Radial Deformation Research Articles

Combined Effect of In Situ Stress Level and Bedding Anisotropy on Hydraulic Fracture Vertical Growth in Deep Marine Shale Revealed via CT Scans and Acoustic Emission

The economic exploitation of unconventional gas and oil in deep shale relies closely on effective hydraulic fracturing stimulations. However, the fracturing operations of deep shale reservoirs face challenges of insufficient fracture growth and a rapid decline in productivity due to the increasing in situ stress level. In addition, the shale strata on the margin of the Sichuan Basin are frequently folded and faulted, and the change in bedding inclinations significantly complicates the process of hydraulic fracturing. The investigation of the combined effect of the in situ stress level and bedding anisotropy on the hydraulic fracture configuration is vital for fracturing engineering design. To analyze this, we conducted hydraulic fracturing tests on shale cores to simulate the hydraulic fracture initiation and growth from a horizontally positioned perforation. By using acoustic emission detection and CT scans, the influence of natural stress levels and the angle of the shale’s bedding on the process of hydraulic fracturing in shale and the resulting fracture geometry were analyzed. The results showed that the area of hydraulic fracture under a higher stress level (σ1 = 50 MPa, σ3 = 40 MPa) was about 13%~23% smaller than that created under the lower stress level (σ1 = 30 MPa, σ3 = 20 MPa) when the bedding angle was smaller than 60°. With the increase in bedding angle, the curves of the fracture area and fracture network index under two different stress levels presented similar decreasing trends. Also, the time from micro-crack generation to sample breakdown was significantly reduced when the bedding orientation changed from the horizontal to vertical position. The increasing stress level significantly increased the breakdown pressure. In particular, the fracturing of shale samples with bedding angles of 0° and 30° required a higher fluid pressure and released more energy than samples with larger bedding inclinations. Additionally, the measurement of the sample radial deformation indicated that the hydraulic fracture opening extent was reduced by about 46%~81% with the increasing stress level.

Detection and localization of LV winding radial deformation in transformers using electromagnetic waves - a feasibility study

Recently, online methods based on electromagnetic waves have been proposed to detect the mechanical defects of high voltage (HV) windings in power transformers. In this article, for the first time, the possibility of online detecting and locating the radial deformation (RD) of low voltage (LV) windings using electromagnetic waves is presented. In the proposed method, a high frequency and wideband signal is sent to a simplified model of transformer winding via small antennas. The antennas are connected to the inner side of the oil tank cover through Radio Frequency (RF) cables, so that online monitoring can be realized with minimal changes in the transformer structure. The data of the reflected signals in different states is recorded in a database and sorted as primary data bank. By comparing the results of the sound state with measured signals, the possible faults can be detected. In this paper, the detection and location of radial deformation is estimated by using regression tree based on three features. Several cases are simulated by Computer Simulation Technology (CST) software, and their verification are conducted by a setup in laboratory. Based on comparison results, it can be claimed that the proposed method has LV windings radial deformation online detecting and locating ability with an acceptable accuracy.

DETERMINATION THE STRESS AND DEFORMATION OF THE CANNON BARREL WHEN FIRED

This paper presents a calculation process of the stress field of the 130M46 cannon barrel when firing under the load of gas pressure and temperature. The paper will focus on calculating the stress of a barrel and solving some disadvantages of previous methods using the finite element method and the simulation tools of the CFD software. The calculation results are the stress and deformation parameters of the barrel such as normal stress, tangential stress, average stress, radial deformation, tangential deformation, and total displacement. These stress values are determined when firing 1 shot and 8 consecutive shots to determine the allowable durability limit of the gun barrel material. The result of this research can be used to study and analyze some similar technical issues in weapons.

Working process and opening characteristics of soft insulator of pulse motor

AbstractIn this paper, a simulation test system for the working process of soft insulation is designed, using equivalent simulated ablation test methods combined with a CCD measuring system and micro electron microscope scanning technology, which can better describe the thermal properties and state of insulation after ablation. At the same time, a test plan for the opening characteristics of the insulator based on different ablation times and different opening structure sizes as the main influencing factors are designed. The experimental results show that the ablation test can well simulate the state of an actual pulse engine compartment after the ablation and the maximum relative error of the ablation rate can be controlled within 5 %. From the influence of ablation time on the opening characteristics of the insulator, it can be seen that the maximum axial deformation of the insulator is different from the relative value of the opening pressure. The radial deformation of the insulator is larger than that of the non‐ablated insulator and larger than the inner diameter of the insulator shell after ablation. From the influence of the size of the opening structure of the insulator (depth of weakening grooves) on the opening characteristics of the insulator, it can be seen that as the weakening groove depth of the compartment deepens, the original pressure change pattern disappears, and the opening pressure and opening time of the insulator decrease significantly.

А particle model of interaction between weakly non-spherical bubbles

A mathematical model of interaction of weakly non-spherical gas bubbles in liquid is proposed. It is a system оf the second order ODEs in the radii of bubbles, the position vectors of their centers and the amplitudes of their small deformations in the form of spherical harmonics. Compared to the available analogs, the proposed model equations are more accurate in terms of the ratio of the radii of bubbles to the distance between their centers. This allows one to study bubble-bubble interaction at smaller distances between the bubbles. The model equations are quite compact, which simplifies their theoretical analysis and construction of algorithms of their solution. Five problems (dynamics of a single bubble under harmonic excitation, bubble collapse near a plane rigid wall, interaction of three synchronized and nonsynchronized bubbles located in line, and interaction between sixteen bubbles with the centers located on a plane surface) are considered for validation. It is shown that in all cases the proposed model results well agree with the corresponding available experimental data and numerical solutions. For demonstration of the applicability, the proposed model is used to analyze radial oscillations, spatial movements and surface deformations of the bubbles in rectilinear, planar and spatial clusters under harmonic forcing. Initially 125, 121 and 125 bubbles of the clusters are located at the nodes of 1D, 2D and 3D uniform grids, respectively. It is found that the monotonically decaying radial oscillations of the 1D cluster bubbles during one period of forcing are quite similar to those of a single bubble. Unlike this, the attenuation of the radial oscillations of the central bubbles in the 2D and 3D clusters is essentially non-monotonic. The maximum pressures in the central bubbles of the 2D and 3D clusters are significantly higher than in the single and 1D cluster bubbles. In all clusters the maximum deformations of bubbles are in the form of the second spherical harmonics, except for the central bubble of the 3D cluster, the maximum deformations of which are in the form of the fourth harmonics.

Analysis of the dynamic evolution behavior of radial deformation and cracks during in-service welding instability based on quasi-in-situ and in-situ experiments

Avoiding the risk of in-service welding instability is the primary problem to be solved to ensure pipeline repair safety. And it is of great importance to develop a model to predict burn-through instability. However, few literatures have investigated the bulge instability behavior based on in-situ or quasi-in-situ experiments, which restricts the development of a unified prediction model. Therefore, in the present paper, the dynamic evolution behavior of both radiation deformation and cracks during in-service welding instability was investigated. The in-service welding instability process was divided into two stages, namely, the bulge instability (i.e. molten pool bulge) stage and the burn-through instability (i.e. bubble-induced molten metal overflow and meltage-effect burn-through) stage. The former revealed the initiation and propagation of cracks under the combined action of temperature effect and strain effect. The latter uncovered that the raised remaining pipe wall metal was melted and the cracks were transformed to melting-corrode pinholes due to the meltage effect. Noted, the radial deformation was the root cause of burn-through instability, which resulted in cracks through the pipe wall and the raised molten pool attracted to the welding arc. Besides, the in-service welding instability zone was divided into four zones, i.e. crack-propagate radial deformation zone, bulge-assisted burn-through hole zone, bulge-assisted opening fracture zone as well as direct burn-through hole zone. Furthermore, the crack failure mode was a mixture of transgranular and intergranular fractures. And the transgranular cracks presented an obvious deflection inside the pro-austenite grains.

Heat transfer-deformation analysis and optimization of air-cooled reciprocating compressor cylinders under heat-flow-solid coupling

Heat transfer deterioration and deformation can jeopardize the operating safety of compressor-air-cooled cylinders. To comprehend the heat transfer-deformation mechanism, enhance the heat dissipation and cooling effects, and reduce the deformation effect, a study on the control and optimization of heat transfer-deformation of compressor cylinders under the influence of multi-field coupling was conducted. The orthogonal experiment method is used to examine the effects of rib height, air chamber width, and working wall thickness on the cylinder's heat transfer properties and deformation effect. The results show that the average temperatures of the exhaust chamber and the working chamber of the air-cooled cylinder are higher, at 99.2 °C and 96 °C, respectively, and the proportion of the hot zone is as high as 44.1 %. The maximum radial deformation of each section of the working chamber and the maximum deformation of the cylinder are 0.223 mm and 0.451 mm, respectively. Through orthogonal experimentation and range analysis, it was found that the height of the cylinder rib plate has the greatest influence on the deformation. Besides, the cylinder structure is optimized, and the average temperatures of the exhaust chamber and the working chamber of the optimized cylinder are reduced to 98.4 °C and 95.5 °C, respectively. The maximum radial deformation is suppressed to 0.193 mm and 0.440 mm, respectively, preventing the sealing failure of the cylinder's working chamber and guaranteeing the compressor's operation efficiency. This study provides theoretical guidance for the optimization of heat transfer, deformation control, and the standardized design of reciprocating compressor cylinders.

Numerical Analysis of Temperature Deformation Characteristics for Super-High Arch Dams considering Solar Radiation Effects

Considering that the effect of solar radiation on the super-high arch dam temperature field remains poorly studied, the calculation accuracy of dam temperature deformation is unable to be guaranteed accordingly. To address the issue, the solar radiation effect is adequately taken into consideration by proposing a practical calculation method based on the ray-tracing algorithm, the precomputation algorithm, and the ASHRAE clear sky model in this paper. With the aid of the ASHRAE clear sky model, the solar radiation received by the super-high arch dam and reservoir water is calculated. The shading effects are calculated by means of the ray-tracing algorithm, and the precomputation technology is introduced to further enhance the computational efficiency. Finally, to guarantee the authenticity of the calculation results, the dam thermodynamic parameters are inversed by employing the hybrid genetic algorithm. Based on the application in a real-life case, we concluded that around one third of the entire dam radial temperature deformation was attributable to solar radiation during continuous sunny days. The analysis results signify a critical role for taking account of the solar radiation in dam deformation calculation. Furthermore, the practicability and utilization prospect of the proposed method was verified.

Structural transition of single-walled carbon nanotube (6, 6) bundles under lateral shocks

Dynamic response of single-walled carbon nanotube (SWCNT) (6,6) bundles under planar shock are investigated using molecular dynamics (MD) simulations. The Hugoniot data indicate that the shock velocity (up) in the range of 0–12 km/s can generate a wide range of shock waves (0–24 km/s), and high pressure up 0–500 GPa. The SWCNT bundles undergo a radial deformation at ∼5 GPa (up=1 km/s). As pressure reaches ∼38 GPa (up=3 km/s), the bundles are activated and transform into a diamond-graphite structure, and a diamond-like mixture at ∼90 GPa (up=5 km/s) is formed, which is partly reversible upon release to atmospheric pressure. Finally, it completely liquefied into an amorphous carbon structure at pressure over 150 GPa (up=6 km/s). Meanwhile, the density functional theory calculations show that structural transition processes of SWCNT (6,6) bundles under lateral compression agree well with the MD simulations. This study provides atomistic insights into the structural transition of SWCNT bundles under shock compressions.

Power Transformer Winding Deformation Diagnosis Based on the Sum of Two‐Way Shortest Distance

Frequency response analysis (FRA) method has been widely used in the world, but the interpretation of its signatures is still a hard problem to solve. This paper introduces a method of the sum of two‐way shortest distance for transformer winding deformation fault diagnosis, which is based on trajectory similarity between FRA signatures. Compared with most existing methods, it does not need order preservation; however, it focuses more on the trajectory itself. The geometric principle of the sum of two‐way shortest distance is introduced and analyzed in detail. By using the circuit analysis software, the equivalent circuit model of the transformer is established, a group of the FRA signatures of three types of transformer winding fault, including axial displacement, radial deformation, and disk space variation fault, are obtained. The distribution of different type of faults is studied by using the sum of two‐way shortest distance to process the FRA signatures in three different frequency bands. Using the sum of two‐way shortest distance as input, the support vector machine (SVM) is employed to train a predictive engine for transformer winding deformation fault diagnosis. Result shows that the proposed method can well classify and diagnose transformer winding deformation fault. © 2023 Institute of Electrical Engineer of Japan and Wiley Periodicals LLC.

Method for processing experimental data when investigating residual stresses by drilling probe holes and digital image correlation

This paper investigates the cutting forces arising when using a single abrasive grain. Analytical studies were carried out using a model of a single abrasive grain in the form of a rod with a radiused apex acting on the workpiece material. The slip-line method (method of characteristics) was used to calculate the deformation intensity of a plastically edged workpiece material under the action of a single grain. Mathematical models were developed for the following factors: plastic deformation of the material, edging of the stagnated zone and its friction against the grain surface when moved upwards in the form of chippings, grain friction against the plastically deformed material, and the action of the dynamic component of plastic deformation. The significance of the dynamic component in the overall balance of forces related to plastic deformation was established by determining the ratio of dynamic stress on the break line and shear yield point. This dependence calculated for D16T and 30HGSA materials showed the feasibility of accounting for the dynamic component subsequently processed by free orthogonal cutting and rolling contact deformation using a special machine with numerical control. Further, using the same machine, drilling of probing holes was performed with video recording of the surface image prior to and following drilling. By varying the speckle images, the displacements of material particles on the sample surface were determined by the digital image correlation method, following which the radial deformations were determined by differentiating the obtained displacement values. Statistical analysis of a sample of radial deformations equidistant from the centre of the hole while varying the rotation angle by Fourier transformation with the calculation of the distribution period showed that the distribution is periodic. It is established that the periodograms constructed using experimental data have local maxima at a period value close to 180 degrees. This determines that the main calculated components of the residual stresses and the angle of their rotation be constant when selected to calculate the values of radial deformations at arbitrary points around the hole. The paper presents an approach that allows residual stresses to be determined by drilling probing holes and assessing the displacement of material particles on the sample surface due to the redistribution of residual stresses. For the analytical description of experimental data, it is proposed that an approximating periodic function be used, and the physical meaning of its coefficients is determined.

Tele-ultrasound in community with limited resources: The association of hypertension on reduced carotid artery circumferential strain

Introduction: Stroke is one of the leading causes of death worldwide, in majority triggered by modifiable risk factors such as hypertension. AIM: to assess relations between hypertension and carotid arteries radial and circumferential deformation, assessing a population of participants after a first ischemic stroke and healthy controls. Methods: Retrospective study, from 2016 to 2017, with a sample of the PAI project control group, an urban population of the São Francisco Valley in the Northeast of Brazil, 105 people between 40-80 years-old, including patients after a first episode of ischemic stroke in the absence of known cardiovascular disease; and a control group of healthy volunteers, matched by age, sex, and presence of hypertension. Asynchronous analysis was performed by tele-ultrasonography of carotid artery ultrasound with images acquisition of EKG-synchronized videos in cross-section of the common carotid artery bilaterally and then strain values were acquired by Speckle Tracking technique, computing the mean circumferential and radial peaks of both carotids. Univariate and multivariable analyses assessed the association between carotid strain and hypertension. Results: 84 participants had analyzable images (29 patients after a first episode of stroke). The mean age was 60.5 + 11.6 years, 46.5% were women, 70.2% had hypertension. Radial deformation was lower but non-significant in participants with hypertension compared to those without hypertension (-3.13% vs. -3.35%, respectively, p = 0.54). There was significantly less circumferential deformation among participants who had hypertension compared to those without hypertension (4.16% vs. 5.3%, respectively, p = 0.003). Hypertension maintained association with lower circumferential strain in multivariate analysis (coef = -1.13; p = 0.019). Conclusion: hypertension was independently associated with the decrease in the carotid artery circumferential deformation. Tele-ultrasound associated with carotid strain analysis shows promising results for the evaluation of subclinical changes in carotid arteries in populations with limited resources in remote regions such as the Northeast of Brazil.

Radial deformation and stress distribution of grinding wheel on surface grinding

Radial deformation and stress distribution of grinding wheel on surface grinding

Design research on the unmeshed thread section structure of engine conrod bolts

In the design standard for hexagonal flange bolts, the reliability of the bolt connection structure varies when different structural forms of bolts are selected. However, there are few studies on the design and selection of bolts with different structural forms, and the design law of the bolt connection structure cannot be summarized comprehensively. In this paper, a finite element model of conrod bolt tightening was established based on the mesh convergence criterion, and the model was verified by comparing the simulation curve of tightening torque-bolt preload with the theoretical curve. The influence of the length of unmeshed thread, the length of thin rod and the diameter of thin rod section on the stress and deformation of conrod bolt was studied, it is found that the increase of the three kinds of structural parameters will reduce the stress concentration and radial deformation at the first thread of engagement, which can guarantee the structural strength of the bolt. At the same time, the fatigue safety factor of the bolt easy-to-failure region was analyzed, and the reliability of different structural forms of bolts was evaluated comprehensively. The results show that when the structure of bolt conforms to the design standard of full thread hexagonal flange bolt, the length of unmeshed thread is 27 mm, the stress value and radial deformation of the first thread are the smallest, and the fatigue safety factor of the bolt easy-to-failure region is the largest, which is not easy to damage. In the design of hexagonal flange bolts, full thread hexagonal flange bolts are used as much as possible.

Theoretical and experimental analysis of electric vehicle motor dynamics under the coupling of harmonic current and temperature excitation

The NVH performance of electric vehicles is crucial for human comfort, and the electric drive system is key to NVH performance. Permanent magnet synchronous motors experience high-temperature increases under high-speed operating conditions, resulting in motor structure deformation at high-temperatures. The radial deformation of the stator alters the airgap dimensions of the motor’s electromagnetic field. The airgap of the motor’s magnetic field has high-sensitivity to these changes aggravating the vibration and noise problems. Harmonic currents in high-speed vehicle motors add to these problems. Therefore, motor dynamics must be studied under the joint influences of airgap distortion and harmonic currents. We proposed a method of modeling permanent magnet synchronous motors under the joint effect of harmonic currents and temperature fields. And established an accurate multi-field coupled vibration response prediction model for permanent magnet synchronous motors. The accuracy of the vibration prediction model was subjected to a bench test. The vibration characteristics of the motor were studied using order and spectrum analyses. We found that the airgap magnetic-field distortion, due to the motor and stator thermal deformation, significantly affected the motor vibration characteristics. The main motor vibration noise was caused by the 24th and 48th order electromagnetic force waves. This provides a reference for establishing an accurate vibration prediction model for permanent magnet synchronous motors.

Energy mechanism for the instability of liquid jets with thermocapillarity

Xu and Davis [J. Fluid Mech. 161, 1–25 (1985)] examined the stability of long axisymmetric liquid jet subjected to an axial temperature gradient, finding capillary, surface-wave, and hydrodynamic modes. They showed that capillary breakup can be retarded or even suppressed for a small Prandtl number (Pr < 1) and a large Biot number (Bi ≥ 1). In the present work, the energy mechanism is carried out for these three kinds of flow instabilities, and the mechanism of suppressing capillary breakup is clarified. When the Reynolds number (RB) is not large, the work done by the pressure on the free surface (PS) is the main energy source of the capillary instability. At small Pr and large Bi, the phase difference between the radial velocity and surface deformation increases with RB, leading to the decrease in PS, which prevents the occurrence of capillary breakup. Meanwhile, the work done by thermocapillary force becomes the main energy source, making hydrodynamic modes unstable. The perturbation flow fields are displayed, which shows that the temperature fluctuations of three modes differ from each other.

A new method for analyzing the impact of winding mechanical defects on the equivalent circuit parameters of power transformers

AbstractCondition monitoring of the power transformer winding and diagnose of the fault in its incipient stages can prevent the spread of defect, and as a result, the unexpected exit of the transformer. Correct and accurate perception of the effects of each defect or winding deformation on the detailed or any other model parameters is essential. In this article, a software based on finite element method is used, in order to increase accuracy of the study to model the transformer in healthy and defected cases. Three types of winding mechanical deformation, that is, axial displacement, radial deformation, and disc space variation , have been simulated for different locations and extents. From the simulation of the finite element model in the healthy and other defected cases, R, L, and C matrices are obtained for each case. Each of the above matrices in defected cases has been compared with the corresponding matrix of the healthy case. The amount and manner of the above matrices’ element variations have been investigated in detail, might help the fault classification in terms of the type, extent and location, and risk assessment of using the transformer in the current defective situation.

Study on the Effect of Large Cross-Section Quasi-Rectangular Pipe Jacking near Side Crossing Viaduct Piles in Soft Soil Areas

Due to its high section use rate and minimal environmental impact, pipe jacking technology is frequently utilized in the building of urban rail transit and other municipal projects. This paper develops a three-dimensional numerical model for the gradual construction of rectangular pipe jacking based on the quasi-rectangular pipe jacking metro station project on Shanghai Line 14 and examines the interaction between the subsequent construction of double line pipe jacking and pile foundation. To analyze the deformation pattern of the tunnel section and the ground surface during the construction period and to confirm the applicability and accuracy of the model, the simulation results are compared with the monitoring data. The findings demonstrate that although the bending moment of the pipe jacking section is distributed as a “butterfly” under the influence of the viaduct piles, the maximum positive and negative bending moments as well as the lateral and vertical radial deformations of the pipe section cross-section are all somewhat diminished. The ground surface settlement curve in the vicinity of the bearing platform exhibits a more pronounced non-uniform settlement when the two pipe jackings pass through the pile foundation in close proximity, one after the other. The largest horizontal displacement of the pile foundation is found inside the jacking pipe tunnel at a depth of roughly 17 m below ground, where pipe jacking II has a greater influence on the lateral displacement of the pile foundation than pipe jacking I. The study’s findings line up with the monitoring data, which can serve as a guide and aid in the development of initiatives of a similar nature.

Effects of Particle Shape and Packing Density on the Mechanical Performance of Recycled Aggregates for Construction Purposes

This paper employs the discrete element method (DEM) to study the mechanical properties of artificial crushed stone. Different grain shapes and gradations are considered, and three types of 3D artificial stone models are generated based on the statistical conclusions in the relevant literature and the observed data. Concurrently, the 3D models of the artificial stones are divided into three groups by their shape parameters (elongation index and flatness index). Furthermore, three types of gradation with different Cu (coefficient of uniformity) and Cc (coefficient of curvature) are also considered. Then, several 3D triaxial compression tests are conducted with the numerical methods to determine the relationship between the grain shapes and their mechanical characteristics. The test results showed that there was a positive correlation between a particles’ angularities and the maximum deviatoric stress in the triaxial compression tests when there were obvious distinctions between the particles. In addition, gradations had a conspicuous impact on the stiffness of the sample. The stress–strain curve possessed a larger slope when the coefficient of curvature was bigger. In terms of shear strength, the results in this paper align well with the traditional shear strength envelope which are convincing for the dependability of the methods used in this paper. The radial deformation capacity and volume strain of the specimen during the triaxial compression tests are also examined. It is believed that there were great differences in deformability between different samples. At the mesoscopic level, the change in coordination number is identified as the fundamental reason for the change in volume strain trend.

Issues of Developing Equal-Strength Two-Layer Spherical Rubber-Metal Hinges

Development of equal-strength two-layer spherical rubber­metal hinges (RMH), described in the paper, is associated with the problem that with an equal thickness of the layers of rubber bushings and an equal opening angle, there is a significant difference in their radial stiffness and relative deformation of the rubber. With hinge dimensions corresponding to those of the hinges used in the undercarriage of locomotives, there is a difference in relative deformation of inner and outer bushings by about 1,5 times. As a result, it is proposed to determine the load capacity of spherical two-layer RMH by the value of relative deformation of the rubber of the most loaded bushing. Also, studies have been carried out on the possibilities of creating a uniformly deformable design of a spherical two-layer RMH.To determine the characteristics of a spherical rubber-metal hinge, applied digital computer modelling based on the finite element method. A proposed parametrised geometric model of a spherical two-layer RMH and a finite element model of an elastic bushing offer the ratio of radial stiffnesses of outer and inner bushings, which is close to the preliminarily determined one, based on the equations of the theory of elasticity in displacements in a spherical coordinate system.It has been established that to achieve uniform elasticity by changing the opening angle, the opening angle of the outer reinforcement of RMH should be approximately 1,5 times less than the opening angle of the inner one. This makes it possible to reduce the width of outer reinforcement of RMH by 25 % but raises the problem of strength and rigidity of outer edges of intermediate reinforcement. Also, equal elasticity of hinge bushings can be achieved due to their different thicknesses, while to achieve non-uniform stiffness of bushings within ± 5 %, it is required to ensure that deviation of the intermediate cage diameter during hinge manufacture is less than ± 0,1 %.The obtained research results prove the practical possibility of creating an equally strong (with equal bushing rigidity) spherical two-layer RMH. The issue of searching for a compromise design of RMS, acceptable from the point of view of loading of the intermediate cage and of the requirements for manufacturing accuracy, requires further study.