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It is proved that the set of closed classes containing some minimal classes in the partially ordered set $${\cal L}_2^3$$ of closed classes in the three-valued logic that can be homomorphically mapped onto the two-valued logic has the cardinality of continuum.

Frictional tests of fuel-rod casings and spacing cells are conducted in various conditions. The frictional coefficients are determined for different loads. The influence of factors such as vibration, the contact load, the sample speed, the atmosphere, and the temperature is considered.

During exploitation, fuel assemblies are subjected to vibration loads caused by vibrations of intracase devices, pressure pulsations, acoustic waves, and turbulent flow of the coolant. Vibrations of the fuel assembly can be the cause of damage to its details, particularly, fuel elements and spacer lattices, because of their wear. Therefore, one requirement for the project of the fuel assembly of AES-2006 reactor installations is vibration strength and resistance throughout the service life of the fuel assembly in the reactor. The vibration strength and fuel assembly strength are substantiated by computational-experimental methods using the results of the experimental modal analysis of the full-scale mockup for verification.

Seismic tests of full-scale mockups of fuel assemblies from the VVER-1000 reactor permit the determination of the transfer characteristics between the stimulus (acceleration of the supports) and the response of the fuel assemblies. No resonant responses of the fuel assemblies to seismic loads are observed.

Intrinsic and forced vibrations of a reactor pile in standing water and in coolant flux are investigated. The eigenfrequencies and damping factors of the intrinsic vibrations and the parameters of forced vibrations of the fuel rods are determined. The influence of the auxiliary spacers on fuel-rod vibrations is discussed.

A procedure and results of seismic stability tests of full-scale models for fuel assemblies of the water-water energetic reactor VVER-1000 are presented. In the course of tests, kinematic loading of fuel assembly supports has been carried out in accordance with accelerograms of the motion of fuel assembly supports during an earthquake, which was obtained by computational methods. Based on the results of measurements of the vibrational response of fuel assemblies, transfer characteristics between the response of fuel assemblies and applied action (support acceleration) are determined. The lack of a resonant response of fuel assemblies at seismic loads is found.

The dynamic characteristics and wear of unattached fuel rods in the lower supporting lattice are investigated. The vibrational eigenfrequencies and dynamic rigidity of the fuel rods in different configurations are determined. The vibrational wear at contact between the fuel rods and the spacing elements is studied.

The wear resistance of fuel assemblies in the VVER-440 water-moderated reactor is investigated, with small fuel-rod diameter. The experimental apparatus, the model of the fuel rods, and the similarity conditions are described; the possibility of applying the experimental results to regular fuel rods is noted.

The methods and results of research to substantiate the wear resistance of VVER-440 fuel assemblies with smaller nominal fuel-element diameters are shown. The results of tests of the fuel elements of VER-1000 fuel assemblies with zirconium spacer grids for fretting corrosion were used for substantiation. The test bench, the test model of the fuel element, the conditions of similarity, and the transferability of the results of experimental tests to standard fuel elements are described. It is shown that spent fuel elements with smaller diameters have significant wear resistance in contact with spacer grids.

Fuel-rod casings and spacing cells are subjected to frictional tests, with variation in the technological and operational factors.

The possible structural deformation of the fuel assembly in a nuclear power plant when dropped during transportation or other operations is considered. The consequences of such damage are studied.

A procedure and findings of investigations of the dynamic characteristics and the wear of fuel elements in the framework of the development of a perspective design of fuel elements without fastening in a lower support grid are presented. At the first phase of the work, natural vibration frequencies and the dynamic rigidity of fuel elements are determined in various design variants of lower spans. Resonance frequencies of spans of fuel elements are revealed by minimums of the dynamic rigidity. At the second phase, investigations of vibrational wear within contact of fuel elements with cells of spacer grids are performed on models of a lower part of a fuel assembly. Four embodiments of the lower part of the fuel assembly are investigated. As a result of the application of high vibrational loads, the wear of fuel element cans and grid cells is observed in more than a half of contact assembles of fuel elements with spacer grids. The most and least wear-resistant designs of the lower part of the fuel assembly are determined by results of tests.

The wear of frictional steel and cast-iron surfaces in high-temperature (400–550°C) liquid-metal coolants in BREST and SVBR nuclear-power units is studied experimentally. It is shown that long life of the surfaces in reactor operation may be ensured by applying and maintaining protective oxide coatings.

The tribological problems posed by heavy liquid-metal heat carriers used in the circuits of nuclear power plants are discussed. The results of experimental study of the vibrational wear of heat-exchanging tubes in the interfaces with the spacing grates are presented. These results are applicable for testing the vibrational strength of the steam generator of a fast neutron reactor with lead heat carrier. Experimental investigation and service-life tests of involute-profile cylindrical tooth gears and sliding bearings working in fast neutron reactors containing the lead heat carrier are conducted. Experimental and theoretical study is performed on the wear of steel and cast-iron sliding bearings in the recycling pumps of reactors operating in lead, eutectic lead-bismuth and lead-lithium alloys. It is shown experimentally that the tooth gears from 40X13 steel and SCh20 grey iron are capable of operating in the lead heat carrier for 500 and 400 hours, respectively, at the temperature 450°C when the concentration of thermodynamically active oxygen in the lead is close to saturation, the contact stress in the gearing is 758 MPa, the gear rotational frequency is 500 min−1 or less, and the gear ratio is 1.5 (the peripheral velocity of the gear and the wheel over the pitchline is 2.1 m/s). The likely causes of destruction of the gear teeth are adhesive wear and insufficient heat resistance (refractorability) of the tooth material at 450–500°C.

The vibrational wear at the junctions of heat-exchanger pipe and spacer grids is studied experimentally, so as to confirm the shock resistance of hot-water generators in fast reactors with lead coolant. Endurance tests of tube and spacer samples are conducted. Metallographic and profilometric data on samples subjected to vibrational wear are presented. The wear mechanism is described. A preliminary estimate is obtained for the pipe life in the steam generator.

Experimental equipment designed for solving tribological problems arising in friction units operating in heavy liquid-metal heat carriers for nuclear-reactor circuits is discussed. In order to study fretting corrosion, a setup has been produced that simulates the wear of a fuel element in contact with a spacer grid cell. Thus, the vibration strength of the steam generator of a fast-neutron reactor with a lead heat carrier is substantiated. An experimental setup for studying and carrying out endurance testing of cylindrical gears with standard circuit and plain bearings operating in fast-neutron reactors in the medium of a lead heat carrier is described. Experimental specimens of circulation pumps for reactor equipment are developed for investigation of the wear of steel and cast-iron plain bearings operating in lead medium and the wear of eutectic lead-bismuth and lead-lithium alloys.

Studies of the frictional interaction between samples of standard elements simulating contact conditions in a friction couple consisting of a fuel cell shell and a spacing grid cell were conducted. The studies were carried out with a special test bench. The effects of the load parameters, the contact geometry of the specimens, and the state of the working surfaces on friction processes were studied. The values of the friction factors for elements made of zirconium alloys were obtained, which are needed for calculation and experimental testing of the strength of a fuel assembly. The presence of protective oxide films on the friction surfaces of specimens is shown to significantly reduce the friction factor and diminish the probability of seizure.

The influence of annealing on bulk samples of Ti49.4Ni50.6 alloy subjected to severe plastic deformation by torsion under high pressure has been studied by transmission electron microscopy and X-ray diffractometry. It is found that a homogeneous nanocrystalline state is formed in the bulk samples after annealing.