Preston Coefficient Research Articles

Surface generating mechanism in surface shape error control for thin copper plate with large-diameter based on chemical mechanical lapping

As metal plane flyer, pure copper thin plate is required with extremely low surface shape error. To achieve this goal, some researchers make a significant attempt to develop a deterministic full-aperture polishing/lapping process. However, the detail relationship of surface shape error and vital machining parameter such as machining time which benefits machining efficiency promotion is not given. Besides, the error rate of surface shape error prediction is high. To solve this problem, the surface shape prediction model considering the influence of pressure and relative velocity distribution on material removal amount is established for thin copper plate. Through the product of pressure distribution, relative velocity distribution, Preston coefficient k and machining time T, material removal distribution is obtained. According to initial surface shape characteristic, through targeted adjustment of eccentricity, lapping pad rotation speed, workpiece rotation speed to control pressure and relative velocity distribution, suitable material removal distribution is formed to smooth surface radial profile, realizing deterministic control of surface shape error. By above method, the flatness of pure copper thin plate (Φ200 mm × 2.2 mm) decreases from PV 54.8 μm to PV 1.9 μm with mean error rate of surface shape error prediction <10 %, realizing deterministic control of surface shape error.

A robotic polishing parameter optimization method considering time-varying wear

In the automatic polishing process, the wear of polishing tools and the change of polishing parameters will affect the Preston coefficient, which makes it difficult to establish an accurate material removal model to achieve stable and excellent polishing quality. In this paper, a robotic polishing parameter optimization method considering time-varying wear is proposed to address these issues. First, combining the rich information in the theoretical modeling method with the data-driven regression method, a material removal regression model incorporating prior knowledge is proposed, which greatly reduces the large amount of experimental data required by the original regression model. The proposed model is able to track the wear variation of the sandpaper as well as the effect of polishing parameters. Then, based on the proposed prediction model, the genetic algorithm is used to optimize the polishing parameters in order to achieve better machining quality and less energy consumption. Finally, the experimental verification is carried out on the hybrid robot polishing test bench. The results show that the proposed material removal regression model incorporating prior knowledge has higher prediction accuracy and less required experimental data than existing models. The proposed robot polishing parameter optimization method can effectively compensate for tool wear and ensure the consistency of material removal during polishing while reducing energy consumption.

Modeling and prediction of generated local surface profile for ultrasonic vibration-assisted polishing of optical glass BK7

• Preston coefficient is affected by ultrasonic amplitude. • Contact pressure is affected by ultrasonic amplitude. • Large ultrasonic amplitude helps to improve the polishing ability. • Local surface profile can be well predicted by the proposed calculation model. • Prediction of surface profile is a basis for free-form surface polishing of UVAP. With the rapid progress of science and technology, many applications of hard and brittle materials require advanced and suitable machining-techniques. One technique in particular, ultrasonic vibration-assisted polishing (UVAP), has been studied intensively by researchers worldwide. These studies indicate that UVAP has the capability to improve the surface quality as well as the machining efficiency. However, few studies focus on the deterministic material-removal of UVAP. The difference between generated and theoretical surface profiles determines the surface accuracy. Therefore, this paper focuses on predicting the generated local surface profile and providing a theoretical basis to reduce this error by controlling the polishing parameters. In addition to the axial ultrasonic vibration of polishing tool, ultrasonic atomization was adopted to provide uniformly distributed polishing slurry. To ensure sufficient surface-accuracy, it is necessary to predict the generated surface profile for a fixed spot as a basis research. This means, to enable accurate predictions the following improvements are realized: (i) A novel model for the elastic spherical contact-deformation of the polishing tool is used to calculate both the polishing force and contact radius. It takes into account the nonlinear elasticity of the polishing tool and the lateral extension of the contact area, which makes it more consistent with the actual deformation. (ii) A novel model for the material-removal distribution function for UVAP is proposed, based on the Preston equation. It considers the periodic changes of polishing force and contact radius caused by ultrasonic vibration. (iii) A series of fixed-spot polishing experiments on BK7 glass are carried out to verify the proposed models. The results show that the Preston coefficient is affected by axial ultrasonic amplitude, and large ultrasonic amplitude improves the polishing ability. In addition, the generated local surface profile, the maximum contact radius, as well as the material-removal depth and material-removal rate (MRR) can be predicted well. The new models not only provide a possibility to realize deterministic material removal but also enables in-depth-understanding of UVAP. It also represents a basic theoretical foundation for future, flat or free-form surface-polishing.

Design of FG/CS-LPP and material removal uniformity experiment on ZrO2 ceramic

A novel processing technology based on the functionally graded and composite structured lapping and polishing plate (FG/CS-LPP) is proposed for effectively improving the material removal uniformity. The FG/CS-LPP has the characteristics of required quasi-continuous distribution of Young's modulus in the radial direction and composite structure in the longitudinal direction. Moreover, the certain variation of Young's modulus does not tend to influence the material removal uniformity and two-step processing technique makes the shrinkage deformation of the composites reduce to 0.03 mm. Based on the Preston equation, the FG/CS-LPP can realize smooth inverse proportional stress distribution and make processing parameters decoupling of K (Preston coefficient) and P (contact stress). Through numerical simulation analysis and experimental verification, the designed FG/CS-LPP successfully achieves material removal uniformity on ZrO2 ceramic.

Nanoplastic removal function and the mechanical nature of colloidal silica slurry polishing

AbstractThe nanomechanical deformations on a broad range of optical material surfaces (single crystals of Al2O3 [sapphire], SiC, Y3Al5O12 [YAG], CaF2, and LiB3O5 [LBO]; a SiO2–Al2O3–P2O5–Li2O glass‐ceramics [Zerodur]; and glasses of SiO2:TiO2 [ULE], SiO2 [fused silica], and P2O5–Al2O3–K2O–BaO [Phosphate]) near the elastic‐plastic load boundary have been measured by nanoindentation and nanoscratching to mimic the nanoplastic removal caused by a single slurry particle during polishing. Nanoindenation in air was performed to determine the workpiece hardness at various loads using a commercial nanoindenter with a Berkovich tip. Similarly, an atomic force microscope (AFM) with a stiff diamond coated tip (150 nm radius) was used to produce nanoplastic scratches in air and aqueous environments over a range of applied loads (~20‐170 μN). The resulting nanoplastic deformation of the nanoscratches were used to calculate the removal function (i.e., depth per pass) which ranged from 0.18 to 3.6 nm per pass for these materials. A linear correlation between the nanoplastic removal function and the polishing rate (using a fixed polishing process with colloidal silica slurry on a polyurethane pad) of these materials was observed implying that: (a) the polishing mechanism using colloidal silica slurry can be dominated by mechanical rather than chemical interactions; and (b) the nanoplastic removal function, as opposed to interface particle interactions, is the controlling factor for the polishing material removal rate. Furthermore, this correlation is consistent with the Ensemble Hertzian Multi‐Gap (EHMG) microscopic material removal rate model described previously. The nanoplastic removal depth was also found to correlate to the measured nanoindentation hardness (H1) of the optical material, scaling as H1−3.5. Two‐dimensional (2D) finite element analysis simulations of nanoindentation showed a similar nonlinear dependence of plastic deformation with the workpiece material hardness. The findings of this study are used to determine an effective Preston coefficient for the material removal rate expression and enhance the predictive nature of the nanoplastic polishing rate for various materials utilizing their material properties.

Effects of the Profile of Workpiece Surface on Material Removal Rate Distribution in Polishing Process

Accurate prediction of the material removal rate (MRR) distribution is very important for the control of the polishing process. However, the widely used prediction method of MRR based on the Preston equation is still incapable of predicting the roll-off phenomenon in polishing process. One of the reasons is that many of the researchers’ neglected the effect of the surface profile of the workpiece on the MRR. In this paper, the evolutionary process of MRR distribution with the change of surface profile using two different polishing pad is studied, it is found that MRR varies gradually with the change of surface profile and tends to be uniform finally. Based on the analysis of contact pressure considering the actual surface profile of workpiece and modified Preston equation, the distribution of MRR is analyzed. It is found that the Preston coefficient distribution on workpiece surface is stable when the surface profile variation is small and shows obvious differences from the center to the edge of the workpiece. Through the comparison it is found that correlation between the regularities of Preston coefficient distribution and the type of polishing pad is significant. The research results in this paper will play an important guiding role in the quantitative prediction method research of polishing process.

Effects of Polishing Parameters on Evolution of Different Wafer Patterns During Cu CMP

Chemical mechanical polishing (CMP) has been widely used in the IC industry. To specify proper polishing parameters for Cu CMP is a very important and difficult task. In this paper, by using the linear system method modeling the relationship between the contact pressure and topography of wafer, the evolutions of the wafer patterns under different polishing parameters are simulated and compared with experimental data. The wafer patterns contain square-wave features with different pitches and pattern densities. The effects and tradeoffs between different polishing parameters on the evolution of different wafer patterns are studied. It is found that high selectivity ratio can achieve small dishing, while small selectivity ratio can help to achieve small erosion and small differences among different patterns. Small down force and large Young’s modulus of pad can achieve a good planar surface. Large Preston coefficient will have small erosion during one-material polishing, while small Preston coefficient will have small erosion in two-material polishing. Time point of changing polishing parameters is important to achieve an efficient polishing process and a planar surface.

Discrete element simulation of micromechanical removal processes during wire sawing

The material removal rate in the wire sawing technology depends on several features of the used abrasives and the complex process of particle movement and interaction inside the kerf. To investigate these micro-mechanical aspects of the wire sawing process, a numerical model is developed in the present paper. The model is based on the discrete element method adjusted to use sharp edged polygonal particles. The crucial procedure of material removal is implemented through concepts of the fracture mechanics of sharp edged indenters. The model allows to study the influence of essential parameters like wire speed, lapping pressure, particle shape, particle size distribution a.o. on the material removal process. A parametric study towards the influence of wire speed and lapping pressure on the amount of material removal is also presented. The parametric numerical studies carried out confirm the phenomenological law of Preston for the removal rate and enable correlations between the Preston coefficient and micro-mechanical process parameters.

Research on Material Removal Modeling and Processing Parameters of Magnetorheological Finishing

Magnetorheological Finishing(MRF) is an advanced optical manufacturing technology, It is a kind of deterministic process. It conquers the defections such as low-efficiency and low-grade surface quality of the traditional method. Deduced from the hydrodynamic lubrication theory of the Bingham plastic flow, the material removal model of MRF is established. The reliability of the model is verified by the experiment. finally, we get the mean Preston coefficient by the theoretical curve and the actual measured curves, the value will be applied to optical components of the computer-controlled MRF operation. Through the magnetorheological finishing experiments , the results that compared with the experimental results in good agreement prove that our proposed model is reasonable.

The Effects of Hardness Variation on a CMP Model of Copper thin Films

AbstractWith the rapid change of materials systems and decreased feature size, thin film microstructure and mechanical properties have become critical parameters for microelectronics reliability. An example of a major driver of this new technology is the data storage community who is pushing for 1 Terabit/square inch on its magnetic disk hard drives. This requires inherent knowledge of the mechanical properties of materials and in depth understanding of the tribological phenomena involved in the manufacturing process. Chemical mechanical polishing (CMP) is a semi-conductor manufacturing process used to remove or planarize ultra-thin metallic, dielectric, or barrier films (copper) on silicon wafers. The material removal rate (MRR), which ultimately effects the surface topography, corresponding to CMP is given by the standard Preston Equation, which contains the load applied, the velocity of the pad, the Preston coefficient which includes chemical dependencies, and the hardness of the material. Typically the hardness, a bulk material constant, is taken as a constant throughout the wafer and thereby included in the Preston coefficient. Through metallurgy studies, on the micro and nano scale, it has been proven that the hardness is dependent upon grain size and orientation. This research served to first relate the crystallographic orientation to a specific hardness value and secondly use the hardness variation in the previously developed particle augmented mixed-lubrication (PAML) model to simulate the surface topography and MRR during CMP. Recent test and results show that currently there is no empirical formula to relate the crystallographic orientation and thereby a critically resolved shear stress (CRSS) to a specific hardness value. The second part of this investigation utilized the variation in hardness values from the initial study and incorporated these results into the PAML numerical model that incorporates all the physics of chemical mechanical polishing (CMP). Incorporation of the variation of hardness resulted in a surface topography with a difference in roughness (Ra) from the bulk constant hardness value of 60 nm. The material removal rate (MRR) of the process differs by 2.17 μm3/s.

A surface roughness predictive model in deterministic polishing of ground glass moulds

The introduction of deterministic NC grinding and polishing operations, in the manufacturing of free-form glass components for precision optics, requires the characterization of surface topography evolution as a function of process parameters. In this work, a model based on Reye's wear hypothesis is proposed for the assessment of surface roughness prediction as a function of operating parameters, in the deterministic polishing process of glass moulds. According to Reye's hypothesis, the removed material per unit area is proportional to the work due to the friction force: the removed material per unit area can be computed by adequately integrating the areal material ratio function (Abbott–Firestone curve) of the surface and can be associated with the amplitude roughness parameter; the work due to the friction force per unit area is proportional to the integral of the product of pressure and velocity in the time interval and can be derived from the process parameters by means of the Hertz theory. The model assessment was performed on ground glass flat samples polished with different operating parameters, mapping the surface roughness using an atomic force microscope (AFM). The developed model shows a satisfactory estimate of surface roughness evolution during the polishing process and confirms the experimental results found in the literature for the Preston coefficient.

Investigation of the material removal model for bonnet tool polishing with precession

Bonnet tool polishing is a novel aspherical polishing method. This paper describes a method to obtain the local removal rate for the polishing process by using bulbous flexible membrane covered with a polishing pad and pressurised by an internal fluid. During the polishing process the precession process, in which the bonnet tool cannot only spines itself but also precesses along the local normal on the specimen surface, was applied. The local removal rate model was established according to the Preston equation. The influence of the precession process on the material removal rate was analysed and also the polishing pressure distribution was obtained according to the experiment data. It is confirmed by the experiments that the dwelling time has a linear relation with the local removal depth. Preston coefficient can be calculated from the experimental data. Finally, the expression of the local removal rate in bonnet tool polishing was acquired experimentally.

Study of Local Material Removal Model of Bonnet Tool Polishing

Bonnet tool polishing is a novel aspherical polishing method. This paper describes a method to obtain the local removal rate for the polishing process using bulbous flexible membrane covered with a polishing pad and pressurized by an internal fluid. According to the principle of bonnet polishing and Preston equation, the local removal rate model was established. It is confirmed by the experiments that the local removal depth has a linear relation with the dwell time. Preston coefficient can be calculated from the experimental data. Finally the expression of the local removal rate in bonnet tool polishing is acquired semi-empirically.

Measurement of the Preston coefficient of resin and bronze bond tools for deterministic microgrinding of glass

Deterministic microgrinding technology applies a bound diamond abrasive tool positioned by a Computer Numerically Controlled (CNC) machine to generate precision optical components. The ease of work material removal during the grinding process is often characterized by the specific energy or the Preston coefficient. For a given part and process, these two parameters also indicate the tool/abrasive performance. The Preston coefficient of a resin bond tool with 2–4 μm diamond abrasives under different process parameter combinations has been measured with BK7 as the test glass. The Preston coefficient of a similar bronze bond tool was also measured for comparison. Experimental measurements show the resin tool behaves qualitatively differently than the bronze tool in a multiple pass grinding process. The measured Preston coefficient of the resin tool was two to three times smaller than that of the bronze tool and decreased rapidly as pass number increased. A plot of the Preston coefficient versus resin tool bond wear suggests that excessive tool wear reduces the tool's cutting efficiency, resulting in a rapid decrease in the Preston coefficient.

Modeling of Pattern Density Dependent Pressure Non-Uniformity at a Die Scale for ILD Chemical Mechanical Planarization

AbstractLocal material removal rate is inversely proportional to the local pattern density in ILD CMP. With the assumption that the local velocity and Preston coefficient are constant across a chip, local MRR non-uniformity is mainly attributed to the local pressure non-uniformity. Pressure distributions on two different test patterns consisting of five different pattern density sections were obtained with a finite element model. These pressure distributions were compared with output from a semi-empirical pattern dependent oxide CMP model (MIT model) with three different weighting functions. Result showed that pressure distribution could be well approximated with the pattern density dependent oxide CMP model. This FEM model was further taken to evaluate the effects of thickness and material properties of each layer on the degree of pattern dependant pressure non-uniformity at a die scale for a typical polishing pad made up of a hard and a soft layer. The analysis shows that the degree of pressure nonuniformity at a die scale increases with the combination of a stiff hard layer and a thick soft layer, while it decreases with the combination of a stiff soft layer and a thick hard layer.

Analysis of chatter in contour grinding of optical materials

Chatter that limits ground surface finish has been observed in the deterministic microgrinding of brittle optical materials. In this article, the classical single degree of freedom model for chatter, accounting for both work and tool regenerative effects, is adapted for contour grinding optical surfaces. A linearized expression for the cutting stiffness is developed for the contour grinding geometry based on Preston’s law. Techniques developed to measure the machine frequency response function (FRF) and the Preston coefficient, needed as inputs to the simulations, are described. Numerical simulations based on this model are used to predict the grinding system behavior and to investigate process parameters affecting chatter stability. The stability limits observed during grinding experiments on optical glasses are in good agreement with the simulation results.

Local material removal mechanism considering curvature effect in the polishing process of the small aspherical lens die

This paper describes a method to obtain the local removal rate for the polishing process of the small aspherical lens die using a spherical tool. When the small spherical polishing tool traverses an aspherical surface, non-uniform polishing area and local removal rate are locally generated around the contacting points according to the curvature change of an aspherical surface. Therefore, an aspherical surface is divided into multiple patches and the local removal rate on the patches is calculated semi-empirically from the Preston equation. Formation of the elliptical polishing area is confirmed experimentally and the Preston coefficient is calculated from the central removal depth and dwell time that has a linear relation with the local removal depth. Finally, using the equivalent radius of two contact bodies, the curvature effect of an aspherical surface on the polishing area is explained.

Micromechanics of diamond composite tools during grinding of glass

Precision optical components are now manufactured by CNC (computer numerically controlled) grinding technology using diamond composite tools. Tooling performance, and in particular consistency of performance, is an important issue in this automation. A key measure of performance is the power/forces required for material removal, often summarized in terms of the specific grinding energy or ‘Preston's coefficient’. In this study measurements of grinding energy were used, along with optical profilometry measurements of tool surface features, to quantitatively characterize the performance and development of a bronze-bond composite diamond tool during grinding of three optical glasses with distinctly different grinding behavior. Evolution of grinding performance is strongly related to both the process conditions and the glass type. These effects can be understood in terms of changes in the relative rates of bond and abrasive wear and the consequent evolution of the tool surface. In particular in certain cases the evolution of tool surfaces can be adjusted toward a state of dynamic equilibrium (‘selfsharpening’) by adjusting process conditions.

Grinding of single crystal sapphire: workpiece roughness correlations

Experiments were performed on single crystal sapphire with a selection of bound abrasive cup tools to produce fine ground surfaces with rms roughness on the order of 1 μm. Both workpiece roughness and the ease of material removal (as quantified by Preston's coefficient or the specific grinding energy) were found to decrease with decreasing chip thickness. However, great variability was observed even for a fixed chip thickness as a result of differences in tool performance. A strong correlation was also found between Preston's coefficient and the workpiece roughness. Data for all tool bond types (resin, metal, and vitrified), abrasive sizes (2–80 μm diamond), surface conditions (as-dressed and glazed), and tool geometries fell on the same curve. This behavior has important practical effects during infeed controlled grinding. Only above a certain ‘critical roughness’, which depended on the workpiece size, was grinding able to remove the programmed infeed depth.

Loose abrasive lapping hardness of optical glasses and its interpretation

We present an interpretation of the lapping hardness of commercially available optical glasses in terms of a micromechanics model of material removal by subsurface lateral cracking. We analyze data on loose abrasive microgrinding, or lapping at fixed nominal pressure, for many commercially available optical glasses in terms of this model. The Schott and Hoya data on lapping hardness are correlated with the results of such a model. Lapping hardness is a function of the mechanical properties of the glass: The volume removal rate increases approximately linearly with Young's modulus, and it decreases with fracture toughness and (approximately) the square of the Knoop hardness. The microroughness induced by lapping depends on the plastic and elastic properties of the glass, depending on abrasive shape. This is in contrast to deterministic microgrinding (fixed infeed rate), where it is determined from the plastic and fracture properties of the glass. We also show that Preston's coefficient has a similar dependence as lapping hardness on glass mechanical properties, as well as a linear dependence on abrasive size for the case of brittle material removal. These observations lead to the definition of an augmented Preston coefficient during brittle material removal. The augmented Preston coefficient does not depend on glass material properties or abrasive size and thus describes the interaction of the glass surface with the coolant-immersed abrasive grain and the backing plate. Numerical simulations of indentation are used to locate the origin of subsurface cracks and the distribution of residual surface and subsurface stresses, known to cause surface (radial) and subsurface (median, lateral) cracks.