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##

## PathSim example of slip-stick system (box on conveyor belt)

##

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# IMPORTS ===============================================================================

import numpy as np

import matplotlib.pyplot as plt

from pathsim import Simulation, Connection

from pathsim.blocks import (

Integrator,

Amplifier,

Function,

Source,

Switch,

Adder,

Scope

)

from pathsim.events import ZeroCrossing

from pathsim.solvers import RKBS32

# SYSTEM DEFINITION =====================================================================

#initial position and velocity

x0, v0 = 0, 0

#system parameters

m = 20.0 # mass

k = 70.0 # spring constant

d = 10.0 # spring damping

mu = 1.5 # friction coefficient

g = 9.81 # gravity

v = 2.0 # belt velocity magnitude

T = 50.0 # excitation period

F_c = mu * m * g # friction force

#function for belt velocity

def v_belt(t):

return v * np.sin(2*np.pi*t/T)

# return v * t / T

# return v * (1 - np.exp(-t/T))

#function for coulomb friction force

def f_coulomb(v, vb):

return F_c * np.sign(vb - v)

# system topology -----------------------------------------------------------------------

#blocks that define the system dynamics

Sr = Source(v_belt) # velocity of the belt

I1 = Integrator(v0) # integrator for velocity

I2 = Integrator(x0) # integrator for position

A1 = Amplifier(-d)

A2 = Amplifier(-k)

A3 = Amplifier(1/m)

Fc = Function(f_coulomb) # coulomb friction (kinetic)

P1 = Adder()

Sw = Switch(0) # selecting port '0' initially

#blocks for visualization

Sc1 = Scope(

labels=[

"belt velocity",

"box velocity",

"box position"

]

)

Sc2 = Scope(

labels=[

"box force",

"coulomb force"

]

)

blocks = [Sr, I1, I2, A1, A2, A3, Fc, P1, Sw, Sc1, Sc2]

#connections between the blocks

connections = [

Connection(I1, Sw[1], Fc[0]),

Connection(Sr, Sw[0], Fc[1], Sc1[0]),

Connection(Sw, I2, A1, Sc1[1]),

Connection(I2, A2, Sc1[2]),

Connection(A1, P1[0]),

Connection(A2, P1[1]),

Connection(Fc, P1[2], Sc2[1]),

Connection(P1, A3, Sc2[0]),

Connection(A3, I1)

]

# event management ----------------------------------------------------------------------

def slip_to_stick_evt(t):

_1, v_box , _2 = Sw()

_1, v_belt, _2 = Sr()

dv = v_box - v_belt

return dv

def slip_to_stick_act(t):

#change switch state

Sw.select(0)

I1.off()

Fc.off()

E_slip_to_stick.off()

E_stick_to_slip.on()

E_slip_to_stick = ZeroCrossing(

func_evt=slip_to_stick_evt,

func_act=slip_to_stick_act,

tolerance=1e-3

)

def stick_to_slip_evt(t):

_1, F, _2 = P1()

return F_c - abs(F)

def stick_to_slip_act(t):

#change switch state

Sw.select(1)

I1.on()

Fc.on()

#set integrator state

_1, v_box , _2 = Sw()

I1.engine.set(v_box)

E_slip_to_stick.on()

E_stick_to_slip.off()

E_stick_to_slip = ZeroCrossing(

func_evt=stick_to_slip_evt,

func_act=stick_to_slip_act,

tolerance=1e-3

)

events = [E_slip_to_stick, E_stick_to_slip]

# simulation setup ----------------------------------------------------------------------

#create a simulation instance from the blocks and connections

Sim = Simulation(

blocks,

connections,

events,

dt=0.01,

dt_max=0.1,

log=True,

Solver=RKBS32,

tolerance_lte_abs=1e-6,

tolerance_lte_rel=1e-4

)

# Run Example ===========================================================================

if __name__ == "__main__":

#run the simulation for some time

Sim.run(2*T)

# visualization ---------------------------------------------------------------------

#plot the results directly from the two scopes

fig, ax = Sc1.plot("-", lw=2)

for t in E_slip_to_stick:

ax.axvline( t , ls="--", c="k")

for t in E_stick_to_slip:

ax.axvline( t , ls=":", c="k")

Sc2.plot("-", lw=2)

plt.show()