A Hybrid Model for Predicting Steering Brake Squeal Based on Multibody Dynamics and Finite Element Methods

In recent years, the problem of automotive brake squeal during steering braking has attracted attention. Under the conditions of squealing, the loading of sprung mass is transferred, and lateral force is generated on the tire, resulting in stress and deformation of the suspension system. To predict the steering brake squeal propensity and explore its mechanism, we established a hybrid model of multibody dynamics and finite element methods to transfer the displacement values of each suspension connection point between two models. We successfully predicted the occurrence of steering brake squeal using the complex eigenvalue analysis method. Thereafter, we analyzed the interface pressure distribution between the pads and disc, and the results showed that the distribution grew uneven with an increase in the steering wheel angle. In addition, changes in the contact and restraint conditions between the pads and disc are the key mechanisms for steering brake squeal.

THEORETICAL COMPLEX ENERGIES OF STARK RESONANCES IN LITHIUM BY OPERATOR PERTURBATION THEORY APPROACH

The theoretical complex energies of the Stark resonances in the lithium atom (non-hydrogenic atomic system) in a DC electric are calculated within the operator form of the modified perturbation theory for the non-H atomic systems. The method includes the physically reasonable distorted-waves approximation in the frame of the formally exact quantum-mechanical procedure. The calculated Stark resonances energies and widths in the lithium atom are calculated and compared with results of calculations on the basis of the method of complex eigenvalue Schrödinger equation by Themelis-Nicolaides, the complex absorbing potential method by Sahoo-Ho and the B-spline-based coordinate rotation method approach by Hui-Yan Meng et al.

Parametric Study of Track Support Structure to Minimize the Occurrence Possibility of Rail Corrugation

Changing the track support structure is an effective method to suppress or eliminate rail corrugation in practical engineering. Rail corrugation on small-radius curves with booted short sleepers is the main research object in the present paper. A relevant finite element model of the wheelset-track system supported by booted short sleepers is built combined with the dynamic analysis of the vehicle-track system. The effects of various parameters of booted short sleeper structure on the wheel–rail friction-induced vibration are investigated by complex eigenvalue analysis. Considering the interaction of multiple parameters in the booted short sleeper structure, the multi-parameter fitting equation forecasting the possibility of rail corrugation is obtained using the least squares algorithm. Results show that wheel–rail friction-induced oscillation is a contributing factor in the formation of rail corrugation. Controlling wheel–rail friction-induced oscillation with a frequency of about 300 Hz is beneficial to suppress the possibility of rail corrugation in sections with booted short sleepers. Lower fastener stiffness or greater vertical fastener damping make it less likely that rail corrugation will occur. Rail corrugation is not generated when the vertical stiffness of the fastener is controlled below 20 MN/m in the booted short sleeper.

On the Stability of Convection in a Non-Newtonian Vertical Fluid Layer in the Presence of Gold Nanoparticles: Drug Agent for Thermotherapy

We consider the effect of gold nanoparticles on the stability properties of convection in a vertical fluid layer saturated by a Jeffreys fluid. The vertical boundaries are rigid and hold at uniform but different temperatures. Brownian diffusion and thermophoresis effects are considered. Due to numerous applications in the biomedical industry, such a study is essential. The linear stability is investigated through the normal mode disturbances. The resulting stability problem is an eighth-order ordinary differential complex eigenvalue problem that is solved numerically using the Chebyshev collection method. Its solution provides the neutral stability curves, defining the threshold of linear instability, and the critical parameters at the onset of instability are determined for various values of control parameters. The results for Newtonian fluid and second-grade fluid are delineated as particular cases from the present study. It is shown that the Newtonian fluid has a more stabilizing effect than the second-grade and the Jeffreys fluids in the presence of gold nanoparticles and, Jeffreys fluid is the least stable.

Transverse Vibration Analysis of Axially Moving Trapezoidal Plates

Transverse vibration of axially moving trapezoidal plates is investigated. The differential equation of transverse vibration for a axially moving trapezoidal plate is established by D'Alembert principle. The original trapezoid region can be replaced by regular square region by the medium parameter method for the convenience of calculation. A generalized complex eigenvalue equation is derived by a discrete method (the differential quadrature method). The complex frequency curve of trapezoidal plate is obtained by calculating the eigenvalue equation. The change of the complex frequencies of the axially moving trapezoidal plates with the dimensionless axially moving speed is analyzed. The effects of the aspect ratio and the trapezoidal angle on instability type of the trapezoidal plate are discussed under different boundary conditions. The results of numerical analysis show that there are two main instability types of axially moving trapezoidal plate: divergence and flutter. The modal orders of the two types of instability are also different, which is related to the trapezoidal angle, aspect ratio and boundary condition of the trapezoidal plate.

Complex Eigenvalue Splitting for the Dirac Operator

We analyze the eigenvalue problem for the semiclassical Dirac (or Zakharov–Shabat) operator on the real line with general analytic potential. We provide Bohr–Sommerfeld quantization conditions near energy levels where the potential exhibits the characteristics of a single or double bump function. From these conditions we infer that near energy levels where the potential (or rather its square) looks like a single bump function, all eigenvalues are purely imaginary. For even or odd potentials we infer that near energy levels where the square of the potential looks like a double bump function, eigenvalues split in pairs exponentially close to reference points on the imaginary axis. For even potentials this splitting is vertical and for odd potentials it is horizontal, meaning that all such eigenvalues are purely imaginary when the potential is even, and no such eigenvalue is purely imaginary when the potential is odd.

Influence of Material-Dependent Damping on Brake Squeal in the Specific Disc Brake System

The connection of two phenomena - non-conservative friction forces and dissipation-induced instability can lead to many interesting engineering problems. The paper studies general material-dependent damping influence on dynamical instability of disc brake systems leading to brake squeal. The effect of general damping is demonstrated on a minimal and complex model of a disc brake. A complex system including material-dependent damping is defined in the commercial finite element software. The finite element model validated by experimental data on the brake-disc test bench is used to compute the influence of a pad and a disc damping variations on system stability by complex eigenvalue analysis. Analyzes show a significant sensitivity of the experimentally verified unstable mode of the system to the ratio of the damping between the disc and the friction material components.

Analysis of influence factors of rail corrugation in small radius curve track

In order to effectively prevent and control the generation and development of rail corrugation, according to the actual line condition of the small radius curve section, the vehicle (with flexible wheel sets)–track space coupled model was established by using the multi-body dynamic software UM (Universal Mechanism), which could consider the coupled relationship in three directions of space, and the dynamic analysis for the corrugation section was carried out by using the model. Then, based on the theory of friction self-excited vibration, the three-dimensional model of a wheel–rail system was established by using the finite-element software ABAQUS, and the complex eigenvalue analysis of influence factors of rail corrugation was conducted based on wheel–rail contact parameters obtained by dynamic calculation. Through the stability analysis of the wheel–rail system with different fastener vertical and lateral stiffnesses, friction coefficients, and superelevation states, we find that properly increasing the fastener vertical and lateral stiffnesses, controlling the wheel–rail friction coefficient below 0.4, and keeping the balanced superelevation state of the track structure can effectively reduce the occurrence possibility of unstable vibration of the wheel–rail system, thus inhibiting the generation and development of rail corrugation. The excess superelevation state of the track structure results in the unstable friction self-excited vibration of the wheel–rail system at the inner wheel–inner rail, while the deficient superelevation state results in the unstable friction self-excited vibration of the wheel–rail system at the outer wheel–outer rail, which shows that the superelevation state of the track structure directly affects the formation of rail corrugation and determines the development order of corrugation of inner and outer rails. This conclusion can well explain the cause of corrugation appearing on only one side rail.