Chapter 3 Passive Protective Schemes for Rail- Counterweight System

Transcription

1 Chapter 3 Passive Protective Schemes for Rail- Counterweight System The analyses in the previous chapter have shown that the rail-counterweight systems are vulnerable to overstressing of the guide rails even under medium earthquakes. Although the parametric study described several possibilities of reducing the stress in the rail such as by changing the gap sizes, by increasing the size of rails, and by the installation of intermediate tie-brackets, some of these can be used and other may have some other problems. For example, the tie brackets may be useful, but changing the gaps may be associated with other mechanical effects and the riding quality in the elevator. Based on the need for having a working elevator all the time, especially in critical facilities like hospitals, the use of more advanced protective system to enhance their performance is much desirable. Structural engineers have used, and considered the use of, the passive and active control methods to protect structural systems from dynamic earthquake effects. One of the passive methods used for reducing seismic responses of a structural system is to increase the energy dissipating capability of the structure with supplemental damping devices placed at several discrete locations on the structure. Other passive schemes that have been used in building 70

2 structures include base isolations and tuned mass dampers. Besides these passive methods, active schemes using external force and semi-active schemes which combined the energy dissipating capability with additional low power changeable reactive force have also been considered in building and bridge structures. It is, therefore, natural to consider some of these methods for mitigation seismic effects on mechanical systems such as the rail-counterweight systems to improve the performance of elevators in strong earthquakes. In this chapter, the use of the damping enhancement schemes with additional damping devices and tuned vibration absorber will be examined. The use of active and semi-active schemes is discussed in the next chapter. 3.1 Supplemental Damping Increasing the damping of a structural system generally will improve its energy dissipation capability and thus reduce its dynamic responses. This is also true for the rail-counterweight system of elevator. Indeed, by merely increasing the modal damping ratio of the system, the response of the rail-counterweight system can be reduced quite significantly. Table 3.1 shows the reduction of maximum stress in the rail under actual Northridge earthquake if the modal damping ratio of the system is increased from the initial value of 2% to 3%, 4%, and 5%. Almost 20% reduction can be achieved when the modal damping ratio is amplified to 5%. Because of the tight space in the rail-counterweight system, however, there is not much space to install the additional discrete dampers. One possibility that is examined in this study is to place the dampers parallel to the spring at the roller guide assemblies. Modal damping ratios obtained after the installation of small viscous dampers of different sizes in parallel with the springs in the roller guide assemblies are shown in Table 3.2. The modal damping ratio of the first mode on the in-plane and out-of-plane direction can be easily increased up to 71

3 5% and more for higher modes. However, these numbers are only valid when the roller guide assemblies are contributing to the vibration of the rail-counterweight system. This is not the case if the clearance between the restraining plate and the rail is closed. When contact happens, the damper becomes ineffective, as it could not have any relative motion to dissipate energy. Thus the dampers become ineffective when the high stresses in the rails usually occur. Table 3.3 shows this clearly where the reductions in the maximum stress in the rails under actual Northridge earthquake for different sizes of discrete dampers are presented. The maximum stress in the rail can only be reduced by about 5%. Thus, the use of the discrete dampers on the roller guide assemblies is not very effective in improving energy dissipation capability of the system. 3.2 Tuned Mass Damper The arrangement of the stacked weights within the frame of the counterweight provides the incentive to use the top part of the weight as a tuned mass damper with minimal changes in the counterweight configuration. The weight blocks are tied together and restrained from moving relative to each other by tie rods that anchor them to the counterweight frame. For the response control purpose, the top portion of the weights can be separated and allowed to move relative to the rest of the counterweight by providing small rollers and making appropriate slot at the location of the tie rods to accommodate the motion of the tuned mass damper. Spring and damper are placed between this isolated mass and the counterweight frame to make it a mass damper system. This is schematically shown in Figure 3.1. Actuator or semi-active device can also be placed between the mass and the frame to provide force to convert the tuned mass damper to an active or a semi-active system. This will be discussed in Chapter 4. 72

4 It is noted that this mass damper can only move in the in-plane direction, thus it will only be effective to reduce the response due to the in-plane motion of the counterweight. However, it has been shown in the previous chapter that the in-plane motion in any case happens to be more critical than the out-of-plane motion, and thus scheme should be able to reduce the more severe seismic effects. In the following subsection, the equations of motion that now include the motion of the tuned mass damper are now developed, followed by a numerical simulation study to examine the effectiveness of the proposed protective scheme Equations of Motion The in-plane equations of motion, equation 2.24, of the counterweight developed in Chapter 2 must now be supplanted to include the motion of the top part of the mass relative to the remaining counterweight mass below. The equation of motion of this separated mass damper can be written as ( 1 ) ( 1 ) µ mu!! c T + ct u! T u! c µ u! e + kt u T uc µ ue = µ mx!! c c (3.1) where µ is the ratio of the damper mass to the total mass of the counterweight m c, k T and c T are the stiffness and damping coefficients of the spring and damper attached between the mass damper and the counterweight frame, respectively, and u T is the displacement of the TMD mass relative to the building. Other variables are the same as used in the previous chapter. The tuned mass damper is assumed to have translation degree of freedom only. In other words, the whole counterweight, including the mass damper, rotates as a single body. The total mass of the counterweight including the mass damper part is assumed to be the same as the original system without TMD. The mass ratio µ also reflects the eccentric placement of 73

5 the TMD with respect to the remaining mass. With this assumption, the effect of the size of the roller bearings under the mass damper to the eccentricity is ignored. Since the motion of the tuned mass damper is only in the in-plane direction of the counterweight and the analysis of in-plane and out-of-plane motions can be carried out separately, the following analysis is performed for the in-plane motion only. The final results of the response, however, take into account both in-plane and out-of-plane motions of the counterweight. Combining (3.1) with the equations of motion of the rail-counterweight system in the inplane direction (2.24), we have Mq!! + Cq! + Kq = Mx!! + f (3.2) i i i i i i i i where the size of mass, damping, and stiffness matrices are now 3 3 and u T is added to the displacement vector q i 1 µ 0 0 M m c 0 γ 1 0 i = (3.3) 0 0 µ T T ( 1 µ ) T ( 1 µ ) ( 1 2 µ ) ( 1 µ ) ( 1 µ ) k11 + k k12 + k k K i = k12 + kt k22 + kt kt (3.4) kt kt k T T T ( 1 µ ) T ( 1 µ ) ( 1 2 µ ) ( 1 µ ) ( 1 µ ) c11 + c c12 + c c C i = c12 + ct c22 + ct ct (3.5) ct ct c T uc q i = ue (3.6) u T 74

6 3.2.2 Numerical Results The effectiveness of the tuned mass damper system is examined by comparing the maximum stress in the rails under the uncontrolled and controlled conditions. The counterweight properties as well as the building are the same as those used in Chapter 2. The damping coefficient for the TMD system is fixed at 5%, while the stiffness is varied to obtain the best tuning frequency. Two recorded earthquake motions, Northridge and El Centro, and an ensemble of 50 synthetic accelerations time histories with broadband frequency characteristics are used as the base motion of the building. One interesting property of the rail-counterweight system is the change of frequency during vibration due to contacts between the restraining plate and the rail and between the frame and the rail. There are several possibilities for the frequency of the system based on these contacts, namely no contacts, contact at the upper or lower roller guide only, contact at both roller guide assemblies, and contact at both roller guides and between the frame and the rail. Each of these cases has different frequency. This creates problem as to which frequency the mass damper system should be tuned. In this study, the fundamental frequency when contact happens at both upper and lower roller guides is chosen as the nominal tuning frequency. The analyses are then carried out for different frequency ratios in order to obtain the most effective value. Figures 3.2 and 3.3 show the ratio of the maximum stress in the rail as a function of frequency ratio for different mass ratio under the actual Northridge and El Centro earthquakes, respectively. The stress ratio in these figures is the ratio between the maximum stress in the rail in the controlled and uncontrolled systems. Under Northridge earthquake, the maximum stress of the rail can be reduced to about 80% of its uncontrolled value for 75

7 frequency ratio of TMD between 0.8 and 1.0. Within this frequency range, there is not much difference in the results of all three mass ratios; with the 20% mass ratio has the best results at the frequency ratio of The results for lower intensity earthquake, represented by the actual El Centro earthquake in Figure 3.3, the best results also fall within the same frequency range but the reduction percentage is somewhat less. The 10% mass ratio gives the best results for this case. In Figure 3.4 the maximum ground acceleration of the El Centro earthquake is normalized to 0.9g to make it more comparable to the Northridge earthquake, and the results indicate similar trends with the Northridge earthquake. The next set of figures present the maximum displacement of the mass damper. This displacement of the mass damper must be checked because there is only limited space within the counterweight frame for the mass damper motion. Figures 3.5 to 3.7 show that the maximum displacement is lower for the TMD with higher frequency ratio. The maximum displacement for the frequency ratio 0.8 to 1.0 that gives the best stress reduction can be considered acceptable. The displacement is less than two inches for the high intensity earthquakes and even less than one inch for the actual El Centro earthquake. Figure 3.8 shows the mean plus one standard deviation of the peak stress in the rail under an ensemble of synthetic acceleration with similar frequency characteristics. The frequency ratio of the system is fixed at 0.9. This figure shows that the tuned mass damper can moderately reduce the peak stress and there is not much difference in the results of different mass ratio. The mean and absolute maximum values of peak displacement of the mass damper are plotted in Figure 3.9, which are low enough to be accommodated in the counterweight frame. The effect of different mass ratio, especially for strong earthquakes, is more evident in the fragility curves shown in Figure 3.10 where the 10% mass ratio performs 76

8 better. The probability of failure of the rail is quite low for ground acceleration lower than 0.5g. They can however be shown on a semi-log scale as in Figure Concluding Remarks The effect of two passive protective methods on the seismic response of the railcounterweight system has been presented in this chapter. Increasing modal damping ratio appears to be useful in reducing the maximum stress in the rail, and installing discrete damper devices parallel to the helical spring in the roller guide assemblies can help in increasing the modal damping ratio. However, the roller guide assemblies (thus, the dampers too) become ineffective when contact between the restraining plate and the rail occurs. Therefore, there is not much reduction in the stress that can be achieved with this method. Another protective method that is moderately effective is utilizing the top part of the weights as tuned mass damper. The numerical results show that a properly designed tuned mass damper can reduce the maximum stress in the rail by about 20%. The optimum choice of the tuning frequency is not very clear, but the best results are achieved when the frequency of the mass damper system is between 0.8 to 1.0 times the frequency of the original system with contact on both upper and lower roller guide assemblies. Within this frequency range, the maximum displacement of the mass damper is also low enough to be accommodated on the system. The TMD with smaller mass (10% and 20% of the total mass) is found to be moderately effective in reducing the response of the counterweight. The performance of this tuned mass damper system can be improved by using it in an active mode. This can be done by installing an actuator between the mass damper and the frame and employing active control scheme to determine the needed external force. This approach is discussed in the next chapter, along with semi-active control method. 77

9 Figure 3.1 Counterweight with part of weights acting as mass damper. 78

10 µ = 10% µ = 20% µ = 30% Stress ratio Frequency ratio Figure 3.2 Stress ratio for different size of mass damper as a function of frequency ratio, Northridge earthquake 0.843g. 79

11 µ = 10% µ = 20% µ = 30% Stress ratio Frequency ratio Figure 3.3 Stress ratio for different size of mass damper as a function of frequency ratio, El Centro earthquake 0.348g. 80

12 µ = 10% µ = 20% µ = 30% Stress ratio Frequency ratio Figure 3.4 Stress ratio for different size of mass damper as a function of frequency ratio, El Centro earthquake 0.9g. 81

13 7 6 µ = 10% µ = 20% µ = 30% 5 Max. TMD displ. [in.] Frequency ratio Figure 3.5 Maximum displacement of different size of mass damper as a function of frequency ratio, Northridge earthquake 0.843g. 82

14 7 6 µ = 10% µ = 20% µ = 30% 5 Max. TMD displ. [in.] Frequency ratio Figure 3.6 Maximum displacement of different size of mass damper as a function of frequency ratio, El Centro 0.348g. 83

15 7 6 µ = 10% µ = 20% µ = 30% 5 Max. TMD displ. [in.] Frequency ratio Figure 3.7 Maximum displacement of different size of mass damper as a function of frequency ratio, El Centro 0.9g 84

16 Stress [ksi] Uncontrolled µ = 10% µ = 20% µ = 30% Max. ground acceleration [g] Figure 3.8 Mean plus one standard deviation of peak stress in the rail 85

17 2.5 2 Displacemen [in.] µ = 10% µ = 20% µ = 30% 0.5 mean absolute max Max. ground acceleration [g] Figure 3.9 Mean and absolute maximum of peak displacement of the mass dampers. 86

18 Uncontrolled µ = 10% µ = 20% µ = 30% 0.01 Probability of failure Max. ground acceleration [g] Figure 3.10 Fragility curves for different size of mass dampers. 87

19 Probability of failure Uncontrolled µ = 10% µ = 20% µ = 30% Max. ground acceleration [g] Figure 3.11 Fragility curves for different size of mass dampers. 88

20 Table 3.1 Reduction in maximum stress in the rail with increasing modal damping ratio, actual Northridge earthquake Damping Ratio Reduction in maximum stress 3% 10.2% 4% 15.9% 5% 19.9% Table 3.2 Modal damping ratio of the rail-counterweight system with additional dampers parallel to the spring at the roller guide assemblies Additional damping In-plane Out-of-plane [lb-s/in] Mode 1 Mode 2 Mode 1 Mode 2 Mode Table 3.3 Reduction in maximum stress with discrete damping devices at the roller guide assemblies, actual Northridge earthquake Additional damping [lb-s/in] Reduction in maximum stress % % % 89