Vibrations of Misaligned Rotor System with Hysteretic Friction Arising from Driveshaft–Stator Contact under Dispersed Viscous Fluid Influences

Dynamic analysis of a combination of misaligned rotors, the disturbance of the Cardan joint and the rotor–stator rubbing within a restricted clearance space in a viscous fluid is complex and can result in persistent vibration anomalies that are often misunderstood. It becomes increasingly important to gain some insights into how the transmission of coupled motion responds dynamically under a variety of conditions. This paper introduces an efficient simulation of the misaligned multi-degree-of-freedom rotor’s model, which was developed to predict the transient dynamic behaviours of a driveshaft deflection. The model accounts for tight clearance as a function of contact deformation according to nonlinear Hertzian contact theory. The paper also examines recent research by considering the influence of parameters such as eccentric masses, applied torques and flexible coupling joint perturbation introduced in the proposed rotor system. The simulation results indicated that the viscous fluid surrounding the driveshaft had sufficient torsional flexibility to dampen the rubbing impact to the driven shaft displacement. In addition, the torsional fluctuations of the flexible coupling abruptly increased, and then significantly impacted the vibration of the submerged driveshaft. Parametric studies involving the interconnected rotor models indicated that the effects of fluid on a close-bounds contact area can create partial disturbance reduction. The high rubbing contact is shown to be lost through the Hooke’s joints during power transmission. The speed-frequency spectrum maps provide valuable information on all the modelled excitations over the frequency of the twice-running speed resonance in a viscous medium. Further, nonlinear characteristics are reconstructed through orbit shapes and can be adopted in the condition monitoring of rotors in engineering practice.

Analysis of Dynamic Response of a Two Degrees of Freedom (2-DOF) Ball Bearing Nonlinear Model

Often the input values used in mathematical models for rolling bearings are in a wide range, i.e., very small values of deformation and damping are confronted with big values of stiffness in the governing equations, which leads to miscalculations. This paper presents a two degrees of freedom (2-DOF) dimensionless mathematical model for ball bearings describing a procedure, which helps to scale the problem and reveal the relationships between dimensionless terms and their influence on the system’s response. The derived mathematical model considers nonlinear features as stiffness, damping, and radial internal clearance referring to the Hertzian contact theory. Further, important features are also taken into account including an external load, the eccentricity of the shaft-bearing system, and shape errors on the raceway investigating variable dynamics of the ball bearing. Analysis of obtained responses with Fast Fourier Transform, phase plots, orbit plots, and recurrences provide a rich source of information about the dynamics of the system and it helped to find the transition between the periodic and chaotic response and how it affects the topology of RPs and recurrence quantificators.

A finite element based simulation framework for robotic grasp analysis

The commonly used grasp simulators such as GraspIt! and OpenRAVE use wrench space formulations and grasp quality metrics such as ϵ and v to identify stable grasps in dynamic conditions. However, wrench space formulations are derived based on static mechanical equilibrium equations, and the physical attributes of the object such as stiffness and mass are also not considered for grasp analysis. Above all, these grasp analysis frameworks cannot be experimentally validated, thereby resulting in grasps that are not reliable. In this paper, an experimentally validatable Finite Element (FE) based grasp analysis framework is proposed for evaluation of robotic grasps in dynamic conditions. By applying standard solutions of Hertzian contact theory to a few robotic grasps, Finite Element Method (FEM) is validated. A real-world grasp situation is then simulated using FEM, and the FE model is validated based on the contact area measured in real-time using a pressure sensor. By applying dynamic perturbations to the validated FE model, the stability of the grasp is evaluated, and the most stable grasp is identified using the contact area based metric, π. It is observed that FE simulations agree with the analytical solutions and experimental results, with a relative error of not more than 7%.

Collision dynamics analysis of lifting the pantograph

An extended pantograph-catenary (PAC) contact collision model is presented in this paper. The catenary is described by a finite element model while the pantograph is described by a multi-body model. The normal collision model is established by using the Hertzian contact theory. A 1:1 PAC collision contact test rig is built to validate the pantograph-lifting model. The dynamic responses of the PAC system during lifting the pantograph with different velocities and positions are studied. The research results show that the velocity and position of lifting the pantograph will affect the pantograph-lifting time, acceleration of collector piece, vertical displacement and contact force in the process of lifting pantograph. When the velocity of lifting the pantograph exceeds 0.5 m/s, the contact force between the pantograph and the contact wire will exceed 250 N, which is the allowed value set in the provisions of EN50367. It is essential to control the velocity of lifting the pantograph below 0.4 m/s to prevent the catenary or contact piece from being damaged due to the excessive impact force. The distribution of the droppers also affects the collision force between the PAC system.

Reinvestigation into railway wheel-track interaction and suspension damage

Without considering either velocity or acceleration effects, the current conventional method presented in literature applies the vertical deflection of a wheel centre caused by a flat defect to the Hertzian contact theory. This method has been numerically and theoretically proved to be inappropriate and can incorrectly predict a higher wheel-rail impact force for a low speed than a high speed. Therefore, under a hypothesis of no wheel bouncing and sliding, two new methods, the velocity-based and the acceleration-based have been proposed. The former method takes the wheel centre deflection change in each computational increment from the Hertzian contact theory while the latter applies the wheel centre acceleration caused by the flat in revolutions to the wheel as a force in dynamic simulation, which interprets the speed effects on impacts precisely. A sensitivity study proves that the velocity-based method is unreliable as opposed to the acceleration-based method. A beam/rigid FE model has also been developed to inspect the wheel-track interaction by performing dynamic analysis in the time domain. It has been found out that the impact responses predicted by the FE analysis and the velocity method are similar and the FE results heavily depend on the compute increment, which implies the FE modelling in ABAQUS may be unreliable for this issue with current applied increments. Finally, the results calculated using the acceleration method have been employed to study the suspension/damper torsional stress caused by a wheel flat. This indicates that a wheel flat may lead to potential fatigue damage if without proper maintenance management.

Erosion Model for Brittle Materials Under Low-Speed Impacts

The erosion of perfectly brittle materials under low-speed impacts is studied by the combination of the Hertzian contact theory and the maximum stress criterion. It is found that the fractional erosion per impact is proportional to the product of the square root of the yield strain and the ratio of the kinetic energy per volume of the impacting body to the critical strain energy density of the target. The novel formula is conceptually extended to the erosion of cracked brittle materials.

Dynamic Model of Planetary Roller Screw Mechanism with Considering Torsional Degree of Freedom

To predict accurately the dynamics performance of planetary roller screw mechanism, it is necessary to establish its streamline and engineering-compliant dynamic model, which is the basis of mechanical design and precision control of the system. In this paper, the relative displacement between roller and ring gear along the line of action is deduced and the relationship between nature frequencies and the number of rollers is discussed. Considering the torsional stiffness of all components and the thread mesh stiffness based on the Hertzian contact theory, the purely torsional model for planetary roller screw mechanism is presented to reveal the natural frequencies and vibration mode characteristics of the system. The results show that the natural properties of undamped system in planetary roller screw mechanism are mainly reflected by two typical vibration modes: rotational mode and roller mode.

Difference between the ideal and combined spherical joints and its effects on parallel manipulators

When using parallel manipulators as machine tools, the spherical joint has been widely used and replaced by a combination of a universal joint and a rotating unit, but the introduced differences and effects have not been studied in detail. In this paper, an approach to establish the mathematical models of the ideal and combined spherical joints is presented, and the differences between the two spherical joints are given from the perspective of constraints, workspace, clearance, and contact deformation. First, the non-interference workspace of a class universal joint is investigated by using a simple and clear projection method, where the constraint domain and workspace of two spherical joints are proposed. Next, the approximate clearance models of these two spherical joints are analyzed, and the corresponding contact deformation models are also given based on the Hertzian Contact theory. Finally, a 1PU + 3UPS parallel manipulator is used to verify the discrepant effects of two spherical joints on parallel manipulators. If the combined spherical joint is used, the results indicate that the improvement in the workspace is significant, but the drop in stiffness is also evident. Thus, this paper provides a theoretical basis for researchers to use combined spherical joints.

Evaluation Method of Surface-Rigidity Distribution in Elastic Body by Surface-Probing

Elasticity distributions in structure is one of the typical physical quantities that it is desired to measure nondestructively. Indentation testing is a useful method for the nondestructive measurement methods; however, devices are necessary to evaluate the distribution of elasticity. In this report, a technique to evaluate the elastic distribution in solid is introduced by the information obtained from a simple indentation device. The evaluation is based on Hertzian contact theory that is applied to calculate elasticity from force measured by this indentation device. However, the non-uniform nature of elasticity distribution makes it difficult to apply Hertzian theory. As a solution to this difficulty, a correcting method of elasticity is discussed by analyzing the variation of force information obtained from the device. This correction depends on the method for determining the correction factor decided by the area of elastic range distributed in the solid; this decision is numerically defined by finite element method (FEM). The usefulness of this correction method is confirmed by evaluating the hardness distribution of wood grain. Trees are a representative material with hardness distribution, whose mechanical characteristics depend deeply on wood grain. Therefore, evaluating the ability of elasticity distribution in wood grain has been checked by the correction method discussed in this report. Then, for the problem related to evaluation based on basic Hertzian theory, the expected result can be obtained using wood grain size coefficient and the specification of the probe. However, it is also necessary to examine to the choice of device specifications such as probe dimensions because the elasticity of wood is relatively high and any measured information will have high sensitivity in elastic analyses. Those recommendtion are discussed by showing the devices developed for this evaluation in this report.

Impact of journal bending on the failure of axle bearings in railroad passenger cars

This research presents a systematic methodology to analyze the failure mechanism of cylindrical roller bearings of railroad passenger cars. Initially, a finite element model is developed to calculate the journal bending and internal contact load distribution, considering multi-interfacial contact parameters. Then, non-Hertzian contact theory is applied to prove the rollers’ abnormal contact behaviors, including load-distribution and displacement. Subsequently, a grease lubrication model is developed to study bearings lubrication under different operating conditions. Additionally, an exact service life model from ISO standards is used to evaluate the effect of journal bending. Finally, a system failure mechanism can be summarized and validated in the experiments, also helpful for axle box system bearings design and assembly.