The hydrolysis of whole casein and isolated casein components were investigated with the purpose of obtaining information concerning the kinetic and specifty of aspartic proteases in rennin, pepsin and 4 microbial rennet substitutes. The velocity of hydrolysis decreased rapidly within the first hour. However, the hydrolysis was not completed after 2 days. A mathematical description of the slope of hydrolysis is possible by use of exponential equations. More than 40 peptides were detected by capillary electrophoresis or PAGE. The characterization of the C- and N-terminal amino acids of peptides shows that the hydrolysis of any peptide bond depends mainly on the structure of the C-terminal side chains of the amino acids. The detection of the basic amino acids lysin and arginin in the C-terminal position of peptides is a new result, furthering the knowledge about the specificity of aspartic proteases. Differences in the reaction velocity or in the extent of hydrolysis are one of the possible explanations for the described differences in the rennet curd yield. It was concluded that the rennet enzymes are active also in the later phases of cheese ripening and are able to support the action of cheese ripening flora.
Modern machine tools are highly optimized with respect to their design and the production processes they are capable to. Now for further advances, especially a detailed knowledge about the thermo-elastic behavior is needed, because the nowadays still existing deficits are mainly related to this. That is why, endeavors in improvement, like the optimization of the design, the evaluation of new materials and the regulation of the production process, particularly rely on accurate computed thermal deformations. One possible approach to increase their quality is to also include the relevant structural variabilities of the machine tools as well as the resulting interactions between the coupled parts within the calculations. In this article, three different numerical methods are presented, which include structural motions in thermoelastic analyses. Thereby, several conflicting criteria, like real-time capability, memory saving issues and accuracy are fulfilled each time in a different manner. Those methods are afterwards compared with respect to their runtime and accuracy. Finally, the paper concludes with a classification of the usability of the methods in real-time control and optimization tasks.
In thermal simulations moving parts can be included by discretely adjusting their position within the steps of a transient analysis, whereby frictional heating is considered as a pre-determined, time-depended NEUMANN-BC within the contact zone. Now when using a coarse time discretization, the rarely conducted update of the actual loaded friction is the reason for one proportion of the occurring lack in result quality. In this paper we present an idea to counter this systematic error source by some low-effort editing of the applied load data. The proposed method is based on the conservation of the provided frictional energy between the continuous and discrete motion and considers the actually used time discretization. Its performance is shown for a simplified case at the end of this paper. Motivation and Basic ApproachThe inclusion of structural variabilities is one approach to increase the result quality of transient thermal analyses, especially in fields like machine tool engineering, where moving parts are of certain relevance. Therefore, discretely adjusting their positions pursuant to a given motion profile s(t) (with corresponding velocity v(t)) within the steps of a transient analysis is a very intuitive method that yields the continuous motion for a vanishing time step size ∆t → 0. A brief explanation of this method including some related mandatory particularities can be found in [1]. Therein, the frictional heat is considered as a pre-determined NEUMANN-BCq F ric (t) applied on the contact zone (with dimensions l M along and w M orthogonal to the direction of motion) beyond the current position of the moving body. Furthermore, in [2] the so-called characteristic motion number η for the theoretical description of such discrete motions was introduced and the need for using a constant displacement step size ∆s between the loadsteps L n with related times t Ln was reasoned:It is easy to see, that for small ∆t the needed effort of these simulations may rapidly reach an unacceptable high amount. Therefore, using a coarse time discretization while correcting the arising deviations in result quality is one approach to also enable such analyses for given problems where a time-convergent solution is not possible in practice. Now the problem about common tribological systems is that their representing friction models are directly depending on the velocity of the friction inducing motion. For an accelerated motion, this leads to a non-constantq F ric (t). As we can see in Fig. 1, in a time discrete analysis at the actual simulation time t Ln , we apply the relatedq Ln =q F ric (t Ln ) on the contact zone [s(t Ln ); s(t Ln ) + l M ]. The energy Q Ln supplied in there in loadstep L n furthermore depends on a relevant loading time ∆t Ln and results to:Therein, we already indicated the inherent problem of the method, namely that in time discrete analyses the energy entry via a contact NEUMANN-BC is generally of incorrect amount (see eq. 2) and furthermore inaccurately located (see Fig. 1). Both systematic errors increa...
Using a coarse time discretisation for saving calculation effort will induce non-uniform heat input within thermal-transient analyses which include translational rigid body motions by the technique of discrete displacement adjustment. We are going to show, why these non-uniformities are generally unavoidable and how a suitable choice of time step size pre-minimizes their consequences. Afterwards, the amount and location of the remaining load-bumps are analytical deduced for an arbitrary motion. With this information, we develop a correction method based on arithmetic calculations to avoid these numerical caused errors. For practical use, the correction is applied as an algorithm to the solution process of analyses with spatial discretized motion partners. We finish by demonstrating the performance of the correction.
The numerical simulation of a moving heat source from a fixed point observer is often done by discretely adjusting its position over the steps of a thermal transient analysis. The efficiency of these simulations is increased when using a coarse temporal discretization whilst maintaining the quality of results. One systematic error source is the rare update of a nonconstant moving heat source with regard to its magnitude and location. In this work, we present an analysis of the error and propose a correction approach based on conserving the specified heat from a continuous motion in analyses with large time-step sizes. Deficiencies associated with the correction in special motion situations are identified by means of performance studies and the approach is extended accordingly. The advantages of applying the proposed correction are demonstrated through examples.
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