Kinematic parameters

It has long been recognized that the kinematic parameters measured in shoek-wave experiments and ean empirieally be described in regions where a substantial phase change in the material does not occur as... 

Table 3.3 summarizes the history of the development of wave-profile measurement devices as they have developed since the early period. The devices are categorized in terms of the kinetic or kinematic parameter actually measured. From the table it should be noted that the earliest devices provided measurements of displacement versus time in either a discrete or continuous mode. The data from such measurements require differentiation to relate them to shock-conservation relations, and, unless constant pressures or particle velocities are involved, considerable accuracy can be lost in data processing. 

When the length scale approaches molecular dimensions, the inner spinning" of molecules will contribute to the lubrication performance. It should be borne in mind that it is not considered in the conventional theory of lubrication. The continuum fluid theories with microstructure were studied in the early 1960s by Stokes [22]. Two concepts were introduced couple stress and microstructure. The notion of couple stress stems from the assumption that the mechanical interaction between two parts of one body is composed of a force distribution and a moment distribution. And the microstructure is a kinematic one. The velocity field is no longer sufficient to determine the kinematic parameters the spin tensor and vorticity will appear. One simplified model of polar fluids is the micropolar theory, which assumes that the fluid particles are rigid and randomly ordered in viscous media. Thus, the viscous action, the effect of couple stress, and... 

We see that the acceleration in the inertial frame P can be represented in terms of the acceleration, components of the velocity and coordinates of the point p in the rotating frame, as well as the angular velocity. This equation is one more example of transformation of the kinematical parameters of a motion, and this procedure does not have any relationship to Newton s laws. Let us rewrite Equation (2.37) in the form... 

In [9] Passman, Nunziato and Walsh presented a multiphase mixture in which each constituent had a simple geometrical structure characterized by a scalar kinematic parameter, its volume fraction. But when the kinematical describer is more complex and takes value on a manifold, it is necessary to consider the more general microstructure introduced, e.g., by Capriz in the essay [3], where materials as liquid crystals, granular and porous media, Cosserat and micromorphic continua are studied. 

A1 and A2 intersection points on axes Kinematic parameter of flow... 

The mixing performance depends significantly on the dimensionless kinematic parameter... 

Figure 4.11 Influence of the kinematic parameter of flow A on the mixing quality [14]...

Figure 4.12 Influence of kinematic parameter of flow A and viscosity on the dispersion degree of Ti02 agglomerates in silicone oil (trials with a single screw extruder) [151...

An important dimensionless screw parameter is the kinematic parameter of flow. 

Figure 6.11 also includes the kinematic parameter of flow, defined in Eq. 6.1. The pressure characteristic also enables us to calculate the length for pressure generation. This is illustrated in Fig. 6.8, where the length for pressure generation is Lg c . 

Figure 7.9 Efficiency of a triple-flighted screw during pressure generation in relation to the kinematic parameter of flow A...

The rotational speed, which only appeared as a parameter in the linear Eqs. 7.1 and 7.4, forms now an independent dimensionless parameter in the form of the Deborah number n . While the dimensionless pressure generation and dimensionless energy only depend on the kinematic parameter of flow for Newtonian liquids, the dimensionless revolution speed appears as an additional influencing variable for shear thinning. This is plausible if we consider that the rotational speed is a measure of the shear stresses on the material, and thus influences the effective viscosity of the material. It is also to be expected that the interaction will assume a non-linear form since the flow curve is already non-linear. 

Figure 9.11 Degree of disaggregation as a function of the kinematic parameter of flow A and the viscosity of the fluid, measured with Ti02 in silicone oil in a single screw extruder [6, 7]...

In scrutinizing the conveying characteristics in Fig. 39, one discovers three typical ranges in which the screw machine can function. They are outlined in Fig. 40. In this representation, the throughput number Q is standardized by the intercept Ax. In other words, this is the numerical value of Q where the screw machine is conveying without pressure formation. With this flow-kinematic parameter, A = Q/ A1 the state of flow of a screw machine can be outlined more distinctly. 

Fig. 40 Subdivision of the typical working ranges of a screw machine by the flow-kinematic parameter A.

The number of scattering channels that partake in molecular reactions may increase very rapidly when chemical species or kinematical parameters are changed. For example rotational channels multiply as the moments of inertia of reactants or products decrease vibrational modes become numerous in polyatomic molecules and generally the number of accessible channels increases with increasing collision energies. In these cases it may not be possible, and sometimes it is not needed, to develop a detailed treatment of cross sections. Rather, one may want to know only averages of cross... 

As it can be concluded from Equation 12.20a, the ideal global trajectory of any point fixed on the end surface of the workpiece is not influenced by the kinematical parameters, but only by the geometrical parameters of the planetary gear system, which are fixed for each setup and machine tool utilized. Conversely, the trajectories of the same point on each active surface of the bottom and upper grinding wheels are, respectively, influenced by the wheel rotational speed, but only when the coefficient from Equation 12.3 is variable. 

The transformation matrix between two consecutive reference frames j-1 and j is obtained on the base of the kinematic parameters as the product of translation and rotation matrices which depend on them ... 

J. Santolaria, J.J. Aguilar, J.A. Yague, J. Pastor, Kinematic parameter estimation technique for calibration and repeatability improvement of articulated arm coordinate measuring machines,... 

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