ISSN 1068798X, Russian Engineering Research, 2011, Vol. 31, No. 11, pp. 1072–1077. © Allerton Press, Inc., 2011. Original Russian Text © Yu.N. Drozdov, V.V. Makarov, A.V. Afanas’ev, I.V. Matvienko, V.N. Puchkov, 2011, published in Vestnik Mashinostroeniya, 2011, No. 11, pp. 36–42.

Friction and Wear of Fuel Assemblies in WaterModerated Reactors Yu. N. Drozdova, V. V. Makarovb, A. V. Afanas’evb, I. V. Matvienkob, and V. N. Puchkova a

Blagonravov Institute of Mechanical Engineering, Russian Academy of Sciences, Moscow b Gidropress Design Office email: [email protected]

Abstract—Static and dynamic processes that involve frictional forces are experimentally studied. The fric tional forces affect the stress of the fuel assembly in all stages of the life cycle. DOI: 10.3103/S1068798X11110062

Friction and wear in machines have been under study since the middle of the last century. At present, all developed nations have scientific societies devoted to tribology, because the wear of machines is responsi ble for enormous economic losses each year, despite the development of very effective preventive measures. The difficulty in preventing wear is that it is a complex nonlinear process. Tribologists adopt a range of con cepts—from mechanics, chemistry, physics, materials science, mathematics, similarity theory, and else where—in describing friction and wear. In atomic power—in particular, within the housing and piles of VVER1000 watermoderated reactors (Fig. 1)—some components operate in frictional con ditions different from those generally encountered in manufacturing equipment. Such distinctive condi tions include the need to use corrosionresistant steel and zirconium alloys in frictional pairs; the inability to use lubricant; high temperatures; operation in a cool ant (water) flux; radiation; and hindrances to mainte nance. In the pile of the VVER1000 reactor, there are several thousand junctions between fuel rods and the spacing grid with free play. On account of elastic defor mation of the fuel rods and the spacing grid, forces and torques from the grid act on the fuel rods. The interac tion between the fuel rods and spacing grid was described, for example, in [1]. The state of these junctions may change from mobile to immobile during pile assembly and opera tion. This is associated with mutual slip and friction of the components. The frictional forces may result in impermissible deformation of the spacing grid and wear of the fuelrod casings, which must be taken into account in the design process. Slip of the fuel rods with respect to the spacing grid occurs in pile assembly; in the course of operation, as a result of nonsynchronous thermomechanical elon gation of the fuel rods and the guide channel; and in fuelrod vibration excited by the coolant flux. To con trol the pile lifecycle from design to removal from ser vice—in particular, to establish the required thermo

mechanical and vibrational strength—we need to understand the friction and wear of its components. This requires experimental study. In pile manufacture, the guide channels and fuel rods are successfully inserted in the cells of a series of fixed spacing grids stacked vertically on a horizontal assembly bench. Lacquer coatings are used to reduce the frictional forces. Without lacquer, the maximum total frictional forces at all the spacing grids may sig nificantly exceed 1000 N. Longitudinal scratches and shavings are formed in slippingfriction zones at the surface of the fuelrod casings. This indicates plastic displacement and cutting. Economic considerations support the elimination of the lacquer but, in that

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(a)

(b)

1 2 3

(c)

4 (d)

5

Fig. 1. Fuel assembly of VVER1000 reactor and its com ponents: (a) fragment of spacing grid and guide channel; (b) spacinggrid cell; (c) spacing grid with fragments of guide channel; (d) framework fragment consisting of guide channel and spacing grid; (1) head; (2) guide channel; (3) fuel rods; (4) spacing grid; (5) tailpiece.

FRICTION AND WEAR OF FUEL ASSEMBLIES IN WATERMODERATED REACTORS

case, some means of reducing the frictional forces and the depth of the damage must be found. Quasistatic frictional forces arise in the nonsyn chronous motion of the fuel rods and guide channel on account of thermal and radiative creep of the material and elongation of the fuelrod casings: 312 fuel rods slip relative to the framework consisting of the guide channel and the spacing grids (soldered to the chan nels), and longitudinal frictional forces are applied to the spacing grids. The frictional forces mainly depend on the clearance between the fuel rod and the sur rounding spacinggrid cell [2]. At the beginning of this century, in order to create a rigid pile with a welded framework, attention focused on the strength of the framework with nonsynchronous thermomechanical elongation of the fuel rods and the guide channel. To assess the thermomechanical strength of the spacing grids, the forcing of a bundle of fuel rods (without pre liminary treatment) through spacing grids soldered to guide channels was tested in doublespan mockups of a reactor pile [3]. These tests provided valuable infor mation. The frictional coefficients of zirconium alloys and the influence of structural, technological, and opera tional factors were unknown. Here the structural fac tors include the tightness and state of the contact sur faces (ground, anodized, with an oxide coating), while operational factors include vibration and the slip rate in thermomechanical elongation. The most conserva tive measures were adopted to ensure thermomechan ical strength of the pile with a welded framework. The bestknown effects of frictional forces in the operation of pressurizedwater reactors are as follows: (1) fretting wear of the fuel rod in contact with the spacinggrid cell when a gap is present; (2) extreme vibration. In a boilingwater reactor, fretting wear by debris is observed—that is, wear of the fuelrod casing in contact with foreign objects. Transverse vibration is due to the interaction of the fuel rods with the longitu dinal–transverse coolant flux. In improving pile design, attention must also be paid to the friction of the upper fuelassembly compo nents with tightening of the upper casing and with clamp attachment of the removable fuelassembly cap to the guide channel. The upper components are rede signed to as to eliminate jamming, by increasing the gap between the mobile components using directional spring covers and clamp linings. In simulation tests of the pile, the frictional forces in the reactor’s active zone and in highspeed removal of fuel assemblies from the reactor were also investi gated. The frictional forces were determined as a func tion of the rate at which a fuelassembly mockup is moved into and out of a cell consisting of six fuel assemblies. Faster motion of the fuel assemblies in and out of the active zone was shown to be beneficial. We now consider the results of investigating friction in the pipe of a VVER1000 reactor. RUSSIAN ENGINEERING RESEARCH

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F, N 600 400

Motion without ultrasound Displacement Application of ultrasound

200 0 40

Motion with ultrasound

45

50

55

60 t, s

Fig. 2. Dependence of the frictional force F on the time t in fuelrod motion with and without ultrasound.

To reduce the frictional forces in pile assembly, we investigate the influence of ultrasound on the friction of the fuelrod casings and spacinggrid cells. To this end, we consider a fragment of the welded pile frame work containing 10 spacing grids and 18 guide chan nels and a fuelrod casing in air at normal tempera ture. The longitudinal (pushing) force is applied to the upper cap of the fuel rod by means of a dynamometer and a longitudinalultrasound emitter. The test results are summarized in Fig. 2. Without ultrasound, the longitudinal force is 700–800 N; with ultrasound, it is 180–210 N. The decrease in the force depends on the ratio of the longitudinal velocity and the ultrasound’s wave velocity and may be attributed to the additional force created by the ultrasound. In some countries, at the end of the twentieth cen tury, there were incidents at pressurizedwater reactors in which the control rods of the safety system jammed in the guide channel of the pile, on account of the increased frictional force in distorted fuel assemblies. In that period, research was conducted in Russia and elsewhere to establish the causes of fuelassembly dis tortion and incorrect triggering of the safety system. On a fullscale mockup of the pile in a VVER1000 reactor, the dependence of the descent time and fric tional forces of the control rods on the curvature of the fuel assemblies was investigated [4]. Data were also obtained for the elastic and inelastic drag forces on the fuel assemblies in transverse flexure. In Fig. 3, we present the frictional force as a function of the height of the control rods in fuel assemblies with typeIII dis tortion and the elasticflexure line of the fuel assem blies. The experiments indicate that the critical parameter determining the jamming of the control rods is the curvature of the guide channel, which is the inverse of the fuel assemblies’ radius of curvature. Sec tions characterized by change in flexure (by inflection) are responsible for secondary local increase in the fric tional force. Fuelassembly flexure of types I and II (types C and S), with limiting amplitude of 25 mm, which is observed in nuclear plants, has almost no influence on the descent time and frictional forces of

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175 125 75 1

25

SG1

0

SG4

1

SG8

2

SG12

3

4 H, m

Fig. 3. Dependence of the frictional force F on the height H of the control rod in the fuel rod with typeIII distortion (2) and line of elastic flexure of fuel assembly (1): SG, spacing grid.

Force, kgf 150 100 y = 24.65x + 0.17 R2 = 0.98

–15

–10

–5

y = 9.28x + 10.99 R2 = 1

50

0 –50

5 10 15 Displacement, mm

–100 –150 Fig. 4. Dependence of the transverse displacement of spac ing grid 7 on the transverse force P for a fuelassembly model with a welded framework.

FRF 4

1

3

2 3

2

5 4

1 0

5

10

15 f, Hz

Fig. 5. Transfer functions of the fuel assembly with the excitation of support vibrations of amplitude 0.2 (1), 0.5 (2), 1 (3), 2.5 (4), and 5 (5) m/s2.

the control rods in guide channels, while typeIII flex ure of amplitude around 13 mm leads to impermissible slowing and jamming of the control rods. Jamming of the control rods may be prevented by eliminating impermissible curvature of the fuel assem blies—specifically, by increasing the flexural rigidity of individual fuel assemblies in a new design with a

welded framework (rigid fuel assemblies) and reducing the longitudinal force on the fuel assemblies. The cre ation of rigid fuel assemblies is associated with flexure tests of dozens of different fuel assemblies under the action of a transverse point force. The appearance of frictional forces is observed in the form of hysteresis loops on the force–displacement diagrams. The dependence of the fuel assemblies’ flexure on the transverse force is nonlinear (Fig. 4) [5]. The characteristics obtained in model flexure have several sections with significantly different values of the reduced rigidity (the ratio of the transverse point force applied to the middle spacing grid of the fuel assembly and the displacement of the middle spacing grid). With a displacement of no more than 1 mm (in the initial section), the rigidity consists of two compo nents: the rigidity of the framework; and the rigidity of the fuel rods that are motionless with respect to the spacinggrid cells. With increase in transverse dis placement, the fuel rods move and begin to turn, with slip relative to the supporting projections of the spac inggrid cells. The angular rigidity of the fuelrod sup port (the torque divided by the angle of rotation) declines [3]; the reduced rigidity of the fuel assemblies also declines. After the fuel rods begin to rotate in the spacing grid, some of the reaction forces and torques of the supports are due to elastic drag of the cells, while the remainder is due to inelastic drag (friction). Fric tion explains the hysteresis of the mockup’s flexural characteristic. In fuelrod rotation with transverse flexure of the fuel assemblies, friction is due to increase in damping and decrease in the frequencies of resonant vibration with increase in the amplitude. These effects are con siderable at large amplitudes of lowfrequency vibra tion—as in seismic activity, for example. The influ ence of the vibrational amplitude on the modal char acteristics of the fuel assemblies has been studied in a model with kinematic loading of the supports by a sinusoidal vibrational load, with variation in the accel eration from 0.2 to 5 m/s2 [6]. With increase in the acceleration (Fig. 5), the resonant frequencies are dis placed to lower frequency, while the amplitude of the transfer function at resonance (the amplitude ratio of the response and stimulation) declines. In some cases, at support accelerations of 1–3 m/s2, the lowfre quency shift of the resonant frequencies practically stops, and the modulus of the transfer function at res onance begins to increase. This may be explained in that, at small vibrational amplitudes, there is no rela tive displacement of the components in the fuel assembly. In other words, the fuel assembly behaves as an integral unit. With increase in vibrational ampli tude, slip and friction of the components in the fuel assembly is observed (for example, slip of the fuel rods on rotation in the spacinggrid cells, displacement of the fuel rods). The number of slipping components increases with increase in vibrational amplitude of the support.

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Analysis of the operational reliability of piles in pressurizedwater reactors and boilingwater reactors indicates that failure is often due to fretting wear, which may be attributed to friction of the slipping fuel rods and spacing grids in coolant (water) that contains oxygen. At Gidropress Design Office, model test methods whose results may be transferred to industrial fuel assemblies have been developed [7]. Fretting wear of fuel rods and spacing grids and the corresponding structural materials have been investigated for coolant temperature, pressure, speed, and chemical composi tion that are close to the industrial standards [8]. These experiments show that the junctions of the fuel rods with both steel and zirconium spacing grids have a considerable margin of vibrational strength in normal operating conditions. When the vibrational amplitude of the fuelrod casings is several times greater than the design values and the joints between the fuel rod and spacing grid contain gaps, their wear is similar to that of regular piles operating with extreme vibration. Tests in a specially designed tribometer and autoclave per mit calculation of the wear coefficients of the zirco nium alloys in the Archard equation. The wear coeffi cient of zirconium fuelrod casings with zirconium counterbodies (spacinggrid cells) is 0.6 × 10–3. To determine the frictional coefficients of zirco nium components, the friction between samples of regular components simulating the contact between a fuelrod casing and a spacinggrid cell in the pile of a VVER1000 reactor was investigated for the first time at Gidropress Design Office in 2006 [9]. A specially designed tribometer was used to measure the frictional coefficients during the reciprocating motion of a fuel rod casing in contact with three fragments of the spac inggrid cell (Fig. 6). The influence of the loading parameters, the length of the contact line, the sample geometry, and the combination of working surfaces on the frictional processes was assessed. For the first time, the frictional coefficients were determined for zirco niumalloy components. The frictional coefficient is 0.55 for the components supplied and a third as much after the formation of a surface oxide film. The influence of the normal contact force, the rel ative velocity, the geometry of the spacinggrid cell, and the state of the contact surfaces on the frictional coefficient was determined in [10]. The basic forms of friction are the friction of surfaces with complete (ffr = 0.5–0.8) or partial (ffr = 0.2–0.5) contact of pure metallic surfaces; and the friction of surfaces with protective films (ffr = 0.1–0.2). The pro tective films are disrupted by the contact pressure, which depends on the normal force and the actual contact area, and the relative velocity of the samples. In terms of the state of the surfaces and the varia tion in frictional coefficients, the tests may be divided into three groups. (1) Frictional pairs with etched and ground sur faces of fuelrod casings and spacinggrid cells as sup RUSSIAN ENGINEERING RESEARCH

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Fcont 1

Fcont Fcont 2

Displacement Fig. 6. Frictional testing of samples with longitudinal vibrational slip: (1) mobile fuelrod casing; (2) counter bodies (fragments of spacinggrid cells).

plied by the plant. This group is characterized by fric tion with complete or partial contact of metallic sur faces over the whole range of contact speeds and normal forces. The mean frictional coefficient is 0.5– 0.6; in some experiments, it is 0.83. (2) Frictional pairs with anodized surfaces of fuel rod casings and spacinggrid cells as supplied by the plant. These pairs are autoclaved in water or oxidized in a thermostat in air at 320°C for 3 h. At the beginning of the process, the frictional coefficient is 0.1–0.2; this is typical of surfaces with protective films. In the course of the process, the protective films are com pletely or partially disrupted. With partial disruption, the frictional coefficient increases to 0.2–0.5; with complete disruption, it reaches the values typical of the first group. (3) Frictional pairs with fuelrod casings and spac inggrid cells subjected to 35h autoclaving in water at 320°C or 15h oxidation in air at 320°C (in a thermo stat). Over the whole range of normal forces and speeds, the frictional coefficients are 0.1–0.2. This indicates relatively high strength of the protective films. Until recently, there had been no formal study of the influence of factors such as transverse vibration, the superlow relative speeds of the samples typical of radiative elongation of the fuel rods, and the tempera ture and the medium present. The influence of these factors on the frictional force of zirconium alloys was determined in [11]. Since the frictional coefficients of zirconium alloys are very different at different stages of the pile’s life cycle, fragments of ground fuelrod cas ings and spacinggrid cells of the TVS2006 pile were considered in the state received from the plant (with out protective films) and with protective films obtained by autoclaving. Fragments of regular fuel

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vibration

0.4

Without vibration

With vibration

0.2 0

0.6

1.2

1.8

2.4

3.0

3.6 X, mm

Fig. 7. Influence of vibration on ffr in the direction of the linear motion: Fcont = 1 N; f = 16.5 Hz.

(а)

Z, µm 180

428 360 Y, µ m

90 0

240 128 256 X, µ 384 m

120 512

(b)

0

Z, µm 428

370 185

240

256 512 X, µ 768 m

Y, µ m

360 0

120 1024

1200 0

Fig. 8. Wear areas of autoclaved fuel rods (a) and spacing grid cell (b): Fcont = 1 N; f = 16.5 Hz.

rod casings and spacinggrid cells with contact projec tions were tested on a UMT3M (CETR) tribometer with motion along the X axis. The test conditions were as follows: temperature 20 or 320°C; friction in the presence of air or water; speed 0.001 and 1 mm/s; con tact force Fcont = 1–10 N; with and without transverse vibration along the Y axis (frequency 16.5 Hz; ampli tude 40 µm); frictional path length (along the X axis) 5 mm. In tests of autoclaved samples without vibra tion, ffr = 0.15–0.20. In tests with vibrations, the fric tional coefficients are anomalously low (0.03) in some regions in the direction of the linear motion (Fig. 7). Such values are only expected for autoclaved samples

with transverse vibration and a longitudinal slip veloc ity of 0.001 mm/s, simulating longitudinal extension of the fuel rods on irradiation. Depending on the load, the temperature, and the frictional path, such behavior is either retained over the whole experiment or replaced by friction with ffr = 0.6 in the direction of linear motion. The increase in the frictional coefficient is due to wear of the protec tive film on the spacinggrid cell (or on both the fuel rod casings and spacinggrid cell) as a result of vibra tion and consequent transition to the friction of clean metal surfaces, for which ffr = 0.6. An anomalously low frictional coefficient is also seen in tests with a regular spacinggrid cell that has three contact projections. The depth of the surface wear after frictional tests is 6– 8 µm, while the thickness of the oxide film is no more than 1 µm. The contact tracks after the tests are shown in Fig. 8. For samples in the state supplied, without trans verse vibration, ffr = 0.5–0.6; with transverse vibration in the direction of the linear motion, the frictional coefficient may vary within the range 0.2–0.6, at twice the frequency of the transverse vibrations. In other words, the transverse vibration is associated with con siderable periodic decrease in frictional force in the direction of the linear motion. The temperature and the medium (air or water) have no statistically signifi cant influence on the frictional coefficient. Thus, factors such as transverse vibration, the low relative speeds of the fuelrod casings and spacinggrid cell, and the oxidized contact surfaces reduce the fric tional force severalfold. Note that normal operation of the pile in the reactor will not be observed without pro tective films on the fuelrod casings and spacinggrid cells, without vibration, and with high longitudinal speed. With 30mm elongation of the fuel rods in three years, the mean speed is 0.02 µm/min. In other words, the distance traveled by the end of the fuel rod each minute is less than the characteristic standard rough ness of the rod surface. If we take account of such low speeds, the nonuniform neutron flux, and the contact elasticity, we would expect the slipping of each fuel rod in each spacinggrid cell to be different, discontinu ous, abrupt, and asynchronous. In other words, it is unlikely that 312 fuel rods will move in the spacing grid and apply frictional force synchronously and at the same rate, in contrast to experiments in which 312 fuel rods were pushed through the spacing grid [3]. Since the likelihood of simultaneous action of these factors is small, we believe that radiative elongation of the fuel rods cannot account for the considerable thermome chanical loads (frictional forces) on the spacing grid and its associated deformation and failure. Note, in conclusion that, together with other mea sures, the creation of rigid fuel assemblies—in other words, conversion of the mobile joints between the guide channel and spacing grid to immobile joints by point welding—prevents distortion of the fuel assem

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blies but creates longitudinal thermomechanical loads on the spacing grid as a result of the frictional forces exerted on the grid by the fuel rods as a result of their asynchronous radiative elongation. Research shows that the existing rigid piles have a considerable margin of strength, which may be utilized in subsequent improved pile designs. For example, options might be to reduce the wall thickness of the spacinggrid cells from 0.3 to 0.25 mm; and to increase the contact length of the spacing grid and the fuel rod, so as to reduce the contact pressure and increase resistance to fretting wear. Application of ultrasound to reduce the frictional forces might facilitate pile assembly. Experimental research at Gidropress Design Office on the static, thermomechanical. and vibrational strength of pile designs for watermoderated reactors shows that the frictional forces in the pile have a signif icant influence on its strength and performance and also on reactor safety. These results have been used to improve the strength and reliability of Gidropress pile designs. Note that all the major producers of reactor fuel study the fretting wear of fuel assemblies and the con tact between the fuel rod and spacing grid so as to improve the structure of such junctions, but not from a tribological perspective. In tribology, we adopt a sys temic approach [12]: in considering the frictional components, we analyze the inputs and loads, the sys tem’s structure (body, counterbody, medium), the use ful outputs (for example, the working life), and the parameter variation over time. These aspects of the contact between the fuel rod and spacing grid and its influence on the strength of the pile have yet to be seri ously studied.

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9.

REFERENCES

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1. d’Uston, B., Nonlinear Vibrations of Fuel Rods under Turbulent Excitation, Kadarash: IAEA, 2004, paper 3.3. 2. Enin, A. and Ustimenko, A.P., Comparative Analysis of the Interaction between Fuel Rods and the Rigid Fuel Assembly in a New Generation of WaterModerated Reactors, Sbornik dokladov 5oi Rossiiskoi konferentsii: Metody i programmnoe obespechenie raschetov na prochnost’ (Proceedings of the Fifth Russian Confer ence on StrengthCalculation Methods and Software), Moscow: FGUP NIKIET, 2010. 3. Ustimenko, A.P. and Shustov, M.A., Mechanical Char acteristics of Reactor Fuel Assemblies from Experi ments on Components and Small Models, Sbornik

11.

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Vol. 31

12.

No. 11

1077

dokladov 2i Rossiiskoi konferentsii “Metody i program mnoe obespechenie raschetov na prochnost’ ” (Proceedings of the Second Russian Conference on StrengthCalcu lation Methods and Software), Moscow: FGUP NIKIET, 2002, pp. 90100. Gushchik, I.A., Makarov, V.V., Seleznev, A.V., and Komarova, S.N., Passage of Flexible Fuel Rods in Deformed Channels, Problemy resursa i bezopasnosti energeticheskogo oborudovaniya (Life and Safety of Power Equipment), Moscow: ImMASh im. Blagonra vova RAN, 1999, pp. 131–136. Vasil’chenko, I.N., Seleznev, A.V., Kobelev, S.N., Makarov, V.V., Afanasjev, A.V., Matvienko, I.V., Enin, A.A., and Ustimenko, A.P., Experimental Verification of FA for WWER1000. Investigations of TVS2M, Seventh International Conference on WWER Fuel Performance, Modelling and Experimental Support, Albena, Bulgaria, 2007. Makarov, V.V., Afanasyev, A.V., Matvienko, I.V., Tutnov, Al.A., Kiselev, Alexander.S., Kiselev, Alexey.S., and Volkov, S.E., WWER FA Modal Analysis under Vibration Force and Kinematic Excitation, Seventh International Conference on WWER Fuel Performance, Modelling and Experimental Support, Albena, Bulgaria, 2007. Drozdov, Yu. and Makarov, V., Method for Investigating Fretting Corrosion of Fuel Elements of Nuclear Power Reactors, Vestn. Mashinostr., 1991, vol. 71, no. 1, pp. 9–12. Makarov, V.V., Afanas’ev, A.V., and Grishakov, A.V., Resistance of VVER440 Reactor Fuel Rods to Fretting Corrosion in Contact with Spacing Grids, Vopr. At. Nauki Tekhn., 2011, no. 29, pp. 34–40. Drozdov, Yu.N., Makarov, V.V., Afanas’ev, A.V., et al., Dynamics of the Frictional Interaction between the FuelRod Casing and the SpacingGrid Cell in a Pile, Vestn. Mashinostr., 2007, no. 3. Makarov, V.V., Afanas’ev, A.V., Matvienko, I.V., et al., Friction at a Single Contact Formed by the FuelRod Casing and the SpacingGrid Cell, 5ya mezhdunarod naya nauchnotekhnicheskaya konferentsiya Obespeche nie bezopasnosti AES s VVER (Fifth International Con ference on the Safety of Nuclear Plants with Water Moderated Reactors), Podolsk: OKB Gidropress, 2007. Puchkov, M.V., Makarov, V.V., Afanas’ev, A.V., et al., Frictional Tests of FuelRod Casings and SpacingGrid Cells with Variation in Structural, Technological, and Operational Factors, Vopr. At. Nauki Tekhn., 2010, no. 27, pp. 53–58. Chihoshi, H., Systems Analysis in Tribonics (Russian translation), Moscow: Mir, 1982.

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