4. B modeling#
4.1. Characteristics of modeling#
In this modeling, we use the operator DYNA_VIBRA (see [U4.53.03]) with the relationship DIS_CHOC. The integration diagram is DEVOGE.
In modeling B, we consider the skate and the plane as two mobile structures. Each structure is then modelled by a node and an element of type POI1. Node \(\mathrm{NO2}\) is supposed to be locked, it materializes the plane of friction. Relationship conditions between degrees of freedom are imposed on node \(\mathrm{NO1}\) (which models the skate) so that the movement is unidirectional in the \(\theta\) direction.
An obstacle of type BI_PLAN_Z (two moving parallel planes separated by a game) is used to simulate the sliding plane. We choose to use the Oy axis as the generator of this plane, i.e. NORM_OBST = (0., 1., 0.). By default, the origin of the obstacle is located halfway between nodes \(\mathrm{NO1}\) and \(\mathit{NO}2\). It remains to define the parameters DIST_1 and DIST_2 which represent the thickness of material around the shock nodes.
For there to be a reaction force from the plane on the system, the system must be slightly pressed into the plane obstacle by a distance \(\mathrm{\delta }n\) such as: \({F}_{n}={K}_{n}\cdot \mathrm{\delta }n\).
Like \({F}_{n}=\mathrm{mg}\), we then have \(\delta n=\mathrm{mg}/{K}_{n}\).
We considered a normal shock stiffness of \(20N/m\) (fictional stiffness that only makes sense to generate a reaction force from the plane on the system), so we have \(\mathrm{\delta }n=\mathrm{0,5}m\). Knowing that the two nodes \(\mathit{NO}1\) and \(\mathit{NO}2\) are geometrically confused, we choose for example:
DIST_1 = DIST_2 = \(\mathrm{\delta }n/2\).
Tangential shock stiffness: \({K}_{T}=400000N/m\): it is greater than the stiffness of the oscillator for the stopping phase to be modelled correctly.
No time used for time integration: \({5.10}^{-4}s\).
4.2. Characteristics of the mesh#
Number of knots: 2
Number of meshes and types: 2 POI1
4.3. Tested sizes and results#
Values of the displacements (in meters) in the direction of the oscillator for the times when the sign of the speed changed over the time period \((0;0.3s)\).
Identification |
moment (s) |
Reference |
\(\mathrm{DY}=\mathrm{r2}\mathrm{cos45}\) |
|
—4.596E—4 |
\(\mathrm{DY}=\mathrm{r3}\mathrm{cos45}\) |
|
3.182E—4 |
\(\mathrm{DY}=\mathrm{r4}\mathrm{cos45}\) |
|
—1.768E—4 |
\(\mathrm{DY}=\mathrm{r5}\mathrm{cos45}\) |
|
3.536E—5 |