Rolling Sphere Research Articles

Longitudinal Motion Controlling for a Spherical Rolling Robot with Soft Shell Based on Feedback Linearization

Longitudinal Motion Controlling for a Spherical Rolling Robot with Soft Shell Based on Feedback Linearization

Improving the design of cages for bearings of high technical level

The structure of roller bearings of axle boxes of freight and passenger cars was analyzed. The type of bearings depends on the operating conditions in a particular country. In the UK, the US, Japan, Poland, railcars are equipped with wheelsets with double-row cylindrical roller bearings. In Austria, bearing assemblies with two cylindrical roller bearings are used, and in Sweden – axle unit with two spherical roller bearings. Conventional, most massive cylindrical roller bearings (almost 99 % of all bearings) of axle boxes of Ukrainian freight and passenger cars were chosen as the basic design taking into account the technical and economic aspects of operation. Structural decomposition of basic bearings according to functions was performed. Structural and functional relationships of the bearing parts and elements of parts were revealed, the structural-functional model was constructed, making it possible to improve the functions of cages of basic bearings. Several new functions of cages appeared – the function of elimination of misalignment of its design, the function of reduction of forces of interaction with rollers and locator ring, the function of slippage reduction of rollers. The design changes in the cage components by increasing the number of windows, the convex shape of side surfaces of jumpers, profile section of the cage rings, which contribute to raising the technological level of bearings within the specified dimensions were grounded.

Mechanical analysis of spherical roller bearings due to surface waviness

This work presents a theoretical model to research the vibration due to surface waviness of spherical roller bearings (SRBs), taking account of the self-aligning feature and the external axial load. The surface waviness is described by cosinoidal functions. The self-aligning features, including the variation law of the self-aligning contact angle and the interaction with the external loads, are introduced into the non-Hertzian contact model. The nonlinear equations are solved by Runge–Kutta method and the proposed model is validated by comparing with the results of the published references. The results show more characteristic frequencies will be excited under the self-aligning operating condition, whereby the improved equations proposed in this paper are recommended to instead of the previous ones to predict characteristic frequencies of the waviness vibration in an SRB. In addition, these characteristic vibrations caused by waviness are obviously influenced by the magnitude and the direction of the self-aligning contact angle. A proper pretightening load should be chosen according to the self-aligning feature or else it will lead to hidden dangers. The radial clearance and the waviness amplitude can both highlight the effect of waviness. And the vibration caused by a larger radial clearance may be fiercer than the vibration due to waviness.

Estimation of the electric fields and dielectric breakdown in non-conductive wind turbine blades subjected to a lightning stepped leader

In this paper, the electric fields in the wind turbine blades due to the lightning stepped leader are studied, and the dielectric breakdown is assessed. The developed finite element analysis (FEA) includes the full length of the leader and enables one to incorporate various uniform and non-uniform charge density models. The lightning striking distance is calculated using the rolling sphere method. The electric field in a horizontal axis wind turbine with three blades representing Sandia 100 m All-glass Baseline Wind Turbine Blades (SNL 100-00) at three different lightning protection levels (LPL) is computed and compared to the dielectric breakdown strength of the blades. The dielectric breakdown strength of the blades is evaluated based on the experimental data. The results show that the tip region of the blade is the most vulnerable to the dielectric breakdown with the safety factor as low as 1.32 at LPL I. Copyright © 2016 John Wiley & Sons, Ltd.

Experimental investigation of the external lightning protection of ships through impulse voltage tests on a scaled‐down ship model

The impacts of a lightning strike are amplified in an environment with special features such as a ship electric grid, especially within the extended integration of electronic systems. In most marine regulations, lightning protection specifications are inadequate in the cases of metallic vessels, regarding the necessity of installing lightning rods and the method for the definition of their protection zone and subsequently of their height. Therefore, impulse voltage experiments on a scaled-down ship model were conducted in order to acquire interception probability distributions of its superstructures and to assess the accuracy of various protection zone models, established for isolated rods, on the given complex topology of a ship. The experimental results highlighted the overestimation of the protection zone even by the well-established rolling sphere model for negative polarity impulses depending on the geometrical conditions and the satisfying performance of statistical models that incorporate proximity effects and lightning interception probability.

Analytic study of a rolling sphere on a rough surface

In this paper it is realized an analytic study of the rolling’s sphere on a rough horizontal plane under the action of its own gravity. The necessities of integration of the system of dynamical equations of motion lead us to find a reference system where the motion equations should be transformed into simpler expressions and which, in the presence of some significant hypothesis to permit the application of some original methods of analytical integration. In technical applications, the bodies may have a free rolling motion or a motion constrained by geometrical relations in assemblies of parts and machine parts. This study involves a lot of investigations in the field of tribology and of applied dynamics accompanied by experiments. Multiple recordings of several trajectories of the sphere, as well as their treatment of images, also followed by statistical processing experimental data allowed highlighting a very good agreement between the theoretical findings and experimental results.

Controller tuning based on optimization algorithms of a novel spherical rolling robot

This study presents the construction process of a novel spherical rolling robot and control strategies that are used to improve robot locomotion. The proposed robot drive mechanism is constructed based on a combination of the pendulum and wheel drive mechanisms. The control model of the proposed robot is developed, and the state space model is calculated based on the obtained control model. Two control strategies are defined to improve the synchronization performance of the proposed robot motors. The proportional-derivative and proportional-integral-derivative controllers are designed based on the pole placement method. The proportional-integral-derivative controller leads to a better step response than the proportional-derivative controller. The controller parameters are tuned with genetic and differential evaluation algorithms. The proportional-integral-derivative controller which is tuned based on the differential evaluation algorithm leads to a better step response than the proportional-integral-derivative controller that is tuned based on genetic algorithm. Fuzzy logics are used to reduce the robot drive mechanism motors synchronizing process time to the end of achieving a high-performance controller. The experimental implementation results of fuzzy-proportional-integral-derivative on the proposed spherical rolling robot resulted in a desirable synchronizing performance in a short time.

Fundamental investigation of heat transfer mechanisms between a rolling sphere and a plate in OpenFOAM® for laminar flow regime

The heat transfer between particles and walls has been topic of research for several decades. In most cases existing correlations were developed empirically for special conditions and applications like fluidized beds or rotary kilns. With a deeper fundamental understanding of the occurring heat transfer mechanisms both design of existing and development of innovative apparatuses, could be more straightforward since the mentioned existing correlations cannot be applied flawlessly to other conditions, due to specific simplifications and assumptions. The aim of this work is to investigate the fundamental heat transfer mechanisms between spherical particles rolling on a plate on the microscale with the lowest level of simplifications. For the identification of the dominating heat transfer mechanisms an approach with Computational Fluid Dynamics (CFD) simulations is chosen. The fundamental investigations are carried out using a basic geometry of a moving sphere on a plate. Due to the lack of a solver which is able to describe the system of a moving sphere on a plate, a new solver is developed in OpenFOAM®. The solver is validated against an existing model as well as own experimental results. Simulations in the laminar flow region show good agreement. Analogically to literature the main transport resistance is identified in the gap between plate and sphere. The heat conduction through the gas layer between sphere and plate is identified as the dominating mechanism.

Fault diagnosis method for spherical roller bearing of wind turbine based on variational mode decomposition and singular value decomposition

For the non-stationary characteristics of the vibration signal of wind turbine’s roller bearing in fault condition, a bearing fault diagnosis method based on variational mode decomposition (VMD) and singular value decomposition (SVD) is proposed. The VMD method is used to decompose wind turbine’s roller bearing’s fault vibration signal into several components. These components are regard as initial feature vector matrix. The singular value decomposition of the matrix is done. The obtained singular value is used as the extracted bearing fault feature vectors. The probabilistic neural network is used as pattern recognition classifier to determine the working state and fault type of wind turbine roller bearings. The result of case study showed that the proposed method can effectively identify the working state and fault type of wind turbine roller bearings.

Dynamic Modeling and Controller Design for a Spherical Rolling Robot Equipped With a Gyro

In this paper, we derive a dynamic model of a spherical rolling robot that has a new driving mechanism equipped with a gyro and design a controller to stabilize a desired translational motion of the robot. Due to the angular momentum of the gyro, nutation motion of the internal mechanism of the robot may be caused. A feedback controller is designed to achieve the stabilization to a straight motion of the robot and nutation damping in the internal mechanism simultaneously. The asymptotic stability is proved using a Lyapunov function, and the effectiveness of the controller is verified by experiments. The controller is also successfully applied to other translational motions such as a circular motion and a meandering motion.

Effect of deposition method on the RCF performance of Cr x N thin film ball coatings

Abstract Cr x N thin films are of interest due to their wear and corrosion-resistant attributes. However, the tribological and functional performance of these coatings greatly depends upon their material properties and deposition processes. In this study, the tribological and functional performance of Cr x N coatings on AISI 52100 spherical rolling elements were evaluated. Two types of deposition processes were used to apply the coatings: a closed-field unbalanced magnetron sputtering system (CFUMS) and an ion beam assisted e-beam deposition (IBAD) system. Whereas the mechanical and compositional properties of the coatings obtained from the two deposition processes were found to be similar, the topographical and microstructural properties of the coatings differed. The tribological performance of the coated specimens was evaluated under boundary layer lubrication in a rolling (three ball-on-rod) contact tribometer, and the functional performance of these coatings on spherical rolling elements was examined in thrust ball bearings. The L 5 0 fatigue life of M50 rods paired with IBAD-coated balls was four times greater than that obtained with the 52100 balls. Significantly, the L 5 0 fatigue life of the M50 rods paired with the IBAD-coated balls was comparable to the fatigue life of M50 rods when paired with high-quality ceramic (Si 3 N 4 ) balls. Finally, bearings with IBAD-coated balls were observed to operate with lower torque than those with CFUMS-coated balls.

Study on the dynamic performance of tilt rotor supported by spherical roller bearings

Tilt rotor supported by rolling bearings is often used in mechanical equipment. In the past, researches on dynamic performance of bearing-rotor were mainly carried out for horizontal rotor, but there is insufficient reported research on the tilting rotors. In this paper, the dynamic performance of a tilt rotor supported by spherical roller bearings is studied. Through the dynamics analysis of the rotor, a transfer matrix dynamics model for the tilt rotor is established. The stiffness and damping calculation model of spherical roller bearings is built. With a calculation example, the effects of tilting angles and some rotor structure parameters on the system’s dynamic performance are studied numerically. The results obtained show that with the increase in the tilt angle, the critical speed of the rotor decreases, and the amplitude increases in the vertical direction of the shaft. With the same tilting angle, the smaller the distance from the disc to the middle point of the rotating shaft, the larger the am...

A case study on relation between roughness, lubrication and fatigue life of rolling bearings

A spherical roller bearing under high radial loading, constant speed and imposed roughness for the contacting surfaces was chosen as case study. Different lubrication regimes were obtained by varying oil viscosity through the operating temperature. For bearings with especially machined contacting surfaces, λ-ratio is firstly determined and its value is used to estimate the particular value of the lubrication parameter κ. Using the λ-ratio approach the paper reveals the relationship between roughness amplitude and the modified rating life of rolling bearings. The roughness values corresponding to good manufacturing practice are possible to be determined for each particular case. Three groups of random Gaussian roughness were generated with the same values for the Ra parameter as used in the modified lives investigations. For medium and especially high radial loads, the contacts between rough surfaces develop, inside the shallow layer, von Mises equivalent stresses higher than the fatigue limit stress. For condition of lack of lubricant or starved lubrication, these findings explain the initiation of the rolling contact fatigue in the shallow layer, close to contacting surfaces.

The role of roughness amplitude on depth distribution of contact stresses

The normal pressure distribution on contact area and depth distribution of von Mises equivalent stress are of major importance in prediction of various failure phenomena (e.g. rolling contact fatigue, scuffing) of the contacting surfaces. The paper reveals the relationship between roughness amplitude and stress state developed in the loaded material. The study was performed on a double rows spherical roller bearing under three levels of radial loading, and three significant values for the surface roughness. The numerical simulation was used to generate Gaussian rough surfaces with imposed values for Ra parameter. A semi-analytical method was used to solve the non-hertzian contact between rough surfaces. For the same loading level, the depth distribution of von Mises stress for rough surfaces is close to the distribution found for smooth surfaces, except the shallow layer close to the contacting surfaces. For medium and especially high loads, the contact between rough surfaces develops, inside this shallow layer, von Mises equivalent stresses higher than the fatigue limit stress.

Modeling of a Rolling Flexible Spherical Shell

The purpose of this paper is to develop the motion equations of a flexible spherical shell rolling without slip on a flat surface. The motivation for this paper stems from tumbleweed rovers, which are envisioned to roll, deform, and bounce on the Martian surface due to the flexible nature of their thin walls. The motion equations are derived using a constrained Lagrangian approach and capture the rolling without slip nonholonomic constraint. Numerical simulations are performed to validate the dynamic model developed and to investigate the effect of the flexibility of the spherical shell on its trajectory.

Closed-form analytical solutions for calculation of loads and contact pressures for roller and ball bearings

Closed-form load distribution solutions for calculation of the loads exerted by the rolling elements on the outer raceway in cylindrical and spherical roller bearings under radial loading are proposed. The analytical solutions are derived from the non-conforming contact solution of Hertz and the conforming contact solution of Persson. The maximum pressures due to the maximum loads of the rolling elements calculated from the analytical solutions are within a few percents of the results from the corresponding two-dimensional and three-dimensional finite element analyses. A simple method to estimate the fatigue lives of bearings based on the analytical solutions is also presented for engineers to compare the fatigue performance of bearings with different designs.

Effect of Diamond-Like Carbon Coatings on Ball Bearing Performance in Normal, Oil-Starved, and Debris-Damaged Conditions

ABSTRACTIn this study, a process was developed to deposit wear-resistant metal-doped diamond-like amorphous hydrocarbon and carbon coatings onto spherical rolling elements. Nanocomposite WC/a-C:H, TiC/a-C, and Ti/a-C:H coatings were applied in a closed-field unbalanced magnetron sputtering system and their mechanical, compositional, and microstructural properties were examined. The ability of the coated spherical rolling elements to affect bearing performance in normal, oil-starved, and debris-damaged conditions was evaluated in thrust bearing tests. WC/a-C:H-coated spherical rolling elements (balls) exhibit the ability to improve bearing performance in normal, oil-starved, and debris-damaged conditions.

Analyzing Hertzian contact stress developed in a double row spherical roller bearing and its effect on fatigue life

Purpose The purpose of this paper is to describe a method permitting the creation of a realistic model of spherical roller bearing with the aim of determining contact stress and fatigue life based on dynamic loading conditions. The paper also aims to recognize the effect of tolerance values on contact stress and fatigue life. Motion and load transmission in spherical roller bearing occurs within the assembly by elliptical curved contacting surfaces. The stress produced by the transmitted load would be very high because of least contacting area between these surfaces. Design/methodology/approach The paper describes a methodology to determine contact stress using analytically as well as finite element method for spherical roller bearing. The comparison for the both each approach for contact stress at different loading condition is carried out. Prediction of fatigue life based on dynamic loading conditions for bearing is also determined using finite element model. The effect on induced contact stress and fatigue life by varying tolerances on inner race dimensions have been found out. Findings The paper suggests that the maximum stress produces at the start or end of the contacting arc under static loading condition in spherical roller bearing. The analytical and finite element approach is in good agreement. The fatigue life prediction is useful for selecting loading conditions for various applications of double row spherical roller bearing. Tolerance level at inner ring raceway radius is kept high because of manufacturing constrain of complex curvature geometric shape. Research limitations/implications The present approach does not consider dynamic loading conditions for contact stress analysis. Therefore, researchers are encouraged to analyze the effect of wear, lubrication and other tribological aspects on bearing life. Originality/value The paper includes determination of contact stress and prediction of fatigue life for spherical roller bearing using analytical as well as finite element approach. The tolerance values at inner race are identified as per manufacturing constraint based on contact stress and fatigue life.

Wind turbine bearing fault diagnosis based on adaptive local iterative filtering and approximate entropy

For the unsteady characteristics of a fault vibration signal from a wind turbine rolling bearing, a bearing fault diagnosis method based on adaptive local iterative filtering and approximate entropy is proposed. The adaptive local iterative filtering method is used to decompose original vibration signals into a finite number of stationary components. The components which comprise major fault information are selected for further analysis. The approximate entropy of the selected components is calculated as a fault feature value and input to a fault classifier. The classifier is based on the nearest neighbor algorithm. The vibration signals from a spherical roller bearing on a wind turbine in its normal state, with an outer race fault, an inner race fault and a roller fault are analyzed. The results show that the proposed method can accurately and efficiently identify the fault modes present in the rolling bearings of a wind turbine.

Mechanical analysis of spherical roller bearings due to misalignments between inner and outer rings

This research presents a theoretical model to analyze the mechanical performance of spherical roller bearings, taking account of the angular and centroidal misalignments between the inner and outer rings. The angular misalignment can be improved by spherical roller bearings self-aligning feature to a certain degree. The interpolation method is used to determine the self-aligning contact angles of the different rollers. The centroidal misalignment is described by the angular and distance deviations. Non-Hertzian contact theory is applied to model and calculate the rollers load-distribution and total contact angles as well as the displacement of the inner ring. The loads of the rollers with the misalignments features and the external loads are included in the equilibrium equations, which is solved by Newton-Raphson method. This research shows spherical roller bearings self-aligning ability can balance the additional bending moment caused by the angular misalignment, which is at the cost of reducing its carrying capacity. But this carrying capacity will be improved to a certain degree by a proper axial load. It also illustrates that any kinds of centroidal misalignments are harmful for the service life of bearings. But the location of the misalignments can be roughly inferred by the external loads and the displacement of the inner ring, which is helpful for spherical roller bearings fault diagnose and elimination.