Search

Rolling bearings are a leading cause of equipment breakdowns in electrical machines, underscoring the significance of predictive maintenance strategies. However, the given methods require high-quality big data, which is challenging to acquire, especially for faulty cases. Simulation models offer an alternative by generating large data sets to complement experimental data. However, bearings involve complex contact-related phenomena, such as slipping and clearance. Therefore, generating realistic data comparable to the real-world necessitates accuracy. Our study presents a multibody simulation system of a motor bearing, incorporating a geometry-based polygonal contact method (PCM), which accurately captures nonlinear bearing dynamics and allows for the simulation of various contact geometries. We introduce a systematic approach to adjust the PCM contact properties for rolling bearings, referencing the well-established Hertzian theory. Both healthy and faulty bearings with a local outer ring fault were simulated. The simulated output was a relative shaft displacement, experimentally validated using a capacitive sensor. Our model successfully demonstrates the potential to employ geometry-based contacts for generating realistic data on faulty bearings with the aim of predictive maintenance. • Simulating rolling bearing dynamics using surface geometry-based polygonal contacts. • Adapting the polygonal contact method to bearings, referencing Hertzian theory. • Successfully imitating common bearing contact phenomena, such as slip and clearance. • Bearing fault analysis validation through experimental shaft displacement data. • Displacement spectrums of outer ring faults correspond to the experimental results. [ABSTRACT FROM AUTHOR]

In this paper, we present a Boundary Element methodology to numerically investigate the operation of a viscoelastic rolling element bearing in steady-state conditions. The methodology is fully general, able to deal with any real linear viscoelastic material, and relies on the ad hoc definition of steady-state viscoelastic Green's functions that intrinsically take into account the circular geometry of the domain. From an applicative point of view, the assessment of this contact problem is crucial: we show that the distribution of the load among the rollers is really different from what is predicted in purely elastic conditions, with some rollers eventually losing the contact with the raceways for some speed values. This has dramatic consequences not only on the rolling element bearing durability but may impact the rotor dynamics of the system supported by the bearing. Furthermore, our analysis assesses the viscoelastic torque pointing out the sources of hysteretic dissipation. Finally, to corroborate our model, numerical predictions for a rolling element bearing with the outer ring made of Polytetrafluoroethylene (PTFE) are compared, with good agreement, to experimental outcomes. • A novel Boundary Element formulation assesses polymer rolling bearings mechanics. • Analysis of the load distribution among the rollers as a function of the speed. • Assessment of the hysteretic dissipation as a function of the load and the speed. • Experimental corroboration for a Polytetrafluoroethylene (PTFE) rolling bearing. [ABSTRACT FROM AUTHOR]

• Presents a comprehensive multibody dynamics model for cross groove ball CVJs. • Offers a novel contact mechanics and friction model for the cage race contact. • Importance of friction coefficient in determining the dynamic response is shown. • Highly varied contact kinematics from pure rolling to pure sliding are predicted. Accurate prediction of constant velocity joint transient contact loading and complex kinematics is necessary to improve joint design and prevent incurring failure from rolling contact fatigue. A detailed multibody dynamic model is presented for cross groove constant velocity joints used in high performance automotive racing applications, hitherto not reported in the open literature. The developed model includes detailed contact mechanics and friction models for all contacts made between the components. A novel semi-Hertzian contact model is adopted for the cage-race conjunction. Local contact kinematics is evaluated based on a methodology used in tribological analysis. The proposed model is validated against available computational models provided in literature for cross groove designs. Using the model, contact pressures occurring in the ball-race and ball-cage contacts are shown to reach levels as high as 4 and 5 GPa, respectively. The assumed value of friction coefficient is shown to have a strong influence on the predicted contact forces. Local contact motions are presented for the ball-race and ball-cage contacts, demonstrating complex motion which varies between pure rolling and pure sliding within a single cycle. [ABSTRACT FROM AUTHOR]

• The complex-number method is applied to planar mechanisms (PMs) with higher pairs. • A general notation for writing the constraint equations of PMs is stated. • A general algorithm for the kinematic analysis of single-DOF PMs is proposed. • The proposed algorithm is simple to present it in graduate/undergraduate courses. • The effectiveness of the proposed algorithm is proved through three case studies. In single-degree-of-freedom (DOF) mechanisms, velocity coefficients (VCs) and their 1st derivative with respect to the generalized coordinate (acceleration coefficients (ACs)) only depend on the mechanism configuration. In addition, if the mechanism is a planar linkage (i.e., a mechanism containing only lower pairs), complex numbers are an easy-to-use tool for writing linkage's loop equations that are formally differentiable and are the only constraint equations of linkages. Actually, the use of complex numbers for systematically writing the constraint equations of planar mechanisms is often limited to linkages. The possible presence of higher pairs in these mechanisms is usually managed through either equivalent linkages or apparent velocity/acceleration equations. Both these methods are simple to implement for a single mechanism configuration, but become cumbersome when continuous motion has to be analyzed. Other approaches use ad hoc auxiliary equations. Here, first, a general notation that brings to select particular auxiliary equations is proposed; then, such notation is adopted to propose an algorithm that systematically uses VCs and ACs for solving the kinematic-analysis problems of single-DOF planar mechanisms. The proposed notation and algorithm, over being efficient enough for constituting the kinematic block of any dynamic model of these mechanisms, are easy to present planar kinematics, with the complex-number method extended to higher pairs, in graduate and/or undergraduate courses. [ABSTRACT FROM AUTHOR]

Rolling-contact mechanisms can provide low-friction motion with unique kinematic paths. We show that developable surfaces can be used as a design tool for rolling-contact mechanisms joined with compliant bands. These mechanisms can exhibit 3D motion paths, couple rotational and translational motions into a single degree of freedom, and can be designed to exhibit various tailored kinetic responses. We set forth developable surface parametrizations well suited to the creation of rolling contacts. We highlight how the geodesic and principal curvatures of the non-ruling principal curves of a developable surface are meaningful design quantities for rolling contacts. We provide kinematic and kinetic analyses and demonstrate several developable compliant-aided rolling-contact mechanisms in physical prototypes. [ABSTRACT FROM AUTHOR]

• A new dynamic model is proposed for inflatable mechanisms with friction and adhesion. • A modified master-master detection approach for rolling contact is presented. • The frictional contact considers stick-slip transition, large sliding and rolling. • An adhesion element with failure mechanism is developed. • Appropriate parameters for adhesion constitutive relationship are obtained. A new modeling approach is proposed for dynamic analysis of inflatable mechanisms with large deformations, involving frictional contact and adhesion. Firstly, the Absolute Nodal Coordinate Formulation (ANCF) shell element is employed to model the flexible appendage. Then, by combining the master-slave and master-master techniques, a frictional contact formulation for the thin shell and the rigid cylinder is presented, which can capture the stick–slip transition and address both large sliding and rolling scenarios. In addition, a modified contact detection approach is proposed by optimizing the contact detection region to effectively avoid mutual over-penetration and improve detection efficiency. Furthermore, an adhesion element with failure mechanism is developed. Finally, a series of numerical examples are carried out to validate the proposed modeling approach. Together with the successful simulation against the resistance controlled deployment of an inflatable mechanism, the advantages of the proposed approach are demonstrated. Moreover, the most appropriate parameters for adhesion constitutive relationship are obtained to serve the adhesion-based controller design. [Display omitted] [ABSTRACT FROM AUTHOR]

This paper presents an original approach using Discrete Element Method (DEM) for predicting the mechanical behavior of a bearing considering rigid and elastic housing. The ability of DEM to describe accurately the mechanical state of a bearinghas been established by means of a comparison with FEM, of mechanical stresses and load distributions in a static case. Specifically, a contact model and a cohesive model are implemented together in 2D simulations. Once static results validated, DEM simulations are conducted in dynamic in order to evaluate Von Mises stresses within the rings. The bearing is decomposed in a macroscopic polydisperse granular media made of rolling elements and cage components. The rings are modeled as a homogeneous continuous material by considering a cohesive granular assembly. Besides the fact that the proposed modeling takes into account all bearing components, it also allows to describe both elastic behavior and loading evolution in dynamic mode. [ABSTRACT FROM AUTHOR]

• A new cycloidal-pin reducer with a rotatable output-pin mechanism is proposed. • Effects of the multi-source geometric errors in modeling of reducer are considered. • A geometric error allocation strategy of the parts in the assembly of reducer is given. • Dynamic transmission errors of the reducers with different tolerance designs are studied. A new type of one-stage precision cycloidal-pin reducer is designed and explored in this study. The design innovatively replaces the fixed output-pin mechanism of conventional cycloidal-pin reducers with a rotatable output-pin mechanism, thereby transforming the sliding contact between the output-pin and the output-hole into a rolling contact. This new structural design is found to significantly improve the transmission efficiency of the reducer. To evaluate the dynamic transmission error (DTE) characteristics of the proposed reducer, a general dynamic model of the cycloidal-pin transmission system considering the influences of multi-source error factors on the geometry of the main components is established. The geometric error of the component is determined by taking random values within a given design-tolerance zone. The geometric error distribution introduced using this method can well match the actual machining situation. Finally, the DTEs of the new reducers with three different tolerance designs are analyzed numerically and tested experimentally. The results show that the new reducer with a reasonable tolerance design can achieve high transmission accuracy and has the potential for application in the joints of industrial robots. [ABSTRACT FROM AUTHOR]

The involute profile is the most commonly used tooth profile for cylindrical gears. However, its counterpart for bevel gears is not commonly used because its generation is not compatible with the use of easy-to-manufacture cutting tools and market-oriented generation methods. Nowadays, with additive manufacturing technology growing across industries to manufacture parts and full-scale products, the spherical involute profile deserves to be given the possibility to become the reference profile for bevel gears generated by additive manufacturing, forging or plastic molding. In this work, both the spherical involute and the octoidal form systems for bevel gears are mathematically defined. The geometry of their respective crown-gears for generation is derived and the computerized modeling of the geometries of the generated bevel gears presented. The comparison between the obtained gear tooth geometries is performed from the point of view of the obtained geometric deviations, their behavior to the change of the shaft angle and the evolution of contact and bending stresses for different values of torque applied to the pinion. The results showed that the spherical involute profile can handle better with the changes in the shaft angle, although the octoidal profile presents lower contact and bending stresses. [ABSTRACT FROM AUTHOR]

• The contact pressure was reduced by changing the geometry of the bodies. • The durability of the bodies with logarithmic profile rised at low and high loads. • The durability barely changed at medium loads using the logarithmic profile. • Utilization of higher durability of logarithmic profile in special applications. Increasing the durability of machines and equipment is very desirable today. It mainly applies for special and economically expensive applications. This can be achieved by new design of its parts. The aim of this research is to increase the durability of curved bodies with line contact by changing their shape. The durability of a rolling element with a fully crowned profile and a logarithmic profile were calculated using the contact stress at the point of contact obtained analytically on the basis of Hertz's theory and numerically using the finite element analysis. The durability was calculated analytically based on the theories of Lundberg-Palmgren, Ioannides-Harris and Zaretsky and then compared. [ABSTRACT FROM AUTHOR]

This paper investigates the rolling dynamics of spherical wheels using the theoretical framework provided by the brush models. The analysis is mainly conducted under the assumption of vanishing sliding inside the contact patch. Different types of kinematics are considered: simply rolling wheels, rolling and tilting, and purely spinning. For the first two cases, a complete solution is derived concerning both the steady-state and transient behaviours. Some qualitative trends for the forces and moments generated inside the contact patch are then provided when accounting for limited friction. For the case of a purely spinning spherical wheel, it is shown that steady-state conditions are never possible owing to the assumption of vanishing sliding. Moreover, it is demonstrated that the shear stresses acting inside the contact patch grow unbounded if the additional contribution relating to the deflection of the bristle is not taken into account when calculating the total sliding velocity. In this case, a stationary solution may be eventually recovered as an asymptotic distribution only by assuming limited friction inside the contact patch. • The kinematics of spherical robots is analysed using the brush theory. • General solutions are provided in steady-state and trainset conditions. • Closed-form expressions for the deformation of the bristles are derived. • Neglecting higher-order terms may lead to unbounded solutions. [ABSTRACT FROM AUTHOR]

This work describes a deployable compliant rolling-contact element joint (D-CORE joint) that employs curved-folding origami techniques to enable transition from a flat to deployed state. These deployable joints can be manufactured from a single sheet of material. Two fundamental configurations of the D-CORE are presented. The first configuration allows for motion similar to that of a Jacob's ladder when the joint is in a planar state while achieving the motion of a CORE when in the deployed state. The second configuration constrains all degrees of freedom to create a static structure when the joint is in the planar state and allows for the motion of a CORE in the deployed state. Curved-folding origami techniques can be used with both configurations to control the cam radius and range of motion of the D-CORE. Physical models are demonstrated in Tyvek®, polycarbonate, polypropylene, and metallic glass. A deployable translating platform constructed of an inversion of the D-CORE is also shown. [ABSTRACT FROM AUTHOR]

This paper is concerned with the possibility of concave thread making by tool of straight line. Geometry of worm thread formed by tapered end mill is presented. Machining of concave worm threads is described. It was found that high compatibility of the shape of the machined profile with theoretical one took place. Surface roughness of worms formed by rotary file is comparable with that of commercial worms. Developed method of machining allows easy concave profiles of worm thread forming using universal commercial tools. [ABSTRACT FROM AUTHOR]

Constant-breadth cam mechanisms are characterized by the fact that the closure of the cam-follower contact is guaranteed thanks to the geometry and, therefore, auxiliary elements as springs are not necessary. On the other hand, cam mechanisms with a negative radius roller follower allow designing simple machines exerting remarkably high forces when the space is restricted. This work proposes a new constant-breadth cam mechanism with a double roller translating follower of negative radius. The cam profile is designed with an optimizing method based on Bézier curves. [ABSTRACT FROM AUTHOR]

• Include surface roughness topography in stress determination. • Include both crack nucleation and propagation descriptions. • Consider realistic mixed EHL operating condition. • Show roughness effect on crack nucleation and propagation. • Compare to experiments to show good correlation. In this study, a rolling contact fatigue model for lubricated gear contacts of rough surfaces is proposed, considering both crack nucleation and propagation stages. A boundary element approach is implemented to describe surface roughness topography effect on near surface stress concentration, with surface tractions yielded from mixed EHL analysis. A fatigue criterion is employed to find crack nucleation position and life. Assuming mode II crack opening mechanism, stress intensity factor range is determined and used to arrive crack propagation life. Through comparisons to experiments, model capability is demonstrated. Simulation results show important roughness effect on crack propagation as well as crack nucleation. [ABSTRACT FROM AUTHOR]

The goal of the paper is to develop the theory of curving meshing and apply it in high performance gear transmission. With this aim, this study investigates the gear geometry and kinematics of space curve meshing in gear design field. Here, definition of conjugate curves and the method of obtaining them are described. What's more, an extended method to get tooth surfaces from a space curve and its conjugate curve is proposed and the meshing characteristics of these tooth surfaces are argued. Then, based on arguments for conjugate curve theorem, this paper proposes the mathematical model of conical-helix bevel gears from the idea of logarithmic spiral bevel gears. To validate this model and investigate the tooth contact characteristics of conical-helix bevel gears, the numerical example of a pair of these gears with specific profiles is represented by applying the general computer program, ANSYS 14.0. Results show that the main characteristics of these gears include loads in the same direction, pure rolling contact and low bending stresses. The results also agree with the theoretical derivations for conjugate curves and conical-helix bevel gears. [ABSTRACT FROM AUTHOR]

Dynamic properties of ball bearing (or any rolling bearing) are varying during operation, especially the stiffness which mostly depends on rotating speed and loads applied. Therefore, in this paper, the notion of rolling bearing speed-varying stiffnesses introduced and explained by studying the relations of load-deflection through the bearing dynamic model which is based on Jones & Harris's efforts. After the acquisition of load-deflection relations, two common numerical (linearization) methods are provided to calculate bearing stiffness, which turned out to be too unstable to get satisfied results. To improve the method of calculating speed-varying stiffness, an analytic model based on the differentiation of implicit function is proposed to calculate the speed-varying stiffness. The comparisons between the results from the numerical method and the proposed method have been made to validate the proposed method. In addition, the results calculated by the proposed method are compared with those which appeared in other literatures or experiments. [ABSTRACT FROM AUTHOR]

This paper presents a new kinematic model based on the Darboux frame for motion control and planning. In this work, we show that an underactuated model of a spin-rolling sphere on a plane with five states and three inputs can be transformed into a fully-actuated one by a given Darboux frame transformation. This nonlinear state transformation establishes a geometric model that is different from conventional state-space ones. First, a kinematic model of the Darboux frame at the contact point of the rolling sphere is established. Next, we propose a virtual surface that is trapped between the sphere and the contact plane. This virtual surface is used for generating arc-length-based inputs for controlling the contact trajectories on the sphere and the plane. Finally, we discuss the controllability of this new model. In the future, we will design a geometric path planning method for the proposed kinematic model. [ABSTRACT FROM AUTHOR]

• A method to map unique contact curves for rolling in-hand manipulation. • Geodesic based contact curves used to ensure rolling constraints. • Geodesic equations modified to bring a slipping in-hand manipulation to rolling. • Generation of guaranteed special contact curves in rolling constraint. The paper focuses on synthesizing optimal contact curves that can be used to ensure a rolling constraint between two bodies in relative motion. We show that geodesic based contact curves generated on both the contacting surfaces are sufficient conditions to ensure rolling. The differential geodesic equations, when modified, can ensure proper disturbance rejection in case the system of interacting bodies is perturbed from the desired curve. A corollary states that geodesic curves are generated on the surface if rolling constraints are satisfied. Simulations in the context of in-hand manipulations of the objects are used as examples. [ABSTRACT FROM AUTHOR]

• An analytical synthesis of pure rolling contact bevel gears is proposed. • Tooth surfaces of pure rolling contact bevel gears are extended. • A direct relationship between the normal pressure angle and normal vector is derived. • A direct derivation process of the curvature relationships is represented. • The analytical model is applied in the logarithmic bevel gears in details. This work attempts to improve the kinematic geometry model of pure-rolling contact spiral bevel gears (PCSBGs). A systematic report on the analytical design and analysis methods for PCSBGs is presented herein. The tooth surface model of PCSBGs are extended, and a direct relationship between the normal vector and normal pressure angle of PCSBGs is derived, which contributes to building a bridge between the basic geometric parameters and contact characteristics of PCSBGs. The curvature relationships between the tooth surfaces of PCSBGs are derived, and simple equations related to the relative normal curvatures of PCSBGs are obtained from tensor analysis. A logarithmic spiral bevel gear is used as a sample case to demonstrate the application of the kinematic geometry model of PCSBGs and to verify the analytical expressions. The numerical analysis results of the logarithmic spiral bevel gears agree with the analytical model. [ABSTRACT FROM AUTHOR]

• A simplified online wheel-rail constraint-based contact method is presented. • The constraint method deals efficiently with the two-point contact scenario. • Equivalent profiles that maintain real wheelset kinematics are defined. • A linear regularization for continuous points from tread to flange is derived. • Contact forces are applied at the exact locations in the two-point contact scenario. This paper presents a rigid contact approach to analyse the two-point wheel-rail contact scenario using the simplified constraint-based contact method called Knife-edge Equivalent Contact method (KEC-method). The proposed approach makes use of the computationally efficient online solution of the KEC constraints, where a single-point rail is in contact with an equivalent wheel profile, and provides an exact relation between the location of the contact points in the equivalent and real profiles. In this context, the two-point contact scenario can be easily dealt by linearly softening the KEC-constraints in the vicinity of the two-point contact, that gives a continuous and unique contact point solution between each wheel-rail pair and avoids finite contact point jumps between tread and flange. This allows an efficient kinematic solution of the two-point contact scenario. However, to properly account for a dynamic equivalence of the two-point contact scenario in the computation of the tangential contact forces, the reaction force acting on the wheel when the contact point lies on the tread-flange transition, is transformed into two contact forces acting on the tread and flange respectively maintaining the resultant equilibrium of forces at the wheel. [ABSTRACT FROM AUTHOR]