Radial Load Research Articles

Multiscale Structural Mechanics of Rotary Shaft Seals: Numerical Studies and Visual Experiments

Although rotary shaft seals have been used successfully in many industrial applications for decades, their tribological behavior is still not completely understood. In-depth knowledge of the structural mechanics is essential for the design and optimization of such sealing systems. High complexity results from the multiscale interactions in the tribological system rotary shaft seal. Large macroscopic deformations occur due to the hyperelastic material behavior of elastomers coupled with microscopic tangential distortions of the sealing edge surface in the contact area. This paper includes both numerical and experimental studies on the tribological behavior of rotary shaft seals. A multiscale finite element model provides the simulation of the macroscopic deformations and the microscopic displacements. A test rig equipped with a hollow glass shaft enables in situ visual contact analyses, qualitative determinations of pressure distributions and quantitative measurements of elastomer surface distortions. The optical phenomenon of frustrated total internal reflection enables qualitative evaluations of the pressure distribution. Particle image velocimetry (PIV) is employed to quantify the tangential distortions. The test rig enables the measurement of the friction torque with the same configuration. The results of the numerical and experimental investigations for the radial load, friction torque and tangential distortions are compared and discussed. This serves to validate the simulation methods and the correlation of the measured parameters. This finally results in a solid and validated basis for further tribological investigations of rotary shaft seals.

The Effects Analysis of Contact Stiffness of Double-Row Tapered Roller Bearing under Composite Loads

Double-row tapered roller bearings have been widely used in various equipment recently due to their compact structure and ability to withstand large loads. The dynamic stiffness is composed of contact stiffness, oil film stiffness and support stiffness, and the contact stiffness has the most significant influence on the dynamic performance of the bearing. There are few studies on the contact stiffness of double-row tapered roller bearings. Firstly, the contact mechanics calculation model of double-row tapered roller bearing under composite loads has been established. On this basis, the influence of load distribution of double-row tapered roller bearing is analyzed, and the calculation model of contact stiffness of double-row tapered roller bearing is obtained according to the relationship between overall stiffness and local stiffness of bearing. Based on the established stiffness model, the influence of different working conditions on the contact stiffness of the bearing is simulated and analyzed, and the effects of radial load, axial load, bending moment load, speed, preload, and deflection angle on the contact stiffness of double row tapered roller bearings have been revealed. Finally, by comparing the results with Adams simulation results, the error is within 8%, which verifies the validity and accuracy of the proposed model and method. The research content of this paper provides theoretical support for the design of double-row tapered roller bearings and the identification of bearing performance parameters under complex loads.

Dynamic characteristics of asymmetrically supported cylindrical roller bearing–rotor coupled system considering variable compliance vibration

This article provides a dynamic model of a cylindrical roller bearing–rotor system by combining the finite element method of the rotor and the interaction between the components of the bearing to study the dynamic response of the rotor with asymmetric support mode. The shaft is discretized by beam elements with five degrees of freedom. The bearing inner ring is consolidated with the journal of the shaft. The simulation results show that variable compliance vibration can stimulate resonance of the rotor in the sub-critical speed region. The variable compliance vibration of the rolling bearings does not occur synchronously on both sides of the asymmetric supported rotor. The increase in radial load and clearance exacerbates variable compliance vibration, while rotor imbalance has a smaller impact on variable compliance vibration. Usually, the presented coupled model can be applied to the comprehensive analysis of the vibration characteristics of all components in any cylindrical roller bearing–rotor system.

Mathematical Modeling and Multi-Criteria Optimization of Design Parameters for the Gyratory Crusher

There are a sufficient number of works devoted to modeling crushing machines. Nevertheless, the fact that there are a large number of working conditions, and the ongoing development of science and technology, require continuous improvement and specification of the models intended for crushing processes and those of the devices concerned. However, there are few studies related to single-roll gyratory crushers. Such crushers are promising for use in mines to crush rocks laid in the developed space. Mathematical modeling and optimization of the design parameters of the working chamber and the executive body (roll) of a single-roll gyratory shaft crusher, designed for crushing strong rocks, was performed in this paper. A differential equation was derived. As a result of its solution, the rational shape of the working chamber cheek of the single-roll gyratory crusher was established, representing a logarithmic spiral arc. Analytical expressions were derived to determine the rational rotation speed and productivity of the crusher under consideration. Expressions for calculating the kinematic load components acting on the roll were formulated. They are the periodic functions of the shaft rotation angle. The Fourier series expansion showed that the loads contained harmonics of the first, second, third and fourth orders. Using the concept of fuzzy sets, a multi-criteria optimization of the design parameters of the working chamber was performed, including the values of the eccentricity and the central angle of the beginning of the cheek profile. The variation coefficients of the kinematic components of the loads acting on the working body reduced, due to the optimal choice of the working chamber profile and the angular coordinates of the installation of the fixed cheeks. The torque reduced 1.67 times, while the radial load decreased 1.2 times.

A simple analytical estimate for the elastic-plastic behavior of two-phase bi-continuous isotropic composites

A simple modeling is proposed to estimate the elastic-plastic behavior of two-phase isotropic composites made of interpenetrated co-continuous phases. This nonlinear modeling, without equivalent so far, is based on the extension of an explicit Laminate System (LS) scheme proposed previously for linear elastic behavior of such co-continuous composites. Considering monotonic radial loadings, the effective nonlinear stiffness of bi-continuous elastic-plastic composites is estimated from stepwise linearizing the composite overall and phase behaviors using a classical secant linearization procedure. The efficiency of this proposed modeling is checked on some comparisons with rare experimental literature data and with other classical analytical homogenization estimate schemes.

Lightweight Design and Structural Analysis of a Wheel Rim Using Finite Element Method and Its Effect on Fuel Economy and Carbon Dioxide Emission

Wheel rims made of metal alloy considerably impact the vehicle’s overall weight. Consequently, employing alloys in the design of wheels results in higher fuel efficiency and lower carbon dioxide emissions. Weight reduction of vehicles also leads to better acceleration. Lightweight automotive design has been increasingly popular in recent years as a means of conserving energy and protecting the environment. The rim is an essential feature of the vehicle since it bears a substantial portion of its overall weight. A vehicle’s weight can be greatly reduced by using a lightweight rim. However, the impact of a lightweight rim on improved fuel economy and reduced carbon dioxide emissions has not been widely explored. In this study, a wheel rim has been designed, and a finite element model has been developed considering radial load, where tire pressure has also been considered. A practical experiment with identical parameters had also been carried out. The values of equivalent stress, strain, and deformation for a metal and an alloy which is steel and cast aluminum alloy (A356.0), respectively, have been compared. In terms of structural stability, steel and cast aluminum alloy have shown fairly similar results based on equivalent stress and deformation. However, the use of cast aluminum alloy has greatly decreased the rim’s weight as a result of its low density and high specific strength. Additionally, the aluminum alloy rim has shown superior fuel efficiency and lower carbon dioxide emissions. According to the findings, cast aluminum alloy rims are more feasible when building a vehicle wheel rim since they minimize the wheel’s and vehicle’s weight while maintaining structural strength. It leads to less fuel consumption, which can save fuel costs and is important for energy conservation.

Experimental study on vibration characteristics due to cage damage of deep groove ball bearing

Currently, few studies focus on vibration characteristics of cage damage. A test rig can simulate cage damage is built. Through two kinds of healthy deep groove ball bearings (Bearing 6210 and Bearing 6011) run for a long time under abnormal load, the cage damage bearing is obtained, and the bearing vibration and temperature signals in full life cycle are collected. The change law of vibration signal with cage damage under different speeds and loads is found. The results show that the damaged cage has periodic impact with the inner and outer ring, and the vibration signal appears frequency component of nfc. The influence of axial load on the vibration of damaged bearing is greater than that of radial load.

Analysis of the Importance of the Filling Material Characteristics Injected Around the Precast Concrete Lining in the Microtunnelling Technology

Microtunnelling is an excavation technique capable of positioning underground pipes with considerable advantages from the point of view of the environment, safety, construction times and also total costs, when the lengths are significant. The technology used is now reliable and is suitable for use in different types of soils and rocks without particular problems. The installation of the concrete lining of the micro-tunnel takes place behind the excavation machine starting from a thrust shaft. A filling material must be injected between the outer surface of the lining and the tunnel wall. This filling material plays a very important role, because it conditions the overall stiffness of the support system and, therefore, influences the radial load applied by the ground to the support system. Therefore, it is necessary to take into account the presence of the filling material in order to correctly size the support system of the micro-tunnel. This paper illustrates a new procedure for analyzing the behavior of the micro-tunnel support system, based on widely used and tested analytical calculation methods. This procedure was applied to a real case, underway in Northern Italy. The results obtained were then compared with those of numerical modeling, which made it possible to simulate the micro-tunnel in detail. From the comparison it was possible to note how the analytical calculation procedure leads to stress states similar (slightly higher) to those of numerical modeling; the first, therefore, can be effectively used in the preliminary stages of the design of micro-tunnels to obtain useful information on the characteristics of the support systems to be adopted to ensure the stability.

Radial impact fracture characteristics and crack initiation criterion of concentric perforated granite after high temperature-water cycle

In this study, the radial impact fracture characteristics and crack initiation criterion of concentric perforated granite after high temperature-water cycle were evaluated based on the engineering environment such as high temperature, water encounter and dynamic disturbance experienced by the wellbore surrounding rock in the energy storage area during deep geothermal energy mining. And the combination of mechanical test, numerical simulation and theoretical analysis was used. The results revealed that the concentric perforated granite treated with high temperature and water soaking under radial impact load successively underwent three stages: transient elastic deformation, stable and unstable expansion of internal cracks. Finally, the tensile failure was produced and the granite was split into four pieces of approximately symmetrical. The main fracture direction of the rock sample was the impact direction revealed by the strain, fracture history and lateral strain clouds of the inner bore wall of the sample. Meanwhile, the tensile cracks firstly sprouted from the inner bore wall of the sample in the impact direction and expanded to the outer wall, and then from the outer wall in the vertical direction to the inner bore wall. Then, based on the test results, the damage variables were defined according to the proportion of damage degree caused by single factor and the law of crack germination inside the rock sample. It was calculated that the damage accumulation rate of concentric perforated granite under radial impact load after high temperature and water immersion experienced three typical stages: “slow-fast-slow”. Finally, the energy structure relationship of the micro-element of concentric perforated granite was constructed. The crack initiation criterion of the rock sample with concentric perforated structure under radial impact load was established by considering the initial damage caused by heating and water immersion and using the parameters such as the energy storage limit of the rock sample and the energy required for crack initiation. In addition, the rationality was also verified. The research can provide a theoretical reference for the formation of heat transfer channel caused by fracture of stored rock mass and the stability control of surrounding rock of geothermal wellbore, which have great engineering practice and scientific significance.

Stress level estimates in coated or uncoated silicon nanoparticles during lithiation

This work is devoted to the modeling of the mechanical behavior of coated or uncoated silicon nanoparticles, which constitute the anode active material in some lithium ion batteries, during their first lithiation at room temperature. The lithiation process induces a large volume expansion of the particles and a high level of stresses, which can lead to the fragmentation of the particles. Several approaches are proposed in order to estimate the volume expansion and the stress levels experienced by the particles. An original semi-analytical small strain model is first presented, which adapts the solution proposed by Seck et al. (2018) of the elastic-viscoplastic composite sphere problem subjected to radial loading, to the lithiated particle problem, in particular by considering the variation of phases properties during lithiation. The lithium concentration in the silicon particle is given by a sigmoid function (called logistic function) in order to mimic the reaction front between the phases. The implementation of the approach using the Hencky strain tensor Miehe et al. (2002) is proposed to take into account the large strains experienced by the particles. A complete description of the formulation is provided and the advantages are discussed. The importance of the large strains model is established by comparing it with the small strain one concerning the predictions of the pushing-out effect and the size effect of particles on their internal stresses during lithiation. Comparisons between our simulations and experimental data from Tardif et al. (2017) measuring the operando strain experienced by the pristine silicon gives the yield stress of the lithiated silicon. In addition, carbon-coated silicon nanoparticles are finally studied. We develop original closed-form expressions to predict the maximal stresses experienced by the coating at the end of the lithiation. Those expressions are used to re-estimate the fracture stress of pyrolitic carbon, considering a critical review of both pyrolitic carbon and lithiated silicon elastic properties. Finally, the mechanical effect of the coating on silicon during lithiation is studied.

Design of an aircraft generator with radial force control.

With the increasing electrical energy demands in aviation propulsion systems, the increase in the onboard generators' power density is inevitable. During the flight, forces coming from the gearbox or gyroscopic forces generated by flight manoeuvres like take-off and landing can act on the generators' bearings, which can lead to wear and fatigue in the bearings. Utilizing the radial force control concept in the electrical machine can relieve loads from the bearings that not only minimize the bearing losses but also increase bearing life. The objective of the MAGLEV project (Measurement and Analysis of Generator bearing Loads and Efficiency with Validation) is to study, demonstrate, and test a new class of high-speed generators with radial force control. In this paper, design steps of this type of generator and its test rig are presented and the measurement methodology used for radial force control is explained. The concept is developed in an electrical machine and is validated on a test rig by measuring required parameters like shaft displacement, vibrations and bearing temperature. Additionally, the friction moment of each generator's bearings is measured and validated in a separate test rig under comparable conditions to the bearing loads in the generator. Therefore, a novel approach to determine precisely the bearing friction in a radial load unit, rotatably supported by an additional needle bearing is used, which shows a good agreement with the calculated friction. Furthermore, new calculation methods for the operating behavior of cylindrical roller bearings with clearance are presented, which are utilized in the generator test rig.

Thermal characteristics of a 90-mm bore cylindrical roller bearings for aerospace applications: All-steel versus hybrid bearings

Modern aircraft engines have to meet rigorous requirements such as thrust to weight ratio, efficiency and new regulations related to environment protection. These requirements affect all engine modules and components, including rolling element bearings. The latter have to withstand severe operating conditions because of the high thermal impact due to elevated rotational speeds and loads. In this study, two test campaigns were carried out under realistic operating conditions of load, speed, and oil flow rate to investigate and compare the thermal characteristics of two distinct cylindrical roller bearings: a hybrid bearing featuring silicon nitride (Si3N4) rollers and an all-steel bearing. Each bearing was instrumented with an array of thermocouples around its circumference to determine temperature profile under various test conditions. In addition, oil supply and drain temperatures were also measured to estimate the power loss. The experiments were conducted on a high-speed rolling-element test rig operating at speeds up to 30,000 rpm and under radial loads of up to 4500N.

Analysis of maximum radial load capacity of hydrostatic journal bearing considering supply pressure limitation by a novel method

The aim of the present study is the numerical analysis of the operating conditions (rotary speed, supply pressure) and structure parameters’ (capillary design parameter, recess wrap angle) influence on the performance of a four-rectangle recessed hydrostatic journal bearing, taking into account the limitation of the recess pressure that is always smaller than supply pressure. A new calculation method is proposed that ensures both lower time consumption than traditional numerical method (FEM, FDM) and higher accuracy than simplified method (Liang’s method). This approach examines the effect of operating conditions and structure parameters on the maximum load capacity, attitude angle, and maximum eccentricity ratio considering the supply pressure limitation. Moreover, the pressure distribution under various operating conditions and structure parameters is also investigated to explore their contributions to the performance of the hydrostatic journal bearing. The results indicate an excellent guiding significance for the design and application of hydrostatic journal bearings.

Variable pitch fan aerodynamic design for reverse thrust operation

Variable pitch low pressure ratio fans could enable higher propulsive efficiency and eliminate the need for heavy thrust reversers. In this paper, the effects of the fan rotor design on reverse thrust capability have been explored by varying key parameters of NASA’s Advanced Ducted Propulsor (ADP) while maintaining cruise point performance. Reverse thrust performance has been assessed using RANS single passage CFD of the variable pitch fan system with an extended domain. This computational approach has been validated using NASA Stage 51B, an experimental variable pitch fan test case. Predicted total pressure and total pressure ratios for this case were found to agree with test data within experimental error, except where large tip region separations occurred at high incidence. Applying individual variations to rotor pitch-to-chord, radial loading distribution, and chordwise camber distribution generated changes to rotor incidence, blockage, and peak surface Mach numbers in reverse operation. An increase in gross reverse thrust of up to 8% was achieved through reductions in rotor pitch-to-chord due to improved loading and lower shock Mach numbers. Controlling section camber distributions was used to move the rotor shock downstream and was found to increase reverse thrust by up to 3%. Increasing rotor loading at the mid span relative to the tip resulted in high tip incidence and a 50% reduction in gross reverse thrust across all rotor speeds. This suggests that tip loaded designs are required for high levels of reverse thrust.

Numerical investigation of the effect of blade distortion laws on the corner flow separation of the axial-flow fan

To study the effect on performance of different blade distortion laws of axial flow fans, the radial distributions of blade stagger angle were fit as Bézier curves, and five distribution laws were established. Three-dimensional numerical simulations were carried out for the fan schemes. The results show that distortion near the blade root can effectively restrain the corner separation vortex from climbing along the blade suction surface, so that the low-energy fluid accumulates in the corner region. Tip distortion rises the pressure difference between the pressure and the suction surface, and the turbulence intensity of the tip leakage is increased. Root distortion inhibits the CV diffusion, resulting the decay of tip leakage vortex, thereby improving the stall margin. Relative to a uniform distortion blade, the blade-root distortion scheme increases the radial load of the blade, while the tip distortion scheme results in a decrease of the blade load coefficient. The maximum load position of the end-zone distorted blade moves to the root area, while the maximum load position of the middle distorted blade shifts to the tip area. The end-zone distortion improves the efficiency and total pressure of the fan without changing the efficient working range, and is considered to be the optimal scheme. The maximum pressure coefficient of the end-zone distortion scheme is increased by 4.97% and the maximum efficiency is increased by 1.28%.

In-Plane Failure Mechanism and Strength Design of Plate-Tube-Connected Circular Steel Arches

The in-plane elastoplastic failure mechanism of plate-tube-connected steel circular arches with inverted triangular cross sections is investigated in this study by using theoretical derivation and numerical simulation. First, the in-plane elastic buckling load formula of the arch under full-span uniform radial load (FSURL) is presented. Then, the limited conditions of avoiding the connecting plate and chord local failure before global elastic instability are derived. Lastly, the elastic–plastic failure mechanisms of arches are studied under FSURL, full-span uniform vertical load (FSUVL), and half-span uniform vertical load (HSUVL). It is found that the arch will experience global failure, chord local failure, combined connecting plate and chord failure, and connecting plate local failure under FSUVL and HSUVL. The failure mode is mainly related to the stiffness of the connecting plate. The corresponding design formulas are proposed for the global failure of arches and local failure of the chord. The proposed formulas and FE results are in good agreement.

Static stability test and simulation of a large-scale modular carbon fiber reinforced polymer wheel-spoke-shaped stiffening ring subjected to multi-point radial loading

To enhance the hoop stiffness of the rigid-flexible integrated airship, a new large-scale wheel-spoke-shaped stiffening ring composed of modular carbon fiber reinforced polymer (CFRP) standard trusses was designed in this work. Particularly, by using the modular assembly technology, the CFRP stiffening ring with a diameter of 40.0 m was integrated assembly, which verified the feasibility of the proposed structural design method. Based on the applied uniformly distributed load form of the CFRP wheel-spoke-shaped stiffening ring during the flight of the rigid-flexible integrated airship, the standard truss module was subjected to a multi-point loading static stability test through a self-developed loading device, while the in-plane buckling failure position and buckling load of the CFRP wheel-spoke-shaped stiffening ring were also determined. Based on the refined multi-layered shell model, the combined eigenmode imperfection method was used for the nonlinear buckling analysis of the CFRP truss module. The buckling failure mode and the buckling load obtained from the simulation results were in good agreement with the test results. The proposed and verified large-scale modular CFRP wheel-spoke-shaped stiffening ring improved the hoop stiffness of the rigid-flexible integrated airship and achieved structural weight reduction and the design goal of the large-scale structure. The refined multi-layered shell model based on the combined eigenmode imperfection method has an important application value and guiding significance for investigating the buckling property of CFRP wheel-spoke-shaped stiffening rings, which provides valuable technical support for the structural design of rigid-flexible integrated airships.

On the asymmetric dynamic response of viscoelastic sector plate made of FG polymer foam

This work provides an analytical investigation of the damped forced vibration behavior of viscoelastic annular sector plates made of porous polymer foam. For this aim, the motion equations are obtained through first-order shear deformation theory (FSDT) in conjunction with the energy method and the calculus of variations. Three distinct types of pore distribution are explored in the plate thickness such as porosity symmetric distribution type 1 (PSDT1), porosity symmetric distribution type 2 (PSDT2), and porosity non-symmetric distribution (PND). Then, the obtained relations are extended to constitutive equations by considering the standard linear solid (SLS) viscoelastic model. The perturbation technique and Fourier series are employed to solve the system of equations with variable coefficients. The equations with variable coefficients are changed to a system with constant coefficients by inserting a new variable, and the asymmetrically dynamic response is computed analytically in a closed-form solution. Then, the transient dynamic behavior of viscoelastic functionally graded porous (VFGP) annular sector plates is detailed for various types of radial and asymmetric circumferential loadings. Furthermore, a user-defined field (USDFLD) code is developed for evaluating the reliability of the analytical findings using finite element (FE) software. Finally, we have benchmarked the effectiveness of our framework by investigating several geometrical parameters, material properties, and loadings types.

Calculation of radially inhomogeneous ring loaded with normal and tangential loads

The aim of the study is to solve the problem of the stress-strain state of a thin ring under radial and ring loads, factoring in the radial inhomogeneity of the ring. Also, the task is to compare the two calculation methods to the example of solving the problem of uneven load distribution along the outer surface of the ring with one-dimensional inhomogenuity. Analytical or numerical-analytical solutions are used in the two-dimensional plane problem of the theory of elasticity in polar coordinates for an inhomogeneous body. Most of these problems consider centrally symmetric circular bodies. As a rule, this is possible when all unknown functions depend on the radius. These tasks correspond with the majority of ring and cylindrical structures. Pipes are suitable for creating pipeline systems and civil engineering, they are used for gas pipelines, in heating networks and water supply systems. The key feature of the work lies in the consideration of uneven radial and ring loads distribution along the outer surface of the ring. Comparison of the calculation results obtained by two methods makes it possible to determine the stressed and deformed states with sufficient accuracy, an indicator of which is the obtaining of the ring stresses.

Application of Active Disturbance Rejection in a Bearingless Machine with Split-Winding

In this paper it is proposed the displacement control of a bearingless induction machine (BIM) with split winding and optimized drive structure using Active Disturbance Rejection Control (ADRC). Considering that the BIM is a multivariable, nonlinear, and time-varying system with coupled variables, advanced control techniques can be useful in order to make the system operate efficiently and with good dynamic performance. The ADRC considers the total disturbance, composed of unmodeled dynamics, nonlinearities, uncertainties, and load variations, as an extended state and estimates it in real-time through a state observer. This increases the overall robustness of the control system to disturbances of different natures. The application of the ADRC technique on the radial position control of the BIM used in this work showed that a Linear version of ADRC is not able to compensate for radial load disturbances but this drawback can be solved by the use of a nonlinear observer in the ADRC structure. Besides that, both control versions of the ADRC were able to make stable the naturally unstable radial displacement of the machine’s rotor.