Gear dynamics

Romanato P, Duttwyler S, Linden A, Baldridge KK, Siegel JS (2010) Intramolecular halogen stabilization of silylium ions directs gearing dynamics. J Am Chem Soc 132 7828... 

Gear elements must be multiplane and dynamically balanced. Where keys are used in couplings, half keys must be in place. The maximum allowable unbalanced force at maximum continuous speed should not exceed 10% of static weight load on the journal. The maximum allowable residual unbalance in the plane of each journal is calculated using the following relationship... 

Analysis parameters should be established to monitor the key indices of the compressor s dynamics and failure modes. These indices should include bearings, gear mesh, rotor passing frequencies, and mnning speed. However, because of its sensitivity to process instability and the normal tendency to thmst, the most critical monitoring parameter is axial movement of the male and female rotors. 

Kahraman, A., Dynamic Analysis of Geared Rotors, NASA, 1990. 

In this section, we switch gears slightly to address another contemporary topic, solvation dynamics coupled into the ESPT reaction. One relevant, important issue of current interest is the ESPT coupled excited-state charge transfer (ESCT) reaction. Seminal theoretical approaches applied by Hynes and coworkers revealed the key features, with descriptions of dynamics and electronic structures of non-adiabatic [119, 120] and adiabatic [121-123] proton transfer reactions. The most recent theoretical advancement has incorporated both solvent reorganization and proton tunneling and made the framework similar to electron transfer reaction, [119-126] such that the proton transfer rate kpt can be categorized into two regimes (a) For nonadiabatic limit [120] ... 

Unfortunately, the dynamic correlation energy is not constant for a given molecule but may vary considerably between different electronic states. Thus, any procedure geared towards quantitative accuracy in predicting excited-state energies must in some way account for these variations. The most economical way to achieve this is to introduce a number of parameters into the model. By scaling those to a set of experimental data... 

It may be pertinent to mention here a recent criticism of the gear effect by methyl groups, since most of the known examples used in the study of the gear effect are in aromatic molecules. Based on dynamic NMR data on the internal rotation of the 9-methyl group in 42, which indicated a far lower barrier for 42a than for 42b, Oki... 

As a part of a study on persilylated 7r-electron systems, particularly on persilylated benzenes66, Sakurai and coworkers67 were interested in hexakis(fluorodimethylsilyl)ben-zene (30) for its possible dynamic properties as a gear-meshed structure68 and for the possible presence of nonclassical neutral pentacoordinate silicon atoms52. The X-ray analysis of 30 was also reported (Figure 10). 

So-called stiff differential equation models are particularly challenging to solve. Stiff models have dynamic behavior that encompasses a wide range of time scales. An example would be fast kinetics combined with long fluid-residence times in a chemical reactor. Gear s method is perhaps the most commonly used technique for solving these types of problems. 

In 2004, Berstorff introduced a combined rubber extruder/gear pump, patent pending, for the production of dynamically cross-linked vulcanized thermoplastic elastomers (TPE-V) (DE 101340701 Al). A short rubber extruder, with a gear pump connected downstream,... 

Obviously, the above algorithms are not suitable when transients of the finer scale model are involved (Raimondeau and Vlachos, 2000), as, for example, during startup, shut down, or at a short time after perturbations in macroscopic variables have occurred. The third coupling algorithm attempts fully dynamic, simultaneous solution of the two models where one passes information back and forth at each time step. This method is computationally more intensive, since it involves continuous calls of the microscopic code but eliminates the need for a priori development of accurate surfaces. As a result, it does not suffer from the problem of accuracy as this is taken care of on-the-fly. In dynamic simulation, one could take advantage of the fast relaxation of a finer (microscopic) model. What the separation of time scales between finer and coarser scale models implies is that in each (macroscopic) time step of the coarse model, one could solve the fine scale model for short (microscopic) time intervals only and pass the information into the coarse model. These ideas have been discussed for model systems in Gear and Kevrekidis (2003), Vanden-Eijnden (2003), and Weinan et al. (2003) but have not been implemented yet in realistic MC simulations. The term projective method was introduced for a specific implementation of this approach (Gear and Kevrekidis, 2003). 

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