Thin-Lin Horng

Comparisons of contact pressures of crowned rollers

Abstract The present work determines the contact pressure and stress concentration between the crowned roller and the raceway by using three-dimensional finite element analysis. A number of crowned profiles with various dimensions were examined. Fine meshes and node-to-Hermit-surface contact elements were used along the contact surface in order to obtain accurate analysis results. A table was generated to show the stress concentration near the roller edge for various crowned profiles and dimensions. This table indicates that the exponential profile is the optimal crowned profile to eliminate stress concentration.

Behaviors of a single crack in multiple bolted joints

This paper examines the pin load ratios and the stress intensity factors (SIFs) of a single crack in the multiple bolted joints by using finite element analyses. Cubic-spline contact elements and rigid links were used to model the contact surface between the bolt and the rigid pin. The least-squares method was used to determine the SIFs. The finite element results indicate that the cracked hole can still sustain the major part of the original loading at the uncracked condition. The first hole sustains the largest pin load and mode-I SIF, which are reduced little for crack propagation. This critical condition cannot be reduced by the arrangement of more pins in the plate. In this paper, two simple formulae were also investigated to fit the load ratios and SIFs of the multiple bolted-joints problems.

A Deformation Formula for Circular Crowned Roller Compressed Between Two Flat Plates

The main purpose of this paper is to develop a deformation equation for the circular crowned roller compressed between two plates. First, the roller is divided into three parts, two crowned parts and one cylindrical part. The superposition method is then introduced to obtain the roller stiffness. The stiffness contribution of the crowned parts is calculated by the classical Hertzian contact solution and the stiffness contribution of the noncrowned part is obtained by the Hoeprichs formula. Comparisons with various finite element results indicate that the deformation equation derived in this paper can be a good deformation formula for the circular crowned roller.

Stiffness of an arbitrarily crowned roller compressed between two plates

Abstract This paper derives a stiffness equation for the arbitrarily crowned roller compressed between two plates. The roller is first divided into three parts: two crowned parts and one cylindrical part. The superposition method is introduced to obtain the roller stiffness. Three-dimensional finite element analyses were used to validate the accuracy of the stiffness equation, in which rollers with circular, quadratic, cubic, fourth-order power and exponential profiles were analysed. Comparisons with finite element results indicate that the accuracy of the stiffness equation derived in this paper is acceptable.

An Analysis of the Pad Deformation for Improved Planarization

For manufacturing of Integrated Circuits (IC), Chemical Mechani cal Polishing (CPM) is the most popular method to reach a global flatness in wafer fabrica tion. One of the most important factors to be concerned in CMP is the polishing pad. The polishing pad needs to be dressed to maintain the quality and the throughput of production. This is due to the wear of polishing pad and the influence of impurities. Particularly important targets in the pa d dressing are to increase the material removal rate (MRR) and a low non-uniformity (N.u.). A higher materia l removal rate (MRR) is achieved by higher stresses acted on to the pad. Meanwhile, stiffness properties of pad are changeable because of depth elimination and deterioration in the non-uniformity (N.u.) of pad surface. Therefore, in order to conduct an improved planarization process with higher MRR and l ower N.u., an investigation of pad deformation is necessary. The goal of this study is to develop pad deformation equations for pad dressing. Firstly, the uniform circular distribution pr essure is used to simulate applied loading on polishing pad done by dresser during dressing process. Then, t he three-dimensional pad deformation depth and stiffness of polishing pad are obtained by using Hertizian contact theorem and principle of elasticity. Finally, the superposit ion method is introduced to calculate the deformation resulted from total dressing force. T h theoretical results reveal that the deformation in the center of dresser is significant. Similar def ormed-shapes are obtained for different pad depth under the same loading. In conclusion, the deformed magnitude is str ongly correlated to the indices such as MRR and Nu. Introduction In order to calculate MRR and to propose an improved polishing process whic h the quality of N.u. index can be well preserved under higher dressing force, the relative approach of pad deformation analyses is of particular importance. One of the principal reasons i that owing to the deformation equation of polishing pad, an improved planarization process with higher MRR and lower N.u. can be reached. Preston [1] demonstrated an empirical method to estimate glass M RR by using the equation related to the pressure and relative velocity. A number of researches [2,3,4,5] w ere conducted to modify the Preston’s equation. In order to calculating MRR accuratly, they found s ome other parameters also must be considered. Those parameters consist of abrasive particle s ize, contact pressure, hardness of surface, the fraction of displaced material, fluid dynamic behavior of slurry, surface roughness, applied shear stress, polish pad shape, etc. However, pad stiffness and pa d deformation seem no complete discussion in those study. In other word, the deduction of pad deformat ion equations during polishing appears to be absent from the literature. In this study, a simple method is proposed to calculate pad deformation. F irst, the uniform circular distribution pressure is used to simulate applied loading on polishing pad done by single dresser during dressing process. Then, the three-dimensional pad deformation equation is obtained by using Hertizian contact theorem and principle of elasticity [6,7,8]. Finall y, The superposition method is introduced to calculate the deformation resulted from total dressing force. The theoretical results reveal that deformation shapes under the effect of dressing force a re obviously, and the deformed Key Engineering Materials Online: 2003-04-15 ISSN: 1662-9795, Vols. 238-239, pp 241-246 doi:10.4028/www.scientific.net/KEM.238-239.241

Vibration Responses of Atomic Force Microscope Cantilevers

In this investigation, the solution of the vibration response of an atomic force microscope cantilever is obtained by using the Timoshenko beam theory and the modal superposition method. In dynamic mode atomic force microscopy (AFM), information about the sample surface is obtained by monitoring the vibration parameters (e.g., amplitude or phase) of an oscillating cantilever which interacts with the sample surface. The atomic force microscope (AFM) cantilever was developed for producing high-resolution images of surface structures of both conductive and insulating samples in both air and liquid environments (Takaharu et al., 2003 ; Kageshima et al., 2002 ; Kobayashi et al., 2002 ; Yaxin & Bharat, 2007). In addition, the AFM cantilever can be applied to nanolithography in micro/nano electromechanical systems (MEMS/NEMS) (Fang & Chang, 2003) and as a nanoindentation tester for evaluating mechanical properties (Miyahara, et al., 1999). Therefore, it is essential to preciously calculate the vibration response of AFM cantilever during the sampling process. In the last few years, there has been growing interest in the dynamic responses of the AFM cantilever. Horng (Horng, 2009) employed the modal superposition method to analyze the vibration responses of AFM cantilevers in tapping mode (TM) operated in a liquid and in air. Lin (Lin, 2005) derived the exact frequency shift of an AFM non-uniform probe with an elastically restrained root, subjected to van der Waals force, and proposed the analytical method to determine the frequency shift of an AFM V-shaped probe scanning the relative inclined surface in noncontact mode (Lin, et al., 2006). Girard et al. (Girard, et al., 2006) studied dynamic atomic force microscopy operation based on high flexure modes vibration of the cantilever. Ilic et al. (Ilic, et al., 2007) explored the dynamic AFM cantilever interaction with high frequency nanomechanical systems and determined the vibration amplitude of the NEMS cantilever at resonance. Chang et al. (Chang & Chu, 2003) found an analytical solution of flexural vibration responses on tapped AFM cantilevers, and obtained the resonance frequency at arbitrary dimensions and tip radii. Wu et al. (Wu, et al., 2004) demonstrated a closed-form expression for the sensitivity of vibration modes using the relationship between the resonant frequency and contact stiffness of the cantilever and the sample. Horng (Horng, 2009) developed an analytical solution to deal with the flexural vibration problem of AFM cantilever during a nanomachining process by using the modal superposition method.