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Chapter 3 ISOLATOR DEVICES AND SYSTEMS
3.4 LEAD EXTRUSION DAMPERS
3.4.2 Properties of the Extrusion Damper
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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.
Figure 3.9: (a) Typical load-displacement hysteresis loops for lead extrusion dampers.
(b) Comparison of hysteresis loops obtained for a constricted-tube lead-extrusion damper tested in 1976 (solid line) and again in 1986 (dashed line). (Cousins & Robinson, 1987.) The force to operate one of the extrusion hysteretic dampers has also been found to be almost independent of both the stroke and the position from which displacement starts. The hysteresis loops in Figure 3.9(b), which shows the behaviour of the same damper at an interval of 10 years (1976 and 1986), confirm the stability of the extrusion dampers (Robinson & Cousins (1987, 1988)).
The extrusion force is rate-dependent, as can be understood on the dislocation model by considering the speeds of dislocation motion and grain boundary sliding. To examine the rate dependence of the extrusion force, for the extrusion energy absorbers, a number of them were tested at speeds ranging from 3x10-10 to 1 m/sec.
(a)
(b)
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Figure 3.10 Rate dependence of lead extrusion hysteretic damper. The force is compared with that corresponding to a speed of 1 m/s, and this load ratio is plotted as a function of speed.
The experimental results for the rate dependence of the energy absorbers are shown in Figure 3.10, in which the ordinate is the 'load ratio' relating the force to that which will cause the damper to yield at a speed of 1 m/s. The damper's performance has two different characteristics, with the change occurring at a speed of 10-4 m/sec. Below this speed, the exponential equation (3.7b) is given by b=0.14. Hence if the rate of cycling is increased by a factor of ten, the load increases by 38 per cent, or the rate must be increased 140 times for the load to be doubled. Above a speed of 10-4 m/s, b = 0.03. In this case a 7% increase in load increases the rate by a factor of ten, while a 40% increase in the load requires the rate to be increased 105 times. The value of 0.14 for b, for rates below 10-4 m/s, agrees well with the figure of 0.13 obtained by Pearson (1944) for lead at 17oC. Loads which cause creep may also be compared with the load at an earthquake-like speed of 10-1 m/sec. At a load ratio F/F(10-
1 m/sec) = 0.2, the creep rate becomes ~10 mm/yr.
The results above 10-4 m/sec indicate that at these speeds the extrusion energy absorbers are nearly rate-independent; for example, at a rate of ~102 m/sec the extrusion force is expected to be 1.15 times that for an earthquake-like speed of 10-1 m/sec.
Above a rate of 2 x 10-2 m/sec, tests on large energy-absorbing devices become difficult because of the large power required. For example, for a 200 kN hysteretic damper operating at 1 Hz with a total stroke of 250 mm, a power of 100 kW must be supplied.
The effect of temperature on the extrusion energy absorber is complex, in that an increase in temperature, due either to ambient changes, or to the absorption of energy during an earthquake, has a twofold effect:
- As the temperature increases the extrusion force decreases.
- The higher the temperature, the more rapidly the lead will undergo recovery, recrystallisation and grain growth, thereby eliminating work hardening and regaining its plasticity.
These factors ensure that the extrusion damper is a stable device which cannot destroy itself by building up excessive forces. A 15 kN constricted-tube extrusion damper was operated continuously at 1 Hz for 1,800 cycles and during this test the temperature on the outside of the orifice reached an equilibrium value of 210oC. The effect of lowering the temperature was checked by cooling an energy absorber to -20oC but no noticeable change in extrusion force, compared to that at 25oC, was observed.
The lifetime of an extrusion energy absorber has been tested by operating a 15 kN constricted- tube device continuously at frequencies of 0.5, 1 and 2 Hz for a total of 3,400 cycles (Robinson and Greenbank (1976)).
After this test, which provided conditions far more severe than those to be expected in service, (during an earthquake the device would be expected to undergo ~10 cycles), the extrusion energy absorber was found to operate as initially at 1.7 x 10-3 m/sec. This result is not surprising since 'hot worked' lead is forever recovering its original mechanical properties. Therefore the extrusion damper should be able to cope with a very large number of earthquakes.
The maximum energy an extrusion damper can absorb in a short time is limited by the heat capacity of the lead and the surrounding steel. To increase the temperature of lead from 20oC to its melting point of 327oC, but without melting it, requires 3.8 x 104 joules/kg of lead. The surrounding steel raises the heat capacity of the device by a factor of ~4 so that the total energy capacity of the extrusion device is ~1.6 x 105 joules/kg (total weight).
An extrusion damper with a 30 mm outside diameter had an extrusion force of ~15 kN while a device with a 150 mm outside diameter required a force of ~150 kN to operate it. The stroke of the extrusion energy absorber is not limited in any way by the basic properties of the device. To date the largest extrusion dampers made had a total stroke of 800 mm (±400 mm) and operated at a force of 250 kN. The total length of a device when at its maximum extension is three to four times the length of its stroke.