Generalized numerical pressure distribution model for smoothing polishing of irregular midspatial frequency errors

Abstract

The smoothing effect of the rigid lap plays an important role in controlling midspatial frequency errors (MSFRs). At present, the pressure distribution between the polishing pad and processed surface is mainly calculated by Mehta's bridging model. However, this classic model does not work for the irregular MSFR. In this paper, a generalized numerical model based on the finite element method (FEM) is proposed to solve this problem. First, the smoothing polishing (SP) process is transformed to a 3D elastic structural FEM model, and the governing matrix equation is gained. By virtue of the boundary conditions applied to the governing matrix equation, the nodal displacement vector and nodal force vector of the pad can be attained, from which the pressure distribution can be extracted. In the partial contact condition, the iterative method is needed. The algorithmic routine is shown, and the applicability of the generalized numerical model is discussed. The detailed simulation is given when the lap is in contact with the irregular surface of different morphologies. A well-designed SP experiment is conducted in our lab to verify the model. A small difference between the experimental data and simulated result shows that the model is totally practicable. The generalized numerical model is applied on a Φ500 mm parabolic surface. The calculated result and measured data after the SP process have been compared, which indicates that the model established in this paper is an effective method to predict the SP process.

Conformal smoothing of mid-spatial frequency surface error for nano-accuracy Continuous Phase Plates (CPP)

“…In this model, the contact between polishing pad and component is considered to be elastic and the component is assumed to be rigid. Effects friction and others are ignored, in order to simplify the model 21,22 .…”

Improving smoothing efficiency of rigid conformal polishing tool using time-dependent smoothing evaluation model

“…In order to understand the source of the high edge pressure, we consider an example using the static FEA to analyze the nominal contact pressure distribution between the tool and workpiece. The static elastic modulus of Silly-Putty is assumed to be 2 MPa at 7 Hz, based on the dynamic mechanical properties of this material [15]. For a 68-N vertical force applied to the drive pin hole, symmetrical FEA models are established for the old and new RC laps (100 mm), using the ABAQUS software.…”

“…This new model discloses the exponential decay of the MSF errors with time during smoothing. Finally, Nie et al constructed a generalized numerical pressure distribution model to solve the superposition of innumerable sinusoidal errors with different frequencies and amplitudes through finite element analysis (FEA) [15].…”

Control of mid-spatial frequency errors considering the pad groove feature in smoothing polishing process

“…The following simplified condition is used in this paper during the simulation: the classic Preston equation is the basic law of the material removal mechanism [29]; the polishing pad and mirror surface keep full contact with each other at all times [16]; the viscoelasticity of the pad, the hydrodynamic lubrication of the slurry, and the friction are not considered [30]; other factors that affect CPD are not considered; and a 95% effective aperture is analyzed to filter the edge effect by virtue of the tool overhang.…”

“…A rigid or semirigid polishing lap [13] is commonly used to generate a pressure difference between the peak and valley area of the surface error. Available models [14][15][16] have been developed to calculate the pressure distribution, which makes the surface error after smoothing predictable. The SP process is well used and studied in depth at the University of Rochester [17], Zeeko Ltd. [18], Optimax Systems, Inc. [19] etc.…”