6. D modeling#
6.1. 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.
This modeling corresponds to modeling B, in which the unidirectional friction option is activated. The skate and the plane are considered to be 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 \(\mathit{NO}1\) 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.
Unidirectional friction implies that the coefficient of friction is no longer isotropic in the plane defined above. It is equal to 0 along the axis specified in NORM_OBST and \(\mathrm{\mu }\) in the perpendicular direction. For an angle \(\theta\) of \(\mathrm{\pi }/2\), this corresponds to dividing the coefficient of friction by \(\sqrt{(2)}\), compared to the B model.
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 \({F}_{n}=\mathit{mg}\), we then have \(\mathrm{\delta }n=\mathit{mg}/{K}_{n}\).
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 combined, 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: \({5.10}^{-4}s\).
6.2. Characteristics of the mesh#
Number of knots: 2
Number of meshes and types: 2 POI1
6.3. Tested sizes and results#
Values of the movements in the direction of the oscillator for the approximate times of change in the sign of the speed over the time period \((0;0.2s)\).
Identification |
moment (s) |
Reference |
\(\mathit{DY}=r2\mathrm{cos}45\) |
|
—5,010E—04 |
\(\mathit{DY}=r3\mathrm{cos}45\) |
|
4,010E—04 |
\(\mathit{DY}=r4\mathrm{cos}45\) |
|
—3,010E—04 |
\(\mathit{DY}=r5\mathrm{cos}45\) |
|
2,010E—04 |