/SLIPRING/SPRING

Block Format Keyword Define 1D slipring for seatbelt elements defined with /MAT/LAW114 and /PROP/TYPE23.

Format

(1)	(2)	(3)	(4)	(5)	(6)	(7)	(9)
/SLIPRING/SPRING/`slipring_ID`/`unit_ID`
`slipring_title`
`El_ID1`	`El_ID2`	`node_ID`₁	`node_ID`₂	`sens_ID`	`Fl_flag`	`A`	`Ed_factor`
`fct_ID`₁	`fct_ID`₂	`Fric_d`		`Xscale`₁		`Yscale`₂	`Xscale`₂
`fct_ID`₃	`fct_ID`₄	`Fric_s`		`Xscale`₃		`Yscale`₄	`Xscale`₄

Definition

Field	Contents	SI Unit Example
`slipring_ID`	Slipring identifier. (Integer, maximum 10 digits)
`unit_ID`	(Optional) Unit identifier. (Integer, maximum 10 digits)
`slipring_title`	Slipring title title. (Character, maximum 100 characters)
`El_ID1`	ID of first element in slipring. (Integer, maximum 10 digits)
`El_ID2`	ID of second element in slipring. (Integer, maximum 10 digits)
`node_ID`₁	ID of anchorage node. (Integer, maximum 10 digits)
`node_ID`₂	Optional ID of node for the orientation of the slipring. (Integer, maximum 10 digits)
`sens_ID`	Sensor identifier used for slipring locking. = 0 The slipring is unlocked. (Integer)
`Fl_flag`	Sliding direction control flag = 0 (Default) Slip in both directions. = 1 Slip from `El_ID1` to `El_ID2` only. = 2 Slip from `El_ID2` to `El_ID1` only. (Integer)
`A`	Coulomb friction scale factor. (Real)
`Ed_factor`	Exponential decay factor for Coulomb friction. (Real)	$[\frac{s}{m}]$
`fct_ID`₁	Function identifier defining dynamic Coulomb friction coefficient as a function of time. (Integer)
`fct_ID`₂	Function identifier defining dynamic Coulomb friction coefficient as a function of normal force. (Integer)
`Fric_d`	Dynamic Coulomb friction coefficient. If `fct_ID`₁ = 0: constant value (Default = 0). If `fct_ID`₁ > 0: ordinate scaling factor for function fct_ID₁ (Default = 1). (Real)
`Xscale`₁	Abcissa scaling factor for function `fct_ID`₁. Default = 1 (Real)
`Yscale`₂	Ordinate scaling factor for function `fct_ID`₂. Default = 1 (Real)
`Xscale`₂	Abcissa scaling factor for function `fct_ID`₂. Default = 1 (Real)
`fct_ID`₃	Function identifier defining static Coulomb friction coefficient as a function of time. (Integer)
`fct_ID`₄	Function identifier defining static Coulomb friction coefficient as a function of normal force. (Integer)	$[s]$
`Fric_s`	Static Coulomb friction coefficient. If `fct_ID`₃= 0: constant value (Default = 0). If `fct_ID`₃> 0: ordinate scaling factor for function `fct_ID`₂ (Default = 1). (Real)	$[N]$
`Xscale`₃	Abcissa scaling factor for function `fct_ID`₃. Default = 1 (Real)
`Yscale`₄	Ordinate scaling factor for function `fct_ID`₄. Default = 1 (Real)	$[s]$
`Xscale`₄	Abcissa scaling factor for function `fct_ID`₄. Default = 1 (Real)	$[N]$

Comments

The slipring is defined by the 2 spring seatbelt elements initially connected to the slipring, El_ID1, El_ID2 and the node node_ID₁ are used to define the position of the slipring. The common node between the 2 elements El_ID1 and EL_ID2 must be at the same coordinates as node_ID₁.
node_ID₁ and node_ID₂ must not be nodes of the seatbelt spring component.
By default, the rotation axis of the slipring is defined by $\vec{n_{d e f}}$ , the normal direction to the plane defined by the two connected elements.
Additionally, the rotation axis of the slipring can be defined by the direction of node_ID₁ and node_ID₂. the angle $γ$ between the direction of node_ID₁ and node_ID₂ and $\vec{n_{d e f}}$ is used to compute the friction.

Figure 1.
The Coulomb friction coefficient is computed with:(1)
$μ = (1 + A γ^{2}) (μ_{d y n} + (μ_{s t a t} - μ_{d y n}) e^{- E d_f a c t o r . | V_{r e l} |})$

Where,

$μ_{s t a t}$

Static friction coefficient

$μ_{d y n}$

Dynamic friction coefficient

$V_{r e l}$

Relative slip velocity

They are respectively computed with:(2)
$μ_{d y n} = F r i c_d . f c t_I D_{1} (\frac{t}{X s c a l e_{1}}) + Y s c a l e_{2} . f c t_I D_{2} (\frac{F n}{X s c a l e_{2}})$
(3)
$μ_{s t a t} = F r i c_s . f c t_I D_{3} (\frac{t}{X s c a l e_{3}}) + Y s c a l e_{4} . f c t_I D_{4} (\frac{F n}{X s c a l e_{4}})$
When the slipring is unlocked, sliding is activated if the difference of force after flow (marked with *) is lower than the difference of force obtained without flow, and material flow $δ L_{0}$ is computed accordingly:
$| F_{k}^{*} - F_{k - 1}^{*} | < | F_{k} - F_{k - 1} |$ with $\frac{F_{k}^{*}}{F_{k - 1}^{*}} = e^{μ θ . s i g n (F_{k}^{*} - F_{k - 1}^{*})}$

Figure 2.
The common node of the 2 strands of the slipring is kinematically attached to the anchorage node of the slipring node_ID₁. No other kinematic condition can be applied to any node of a seatbelt element which can enter the slipring.
When the length of one strand reaches zero, the slipring is updated. This strand reappears on the other side of the slipring and the previously connected strand on that side leaves the slipring. At the same time, a new spring enters the slipring replacing the one that has moved. The kinematic condition with the anchorage node is also switched to the new common node of the strands. The previous common node is released with an initial velocity computed from the material flow and direction of the released element, such that the two directions of the slipring $\vec{n_{1}}$ and $\vec{n_{2}}$ and the angle $θ$ are not modified by the update.(4)
$\vec{V_{i n i}} = \frac{δ L_{0}}{d t} \vec{n_{k}}$

Figure 3.
To ensure element and time step stability, maximum stiffness value is computed from $L_{\min}$ defined in seatbelt material (/MAT/LAW114) and spring element reference length $L_{0}$ .(5)
$K = \frac{k}{\max (L_{\min}, L_{0})}$
When a spring element is in the slipring, viscosity is deactivated.