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1. On the Friction Isolator for Precision Motion Control and its Dynamics

   https://doi.org/10.1115/DETC2019-98354  

   Dong, Xin; Okwudire, Chinedum; Wang, Jiamin; Barry, Oumar (August 2019, ASME 2019 International Design Engineering Technical Conferences and Computers and Information in Engineering Conference)

   Abstract Motion stages are widely used for precision positioning in manufacturing and metrology applications. However, they suffer from nonlinear pre-motion (i.e., “static”) friction which adversely affects their precision and motion speed. Existing friction compensation methods are not robust enough to handle the highly nonlinear and variable dynamic behavior of pre-motion friction. Therefore, the first two authors have proposed the concept of a friction isolator as a simple and robust solution to mitigate the undesirable effects of pre-motion friction in precision motion stages. They experimentally demonstrated that a motion stage with friction isolator can achieve significantly improved precision, speed and robustness to variations in pre-motion friction. However, a theoretical study was not carried out to fundamentally understand the dynamic phenomena associated with using a friction isolator on a motion stage. This introductory paper investigates the dynamics of a PD-controlled motion stage with friction isolator. The influence of the friction isolator on the response and stability of the system is examined through theoretical and numerical analysis. It is shown, using a case study, that the addition of a friction isolator shrinks the range of P and D gains that can stabilize the motion stage. Several other case studies that include the effects of external excitation and integral controller are carried out to motivate deeper dynamic analyses of the friction isolator for precision motion control. 

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2. BIFURCATION ANALYSIS OF A PD CONTROLLED MOTION STAGE WITH A NONLINEAR FRICTION ISOLATOR

   Ehab E. Basta, Sunit K. (January 2023, ASME: IDETC-CIE 2022)

   The utilization of mechanical-bearing-based precision motion stages (MBMS) is prevalent in the advanced manufacturing industries. However, the productivity of the MBMS is plagued by friction-induced vibrations, which can be controlled to a certain extent using a friction isolator. Earlier works investigating the dynamics of MBMS with a friction isolator considered a linear friction isolator, and the source of nonlinearity in the system was realized through the friction model only. In this work, we present the nonlinear analysis of the MBMS with a nonlinear friction isolator for the first time. We consider a two-degree-of-freedom spring-mass-damper system to model the servo-controlled motion stage with a nonlinear friction isolator. The characteristic of the dynamical friction in the system is captured using the LuGre friction model. The system’s stability and nonlinear analysis are carried out using analytical methods. More specifically, the method of multiple scales is used to determine the nature of Hopf bifurcation on the stability lobe. The analytical results indicate the existence of subcritical and supercritical Hopf bifurcations in the system, which are later validated through numerical bifurcation. This observation implies that the nonlinearity in the system can be stabilizing or destabilizing in nature, depending on the choice of operating parameters. 

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3. Stability and Bifurcation Analysis of Precision Motion Stage With Nonlinear Friction Isolator

   https://doi.org/10.1115/1.4062266  

   Gupta, Sunit K.; Basta, Ehab E.; Barry, Oumar R. (August 2023, Journal of Computational and Nonlinear Dynamics)

   Abstract The application of servocontrolled mechanical-bearing-based precision motion stages (MBMS) is well-established in advanced manufacturing, semiconductor industries, and metrological applications. Nevertheless, the performance of the motion stage is plagued by self-excited friction-induced vibrations. Recently, a passive mechanical friction isolator (FI) has been introduced to reduce the adverse impact of friction in MBMS, and accordingly, the dynamics of MBMS with FI were analyzed in the previous works. However, in the previous works, the nonlinear dynamics components of FI were not considered for the dynamical analysis of MBMS. This work presents a comprehensive, thorough analysis of an MBMS with a nonlinear FI. A servocontrolled MBMS with a nonlinear FI is modeled as a two DOF spring-mass-damper lumped parameter system. The linear stability analysis in the parametric space of reference velocity signal and differential gain reveals that including nonlinearity in FI significantly increases the local stability of the system's fixed-points. This further allows the implementation of larger differential gains in the servocontrolled motion stage. Furthermore, we perform a nonlinear analysis of the system and observe the existence of sub and supercritical Hopf bifurcation with or without any nonlinearity in the friction isolator. However, the region of sub and supercritical Hopf bifurcation on stability curves depends on the nonlinearity in FI. These observations are further verified by a detailed numerical bifurcation, which reveals the existence of nonlinear attractors in the system. 

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4. On the Effect of Surface Friction and Upward Radiation of Energy on Equatorial Waves

   https://doi.org/10.1175/JAS-D-21-0199.1  

   Lin, Jonathan; Emanuel, Kerry (March 2022, Journal of the Atmospheric Sciences)

   Abstract In theoretical models of tropical dynamics, the effects of both surface friction and upward wave radiation through interaction with the stratosphere are oft-ignored, as they greatly complicate mathematical analysis. In this study, we relax the rigid-lid assumption and impose surface drag, which allows the barotropic mode to be excited in equatorial waves. In particular, a previously developed set of linear, strict quasi-equilibrium tropospheric equations is coupled with a dry, passive stratosphere, and surface drag is added to the troposphere momentum equations. Theoretical and numerical model analysis is performed on the model in the limits of an inviscid surface coupled to a stratosphere, as well as a frictional surface under a rigid lid. This study confirms and extends previous research that shows the presence of a stratosphere strongly shifts the growth rates of fast-propagating equatorial waves to larger scales, reddening the equatorial power spectrum. The growth rates of modes that are slowly propagating and highly interactive with cloud radiation are shown to be negligibly affected by the presence of a stratosphere. Surface friction in this model framework acts as purely a damping mechanism and couples the baroclinic mode to the barotropic mode, increasing the poleward extent of the equatorial waves. Numerical solutions of the coupled troposphere–stratosphere model with surface friction show that the stratosphere stratification controls the extent of tropospheric trapping of the barotropic mode, and thus the poleward extent of the wave. The superposition of phase-shifted barotropic and first baroclinic modes is also shown to lead to an eastward vertical tilt in the dynamical fields of Kelvin wave–like modes. 

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5. Effects of spatially-varying substrate anchoring on instabilities and dewetting of thin nematic liquid crystal films

   https://doi.org/10.1039/d0sm01416h  

   Lam, Michael-Angelo Y.-H.; Kondic, Lou; Cummings, Linda J. (November 2020, Soft Matter)

   null (Ed.)

   Partially wetting nematic liquid crystal (NLC) films on substrates are unstable to dewetting-type instabilities due to destabilizing solid/NLC interaction forces. These instabilities are modified by the nematic nature of the films, which influences the effective solid/NLC interaction. In this work, we focus on the influence of imposed substrate anchoring on the instability development. The analysis is carried out within a long-wave formulation based on the Leslie–Ericksen description of NLC films. Linear stability analysis of the resulting equations shows that some features of the instability, such as emerging wavelengths, may not be influenced by the imposed substrate anchoring. Going further into the nonlinear regime, considered via large-scale GPU-based simulations, shows however that nonlinear effects may play an important role, in particular in the case of strong substrate anchoring anisotropy. Our simulations show that instability of the film develops in two stages: the first stage involves formation of ridges that are perpendicular to the local anchoring direction; and the second involves breakup of these ridges and formation of drops, whose final distribution is influenced by the anisotropy imposed by the substrate. Finally, we show that imposing more complex substrate anisotropy patterns allows us to reach basic understanding of the influence of substrate-imposed defects in director orientation on the instability evolution. 

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