Finiteness Theorems for Binary Forms with Given Discriminant

Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/135212/1/plms0385.pd

Evaluation of feasibility of measuring EHD film thickness associated with cryogenic fluids

The feasibility of measuring elastohydrodynamic (EHD) films as formed with a cryogenic (LN2) fluid is evaluated. Modifications were made to an existing twin disk EHD apparatus to allow for disk lubrication with liquid nitrogen. This disk apparatus is equipped with an X-ray system for measuring the thickness of any lubricant film that is formed between the disks. Several film thickness experiments were conducted with the apparatus which indicate that good lubrication films are filmed with LN2. In addition to the film thickness studies, failure analyses of three bearings were conducted. The HPOTP turbine end bearings had experienced axial loads of 36,000 to 44,000 N (8,000 to 10,000 lb). High continuous radial loads were also experienced, which were most likely caused by thermal growth of the inner race. The resulting high internal loads caused race spalling and ball wear to occur

Investigation of instability, dynamic forces, and effect of dynamic loading on strength of cages for the bearings in the high pressure oxygen turbopumps for the space shuttle main engine

Experiments were performed to determine the effect of cyclic loading on bearing cage strength. A long term working tensile load of approximately 1300 N (300 lbs) was found to be the likely maximum. Higher loads caused a decrease in cage tensile strength after the 125,000 cycle testing period. Poisson's ratio in compression was found to be highly dependent upon the direction of the fiberglass plies. At room temperature the value was 0.15 with the plies and 0.68 across the plies. At -196 C (-321 F), the value with the plies was 0.20. The results of the analyses conducted have again demonstrated the critical need for improved lubrication in the high pressure oxygen turbopump bearings. Lubricant films with low shear strength and low friction coefficients promote cage stability and decrease ball/cage forces during marginal operating conditions. The analysis of the effect of combined bearing loads on ball/cage loads has identified a radial load of 3600 N (800 lbs) as the maximum for the current clearance of the balls and cage pockets. Liquid oxygen impinging on the cage in the direction of rotation was found to enhance cage stability

Back-reacted saponite in Jurassic mudstones and limestones intruded by a Tertiary sill, Isle of Skye

The Lón Ostatoin stream section, Trotternish Peninsula, Isle of Skye, exposes a sequence of Middle Jurassic mudstones and limestones which have been locally metasomatized by a transgressive sill of Tertiary age. Limestones in the sequence, including some previously reported as bentonite, have been altered to an unusual assemblage of grossular garnet and saponite clay. The mudstones also contain large proportions of saponite together with pyroxene and zeolites. Saponite also occurs within the basalt intrusion. Grossular and pyroxene represent artifacts of relatively high-temperature assemblages that formed during an early phase of alteration. As the intrusion and adjacent altered country rocks cooled, lower-temperature fluids flowed through a late set of contraction (micro)fractures. Back-reacted saponite, analcime and clinoptilolite were formed, possibly as alteration products of the unstable higher-temperature minerals. The lower-temperature mineral assemblage eventually sealed the late fracture system. This paper highlights an important concept for the study of analogue sites used to investigate thermal effects on engineered liners or barrier host rocks for the landfill and radioactive-waste industries. This is that the original thermally altered mineral assemblage may be overprinted by later, lower-temperature back-reactions. A detailed understanding of both processes is necessary in order to construct a sensible model for the thermal and mineralogical evolution of the site

Measurements of elastohydrodynamic film thickness, wear and tempering behavior of high pressure oxygen turbopump bearings

The reusable design of the Space Shuttle requires a target life of 7.5 hours for the turbopumps of the Space Shuttle main engine (SSME). This large increase from the few hundred seconds required in single-use rockets has caused various problems with the bearings of the turbopumps. The berings of the high pressure oxygen turbopump (HPOTP) were of particular concern because of wear, spalling, and cage failures at service time well below the required 7.5 hours. Lubrication and wear data were developed for the bearings. Since the HPOTP bearings operate in liquid oxygen, conventional liquid lubricants cannot be applied. Therefore, solid lubricant coatings and lubricant transfer from the polytetrafluorethylene (FTFE) cage were the primary lubrication approaches for the bearings. Measurements were made using liquid nitrogen in a rolling disk machine to determine whether usable elastohydrodynamic films could be generated to assist in the bearing lubrication

On several families of elliptic curves with arbitrary large Selmer groups

In this paper, we calculate the $\phi (\hat{\phi})-$Selmer groups S^{(\phi)} (E / \Q) and S^{(\hat{\varphi})} (E^{\prime} / \Q) of elliptic curves $y^{2} = x (x + \epsilon p D) (x + \epsilon q D)$ via descent theory (see [S, Chapter X]), in particular, we obtain that the Selmer groups of several families of such elliptic curves can be arbitrary large.Comment: 22 page

Evaluation of outer race tilt and lubrication on ball wear and SSME bearing life reductions

Several aspects of the SSME bearing operation were evaluated. The possibility of elastohydrodynamics (EHD) lubrication with a cryogenic fluid was analyzed. Films as thick as .61 microns were predicted with one theory which may be thick enough to provide hydrodynamic support. The film formation, however, is heavily dependent on good surface finish and a low bulk bearing temperature. Bearing dynamics to determine if the radial stiffness of a bearing which are dependent on bearing misalignment were analyzed. Four ball tests were conducted at several environmental conditions from an LN2 bath to 426 C in air. Surface coatings and ball materials are evaluated. Severe wear and high friction are measured for all ball materials except when the balls have surface lubricant coatings

The PTPN22 Locus and Rheumatoid Arthritis: No Evidence for an Effect on Risk Independent of Arg620Trp

The Trp(620) allotype of PTPN22 confers susceptibility to rheumatoid arthritis (RA) and certain other classical autoimmune diseases. There has been a report of other variants within the PTPN22 locus that alter risk of RA; protective haplotype '5', haplotype group '6-10' and susceptibility haplotype '4', suggesting the possibility of other PTPN22 variants involved in the pathogenesis of RA independent of R620W (rs2476601). Our aim was to further investigate this possibility.A total of 4,460 RA cases and 4,481 controls, all European, were analysed. Single nucleotide polymorphisms rs3789607, rs12144309, rs3811021 and rs12566340 were genotyped over New Zealand (NZ) and UK samples. Publically-available Wellcome Trust Case Control Consortium (WTCCC) genotype data were used.The protective effect of haplotype 5 was confirmed (rs3789607; (OR = 0.91, P = 0.016), and a second protective effect (possibly of haplotype 6) was observed (rs12144309; OR = 0.90, P = 0.021). The previously reported susceptibility effect of haplotype 4 was not replicated; instead a protective effect was observed (rs3811021; OR = 0.85, P = 1.4×10(-5)). Haplotypes defined by rs3789607, rs12144309 and rs3811021 coalesced with the major allele of rs12566340 within the adjacent BFK (B-cell lymphoma 2 (BCL2) family kin) gene. We, therefore, tested rs12566340 for association with RA conditional on rs2476601; there was no evidence for an independent effect at rs12566340 (P = 0.76). Similarly, there was no evidence for an independent effect at rs12566340 in type 1 diabetes (P = 0.85).We have no evidence for a common variant additional to rs2476601 within the PTPN22 locus that influences the risk of RA. Arg620Trp is almost certainly the single common causal variant