INDEX torque

Techniques for evaluating processing stabiHty and mechanochemical effects include using a Brabender torque rheometer (29,30), injection mol ding (26,28), capillary rheometry (26,28), and measuring melt index as a function of residence time (26). 

Transient torques Gears with indexing or positioning errors. 

Figure 14-8. Scoring based on flash temperature index related to speed and torque. (Courtesy of Lufkin Industries, Inc.)...

The shear-stress convention is a bit more complicated to explain. In a differential control volume, the shear stresses act as a couple that produces a torque on the volume. The sign of the torques defines the positive directions of the shear stresses. Assume a right-handed coordinate system, here defined by (z, r, 9). The shear-stress sign convention is related to ordering of the coordinate indexes as follows a positive shear xzr produces a torque in the direction, a positive xrg produces a torque in the z direction, and a positive x z produces a torque in the r direction. Note also, for example, that a positive xrz produces a torque in the negative 6 direction. 

High Density Polyethylene - [Both regular and high molecular weight (HMW)]. The time to increase in torque at 220°C. by the Brabender Plasticorder was determined as a measure of crosslinking. Yellowness Index after the Brabender test at 220°C. and after the first extrusion at 260°C. were also performed. 

Some of the test methods being used to measure the processing stability of polypropylene include melt flow drift measurements at elevated temperatures using an extrusion plastometer (melt indexer), melt viscosity retention measurements using a torque rheometer, retention of melt flow after repeated extrusions, and injection molded spiral test measured by the flow in inches at various temperatures and the retention of melt flow of the injected spirals. The nine commercial resins were evaluated by these methods. 

For foods that follow the simple power law model, the flow behavior index is determined as the slope of a double logarithmic plot of log N (abscissa) versus log torque (ordinate). In order to determine the consistency index, magnitudes of torque must be determined in the same container for the test fluid and for a standard fluid whose... 

Power consumption or torque fluctuations are influenced by granule properties (PSD, shape index, and apparent density) and the granulation time. Fluctuation of torque/power consumption and intensity of spectrum obtained by FFT analysis can be used for end-point determination. 

In this relation, M is the torque, K is the familiar consistency index from viscosity versus shear rate relationships, S is the rotor speed, and n is the power-law index, also familiar from viscosity versus shear rate plots. It can be seen from Equation 1 that a log-log plot of torque versus rotor speed should yield a straight line with intercept given by log (K C(n)) and slope given by n, the power-law index. 

Anisotropic molecules show optically isotropic behavior in the bulk when they are disordered and randomly oriented, for instance in solutions or liquid crystal above the transition temperature. Under the influence of a strong beam, the induced dipole moment of the molecules feels a torque that tends to orient the molecule. The reorientation of the molecular dipoles induces a change in the refractive index. The typical values for molecular susceptibilities and the time-responses vary depending on the type of systems. For small anisotropic molecular systems, x 10 esu, with a time response 10 s. However, in the nematic phase, liquid crystal molecules are strongly correlated, resulting in much higher values, x 10 esu,... 

The vector T will simply be called the torque in the following, without specifying any index. Note also that G, = G2 = G. 

Two properties were recorded as a result of processing each sample in the Brabender Plasticoder (1) time in minutes to reach a rapid increase in torque and (2) the color of each test sample as determined by yellowness index (ASTM D1925-70). 

Eq. 4.1 can be obtained from several mechanics textbooks (e.g., [20, 21]) and is shown here in 3-dimensional vector notation under consideration of relative motion. J is the matrix of the probe mass s moment of inertia 0,2 and eo0,2 are the angular acceleration and velocity of the probe mass s coordinate system (index 2) with respect to the inertial frame (index 0) 0,i and (001 are the angular acceleration and velocity of the reference system (index 1) with respect to the inertial frame. The reference system is attached to the sensing element s substrate and therefore also to the vehicle whose motion is to be measured. 2 and oi12 belong to the probe mass with respect to the reference system. M is the torque applied to the probe mass and is composed of the driving stimulus as well as the stiffness of the suspension beams and the damping of the mechanical resonator. 

Qiu and Rao (Qiu, C. G. and Rao, M. A. J. Texture Stud., submitted) determined slip coefficients and slip velocities for apple sauce in a concentric cylinder viscometer as well as the effect of insoluble solids content on them. Three concentric cylinder units specified in the theory of Mooney (42.) were employed. Rotational speeds were determined with the different concentric cylinder systems at the same magnitude of torque. Figure 2 shows, for one sample of apple sauce, the shear rates uncorrected and corrected for slip plotted against the shear stress. The magnitudes of the flow behavior index of the power law model (Equation 2) did not change significantly due to correction for wall slip however, the magnitudes of the consistency index increased due to wall slip corrections. 

The dyadics and are two-index, symbolic operators termed the multiparticle force and torque operators. They are defined by the relations... 

Flexion of a joint is defined to be the positive direction for angular changes hence, the flexor torque is assumed to be positive. Index/ is for the equivalent flexor muscle, and index e for the equivalent extensor muscle. The contribution of passive tissue crossing the joints is included by a resistive torque (index r), which will be described below. 

Melt viscosity can also be used for molar mass estimates. The measurements are, however, somewhat less precise because of the high viscosities due to entanglements of the molecules, and it is inconvenient to work at the higher temperatures needed to melt the polymer. A frequent measurement is that of the melt index. A basic extrusion-capillary is used to determine the (mass) rate of flow of the polymer through a specified capillary under controlled conditions of temperature and pressure. Similarly, the Mooney viscometer gives a measure of the torque to revolve a rotor at constant speed in a polymer at constant speed, which is linked ultimately to molar mass. The Mooney viscometer has found application in the rabber industry as an empirical measure of molar mass. Somewhat more information on melt viscosity is given in Sect. 5.6.6. 

The list could be made longer, taking the idea of electrokinetics in a wide sense (response of the colloidal system to an external field that affects differently to particles and liquid). Thus, we could include electroviscous effects (the presence of the EDL alters the viscosity of a suspension in the Newtonian range) suspension conductivity (the effect of the solid-liquid interface on the direct current (DC) conductivity of the suspension) particle electroorientation (the torque exerted by an external field on anisotropic particles will provoke their orientation this affects the refractive index of the suspension, and its variation, if it is alternating, is related to the double-layer characteristics). 

Sample Maximum torque (Mh) (dNm) Delta torque (dNm) Cure time (tgo) (min) Cure rate index (CRI) (min- )... 

Cure time corresponds to the time required for optimum vulcanization of samples. NR filled with different silica types (precipitated silica, PSi and fumed silica, FSi) have been prepared and their cure characteristics features were analyzed. The corresponding data related to the cure characteristics, scorch time (ts2), cure time (tc9o) cure rate index (CRI) and minimum torque (Ml) are recorded in Table 18.10. It can be seen that compared to PSi/NR compounds, degree of reversion and viscosity are higher for FSi/NR compounds at the same... 

Salaeh et al investigated the curing characteristics of the gum rubber compound and the ceramic/NR composites in terms of minimum, maximum and delta torques, scorch time, cure time, and cure rate index (CRI) are summarized in Table 18.11. This suggests that longer cure time but lower CRI in the BaTiOs composites compared with the PbTiOs composites. This indicated lower rate of vulcanization in the BaTi03 compounds. Furthermore,... 

Let both the helical axis and the electric field are parallel to the normal z of a cholesteric liquid crystal layer of thickness d and >0. In the case of a very weak field the elastic forces tend to preserve the original stack-like arrangement of the cholesteric quasi-layers as shown in Fig. 12.15a. On the contrary, in a very strong field, the dielectric torque causes the local directors to be parallel to the cell normal, as shown in Fig. 12.15c. At intermediate fields, due to competition of the elastic and electric forces an undulation pattern appears pictured in Fig. 12.15b. Such a structure has two wavevectors, one along the z-axis (nld) and the other along the arbitrary direction x within the xy-plane. The periodicity of the director pattern results in periodicity in the distribution of the refractive index. Hence, a diffraction grating forms. Let us find a threshold field for this instability. 

The solutiOTi of Eq. (13.48) depends on further simplifications. If we assume that the director in the odd layers with i = 0 is unaffected by an external field and only the azimuth in the even layers is changed from Jt to 0, then, for an infinitely thick sample (x —> oo), the free energy is independent of both x and Oi. The corresponding torque balance equation reduces to the form with index (/ -P 1) omitted ... 

A paper presented at the 1990 SPE ANTEC (5) discussed techniques for compounding highly filled polymers with corotating twin-screw extruders. The fusion time as measured in a torque rheometer of 40 wt% filled polypropylene with melt flow index (MFI) of 15 was 2.4 min for glass fibers, 8 min for mica, and 13.5 min for talc. For a 30 wt% loading of mica, fusion time was reduced to about 5 min. 

The new spring was evaluated by subjecting it to the standard performance requirements of the Rediffusion specification. This specification contains a large number of performance requirements and test procedures, covering the various components and the functioning of the assembled switch. The items which are of particular relevance to the indexing spring are a life test which tests its durability, and a torque test which ensures that the action of the switch is not too stiff. 

Note that force-dimensioning ellipsoids, as well as manipulability ones, also allow computing the local isotropy index of the device as = Vax/Vin- global index over the work space can also be computed, taking into account either its mean value or the worst case. The robot s architecture, dimensions, and actuators can be adjusted to reach a desired force/torque capacity and a predefined isotropy. Also, as the total work space of the robot is usually larger than the specified useful one, the position of the latter relative to the base of the robot can be optimized, i.e., placed where the force/torque capacity is maximum and/or where it is the most isotropic (the same holds for apparent stiffness and mass). 

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