Spring TYPE12 - Pulley (/PROP/SPR_PUL)

Spring TYPE12 is used to model a pulley. When used in a seat belt model, it is defined with three nodes.

Node 2 is located at the pulley, and a deformable rope is joining the three nodes (Figure 1). The spring mass is distributed on the three nodes with ¼ at node 1 and node 3 and ½ at node 2.

A Coulomb friction can be applied at node 2, taking into account the angle between the two strands. Without friction, forces are computed as:(1)

| F_{1} | = | F_{2} | = K δ

With,

$δ$: Total rope elongation
$K$: Stiffness

If the Coulomb friction is used, forces are computed as:(2)

F_{f r} = \min {| Δ F |, \max [0, (| F_{1} | + | F_{2} |) \cdot \tanh (\frac{β \cdot μ}{2})]} \cdot s i g (Δ F)

Where,

$μ = f_{f r} (\frac{Δ F}{X s c a l e_F}) \cdot Y s c a l e_F$
$β$: Angle (radians unit)
$f_{f r}$: Function of fct_ID_fr

I_fr =0 (symmetrical behavior)(3)
$Δ F = | F_{1} - F_{2} |$
I_fr =1 (non-symmetrical behavior)(4)
$Δ F = F_{1} - F_{2}$

δ_{1}

is the elongation of strand 1-2 and

δ_{2}

of strand 2-3.

Time step is computed with the same equation that for spring TYPE4, but the stiffness is replaced with twice the stiffness to ensure stability with high friction coefficients.

Note: The two strands have to be long enough to avoid node 1, or node 3 slides up to node 2. Nodes 1 and 3 will be stopped at node 2, if there is a knot at nodes 1 and 3.

For further information, refer to the Radioss Theory Manual.