Linear taper

These designs avoid the possible stress developed in stepped horns. The amplification factor for either a linear or an exponential horn is the ratio of the end diameters (not areas as with stepped). The linear taper is the easier design to manufacture but its potential magnification is normally restricted to a factor of approx. 4-fold. The exponential taper offers higher magnification factors than the linear taper. Its shape makes it more difficult to manufacture but the small diameter of the working end and its length make it particularly suited to micro applications. 

For the analysis of the matrix flow in pultrusion, the linearly tapered, constant-width die of Figure 11.6 is considered. The treatment herein applies to an idealized process at steady state it is assumed that all fibers in the oversaturated and void-free bundle that enters this heated die are parallel to one another and to the pulling direction throughout the die, and that matrix flows parallel to the fibers only. The tapered section of a die is normally followed by a... 

Figure 11.6 Linearly tapered die considered in pressure and pulling resistance analyses...

Figure 11.7 Dimensionless matrix flow relative to the fibers in a linearly tapered die as a function of initial fiber volume fraction (thermoset pultrusion)...

Linear, Taper-Shaped, and Dendritic Molecules with RF-Chains... 

For a linearly tapered tube with a diameter at the bottom about equal to the float diameter, the area for flow is a quadratic function of the height of the float h ... 

ABS/PVC blends (e.g., Triax CBE, Enplex tm) are formulated to provide a broad window of molding conditions. Because of the presence of PVC, shear or thermal degradation must be minimized. Shot size should be about 50% of machine capacity — less than 35% will result in a long residence time, whereas in excess of 65% will increase plasticating time, both of which create conditions for resin degradation. High compression screws should be avoided since they generate excessive shear heat — a linear taper screw with a compression ratio between 1.5 and... 

Table 8 Compliance Rate Change of Linear Tapered Specimens...

If this pot is of the "linear taper" type, then according to equation 4.3, the voltmeter will read somewhere between 4.5 and 5 volts. However, some pots have an "audio taper," in which case the resistance versus rotation is logarithmic, and the 5 volt point will not be an5rwhere near the middle. 

One of the difficulties encountered in the application of extrusion dies is that dies are very sensitive to production variations. Liu et al. [1] analyzed the effects of several production variations on flow uniformity for a linearly tapered coat-hanger die. They found that as a production variation arises, the uniformity of the thin liquid layer generated by the die deteriorates rapidly. 

We shall illustrate the variations of the choker bar taper function l y) by some sample calculations. The following geometric parameters of a linearly tapered coat-hanger die are selected for demonstration ... 

Liu et al. [ 1 ] found that the flow uniformity is very sensitive to the variation of the power-law index in a linearly tapered coat-hanger die. If a die was originally designed based on n=0.5 and suddenly n was changed to 0.6, a W-type flow distribution would appear. On the other hand, if n dropped to 0.4, an M-type flow pattern would appear instead. The design equation (17) can be applied to offset the ffow uniformities caused by the variation of w. We fixed =0.5 and made proper selections of ho and h. Then n was varied to n = 0.6 and 0.4. l iy) was computed based on Eq. (17) and then a choker bar with the taper function l y) could be constructed to correct ffow nonuniformities. The effect of n on l y) is displayed in Fig. 7. For the case /I=0.6 >0.5, l y) has to decrease from the die end to the die center to eliminate the ffow nonuniformities if n=0.4 <0.5, then l iy) will increase from the die end to the die center instead. If is longer, the variation of hiy) will be smaller. 

In this chapter, we have described a novel design approach to correct flow nonuniformities caused by four types of production variations in a linearly tapered coat-hanger die. The theoretical approach is based on the onedimensional lubrication approximation and can be used to predict the taper function of an adjustable choker bar. Once a choker bar is constructed based on the prediction of the mathematical model, the flow nonuniformities can be properly eliminated by inserting this bar into the die. A choker bar can be tapered in different ways as indicated in Fig. 3. The shape displayed in Fig. 3a may be easier to machine and was selected for illustration. The four production variations we have considered include (i) enlarging the manifold, (ii) including the fluid inertial terms, (iii) varying the viscosity of the polymeric liquids, and (iv) narrowing the liquid film width to meet production requirements. All these four production variations can be properly handled, but if the fluid inertia becomes dominant, or the Reynolds number is not small, the present method may not be applicable. 

The data reduction for the tapered ENF (TENF) specimen can take the form of an experimental compliance or a simple beam theory approach, as reported by Edde and Verrenman (1995) or a corrected beam theory approach following the work of Qiao et al. (2003), using a beam on an elastic foundation model. These authors showed that substrates with a linear taper gave an almost linear relationship between compliance and crack length, within a certain range of crack lengths. 

The parameters for the linear taper of Fig. 5-6(a) are identical with those of the previous example and the taper angle is SI We can determine very simply the minimum taper length for total power transmission when a meridional ray enters the taper at z = —L and makes angle 0q with the axis. This result apphes to both direct on-axis illumination by a collimated beam, i.e. 0q = 0, and the inclusion of a lens, as discussed in Section 4-11, which transforms the on-axis beam into acone of meridional rays at angle d(, > 0. 

Fig. 5-6 (a) Step-profile linear taper with taper angle Q and (b) the equivalent geometrical path. 

For an on-axis beam Og = 0, in which case Eqs. (5-58) and (5-59b) show that the minimum length parabolic taper is longer than the corresponding linear taper by a factor (po + p)/(Po — p) provided the taper angle is small and the fiber is weakly guiding. 

We can quantify the accuracy of Eq. (5-60) for the linear taper of the previous section. At the minimum taper length of Eq. (5-59b) we deduce from Eq. (5-59a) that for meridional rays... 

Figure46.3 Suggested and actual linear taper currents obtained during 16h voltage-limtted taper current charging of 15V, 5Ah Eveready 561 alkaline manganese dioxide battery (Courtesy of Union Carbide)...

The suggested linear taper current for the 561 battery and actual current characteristic obtained with the... 

Feed section 3.2 turns and 0.5 in. channel depth Compression section 12 turns with a linear taper... 

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