Automotive disc brake squeal

https://escholarship.org/content/qt7hd8r1ft/qt7hd8r1ft.pdf

Advancing Cutting Technology

This paper presents a framework to investigate the dynamics of overall vehicle-track systems with emphasis on theoretical modelling, numerical simulation and experimental validation. A three-dimensional vehicle-track coupled dynamics model is developed in which a typical railway passenger vehicle is modelled as a 35-degree-of-freedom multi-body system. A traditional ballasted track is modelled as two parallel continuous beams supported by a discrete-elastic foundation of three layers with sleepers and ballasts included. The non-ballasted slab track is modelled as two parallel continuous beams supported by a series of elastic rectangle plates on a viscoelastic foundation. The vehicle subsystem and the track subsystem are coupled through a wheel-rail spatial coupling model that considers rail vibrations in vertical, lateral and torsional directions. Random track irregularities expressed by track spectra are considered as system excitations by means of a time-frequency transformation technique. A fast explicit integration method is applied to solve the large nonlinear equations of motion of the system in the time domain. A computer program named TTISIM is developed to predict the vertical and lateral dynamic responses of the vehicle-track coupled system. The theoretical model is validated by full-scale field experiments, including the speed-up test on the Beijing-Qinhuangdao line and the high-speed running test on the Qinhuangdao-Shenyang line. Differences in the dynamic responses analysed by the vehicle-track coupled dynamics and by the classical vehicle dynamics are ascertained in the case of vehicles passing through curved tracks.

https://www.tandfonline.com/doi/pdf/10.1080/00423110802621561

Fundamentals of vehicle–track coupled dynamics

Hilbert transform in vibration analysis

We give an overview of all codim 1 bifurcations in generic planar discontinuous piecewise smooth autonomous systems, here called Filippov systems. Bifurcations are defined using the classical approach of topological equivalence. This allows the development of a simple geometric criterion for classifying sliding bifurcations, i.e. bifurcations in which some sliding on the discontinuity boundary is critically involved. The full catalog of local and global bifurcations is given, together with explicit topological normal forms for the local ones. Moreover, for each bifurcation, a defining system is proposed that can be used to numerically compute the corresponding bifurcation curve with standard continuation techniques. A problem of exploitation of a predator–prey community is analyzed with the proposed methods.

https://www.staff.science.uu.nl/~kouzn101/MiniFilippov/Filippov2D.pdf

One-Parameter Bifurcations in Planar Filippov Systems

This article gives a historical overview of structural and mechanical systems with friction. Friction forces between sliding surfaces arise due to complex mechanisms and lead to mathematical models which are highly nonlinear, discontinuous and nonsmooth. Humankind has a long history of magnificent usage of friction in machines, buildings and transportation. Regardless, our state of knowledge of the friction-influenced dynamics occurring in such systems as well as in our daily lives was, until recently, rather primitive. To represent our understanding of friction in nonlinear dynamics, we first trace examples from the earliest prehistoric technologies and the formulation of dissipation laws in mechanics. The work culminates with examples of friction oscillators and stick-slip. This review article contains 304 references.

A Historical Review on Dry Friction and Stick-Slip Phenomena

On the modelling of friction oscillators

During the last years railway companies have observed increasing problems with track damage like rail corrugation, deterioration of ballast or unround wheels. Since the origin of these damages is suspected in the mid-frequency dynamics, research activities in the frequency range from 50 up to 500 Hz have been initiated. The article demonstrates that in comparison to the low and high frequency range the knowledge about physical effects in the mid-frequency range is poor. Apart from a historical literature review on vehicle and track modelling, recently published methods and models are collated and problems in their mathematical treatise are mentioned. Regarding the vehicle, the paper shows the development starting with Klingel's massless wheelset model and ending with sophisticated elastic multibody system models. Concerning the track, different mathematical approaches in frequency and time domain are compared. In the mid-frequency range the pad, ballast and subsoil properties play an important role. Hence...

Vehicle-Track Dynamics in the Mid-Frequency Range

In the present paper two types of nonsmooth oscillators are investigated: an impact oscillator and a self-sustained friction oscillator. Both are nonsmooth one degree of freedom oscillators with harmonic external excitation. Here the different types of motion, bifurcation diagrams and Poincare maps are determined from experiments. These results will be compared with numerical results on the basis of the identified impact and friction models. The nonsmooth third-order systems show rich bifurcational behaviour which is analysed by numerical simulations but also using mapping approaches. Two different formalisms for the calculation of the Lyapunov exponents are applied. The latter one requires special considerations in the given case of nonsmooth systems. Furthermore, the embedding dimension is gained applying the method of false nearest neighbours. In the case of coexisting solutions further analysis is done by means of bifurcation and stability analysis and the cell-mapping approach.

Dynamics of oscillators with impact and friction

Friction-induced self-sustained oscillations, also known as stick-slip vibrations, occur in mechanical systems as well as in everyday life. On the basis of a one-dimensional map, the bifurcation behaviour including unstable branches is investigated for a friction oscillator with simultaneous self-and external excitation. The chosen way of mapping also allows a simple determination of Lyapunov exponents.

Karl Popp

Papers

A Historical Review on Dry Friction and Stick-Slip Phenomena

On the modelling of friction oscillators

Vehicle-Track Dynamics in the Mid-Frequency Range

Dynamics of oscillators with impact and friction

Bifurcation and stability analysis for a non-smooth friction oscillator