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At least 37 records · Page 2
All sourcesNASA NTRSDOE OSTI
NASA NTRS2003

Tool Forces Developed During Friction Stir Welding

This paper will describe a technique for measuring the various forces and the torque that exist on the Friction Stir Welding pin tool. Results for various plunge depths, weld speeds, rotational speed, and tool configurations will be presented. Welds made on 6061 aluminum with typical welding conditions require a downward force of 2800 lbs. (12.5 kN) a longitudinal force in the direction of motion of 300 lbs (1.33 kN), a transverse force in the omega x v direction of 30 lbs (135 N). Aluminum 2195 under typical weld conditions requires a downward force of 3100 lbs. (1.38 kN), a longitudinal force of 920 lbs. (4.1 kN), and a transverse force of 45 lbs. (200 N) in the omega x v direction.

Melendez, M.↗
DOE OSTI2024

Bayesian inference of multi-messenger astrophysical data: Joint and coherent inference of gravitational waves and kilonovae

Multi-messenger observations of binary neutron star mergers can provide information on the neutron star’s equation of state (EOS) above the nuclear saturation density by directly constraining the mass-radius diagram. We present a Bayesian framework for joint and coherent analyses of multi-messenger binary neutron star signals. As a first application, we analyze the gravitational-wave GW170817 and the kilonova (kN) AT2017gfo data. These results are then combined with the most recent X-ray pulsar analyses of PSR J0030+0451 and PSR J0740+6620 to obtain new EOS constraints.We extend the bajes infrastructure with a joint likelihood for multiple datasets, support for various semi-analytical kN models, and numerical-relativity (NR)-informed relations for the mass ejecta, as well as a technique to include and marginalize over modeling uncertainties. The analysis of GW170817 used the TEOBResumS effective-one-body waveform template to model the gravitational-wave signal. The analysis of AT2017gfo used a baseline multicomponent spherically symmetric model for the kN light curves. Various constraints on the mass-radius diagram and neutron star properties were then obtained by resampling over a set of ten million parameterized EOSs, which was built under minimal assumptions (general relativity and causality).

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2021

r-Process Radioisotopes from Near-Earth Supernovae and Kilonovae

The astrophysical sites where r-process elements are synthesized remain mysterious: it is clear that neutron star mergers (kilonovae (KNe)) contribute, and some classes of core-collapse supernovae (SNe) are also possible sources of at least the lighter r-process species. The discovery of 60Fe on the Earth and Moon implies that one or more astrophysical explosions have occurred near the Earth within the last few million years, probably SNe. Intriguingly, 244 Pu has now been detected, mostly overlapping with 60 Fe pulses. However, the 244 Pu flux may extend to before 12 Myr ago, pointing to a different origin. Here, motivated by these observations and difficulties for r-process nucleosynthesis in SN models, we propose that ejecta from a KN enriched the giant molecular cloud that gave rise to the Local Bubble, where the Sun resides. Accelerator mass spectrometry (AMS) measurements of 244 Pu and searches for other live isotopes could probe the origins of the r-process and the history of the solar neighborhood, including triggers for mass extinctions, e.g., that at the end of the Devonian epoch, motivating the calculations of the abundances of live r-process radioisotopes produced in SNe and KNe that we present here. Given the presence of 244 Pu, other r-process species such as 93 Zr, 107 Pd, 129 I, 135 Cs, 182 Hf, 236 U, 237 Np, and 247 Cm should be present. Their abundances and well-resolved time histories could distinguish between the SN and KN scenarios, and we discuss prospects for their detection in deep-ocean deposits and the lunar regolith. We show that AMS 129 I measurements in Fe–Mn crusts already constrain a possible nearby KN scenario.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2024

On a Spectral Method for β -particle Bound Excitation Collisions in Kilonovae

The interaction of β-particles with the weakly ionized plasma background is an important mechanism for powering the kilonova (KN) transient signal from neutron star mergers. For this purpose, we present an implementation of the approximate fast-particle collision kernel, described by Inokuti following the seminal formulation of Bethe, in a spectral solver of the Vlasov–Maxwell–Boltzmann equation. In particular, we expand the fast-particle plane-wave atomic excitation kernel into coefficients of the Hermite basis, and derive the relevant discrete spectral system. In this fast-particle limit, the approach permits the direct use of atomic data, including optical oscillator strengths, normally applied to photon–matter interaction. The resulting spectral matrix is implemented in the MASS-APP spectral solver framework, in a way that avoids full matrix storage per spatial zone. We numerically verify aspects of the matrix construction, and present a proof-of-principle 3D simulation of a 2D axisymmetric KN ejecta snapshot. Our preliminary numerical results indicate that a reasonable choice of Hermite basis parameters for β-particles in the KN is a bulk velocity parameter u = 0, a thermal velocity parameter α = 0.5c, and a 9 × 9 × 9 mode velocity basis set (Hermite orders of 0–8 in each dimension). For interior-ejecta sample zones, we estimate that the ratio of thermalization from large-angle (≳2fdg5) bound excitation scattering to total thermalization is ~0.002–0.003.

79 ASTRONOMY AND ASTROPHYSICS↗
NASA NTRS1978

Effects of laminar flow control on the performance of a large span-distributed-load flying-wing cargo airplane concept

The effects of laminar flow control (LFC) on the performance of a large span-distributed-load flying-wing cargo airplane concept having a design payload of 2.669 MN and range of 5.93 Mm were determined. Two configurations were considered. One employed laminarized flow over the entire surfaces of the wing and vertical tails, with the exception of the estimated areas of interference due to the fuselage and engines. The other case differed only in that laminar flow was not applied to the flaps, elevons, spoilers, or rudders. The two cases are referred to as the 100 percent and 80 percent laminar configurations, respectively. The utilization of laminar flow control results in reductions in the standard day, sea level installed maximum static thrust per engine from 240 kN for the non-LFC configuration to 205 kN for the 100 percent laminar configuration and 209 kN for the 80 percent case. Weight increases due to the LFC systems cause increases in the operating empty weights of approximately 3 to 4 percent. The design takeoff gross weights decrease approximately 3 to 5 percent. The FAR-25 takeoff field distances for the LFC configurations are greater by about 6 to 7 percent. Fuel efficiencies for the respective configurations are increased 33 percent and 23 percent.

Jernell, L. S.↗
NASA NTRS1988

Alignment verification procedures

In alignment verification procedures each laboratory is required to align its test machines and gripping fixtures to produce a nearly uniform tensile stress field on an un-notched sheet specimen. The blank specimens (50 mm w X 305 mm l X 2.3 mm th) supplied by the coordinators were strain gauged. Strain gauge readings were taken at all gauges (n = 1 through 10). The alignment verification procedures are as follows: (1) zero all strain gauges while specimen is in a free-supported condition; (2) put strain-gauged specimen in the test machine so that specimen front face (face 1) is in contact with reference jaw (standard position of specimen), tighten grips, and at zero load measure strains on all gauges. (epsilon sub nS0 is strain at gauge n, standard position, zero load); (3) with specimen in machine and at a tensile load of 10 kN measure strains (specimen in standard position). (Strain = epsilon sub nS10); (4) remove specimen from machine. Put specimen in machine so that specimen back face (face 2) is in contact with reference jaw (reverse position of specimen), tighten grips, and at zero load measure strains on all gauges. (Strain - epsilon sub nR0); and (5) with specimen in machine and at tensile load of 10 kN measure strains (specimen in reverse position). (epsilon sub nR10 is strain at gauge n, reverse position, 10 kN load).

Edwards, P. R.↗
NASA NTRS2003

Experimental High Temperature Characterization of a Magnetic Bearing for Turbomachinery

Open loop, experimental force and power measurements of a radial, redundant-axis, magnetic bearing at temperatures to 1000 F (538 C) and rotor speeds to 15,000 RPM along with theoretical temperature and force models are presented in this paper. The experimentally measured force produced by a single C-core using 22A was 600 lb. (2.67 kN) at room temperature and 380 lb. (1.69 kN) at 1000 F (538 C). These values were compared with force predictions based on a 1D magnetic circuit analysis and a thermal analysis of gap growth as a function of temperature. Tests under rotating conditions showed that rotor speed has a negligible effect on the bearing s load capacity. One C-core required approximately 340 W of power to generate 190 lb. (8.45 kN) of magnetic force at 1000 F (538 C); however the magnetic air gap was much larger than at room temperature. The data presented is after the bearing had already operated six thermal cycles and eleven total (not consecutive) hours at 1000 F (538 C).

Montague, Gerald↗
NASA NTRS2025

The Shape Effect: Influence of 1D and 2D Boron Nitride Nanostructures on the Radiation Shielding, Thermal, and Damping Properties of High-Temperature Epoxy Composites

In space exploration, lightweight multifunctional materials capable of shielding neutron radiation, dissipating heat, and providing damping are essential. Polymer composites reinforced with boron nitride (BN) nanomaterials—specifically one-dimensional boron nitride nanotubes (BNNTs) and two-dimensional boron nitride nanoplatelets (BNNPs)—offer promising solutions. This study investigates how BN nanomaterial morphology influences the performance of high-temperature (HT) epoxy composites. We developed ultralightweight, three-dimensional BN foams comprising 1D BNNTs, 2D BNNPs, and hybrid 1D BNNT/2D BNNP structures via freeze-drying, then infiltrated them with HT epoxy to form dense composites. The BNNT foam exhibited the highest neutron radiation shielding, with a mass absorption coefficient of 26.64 cm2 g −1 , outperforming the hybrid foam (18.18 cm 2 g −1 ) and the BNNP foam (11.12 cm 2 g −1 ). A similar trend was observed in the HT epoxy composites; incorporating these foams at least doubled the mass absorption coefficient compared to the neat polymer. In terms of thermal conductivity, the BNNT/BNNP foam-epoxy composite achieved the highest value of 0.34 W m −1 K −1 , a 2.13-fold increase over neat HT epoxy. The BNNT/BNNP foam-epoxy composites also improved by 1.88 and 1.75 times, respectively. Mechanical testing revealed that BNNP foams withstood the highest loads during nanoindentation (3.53 kN), followed by BNNT/BNNP foams (1.93 kN) and BNNT foams (1.56 kN). All BN foam-epoxy composites exhibited enhanced damping properties, with tan δ increasing by at least 30 % compared to neat HT epoxy. These findings elucidate the impact of BN nanomaterial morphology on the multifunctional performance of HT epoxy composites, offering insights for developing high-performance, tailorable materials for demanding environments.

Kazue Orikasa↗
DOE OSTI2023

Linear growth of circuit complexity from Brownian dynamics

How rapidly can a many-body quantum system generate randomness? Using path integral methods, we demonstrate that Brownian quantum systems have circuit complexity that grows linearly with time. In particular, we study Brownian clusters of N spins or fermions with time-dependent all-to-all interactions, and calculate the Frame Potential to characterize complexity growth in these models. In both cases the problem can be mapped to an effective statistical mechanics problem which we study using path integral methods. Within this framework it is straightforward to show that the kth Frame Potential comes within ϵ of the Haar value after a time of order t ~ kN + k log k + log ϵ –1 . Using a bound on the diamond norm, this implies that such circuits are capable of coming very close to a unitary k-design after a time of order t ~ kN. We also consider the same question for systems with a time-independent Hamiltonian and argue that a small amount of time-dependent randomness is sufficient to generate a k-design in linear time provided the underlying Hamiltonian is quantum chaotic. These models provide explicit examples of linear complexity growth that are analytically tractable and are directly applicable to practical applications calling for unitary k-designs.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗
DOE OSTI2020

Adaptive simulations enable computational design of electron beam processing of nanomaterials with supersonic micro-jet precursor

Focused Electron Beam Induced Processing (FEBIP) is a powerful tool for the “direct-write” of nanomaterials with the possibility of atomistic control on suspended 2D material substrates. FEBIP capabilities have been significantly expanded by using a localized jet-based delivery of precursors, and especially when a thermally energized supersonic micro-jet enhances the delivery of mass flux along with controlling the far-from-equilibrium thermodynamic state of adsorbed adatoms. The possibilities of growing nanomaterials with “dialed-in” composition with ultra-high growth rates and aspect ratios up to 100:1 have been demonstrated using the supersonic micro-jet-FEBIP. Bringing this scientific discovery to the level of maturity required for practical applications in additive nanomanufacturing requires simulation tools that are capable of capturing the complex flow physics of micro-jet-substrate interactions that bridge a wide range of flow regimes from the high-density gas micro-jet expanding into the vacuum environment of FEBIP. To address this significant computational challenge, a new approach has been developed and described in this work for a multiscale adaptive DSMC (Direct Simulation Monte Carlo) algorithm to predict the micro-jet gas dynamics in an FEBIP environment, spanning the full range of flow regimes from low Knudsen (Kn) number O(0.01) continuum flow to high Kn of O(10) for the molecular flow within a unified computational framework. Here, the fundamental principles of the adaptive DSMC algorithm are described, its viability as a DSMC technique is demonstrated, and computational improvements for the benchmark cases are discussed in the context of advancing 3D nanofabrication with FEBIP. Ultimately, combining the first principle simulations via adaptive DSMC with the complementary experimental data will enable the creation of the powerful CAD tools for in silico design and optimal operation of micro-jet-FEBIP.

36 MATERIALS SCIENCE↗
DOE OSTI2024

Microstructure and mechanical properties of ultrasonic spot welding of AA7075-T6 and A380 casting aluminum alloy

Ultrasonic spot welding (USW) was employed to join AA7075-T6 and casting Al alloy A380. Under a constant welding power, the influence of the welding time duration (from 1 s to 3 s) on peak temperature, microstructure, hardness, and mechanical strength of the joints were studied. It was found that the peak temperature increased with welding time. A sound solid-state metallurgical bonding was obtained at the joint interface. The cracks occurred at the edge of the joints were eventually eliminated as the welding time increased. A layer of refined grains formed in A380 adjacent to the bonding line. Further, hardness reduction occurred in AA7075 at the joint interface and the degree of hardness reduction and the volume increased with the peak temperature. By increasing welding time, lap shear tensile tests show that the peak load increased from 5.3 kN to 6.55 kN. The corresponding interfacial shear strength ranged from 96.29 MPa to 99.72 MPa, lower than the shear strength of both base materials (331 MPa for AA7075 and 185 MPa for A380). All joint samples exhibited interfacial fracture after lap shear tensile testing, with a thin layer of A380 remnant attached to AA7075 at the center of the fractured surface.

36 MATERIALS SCIENCE↗
DOE OSTI2024

Effect of die design on microstructure and mechanical joint strength in friction self-piercing riveted AA7055-T76 and AA7055-T76

In the present study, a unique friction self-piercing riveting (F-SPR) was applied to join high-strength, low-ductility aluminum alloy (AA) 7055-T76 and AA7055-T76 to mitigate a cracking issue. Also, the effect of die design on both joint formation and the mechanical joint performance were investigated. A crack-free joint was achieved when joining AA7055-T76 and AA7055-T76 by F-SPR. As the bottom diameter of the die increased, the mechanical interlocking distance initially increased then became almost saturated. At the same time, the solid-state bonding gradually disappeared, and the lap-shear fracture changed from bottom aluminum fracture to rivet pull-out with partial bottom aluminum fracture. The average maximum lap-shear joint strength of 11.57 kN and cross tension of 5.65 kN were achieved from the D2 die design owing to the combined contributions from high mechanical interlocking distance and good solid-state bonding at the joint interface. Ultrafine grain refinement was observed at the region next to the rivet shank outer surface and along the materials flow line between the top and bottom aluminum sheet in the rivet cavity. Further, because of the same joint-process parameters, the hardness profile at the joints made by different dies did not show obvious differences. As the distance from the base metal to the rivet outer surface decreased, frictional heat caused the hardness to initially decrease from 190 to 150 HV in the heat-affected zone. Hardness increased up to 175 HV in the thermomechanical affected zone (TMAZ-I) owing to large plastic deformation.

36 MATERIALS SCIENCE↗
DOE OSTI2022

Validation of SOLPS-ITER simulations with kinetic, fluid, and hybrid neutral models for JET-ILW low-confinement mode plasmas

For JET L-mode plasmas in low-recycling conditions (electron temperature at the outer strike point, T e,ot ≳ 30 eV ), SOLPS-ITER simulations agree within the error bars for the experimental profiles at the low-field side (LFS) divertor target. The peak Balmer-α (Dα ) emission in the LFS divertor agrees within the error bars of the KS3 filterscope diagnostic, but is approximately 30% lower than the peak value of the KT1 spectrometer. Simulations have been performed with fluid, kinetic, and hybrid models for the neutrals. The large fluid-kinetic discrepancies of more than a factor 2 are successfully corrected by using a hybrid fluid-kinetic approach, for which kinetic atoms are transferred to the fluid population when the local Knudsen number of the atom becomes smaller than a user-defined transition Knudsen number Kn t . The hybrid-kinetic discrepancies are limited to a few % for Kn t ≤ 100 . When increasing the upstream density to high-recycling conditions, at the onset of detachment ( T e,ot ≈ 5 eV ), the simulations predict more than a factor 2 lower peak ion saturation current to the LFS divertor than the experiments. Also the Dα emission is underpredicted with approximately a factor 2. For these high-recycling conditions, the fluid-kinetic discrepancies are limited to maximum 50%, which are again corrected by using the hybrid approach.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
DOE OSTI2022

Preliminary conceptual design of fast neutron spectrum nuclear thermal rocket cores using monolithic uranium nitride fuel

This paper presents a few nuclear thermal rocket (NTR) reactor core preliminary conceptual designs based on the use of monolithic uranium nitride (UN) fuel plates or pins clad with tungsten (W), alloyed or unalloyed as needed. High-assay low-enriched uranium (HALEU) as well as high-enriched uranium (HEU) are considered. Nominal core thermal powers are between 300 and 1100 MW corresponding to thrusts between 66 kN and 240 kN. The estimated thrust-to-reactor-weight ratios (T/WRx) achievable with the HEU plate and pin configurations are between 3.8 and 10.9. The T/WRx achievable with the HALEU plate and pin configurations are lower, 1.9–4.0, than those achievable with HEU. It is noteworthy that even a relatively modest increase in fuel enrichment above the HALEU limit enables a significant increase in T/WRx. It must be emphasized that these results do not yet account for uncertainties and that the appropriateness of the assumed fuel thermal design limits for normal operation (i.e., peak centerline temperature of 3100 K) will need to be confirmed. Finally, just like for the other UN-based fuels currently considered for NTR applications (i.e., CERMET and CERCER), the proposed UN fuel systems need significant testing in prototypic conditions to confirm the appropriate performance for safe NTR applications. However, the monolithic fuel systems may have, overall, a higher technology readiness level (TRL), and, consequently, shorter fuel development and validation time may result.

22 GENERAL STUDIES OF NUCLEAR REACTORS↗
DOE OSTI2024

Macroscopic modeling of gas permeability in hierarchical micro/nanoporous media: A unified characterization of rarefaction using Klinkenberg theory and equivalent diameter

Estimating gas transport through a hierarchical micro/nanoporous system is challenging due to non-equilibrium gas dynamics. The primary difficulty lies in determining the rarefaction level, because identifying a representative flow dimension in a complex porous system with multiple pore scales is not straightforward. Our study performed a pore-level analysis for gas permeability in dual-scale porous media with varying porosity, throat size, and secondary pore size under different rarefaction conditions. We found that secondary porosity negatively affects permeability due to increased friction forces, with this influence growing as the secondary pore size and porosity increase until the secondary pore becomes comparable to the throat. However, rarefaction reduces the effects of secondary pores due to boundary slip. Traditional Knudsen number (Kn) calculations based on Darcy-defined height failed to accurately describe the rarefaction effects on gas permeability. Instead, we introduced an equivalent diameter to calculate the Kn, which provided an accurate normalization of apparent gas permeability independent of pore geometry. Furthermore, the extended Kozeny–Carman–Klinkenberg model developed in our previous study successfully yielded a macroscopic model for apparent gas permeability in hierarchical micro/nanoporous systems as a function of the traditional Darcy height and porosity.

04 OIL SHALES AND TAR SANDS↗
DOE OSTI2024

Actinide signatures in low electron fraction kilonova ejecta

ABSTRACT Neutron star (NS) mergers are known to produce heavy elements through rapid neutron capture (r-process) nucleosynthesis. Actinides are expected to be created solely by the r-process in the most neutron-rich environments. Confirming if NS mergers provide the requisite conditions for actinide creation is therefore central to determining their origin in the Universe. Actinide signatures in kilonova (KN) spectra may yield an answer, provided adequate models are available in order to interpret observational data. In this study, we investigate actinide signatures in neutron-rich merger ejecta. We use three ejecta models with different compositions and radioactive power, generated by nucleosynthesis calculations using the same initial electron fraction ($Y_e = 0.15$) but with different nuclear physics inputs and thermodynamic expansion history. These are evolved from 10 to 100 d after merger using the sumo non-local thermodynamic equilibrium (NLTE) radiative transfer code. We highlight how uncertainties in nuclear properties, as well as choices in thermodynamic trajectory, may yield entirely different outputs for equal values of $Y_e$. We consider an actinide-free model and two actinide-rich models, and find that the emergent spectra and light-curve evolution are significantly different depending on the amount of actinides present, and the overall decay properties of the models. We also present potential key actinide spectral signatures, of which doubly ionized $_{89}$Ac and $_{90}$Th may be particularly interesting as spectral indicators of actinide presence in KN ejecta.

Pognan, Quentin (ORCID:0000000152550782)↗
DOE OSTI2020

Mechanical and Corrosion Assessment of Friction Self-Piercing Rivet Joint of Carbon Fiber-Reinforced Polymer and Magnesium Alloy AZ31B

In the present work, thermoset carbon fiber–reinforced polymer (CFRP) was spot joined to magnesium alloy AZ31B by a friction self-piercing riveting (F-SPR) process. Lap shear tensile and cross-tension testing were used to evaluate the mechanical joint performance. An average lap shear tensile load of 5.18 kN was achieved, while an average of 2.81 kN was found from cross-tension testing. All F-SPR samples showed a pullout of AZ31B after mechanical testing, indicating good mechanical interlocking between the steel rivet and AZ31B. Corrosion potential was measured for each material to establish the galvanic corrosion characteristics. As expected, AZ31B was found to be the most active, while thermoset CFRP was the most noble. The steel rivet fell between the AZ31B (active) and the thermoset CFRP (noble). Salt fog corrosion testing (ASTM B-117) was performed to evaluate the corrosion performance of the uncoated F-SPR joint. With up to 200 h of exposure, the post-corroded F-SPR joint integrity retained 81.2% of the pre-exposure F-SPR joint strength with AZ31B pullout failure mode. From cross-sectional analysis of the F-SPR joint, extensive corrosion of AZ31B was observed at the joint and other exposure areas. However, steel rivet was not significantly corroded due to sacrificial anode effect by which AZ31B corroded first in the galvanic couple.

36 MATERIALS SCIENCE↗
DOE OSTI2021

Additively Manufactured Compliant Hybrid Gas Thrust Bearing for Supercritical Carbon Dioxide Turbomachinery: Design and Proof of Concept Testing

The following paper presents a new type of gas lubricated thrust bearing that utilizes additive manufacturing or also known as direct metal laser melting (DMLM) to fabricate the bearing. The motivation for the new bearing concept is derived from the need for highly efficient supercritical carbon dioxide (sCO2) turbomachinery in the mega-watt power range. The paper provides a review of existing gas thrust-bearing technology, outlines the need for the new DMLM concept, and discusses proof-of-concept testing results. The new concept combines hydrostatic pressurization with individual tilting pads that are flexibly mounted using hermetic squeeze film dampers (HSFD) in the bearing-pad support. This paper describes the thrust-bearing concept and discusses the final design approach. Proof-of-concept testing in air for a 6.8 in. (173 mm) outer diameter thrust gas bearing was performed; with thrust loading, up to 1500 lbs (6.67 kN) and a thrust runner speed of 10krpm (91 m/s tip speed). The experiments were performed with a bent shaft resulting in thrust runner axial vibration magnitudes of 2.9 mils (74 μm) p-p and dynamic thrust loads of 270 lbs (1.2 kN) p-p. In addition, force deflection characteristics and stiffness coefficients of the bearing system are presented for an inlet hydrostatic pressure of 380 psi (2.62 MPa). Results at 10 krpm show that the pad support architecture was able to sustain high levels of dynamic misalignment equaling 6 times the nominal film clearance while demonstrating a unit load-carrying capacity of 55 psi (0.34 Mpa). Gas-film force deflection tests portrayed nonlinear behavior like a hardening spring, while the bearing pad support stiffness was measured to be linear and independent of gas film thickness.

Engineering↗