Variable restoring force isolator

Abstract

A variable restoring force (VRF) isolator and related system and method adapted to protect equipment from forces such as during an earthquake. One embodiment for protecting equipment is through isolation, where individual pieces of equipment, or equipment sets, are isolated from the building motion. Because critical equipment often contains acceleration-sensitive components that can be damaged during an earthquake, it is necessary to limit the inertial forces experienced by the equipment during an event. This can be achieved using a special isolator with a restoring force that can be shaped according to the isolator displacement, that is, the variable restoring force (VRF) isolator. An example of a VRF isolator may have a force-displacement relationship characterized by high stiffness at small and large displacements, and low stiffness in between.

Description

VARIABLE RESTORING FORCE ISOLATOR Inventor: Kenneth K. Walsh, Ph.D. BACKGROUND AND SUMMARY OF THE INVENTION

[0001] Exemplary embodiments of the present invention relate generally to systems, devices, and methods adapted to protect equipment during forces such as may be caused during an earthquake.

[0002] Protecting critical equipment in seismically excited buildings is essential for maintaining their functionality after an earthquake. For instance, electronic equipment and computers are particularly susceptible to damage during an earthquake or other forces. Other types of equipment may also be damaged such as during an earthquake.

[0003] Exemplary embodiments of a variable restoring force (VRF) isolator and related system and method of the present invention may satisfy the need to protect equipment from forces such as during an earthquake. One approach of an exemplary embodiment for protecting equipment is through isolation, where individual pieces of equipment, or equipment sets, are isolated from the building motion. Because critical equipment often contains acceleration- sensitive components that can be damaged during an earthquake, it is necessary to limit the inertial forces experienced by the equipment during an event. This can be achieved using a special isolator with a restoring force that can be shaped according to the isolator displacement, that is, the variable restoring force (VRF) isolator. The VRF isolator has a force-displacement relationship characterized by high stiffness at small and large displacements, and low stiffness in between. To validate the VRF isolator concept, a small-scale prototype was constructed, and itsforce-displacement properties were observed for cyclic loading. A model was developed that predicts the relationship between the VRF isolator force and displacement with good accuracy. Numerical analyses were conducted for horizontal isolation of equipment installed on different levels of multi-story seismically excited buildings. Floor acceleration records from historical ground motions were used as inputs to the system, and the VRF isolator performance was evaluated based on the absolute acceleration response of the isolated equipment.

[0004] In addition to the novel features and advantages mentioned above, other benefits will be readily apparent from the following descriptions of the drawings and exemplary embodiments. BRIEF DESCRIPTION OF THE DRAWINGS

[0005] Figures 1 is a schematic drawing of (a) an example of use of an exemplary embodiment of a VRF isolator, and (b) an isolated view of the VRF isolator.

[0006] Figure 2 is force-displacement curve for examples of (a) an ideal and (b) a prototype VRF isolator.

[0007] Figure 3 is a photograph of a portion of exemplary components of a VRF isolator.

[0008] Figure 4 is photographs of portions of the VRF isolator of Figure 3 wherein an example of an upper rail is (a) in a starting position and (b) moved to the left.

[0009] Figure 5 is a schematic drawing of examples of an upper rail, cable, and pulley of an exemplary embodiment of a VRF isolator.

[0010] Figure 6 is schematic drawings of examples of (a) reel, (b) geartrain, (c) VDS, and (d) VPS of an exemplary embodiment of a VRF isolator.

[0011] Figure 7 is a schematic drawing of an example of VDS for defining variable radius.

[0012] Figure 8 is a graph of non-dimensional force vs. displacement for an example of a VRF isolator considering different values of β.

[0013] Figure 9 is graphs of exemplary variations in absolute acceleration and instantaneous period with time for the (a) ground, (b) 3rd floor, (c) case 1, (d) case 2, (e) case 3, and (f) case 4.

[0014] Figure 10 is graphs of exemplary force-displacement loops for the exemplary embodiments of VRF isolators in (a) case 1, (b) case (2), (c) case 3, (d) and case 4.

[0015] Figure 11 is graphs of exemplary variations in absolute acceleration and instantaneous period with time for examples of the (a) roof and (b) equipment for 20% damping in the EW direction.

[0016] Figure 12 is graphs of exemplary variations in absolute acceleration and instantaneous period with time for examples of the (a) roof and (b) equipment for 10% damping in the NS direction.

[0017] Figure 13 is graphs of exemplary force versus displacement for exemplary embodiments of VRF isolators with (a) 20% damping in the EW direction and with (b) 10% damping in the NS direction.

[0018] Figure 14 is a schematic view of another exemplary embodiment of a VRF isolator.DETAILED DESCRIPTION OF EXEMPLARY EMBODIMENT(S)

[0019] Exemplary embodiments of the present invention are directed to a device and related system and method for protecting equipment from unwanted forces such as an earthquake.

[0020] A schematic of an equipment isolation platform with an example of a VRF isolator 10 of the present invention installed at the isolation level is shown in Fig.1a. The VRF isolator 10 comprises a base plate 20 on which a VRF device 30 is mounted along with an arrangement of rails 40 (namely lower rails 42 and upper rail 44) and sliders 50 (namely slider 52 and slider 54), as shown in Fig. 1b. Upper rail 44 is mounted on the sliders 50, which in turn are mounted on lower rails 42 such that the upper rail 44 may move in the horizontal direction of motion. The VRF device 30 is connected between the base plate 20 and the upper rail 44, which is then connected to the bottom of the isolation platform. The VRF isolator 10 is adapted to produce a horizontal force on the isolation platform that always acts to restore it to its original position, i.e., a restoring force.

[0021] The aforementioned isolation platform may be considered to be in a system with the VRF isolator 10. This example of an isolation platform comprises rollers. Other embodiments of an isolation platform may comprise any suitable features that facilitate isolation of equipment and operation with a VRF isolator. Variable Restoring Force (VRF) Isolator Overview

[0022] The VRF isolator 10 is adapted to produce a trilinear elastic restoring force with different loading and unloading paths. An example force-displacement curve for the VRF isolator10 is presented in Fig. 2(a), where three different regions of the curve have been identified. At small VRF isolator displacements (region 1), high stiffness (k1) ensures the stability of the isolation system under service loading. At large VRF isolator displacements (region 3), high stiffness (k3) limits excessive isolator displacements due to extreme seismic loading. In between small and large VRF isolator displacements (region 2), low stiffness (k2) limits acceleration of the isolated equipment at the design level earthquake. It will be shown that the force-displacement characteristics of the VRF isolator 10 can be controlled through proper selection of its component geometry to produce a wide range of isolator responses. Other features of this example of VRF isolator 10 are as follows:

[0023] · Restoring force is independent of the payload weight.

[0024] · Capable of accommodating large isolator displacements within a compact design for installation of isolator on upper floors.

[0025] · Robust with respect to ground motion characteristics allowing for installation of isolator on lower floors.

[0026] · Utilizes basic materials and simple machine components to minimize cost and enhance reliability.

[0027] · Restoring force elements operate within the elastic range to eliminate the need for component replacement after an event.

[0028] · Low profile to reduce platform height.Prototype Description

[0029] To provide proof-of-concept for the VRF isolator, a small-scale prototype 100 was constructed and tested. A picture of the prototype 100 is shown in Fig. 3 where the relevant components have all been identified. A description of the components is as follows: · Constant force spring (CFS) 110 produces a nearly constant force during spring deformation. · Variable pitch shaft (VPS) 120 has a constant diameter and a helical groove 122 over a given length of the shaft. The distance between grooves, or pitch, varies with the shaft length. The remaining length of the shaft is smooth (without groove). · Variable diameter shaft (VDS) 130 has a variable diameter and a helical groove 132 running the length of the shaft. The groove pitch is constant while the shaft diameter varies with the shaft length. · Cable 2140 connects the VPS 120 to the VDS 130. · Geartrain 150 connects the VDS 130 to the storage reel 160. · Cable 1170 is stored on the storage reel, extends between pulleys 180, and is attached to the upper rail 190. · Upper rail 190 mounted on sliders 200, which in turn are mounted on lower rails 210 (only one rail / slider 210 shown) that allow for unidirectional horizontal motion. Operation

[0030] The restoring force in the VRF isolator 100 is generated by wrapping the cables 112, 114 from the constant force springs (CFSs) 110 around the smooth portion of the variable pitch shaft (VPS) 120. This produces a constant torque that resists the rotation of the shaft 120in one direction, resulting in a constant tensile force in Cable 2140. The constant force in Cable 2140 creates a torque on the variable diameter shaft (VDS) 130 that varies with its diameter. The variable torque on the VDS 130 is amplified through the geartrain 150 to the storage reel 160, resulting in a variable tensile force in Cable 1170 that is transmitted to the upper rail 190.

[0031] The relationship between the force transmitted to the upper rail 190 and the upper rail displacement is determined by the position of Cable 2 140 along the VDS 130 and VPS 120. The initial position of Cable 2140 is at the near end of the VDS 130 and VPS 120 (smaller end of VDS 130 in Fig.3). Movement of the upper rail 190 away from its starting position causes rotation of the VDS 130 , which in turn causes rotation of the VPS 120 via Cable 2140. As the VDS 130 and VPS 120 rotate together, Cable 2 140 winds around the VDS 130 and unwinds from around the VPS 120, moving from the near end toward the far end of the shafts (smaller to larger end of VDS 130 in Fig.3). As Cable 2140 moves up the larger diameter of the VDS 130, it increases the torque on the shaft and the force transmitted to the upper rail 190. When the upper rail 190 changes direction and moves back toward the starting position, Cable 2140 moves back down the shafts of the VDS 130 and VPS 120, and the force on the upper rail 190 decreases.

[0032] As Cable 2140 moves up the larger diameter of the VDS 130 , the VPS 120 will spin faster than the VDS 130. To maintain the orientation of Cable 2140 relative to the longitudinal axes of the VDS 130 and VPS 120, and ensure the cable 140 stays in the shaft grooves 122, 132, the pitch of the VPS 120 must decrease along the shaft length, i.e. the variable pitch shaft (VPS) 120. Figure 4(a) shows the VRF isolator prototype 100 with the upper rail 190 and Cable 2140 in the starting position. Figures 4(b) and 3 show Cable 2140 moving from the near end to the farend of the VDS 130 and VPS 120 as the upper rail 190 moves to the left and right of the starting position, respectively. Experimental Validation

[0033] The VRF isolator prototype 100 was subjected to a sinusoidal displacement with constant amplitude and frequency. The upper rail force versus displacement for ten cycles of motion is plotted in Fig 2(b), which shows that the VRF isolator 100 is working as intended. That is, the force-displacement characteristics are defined by high stiffness over small and large displacements with lower stiffness in between. Figure 2(b) shows some periodic fluctuation in the VRF isolator force during loading and unloading. This can be attributed to defects in the VDS and VPS shafts resulting from the 3D printing process. Such defects can be eliminated by machining the VDS 130 and VPS 120 from a harder material in place of using 3D printing.

[0034] The difference between the loading and unloading curve of the VRF isolator 100 in Fig.2(b) can be attributed to friction in and between the prototype components. The friction increases the force on the upper rail 190 as it moves away from the starting position and decreases the force on the upper rail 190 as it moves back toward the starting position. Friction in and between the prototype components leads to a significant amount of damping, which tends to dominate the force-displacement response presented in Fig. 2(b). However, it is not anticipated that this will be the case in a full-scale isolator for the following reasons: (1) the restoring force from the constant force springs (CFSs) will be significantly higher and (2) improved materials, fabrication, and component alignment will reduce friction in and between components.

[0035] A reduction of component friction in the full-scale isolator will reduce damping, thereby making it necessary to incorporate a supplemental damping element. For this purpose, a mechanical slip clutch will be mounted to the base plate and connected at the end of the VPS. The slip clutch will convert rotation of the VPS to a constant torque generated by friction within the clutch. The friction added to the full-scale isolator will have the same effect as the component friction in the prototype, that is, to increase the force on the upper rail during loading and decrease the force on the upper rail during unloading. Mechanical slip clutches are available in a wide range of torques to meet the damping requirement for a full-scale isolator. Model

[0036] To derive a mathematical expression describing the force-displacement relationship for the VRF isolator, only the upper rail, cable and pulley shown in Fig. 5 are first considered. It should be noted that only one pulley is shown for clarity, and the derivation will be provided for displacement of the upper rail in the positive x-direction (to the right in Fig. 5). Furthermore, the friction between, and inertia of, the isolator components is neglected. Cable 1 is initially in the vertical position, with one end attached to the upper rail at A and the other end tangent to the reel (not shown) at B. As the upper rail moves from point A to A’, the cable wraps around the pulley and the end tangent to the reel moves from point B to B’. The horizontal force F acting on the upper rail can be expressed in terms of the force Fc1 in Cable 1 by the following:In Eq.2, x is the upper rail displacement, rp is the radius of the pulley, and d is the distance between the center of the pulley and the upper rail.

[0037] The force Fc1in Cable 1 acting down on the pulley in Fig. 5 acts up on the reel in Fig.6(a). The reel is then connected through the geartrain in Fig.6(b) to the VDS in Fig.6(c), which in turn is connected to the VPS in Fig.6(d) through Cable 2. The VPS is connected to the constant force spring and the mechanical slip clutch, which generate the restoring force and damping force in the isolator, respectively. The relationship between the force Fc1in Cable 1 and the torques TSand TD produced by the constant force springs and the slip clutch is given by:

[0038] The force-displacement characteristics of the VRF isolator are derived from the variable torque on the VDS, which in turn, depends on the change in shaft diameter along the shaft length. The radius rVDof the shaft varies with the shaft length and may be defined as afunction of the shaft rotation θVD. Consider the schematic of the VDS shown in Fig.7. If the VDS has a base radius roand consists of n sections with the length and slope of the ithsection given by liand mi, respectively, then the radius of the ithsection is given by:where the contact angle φ in Eq. (6) is a function of the upper rail displacement x, as shown in Eq. (2). Design

[0039] The variable restoring force of the VRF isolator depends primarily on the pulley radii rpand their location d relative to the upper rail, as well as the variable diameter of the VDS. To determine the design parameters leading to the desired force-displacement chararacteristics of the VRF isolator, it is convenient to first express the force on the upper rail in the following nondimensional form:

[0040] To isolate the effect of the pulley radii rpand location d on the restoring force, the slope mi for all n sections of the VDS are set equal to zero (C1=C2=0), and the non-dimensional force on the upper rail simplifies to:Eq. 17 shows that the initial non-dimensional stiffness of the VRF isolator depends on β, or the ratio of the pulley radii rpto their location d relative to the upper rail. To examine the effect , the gear ratio of the geartrain is set to unity (f=1), the base radius of the VDS is setequal to the radius of the VPS (fo=1), and the non-dimensional force F* versus non-dimensionaldisplacement γ is plotted for various values of β in Fig.8. Figure 8 reveals that the nondimensional force is asymptotic, approaching unity with increasing non-dimensional displacement. Figure 8 also shows that higher values of β lead to a higher initial non-dimensional stiffness and a faster rate of transition of F*to unity.

[0041] Figure 8 shows that the initial non-dimensional stiffness of the VRF isolator is determined by the pulley radii rp along with their location d relative toupper rail, without any contribution from the VDS geometry. Therefore, the dimensional stiffness k1of the VRF isolator corresponding to the first region of the force-displacement curve may be designed by setting the initial slope of the VDS equal to zero (m1=0), and then selecting the isolator parameters to produce the desired stiffness for the initial portion of the force-displacement curve. The initial stiffness k1of the VRF isolator is determined by:

[0042] The stiffness of the VRF isolator for subsequent regions of the force-displacement curve may be designed by considering the asymptotic nature of the non-dimensional force F* in Fig. 8, which becomes nearly constant after some value of the non-dimensional displacement, depending on the value of β. For regions of the curve where the non-dimensional force F*is nearly constant, the isolator stiffness can be designed through the VDS geometry by selecting the slopes m2 through mn for the remaining sections of the shaft to achieve the desired stiffness. In these regions, the non-dimensional force from Eq.7 simplifies to:a e o - e so a s ess co espo g o ethsec o o e s gve y:of the VDS is:

[0043] Equations 18 and 21 show that the VRF isolator parameters may be selected to achieve a desired stiffness over different ranges of the isolator displacement. While many of the geometric parameters (i.e. d, rp, rR, ro, rVP, lVD) will be constrained in the interest of making the isolator compact, there isflexibility in the applied torques TS and TD, and the gear ratio f. That is because these components are readily available in a wide range of capacities.

[0044] Equations 18 and 21 show that the stiffness of the VRF isolator for different ranges of the isolator displacement depends on the sum of the restoring torque Ts from the constant force springs and the damping torque TD from the mechanical slip clutch. During loading, the damping torque TDadds to the restoring torque Ts(i.e. TD>0 in Eqs.18 and 21), thereby increasing the stiffness of the isolator. During unloading, the damping torque TD substracts from the restoring torque Ts (i.e. TD<0 in Eqs. 18 and 21), thereby decreasing the stiffness of the isolator. The difference in the loading and unloading stiffness indicates the amount of damping in the isolator (see Fig.2), which can be controlled by increasing or decreasing the damping torque TD. One benefit of the VRF isolator is that the damping can be increased or decreased withoutchanging the loading stiffness. This can be achieved by increasing and decreasing the damping and restoring torques proportionately so that the total torque during loading remains constant. As a result, the loading stiffness and damping of the isolator are independent of one another. It should be noted that there is a practical limit to the amount of damping torque TD that can be added to the isolator. To ensure that Cable 1 and 2 always remain in tension, the damping torque TDshould always be less than the restoring torque Ts(TD< Ts).

[0045] A force versus displacement plot generated using the VRF isolator model is shown in Fig. 2b, where it can be compared with the experimental results from the VRF isolator prototype. In the model, the torque from the mechanical clip clutch was adjusted to represent the friction observed in the prototype during testing, until good agreement between the model and experiment was obtained. Comparison of the results from the VRF isolator model and prototype show that the model is able to predict the VRF isolator force with good accuracy. Numerical Analysis

[0046] Numerical analyses were performed for two applications of the VRF isolator to evaluate its effectiveness for horizontal isolation of equipment. In each application, the isolated equipment was modeled as a single-degree-of-freedom (SDOF) system mounted on the floor of a building and only subject to one horizontal direction of building motion. The governing equation of motion for the system is:where m is the total isolated mass (i.e. equipment + platform), is the acceleration of the mass relative to the floor on which it is located, is theacceleration, and F(t) is the nonlinear restoring force of the VRF isolator exerted on the mass. The following assumptions were made in the analyses: (1) the isolation system consisted of an isolation platform supporting equipment with a VRF isolator installed at the isolation level, (2) the VRF isolator was assumed to have some initial stiffness in the first region of the force-displacement curve and zero stiffness thereafter, corresponding to an isolation system operating at the design level earthquake, and (3) the total isolated weight (i.e. platform + equipment) was 3000 lb.

[0047] Design of the VRF isolator for each application was determined from a parametric study in which the equipment peak displacement and absolute acceleration responses were obtained for different values of the isolator initial stiffness (i.e., restoring and damping torques). The inputs for the study were historical records of the floor accelerations corresponding to the locations on the buildings where the isolation systems were assumed to be installed. The initial stiffness and damping for each VRF isolator were selected by considering a balance between mitigating the equipment peak absolute acceleration and displacement responses. The selected values for each application are provided in the subsequent section along with a description of the buildings in which the isolation systems were installed and the floor acceleration inputs. 5-story RC building

[0048] The first numerical application is based on the full-scale five-story reinforced concrete (RC) building that was tested on the outdoor shake table at the University of California San Diego (UCSD). The building was fully furnished with nonstructural components and systems (NSCS), including a computer server that was rigidly connected to the third floor. Notably, resultsfrom experiments on the fixed-base building subjected to 100% of the ground acceleration record from the Pisco-Chincha (Ica) earthquake showed that the top of the computer server experienced a peak acceleration of 0.81g, which was more than double the peak floor acceleration (PFA) of 0.37g measured at the third floor during the same shaking.

[0049] In the numerical analyses it was assumed that the horizontal isolation system with the VRF isolator was installed on the third floor of the UCSD building and subjected to the same floor acceleration record from the Pisco-Chincha earthquake (PFA=0.37g). Results of the parametric study to determine the initial stiffness and damping of the VRF isolator for four different cases are shown in Table 1. The four cases correspond to equipment peak displacements (xmax) of 20 cm (8 in.) and 25 cm (10 in.) for 10% damping, and 18 cm (7 in.) and 25 cm (10 in.) for 20% damping. Also shown in the table is parameter x1, which is the VRF isolator displacement over which the initial stiffness is defined. This distance was chosen to be small to increase the range of displacement over which the VRF isolator operates with zero tangential stiffness, a strategy that aims to mitigate the acceleration response of the equipment.

[0050] Table 1. VRF isolator parameters and equipment peak responses at third floor of UCSD building with PFA=0.37g.

[0051] The results of the numerical analyses for the 5-story RC building with a 3rd floor PFA of 0.37g are shown in Table 1. They include the equipment peak absolute acceleration and displacement for each case considered. Percent reductions for the peak absolute acceleration of the equipment are also provided. The percent reduction R3 is calculated relative to the 3rd floor peak absolute acceleration, while the percent reduction Rcis calculated relative to the peak absolute acceleration at the top of the computer server (Rc) that was measured during the UCSD experiments. The percent reductions R3 show that the VRF isolator limited the transmission of the floor acceleration to the equipment, with values ranging from 84% in case 1 to 95% in cases 2 and 4. Higher reductions were observed for Rc, with values ranging from 93% to 98% for the same cases.

[0052] When seismic excitations travel through a building, they generate floor accelerations that are transmitted to any floor-mounted equipment. Without an isolation system, the acceleration experienced by the equipment can be of great magnitude since it vibrates near the fundamental frequency of the building, amplifying the seismic effects. It was previously shown that the peak absolute acceleration measured at the top of the floor-mounted computer server during the UCSD experiments was 0.81g, which was over double the peak absolute acceleration measured at the 3rd floor. However, the results of the numerical analyses show that with the VRF isolator in place, the flexible system and damping element absorb much of the seismic energy and reduce the amplitude of the accelerations transmitted to the equipment. This is further exemplified by the plots of the time-history absolute accelerations for the ground, 3rd floor, and equipment shown in Fig.9. Comparison of Figs.1(a) and (b) shows the amplification of the ground acceleration to the 3rdfloor of the UCSD building, where the peakabsolute acceleration increased from 0.20g to 0.37g. The 3rd floor peak absolute acceleration is then amplified to the top of the computer server where a peak absolute acceleration of 0.81g was measured. However, comparison of Figs. 1(a-b) with Figs.1(c-f) shows that transmission of 3rd floor absolute accelerations to the isolated equipment is limited by the VRF isolator, with the equipment experiencing peak absolute accelerations of 0.06g or less for all cases considered in the analysis.

[0053] For each absolute acceleration time history shown in Fig. 9, there is a corresponding time history of the instantaneous period of the signal along with an average period. Together, these time histories show that the proposed VRF isolator transforms the seismic acceleration profile from a high amplitude and frequency signal to one with a low quasi- constant amplitude and low frequency. The low frequency of the equipment absolute acceleration response shown in Fig.9 is due to the reduction in the VRF isolator effective stiffness when it oscillates in the zero-stiffness region of the force-displacement curve. The larger the displacement response of the isolator is, the lower the effective stiffness and the higher the effective period. It is interesting to note that for each VRF isolator in Fig.9, there is an increase in the effective period beginning around 25s, which corresponds to the highest intensity of floor shaking (see Fig.9 (b)). During this intense shaking, the isolators experience large displacements, a reduction in their effective stiffness, and an increase in their effective period. Therefore, the VRF isolator acts as a low-pass filter under the most intense time window of the floor acceleration, allowing low-frequency vibrations to pass through while attenuating higher- frequency excitations. This results in an equipment absolute acceleration response with a lower amplitude and frequency content than the floor acceleration. It is worth noting that theamplitude of the VRF isolator response is also bounded because the absolute accelerations of the isolators are proportional to their restoring force, which has a constant amplitude in the zero- stiffness region of the force-displacement curve. This is shown in the force-displacement loop for each VRF isolator in Fig.10, where a constant amplitude is observed in the zero-stiffness region of the curve. 10-story RC Building

[0054] The second numerical application is based on a ten-story reinforced concrete commercial building located in San Jose, California, and instrumented under the Strong Motion Instrumentation Program (CSMIP, Station 57355). The building was determined to have a fundamental period of 0.97s in the north-south (NS) direction and 0.85s in the east-west (EW) direction with minimal torsional effects. Three VRF isolators are defined in each direction to protect equipment on the roof, the fifth floor, and the basement of the building.

[0055] Results of the parametric study to determine the VRF isolator parameters at each floor and in each direction of the 10-story RC building are shown in Table 2. Also included in the table are the equipment peak absolute accelerations and displacements, isolator peak restoring forces, and percent reductions between the equipment and floor peak absolute accelerations. The VRF isolator parameters were selected considering the balance between mitigating the equipment peak absolute accelerations and displacements. It is interesting to note that the values of the isolator initial stiffness k1were higher in the NS direction than the EW direction at the 5th (5) floor and roof (R), while the opposite was found to be true at the basement (B). Furthermore, 20% damping resulted in lower equipment peak absolute accelerations than 10% damping at the upper floors in the EW direction but resulted in higher equipment peak absoluteaccelerations than 10% damping at the same floors in the NS direction. Meanwhile, 20% damping resulted in lower equipment peak absolute accelerations than 10% damping in both directions at the basement.

[0056] Percent reductions in the equipment peak absolute acceleration responses shown in Table 2 show that the VRF isolator limits the transmission of the floor accelerations to the equipment. The largest reductions were observed at the 5thfloor and roof in the EW direction of the building, where the reductions were 75% and 71%, respectively. In the NS direction, the percent reductions at the upper levels were smaller, and ranged from 26% to 46%. At the basement, percent reductions in the EW and NS directions were similar, with around a 25% reduction for the 10% damping case and a 54% reduction for the 20% damping case.

[0057] Table 2. VRF isolator parameters and equipment peak responses at each level and in each direction of 10-story RC building.

[0058] Time histories of the roof and equipment absolute accelerations and instantaneous periods are shown in Figs. 11-12 for the EW and NS directions. Time histories atthe roof are shown as this level experienced the highest intensity shaking and the VRF isolators achieved significant reductions in the peak acceleration responses. Also, only the VRF isolators that achieved the largest reductions in each direction are shown, that is, the isolator with 20% damping in the EW direction and 10% damping in the NS direction. The force versus displacement plots for these VRF isolators are also provided in Fig.13. Comparison of the absolute acceleration responses of the roof and the equipment in both directions again showed that the VRF isolators transformed the high amplitude and frequency floor accelerations to equipment accelerations with a low bounded amplitude and low frequency. As previously explained, the bounded amplitude is due to the constant VRF isolator force (see Fig.13), and the lower frequency is due to the reduction in the isolator effective stiffness, in the zero-stiffness region of the force- displacement curve. From the time histories of the instantaneous periods of the equipment acceleration, it is once again observed that the shift in period corresponds with the most intense seismic floor shaking. Alternate Embodiment of VRF isolator

[0059] In an alternate embodiment of the VRF isolator 300, the VPS, VDS, Cable 2, Geartrain, Reel, and Cable 1 are removed relative to the prototype 100, leaving only the base plate 310, constant force springs (CFS) 320 (each comprising a CFS drum 322), mechanical slip clutches (MSC) 330, pulleys 340, lower rails 350, sliders 360, and upper rail 370 as shown in Fig. 14. A second set of pulleys 342 is also added, and all four pulleys 340, 342 are mounted directly to the base plate 310 such that the plane of the pulleys 340, 342 and the plane of the base plate 310 are parallel (these planes are perpendicular in Fig. 3). One CFS 320 and one MSC 330 are, respectively, located on opposite sides of the pulleys 340, 342. The CFSs 320 are mounted to thebase plate 310 while the MSCs 330 are mounted to the CFSs 320 such that rotation of the CFS drum 322 causes the same rotation within the MSC 330. The cables 380, 390 of the CFSs 320, respectively, extend between the pulleys 340, 342 and are attached to a column 400 that extends down from the upper rail 370.

[0060] Displacement of the upper rail 370 in the direction of isolation causes the cables 380, 390 from the constant force springs 320 to wrap around the pulleys 340, 342 (see Fig.5) and causes rotation of the CFS drums 322. Rotation of the CFS drums 322 causes corresponding rotation of the MSCs 330, and the resulting CFS cable forces have a restoring component due to the springs 320 and a damping component due to the friction in the clutches 330. The force from the MSC 330 adds to the restoring force when the upper rail 370 is moving away from its starting position and subtracts from the restoring force when the upper rail 370 is moving toward its starting position.

[0061] In this embodiment of the VRF isolator 300, the horizontal force acting on the upper rail 370 varies with the upper rail displacement based on the geometry of the pulleys 340, 342, that is, the respective radii rpof the pulleys 340, 342 and the respective distance d (indicated in Fig. 14) from the center of the pulleys 340, 342 to the CFS cable attachment point on the column 400. This relationship is described by Eqs.1-2, where now the force Fc1 is the force in the cables 380, 390 of the CFSs 320 due to the deformation of the springs 320 and MSCs 330. The force-displacement curve for the alternate embodiment of the VRF isolator 300 is characterized by an increase in the isolator force over small isolator displacements followed by a constant force thereafter. These characteristics are the same as those of the VRF isolator model studied in the previously described numerical analysis (see Figs. 10 and 13). Therefore, similar isolationperformance to that observed in the numerical analysis is anticipated using the alternate embodiment.

[0062] Any embodiment of the present invention may include any of the optional or preferred features of the other embodiments of the present invention. The exemplary embodiments herein disclosed are not intended to be exhaustive or to unnecessarily limit the scope of the invention. The exemplary embodiments were chosen and described in order to explain some of the principles of the present invention so that others skilled in the art may practice the invention. Having shown and described exemplary embodiments of the present invention, those skilled in the art will realize that many variations and modifications may be made to the described invention. Many of those variations and modifications will provide the same result and fall within the spirit of the claimed invention. It is the intention, therefore, to limit the invention only as indicated by the scope of the claims.

Claims

WHAT IS CLAIMED IS:

1. A system adapted to provide variable restoring force isolation, said system comprising: a set of lower rails comprising a first lower rail and a second lower rail; a set of sliders comprising a first slider and a second slider, said first slider adapted to slide on said first lower rail, and said second slider adapted to slide on said second lower rail; an upper rail associated with said set of sliders such that said upper rail extends between said first slider and said second slider; and a variable restoring force device associated with said upper rail such that said variable restoring force device is adapted to provide a force to said upper rail such that said upper rail is adapted to slide relative to said set of lower rails.

2. The system of claim 1 further comprising an isolation platform, said upper rail associated with said isolation platform such that said isolation platform is adapted to move with said upper rail.

3. The system of claim 1 wherein said variable restoring force device comprises: a spring adapted to produce a substantially constant force; a first shaft having a variable pitch, said first shaft associated with said spring; and a second shaft having a variable diameter, said second shaft associated with said first shaft.

4. The system of claim 1 wherein said variable restoring force device comprises: a spring adapted to produce a substantially constant force; and a mechanical slip clutch associated with said spring.

5. The system of claim 1 further comprising at least at least one additional upper rail adapted to operate similarly to said upper rail.

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