External Radial Load Research Articles

Connection strength analysis and prediction of external swaging based on tube deformation measurement

Fittings have extensive use in the aerospace, automotive, and other industries as they serve as sealing and connecting components for tube systems. External Swaging (ES) forming creates a permanent joint through plastic deformation of the metal. This technique is not dependent on the tube's wall thickness and offers benefits such as high-pressure resistance and effective sealing. Using the forming process of a 10 mm Ti-3Al-2.5 V tube with an adapted 21-6-9 fitting as an illustration, a three-dimensional finite element model for the entire assembly was developed. The model consists of the tube, fitting, elastic clamp, and crimping tool. The formation mechanism and joint strength of external swaging are analyzed by numerical simulation and experimental testing. The results show that during the extrusion process, the tangential contact between the extrusion tool and the elastic clamps converts external radial loads into circumferential loads, resulting in circumferential strains in the tube. Circumferential strain creates an arched sealing area between the tube and fitting contact surfaces, providing sealing and joint strength. The joint strength of 10.60 kN was determined through finite element simulation. The load required for forming is determined by analysis to be 80.13 kN. and the relationship between squeeze load, crimp volume and joint strength is clarified. The study revealed that the height of the arch area aligns with the connection strength's change rule concerning extrusion load, fitting the two found that when the external extrusion load changes, the two are linear rule of changing. Based on this, a method is suggested for forecasting the strength of a joint by measuring the height of the arch in the tube after forming.

Effects of prestress in the coating of an elastic disk

An elastic disk is coated with an elastic rod, uniformly prestressed with a tensile or compressive axial force. The prestress state is assumed to be induced by three different models of external radial load or by ‘shrink-fit’ forcing the coating onto the disk. The prestressed coating/disk system, when loaded with an additional and arbitrary incremental external load, experiences incremental displacement, strain, and stress, which are solved via complex potentials. The analysis incorporates models for both perfect and imperfect bonding at the coating/disk interface. The derived solution highlights the significant influence not only of the prestress but also of the method employed to generate it. These two factors lead, in different ways, to a loss or an increase in incremental stiffness for compressive or tensile prestress. The first bifurcation load of the structure (which differs for different prestress generations) is determined in a perturbative way. The results emphasize the importance of modelling the load and may find applications in flexible electronics and robot arms subject to pressure or uniformly-distributed radial forces.

Deformable hard tissue with high fatigue resistance in the hinge of bivalve Cristaria plicata.

The hinge of bivalve shells can sustain hundreds of thousands of repeating opening-and-closing valve motions throughout their lifetime. We studied the hierarchical design of the mineralized tissue in the hinge of the bivalve Cristaria plicata, which endows the tissue with deformability and fatigue resistance and consequently underlies the repeating motion capability. This folding fan-shaped tissue consists of radially aligned, brittle aragonite nanowires embedded in a resilient matrix and can translate external radial loads to circumferential deformation. The hard-soft complex microstructure can suppress stress concentration within the tissue. Coherent nanotwin boundaries along the longitudinal direction of the nanowires increase their resistance to bending fracture. The unusual biomineral, which exploits the inherent properties of each component through multiscale structural design, provides insights into the evolution of antifatigue structural materials.

Dynamics Modeling and Analysis of Rolling Bearings Variable Stiffness System with Local Faults

By analyzing the support of load-carrying rolling elements when the rolling elements fall into the fault position, the dynamics model of a rolling bearing variable stiffness system with local faults is proposed, considering the retention factor of the contact deformation. Then, this paper researches the change of effective contact stiffness, contact deformation, contact force, and the total effective stiffness of the rolling elements. The results show that the contact stiffness of the rolling elements abruptly decreases when the rolling elements fall into the fault position. The contact deformation and contact force of the load-carrying rolling elements in the load zone increase, rebalancing the external radial load while causing a sudden reduction in the total effective stiffness, resulting in the vibration of the system. When different rolling elements fall into the outer ring fault position, the change in total effective stiffness and the system response are equal in magnitude. Additionally, there is a significant outer race fault characteristic frequency accompanied by frequency multiplication in the fault characteristic spectrums. When different rolling elements fall into the inner race fault position, the total effective stiffness is modulated by the inner race rotation and varies dramatically, resulting in the amplitude of the system time domain vibration response also being modulated by the inner race rotation and varying dramatically. Additionally, there is a significant inner race rotational frequency accompanied by frequency multiplication, an inner race fault characteristic frequency accompanied by frequency multiplication, and a side frequency in the fault characteristic spectrums. The research can provide some reference for the effective diagnosis of the rolling bearing fault.

A New Approach for the Load Calculation of the Most-Loaded Rolling Element of the Rolling Bearing with Internal Radial Clearance—A Case Study

One of the most important factors influencing the study of the tribological behaviour of a rolling bearing is the calculation of the loads transmitted by individual rolling elements of the bearing. However, the calculation of the internal load distribution of rolling bearings is quite complicated. It is a nonlinear, statically indeterminate problem, which can only be solved numerically, through a number of iterations. This is often a problem in analysis because it complicates the mathematical model. This paper is presenting a case study with the goal to show the benefits of the application of a new approach for the calculation of the load of the most-loaded rolling element in the rolling bearing with the internal radial clearance. The calculation is based on the so-called load factors. By multiplying the load factors with the value of the external radial load, the load that is transferred by the most-loaded rolling element of the bearing is obtained. The accuracy of the results largely depends on the correct choice of the load factor. The case study aims to define guidelines for the correct choice of load factors. The case study is made for two types of bearings: the ball bearing and the roller bearing. Obtained results were compared with the results obtained based on the calculation using some of the most commonly used methods so far. The analysis showed greater precision of the considered model with the same or much simpler use. For this reason, the proposed model is considered very suitable for practical application.

Performance of water-lubricated ceramic journal hybrid bearing

Strong shear force developed in the lubrication film in the high-speed spindles will resulting high temperature rise and expanding the mandrel, which would arouse safe servicing problem. This study aimed to address the temperature rise issue in spindles through the use of substitutes in the spindle bearing material. To this end, we developed a spindle with a water-lubricated ceramic hydrodynamic and hydrostatic journal bearing. To support the selection of ceramic materials for the water-lubricated journal bearing, we initially performed application-oriented tests; to this end, the water absorption and porosity among alumina, silicon nitride, and silicon carbide were considered. To investigate the performance, and particularly the temperature characteristics of the hybrid bearing, a water-lubricated ceramic hydrodynamic and hydrostatic bearing test rig was designed to include temperature sensors. At the test rig, the radial clearance was measured for solving the temperature distribution of the bearing during the simulation. The experimental results helped verify that the water temperature increased by approximately 0.7°C as the rotation speed increased from 1200 rpm to 5400 rpm without an external radial load. The increase in temperature with and without radial load under a rotation speed of 3600 rpm was compared, and the results revealed a difference of 0.14°C. This indicates that the developed ceramic bearing improves the thermal stability of the spindle which shows its potential for industrial application in machine tools or other high rotation speed machines.

Study of Bondura® Expanding PIN System – Combined Axial and Radial Locking System

Bolted connections are widely used in parallel plates and flanged joints to axially lock using the preload generated by the tightening torque and to constrain radial movements of the flanges by the surface friction between mating surfaces. The surface friction depends on the micro-asperities of mating surfaces; under the influence of vibrations and other external radial loads, these asperities tend to deform over time, resulting in the failure of the connection. The Bondura expanding pin system presented in this article is an innovative axial and radial locking system, in which the failure of bolted connections due to radial movements is eliminated by relying on the mechanical strength of the pin system along with the surface friction. The present study describes an experimental design to verify the maximum possible preload on the axial-radial pin at different levels of applied torque. The article also provides a realistic comparison of the pin system with standard bolts in terms of handling axial and radial loads. With some alterations in the axial-radial pin system’s design, the joint’s capability to resist failure improved appreciably compared with the original design and standard bolts with higher preload. As a result, the estimated capability improvement of the joint against the connection failure due to the external radial load by the axial-radial pin is observed to be more than 200 % compared to standard bolts. Considering the pros and cons of both fasteners, i.e., axial-radial pin and standard bolts, a practical solution can be chosen in which both fasteners are used in a connection, and an optimized situation can be developed based on the working conditions.

Analysis of Radial Roller Bearing Rating Life in Complex Loading Conditions

Abstract An approach for accurate life analysis of radial roller bearings in complex loading conditions is presented. It employs ISO 16281 and accounts not only for external radial loads applied to the inner ring but also for (i) internal bearing clearance, (ii) flexibility of the bearing rings, (iii) rings out-of-roundness, (iv) inertia effects, (v) rolling elements profile, and (vi) rings misalignment. In the last decades, these factors have been becoming more and more important for modern high-performance jet engines, whose shafts are commonly hollow and the housing and the rings thicknesses may be of comparable magnitudes. To obtain the distribution of internal contact forces, an advanced static model of a bearing with deformable, potentially misaligned, rings is developed. The bending deformations of the rings are reproduced superimposing deformed shapes from each of the arising internal contact force applied individually. Bearing rollers are allowed to have non-cylindrical profile, and its geometry is approximated by means of slices each having constant diameter. A robust numerical scheme for solving the resultant set of equations with the aid of the barrier functions method is constructed. To increase even further the accuracy of rating life analysis, distributions of the contact stresses between the roller and the ring surfaces, obtained by solving numerically the problem of non-Hertzian interaction, are added to computations. A numerical benchmark test is presented to demonstrate the applicability of the developed approach. It shows how the aforementioned factors influence the bearing contact forces and its rating life.

Experimental Study on Cage Dynamic Characteristics of Angular Contact Ball Bearing in Acceleration and Deceleration Process

During acceleration and deceleration processes of a bearing, the kinetic relationship of collision and friction between the cage and the rolling element is complex, which has an important influence on the dynamic characteristics and stability of the rolling bearing. In this study, experimental investigation of the dynamic motions of a cage under various external radial loads was performed during acceleration and deceleration for an angular contact ball bearing with a constant axial load of 100 N. In a bearing test rig, cage motion in the axial and radial directions is measured via laser sensors; the bearing inner ring speed and the cage speed are measured by using eddy current and photoelectric speed sensors, respectively. The results reveal that acceleration and deceleration of the bearing significantly affect the dynamic characteristics of the cage. During the acceleration process, there is a critical speed at which the cage forms a circular whirl orbit. When the inner ring speed is lower than the critical speed, the mass center of the cage swings along the guide land but enters a circular whirl orbit once the critical speed is exceeded. Further, the greater the acceleration and radial load, the higher the critical speed. Similar results are revealed during the deceleration process. In addition, the cage slip ratio is proportional to the acceleration. Conversely, the cage slip ratio is inversely proportional to the radial load; however, the increasing radial load has minimal effect on cage slip rate when the radial load is greater than 100 N.

Load Calculation of the Most Loaded Rolling Element for a Rolling Bearing with Internal Radial Clearance

This paper presents a new model for calculation of load for the most loaded rolling element in a rolling bearing with internal radial clearance. The calculation is based on a so-called load factor. By multiplying this factor by the value of the external radial load, the load transferred by the most loaded rolling element of the bearing is obtained. The values of the load factor are shown in the tables and diagrams, which makes the model very suitable for practical use. The load factors are shown for a ball bearing as well as for a roller bearing. The model considers two support positions of the inner ring on an even and odd number of rolling elements. The new model was compared with the most commonly used models up to now. The results showed greater accuracy of the studied model.

Calculation method for comprehensive damping of ball bearings based on multigrid method

PurposeAs an important part of the rotor system, the damping coefficient of ball bearing has a great influence on the dynamic characteristics of the system. This study aims to propose a theoretical calculation method and an experimental test method to obtain the damping coefficient of ball bearing.Design/methodology/approachBased on Hertzian contact theory and elastohydrodynamic lubrication theory, the point contact oil film damping analysis model of ball bearing is established. The comprehensive damping calculation method considering external radial load, centrifugal force, ball spin, rotational speed and lubricating oil film is derived. The multigrid method is used to obtain the oil film pressure and thickness distribution in the contact zone. The variation trend of comprehensive damping with bearing radial load, rotational speed, oil film thickness and viscosity is analyzed. The test platform is designed and the influencing factors of damping are tested.FindingsThe validity of the model and reliability of the test device are verified by comparing the good consistency obtained in the work. The results show that the comprehensive damping of ball bearing increases with the increase of radial load and decreases with the increase of rotational speed.Originality/valueAt present, the existing bearing damping model can achieve approximate calculation of damping, but the factors considered in these models are not comprehensive enough. Besides, few studies exist regarding test platform of bearing damping, and a perfect test plan has not yet been formed. In this paper, the comprehensive damping calculation model of ball bearing is improved, and a complete experimental scheme is proposed to provide reference for the comprehensive damping theory and experimental research of bearing.Peer reviewThe peer review history for this article is available at: https://publons.com/publon/10.1108/ILT-08-2019-0342/

A Simplified Mathematical Model for the Analysis of Varying Compliance Vibrations of a Rolling Bearing

In this paper, a simplified approach in the analysis of the varying compliance vibrations of a rolling bearing is presented. This approach analyses the generation of vibrations in relation to two boundary positions of the inner ring support on an even and an odd number of the rolling element of a bearing. In this paper, a mathematical model for the calculation of amplitude and frequency of vibrations of a rigid rotor in a rolling bearing is presented. The model is characterized by a big simplicity which makes it very convenient for a practical application. Based on the presented mathematical model a parametric analysis of the influence of the internal radial clearance, external radial load and the total number of rolling elements on the varying compliance vibrations of rolling bearing was conducted. These parameters are the most influential factors for generating varying compliance vibrations. The results of the parametric analysis demonstrate that with the proper choice of the size of the internal radial clearance and external radial load, the level of the varying compliance vibrations in a rolling bearing can be theoretically reduced to zero. This result opposes the opinion that varying compliance vibrations of rolling bearing cannot be avoided, even for geometrically ideally produced bearing.

Free vibration and buckling analyses of functionally graded annular thin sector plate in-plane loads using GDQM

In the present study, buckling and free vibration analyses of annular thin sector plate made of functionally graded materials (FGMs) resting on visco-elastic Pasternak foundation, subjected to external radial, circumferential and shear in-plane loads is investigated. Material properties are assumed to vary along the thickness according to an power law with Poisson\'s ratio held constant. First, based on the classical plate theory (CPT), the governing equation of motion is derived using Hamilton\'s principle and then is solved using the generalized differential quadrature method (GDQM). Numerical results are compared to those available in the literature to validate the convergence and accuracy of the present approach. Finally, the effects of power-law exponent, ratio of radii, thickness of the plate, sector angle, and coefficients of foundation on the fundamental and higher natural frequencies of transverse vibration and critical buckling loads are considered for various boundary conditions. Also, vibration and buckling mode shapes of functionally graded (FG) sector plate have been shown in this research. One of the important obtained results from this work show that ratio of the frequency of FG annular sector plate to the corresponding values of homogeneous plate are independent from boundary conditions and frequency number.

An Analytical Dynamic Model of a Hollow Cylindrical Roller Bearing

Hollow cylindrical roller bearings (HCRBs) have obtained much attention from design engineers in bearing industries since they can perform better than solid cylindrical roller bearings (SCRBs) in centrifugal forces, contact stiffness, cooling ability, fatigue life, etc. In this study, an analytical dynamic model of a lubricated HCRB is presented to analyze the influences of the radial load, the shaft speed, and the hollowness percentage of the roller on the bearing vibrations, which cannot be formulated by the methods in the reported literature. Both the support stiffness of the shaft and the roller mass are formulated in the presented dynamic model. The hollow hole in the roller is modeled as a uniform one. Numerical results show that the hollowness percentage of the roller has a great influence on the vibrations of the roller and the inner race of the HCRB. Moreover, the vibrations of the components of the HCRB are not only determined by the hollowness percentage of the roller, but also depended on the external radial load and shaft speed. Therefore, during the design process for the hollowness percentage of the roller, the influences of the radial load and the shaft speed on the vibrations of the bearing components should be considered, except for the fatigue life. The results show that this work can give a new dynamic method for analyzing the vibrations of the HCRBs. Moreover, it can give some guidance for the design method for the HCRBs.

A numerical investigation of the plastic deformation at the spall edge for a roller bearing

Abstract A clear understanding of dynamic contact characteristics in roller bearings (RBs) is a primary task for vibration analysis of the machineries, especially in the presence of spall failures. This work presents a new dynamic modelling method for a RB with a spall on the races to predict the time-varying plastic deformation at the spall edge. An improved two-degree-of-freedom dynamic model is used to calculate vibrations of the RB. Effects of the spall length, spall edge radius, external radial load, and rotor speed on the dynamic impact force between the spall edge and roller, maximum contact stress at the spall edge, total contact deformation between the spall edge and roller, plastic deformation at the spall edge, and spall edge propagation rate are analyzed. The proposed method is validated by a finite element (FE) method. The numerical results illustrate that the spall edge shape, external radial load, and rotor speed have a significant influence on the dynamic impact force, maximum contact stress, total contact deformation, plastic deformation, and spall edge propagation rate. This paper provides a greater understanding of the effects of the spall sizes and the spall edge shape on the contact characteristics and the vibrations for the RBs.

Experimental Investigation of Shaft Radial Load Effect on Bearing Fault Signatures Detection

This paper investigates the influence of external radial load applied to the shaft on bearing fault detection based on vibration or current in induction motors operating under different conditions. This paper details the results of a laboratory trial comprising different test sets on the condition monitoring and fault diagnostic of a six-poles induction motor using a design of experiment (DOE) approach. The dedicated test setup comprises a custom-made fixture that allows us to dynamically vary the radial load applied to the output shaft. The aim is to investigate the effects of radial load on the fault diagnosis of shaft bearings and the interactions between other operating parameters, such as output torque. Specific scalar parameters have been proposed for the condition monitoring of the test motor from vibration and current data. The correct choice of the significant parameters is proven by the strong dependence on the damage returned by DOE results.

Effect of radial loads on the natural frequencies of thin-walled circular cylindrical shells

In this paper, we study the variation of natural frequencies for thin walled circular cylindrical shells subject to external radial load (uniform and hydrostatic pressure). The study has been performed for four different types of boundary conditions viz. pinned-pinned, pinned-free, clamped-free and one end is pinned and other end axially constrained. Towards this, we have used approximate shape functions and Galerkin projections of the PDEs governing the shell motion, linearized about a steady state solution due to the applied mean radial pressure. Our results have very good agreement with the experimental and theoretical results available in literature. They have also been verified against finite element analysis (FEA) using ABAQUS. We have found that with increasing magnitude of inward radial load, the natural frequency decreases, however, the circumferential wavenumber corresponding to the lowest natural frequency increases. For outward radial load the opposite happens. Furthermore, the circumferential wavenumbers corresponding to lowest natural frequency and first buckling mode are different for short cylinders with the difference decreasing with increasing length of the cylinder. We have also found an interesting result for the beam mode vibration of cylindrical shells. For short cylinders, the natural frequency of the beam mode increases (decreases) with internal (external) pressure, which is consistent with other circumferential modes. Subsequently, we obtain a critical length at which the applied radial pressure has no effect on the natural frequency. For cylinders longer than the critical length, the effect of the radial load is opposite of that observed for the short cylinders, and this is contrary to the behavior of the other circumferential modes. As a result, buckling of the beam mode happens for an outward radial (internal) pressure.

Orifice compensated performance characteristics of hybrid hole-entry conical journal bearing

Influence of semi-cone angles on the performance of the non-recessed hybrid/hydrostatic hole-entry conical journal bearing compensated with orifice restrictor has been carried out analytically. The analysis comprises two rows of symmetric hole-entry contour in the circumferential direction of hybrid/hydrostatic conical journal bearing. An orifice restrictor is used in the hole-entry contour to allow the restricted flow in the clearance space of a journal and bearing. Well-known finite element method and Newton–Raphson method for restrictor have been used to solve the Reynolds equation, governing the fluid flow in the clearance space of a hybrid/hydrostatic conical journal and bearing. Further, the spherical coordinate system has been employed to solve Reynolds equation instead of cylindrical coordinate system. Performance characteristics in terms of stiffness coefficient, damping coefficient, bearing pressure, bearing flow, and minimum fluid film thickness have been discussed for variable external radial load ([Formula: see text]) = 0.25–1.5. The performance characteristics in terms of [Formula: see text], [Formula: see text], and [Formula: see text] is found to be quite significant for hybrid hole-entry conical journal bearing when compared with hydrostatic hole-entry conical journal bearing, which allows the designer to choose appropriate non-recessed hybrid hole-entry conical journal bearing.

각 어긋남을 고려한 각접촉 볼베어링의 피로수명 해석

Angular misalignment has a significant effect on the characteristics of angular contact ball bearings (ACBBs). This paper presents an analysis of fatigue life for ACBBs subjected to angular misalignment. A simulation model is developed with de Mul’s bearing model and the ISO basic reference rating life model. Simulation is performed to calculate the life of the ACBBs subjected to angular misalignment. The numerical results show that angular misalignment influences the load distribution significantly, thus reducing the bearing rating life. The fatigue life of ACBBs is decreased by angular misalignment regardless of axial preload, external radial load and rotational speed. The results show that angular misalignment should be maintained at less than 1mrad for ACBBs.

Stability and Nonlinear Vibrations of Closed Cylindrical Shells Interacting with a Fluid Flow (Review)

Results of systematic study of the stability and nonlinear vibrations of thin cylindrical shells interacting with a fluid flow are presented. The main patterns of dynamical deformation of shells during divergence and flutter are considered. The effect of different structural features (initial geometrical imperfections, added concentrated masses, boundary conditions, longitudinal and transverse static loads) on the critical (divergence and flutter) velocities is analyzed. The amplitude–frequency response of shells to external periodic radial loads and internal periodic pressure caused by small pulsations of the fluid velocity is determined. A method is proposed to solve nonlinear problems describing nonstationary processes of passing resonance zones by shells interacting with the fluid flow