/PROP/TYPE12 (SPR_PUL)
Block Format Keyword The pulley spring property set (with one translational DOF) is used to model a pulley.
Format
(1)  (2)  (3)  (4)  (5)  (6)  (7)  (8)  (9)  (10) 

/PROP/TYPE12/prop_ID/unit_ID or /PROP/SPR_PUL/prop_ID/unit_ID  
prop_title  
Mass  sens_ID  I_{sflag}  I_{leng}  Fric  
K_{1}  C_{1}  A_{1}  B_{1}  D_{1}  
fct_ID_{11}  H_{1}  fct_ID_{21}  fct_ID_{31}  fct_ID_{41}  ${\delta}_{\mathrm{min}}^{1}$  ${\delta}_{\mathrm{max}}^{1}$  
F_{1}  E_{1}  Ascale_{1}  Hscale_{1}  
fct_ID_{fr}  I_{fr}  Yscale_F  Xscale_F  F_min  F_max 
Definitions
Field  Contents  SI Unit Example 

prop_ID  Property identifier (Integer, maximum 10 digits) 

unit_ID  Unit Identifier (Integer, maximum 10 digits) 

prop_title  Property title (Character, maximum 100 characters) 

Mass  Mass.
(Real) 
$\left[\text{kg}\right]$ or $\left[\mathrm{kg}\cdot m\right]$ 
sens_ID  Sensor
identifier. (Integer) 

I_{sflag}  Sensor flag. 4
5
(Integer) 

I_{leng}  Input per unit length flag.
(Integer) 

Fric  Coulomb friction. 6 (Real) 

K_{1}  Stiffness
$K$
with I_{leng}= 0.
(Real) 
$\left[\frac{\text{N}}{\text{s}}\right]$ 
Stiffness
$\frac{K}{{l}_{0}}$
with I_{leng}= 1.
(Real) 
$\left[\frac{N}{\mathrm{m}\cdot s}\right]$  
C_{1}  Damping
$C$
with I_{leng}= 0. (Real) 
$\left[\frac{\text{Ns}}{\text{m}}\right]$ 
Damping
$\frac{C}{{l}_{0}}$
with I_{leng}= 1. (Real) 
$\left[Ns\right]$  
A_{1}  Coefficient for strain rate effect in
tension (homogeneous to a force). Default = 1.0 (Real) 
$\left[\text{N}\right]$ 
B_{1}  Logarithmic coefficient for strain rate
effect in tension (homogeneous to a force). (Real) 
$\left[\text{N}\right]$ 
D_{1}  Scale coefficients for elongation
velocity. Default = 1.0 (Real) 
$\left[\frac{\text{m}}{\text{s}}\right]$ 
fct_ID_{11}  Stiffness function identifier defining
$\mathrm{f}\left(\delta \right)$
with I_{leng}= 0 or
$\mathrm{f}\left(\epsilon \right)$
with I_{leng}= 1.
(Integer) 

H_{1}  Hardening flag for nonlinear spring.
(Integer) 

fct_ID_{21}  Function defining the change in force
with spring displacement (or rotation) rate in
$\mathrm{g}\left(\dot{\delta}\right)$
with I_{leng}= 0 or
$\mathrm{g}\left(\dot{\epsilon}\right)$
with I_{leng}=1. (Integer) 

fct_ID_{31}  Function used only for unloading. If H_{1}=4: Function identifier defining lower yield curve. If H_{1}=5: Function identifier defining residual displacement versus maximum displacement. If H_{1}=6: Function identifier defining nonlinear unloading curve. If H_{1}=7: Function identifier defining nonlinear unloading curve. (Integer) 

fct_ID_{41}  Function to consider velocity or
deformation velocity dependency damping in
$\mathrm{h}\left(\dot{\delta}\right)$
with I_{leng}= 0 or $\mathrm{h}\left(\dot{\epsilon}\right)$
with I_{leng}=1. (Integer) 

${\delta}_{\mathrm{min}}^{1}$  Negative failure displacement (if I_{leng}=0), or Negative failure displacement multiply ${l}_{0}$ if I_{leng}=1). Default = 10^{30} (Real) 
$\left[\text{m}\right]$ 
${\delta}_{\mathrm{max}}^{1}$  Positive failure displacement (if I_{leng}=0), or Positive failure displacement multiply ${l}_{0}$ if I_{leng}=1). Default = 10^{30} (Real) 
$\left[\text{m}\right]$ 
F_{1}  Scale factor for
$\delta $
or
$\dot{\epsilon}$
(abscissa of fct_ID_{21} function
for
$\mathrm{g}\left(\dot{\delta}\right)$
or
$\mathrm{g}\left(\dot{\epsilon}\right)$
). (Real) 
$\left[\frac{\text{m}}{\text{s}}\right]$ 
E_{1}  Scale factor for
$\mathrm{g}\left(\dot{\delta}\right)$
or
$\mathrm{g}\left(\dot{\epsilon}\right)$
(fct_ID_{21} function) which is coefficient for strain
rate effect (homogeneous to a force). (Real) 
$\left[\text{N}\right]$ 
Ascale_{1}  Scale factor for
$\delta $
or
$\text{\epsilon}$
(abscissa of fct_ID_{11} function
for
$\mathrm{f}\left(\delta \right)$
or
$\mathrm{f}\left(\epsilon \right)$
). (Real) 
$\left[\text{m}\right]$ 
Hscale_{1}  Scale factor for
$\mathrm{h}\left(\dot{\delta}\right)$
or
$\mathrm{h}\left(\dot{\epsilon}\right)$
(fct_ID_{41} function) homogeneous to a
force. Default = 1.0 (Real) 

fct_ID_{fr}  Function identifier defining scaling of
friction coefficient Fric as function of force difference
between left and right arms of the pulley. (Integer) 

I_{fr}  Friction model flag. 6
(Integer) 

Yscale_F  Ordinate scale for function
fct_ID_{fr}. Default = 1.0 (Real) 

Xscale_F  Abscissa scale for function
fct_ID_{fr}. Default = 0.0 (Real) 
$\left[\text{N}\right]$ 
F_min  Negative limit force for nonreversible
friction model. Used only for I_{fr} = 1. 6 Default = 10^{30} (Real) 
$\left[\text{N}\right]$ 
F_max  Positive limit force for nonreversible
friction model. Used only for I_{fr} = 1. 6 Default = 10^{30} (Real) 
$\left[\text{N}\right]$ 
Example
/UNIT/2
unit for prop
Mg mm s
#12345678910
/PROP/SPR_PUL/1/2
pulley spring example with friction
# Mass sensor_ID Isflag Ileng Fric
2.7e5 0 0 0 1
# K C A B D
10000 .001 0 0 0
#funct_ID1 H funct_ID2 funct_ID3 funct_ID4 delta_min delta_max
1 0 0 0 0 0 0
# Fscale1 E Ascalex H4
0 0 0 0
# Fct_IDfr Ifr Yscale_F Xscale_F F_MIN F_MAX
2 1 0 0 800 4500
#12345678910
/FUNCT/1
nonlinear elastic
# Disp. Force
# X Y
1 0.1
0 0
1 10000
#12345678910
/FUNCT/2
friction function
# Force Fric
# X Y
1000 0.2
1000 0.2
2000 0.3
4000 0.9
5000 1.0
10000 1.0
#12345678910
#ENDDATA
Comments
 This property is modeled using
a 3 node /SPRING element where node 1 and node 3 are the ends of the
rope and node 2 is the pully location.
Once node 1 slides to node 2 locking occurs as if there is a knot at node 1 that cannot move through the pully.
 Force computation:
 In case of I_{leng} =0 (flag I_{leng} is defined in Line 3), the force
in the spring is computed as:
(1) $$F=\mathrm{f}\left(\frac{{\delta}^{1}}{Ascal{e}_{1}}\right)\left[{A}_{1}+{B}_{1}\mathrm{ln}\left(\mathrm{max}\left(1,\left\frac{{\dot{\delta}}^{1}}{{D}_{1}}\right\right)\right)+{E}_{1}\mathrm{g}\left(\frac{{\dot{\delta}}^{1}}{{F}_{1}}\right)\right]+{C}_{1}{\dot{\delta}}^{1}+Hscal{e}_{1}\mathrm{h}\left(\frac{{\dot{\delta}}^{1}}{{F}_{1}}\right)$$With ${l}_{0}<{\delta}^{1}<+\infty $
Where, $\delta =l{l}_{0}$ is the difference between the current length and the initial length of the spring element.
 If I_{leng}=1, all input are per unit length.
Spring mass = $M\cdot {l}_{0}$
Spring stiffness = $\frac{K}{{l}_{0}}$
Spring damping = $\frac{C}{{l}_{0}}$
Spring inertia = $I\cdot {l}_{0}$
Where, ${l}_{0}$ is the spring reference length.
 The value of force in the spring is computed as:
(2) $$F=\mathrm{f}\left(\frac{\epsilon}{Ascal{e}_{1}}\right)\left[{A}_{1}+{B}_{1}\mathrm{ln}\left(\mathrm{max}\left(1,\left\frac{\dot{\epsilon}}{{D}_{1}}\right\right)\right)+{E}_{1}\mathrm{g}\left(\frac{\dot{\epsilon}}{{F}_{1}}\right)\right]+{C}_{1}\dot{\epsilon}+Hscal{e}_{1}\mathrm{h}\left(\frac{\dot{\epsilon}}{{F}_{1}}\right)$$Where, $\text{\epsilon}$ is the engineering strain:(3) $$\epsilon =\frac{\delta}{{l}_{0}}$$Force functions are given versus engineering strain and engineering strain rate.
Failure criteria are defined with respect to strain. Input of negative/positive failure limit should be related to initial length ${l}_{0}$
 In case of I_{leng} =0 (flag I_{leng} is defined in Line 3), the force
in the spring is computed as:
 If ${\delta}_{\mathrm{min}}^{1}$ (resp ${\delta}_{\mathrm{max}}^{1}$ ) is 0, no failure in the direction. The ${\delta}_{\mathrm{min}}^{1}$ must be negative. For linear springs, $\mathrm{f}\left(\delta \right)$ and $\mathrm{g}\left(\dot{\delta}\right)$ are null functions and A_{1}, B_{1} and E_{1} are not taken into account.
 Spring is activated and/or
deactivated by sensor:
 If sens_ID ≠ 0 and I_{sflag} = 0, the spring element is activated by the sens_ID.
 If sens_ID ≠ 0 and I_{sflag} = 1, the spring element is deactivated by the sens_ID.
 If sens_ID
$\ne $
0 and I_{sflag} = 2, then:
 The spring is activated and/or, deactivated by sens_ID. (if sensor is ON, spring is ON; if sensor is OFF, spring is OFF).
 The spring reference length ( ${l}_{0}$ ) is the distance between spring node N1 and N2 at the time of the sensor's activation.
 If a sensor is used for activating or deactivating a spring, the reference length of the spring at sensor activation (or deactivation) is equal to the nodal distance at time =0; except if sensor flag is equal to 2.
 Friction models definition:
 If fct_ID_{fr} and Fric = 0 (no friction), then $\left{F}_{1}\right=\left{F}_{2}\right$ .
 If fct_ID_{fr} = 0 and Fric > 0, then constant Coulomb friction coefficient used: $\mu =Fric=\mathrm{const}.$
 If fct_ID_{fr} > 0, then variable
friction is calculated as a function on relative force between two pulley
branches:
I_{fr} = 0 (symmetrical behavior), $\text{\Delta}F=\left{F}_{1}{F}_{2}\right$
I_{fr} = 1 (nonsymmetrical behavior), $\text{\Delta}F={F}_{1}{F}_{2}$
Friction force ${F}_{fr}$ is computed as:(4) $${F}_{fr}=\mathrm{min}\left\{\left\text{\Delta}F\right,\mathrm{max}\left[0,\left({F}_{1}+{F}_{2}\right)\cdot \mathrm{tanh}\left(\frac{\beta \cdot \mu}{2}\right)\right]\right\}\cdot sig\left(\text{\Delta}F\right)$$Where,(5) $$\mu ={\text{f}}_{fr}\left(\frac{\text{\Delta}F}{Xscale\_F}\right)\cdot Yscale\_F$$ $\beta $
 Angle (radians unit)
 ${f}_{fr}$
 Function of fct_ID_{fr}
 If I_{fr} = 1 (nonsymmetrical
behavior) and when F_min (or F_max) is reached,
friction is switching permanently from the function definition to the constant value
Fric.
Otherwise, the friction value is defined according to the input function fct_ID_{fr}.