [CrossRef]
23. H. Zhang, X. Zhang, Z. Li, et al., “Removing single-point diamond turning marks using form-preserving active fluid jet polishing,” Precis. Eng. 76, 237–254 (2022). [CrossRef]
24. J. Luo and D. A. Dornfeld, “Material removal mechanism in chemical mechanical polishing: theory and modeling,” IEEE Trans. Semicond. Manufact. 14(2), 112–133 (2001). [CrossRef]
25. W. Zhu and A. Beaucamp, “Generic three-dimensional model of freeform surface polishing with non-Newtonian fluids,” Int. J. Mach. Tools Manuf. 172, 103837 (2022). [CrossRef]
26. C. L. He, W. J. Zong, C. X. Xue, et al., “An accurate 3D surface topography model for single-point diamond turning,” Int. J. Mach. Tools Manuf. 134, 42–68 (2018). [CrossRef]
