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146 lines
6.5 KiB
146 lines
6.5 KiB
\chapter{Effect of Friction on Slapdown Severity}
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\section{Introduction}
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Friction between the initial impact point and the target can have
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a significant effect on the secondary impact severity in a
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shallow angle slapdown event. The coefficient of friction
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is a significant parameter influencing the importance of friction.
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However, the radius at which the friction force acts (distance between
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the contact point and the axial centerline of the object) also plays a
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significant role. These two parameters are investigated here.
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The solid cylinder with length of 120 and radius to the edge of
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the spring of 40 was used. The mass was 80, the moment of inertia was
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114,000, the initial vertical velocity was -527.5 and the initial
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angle was 15$^\circ$. The moderate stiffness linear elastic and the
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nonlinear plastic springs described in the section on nose spring
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effects (Chapter 5) were used.
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\begin{figure}
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\vspace{3.5 in}
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\caption{Effect of Friction on Slapdown Severity}
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\end{figure}
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\section{Coefficient of Friction}
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The results of a study on the effect of coefficient of friction
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are shown in Table 6.1 and Figure 6.1.
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Friction had a much
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greater effect for the linear elastic spring than for the nonlinear
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plastic spring. Two parameters contributed to this difference. The
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normal forces, and thus the frictional forces, were much higher for the
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linear elastic spring. In addition, no energy was absorbed for the
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linear elastic spring compared to the large amount absorbed in the
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nonlinear plastic spring. Thus, energy dissipation due to friction
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had a proportionally greater effect on the linear
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elastic spring than on the nonlinear plastic spring. The increase in
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tail velocity for coefficient of friction of 0.4 over that of 0.3 for
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the linear elastic spring is due to the development of sufficient
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frictional force that the nose sticks (nose velocity in the x
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direction goes to zero). When nose sticking occurs, no further energy
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is dissipated by friction. Therefore, more energy remains to
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accelerate the tail resulting in higher tail velocities.
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\begin{figure}
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\vspace{3.5 in}
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\caption{Effect of Spring Radius (Moment Arm) on the Modification of
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Slapdown Severity by Friction}
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\end{figure}
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\begin{table}
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\begin{center}
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\caption{Effect of Increasing Coefficient Friction on Secondary
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Impact}
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\begin{tabular}{||c|c|c||}
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\hline
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\multicolumn{1}{||l|}{Linear Elastic Spring} & &\\
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Coefficient &Tail &Tail\\
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of Friction &Velocity &Displacement\\
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0.0 &-979 &6.028\\
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0.1 &-938 &5.777\\
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0.2 &-891 &5.490\\
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0.3 &-852 &5.251\\
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0.4 &-865 &5.331\\
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\hline
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\multicolumn{1}{||l|}{Nonlinear Plastic Spring} & & \\
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Coefficient &Tail &Tail\\
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of Friction &Velocity &Displacement\\
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0.0 &-752 &5.103\\
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0.1 &-733 &4.993\\
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0.2 &-711 &4.894\\
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0.3 &-690 &4.756\\
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0.4 &-686 &4.760\\
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\hline
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\end{tabular}
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\end{center}
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\end{table}
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\section{Radius of Spring}
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The effect of spring radius (distance between the contact point
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and the axial centerline of the object)
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is shown in Table 6.2 and Figure 6.2.
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The secondary impact severity decreases almost linearly with
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increasing spring radius for both linear and nonlinear springs. As in
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the coefficient of friction study (Section 6.2),
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and for the same reasons, the
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effect of spring radius was more pronounced for the linear elastic
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spring than for the nonlinear plastic spring. The spring radius is
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proportional to the moment arm over which the frictional forces act.
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Thus, increasing spring radius serves to retard rotation. Retardation
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of rotation decreases the secondary impact severity at the
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expense of increasing the initial impact severity (energy is
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shifted from secondary impact to primary impact).
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\begin{table}
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\begin{center}
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\caption{Effect of Increasing Spring Radius on Secondary Impact}
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\begin{tabular}{||c|c|c||}
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\hline
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\multicolumn{1}{||l|}{Linear Elastic Spring} & &\\
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\multicolumn{1}{||l|}{Coefficient of Friction 0.2} & &\\
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Radius &Tail &Tail\\
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of Spring &Velocity &Displacement\\
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40. &-891 &5.490\\
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50. &-871 &5.365\\
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60. &-849 &5.232\\
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80. &-802 &4.942\\
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100. &-748 &4.614\\
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120. &-689 &4.250\\
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240. &-455 &2.828\\
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360. &-261 &1.661\\
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\hline
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\multicolumn{1}{||l|}{Nonlinear Plastic Spring} & & \\
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\multicolumn{1}{||l|}{Coefficient of Friction 0.2} & & \\
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Radius &Tail &Tail\\
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of Spring &Velocity &Displacement\\
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40. &-711 &4.894\\
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50. &-702 &4.832\\
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60. &-692 &4.787\\
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80. &-670 &4.652\\
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100. &-645 &4.504\\
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120. &-617 &4.325\\
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240. &-502 &3.630\\
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360. &-430 &3.069\\
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\hline
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\end{tabular}
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\end{center}
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\end{table}
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\section{Conclusions}
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It is difficult to make broad generalizations covering the
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effects of friction on the shallow angle slapdown problem. While
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friction always serves to decrease the severity of the secondary
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impact, in certain extreme cases, friction can increase the severity
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of the initial impact sufficiently that the initial impact is more
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severe than the secondary
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impact. In general, for geometries, impact
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limiter behavior, and coefficients of friction anticipated in
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transportation of radioactive materials, it will be conservative to
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neglect friction in the analysis of shallow angle slapdown events.
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However, if the impact limiter radius is large compared to the package
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length or the coefficient of friction is anticipated to exceed 0.3,
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neglecting friction can lead to significantly
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unconservative initial impact predictions.
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