Strömberg, N., "A Virtual Test Rig for Disc Brake Systems by Adopting a Thermo-Flexible Multi-Body Approach," SAE Technical Paper 2016-01-1932, 2016, doi:10.4271/2016-01-1932.
During several years a toolbox for performing virtual rig tests of disc brake systems has been developed by the author. A thermo-flexible multi-body model of a test rig is derived and implemented by coupling two types of models: a finite element model and a multi-body model. The finite element model is a thermo-mechanical model of the pad-disc system that is formulated including thermo-elasticity, frictional contact and wear. The energy balance of the contact interface is governed by contact conductance that depends linearly on the contact pressure and the frictional heat depends on a temperature dependent coefficient of friction. Instead of adopting a standard Lagrangian approach, the disc is formulated in an Eulerian frame like a fluid. This is then coupled to the pad most accurately by using Signorini’s contact conditions, Coulomb’s law of friction and Archard’s law of wear. The numerical treatment of these laws are performed by applying an augmented Lagrangian formulation, which in turn is solved with a non-smooth Newton method. The advantage with the Eulerian formulation is that the contact conditions don't have to be updated, which of course must be done when using a classical Lagrangian formulation. In such manner, a toolbox with extremely good performance is obtained. The disc-pad system is then coupled to a flexible multi-body model of the rig. In conclusion, these two model approaches constitute together a thermo-flexible multi-body model of a test rig for disc brake systems, which have been implemented as a Matlab toolbox using Intel Fortran on Windows. The toolbox has been used to study brake cycles for a real disc brake to a heavy truck. Results from that study is presented in the paper as well as the governing equations of the model.