In this paper a coupled thermo-flexible multi-body model of a test rig including
a brake disc with pads is proposed. The dynamics of the system is modeled by two
rotors connected via a torsional spring. The rotors represent the brake disc and the flywheel
of the rig. The brake moment acting on the disc is governed by thermo-mechanical
finite element analysis of the frictional contact between the pad and the disc. The finite
element model is formulated by treating the disc in an Eulerian framework. The frictional
power is calculated most accurately by solving Signorini’s contact conditions and
Coulomb’s law of friction by using the augmented Lagrangian approach. This is done
by including thermal expansion of the pad and the disc in the equilibrium equations and
using a temperature dependent friction coefficient. The heat due to the frictional power is
then transported with convection defined by the angular velocity of the disc. Distortions
in the solution due to the non-symmetry of the convection matrix is stabilized by using
the streamline-upwind approach. Summarized, the proposed virtual test rig of brake discs
is modeled by three system of equations, i.e. the dynamic equations of the multi-body
system, the energy balance of the pad and the disc, and the frictional contact of the pad
and the disc. In order to obtain a robust and efficient approach, these three equation
systems are solved sequentially by using Newmark’s method, the trapezoidal approach
and Newton’s method. In such manner, temperatures, brake power and angular velocities
can be generated accurately at low computational costs for different braking scenarios.
This is demonstrated for a real pad-disc system to a heavy truck
