Seismic Upgrade Conceptual Design material Shawn Callahan Mike Pollard 3/2/1011

“Brain storming” material At the end of the seismic restraint requirement review we agreed to have a brainstorming session to discuss conceptual designs. The following support material is supplied as back ground material.

Project Milestones (as of 2/25/11) System req review (completed 2/25/11) PDR 3/29/11 DDR 5/3/11 K1 installation and testing complete 7/19/11 K2 installation and testing complete 8/23/11 Documentation complete 8/30/11 ORR 9/5/11

USGS data 10/15/2006 collected on summit of Mauna Kea Overview: Ground movement graphs (slide 5) Acceleration data: N-S, E-W, and vertical (slide 6) Fast Fourier Transform of E-W accelerations (slide 7)

For USGS accelerometer data see: \TSD Planning\TSD Development Projects\Seismic Upgrade\Seismometer data from 2006 seismic event

FFT of E-W accelerations. First 20 seconds during the maximum intensity. note: over time the peak frequency varies about +/- 1 Hz with a broad range to excite many resonances in telescope

Existing azimuth restraints Keck 1 and Keck 2 have different seismic restraints systems! Keck 2 restraints built into radial hydrostatic support. (slide 10, 11) Keck 1 has additional large (white) radial restraints. (Slide 9) ½” MHMV pads provides crushable interface between the radial hydrostatic pad supports and the az journal (K1&K2) Uplift restraint is supplied by radial pads (K1 &K2) (see slide 11, 12)

K1 Seismic Restraint note: white nylon(?) pad between restraint and journal bearing

Keck 1 restraint system

Hydrostatic radial support

Damage from 2006 earthquake.

FEA model were made of the K2 HBS radial pad support to understand the forces exerted during the 2006 earthquake. Slide 12 shows ~16mm permanent distortion. Supports starts to yield at 100,000 lbs radial load (far exceeded) MathCAD model of seismic acceleration applied to 300T telescope estimates support saw > 150,000 lbs. Note: stress in UHMV pad ~70,000 psi. (yields at 5800 psi.) Bolt heads restraining pad could damage journal?

FEA models of K2 hydrostatic bearing support. Mesh model (slide 15) Von-Mises Equivalent Stress (slide 16)

von-Mises stress (16mm deflection)

FEA models were made of the of AZ journal assembly and grout to understand how forces were distributed. Mesh model of grout and anchors (slide 18) Mesh model radial support applying load to azimuth journal (slide 19) 300T dummy load (note does not model overturning moment) with 0.4g acceleration (slide 20) Resulting Von-Mises stress in radial support (slide 21) Stress in grout (HBS on) (slide 22, 23)

Model of grout with anchor hardware

Journal bearing, grout, and radial pad support

0.4 g acceleration vector

Von Mises Stress (way) beyond yield strength of UHMW (5800 psi) pads and steel (70kpsi) radial pad supports

Stress in grout ~3x yield stress frictionless journal to grout

Grout stress >20kpsi Grout strength ~6-8kpsi

Conclusions: current system In a zone 4 “rare earthquake” event: journal bearing slips Grout under journal yields (cracks) Anchor bolts securing journal bend or break. In zone 4 “very rare earthquake” uplift restraint failure likely (need further analysis)

The azimuth journal drawings KE sheet 2 of 3 shows a cross section of the az bearing journal. The center of the telescope is to the left. Sheet 1 shows the top down view of the journal bearing.

Eccentricity of track Tomas Krasuski et. al. measured the radial run out of az journal 3/29/2009 (slide 29) Based on telescope logs showing telescope position during 2006 earthquake, journal shape is elongated along direction of quake

What happens if HBS off? Add friction and add overturning moment due to telescope weight above azimuth restraints. Model parameters Frictional contact elements between hydrostatic pad and journal (COF= 0.08) Frictional contact elements between grout and journal (COF 0.45) dummy mass wt. 300 tons 150,000 lbs weight applied to top of HBS pad Horizontal acceleration 0.4g (154 in/s^2) in y-direction (Zone 4 rare earthquake requirement) Grout fixed at bottom Dummy telescope vertical displacement fixed (assume only horizontal displacement)

FEA model results Mesh model showing loads Mesh model showing grout Stress in grout (beyond yield) Minimum principal stress (tensile) detail

Course mesh model refined mesh at grout holes

Course mesh of grout (Journal surface hidden) Coefficient of friction (COF) COF grout-steel 0.45 COF lubed steel-steel 0.08

Minimum principal stress in grout stress concentration at anchor holes beyond yield

Minimum principal stress

Conceptual Design questions Can we spread the load over more of the journal/ anchor bolts? The current clearance is only ~11 mm. Can we increase clearance to decrease accelerations? (Acceleration inversely proportional to stopping distance)

Conceptual Design Strategies: active control: Magneto restrictive An active control system is designed to induce artificial damping to the isolation structure of a building without increasing its stiffness. The control forces needed are exerted only on the base of the structure, and the system is quite practical. This control system can operate efficiently if the time delay that exists in the actual system does not exceed its critical value. The critical delay time depends on both the fundamental frequencies of the structure and the artificial damping introduced by the control system.

Active Restraints Pros: Active isolators provide excellent energy dissipation over a wide range of frequencies. Damping does not add to system stiffness. Tunable to allow improved radial stiffness during operations yet use the maximum travel during a seismic event. Cons: Expensive Complex systems: requires ultra high reliability Must be maintained

Passive restraints (Pros) Pros: Relatively inexpensive Simple systems Little maintenance Cons: Damping increases natural frequency Effectiveness dependant on seismic input frequencies. Resonant maximum natural frequency close to seismic excitation frequencies: “Reduction in transfer of vibratory forces is obtained only when the ratio of the disturbing frequency to the natural frequency is greater than 1.414”

Ordinate: 2006 seismic excitation frequencies between 2-10 Hz. Minimum stiffness (K) set by our 7/16” travel. Abscissa: Calculated static deflection is 1.5” (just off right of chart) It will be difficult to get above the region of “magnification factor” or resonances with passive restraints. (Sorry, still looking for a clearer graphic.)

Adding damping: Shocks Damping c is conveniently referenced to Critical Damping c c which is the value of damping at which a system will not oscillate when disturbed from equilibrium. See: m/page306.html

under-damped oscillator Adding damping increases the “damped natural frequency”. This means we need to lower the stiffness of the system to achieve the same accelerations (fragility factor). This is counter productive to our goal to increase operational radial rigidity.

Recommended reading Excellent survey of questions and answers from designers of passive seismic restraint. Hysteretic Damping Devices: Testing of seismic isolators and dampers-Consierations and Limitations by Ian D. Aiken

End of presentation