A vibration model of a rotor system with the sinusoidal waviness by using the non-Hertzian solution

The nonlinear contact forces and deformations between the balls and raceways can cause very complex vibration behaviours of rotor systems with the waviness in the support bearings. However, almost all previous works that used sinusoidal waviness took the Hertzian solution as the calculation method, which is not an accurate method based on Johnson’s formulation since the changes in the curvature at the sinusoidal contact surfaces. To overcome this issue, a new dynamic model of a rigid rotor system with the waviness in the support bearings is proposed. To provide a more accurate nonlinear contact force formulation for the sinusoidal waviness profile, the model used the Johnson’s extended Hertzian contact model to replace Hertzian contact model. This model can consider the time-varying curvature between the mating sinusoidal surfaces. The lubricating condition in the support bearing is also considered. A comparative study on the effects of Hertzian contact model, simplified Hertzian contact model, and Johnson's extended Hertzian contact model on the nonlinear vibrations of the rotor system is developed. The effects of the waviness amplitude and orders on the vibrations of the rotor system are discussed. The comparative simulations show that the proposed model can provide a more reasonable approach for predicting the vibrations of the rigid rotor system. Moreover, the simulations give that the nonlinear contact forces in the support bearings can greatly affect the system vibrations.

Study on Dynamic Characteristics and Parameter Influence of a Kind of Bilateral Restraint Impact Vibration System

In this paper, the hinge in the articulated structure is studied, the gap hinge is described as a nonlinear bilateral constraint, and the equivalent modeling and analysis of the hinge connection collision vibration are carried out based on the Lankarani–Nikravesh nonlinear contact force model. With the help of the method of nonlinear system dynamics analysis research, the Poincaré mapping of hinge joint collision vibration is constructed, the bifurcation diagram of the system with different parameters is solved, and the variation law of the system motion and the influence of parameters are analyzed by combining the time response diagram, phase diagram, Poincaré cross section diagram, and spectrum diagram of the typical motion of the system. The simulation results show that the system moves in a single degree of freedom and varies with parameters with multiplicative period bifurcation and rubbing edge bifurcation leading to chaos; the system’s periodic motion has shock state mutation and mirror jump transformation.

Mapping Relation between Rail and Bridge Deformation Considering Nonlinear Contact of Interlayer

This paper examines the effect of structural deformation on the unit slab-type ballastless track structure of high-speed railway. The principle of stationary potential energy was used to map the relation between girder vertical deformation and rail deformation considering the effect of subgrade boundary conditions and the nonlinear contact of interlayer. The theoretical model was verified by comparing with the finite element analysis and experimental results. The theoretical model was used to analyze the effects of several key parameters on the rail deformation, such as vertical deformation amplitude, elastic modulus of the mortar layer, and vertical stiffness of the fasteners. The results show that the track slabs suffered significant disengagement, which makes the deformation of the track structure at the position of the beam joint tend to be gentle when nonlinear contact between the mortar layer and the track slabs was considered. The track slabs disengagement mainly occurs near the beam joints (the side of the deformed beam). As the deflection amplitude of the girder increases, the track deformation, the fastener forces and the disengagement length of the track slabs are obviously nonlinear. When the vertical stiffness of the fastener and/or the elastic modulus of the mortar layer increase, the fastener force and the track plate disengagement length increase monotonically and nonlinearly, which will adversely affect the life and safety of the track structure.

Nonlinear behavior of disk spring with complex contact state

Disk springs are widely used as preload and isolation due to their unique mechanical properties. In the prior research, the effect of linear friction on the disk spring was considered, but contact stiffness, another nonlinear contact factor, is ignored. Accordingly, in this paper, the asymmetric displacements of the contact edges are first derived, and the accurate friction dissipations are obtained, as a way to evaluate the effect of friction on the system. Then the velocity of the edges was obtained to establish a dynamic friction model. Meanwhile, the contact displacement and contact stiffness of the edge are obtained by fractal contact theory. Then the nonlinear static and dynamic models of disk spring with friction and contact stiffness are established by the energy method. The load–deflection relationship, stiffness, and hysteresis of disk spring are studied with different contact states. The results show that the model considering contact stiffness and asymmetric friction dissipation can effectively evaluate the static properties of the disk spring. Friction reinforces the nonlinear behavior of the system, while contact stiffness weakens the nonlinearity of the system. And due to the influence of nonlinear contact factors, the transmissibility curves produce multiple resonance peaks.

High Precision Contact Model for Ball Bearings With Waviness

Studying high precision ball bearings requires the development of predictive models. In presence of waviness on the rings, geometrical and also mechanical parameters will vary according to the angular position. To consider these modifications, a nonlinear contact model is proposed with normal and tangential forces calculation using Hertz and Dahl’s models. To solve the static equilibrium of the bearing, a highly modular energy method is developed. It allows the determination of both local and global parameters using the same equation. The 2D developed approach can be used to study different waviness orders and magnitudes to get a better understanding on how this affects the bearing behavior (contact load, balls gaping, pointing defects...). The presented results show that even small contact direction reorientation can create tangential forces. This modifies the bearing deflections and induces a residual moment. These phenomena can only be observed when the contact is accurately modeled.

Dynamic modeling and simulation of a flexible-rotor ball bearing system

This work proposes a comprehensive numerical dynamic model of a flexible-rotor bearing system based on the Hertzian and cubic polynomial nonlinear contact force methods. The model can consider the influences of the nonlinear bearing contact forces and unbalanced force caused by the rotor offset. The displacements and spectrums of the flexible-rotor bearing system from the Hertzian and cubic polynomial nonlinear contact force methods are discussed. The influences of the radial clearance, eccentricity, mass, and deformation of the rotor on the frequency–amplitude characteristics of the flexible-rotor bearing system considering a large speed range are analyzed. The results show that the dynamic and vibration characteristics of the flexible-rotor bearing system from the Hertzian and cubic polynomial nonlinear contact force methods are different. The differences of the frequency–amplitude characteristics between the flexible- and rigid-rotor bearing system are small in a lower speed stage; however, their differences are very large in a higher speed stage. This method can be applied to the nonlinear dynamic modeling and simulation of the flexible-rotor bearing system, which can predict the dynamics and prevent the system failures during the design processing of rotor system.

Modeling and Simulation for Wear Prediction in Planar Mechanical Systems with Multiple Clearance Joints

The main goal of this work is to develop a comprehensive methodology for predicting wear in planar mechanical systems with multiple clearance joints and investigating the interaction between the joint clearance, driving condition and wear. In the process, an effective contact surface discretization method together with Lagrangian method are used to establish the dynamic equation of the multibody system. Considering the change of the contact surface, an improved nonlinear contact-force model suitable for the complicated contact conditions is utilized to evaluate the intrajoint forces, and the friction effects between the inter-connecting bodies are discussed using LuGre model. Next, the contact forces developed are integrated into the Archard model to compute the wear depth caused by the relative sliding and the geometry of the bearing is updated. Then, a crank slider mechanism with multiple clearance joints is employed to perform numerical simulations in order to demonstrate the efficiency of the dynamic procedures adopted throughout this work. The correctness of the proposed method is verified by comparing with other literature and simulation results. This study is helpful for predicting joint wear of mechanical systems with clearance and optimize the mechanism’s design.