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Chapter 3 ISOLATOR DEVICES AND SYSTEMS
3.4 LEAD EXTRUSION DAMPERS
3.4.1 General
Another type of damper utilising the hysteretic energy dissipation properties of metals is the Lead Extrusion Damper, developed at PEL (DSIR) (the Physics and Engineering Laboratory of the NZ Department of Scientific and Industrial Research). The cyclic extrusion damper was invented in April 1971 by Bill Robinson, immediately after he had a morning-tea discussion with Ivan Skinner on the problems associated with the use of steel in devices to absorb the energy of motion of a structure during an earthquake.
The process of extrusion consists of forcing or extruding a material through a hole or orifice, thereby changing its shape (Figure 3.7). The process is an old one. Possibly the first design of an extrusion press was that of Joseph Bramah who in 1797 was granted a patent for a press "for making pipes of lead or other soft metals of all dimensions and of any given length without joints", (Pearson, 1944).
Figure 3.7: A representation of the extrusion of a metal, showing the changes in microstructure. (Robinson, 1976.)
A lower bound for the extrusion pressure p may be derived from the yield stress y of the material under simple axial load, following Johnson & Mellor (1975). Simple extrusion involves a reduction in the cross-sectional area of a solid prism from A1 to A2 by plastic deformation, with an increase in length corresponding to little volume change. The process may be idealised as the frictionless extrusion of an incompressible elastic-plastic solid which has a constant yield stress y. The minimum work W, required to change the section from A1 to A2, or the equal minimum work to change the section from A2 to A1, arises when A1 and A2 have the same shape and when the deformation involves plane strain. Such plane strain occurs when plane sections prior to deformation remain plane throughout the deformation process.
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The work W of plane-strain deformation can be derived by considering a prism of section A2
which is compressed between frictionless parallel anvils to form a prism of section A1. The yield force increases with the increasing sectional area to give the work W as
where L1 is the length when the prism area is A1. Indeed, equation (3.6a) can be used as a basis for the experimental determination of the simple-strain yield stress y for lead, since a suitably lubricated lead cylinder, compressed between smooth anvils, deforms in almost true plane strain.
The work required to cause the reverse change in area by simple frictionless extrusion would be greater than W by an amount which depends on the departures from plane-strain, which should not be great with a gradually-tapered extrusion orifice.
For this almost plane-strain case, a result which appears to have been first put forward in 1931 by Siebel and Fangmeier, the extrusion pressure p follows simply from equation (3.6a), giving
where the extrusion ratio ER = A1/A2
and exceeds 1.0 by a small amount which arises from the departure from plane-strain deformation.
A practical extrusion process will involve significant surface friction which will give a further departure from plane-strain and hence an increase in , beyond the zero-friction value. A further increase in pressure occurs in reaction to the axial component of the surface friction forces.
If there are significant changes in y over sections of the extruded material, as may well arise when hysteretic heating causes temperature differences, this may change the pattern of extrusion strains substantially, a factor which may be significant with cyclic extrusion.
When a back-pressure and a re-expansion throat are included to return a lead plug to its original sectional area A1, as shown in the schematic sketch of an extrusion damper in Figure 3.8, the theoretical frictionless pressure of equation (3.6b) is doubled. For a practical system with effective lubrication, the extrusion pressure, as given by equation (3.6b), should also be roughly doubled when the contraction from area A1 to A2 is followed by an expansion from area A2 to A1.
/ A n A L
A
=
W
1 1
y
1 2 (3.6a)ER n
=
p
y
(3.6b)(a)
Figure 3.8: (a) Longitudinal section of cyclic lead extrusion damper: constricted-tube type.
(Robinson, 1976.)
(b) Longitudinal section of cyclic lead extrusion damper: bulged-shaft type.
When the throat profile is well designed, and the lead-surface lubrication is effective, the pressure should be given approximately by
Another result of interest is the relation between extrusion pressure p and the speed of extrusion v, or the strain rate (Pearson (1944), Pugh (1970)). This is found to be
where b = 0.12 for lead at 17oC, so that for an increase in extrusion speed by a factor of 10, it is necessary to increase the extrusion pressure by 36 per cent. More complete discussions of the behaviour of metals during plastic deformation are found in Nadai (1950), Mendelsson (1968) &
Schey (1970).
Deformation of a polycrystalline metal results in elongation of the grains and a large increase in the number of defects (such as dislocations and vacancies) in each grain. After some time the metal may, if the temperature is high enough, return to a state free from the effects of plastic strain by the three interrelated processes of recovery, recrystallisation and grain growth (Wulff et al (1956), Birchenall (1959), Jones et al (1969)). During the process of recovery, the stored energy of the deformed grains is reduced by the dislocations moving, to form lower energy configurations such as subgrain boundaries, and by the annihilation of vacancies at internal and external surfaces.
Recrystallisation occurs when small, new, undeformed grains nucleate among the deformed grains and then grow at their expense. Further grain growth occurs as some of the new grains grow at the expense of others. The driving force for recrystallisation is the stored energy of deformation of the extruded grains, while the decrease in the surface energy of the many recrystallised grains causes grain growth to occur. The temperature which is sufficient to cause 50% recrystallisation during one hour is called the recrystallisation temperature (Wulff et al (1956), Van Vlack (1985)). For lead this temperature is well below 20oC, while for aluminium, copper and iron it is 150oC, 200oC and 450oC respectively. The rate at which recrystallisation occurs is strongly dependent on temperature.
For example, copper which has been reduced in thickness by 71 per cent, by cold rolling, has a recrystallisation time of 12 min at 300oC, 10.4 days at 200oC and 290 yr at 100oC (Wulff et al (1956)). The rate at which recrystallisation occurs also increases with the amount of deformation.
p A + A / n
=
p
1
y
1 2 o (3.7a)a v
=
p
b (3.7b)(b)
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Since the recrystallisation temperature of lead is below room temperature, any deformation of lead at or above room temperature is in fact 'hot work' in which the processes of recovery, recrystallisation and grain growth occur simultaneously. Working lead at room temperature is equivalent to working a piece of iron or steel at a temperature of more than 400oC. Indeed, lead is the only common metal which need not suffer progressive fatigue when cycled plastically at room temperature.
A device which acts as a hysteretic damper by utilizing this property of lead (Robinson &
Greenbank (1976); Robinson & Cousins (1987, 1988), is shown in Figure 3.8(a). It consists of a thick-walled tube co-axial with a shaft which carries two pistons. There is constriction on the tube between the pistons, and the space between the pistons is filled with lead. The lead is separated from the tube by a thin layer of lubricant kept in place by hydraulic seals around the pistons. The central shaft extends beyond one end of the tube. During operation, axial loads are applied with one attachment point at the protruding end of the central shaft and the other at the far end of the tube. The hysteretic damper is fixed between a point on the structure and a point on the earth, which move relative to one another during an earthquake. As the attachment points move to and fro, the pistons move along the tube and the captive lead is forced to extrude back and forth through the orifice formed by the constriction in the tube.
Since extrusion is a process of plastic deformation, work is done, while very little energy is stored elastically, as the lead is forced through the orifice during structural deformation. Thus during an earthquake such a device, by absorbing energy, limits the build-up of destructive oscillations in a typical structure.
The successful operation of this hysteretic damper depends on the use of a material, in this case lead, which recovers and recrystallised rapidly at the operating temperature, so that the force required to extrude it is practically the same on each successive cycle. If the extruded material had a recrystallisation temperature much above the operating temperature, it would work- harden and be subject to low-cycle fatigue. Moreover, such materials typically have much higher stresses which would present very severe problems for containment, piston sealing and lubrication in a cyclic extrusion device.
A hysteretic damper which operates on this same principle but has different construction details is shown in Figure 3.8(b). Here the extrusion orifice is formed by a bulge on the central shaft rather than by a constriction in the outer tube. The central shaft is located by bearings which also serve to hold the lead in place. As the shaft moves relative to the tube, the lead must extrude through the orifice formed by the bulge and the tube.