7. E modeling#
7.1. Characteristics of modeling#
In this modeling, we use the operator DYNA_NON_LINE (see [U4.53.01]) with the relationship DIS_CONTACT. The integration diagram is NEWMARK.
This modeling corresponds to the direct transient response of the friction pad. It validates the orientation of the discrete as well as the initial interpenetration.
For the first case: The normal contact direction is the global axis \(X\) which corresponds in the test case to the global axis \(X\). The sliding plane is the local plane \((Y,Z)\), i.e. the plane \((Y,Z)\) in the global coordinate system. We therefore direct the shock element to a node, with the keyword ORIENTATION from the AFFE_CARA_ELEM operator in the following way:
ORIENTATION =_F (MAILLE =” EL1 “, CARA =” VECT_X_Y “,
VALE =( 1.0, 0.0, 0.0, 0.0, 0.0, 0.0 ), )) ,) **,
The tangential shock stiffness considered is \({K}_{T}=4\phantom{\rule{0ex}{0ex}}000000N/m\), the Coulomb coefficient is \(\mathrm{\mu }=\mathrm{0,1}\). The normal shock stiffness is \(20N/m\)
The law of shock behavior is therefore defined as follows in DEFI_MATERIAU:
MATCH1 = DEFI_MATERIAU (
DIS_CONTACT =_F (RIGI_NOR =20.0, RIGI_TAN =4000000.0, COULOMB =0.1), **
)
To be able to obtain a reaction force from the plane on the system, the system must be slightly pressed into the plane obstacle by a distance \(\delta n\) such as: \({F}_{n}={K}_{n}\cdot \delta n\).
The reaction balances the weight of the skate, so we have: \({F}_{n}=\mathrm{mg}\) i.e. \(\mathrm{\delta }n=\mathit{mg}/{K}_{n}\). The first loading steps achieve this sinking.
For the second case: The normal direction of contact is the local axis \(X\) which corresponds in the test case to the global axis \(Z\). The sliding plane is the local plane \((Y,Z)\), i.e. the plane \((X,Y)\) in the global coordinate system. We therefore direct the shock element to a node, with the keyword ORIENTATION from the AFFE_CARA_ELEM operator in the following way:
ORIENTATION =_F (MAILLE =” EL1 “, CARA =” VECT_X_Y “,
VALE =( 0.0, 0.0, 1.0, 1.0, 1.0, 0.0 ), )) ,) **,
To be able to obtain 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: \({F}_{n}={K}_{n}\cdot \mathrm{\delta }n\).
The reaction balances the weight of the skate, so we have: \({F}_{n}=\mathit{mg}\) i.e. \(\mathrm{\delta }n=\mathit{mg}/{K}_{n}\).
We considered a normal shock stiffness of \(20N/m\) so we have \(\delta n=\mathrm{0,5}\) from where \(\mathit{DIST}\underline{\phantom{\rule{2em}{0ex}}}1=0.5\).
MATCH2 = DEFI_MATERIAU (
DIS_CONTACT =_F (RIGI_NOR =20.0, RIGI_TAN =4000000.0,
COULOMB =0.10, DIST_1 =0.50),
)
7.2. Characteristics of the mesh#
Number of knots: 1
Number of meshes and types: 1 POI1
7.3. Tested sizes and results#
Values of the movements in the direction of the oscillator for the times when the sign of the speed changes and when the mass stops.
instant |
reference value |
Tolerance |
\(\mathrm{\pi }/100\) |
|
1.0e-04 |
\(2.0\mathrm{\pi }/100\) |
|
1.0e-04 |
\(3.0\mathrm{\pi }/100\) |
|
1.5e-04 |
\(4.0\mathrm{\pi }/100\) |
|
1.0e-03 |
Figure 7.3-a : Mass displacement.
Figure 7.3-b : Mass velocity.