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At least 127 records · Page 7

Stiffener attachment concepts for graphite-epoxy panels designed for postbuckling strength

Stiffener attachment concepts for suppressing or delaying the onset of the skin-stiffener separation failure mode in graphite-epoxy compression panels designed for postbuckling strength were experimentally studied. The effectiveness of these concepts was evaluated using panels with 16-ply skins and a single centrally-located I-shaped stiffener with both static and cyclic compressive loadings. Analytical results suggest that tailoring the relative thicknesses of the panel skin, stiffener attachment flange, and the stiffener web rotational stiffness can minimize the adverse effects of high interface shear and normal stresses. Interface stress levels may be reduced by tapering the thickness of the stiffener attachment flange and properly selecting the stacking sequences of the skin and stiffener attachment flange laminates.

Dickson, John N.↗

Development of a new seal for use on large openings of pressurized spacecraft

The goal of this project was to design, build, and test an example of the seal invented by the author for use on Space Station Freedom and patented in 1991. The seal features a metallic spring core and replaceable elastomeric sealing elements. The metallic spring is designed to retain the sealing force of the elastomeric element against both sides of face seal gland for any specified amount of waviness or separation of the glands. A seal able to tolerate at least 1.3 mm (0.05 in) of flange distortion or separation and a test fixture of this seal which allowed direct comparison testing of O-rings were built. These designs were tested to compare leakage at different amounts of flange deflection. Results of the testing show the development seal exceeded its requirement to seal 1.3 mm of flange separation by 1 mm. This compared with the O-ring leakage, increasing dramatically at 0.5 mm of separation. The development seal also leaked at a lower rate than the O-ring seals in all tests.

Weddendorf, B.↗

MPLM On-Orbit Interface Dynamic Flexibility Modal Test

Now that the International Space Station (ISS) is being constructed, payload developers have to not only verify the Shuttle-to-payload interface, but also the interfaces their payload will have with the ISS. The Multi Purpose Logistic Module (MPLM) being designed and built by Alenia Spazio in Torino, Italy is one such payload. The MPLM is the primary carrier for the ISS Payload Racks, Re-supply Stowage Racks, and the Resupply Stowage Platforms to re-supply the ISS with food, water, experiments, maintenance equipment and etc. During the development of the MPLM there was no requirement for verification of the on-orbit interfaces with the ISS. When this oversight was discovered, all the dynamic test stands had already been disassembled. A method was needed that would not require an extensive testing stand and could be completed in a short amount of time. The residual flexibility testing technique was chosen. The residual flexibility modal testing method consists of measuring the free-free natural frequencies and mode shapes along with the interface frequency response functions (FRF's). Analytically, the residual flexibility method has been investigated in detail by, MacNeal, Martinez, Carne, and Miller, and Rubin, but has not been implemented extensively for model correlation due to difficulties in data acquisition. In recent years improvement of data acquisition equipment has made possible the implementation of the residual flexibility method as in Admire, Tinker, and Ivey, and Klosterman and Lemon. The residual flexibility modal testing technique is applicable to a structure with distinct points (DOF) of contact with its environment, such as the MPLM-to-Station interface through the Common Berthing Mechanism (CBM). The CBM is bolted to a flange on the forward cone of the MPLM. During the fixed base test (to verify Shuttle interfaces) some data was gathered on the forward cone panels. Even though there was some data on the forward cones, an additional modal test was performed to better characterize its behavior. The CBM mounting flange is the only remaining structure of the MPLM that no test data was available. This paper discusses the implementation of the residual flexibility modal testing technique on the CBM flange and the modal test of the forward cone panels.

Bookout, Paul S.↗

Cooling of Gas Turbines I - Effects of Addition of Fins to Blade Tips and Rotor, Admission of Cooling Air Through Part of Nozzles, and Change in Thermal Conductivity of Turbine Components

An analysis was developed for calculating the radial temperature distribution in a gas turbine with only the temperatures of the gas and the cooling air and the surface heat-transfer coefficient known. This analysis was applied to determine the temperatures of a complete wheel of a conventional single-stage impulse exhaust-gas turbine. The temperatures were first calculated for the case of the turbine operating at design conditions of speed, gas flow, etc. and with only the customary cooling arising from exposure of the outer blade flange and one face of the rotor to the air. Calculations were next made for the case of fins applied to the outer blade flange and the rotor. Finally the effects of using part of the nozzles (from 0 to 40 percent) for supplying cooling air and the effects of varying the metal thermal conductivity from 12 to 260 Btu per hour per foot per degree Farenheit on the wheel temperatures were determined. The gas temperatures at the nozzle box used in the calculations ranged from 1600F to 2000F. The results showed that if more than a few hundred degrees of cooling of turbine blades are required other means than indirect cooling with fins on the rotor and outer blade flange would be necessary. The amount of cooling indicated for the type of finning used could produce some improvement in efficiency and a large increase in durability of the wheel. The results also showed that if a large difference is to exist between the effective temperature of the exhaust gas and that of the blade material, as must be the case with present turbine materials and the high exhaust-gas temperatures desired (2000F and above), two alternatives are suggested: (a) If metal with a thermal conductivity comparable with copper is used, then the blade temperature can be reduced by strong cooling at both the blade tip and root. The center of the blade will be less than 2000F hotter than the ends; (b) With low conductivity materials some method of direct cooling other than partial admission of cooling air is essential. From this study, it can be deduced that indirect cooling of turbine blades will not make possible large increases in gas temperature.

Brown, Byron↗

Improving Strength of Postbuckled Panels Through Stitching

The behavior of blade-stiffened graphite-epoxy panels with impact damage is examined to determine the effect of adding through-the-thickness stitches in the stiffener flange-to-skin interface. The influence of stitches is evaluated by examining buckling and failure for panels with failure loads up to 3.5 times greater than buckling loads. Analytical and experimental results from four configurations of panel specimens are presented. For each configuration, two panels were manufactured with skin and flanges held together with through-the-thickness stitches introduced prior to resin infusion and curing and one panel was manufactured with no stitches holding the flange to the skin. No mechanical fasteners were used for the assembly of any of these panels. Panels with and without low-speed impact damage were loaded to failure in compression. Buckling and failure modes are discussed. Stitching had little effect on buckling loads but increased the failure loads of impact-damaged panels by up to 30%.

Jegley, Dawn C.↗

Low NO.sub.x combustor

A combustor includes a dome assembly having radially outer and inner liners joined thereto and defining therebetween a combustion zone. The dome assembly includes at least one annular dome having a pair of axially extending first flanges between which are disposed a plurality of circumferentially spaced apart carburetors for discharging a fuel/air mixture into the combustion zone for generating combustion gases. An annular heat shield includes a pair of axially extending legs integrally joined to a radially extending face in a generally U-shaped configuration, with the face including a plurality of circumferentially spaced apart ports disposed concentrically with perspective ones of the carburetors for allowing the fuel/air mixture to be discharged therefrom through the heat shield. At least one of the heat shield legs includes a plurality of circumferentially spaced apart mounting holes disposed adjacent to a respective one of the dome flanges, and a plurality of mounting pins are fixedly joined to the dome flange and extend radially through respective ones of the mounting holes without interference therewith for allowing unrestrained thermal movement between the heat shield and the dome while supporting the heat shield against axial pressure loads thereon. In a preferred embodiment, the dome assembly includes three domes having respective ones of the heat shield, and respective baffles are spaced from the heat shields for providing impingement cooling thereof.

Halila, Ely E.↗

Self-locking double retention redundant pull pin release

A double-retention redundant pull pin release system is disclosed. The system responds to a single pull during an intentional release operation. A spiral-threaded main pin is seated in a mating bore in a housing, which main pin has a flange fastened thereon at the part of the main pin which is exterior to the housing. Accidental release tends to rotate the main pin. A secondary pin passes through a slightly oversized opening in the flange and is seated in a second bore in the housing. The pins counteract against one another to prevent accidental release. A frictional lock is shared between the main and secondary pins to enhance further locking of the system. The secondary pin, in response to a first pull, is fully retracted from its bore and flange hole. Thereafter the pull causes the main pin to rotate free of the housing to release, for example, a parachute mechanism.

Killgrove, Thomas O.↗

High speed rotor assembly shroud

An improved rotor assembly shroud includes at least one reinforcing flange on the upper surface of the shroud. The strength provided by the reinforcing flange allows for a smaller shroud thickness resulting in a net reduction of shroud mass. The lower shroud mass reduces the centrifugal stress on the rotor assembly blade during operation. The strength provided by the reinforcing flanges also significantly reduces the centrifugal bending stress on the shroud during operation. The shroud mass may be further reduced by tapering the shroud leading and trailing edges or, for shrouds incorporating a damper, by providing a damper cavity with a lower diameter surface defining an opening therethrough.

Miller, Jeff H.↗

Characterization of Fatigue Damage for Bonded Composite Skin/Stringer Configurations

The fatigue damage was characterized in specimens which consisted of a tapered composite flange bonded onto a composite skin. Quasi-static tension tests were performed first to determine the failure load. Subsequently, tension fatigue tests were performed at 40%, 50%, 60% and 70% of the failure load to evaluate the debonding mechanisms. For four specimens, the cycling loading was stopped at intervals. Photographs of the polished specimen edges were taken under a light microscope to document the damage. At two diagonally opposite corners of the flange, a delamination appeared to initiate at the flange tip from a matrix crack in the top 45deg skin ply and propagated at the top 45deg/-45deg skin ply interface. At the other two diagonally opposite corners, a delamination running in the bondline initiated from a matrix crack in the adhesive pocket. In addition, two specimens were cut longitudinally into several sections. Micrographs revealed a more complex pattern inside the specimen where the two delamination patterns observed at the edges are present simultaneously across most of the width of the specimen. The observations suggest that a more sophisticated nondestructive evaluation technique is required to capture the complex damage pattern of matrix cracking and multi-level delaminations.

Paris, Isabelle↗

Assessment of Composite Delamination Self-Healing Via Micro-Encapsulation

Composite skin/stringer flange debond specimens manufactured from composite prepreg containing interleaf layers with a polymer based healing agent encapsulated in thin walled spheres were tested. As a crack develops and grows in the base polymer, the spheres fracture releasing the healing agent. The agent reacts with catalyst and polymerizes healing the crack. In addition, through-thickness reinforcement, in the form of pultruded carbon z-pins were included near the flange tips to improve the resistance to debonding. Specimens were manufactured with 14 plies in the skin and 10 plies in the stiffener flange. Three-point bend tests were performed to measure the skin/stiffener debonding strength and the recovered strength after healing. The first three tests performed indicated no healing following unloading and reloading. Micrographs showed that delaminations could migrate to the top of the interleaf layer due to the asymmetric loading, and hence, bypass most of the embedded capsules. For two subsequent tests, specimens were clamped in reverse bending before reloading. In one case, healing was observed as evidenced by healing agent that leaked to the specimen edge forming a visible "scar". The residual strength measured upon reloading was 96% of the original strength indicating healing had occurred. Hence, self-healing is possible in fiber reinforced composite material under controlled conditions, i.e., given enough time and contact with pressure on the crack surfaces. The micro-encapsulation technique may prove more robust when capsule sizes can be produced that are small enough to be embedded in the matrix resin without the need for using an interleaf layer. However, in either configuration, the amount of healing that can occur may be limited to the volume of healing agent available relative to the crack volume that must be filled.

O'Brien, T. Kevin↗

Using Aerogel-Based Insulation Material To Prevent Foam Loss on the Liquid-Hydrogen Intertank

Uninsulated areas on cryogenic propellant tanks and feedlines cause moisture in the air to condense or ice to form. Flange joints, bracket supports, expansion bellows, and other cavities are uninsulated by design. These areas cannot be sealed because conventional thermal insulation materials would restrict mechanical articulations. Aerogel-based thermal insulation systems are able to seal critical locations such as the liquid-oxygen (LO2) feedline bellows. A new thermal insulation system was also necessary between the intertank wall, flange, and the liquid-hydrogen (LH2) tank dome, where there is a cavity (or crevice) with an exposed 20-K surface. When nitrogen gas is used for purging within the intertank volume, it condenses on this cold surface. Some solid nitrogen may also form on the colder side of the crevice. Voids or discontinuities within the foam can pressurize and cause areas of foam to weaken and break off, reducing thermal efficiency and creating potentially dangerous debris. To prevent this foam loss, we developed a thermal insulation system using bulk-fill aerogel material and demonstrated it with a one-tenth-scale model of the LH2 intertank flange area

Source record↗

In-Situ Focusing Inside a Thermal Vacuum Chamber

Traditionally, infrared (IR) space instruments have been focused by iterating with a number of different thickness shim rings in a thermal vacuum chamber until the focus meets requirements. This has required a number of thermal cycles that are very expensive as they tie up many integration and test (I&T)/ environmental technicians/engi neers work ing three shifts for weeks. Rather than creating a test shim for each iteration, this innovation replaces the test shim and can focus the instrument while in the thermal vacuum chamber. The focus tool consists of three small, piezo-actuated motors that drive two sets of mechanical interface flanges between the instrument optics and the focal- plane assembly, and three optical-displacement metrology sensors that can be read from outside the thermal vacuum chamber. The motors are used to drive the focal planes to different focal distances and acquire images, from which it is possible to determine the best focus. At the best focus position, the three optical displacement metrology sensors are used to determine the shim thickness needed. After the instrument leaves the thermal vacuum chamber, the focus tool is replaced with the precision-ground shim ring. The focus tool consists of two sets of collars, one that mounts to the backside of the interface flange of the instrument optics, and one that mounts to the backside of the interface flange of the focal plane modules. The collars on the instrument optics side have the three small piezo-actuated motors and the three optical displacement metrology systems. Before the instrument is focused, there is no shim ring in place and, therefore, no fasteners holding the focal plane modules to the cameras. Two focus tooling collars are held together by three strong springs. The Orbiting Carbon Observatory (OCO) mission spectrometer was focused this way (see figure). The motor described here had to be moved five times to reach an acceptable focus, all during the same thermal cycle, which was verified using pupil slicing techniques. A focus accuracy of .20.100 microns was achieved.

Liebe, Carl Christian↗

Tool for Insertion of a Fiber-Optic Terminus in a Connector

A tool has been developed for the special purpose of inserting the terminus of an optical fiber in a cable connector that conforms to NASA Specification SSQ- 21635. What prompted the development of the tool was the observation that because of some aspects of the designs of fiber-optic termini and of springs, sealing rings, and a grommet inside the shell of such a connector, there is a tendency for the grommet to become damaged and detached from the sealing rings during installation. It is necessary to ensure the integrity of the grommet for proper sealing and proper functioning of the connector. The special-purpose tool provides the needed protection for the grommet. The grommet-protection tool resembles a funnel into which an axial slit has been cut (see figure). Prior to insertion, the grommet-protection tool is rolled so that one side of the slit overlaps the other side. The rolled-up grommet-protection tool is inserted in one of the connector holes that accommodate the fiber-optic termini and is pushed in until the flange (the wider of the two conical portions) of the tool becomes seated on the connector grommet. Then a special-purpose installation tool is inserted in the flange of the grommet-protection tool and pressed in until it becomes seated in the flange. This operation expands the narrower of the two conical portions of the grommet-protection tool. The installation tool is removed and the grommet-protection tool remains expanded due to the flat surfaces on the axial slit. By use of a standard contact-insertion tool, a fiber-optic terminus is inserted, through the grommet-protection tool, into the connector cavity. By use of a pair of forceps or needle-nose pliers, the grommet-protection tool is then pulled out of the cavity. Finally, the grommet-protection tool is removed from around the installed fiber-optic cable by pulling the cable through the axial slit. Unlike in some prior procedures for installing the fiber-optic termini in the connector, the procedure that involves the use of the present grommet-protection tool does not include the use of lubricants that can contaminate the interior of the connector. The grommet-protection tool is made of a fluoropolymer, taking advantage of the flexibility of such polymers and further taking advantage of the inherent slipperiness of fluoropolymers. Although the tool is designed primarily for insertion of a fiber-optic terminus, it might also be useful for extracting a previously installed fiber-optic terminus.

King, Wes↗

Bubble Eliminator Based on Centrifugal Flow

The fluid bubble eliminator (FBE) is a device that removes gas bubbles from a flowing liquid. The FBE contains no moving parts and does not require any power input beyond that needed to pump the liquid. In the FBE, the buoyant force for separating the gas from the liquid is provided by a radial pressure gradient associated with a centrifugal flow of the liquid and any entrained bubbles. A device based on a similar principle is described in Centrifugal Adsorption Cartridge System (MSC- 22863), which appears on page 48 of this issue. The FBE was originally intended for use in filtering bubbles out of a liquid flowing relatively slowly in a bioreactor system in microgravity. Versions that operate in normal Earth gravitation at greater flow speeds may also be feasible. The FBE (see figure) is constructed as a cartridge that includes two concentric cylinders with flanges at the ends. The outer cylinder is an impermeable housing; the inner cylinder comprises a gas-permeable, liquid-impermeable membrane covering a perforated inner tube. Multiple spiral disks that collectively constitute a spiral ramp are mounted in the space between the inner and outer cylinders. The liquid enters the FBE through an end flange, flows in the annular space between the cylinders, and leaves through the opposite end flange. The spiral disks channel the liquid into a spiral flow, the circumferential component of which gives rise to the desired centrifugal effect. The resulting radial pressure gradient forces the bubbles radially inward; that is, toward the inner cylinder. At the inner cylinder, the gas-permeable, liquid-impermeable membrane allows the bubbles to enter the perforated inner tube while keeping the liquid in the space between the inner and outer cylinders. The gas thus collected can be vented via an endflange connection to the inner tube. The centripetal acceleration (and thus the radial pressure gradient) is approximately proportional to the square of the flow speed and approximately inversely proportional to an effective radius of the annular space. For a given FBE geometry, one could increase the maximum rate at which gas could be removed by increasing the rate of flow to obtain more centripetal acceleration. In experiments and calculations oriented toward the original microgravitational application, centripetal accelerations between 0.001 and 0.012 g [where g normal Earth gravitation (.9.8 m/s2)] were considered. For operation in normal Earth gravitation, it would likely be necessary to choose the FBE geometry and the rate of flow to obtain centripetal acceleration comparable to or greater than g.

Gonda, Steve R.↗

A Comparison of Candidate Seal Designs for Future Docking Systems

NASA is developing a new docking system to support future space exploration missions to low Earth orbit, the Moon, and other destinations. A key component of this system is the seal at the main docking interface which inhibits the loss of cabin air once docking is complete. Depending on the mission, the seal must be able to dock in either a seal-on-flange or seal-on-seal configuration. Seal-on-flange mating would occur when a docking system equipped with a seal docks to a system with a flat metal flange. This would occur when a vehicle docks to a node on the International Space Station. Seal-on-seal mating would occur when two docking systems equipped with seals dock to each other. Two types of seal designs were identified for this application: Gask-O-seals and multi-piece seals. Both types of seals had a pair of seal bulbs to satisfy the redundancy requirement. A series of performance assessments and comparisons were made between the candidate seal designs indicating that they meet the requirements for leak rate and compression and adhesion loads under a range of operating conditions. Other design factors such as part count, integration into the docking system tunnel, seal-on-seal mating, and cost were also considered leading to the selection of the multi-piece seal design for the new docking system. The results of this study can be used by designers of future docking systems and other habitable volumes to select the seal design best-suited for their particular application.

Dunlap, Patrick, H., Jr.↗

Pressure Dome for High-Pressure Electrolyzer

A high-strength, low-weight pressure vessel dome was designed specifically to house a high-pressure [2,000 psi (approx. = 13.8 MPa)] electrolyzer. In operation, the dome is filled with an inert gas pressurized to roughly 100 psi (approx. = 690 kPa) above the high, balanced pressure product oxygen and hydrogen gas streams. The inert gas acts to reduce the clamping load on electrolyzer stack tie bolts since the dome pressure acting axially inward helps offset the outward axial forces from the stack gas pressure. Likewise, radial and circumferential stresses on electrolyzer frames are minimized. Because the dome is operated at a higher pressure than the electrolyzer product gas, any external electrolyzer leak prevents oxygen or hydrogen from leaking into the dome. Instead the affected stack gas stream pressure rises detectably, thereby enabling a system shutdown. All electrical and fluid connections to the stack are made inside the pressure dome and require special plumbing and electrical dome interfaces for this to be accomplished. Further benefits of the dome are that it can act as a containment shield in the unlikely event of a catastrophic failure. Studies indicate that, for a given active area (and hence, cell ID), frame outside diameter must become ever larger to support stresses at higher operating pressures. This can lead to a large footprint and increased costs associated with thicker and/or larger diameter end-plates, tie-rods, and the frames themselves. One solution is to employ rings that fit snugly around the frame. This complicates stack assembly and is sometimes difficult to achieve in practice, as its success is strongly dependent on frame and ring tolerances, gas pressure, and operating temperature. A pressure dome permits an otherwise low-pressure stack to operate at higher pressures without growing the electrolyzer hardware. The pressure dome consists of two machined segments. An O-ring is placed in an O-ring groove in the flange of the bottom segment and is trapped by the flange on the top dome segment when these components are bolted together with high-strength bolts. The pressure dome has several unique features. It is made (to ASME Pressure Vessel guidelines) in a high-strength aluminum alloy with the strength of stainless steel and the weight benefits of aluminum. The flange of the upper dome portion contains specially machined flats for mounting the dome, and other flats dedicated to the special feedthroughs for electrical connections. A pressure dome can be increased in length to house larger stacks (more cells) of the same diameter with the simple addition of a cylindrical segment. To aid in dome assembly, two stainless steel rings are employed. One is used beneath the heads of the high-strength bolts in lieu of individual hardened washers, and another is used instead of individual nuts. Like electrolyzers could be operated at low or high pressures simply by operating the electrolyzer outside or inside a pressurized dome.

Norman, Timothy↗

High-Reliability Waveguide Vacuum/Pressure Window

The NASA Deep Space Network (DSN) uses commercial waveguide windows on the output waveguide of Ka-band (32 GHz) low-noise amplifiers. Mechanical failure of these windows resulted in an unacceptable loss in tracking time. To address this issue, a new Ka-band WR-28 waveguide window has been designed, fabricated, and tested. The window uses a slab of low-loss, low-dielectric constant foam that is bonded into a 1/2-wave-thick waveguide/flange. The foam is a commercially available, rigid, closed-cell polymethacrylimide. It has excellent electrical properties with a dielectric constant of 1.04, and a loss tangent of 0.01. It is relatively strong with a tensile strength of 1 MPa. The material is virtually impermeable to helium. The finished window exhibits a leak rate of less than 3x10(exp -3)cu cm/s with helium. The material is also chemically resistant and can be cleaned with acetone. The window is constructed by fabricating a window body by brazing a short length of WR-28 copper waveguide into a standard rectangular flange, and machining the resulting part to a thickness of 4.6 mm. The foam is machined to a rectangular shape with a dimension of 7.06x3.53 mm. The foam is bonded into the body with a two-part epoxy. After curing, the excess glue and foam are knife-trimmed by hand. The finished window has a loss of less than 0.08 dB (2%) and a return loss of greater than 25 dB at 32 GHz. This meets the requirements for the DSN application. The window is usable for most applications over the entire 26-to-40-GHz waveguide band. The window return loss can be tuned to a required frequency by var y in g the thickness of the window slightly. Most standard waveguide windows use a thin membrane of material bonded into a recess in a waveguide flange, or sandwiched between two flanges with a polymer seal. Designs using the recessed window are prone to mechanical failure over time due to constraints on the dimensions of the recess that allow the bond to fail. Designs using the sandwich method are often permeable to helium, which prohibits the use of helium leak detection. At the time of this reporting, 40 windows have been produced. Twelve are in operation with a combined operating time of over 30,000 hours without a failure.

Britcliffe, Michael J.↗

Ultrasonic Measurement and Monitoring of Loads in Bolts used in Structural Joints

The paper is an overview of work by the author in measuring and monitoring loads in bolts using an ultrasonic extensometer. A number of cases of bolted joints are covered. These include, a clamped joint with clearance fit between the bolt and hole, a clamped joint with the bolt in an interference fit with the hole, a flanged joint which allows the flange and bolt to bend; and a shear joint in a clevis and tang configuration. These applications were initially developed for measuring and monitoring preload in the NASA Space Shuttle Orbiter critical joints but are also applicable for monitoring loads in other critical bolted joints of structures such as transportation bridges and other aerospace structures. The paper explains how to set‐up a model to estimate the load factor and accuracy for the ultrasonic preload application in a clamped joint with clearance fit. The ultrasonic preload application for clamped joint with bolt in an interference fit can also be used to measure diametrical interference between the bolt shank and hole; and interference pressure on the bolt shank. Model and experimental data are given to demonstrate use of ultrasonic measurements in a shear joint. A bolt in a flanged joint experiences both tensile and bending loads. This application involves measurement of bending and tensile preload in a bolt. The ultrasonic beam bends due to the bending load on the bolt. A numerical technique to compute the trace of ultrasonic ray is presented.

Koshti, Ajay↗