def __init__(self, length, radius, mass, endmass):
self.length = length
self.radius = radius
self.mass = mass
self.endmass = endmass
Jz = radius**2 / 2
Jxy = (3 * radius**2 + length**2) / 12
inertia = mass * np.diag([Jxy, Jxy, Jz])
self.A = mass * Jxy + endmass * (length / 2)**2
self.C = mass * Jz
self.pivot = Hinge('pivot', [0, 1, 0])
self.axis = Hinge('axis', [0, 0, 1])
self.body = RigidBody('body', mass, inertia)
self.offset = RigidConnection('offset', [0, 0, length / 2])
self.endbody = RigidBody('end', endmass)
self.pivot.add_leaf(self.axis)
self.axis.add_leaf(self.body)
self.pivot.add_leaf(self.offset)
self.offset.add_leaf(self.endbody)
self.system = System(self.pivot)
# Prescribed DOF accelerations
self.system.prescribe(self.axis, acc=0.0) # constant rotational speed
def __init__(self, length, radius, mass, spin):
self.length = length
self.radius = radius
self.mass = mass
self.spin = spin
x = np.linspace(0, length)
modes = linearisation.ModalRepresentation(
x=x,
shapes=np.zeros((len(x), 3, 0)),
rotations=np.zeros((len(x), 3, 0)),
density=np.ones_like(x) * mass / length,
mass_axis=np.zeros((len(x), 2)),
section_inertia=np.ones_like(x) * radius**2 / 4,
freqs=np.zeros((0, )),
)
self.bearing = Hinge('bearing', [0, 0, 1])
self.pivot = Hinge('pivot', [0, 1, 0])
self.axis = Hinge('axis', [1, 0, 0])
self.body = ModalElement('body', modes)
self.bearing.add_leaf(self.pivot)
self.pivot.add_leaf(self.axis)
self.axis.add_leaf(self.body)
self.system = System(self.bearing)
# Prescribed DOF accelerations
self.system.prescribe(self.axis.istrain,
0.0) # constant rotational speed
class BeamGyroscope(Gyroscope):
def __init__(self, length, radius, mass, spin, endmass):
self.length = length
self.radius = radius
self.mass = mass
self.spin = spin
self.endmass = endmass
Jx = mass * radius**2 / 2
self.bearing = Hinge('bearing', [0,0,1])
self.pivot = Hinge('pivot', [0,1,0])
self.offset = RigidConnection('offset', [-length/2,0,0])
self.axis = Hinge('axis', [1,0,0])
self.body = UniformBeam('body', length, mass/length,
1, 1, 1, Jx=Jx/2) # /2 because added to both ends
self.endbody = RigidBody('end', endmass)
self.bearing.add_leaf(self.pivot)
self.pivot.add_leaf(self.offset)
self.offset.add_leaf(self.axis)
self.axis.add_leaf(self.body)
self.offset.add_leaf(self.endbody)
self.system = System(self.bearing)
# Prescribed DOF accelerations
self.system.prescribe(self.axis, acc=0.0) # constant rotational speed
self.system.prescribe(self.body, acc=0.0) # rigid beam
def __init__(self, length, radius, mass, endmass):
self.length = length
self.radius = radius
self.mass = mass
self.endmass = endmass
Jx = mass * radius**2 / 2
Jyz = mass * (3 * radius**2 + length**2) / 12
self.A = Jyz + endmass * (length / 2)**2
self.C = Jx
self.pivot = Hinge('pivot', [0, 1, 0])
self.offset = RigidConnection('offset', [0, 0, -length / 2])
self.axis = Hinge('axis', [0, 0, 1], rotmat_y(-np.pi / 2))
self.body = UniformBeam('body',
length,
mass / length,
1,
1,
1,
Jx=Jx / 2) # /2 because added to both ends
self.endoffset = RigidConnection('endoffset', [0, 0, length / 2])
self.endbody = RigidBody('end', endmass)
self.pivot.add_leaf(self.offset)
self.offset.add_leaf(self.axis)
self.axis.add_leaf(self.body)
self.pivot.add_leaf(self.endoffset)
self.endoffset.add_leaf(self.endbody)
self.system = System(self.pivot)
# Prescribed DOF accelerations
self.system.prescribe(self.axis, acc=0.0) # constant rotational speed
self.system.prescribe(self.body, acc=0.0) # rigid beam
def __init__(self, length, radius, mass, spin):
self.length = length
self.radius = radius
self.mass = mass
self.spin = spin
Jx = mass * radius**2 / 2
self.bearing = Hinge('bearing', [0, 0, 1])
self.pivot = Hinge('pivot', [0, 1, 0])
self.axis = Hinge('axis', [1, 0, 0])
self.body = UniformBeam('body',
length,
mass / length,
1,
1,
1,
Jx=Jx / 2) # /2 because added to both ends
self.bearing.add_leaf(self.pivot)
self.pivot.add_leaf(self.axis)
self.axis.add_leaf(self.body)
self.system = System(self.bearing)
# Prescribed DOF accelerations
self.system.prescribe(self.axis.istrain,
0.0) # constant rotational speed
self.system.prescribe(self.body.istrain, 0.0) # rigid beam
class BeamGyroscope(Gyroscope):
def __init__(self, length, radius, mass, endmass):
self.length = length
self.radius = radius
self.mass = mass
self.endmass = endmass
Jx = mass * radius**2 / 2
Jyz = mass*(3*radius**2 + length**2) / 12
self.A = Jyz + endmass*(length/2)**2
self.C = Jx
self.pivot = Hinge('pivot', [0,1,0])
self.offset = RigidConnection('offset', [0,0,-length/2])
self.axis = Hinge('axis', [0,0,1], rotmat_y(-np.pi/2))
self.body = UniformBeam('body', length, mass/length,
1, 1, 1, Jx=Jx/2) # /2 because added to both ends
self.endoffset = RigidConnection('endoffset', [0,0,length/2])
self.endbody = RigidBody('end', endmass)
self.pivot.add_leaf(self.offset)
self.offset.add_leaf(self.axis)
self.axis.add_leaf(self.body)
self.pivot.add_leaf(self.endoffset)
self.endoffset.add_leaf(self.endbody)
self.system = System(self.pivot)
# Prescribed DOF accelerations
self.system.prescribe(self.axis, acc=0.0) # constant rotational speed
self.system.prescribe(self.body, acc=0.0) # rigid beam
def __init__(self, length, radius, mass, spin, endmass):
self.length = length
self.radius = radius
self.mass = mass
self.spin = spin
self.endmass = endmass
x = np.linspace(-length / 2, length / 2)
modes = linearisation.ModalRepresentation(
x=x,
shapes=np.zeros((len(x), 3, 0)),
rotations=np.zeros((len(x), 3, 0)),
density=np.ones_like(x) * mass / length,
mass_axis=np.zeros((len(x), 2)),
section_inertia=np.ones_like(x) * radius**2 / 4,
freqs=np.zeros((0, )),
)
self.bearing = Hinge('bearing', [0, 0, 1])
self.pivot = Hinge('pivot', [0, 1, 0])
self.axis = Hinge('axis', [0, 0, 1], rotmat_y(-np.pi / 2))
self.body = ModalElement('body', modes)
self.offset = RigidConnection('offset', [0, 0, length / 2])
self.endbody = RigidBody('end', endmass)
self.bearing.add_leaf(self.pivot)
self.pivot.add_leaf(self.axis)
self.axis.add_leaf(self.body)
self.pivot.add_leaf(self.offset)
self.offset.add_leaf(self.endbody)
self.system = System(self.bearing)
# Prescribed DOF accelerations
self.system.prescribe(self.axis, acc=0.0) # constant rotational speed
def __init__(self, length, radius, mass, spin, endmass):
self.length = length
self.radius = radius
self.mass = mass
self.spin = spin
self.endmass = endmass
Jx = mass * radius**2 / 2
self.bearing = Hinge('bearing', [0, 0, 1])
self.pivot = Hinge('pivot', [0, 1, 0])
self.offset = RigidConnection('offset', [-length / 2, 0, 0])
self.axis = Hinge('axis', [1, 0, 0])
self.body = UniformBeam('body',
length,
mass / length,
1,
1,
1,
Jx=Jx / 2) # /2 because added to both ends
self.endbody = RigidBody('end', endmass)
self.bearing.add_leaf(self.pivot)
self.pivot.add_leaf(self.offset)
self.offset.add_leaf(self.axis)
self.axis.add_leaf(self.body)
self.offset.add_leaf(self.endbody)
self.system = System(self.bearing)
# Prescribed DOF accelerations
self.system.prescribe(self.axis, acc=0.0) # constant rotational speed
self.system.prescribe(self.body, acc=0.0) # rigid beam
class ModalGyroscope(Gyroscope):
def __init__(self, length, radius, mass, spin):
self.length = length
self.radius = radius
self.mass = mass
self.spin = spin
x = np.linspace(0, length)
modes = linearisation.ModalRepresentation(
x =x,
shapes =np.zeros((len(x),3,0)),
rotations =np.zeros((len(x),3,0)),
density =np.ones_like(x) * mass/length,
mass_axis =np.zeros((len(x),2)),
section_inertia=np.ones_like(x) * radius**2 / 4,
freqs =np.zeros((0,)),
)
self.bearing = Hinge('bearing', [0,0,1])
self.pivot = Hinge('pivot', [0,1,0])
self.axis = Hinge('axis', [1,0,0])
self.body = ModalElement('body', modes)
self.bearing.add_leaf(self.pivot)
self.pivot.add_leaf(self.axis)
self.axis.add_leaf(self.body)
self.system = System(self.bearing)
# Prescribed DOF accelerations
self.system.prescribe(self.axis, acc=0.0) # constant rotational speed
class Gyroscope(object):
def __init__(self, length, radius, mass, spin, endmass):
self.length = length
self.radius = radius
self.mass = mass
self.spin = spin
self.endmass = endmass
Jz = radius**2 / 2
Jxy = (3*radius**2 + length**2) / 12
inertia = mass * np.diag([Jxy, Jxy, Jz])
self.bearing = Hinge('bearing', [0,0,1])
self.pivot = Hinge('pivot', [0,1,0])
self.axis = Hinge('axis', [0,0,1])
self.body = RigidBody('body', mass, inertia)
self.offset = RigidConnection('offset', [0,0,length/2])
self.endbody = RigidBody('end', endmass)
self.bearing.add_leaf(self.pivot)
self.pivot.add_leaf(self.axis)
self.axis.add_leaf(self.body)
self.pivot.add_leaf(self.offset)
self.offset.add_leaf(self.endbody)
self.system = System(self.bearing)
# Prescribed DOF accelerations
self.system.prescribe(self.axis, acc=0.0) # constant rotational speed
def simulate(self, xpivot=0.0, vprec=0.0, t1=10, dt=0.05):
# reset
self.system.q [:] = 0.0
self.system.qd[:] = 0.0
# initial conditions
self.system.q [self.pivot.istrain][0] = xpivot # initial elevation
self.system.qd[self.bearing.istrain][0] = vprec # initial azimuth spd
self.system.qd[self.axis.istrain][0] = self.spin # initial rotation speed
self.integ = Integrator(self.system, ('pos','vel'))
self.integ.add_output(dynamics.LoadOutput(self.axis.iprox))
self.integ.add_output(dynamics.LoadOutput(self.pivot.iprox))
self.integ.add_output(dynamics.LoadOutput(self.bearing.iprox))
#integ.add_output(dynamics.CustomOutput(
# lambda s: np.dot(self.axis.mass_vv, self.system.qdd[el.iprox+el.idist]) + \
# np.dot(el.mass_ve, self.system.qdd[el.istrain])))
# simulate
if t1 > 0:
self.t, self.y = self.integ.integrate(t1, dt)
for i,lab in enumerate(self.integ.labels()):
print "%2d %s" % (i,lab)
return self.t, self.y
def ani(self, vs=1):
l = self.length * 1.1
return dynvis.anim(self.system, self.t, self.y,
(0,vs), (-l,l), (-l,l), velocities=False)
class Gyroscope(object):
def __init__(self, length, radius, mass, spin):
self.length = length
self.radius = radius
self.mass = mass
self.spin = spin
Jx = radius**2 / 2
Jyz = (3 * radius**2 + length**2) / 12
Jyz_0 = Jyz + (length / 2)**2 # parallel axis theorem
inertia = mass * np.diag([Jx, Jyz_0, Jyz_0])
self.bearing = Hinge('bearing', [0, 0, 1])
self.pivot = Hinge('pivot', [0, 1, 0])
self.axis = Hinge('axis', [1, 0, 0])
self.body = RigidBody('body', mass, inertia, [length / 2, 0, 0])
self.bearing.add_leaf(self.pivot)
self.pivot.add_leaf(self.axis)
self.axis.add_leaf(self.body)
self.system = System(self.bearing)
# Prescribed DOF accelerations
self.system.prescribe(self.axis, acc=0.0) # constant rotational speed
def simulate(self, xpivot=0.0, vprec=0.0, t1=10, dt=0.05):
# reset
self.system.q[:] = 0.0
self.system.qd[:] = 0.0
# initial conditions
self.system.q[self.pivot.istrain][0] = xpivot # initial elevation
self.system.qd[
self.bearing.istrain][0] = vprec # initial elevation spd
self.system.qd[
self.axis.istrain][0] = self.spin # initial rotation speed
self.integ = Integrator(self.system, ('pos', 'vel'))
self.integ.add_output(dynamics.LoadOutput(self.axis.iprox))
self.integ.add_output(dynamics.LoadOutput(self.pivot.iprox))
self.integ.add_output(dynamics.LoadOutput(self.bearing.iprox))
# simulate
if t1 > 0:
self.t, self.y = self.integ.integrate(t1, dt)
for i, lab in enumerate(self.integ.labels()):
print "%2d %s" % (i, lab)
return self.t, self.y
def ani(self, vs=1):
l = self.length * 1.1
return dynvis.anim(self.system,
self.t,
self.y, (0, vs), (-l, l), (-l, l),
velocities=False)
class Gyroscope(object):
def __init__(self, length, radius, mass, spin):
self.length = length
self.radius = radius
self.mass = mass
self.spin = spin
Jx = radius**2 / 2
Jyz = (3*radius**2 + length**2) / 12
Jyz_0 = Jyz + (length/2)**2 # parallel axis theorem
inertia = mass * np.diag([Jx, Jyz_0, Jyz_0])
self.bearing = Hinge('bearing', [0,0,1])
self.pivot = Hinge('pivot', [0,1,0])
self.axis = Hinge('axis', [1,0,0])
self.body = RigidBody('body', mass, inertia, [length/2, 0, 0])
self.bearing.add_leaf(self.pivot)
self.pivot.add_leaf(self.axis)
self.axis.add_leaf(self.body)
self.system = System(self.bearing)
# Prescribed DOF accelerations
self.system.prescribe(self.axis, acc=0.0) # constant rotational speed
def simulate(self, xpivot=0.0, vprec=0.0, t1=10, dt=0.05):
# reset
self.system.q [:] = 0.0
self.system.qd[:] = 0.0
# initial conditions
self.system.q [self.pivot.istrain][0] = xpivot # initial elevation
self.system.qd[self.bearing.istrain][0] = vprec # initial elevation spd
self.system.qd[self.axis .istrain][0] = self.spin # initial rotation speed
self.integ = Integrator(self.system, ('pos','vel'))
self.integ.add_output(dynamics.LoadOutput(self.axis.iprox))
self.integ.add_output(dynamics.LoadOutput(self.pivot.iprox))
self.integ.add_output(dynamics.LoadOutput(self.bearing.iprox))
# simulate
if t1 > 0:
self.t, self.y = self.integ.integrate(t1, dt)
for i,lab in enumerate(self.integ.labels()):
print "%2d %s" % (i,lab)
return self.t, self.y
def ani(self, vs=1):
l = self.length * 1.1
return dynvis.anim(self.system, self.t, self.y,
(0,vs), (-l,l), (-l,l), velocities=False)
def __init__(self, mode_source_file, root_length=0):
# Modal element using data from Bladed model
print "Loading modes from '%s'..." % mode_source_file
self.modes = ModalRepresentation.from_Bladed(mode_source_file)
self.bearing = Hinge('bearing', [0, 0, 1])
self.offset = RigidConnection('offset', [root_length, 0, 0])
self.blade = ModalElement('blade', self.modes)
self.bearing.add_leaf(self.offset)
self.offset.add_leaf(self.blade)
self.system = System(self.bearing)
# Prescribed DOF accelerations
self.system.prescribe(self.bearing.istrain, vel=0.0,
acc=0.0) # constant spin speed
def __init__(self, length, radius, mass, endmass):
self.length = length
self.radius = radius
self.mass = mass
self.endmass = endmass
Jz = radius**2 / 2
Jxy = (3*radius**2 + length**2) / 12
inertia = mass * np.diag([Jxy, Jxy, Jz])
self.A = mass*Jxy + endmass*(length/2)**2
self.C = mass*Jz
self.pivot = Hinge('pivot', [0,1,0])
self.axis = Hinge('axis', [0,0,1])
self.body = RigidBody('body', mass, inertia)
self.offset = RigidConnection('offset', [0,0,length/2])
self.endbody = RigidBody('end', endmass)
self.pivot.add_leaf(self.axis)
self.axis.add_leaf(self.body)
self.pivot.add_leaf(self.offset)
self.offset.add_leaf(self.endbody)
self.system = System(self.pivot)
# Prescribed DOF accelerations
self.system.prescribe(self.axis, acc=0.0) # constant rotational speed
def __init__(self, length, radius, mass, spin, endmass):
self.length = length
self.radius = radius
self.mass = mass
self.spin = spin
self.endmass = endmass
x = np.linspace(-length/2, length/2)
modes = linearisation.ModalRepresentation(
x =x,
shapes =np.zeros((len(x),3,0)),
rotations =np.zeros((len(x),3,0)),
density =np.ones_like(x) * mass/length,
mass_axis =np.zeros((len(x),2)),
section_inertia=np.ones_like(x) * radius**2 / 4,
freqs =np.zeros((0,)),
)
self.bearing = Hinge('bearing', [0,0,1])
self.pivot = Hinge('pivot', [0,1,0])
self.axis = Hinge('axis', [0,0,1], rotmat_y(-np.pi/2))
self.body = ModalElement('body', modes)
self.offset = RigidConnection('offset', [0,0,length/2])
self.endbody = RigidBody('end', endmass)
self.bearing.add_leaf(self.pivot)
self.pivot.add_leaf(self.axis)
self.axis.add_leaf(self.body)
self.pivot.add_leaf(self.offset)
self.offset.add_leaf(self.endbody)
self.system = System(self.bearing)
# Prescribed DOF accelerations
self.system.prescribe(self.axis, acc=0.0) # constant rotational speed
class Gyroscope(object):
def __init__(self, length, radius, mass, spin):
self.length = length
self.radius = radius
self.mass = mass
self.spin = spin
Jx = radius**2 / 2
Jyz = (3 * radius**2 + length**2) / 12
Jyz_0 = Jyz + (length / 2)**2 # parallel axis theorem
inertia = mass * np.diag([Jx, Jyz_0, Jyz_0])
self.bearing = Hinge('bearing', [0, 0, 1])
self.pivot = Hinge('pivot', [0, 1, 0])
self.axis = Hinge('axis', [1, 0, 0])
self.body = RigidBody('body', mass, inertia, [length / 2, 0, 0])
self.bearing.add_leaf(self.pivot)
self.pivot.add_leaf(self.axis)
self.axis.add_leaf(self.body)
self.system = System(self.bearing)
# Prescribed DOF accelerations
self.system.prescribe(self.axis.istrain,
0.0) # constant rotational speed
def simulate(self, xpivot=0.0, vpivot=0.0, t1=1.5, dt=0.01):
# reset
self.system.q[:] = 0.0
self.system.qd[:] = 0.0
# initial conditions
self.system.q[self.pivot.istrain[0]] = xpivot # initial elevation
self.system.qd[self.pivot.istrain[0]] = vpivot # initial elevation spd
self.system.qd[
self.axis.istrain[0]] = self.spin # initial rotation speed
# simulate
self.t = np.arange(0, t1, dt)
self.y = solve_system(self.system, self.t, outputs='vels')
def ani(self, vs=1):
l = self.length * 1.1
return dynvis.anim(self.system,
self.t,
self.y, (0, vs), (-l, l), (-l, l),
velocities=False)
def __init__(self, mode_source_file, root_length=0):
# Modal element using data from Bladed model
print "Loading modes from '%s'..." % mode_source_file
self.modes = ModalRepresentation.from_Bladed(mode_source_file)
Ry = rotmat_y(-pi / 2)
Rhb1 = rotmat_x(0 * 2 * pi / 3)
Rhb2 = rotmat_x(1 * 2 * pi / 3)
Rhb3 = rotmat_x(2 * 2 * pi / 3)
self.bearing = Hinge('bearing', [1, 0, 0])
root1 = RigidConnection('root1', root_length * np.dot(Rhb1, [0, 0, 1]),
dot(Rhb1, Ry))
root2 = RigidConnection('root2', root_length * np.dot(Rhb2, [0, 0, 1]),
dot(Rhb2, Ry))
root3 = RigidConnection('root3', root_length * np.dot(Rhb3, [0, 0, 1]),
dot(Rhb3, Ry))
self.blade1 = ModalElement('blade1', self.modes)
self.blade2 = ModalElement('blade2', self.modes)
self.blade3 = ModalElement('blade3', self.modes)
self.bearing.add_leaf(root1)
self.bearing.add_leaf(root2)
self.bearing.add_leaf(root3)
root1.add_leaf(self.blade1)
root2.add_leaf(self.blade2)
root3.add_leaf(self.blade3)
self.system = System(self.bearing)
# Prescribed DOF accelerations - constant rotor speed
self.system.prescribe(self.bearing.istrain, vel=0.0, acc=0.0)
# setup integrator
self.integ = Integrator(self.system, ('pos', 'vel'))
self.integ.add_output(dynamics.LoadOutput(self.bearing.iprox))
for b in (self.blade1, self.blade2, self.blade3):
self.integ.add_output(dynamics.LoadOutput(b.iprox, local=True))
for b in (self.blade1, self.blade2, self.blade3):
self.integ.add_output(
dynamics.CustomOutput(lambda s: b.station_positions()[-1],
label="{} tip defl".format(b)))
for b in (self.blade1, self.blade2, self.blade3):
self.integ.add_output(
dynamics.CustomOutput(lambda s: dot(b.Rp,
b.station_positions()[-1]),
label="{} tip pos".format(b)))
class Gyroscope(object):
def __init__(self, length, radius, mass, spin):
self.length = length
self.radius = radius
self.mass = mass
self.spin = spin
Jx = radius**2 / 2
Jyz = (3*radius**2 + length**2) / 12
Jyz_0 = Jyz + (length/2)**2 # parallel axis theorem
inertia = mass * np.diag([Jx, Jyz_0, Jyz_0])
self.bearing = Hinge('bearing', [0,0,1])
self.pivot = Hinge('pivot', [0,1,0])
self.axis = Hinge('axis', [1,0,0])
self.body = RigidBody('body', mass, inertia, [length/2, 0, 0])
self.bearing.add_leaf(self.pivot)
self.pivot.add_leaf(self.axis)
self.axis.add_leaf(self.body)
self.system = System(self.bearing)
# Prescribed DOF accelerations
self.system.prescribe(self.axis.istrain, 0.0) # constant rotational speed
def simulate(self, xpivot=0.0, vpivot=0.0, t1=1.5, dt=0.01):
# reset
self.system.q [:] = 0.0
self.system.qd[:] = 0.0
# initial conditions
self.system.q [self.pivot.istrain[0]] = xpivot # initial elevation
self.system.qd[self.pivot.istrain[0]] = vpivot # initial elevation spd
self.system.qd[self.axis .istrain[0]] = self.spin # initial rotation speed
# simulate
self.t = np.arange(0, t1, dt)
self.y = solve_system(self.system, self.t, outputs='vels')
def ani(self, vs=1):
l = self.length * 1.1
return dynvis.anim(self.system, self.t, self.y,
(0,vs), (-l,l), (-l,l), velocities=False)
def __init__(self, bladed_file, root_length=0, rigid=False):
# Modal element using data from Bladed model
print "Loading modes from '%s'..." % bladed_file
self.blade = Blade(bladed_file)
self.tower = Tower(bladed_file)
self.modes = self.blade.modal_rep()
#self.tmodes = self.tower.modal_rep()
Ry = rotmat_y(-pi/2)
Rhb1 = rotmat_x(0 * 2*pi/3)
Rhb2 = rotmat_x(1 * 2*pi/3)
Rhb3 = rotmat_x(2 * 2*pi/3)
self.base = FreeJoint('base')
self.towerlink = RigidConnection('tower', [0,0,self.tower.hubheight])
self.bearing = Hinge('bearing', [1,0,0])
root1 = RigidConnection('root1', root_length*np.dot(Rhb1,[0,0,1]), dot(Rhb1,Ry))
root2 = RigidConnection('root2', root_length*np.dot(Rhb2,[0,0,1]), dot(Rhb2,Ry))
root3 = RigidConnection('root3', root_length*np.dot(Rhb3,[0,0,1]), dot(Rhb3,Ry))
self.blade1 = ModalElement('blade1', self.modes)
self.blade2 = ModalElement('blade2', self.modes)
self.blade3 = ModalElement('blade3', self.modes)
self.base.add_leaf(self.towerlink)
self.towerlink.add_leaf(self.bearing)
self.bearing.add_leaf(root1)
self.bearing.add_leaf(root2)
self.bearing.add_leaf(root3)
root1.add_leaf(self.blade1)
root2.add_leaf(self.blade2)
root3.add_leaf(self.blade3)
self.system = System(self.base)
# Prescribed DOF accelerations - constant rotor speed
self.base_motion = None
self.base_motion_amp = 0
self.system.prescribe(self.bearing, vel=0)
self.system.prescribe(self.base, vel=0)
if rigid:
for b in (self.blade1, self.blade2, self.blade3):
self.system.prescribe(b, vel=0)
# setup integrator
self.integ = Integrator(self.system, ('pos','vel','acc'))
self.integ.add_output(dynamics.LoadOutput(self.base.iprox))
self.integ.add_output(dynamics.LoadOutput(self.towerlink.iprox))
self.integ.add_output(dynamics.LoadOutput(self.bearing.iprox))
for b in (self.blade1, self.blade2, self.blade3):
self.integ.add_output(dynamics.LoadOutput(b.iprox, local=True))
for b in (self.blade1, self.blade2, self.blade3):
self.integ.add_output(b.output_deflections())
for b in (self.blade1, self.blade2, self.blade3):
self.integ.add_output(b.output_positions())
for b in (self.blade1, self.blade2, self.blade3):
self.integ.add_output(dynamics.NodeOutput(b.iprox, local=True, deriv=2))
def __init__(self, mode_source_file, root_length=0, wind_table=None):
# Modal element using data from Bladed model
print "Loading modes from '%s'..." % mode_source_file
self.blade = Blade(mode_source_file)
self.modes = self.blade.modal_rep()
if wind_table is not None:
loading = BladeLoading(self.blade, wind_table, None)
else:
loading = None
Ry = rotmat_y(-pi/2)
Rhb1 = rotmat_x(0 * 2*pi/3)
Rhb2 = rotmat_x(1 * 2*pi/3)
Rhb3 = rotmat_x(2 * 2*pi/3)
self.bearing = Hinge('bearing', [1,0,0])
root1 = RigidConnection('root1', root_length*np.dot(Rhb1,[0,0,1]), dot(Rhb1,Ry))
root2 = RigidConnection('root2', root_length*np.dot(Rhb2,[0,0,1]), dot(Rhb2,Ry))
root3 = RigidConnection('root3', root_length*np.dot(Rhb3,[0,0,1]), dot(Rhb3,Ry))
self.blade1 = ModalElement('blade1', self.modes, loading)
self.blade2 = ModalElement('blade2', self.modes)
self.blade3 = ModalElement('blade3', self.modes)
self.bearing.add_leaf(root1)
self.bearing.add_leaf(root2)
self.bearing.add_leaf(root3)
root1.add_leaf(self.blade1)
root2.add_leaf(self.blade2)
root3.add_leaf(self.blade3)
self.system = System(self.bearing)
# Prescribed DOF accelerations - constant rotor speed
self.system.prescribe(self.bearing, vel=0.0, acc=0.0)
# setup integrator
self.integ = Integrator(self.system, ('pos','vel'))
self.integ.add_output(dynamics.LoadOutput(self.bearing.iprox))
self.integ.add_output(dynamics.LoadOutput(self.blade1.iprox, local=True))
self.integ.add_output(self.blade1.output_deflections())
self.integ.add_output(self.blade1.output_positions())
class LumpedGyroscope(Gyroscope):
def __init__(self, length, radius, mass, endmass):
self.length = length
self.radius = radius
self.mass = mass
self.endmass = endmass
# corrected radius for lumped masses
mr = radius / np.sqrt(2)
root3 = np.sqrt(3)
self.A = 3 * (mass/3) * mr**2 / 2 + endmass*(length/2)**2
self.C = 3 * (mass/3) * mr**2
self.pivot = Hinge('pivot', [0,1,0])
self.axis = Hinge('axis', [0,0,1])
self.arm1 = RigidConnection('arm1', [mr,0,0])
self.arm2 = RigidConnection('arm2', [-mr/2, mr*root3/2,0])
self.arm3 = RigidConnection('arm3', [-mr/2,-mr*root3/2,0])
self.body = RigidBody('body', mass/3)
self.body2 = RigidBody('body2', mass/3)
self.body3 = RigidBody('body3', mass/3)
self.offset = RigidConnection('offset', [0,0,length/2])
self.endbody = RigidBody('end', endmass)
self.pivot.add_leaf(self.axis)
self.axis.add_leaf(self.arm1)
self.axis.add_leaf(self.arm2)
self.axis.add_leaf(self.arm3)
self.arm1.add_leaf(self.body)
self.arm2.add_leaf(self.body2)
self.arm3.add_leaf(self.body3)
self.pivot.add_leaf(self.offset)
self.offset.add_leaf(self.endbody)
self.system = System(self.pivot)
# Prescribed DOF accelerations
self.system.prescribe(self.axis, acc=0.0) # constant rotational speed
class LumpedGyroscope(Gyroscope):
def __init__(self, length, radius, mass, endmass):
self.length = length
self.radius = radius
self.mass = mass
self.endmass = endmass
# corrected radius for lumped masses
mr = radius / np.sqrt(2)
root3 = np.sqrt(3)
self.A = 3 * (mass / 3) * mr**2 / 2 + endmass * (length / 2)**2
self.C = 3 * (mass / 3) * mr**2
self.pivot = Hinge('pivot', [0, 1, 0])
self.axis = Hinge('axis', [0, 0, 1])
self.arm1 = RigidConnection('arm1', [mr, 0, 0])
self.arm2 = RigidConnection('arm2', [-mr / 2, mr * root3 / 2, 0])
self.arm3 = RigidConnection('arm3', [-mr / 2, -mr * root3 / 2, 0])
self.body = RigidBody('body', mass / 3)
self.body2 = RigidBody('body2', mass / 3)
self.body3 = RigidBody('body3', mass / 3)
self.offset = RigidConnection('offset', [0, 0, length / 2])
self.endbody = RigidBody('end', endmass)
self.pivot.add_leaf(self.axis)
self.axis.add_leaf(self.arm1)
self.axis.add_leaf(self.arm2)
self.axis.add_leaf(self.arm3)
self.arm1.add_leaf(self.body)
self.arm2.add_leaf(self.body2)
self.arm3.add_leaf(self.body3)
self.pivot.add_leaf(self.offset)
self.offset.add_leaf(self.endbody)
self.system = System(self.pivot)
# Prescribed DOF accelerations
self.system.prescribe(self.axis, acc=0.0) # constant rotational speed
class BeamGyroscope(Gyroscope):
def __init__(self, length, radius, mass, spin):
self.length = length
self.radius = radius
self.mass = mass
self.spin = spin
Jx = mass * radius**2 / 2
self.bearing = Hinge('bearing', [0,0,1])
self.pivot = Hinge('pivot', [0,1,0])
self.axis = Hinge('axis', [1,0,0])
self.body = UniformBeam('body', length, mass/length,
1, 1, 1, Jx=Jx/2) # /2 because added to both ends
self.bearing.add_leaf(self.pivot)
self.pivot.add_leaf(self.axis)
self.axis.add_leaf(self.body)
self.system = System(self.bearing)
# Prescribed DOF accelerations
self.system.prescribe(self.axis.istrain, 0.0) # constant rotational speed
self.system.prescribe(self.body.istrain, 0.0) # rigid beam
def __init__(self, mode_source_file, root_length=0):
# Modal element using data from Bladed model
print "Loading modes from '%s'..." % mode_source_file
self.modes = ModalRepresentation.from_Bladed(mode_source_file)
self.bearing = Hinge('bearing', [0,0,1])
self.offset = RigidConnection('offset', [root_length, 0, 0])
self.blade = ModalElement('blade', self.modes)
self.bearing.add_leaf(self.offset)
self.offset.add_leaf(self.blade)
self.system = System(self.bearing)
# Prescribed DOF accelerations
self.system.prescribe(self.bearing.istrain, vel=0.0, acc=0.0) # constant spin speed
def __init__(self, length, radius, mass, spin):
self.length = length
self.radius = radius
self.mass = mass
self.spin = spin
Jx = radius**2 / 2
Jyz = (3 * radius**2 + length**2) / 12
Jyz_0 = Jyz + (length / 2)**2 # parallel axis theorem
inertia = mass * np.diag([Jx, Jyz_0, Jyz_0])
self.bearing = Hinge('bearing', [0, 0, 1])
self.pivot = Hinge('pivot', [0, 1, 0])
self.axis = Hinge('axis', [1, 0, 0])
self.body = RigidBody('body', mass, inertia, [length / 2, 0, 0])
self.bearing.add_leaf(self.pivot)
self.pivot.add_leaf(self.axis)
self.axis.add_leaf(self.body)
self.system = System(self.bearing)
# Prescribed DOF accelerations
self.system.prescribe(self.axis, acc=0.0) # constant rotational speed
class Rotor(object):
def __init__(self, mode_source_file, root_length=0):
# Modal element using data from Bladed model
print "Loading modes from '%s'..." % mode_source_file
self.modes = ModalRepresentation.from_Bladed(mode_source_file)
self.bearing = Hinge('bearing', [0,0,1])
self.offset = RigidConnection('offset', [root_length, 0, 0])
self.blade = ModalElement('blade', self.modes)
self.bearing.add_leaf(self.offset)
self.offset.add_leaf(self.blade)
self.system = System(self.bearing)
# Prescribed DOF accelerations
self.system.prescribe(self.bearing.istrain, vel=0.0, acc=0.0) # constant spin speed
def simulate(self, qm0, spin=10.0, t1=1.5, dt=0.01):
# reset
self.system.q [:] = 0.0
self.system.qd[:] = 0.0
# initial conditions
self.system.q[self.blade.istrain] = qm0 # initial modal amplitudes
self.system.prescribe(self.bearing.istrain, vel=spin, acc=0.0) #acc=spin/t1)
# setup integrator
self.integ = Integrator(self.system, ('pos','vel'))
self.integ.add_output(dynamics.LoadOutput(self.bearing.iprox))
self.integ.add_output(dynamics.LoadOutput(self.blade.iprox))
self.integ.add_output(dynamics.LoadOutput(self.blade.iprox, local=True))
self.integ.add_output(dynamics.CustomOutput(
lambda s: self.blade.station_positions()[-1], label="Tip pos"))
self.integ.add_output(dynamics.CustomOutput(
lambda s: self.blade.quad_stress, label="Quad stress"))
# simulate
self.t,self.y = self.integ.integrate(t1, dt)
return self.t, self.y
def lin(self, qm0, spin=10.0):
# reset
self.system.q [:] = 0.0
self.system.qd[:] = 0.0
# initial conditions
self.system.q[self.blade.istrain] = qm0 # initial modal amplitudes
self.system.prescribe(self.bearing.istrain, vel=spin, acc=0.0) # constant speed
linsys = linearisation.LinearisedSystem(self.system, qm0)
return linsys
def ani(self, vs=1):
l = 40
return dynvis.anim(self.system, self.t, self.y,
(0,vs), (-l,l), (-l,l), velocities=False, only_free=True)
def __init__(self, mode_source_file, root_length=0):
# Modal element using data from Bladed model
print "Loading modes from '%s'..." % mode_source_file
self.modes = ModalRepresentation.from_Bladed(mode_source_file)
Ry = rotmat_y(-pi/2)
Rhb1 = rotmat_x(0 * 2*pi/3)
Rhb2 = rotmat_x(1 * 2*pi/3)
Rhb3 = rotmat_x(2 * 2*pi/3)
self.bearing = Hinge('bearing', [1,0,0])
root1 = RigidConnection('root1', root_length*np.dot(Rhb1,[0,0,1]), dot(Rhb1,Ry))
root2 = RigidConnection('root2', root_length*np.dot(Rhb2,[0,0,1]), dot(Rhb2,Ry))
root3 = RigidConnection('root3', root_length*np.dot(Rhb3,[0,0,1]), dot(Rhb3,Ry))
self.blade1 = ModalElement('blade1', self.modes)
self.blade2 = ModalElement('blade2', self.modes)
self.blade3 = ModalElement('blade3', self.modes)
self.bearing.add_leaf(root1)
self.bearing.add_leaf(root2)
self.bearing.add_leaf(root3)
root1.add_leaf(self.blade1)
root2.add_leaf(self.blade2)
root3.add_leaf(self.blade3)
self.system = System(self.bearing)
# Prescribed DOF accelerations - constant rotor speed
self.system.prescribe(self.bearing.istrain, vel=0.0, acc=0.0)
# setup integrator
self.integ = Integrator(self.system, ('pos','vel'))
self.integ.add_output(dynamics.LoadOutput(self.bearing.iprox))
for b in (self.blade1, self.blade2, self.blade3):
self.integ.add_output(dynamics.LoadOutput(b.iprox, local=True))
for b in (self.blade1, self.blade2, self.blade3):
self.integ.add_output(dynamics.CustomOutput(
lambda s: b.station_positions()[-1], label="{} tip defl".format(b)))
for b in (self.blade1, self.blade2, self.blade3):
self.integ.add_output(dynamics.CustomOutput(
lambda s: dot(b.Rp, b.station_positions()[-1]), label="{} tip pos".format(b)))
def __init__(self, length, radius, mass, spin):
self.length = length
self.radius = radius
self.mass = mass
self.spin = spin
Jx = radius**2 / 2
Jyz = (3*radius**2 + length**2) / 12
Jyz_0 = Jyz + (length/2)**2 # parallel axis theorem
inertia = mass * np.diag([Jx, Jyz_0, Jyz_0])
self.bearing = Hinge('bearing', [0,0,1])
self.pivot = Hinge('pivot', [0,1,0])
self.axis = Hinge('axis', [1,0,0])
self.body = RigidBody('body', mass, inertia, [length/2, 0, 0])
self.bearing.add_leaf(self.pivot)
self.pivot.add_leaf(self.axis)
self.axis.add_leaf(self.body)
self.system = System(self.bearing)
# Prescribed DOF accelerations
self.system.prescribe(self.axis, acc=0.0) # constant rotational speed
class Gyroscope(object):
def __init__(self, length, radius, mass, endmass):
self.length = length
self.radius = radius
self.mass = mass
self.endmass = endmass
Jz = radius**2 / 2
Jxy = (3 * radius**2 + length**2) / 12
inertia = mass * np.diag([Jxy, Jxy, Jz])
self.A = mass * Jxy + endmass * (length / 2)**2
self.C = mass * Jz
self.pivot = Hinge('pivot', [0, 1, 0])
self.axis = Hinge('axis', [0, 0, 1])
self.body = RigidBody('body', mass, inertia)
self.offset = RigidConnection('offset', [0, 0, length / 2])
self.endbody = RigidBody('end', endmass)
self.pivot.add_leaf(self.axis)
self.axis.add_leaf(self.body)
self.pivot.add_leaf(self.offset)
self.offset.add_leaf(self.endbody)
self.system = System(self.pivot)
# Prescribed DOF accelerations
self.system.prescribe(self.axis, acc=0.0) # constant rotational speed
def applied_torque(self, s):
# applied torque about y axis, Q2
elevation = s.q[self.pivot.istrain][0]
return self.endmass * dynamics.gravity * self.length / 2 * np.sin(
elevation)
def thetadotdot(self, s):
# acceleration about y axis, thetadotdot
Q2 = self.applied_torque(s)
return Q2 / self.A
def gyro_torque(self, s):
# gyroscopic sideways torque, Q1
spin = s.qd[self.axis.istrain][0] # spin speed
thetadot = s.qd[self.pivot.istrain][0]
return self.C * spin * thetadot
def simulate(self, xpivot=0.0, spin=10.0, t1=1.5, dt=0.01):
# reset
self.system.q[:] = 0.0
self.system.qd[:] = 0.0
# initial conditions
self.system.q[self.pivot.istrain][0] = xpivot # initial elevation
self.system.qd[self.axis.istrain][0] = spin # initial rotation speed
# setup integrator
#self.integ = Integrator(self.system, ('pos','vel','acc'))
self.integ = Integrator(self.system, ())
for istrain in (self.pivot.istrain, self.axis.istrain):
self.integ.add_output(dynamics.StrainOutput(istrain, deriv=0))
self.integ.add_output(dynamics.StrainOutput(istrain, deriv=1))
self.integ.add_output(dynamics.StrainOutput(istrain, deriv=2))
self.integ.add_output(dynamics.LoadOutput(self.pivot.idist[0]))
self.integ.add_output(
dynamics.LoadOutput(self.pivot.idist[0], local=True))
self.integ.add_output(dynamics.LoadOutput(self.body.iprox))
self.integ.add_output(dynamics.LoadOutput(self.endbody.iprox))
self.integ.add_output(dynamics.CustomOutput(self.applied_torque, "Q2"))
self.integ.add_output(
dynamics.CustomOutput(self.thetadotdot, "thetadotdot"))
self.integ.add_output(dynamics.CustomOutput(self.gyro_torque, "Q1"))
# simulate
if t1 > 0:
self.t, self.y = self.integ.integrate(t1, dt)
def ani(self, vs=1):
l = self.length * 1.1
return dynvis.anim(self.system,
self.t,
self.y, (0, vs), (-l, l), (-l, l),
velocities=False,
only_free=True)
# Blade loading
wind_table = np.array([
[0, 1, 2, 10], # time
[0, 0, 0, 0 ], # x
[0, 0, 20, 20], # y
[0, 0, 0, 0 ], # z
])
loading = BladeLoading(modes.x, wind_table, None)
rotorspeed = 10 * np.pi/30 # 10 rpm
# Modal element
bearing = Hinge('bearing', [0,1,0])
el = ModalElement('el', modes, loading)
bearing.add_leaf(el)
system = System(bearing)
# Prescribe rotation speed
system.prescribe(bearing.istrain, 0.0)
system.qd[bearing.istrain] = rotorspeed
system.find_equilibrium()
integ = Integrator(system, ())
integ.add_position_output(bearing.istrain)
integ.add_custom_output(lambda s: el.modes.X(el.xstrain)[(16,32),1:3].flatten(), 'defl')
integ.add_custom_output(lambda s: el._get_loading()[16,:], 'loading')
integ.add_custom_output(lambda s: el.quad_forces, 'quad_forces')
integ.add_custom_output(lambda s: el.quad_stress, 'quad_stress')
# Load Bladed data for comparison
thrust_time = [0, 1, 2, 10]
thrust_force = [0, 0, 10e3, 10e3]
thrust = np.c_[thrust_force, np.zeros((4, 2))].T
loadfunc = scipy.interpolate.interp1d(thrust_time, thrust)
# Modal element
base = RigidConnection('base', rotation=rotmat_y(-np.pi / 2))
el = DistalModalElement('el', modes, distal=True, damping_freqs=modes2.freqs)
#el = ModalElement('el', modes, distal=True, damping_freqs=modes2.freqs)
rna = RigidBody('rna',
24000,
np.diag([6400003, 6400003, 4266667]),
nodal_load=loadfunc)
base.add_leaf(el)
el.add_leaf(rna)
system = System(base)
system.prescribe(el, vel=0, part=[0, 3])
integ = Integrator(system)
integ.add_output(el.output_deflections())
integ.add_output(el.output_rotations())
integ.add_output(dynamics.LoadOutput(rna.iprox))
linsys = LinearisedSystem(system)
def ani_xy(s, t, y):
return dynvis.anim(s, t, y, (0, 1), (-5, 45), (-5, 5), velocities=False)
class FlappedBladeTurbine(object):
def __init__(self, bladed_file, root_length=0):
# Load modes but use a simple flapped blade
print "Loading modes from '%s'..." % bladed_file
self.blade = Blade(bladed_file)
self.tower = Tower(bladed_file)
self.modes = self.blade.modal_rep()
# Calculate equivalent blade properties
I1 = self.modes.I0[0]
I2 = self.modes.J0[0, 0]
print I1, I2
wflap = self.modes.freqs[0]
bmass = self.modes.mass
inertia = self.modes.inertia_tensor(np.zeros(len(self.modes.freqs)))
Xc = [I1 / bmass, 0, 0]
kflap = I2 * wflap**2
Ry = rotmat_y(-pi / 2)
Rhb1 = rotmat_x(0 * 2 * pi / 3)
Rhb2 = rotmat_x(1 * 2 * pi / 3)
Rhb3 = rotmat_x(2 * 2 * pi / 3)
self.base = FreeJoint('base')
self.towerlink = RigidConnection('tower', [0, 0, self.tower.hubheight])
self.bearing = Hinge('bearing', [1, 0, 0])
root1 = RigidConnection('root1', root_length * np.dot(Rhb1, [0, 0, 1]),
dot(Rhb1, Ry))
root2 = RigidConnection('root2', root_length * np.dot(Rhb2, [0, 0, 1]),
dot(Rhb2, Ry))
root3 = RigidConnection('root3', root_length * np.dot(Rhb3, [0, 0, 1]),
dot(Rhb3, Ry))
self.flap1 = Hinge('flap1', [0, 1, 0])
self.flap2 = Hinge('flap2', [0, 1, 0])
self.flap3 = Hinge('flap3', [0, 1, 0])
self.blade1 = RigidBody('blade1', bmass, inertia, Xc)
self.blade2 = RigidBody('blade2', bmass, inertia, Xc)
self.blade3 = RigidBody('blade3', bmass, inertia, Xc)
self.flap1.stiffness = self.flap2.stiffness = self.flap3.stiffness = kflap
self.base.add_leaf(self.towerlink)
self.towerlink.add_leaf(self.bearing)
self.bearing.add_leaf(root1)
self.bearing.add_leaf(root2)
self.bearing.add_leaf(root3)
root1.add_leaf(self.flap1)
root2.add_leaf(self.flap2)
root3.add_leaf(self.flap3)
self.flap1.add_leaf(self.blade1)
self.flap2.add_leaf(self.blade2)
self.flap3.add_leaf(self.blade3)
self.system = System(self.base)
# Prescribed DOF accelerations - constant rotor speed
self.base_motion = None
self.base_motion_amp = 0
self.system.prescribe(self.bearing, vel=0)
self.system.prescribe(self.base, vel=0)
# setup integrator
self.integ = Integrator(self.system, ('pos', 'vel', 'acc'))
self.integ.add_output(dynamics.LoadOutput(self.base.iprox))
self.integ.add_output(dynamics.LoadOutput(self.towerlink.iprox))
self.integ.add_output(
dynamics.LoadOutput(self.bearing.iprox, local=True))
self.integ.add_output(
dynamics.LoadOutput(self.bearing.idist[0], local=True))
for b in (self.blade1, self.blade2, self.blade3):
self.integ.add_output(dynamics.LoadOutput(b.iprox, local=True))
for b in (self.blade1, self.blade2, self.blade3):
self.integ.add_output(
dynamics.NodeOutput(b.iprox, local=True, deriv=2))
def set_base_motion(self, dof, w, amp):
self.base_motion = dof
self.base_motion_amp = amp
self.system.prescribe(self.base,
part=dof,
vel=lambda t: -w * amp * np.sin(w * t),
acc=lambda t: -w**2 * amp * np.cos(w * t))
def set_initial_conditions(self, qm0=None, az0=None, rotor_speed=None):
# initial conditions
if qm0 is not None: # initial hinge angle
self.system.q[self.flap1.istrain][0] = qm0
self.system.q[self.flap2.istrain][0] = qm0
self.system.q[self.flap3.istrain][0] = qm0
if az0 is not None:
self.system.q[self.bearing.istrain][0] = az0
if self.base_motion is not None:
self.system.q[self.base.istrain][
self.base_motion] = self.base_motion_amp
if rotor_speed is not None:
self.system.prescribe(self.bearing, vel=rotor_speed)
def simulate(self,
qm0=None,
az0=0.0,
rotor_speed=10.0,
t1=None,
dt=0.01,
t0=0.0,
init=False):
# reset
self.system.q[:] = 0.0
self.system.qd[:] = 0.0
self.set_initial_conditions(qm0, az0, rotor_speed)
if t1 is None:
t1 = 4 * pi / rotor_speed if (rotor_speed != 0.0) else 2
if init:
self.system.find_equilibrium()
# simulate
t, y = self.integ.integrate(t1, dt, t0)
#for i,lab in enumerate(self.integ.labels):
# print "%2d %s" % (i,lab)
#return self.t, self.y
# Build results structure
results = FlappedTurbineResults(t, y)
return results
def lin(self, qm0=None, az0=None, rotor_speed=None, init=False):
# reset
self.system.q[:] = 0.0
self.system.qd[:] = 0.0
self.set_initial_conditions(qm0, az0, rotor_speed)
if init:
self.system.find_equilibrium()
# need initial amplitudes for linearisation point
if qm0 is None:
qm0 = self.system.q[self.blade1.istrain]
linsys = linearisation.LinearisedSystem(self.system, np.tile(qm0, 3))
return linsys
def ani(self, results, x=0, y=1):
H = self.tower.hubheight + self.blade.radii[-1]
limits = [(-H, H), (-H, H), (-5, H + 5)]
return dynvis.anim(self.system, results.t, results.strains.as_matrix(),
(x, y), limits[x], limits[y])
class Rotor(object):
def __init__(self, mode_source_file, root_length=0):
# Modal element using data from Bladed model
print "Loading modes from '%s'..." % mode_source_file
self.blade = Blade(mode_source_file)
self.modes = self.blade.modal_rep()
Ry = rotmat_y(-pi/2)
Rhb1 = rotmat_x(0 * 2*pi/3)
Rhb2 = rotmat_x(1 * 2*pi/3)
Rhb3 = rotmat_x(2 * 2*pi/3)
self.bearing = Hinge('bearing', [1,0,0])
root1 = RigidConnection('root1', root_length*np.dot(Rhb1,[0,0,1]), dot(Rhb1,Ry))
root2 = RigidConnection('root2', root_length*np.dot(Rhb2,[0,0,1]), dot(Rhb2,Ry))
root3 = RigidConnection('root3', root_length*np.dot(Rhb3,[0,0,1]), dot(Rhb3,Ry))
self.blade1 = ModalElement('blade1', self.modes)
self.blade2 = ModalElement('blade2', self.modes)
self.blade3 = ModalElement('blade3', self.modes)
self.bearing.add_leaf(root1)
self.bearing.add_leaf(root2)
self.bearing.add_leaf(root3)
root1.add_leaf(self.blade1)
root2.add_leaf(self.blade2)
root3.add_leaf(self.blade3)
self.system = System(self.bearing)
# Prescribed DOF accelerations - constant rotor speed
self.system.prescribe(self.bearing, acc=0.0)
# setup integrator
self.integ = Integrator(self.system, ('pos','vel'))
self.integ.add_output(dynamics.LoadOutput(self.bearing.iprox))
self.integ.add_output(dynamics.LoadOutput(self.blade1.iprox, local=True))
self.integ.add_output(self.blade1.output_deflections())
self.integ.add_output(self.blade1.output_positions())
def simulate(self, qm0=None, spin=10.0, t1=1.5, dt=0.01):
# reset
self.system.q [:] = 0.0
self.system.qd[:] = 0.0
# initial conditions
if qm0 is not None: # initial modal amplitudes
self.system.q[self.blade1.istrain] = qm0
self.system.q[self.blade2.istrain] = qm0
self.system.q[self.blade3.istrain] = qm0
self.system.qd[self.bearing.istrain][0] = spin
# simulate
self.t,self.y = self.integ.integrate(t1, dt)
for i,lab in enumerate(self.integ.labels()):
print "%2d %s" % (i,lab)
return self.t, self.y
def lin(self, qm0=None, spin=10.0):
# reset
self.system.q [:] = 0.0
self.system.qd[:] = 0.0
# initial conditions
if qm0 is not None: # initial modal amplitudes
self.system.q[self.blade1.istrain] = qm0
self.system.q[self.blade2.istrain] = qm0
self.system.q[self.blade3.istrain] = qm0
else:
qm0 = np.zeros(self.blade1._nstrain * 3)
self.system.prescribe(self.bearing, vel=spin, acc=0.0)
self.system.qd[self.bearing.istrain][0] = spin
linsys = linearisation.LinearisedSystem(self.system, qm0)
return linsys
def ani(self, t=None, y=None, planview=True):
if t is None: t = self.t
if y is None: y = self.y
l = 40
if planview:
return dynvis.anim(self.system, t, y, (1,2), (-l,l), (-l,l))
else:
return dynvis.anim(self.system, t, y, (0,1), (-l,l), (-5,5))
class Rotor(object):
def __init__(self, mode_source_file, root_length=0):
# Modal element using data from Bladed model
print "Loading modes from '%s'..." % mode_source_file
self.blade = Blade(mode_source_file)
self.modes = self.blade.modal_rep()
Ry = rotmat_y(-pi / 2)
Rhb1 = rotmat_x(0 * 2 * pi / 3)
Rhb2 = rotmat_x(1 * 2 * pi / 3)
Rhb3 = rotmat_x(2 * 2 * pi / 3)
self.bearing = Hinge('bearing', [1, 0, 0])
root1 = RigidConnection('root1', root_length * np.dot(Rhb1, [0, 0, 1]),
dot(Rhb1, Ry))
root2 = RigidConnection('root2', root_length * np.dot(Rhb2, [0, 0, 1]),
dot(Rhb2, Ry))
root3 = RigidConnection('root3', root_length * np.dot(Rhb3, [0, 0, 1]),
dot(Rhb3, Ry))
self.blade1 = ModalElement('blade1', self.modes)
self.blade2 = ModalElement('blade2', self.modes)
self.blade3 = ModalElement('blade3', self.modes)
self.bearing.add_leaf(root1)
self.bearing.add_leaf(root2)
self.bearing.add_leaf(root3)
root1.add_leaf(self.blade1)
root2.add_leaf(self.blade2)
root3.add_leaf(self.blade3)
self.system = System(self.bearing)
# Prescribed DOF accelerations - constant rotor speed
self.system.prescribe(self.bearing, acc=0.0)
# setup integrator
self.integ = Integrator(self.system, ('pos', 'vel'))
self.integ.add_output(dynamics.LoadOutput(self.bearing.iprox))
self.integ.add_output(
dynamics.LoadOutput(self.blade1.iprox, local=True))
self.integ.add_output(self.blade1.output_deflections())
self.integ.add_output(self.blade1.output_positions())
def simulate(self, qm0=None, spin=10.0, t1=1.5, dt=0.01):
# reset
self.system.q[:] = 0.0
self.system.qd[:] = 0.0
# initial conditions
if qm0 is not None: # initial modal amplitudes
self.system.q[self.blade1.istrain] = qm0
self.system.q[self.blade2.istrain] = qm0
self.system.q[self.blade3.istrain] = qm0
self.system.qd[self.bearing.istrain][0] = spin
# simulate
self.t, self.y = self.integ.integrate(t1, dt)
for i, lab in enumerate(self.integ.labels()):
print "%2d %s" % (i, lab)
return self.t, self.y
def lin(self, qm0=None, spin=10.0):
# reset
self.system.q[:] = 0.0
self.system.qd[:] = 0.0
# initial conditions
if qm0 is not None: # initial modal amplitudes
self.system.q[self.blade1.istrain] = qm0
self.system.q[self.blade2.istrain] = qm0
self.system.q[self.blade3.istrain] = qm0
else:
qm0 = np.zeros(self.blade1._nstrain * 3)
self.system.prescribe(self.bearing, vel=spin, acc=0.0)
self.system.qd[self.bearing.istrain][0] = spin
linsys = linearisation.LinearisedSystem(self.system, qm0)
return linsys
def ani(self, t=None, y=None, planview=True):
if t is None: t = self.t
if y is None: y = self.y
l = 40
if planview:
return dynvis.anim(self.system, t, y, (1, 2), (-l, l), (-l, l))
else:
return dynvis.anim(self.system, t, y, (0, 1), (-l, l), (-5, 5))
some demographic stuff
demo = initial total population of each node
tot_pop total population of the graph
then the dynamical system is initialized with the varaible F
avg_population will be used in the evolution as an "escape parameter" in the markov process
see dynamics.py
"""
demo = np.sum(Z0, 1).astype(int)
tot_pop = np.sum(demo)
avg_pop = tot_pop / communities
print("Total initial populaiton: ", tot_pop)
F = System(Z0)
print(" ========= NET =========")
"""
this section builds the network matrix containing the weights
they are initialized randomly with uniform distribution
and then normalized in the tranport.py file in order to build the transport process
network is a sparse scipy matrix, the networkx stuff is just for visualization
see mat.py
"""
#network = random_network(communities,6000)
network = scale_free_network(communities)
G = nx.Graph(network)
# Modal element using data from Bladed model
print "Loading modes from '%s'..." % bladedpath
modes = ModalRepresentation.from_Bladed(bladedpath+'.$pj')
rotorspeed = 10 * np.pi/30 # 10 rpm
overhang = 1 # 1m
# Modal element
yaw = Hinge('yaw', [0,0,1])
overhang = RigidConnection('overhang', [-overhang,0,0])
bearing = Hinge('bearing', [1,0,0],np.dot(rotmat_y(-np.pi/2), rotmat_x(-np.pi/2)))
el = ModalElement('el', modes)
yaw.add_leaf(overhang)
overhang.add_leaf(bearing)
bearing.add_leaf(el)
system = System(yaw)
# Prescribe rotation speed
system.prescribe(bearing.istrain, 0.0)
system.qd[bearing.istrain] = rotorspeed
# Prescribed yaw angle
acc_period = 0.1
yaw_time1 = 3.0
yaw_time2 = 6.0
dvyaw = 10 * np.pi/180
system.prescribe(yaw.istrain,
acc=lambda t: (t>=yaw_time1 and t<(yaw_time1+acc_period)) and dvyaw/acc_period or 0 +\
(t>yaw_time2 and t<=(yaw_time2+acc_period)) and -dvyaw/acc_period or 0)
system.find_equilibrium()
#loading = PointLoading(blade, wind_table, None)
thrust_time = [0, 1, 2, 10]
thrust_force = [0, 0, 10e3, 10e3]
thrust = np.c_[thrust_force, np.zeros((4, 2))].T
loadfunc = scipy.interpolate.interp1d(thrust_time, thrust)
# Modal element
base = RigidConnection('base', rotation=rotmat_y(-np.pi / 2))
el = ModalElement('el', modes, distal=True, damping_freqs=[8.269, 10.248])
rna = RigidBody('rna',
24000,
np.diag([6400003, 6400003, 4266667]),
nodal_load=loadfunc)
base.add_leaf(el)
el.add_leaf(rna)
system = System(base)
integ = Integrator(system)
integ.add_output(el.output_deflections())
integ.add_output(el.output_rotations())
integ.add_output(dynamics.LoadOutput(rna.iprox))
linsys = LinearisedSystem(system)
def ani_xy(s, t, y):
return dynvis.anim(s, t, y, (0, 1), (-5, 45), (-5, 5), velocities=False)
def ani_xz(s, t, y):
return dynvis.anim(s, t, y, (0, 2), (-5, 45), (-5, 5), velocities=False)
def __init__(self, bladed_file, root_length=0):
# Load modes but use a simple flapped blade
print "Loading modes from '%s'..." % bladed_file
self.blade = Blade(bladed_file)
self.tower = Tower(bladed_file)
self.modes = self.blade.modal_rep()
# Calculate equivalent blade properties
I1 = self.modes.I0[0]
I2 = self.modes.J0[0, 0]
print I1, I2
wflap = self.modes.freqs[0]
bmass = self.modes.mass
inertia = self.modes.inertia_tensor(np.zeros(len(self.modes.freqs)))
Xc = [I1 / bmass, 0, 0]
kflap = I2 * wflap**2
Ry = rotmat_y(-pi / 2)
Rhb1 = rotmat_x(0 * 2 * pi / 3)
Rhb2 = rotmat_x(1 * 2 * pi / 3)
Rhb3 = rotmat_x(2 * 2 * pi / 3)
self.base = FreeJoint('base')
self.towerlink = RigidConnection('tower', [0, 0, self.tower.hubheight])
self.bearing = Hinge('bearing', [1, 0, 0])
root1 = RigidConnection('root1', root_length * np.dot(Rhb1, [0, 0, 1]),
dot(Rhb1, Ry))
root2 = RigidConnection('root2', root_length * np.dot(Rhb2, [0, 0, 1]),
dot(Rhb2, Ry))
root3 = RigidConnection('root3', root_length * np.dot(Rhb3, [0, 0, 1]),
dot(Rhb3, Ry))
self.flap1 = Hinge('flap1', [0, 1, 0])
self.flap2 = Hinge('flap2', [0, 1, 0])
self.flap3 = Hinge('flap3', [0, 1, 0])
self.blade1 = RigidBody('blade1', bmass, inertia, Xc)
self.blade2 = RigidBody('blade2', bmass, inertia, Xc)
self.blade3 = RigidBody('blade3', bmass, inertia, Xc)
self.flap1.stiffness = self.flap2.stiffness = self.flap3.stiffness = kflap
self.base.add_leaf(self.towerlink)
self.towerlink.add_leaf(self.bearing)
self.bearing.add_leaf(root1)
self.bearing.add_leaf(root2)
self.bearing.add_leaf(root3)
root1.add_leaf(self.flap1)
root2.add_leaf(self.flap2)
root3.add_leaf(self.flap3)
self.flap1.add_leaf(self.blade1)
self.flap2.add_leaf(self.blade2)
self.flap3.add_leaf(self.blade3)
self.system = System(self.base)
# Prescribed DOF accelerations - constant rotor speed
self.base_motion = None
self.base_motion_amp = 0
self.system.prescribe(self.bearing, vel=0)
self.system.prescribe(self.base, vel=0)
# setup integrator
self.integ = Integrator(self.system, ('pos', 'vel', 'acc'))
self.integ.add_output(dynamics.LoadOutput(self.base.iprox))
self.integ.add_output(dynamics.LoadOutput(self.towerlink.iprox))
self.integ.add_output(
dynamics.LoadOutput(self.bearing.iprox, local=True))
self.integ.add_output(
dynamics.LoadOutput(self.bearing.idist[0], local=True))
for b in (self.blade1, self.blade2, self.blade3):
self.integ.add_output(dynamics.LoadOutput(b.iprox, local=True))
for b in (self.blade1, self.blade2, self.blade3):
self.integ.add_output(
dynamics.NodeOutput(b.iprox, local=True, deriv=2))
print "Loading modes from '%s'..." % bladedpath
modes = ModalRepresentation.from_Bladed(bladedpath + '.$pj')
rotorspeed = 10 * np.pi / 30 # 10 rpm
overhang = 1 # 1m
# Modal element
yaw = Hinge('yaw', [0, 0, 1])
overhang = RigidConnection('overhang', [-overhang, 0, 0])
bearing = Hinge('bearing', [1, 0, 0],
np.dot(rotmat_y(-np.pi / 2), rotmat_x(-np.pi / 2)))
el = ModalElement('el', modes)
yaw.add_leaf(overhang)
overhang.add_leaf(bearing)
bearing.add_leaf(el)
system = System(yaw)
# Prescribe rotation speed
system.prescribe(bearing.istrain, 0.0)
system.qd[bearing.istrain] = rotorspeed
# Prescribed yaw angle
acc_period = 0.1
yaw_time1 = 3.0
yaw_time2 = 6.0
dvyaw = 10 * np.pi / 180
system.prescribe(yaw.istrain,
acc=lambda t: (t>=yaw_time1 and t<(yaw_time1+acc_period)) and dvyaw/acc_period or 0 +\
(t>yaw_time2 and t<=(yaw_time2+acc_period)) and -dvyaw/acc_period or 0)
system.find_equilibrium()
class Gyroscope(object):
def __init__(self, length, radius, mass, endmass):
self.length = length
self.radius = radius
self.mass = mass
self.endmass = endmass
Jz = radius**2 / 2
Jxy = (3*radius**2 + length**2) / 12
inertia = mass * np.diag([Jxy, Jxy, Jz])
self.A = mass*Jxy + endmass*(length/2)**2
self.C = mass*Jz
self.pivot = Hinge('pivot', [0,1,0])
self.axis = Hinge('axis', [0,0,1])
self.body = RigidBody('body', mass, inertia)
self.offset = RigidConnection('offset', [0,0,length/2])
self.endbody = RigidBody('end', endmass)
self.pivot.add_leaf(self.axis)
self.axis.add_leaf(self.body)
self.pivot.add_leaf(self.offset)
self.offset.add_leaf(self.endbody)
self.system = System(self.pivot)
# Prescribed DOF accelerations
self.system.prescribe(self.axis, acc=0.0) # constant rotational speed
def applied_torque(self, s):
# applied torque about y axis, Q2
elevation = s.q[self.pivot.istrain][0]
return self.endmass * dynamics.gravity * self.length/2 * np.sin(elevation)
def thetadotdot(self, s):
# acceleration about y axis, thetadotdot
Q2 = self.applied_torque(s)
return Q2 / self.A
def gyro_torque(self, s):
# gyroscopic sideways torque, Q1
spin = s.qd[self.axis.istrain][0] # spin speed
thetadot = s.qd[self.pivot.istrain][0]
return self.C * spin * thetadot
def simulate(self, xpivot=0.0, spin=10.0, t1=1.5, dt=0.01):
# reset
self.system.q [:] = 0.0
self.system.qd[:] = 0.0
# initial conditions
self.system.q [self.pivot.istrain][0] = xpivot # initial elevation
self.system.qd[self.axis .istrain][0] = spin # initial rotation speed
# setup integrator
#self.integ = Integrator(self.system, ('pos','vel','acc'))
self.integ = Integrator(self.system, ())
for istrain in (self.pivot.istrain, self.axis.istrain):
self.integ.add_output(dynamics.StrainOutput(istrain, deriv=0))
self.integ.add_output(dynamics.StrainOutput(istrain, deriv=1))
self.integ.add_output(dynamics.StrainOutput(istrain, deriv=2))
self.integ.add_output(dynamics.LoadOutput(self.pivot.idist[0]))
self.integ.add_output(dynamics.LoadOutput(self.pivot.idist[0], local=True))
self.integ.add_output(dynamics.LoadOutput(self.body.iprox))
self.integ.add_output(dynamics.LoadOutput(self.endbody.iprox))
self.integ.add_output(dynamics.CustomOutput(self.applied_torque, "Q2"))
self.integ.add_output(dynamics.CustomOutput(self.thetadotdot, "thetadotdot"))
self.integ.add_output(dynamics.CustomOutput(self.gyro_torque, "Q1"))
# simulate
if t1 > 0:
self.t,self.y = self.integ.integrate(t1, dt)
def ani(self, vs=1):
l = self.length * 1.1
return dynvis.anim(self.system, self.t, self.y,
(0,vs), (-l,l), (-l,l), velocities=False, only_free=True)
class Rotor(object):
def __init__(self, mode_source_file, root_length=0):
# Modal element using data from Bladed model
print "Loading modes from '%s'..." % mode_source_file
self.modes = ModalRepresentation.from_Bladed(mode_source_file)
Ry = rotmat_y(-pi/2)
Rhb1 = rotmat_x(0 * 2*pi/3)
Rhb2 = rotmat_x(1 * 2*pi/3)
Rhb3 = rotmat_x(2 * 2*pi/3)
self.bearing = Hinge('bearing', [1,0,0])
root1 = RigidConnection('root1', root_length*np.dot(Rhb1,[0,0,1]), dot(Rhb1,Ry))
root2 = RigidConnection('root2', root_length*np.dot(Rhb2,[0,0,1]), dot(Rhb2,Ry))
root3 = RigidConnection('root3', root_length*np.dot(Rhb3,[0,0,1]), dot(Rhb3,Ry))
self.blade1 = ModalElement('blade1', self.modes)
self.blade2 = ModalElement('blade2', self.modes)
self.blade3 = ModalElement('blade3', self.modes)
self.bearing.add_leaf(root1)
self.bearing.add_leaf(root2)
self.bearing.add_leaf(root3)
root1.add_leaf(self.blade1)
root2.add_leaf(self.blade2)
root3.add_leaf(self.blade3)
self.system = System(self.bearing)
# Prescribed DOF accelerations - constant rotor speed
self.system.prescribe(self.bearing.istrain, vel=0.0, acc=0.0)
# setup integrator
self.integ = Integrator(self.system, ('pos','vel'))
self.integ.add_output(dynamics.LoadOutput(self.bearing.iprox))
for b in (self.blade1, self.blade2, self.blade3):
self.integ.add_output(dynamics.LoadOutput(b.iprox, local=True))
for b in (self.blade1, self.blade2, self.blade3):
self.integ.add_output(dynamics.CustomOutput(
lambda s: b.station_positions()[-1], label="{} tip defl".format(b)))
for b in (self.blade1, self.blade2, self.blade3):
self.integ.add_output(dynamics.CustomOutput(
lambda s: dot(b.Rp, b.station_positions()[-1]), label="{} tip pos".format(b)))
def simulate(self, qm0=None, spin=10.0, t1=1.5, dt=0.01):
# reset
self.system.q [:] = 0.0
self.system.qd[:] = 0.0
# initial conditions
if qm0 is not None: # initial modal amplitudes
self.system.q[self.blade1.istrain] = qm0
self.system.q[self.blade2.istrain] = qm0
self.system.q[self.blade3.istrain] = qm0
self.system.prescribe(self.bearing.istrain, vel=spin, acc=0.0)
# simulate
self.t,self.y = self.integ.integrate(t1, dt)
return self.t, self.y
def lin(self, qm0=None, spin=10.0):
# reset
self.system.q [:] = 0.0
self.system.qd[:] = 0.0
# initial conditions
if qm0 is not None: # initial modal amplitudes
self.system.q[self.blade1.istrain] = qm0
self.system.q[self.blade2.istrain] = qm0
self.system.q[self.blade3.istrain] = qm0
else:
qm0 = np.zeros(self.blade1._nstrain * 3)
self.system.prescribe(self.bearing.istrain, vel=spin, acc=0.0)
linsys = linearisation.LinearisedSystem(self.system, qm0)
return linsys
def ani(self, vs=1):
l = 40
return dynvis.anim(self.system, self.t, self.y, (0,vs), (-l,l), (-l,l))
class Rotor(object):
def __init__(self, mode_source_file, root_length=0):
# Modal element using data from Bladed model
print "Loading modes from '%s'..." % mode_source_file
self.modes = ModalRepresentation.from_Bladed(mode_source_file)
self.bearing = Hinge('bearing', [0, 0, 1])
self.offset = RigidConnection('offset', [root_length, 0, 0])
self.blade = ModalElement('blade', self.modes)
self.bearing.add_leaf(self.offset)
self.offset.add_leaf(self.blade)
self.system = System(self.bearing)
# Prescribed DOF accelerations
self.system.prescribe(self.bearing.istrain, vel=0.0,
acc=0.0) # constant spin speed
def simulate(self, qm0, spin=10.0, t1=1.5, dt=0.01):
# reset
self.system.q[:] = 0.0
self.system.qd[:] = 0.0
# initial conditions
self.system.q[self.blade.istrain] = qm0 # initial modal amplitudes
self.system.prescribe(self.bearing.istrain, vel=spin,
acc=0.0) #acc=spin/t1)
# setup integrator
self.integ = Integrator(self.system, ('pos', 'vel'))
self.integ.add_output(dynamics.LoadOutput(self.bearing.iprox))
self.integ.add_output(dynamics.LoadOutput(self.blade.iprox))
self.integ.add_output(dynamics.LoadOutput(self.blade.iprox,
local=True))
self.integ.add_output(
dynamics.CustomOutput(lambda s: self.blade.station_positions()[-1],
label="Tip pos"))
self.integ.add_output(
dynamics.CustomOutput(lambda s: self.blade.quad_stress,
label="Quad stress"))
# simulate
self.t, self.y = self.integ.integrate(t1, dt)
return self.t, self.y
def lin(self, qm0, spin=10.0):
# reset
self.system.q[:] = 0.0
self.system.qd[:] = 0.0
# initial conditions
self.system.q[self.blade.istrain] = qm0 # initial modal amplitudes
self.system.prescribe(self.bearing.istrain, vel=spin,
acc=0.0) # constant speed
linsys = linearisation.LinearisedSystem(self.system, qm0)
return linsys
def ani(self, vs=1):
l = 40
return dynvis.anim(self.system,
self.t,
self.y, (0, vs), (-l, l), (-l, l),
velocities=False,
only_free=True)
# Options
dynamics.OPT_GRAVITY = True
dynamics.OPT_GEOMETRIC_STIFFNESS = False
# Create model
bladed_file = r'C:\Users\Rick Lupton\Dropbox\phd\Bladed\Models\OC3-Hywind_SparBuoy_NREL5MW.prj'
print "Loading modes from '%s'..." % bladed_file
towerdef = Tower(bladed_file)
modes = towerdef.modal_rep()
endmass = 100000
endinertia = 100
el1 = ModalElement('el', modes, distal=False)
system1 = System(el1)
el2 = ModalElement('el', modes, distal=True)
body = RigidBody('body', endmass, inertia=endinertia * np.eye(3))
el2.add_leaf(body)
system2 = System(el2)
integ1 = Integrator(system1)
integ1.add_output(el1.output_positions())
integ2 = Integrator(system2, outputs=('pos', 'vel', 'acc'))
integ2.add_output(el2.output_positions())
integ2.add_output(dynamics.NodeOutput(body.iprox))
integ2.add_output(dynamics.NodeOutput(body.iprox, deriv=2))
integ2.add_output(dynamics.LoadOutput(body.iprox))
integ2.add_output(dynamics.StrainOutput(el2.imult))
class Gyroscope(object):
def __init__(self, length, radius, mass, spin, endmass):
self.length = length
self.radius = radius
self.mass = mass
self.spin = spin
self.endmass = endmass
Jz = radius**2 / 2
Jxy = (3 * radius**2 + length**2) / 12
inertia = mass * np.diag([Jxy, Jxy, Jz])
self.bearing = Hinge('bearing', [0, 0, 1])
self.pivot = Hinge('pivot', [0, 1, 0])
self.axis = Hinge('axis', [0, 0, 1])
self.body = RigidBody('body', mass, inertia)
self.offset = RigidConnection('offset', [0, 0, length / 2])
self.endbody = RigidBody('end', endmass)
self.bearing.add_leaf(self.pivot)
self.pivot.add_leaf(self.axis)
self.axis.add_leaf(self.body)
self.pivot.add_leaf(self.offset)
self.offset.add_leaf(self.endbody)
self.system = System(self.bearing)
# Prescribed DOF accelerations
self.system.prescribe(self.axis, acc=0.0) # constant rotational speed
def simulate(self, xpivot=0.0, vprec=0.0, t1=10, dt=0.05):
# reset
self.system.q[:] = 0.0
self.system.qd[:] = 0.0
# initial conditions
self.system.q[self.pivot.istrain][0] = xpivot # initial elevation
self.system.qd[self.bearing.istrain][0] = vprec # initial azimuth spd
self.system.qd[
self.axis.istrain][0] = self.spin # initial rotation speed
self.integ = Integrator(self.system, ('pos', 'vel'))
self.integ.add_output(dynamics.LoadOutput(self.axis.iprox))
self.integ.add_output(dynamics.LoadOutput(self.pivot.iprox))
self.integ.add_output(dynamics.LoadOutput(self.bearing.iprox))
#integ.add_output(dynamics.CustomOutput(
# lambda s: np.dot(self.axis.mass_vv, self.system.qdd[el.iprox+el.idist]) + \
# np.dot(el.mass_ve, self.system.qdd[el.istrain])))
# simulate
if t1 > 0:
self.t, self.y = self.integ.integrate(t1, dt)
for i, lab in enumerate(self.integ.labels()):
print "%2d %s" % (i, lab)
return self.t, self.y
def ani(self, vs=1):
l = self.length * 1.1
return dynvis.anim(self.system,
self.t,
self.y, (0, vs), (-l, l), (-l, l),
velocities=False)
class Turbine(object):
def __init__(self, bladed_file, root_length=0, rigid=False):
# Modal element using data from Bladed model
print "Loading modes from '%s'..." % bladed_file
self.blade = Blade(bladed_file)
self.tower = Tower(bladed_file)
self.modes = self.blade.modal_rep()
#self.tmodes = self.tower.modal_rep()
Ry = rotmat_y(-pi/2)
Rhb1 = rotmat_x(0 * 2*pi/3)
Rhb2 = rotmat_x(1 * 2*pi/3)
Rhb3 = rotmat_x(2 * 2*pi/3)
self.base = FreeJoint('base')
self.towerlink = RigidConnection('tower', [0,0,self.tower.hubheight])
self.bearing = Hinge('bearing', [1,0,0])
root1 = RigidConnection('root1', root_length*np.dot(Rhb1,[0,0,1]), dot(Rhb1,Ry))
root2 = RigidConnection('root2', root_length*np.dot(Rhb2,[0,0,1]), dot(Rhb2,Ry))
root3 = RigidConnection('root3', root_length*np.dot(Rhb3,[0,0,1]), dot(Rhb3,Ry))
self.blade1 = ModalElement('blade1', self.modes)
self.blade2 = ModalElement('blade2', self.modes)
self.blade3 = ModalElement('blade3', self.modes)
self.base.add_leaf(self.towerlink)
self.towerlink.add_leaf(self.bearing)
self.bearing.add_leaf(root1)
self.bearing.add_leaf(root2)
self.bearing.add_leaf(root3)
root1.add_leaf(self.blade1)
root2.add_leaf(self.blade2)
root3.add_leaf(self.blade3)
self.system = System(self.base)
# Prescribed DOF accelerations - constant rotor speed
self.base_motion = None
self.base_motion_amp = 0
self.system.prescribe(self.bearing, vel=0)
self.system.prescribe(self.base, vel=0)
if rigid:
for b in (self.blade1, self.blade2, self.blade3):
self.system.prescribe(b, vel=0)
# setup integrator
self.integ = Integrator(self.system, ('pos','vel','acc'))
self.integ.add_output(dynamics.LoadOutput(self.base.iprox))
self.integ.add_output(dynamics.LoadOutput(self.towerlink.iprox))
self.integ.add_output(dynamics.LoadOutput(self.bearing.iprox))
for b in (self.blade1, self.blade2, self.blade3):
self.integ.add_output(dynamics.LoadOutput(b.iprox, local=True))
for b in (self.blade1, self.blade2, self.blade3):
self.integ.add_output(b.output_deflections())
for b in (self.blade1, self.blade2, self.blade3):
self.integ.add_output(b.output_positions())
for b in (self.blade1, self.blade2, self.blade3):
self.integ.add_output(dynamics.NodeOutput(b.iprox, local=True, deriv=2))
@property
def mass(self):
"""Total mass of turbine"""
return self.tower.total_mass + self.modes.mass * 3
@property
def inertia(self):
"""Total rotational inertia of turbine about base"""
inertia = self.tower.total_inertia
inertia[(0,1),(0,1)] = self.modes.mass * 3 * self.tower.hubheight
return inertia
# XXX neglecting rotor rotational inertia
def set_base_motion(self, dof, w, amp):
self.base_motion = dof
self.base_motion_amp = amp
self.system.prescribe(self.base, part=dof,
vel=lambda t: -w *amp*np.sin(w*t),
acc=lambda t: -w**2*amp*np.cos(w*t))
def set_initial_conditions(self, qm0=None, az0=None, rotor_speed=None):
# initial conditions
if qm0 is not None: # initial modal amplitudes
self.system.q[self.blade1.istrain] = qm0
self.system.q[self.blade2.istrain] = qm0
self.system.q[self.blade3.istrain] = qm0
if az0 is not None:
self.system.q[self.bearing.istrain][0] = az0
if self.base_motion is not None:
self.system.q[self.base.istrain][self.base_motion] = self.base_motion_amp
if rotor_speed is not None:
self.system.prescribe(self.bearing, vel=rotor_speed)
def simulate(self, qm0=None, az0=0.0, rotor_speed=10.0, t1=None,
dt=0.01, t0=0.0, init=False):
# reset
self.system.q [:] = 0.0
self.system.qd[:] = 0.0
self.set_initial_conditions(qm0, az0, rotor_speed)
if t1 is None:
t1 = 4*pi/rotor_speed if (rotor_speed != 0.0) else 2
if init:
self.system.find_equilibrium()
# simulate
self.t,self.y = self.integ.integrate(t1, dt, t0)
for i,lab in enumerate(self.integ.labels()):
print "%2d %s" % (i,lab)
return self.t, self.y
def lin(self, qm0=None, az0=None, rotor_speed=None, init=False):
# reset
self.system.q [:] = 0.0
self.system.qd[:] = 0.0
self.set_initial_conditions(qm0, az0, rotor_speed)
if init:
self.system.find_equilibrium()
linsys = linearisation.LinearisedSystem(self.system)
return linsys
def ani(self, vs=(0,1), t=None, y=None):
if t is None: t = self.t
if y is None: y = self.y
limits = [(-10,10), (-42,42), (-5,110)]
return dynvis.anim(self.system, t, y, vs, limits[vs[0]], limits[vs[1]])
import numpy as np
from scipy.linalg import eig
import matplotlib.pyplot as plt
import dynamics
from dynamics import System, ModalElement, solve_system
from linearisation import LinearisedSystem, ModalRepresentation
import dynvis
dynamics.gravity = 0
# Modal element using data from Bladed model
print "Loading modes from 'demo_a.prj'..."
modes = ModalRepresentation.from_Bladed('demo_a_simplified.prj')
el = ModalElement('el', modes)
system = System(el)
# Linearise system and find modes - should match with original
print "Linearising..."
linsys = LinearisedSystem(system)
w, v = eig(linsys.K, linsys.M)
order = np.argsort(w)
w = np.sqrt(np.real(w[order]))
f = w / 2 / np.pi
v = v[:, order]
# Check that modes come out matching what went in
assert np.allclose(modes.freqs, w), "Linearised freqs should match"
ventries = np.nonzero(abs(v) > 1e-2)[0]
assert len(ventries) == len(w) and (ventries == np.arange(4)).all(), \
"Modes should be orthogonal"
class Turbine(object):
def __init__(self, bladed_file, root_length=0, rigid=False):
# Modal element using data from Bladed model
print "Loading modes from '%s'..." % bladed_file
self.blade = Blade(bladed_file)
self.tower = Tower(bladed_file)
self.modes = self.blade.modal_rep()
Ry = rotmat_y(-pi / 2)
Rhb1 = rotmat_x(0 * 2 * pi / 3)
Rhb2 = rotmat_x(1 * 2 * pi / 3)
Rhb3 = rotmat_x(2 * 2 * pi / 3)
self.base = FreeJoint('base')
self.towerlink = RigidConnection('tower', [0, 0, self.tower.hubheight])
self.bearing = Hinge('bearing', [1, 0, 0])
root1 = RigidConnection('root1', root_length * np.dot(Rhb1, [0, 0, 1]),
dot(Rhb1, Ry))
root2 = RigidConnection('root2', root_length * np.dot(Rhb2, [0, 0, 1]),
dot(Rhb2, Ry))
root3 = RigidConnection('root3', root_length * np.dot(Rhb3, [0, 0, 1]),
dot(Rhb3, Ry))
self.blade1 = ModalElement('blade1', self.modes)
self.blade2 = ModalElement('blade2', self.modes)
self.blade3 = ModalElement('blade3', self.modes)
self.base.add_leaf(self.towerlink)
self.towerlink.add_leaf(self.bearing)
self.bearing.add_leaf(root1)
self.bearing.add_leaf(root2)
self.bearing.add_leaf(root3)
root1.add_leaf(self.blade1)
root2.add_leaf(self.blade2)
root3.add_leaf(self.blade3)
self.system = System(self.base)
# Prescribed DOF accelerations - constant rotor speed
self.base_motion = None
self.base_motion_amp = 0
self.system.prescribe(self.bearing, vel=0)
self.system.prescribe(self.base, vel=0)
if rigid:
for b in (self.blade1, self.blade2, self.blade3):
self.system.prescribe(b, vel=0)
# setup integrator
self.integ = Integrator(self.system, ('pos', 'vel', 'acc'))
self.integ.add_output(dynamics.LoadOutput(self.base.iprox))
self.integ.add_output(dynamics.LoadOutput(self.towerlink.iprox))
self.integ.add_output(
dynamics.LoadOutput(self.bearing.iprox, local=True))
self.integ.add_output(
dynamics.LoadOutput(self.bearing.idist[0], local=True))
for b in (self.blade1, self.blade2, self.blade3):
self.integ.add_output(dynamics.LoadOutput(b.iprox, local=True))
for b in (self.blade1, self.blade2, self.blade3):
self.integ.add_output(b.output_deflections())
for b in (self.blade1, self.blade2, self.blade3):
self.integ.add_output(b.output_positions())
for b in (self.blade1, self.blade2, self.blade3):
self.integ.add_output(
dynamics.NodeOutput(b.iprox, local=True, deriv=2))
def set_base_motion(self, dof, w, amp):
self.base_motion = dof
self.base_motion_amp = amp
self.system.prescribe(self.base,
part=dof,
vel=lambda t: -w * amp * np.sin(w * t),
acc=lambda t: -w**2 * amp * np.cos(w * t))
def set_initial_conditions(self, qm0=None, az0=None, rotor_speed=None):
# initial conditions
if qm0 is not None: # initial modal amplitudes
self.system.q[self.blade1.istrain] = qm0
self.system.q[self.blade2.istrain] = qm0
self.system.q[self.blade3.istrain] = qm0
if az0 is not None:
self.system.q[self.bearing.istrain][0] = az0
if self.base_motion is not None:
self.system.q[self.base.istrain][
self.base_motion] = self.base_motion_amp
if rotor_speed is not None:
self.system.prescribe(self.bearing, vel=rotor_speed)
def simulate(self,
qm0=None,
az0=0.0,
rotor_speed=10.0,
t1=None,
dt=0.01,
t0=0.0,
init=False):
# reset
self.system.q[:] = 0.0
self.system.qd[:] = 0.0
self.set_initial_conditions(qm0, az0, rotor_speed)
if t1 is None:
t1 = 4 * pi / rotor_speed if (rotor_speed != 0.0) else 2
if init:
self.system.find_equilibrium()
# simulate
t, y = self.integ.integrate(t1, dt, t0)
#for i,lab in enumerate(self.integ.labels):
# print "%2d %s" % (i,lab)
#return self.t, self.y
# Build results structure
results = TurbineResults(t, y, self.modes.mode_names)
return results
def lin(self, qm0=None, az0=None, rotor_speed=None, init=False):
# reset
self.system.q[:] = 0.0
self.system.qd[:] = 0.0
self.set_initial_conditions(qm0, az0, rotor_speed)
if init:
self.system.find_equilibrium()
# need initial amplitudes for linearisation point
if qm0 is None:
qm0 = self.system.q[self.blade1.istrain]
linsys = linearisation.LinearisedSystem(self.system, np.tile(qm0, 3))
return linsys
def ani(self, results, x=0, y=1):
H = self.tower.hubheight + self.blade.radii[-1]
limits = [(-H, H), (-H, H), (-5, H + 5)]
return dynvis.anim(self.system, results.t, results.strains.as_matrix(),
(x, y), limits[x], limits[y])
modes = ModalRepresentation.from_Bladed(path_damped+'.$pj')
print "Loading modes from '%s'..." % path_undamped
modes0 = ModalRepresentation.from_Bladed(path_undamped+'.$pj')
# Blade loading
wind_table = np.array([
[0, 1, 2, 10], # time
[0, 0, 0, 0 ], # x
[0, 0, 20, 20], # y
[0, 0, 0, 0 ], # z
])
loading = BladeLoading(modes.x, wind_table, None)
# Modal element
el = ModalElement('el', modes, loading)
system = System(el)
el0 = ModalElement('el0', modes0, loading)
system0 = System(el0)
integ = Integrator(system)
integ0 = Integrator(system0)
integ.add_output(el.output_positions(stations=[16,32]))
integ0.add_output(el0.output_positions(stations=[16,32]))
#def simulate(system, t1=2.0, dt=0.005):
# Load Bladed data for comparison
import pybladed.data
brun = pybladed.data.BladedRun(path_damped)
bladed_defl = np.c_[
brun.get('blade 1 x-deflection;2'),
class Rotor(object):
def __init__(self, mode_source_file, root_length=0):
# Modal element using data from Bladed model
print "Loading modes from '%s'..." % mode_source_file
self.modes = ModalRepresentation.from_Bladed(mode_source_file)
Ry = rotmat_y(-pi / 2)
Rhb1 = rotmat_x(0 * 2 * pi / 3)
Rhb2 = rotmat_x(1 * 2 * pi / 3)
Rhb3 = rotmat_x(2 * 2 * pi / 3)
self.bearing = Hinge('bearing', [1, 0, 0])
root1 = RigidConnection('root1', root_length * np.dot(Rhb1, [0, 0, 1]),
dot(Rhb1, Ry))
root2 = RigidConnection('root2', root_length * np.dot(Rhb2, [0, 0, 1]),
dot(Rhb2, Ry))
root3 = RigidConnection('root3', root_length * np.dot(Rhb3, [0, 0, 1]),
dot(Rhb3, Ry))
self.blade1 = ModalElement('blade1', self.modes)
self.blade2 = ModalElement('blade2', self.modes)
self.blade3 = ModalElement('blade3', self.modes)
self.bearing.add_leaf(root1)
self.bearing.add_leaf(root2)
self.bearing.add_leaf(root3)
root1.add_leaf(self.blade1)
root2.add_leaf(self.blade2)
root3.add_leaf(self.blade3)
self.system = System(self.bearing)
# Prescribed DOF accelerations - constant rotor speed
self.system.prescribe(self.bearing.istrain, vel=0.0, acc=0.0)
# setup integrator
self.integ = Integrator(self.system, ('pos', 'vel'))
self.integ.add_output(dynamics.LoadOutput(self.bearing.iprox))
for b in (self.blade1, self.blade2, self.blade3):
self.integ.add_output(dynamics.LoadOutput(b.iprox, local=True))
for b in (self.blade1, self.blade2, self.blade3):
self.integ.add_output(
dynamics.CustomOutput(lambda s: b.station_positions()[-1],
label="{} tip defl".format(b)))
for b in (self.blade1, self.blade2, self.blade3):
self.integ.add_output(
dynamics.CustomOutput(lambda s: dot(b.Rp,
b.station_positions()[-1]),
label="{} tip pos".format(b)))
def simulate(self, qm0=None, spin=10.0, t1=1.5, dt=0.01):
# reset
self.system.q[:] = 0.0
self.system.qd[:] = 0.0
# initial conditions
if qm0 is not None: # initial modal amplitudes
self.system.q[self.blade1.istrain] = qm0
self.system.q[self.blade2.istrain] = qm0
self.system.q[self.blade3.istrain] = qm0
self.system.prescribe(self.bearing.istrain, vel=spin, acc=0.0)
# simulate
self.t, self.y = self.integ.integrate(t1, dt)
return self.t, self.y
def lin(self, qm0=None, spin=10.0):
# reset
self.system.q[:] = 0.0
self.system.qd[:] = 0.0
# initial conditions
if qm0 is not None: # initial modal amplitudes
self.system.q[self.blade1.istrain] = qm0
self.system.q[self.blade2.istrain] = qm0
self.system.q[self.blade3.istrain] = qm0
else:
qm0 = np.zeros(self.blade1._nstrain * 3)
self.system.prescribe(self.bearing.istrain, vel=spin, acc=0.0)
linsys = linearisation.LinearisedSystem(self.system, qm0)
return linsys
def ani(self, vs=1):
l = 40
return dynvis.anim(self.system, self.t, self.y, (0, vs), (-l, l),
(-l, l))
class FlappedBladeTurbine(object):
def __init__(self, bladed_file, root_length=0):
# Load modes but use a simple flapped blade
print "Loading modes from '%s'..." % bladed_file
self.blade = Blade(bladed_file)
self.tower = Tower(bladed_file)
self.modes = self.blade.modal_rep()
# Calculate equivalent blade properties
I1 = self.modes.I0[0]
I2 = self.modes.J0[0,0]
print I1, I2
wflap = self.modes.freqs[0]
bmass = self.modes.mass
inertia = self.modes.inertia_tensor(np.zeros(len(self.modes.freqs)))
Xc = [I1 / bmass, 0, 0]
kflap = I2 * wflap**2
Ry = rotmat_y(-pi/2)
Rhb1 = rotmat_x(0 * 2*pi/3)
Rhb2 = rotmat_x(1 * 2*pi/3)
Rhb3 = rotmat_x(2 * 2*pi/3)
self.base = FreeJoint('base')
self.towerlink = RigidConnection('tower', [0,0,self.tower.hubheight])
self.bearing = Hinge('bearing', [1,0,0])
root1 = RigidConnection('root1', root_length*np.dot(Rhb1,[0,0,1]), dot(Rhb1,Ry))
root2 = RigidConnection('root2', root_length*np.dot(Rhb2,[0,0,1]), dot(Rhb2,Ry))
root3 = RigidConnection('root3', root_length*np.dot(Rhb3,[0,0,1]), dot(Rhb3,Ry))
self.flap1 = Hinge('flap1', [0,1,0])
self.flap2 = Hinge('flap2', [0,1,0])
self.flap3 = Hinge('flap3', [0,1,0])
self.blade1 = RigidBody('blade1', bmass, inertia, Xc)
self.blade2 = RigidBody('blade2', bmass, inertia, Xc)
self.blade3 = RigidBody('blade3', bmass, inertia, Xc)
self.flap1.stiffness = self.flap2.stiffness = self.flap3.stiffness = kflap
self.base.add_leaf(self.towerlink)
self.towerlink.add_leaf(self.bearing)
self.bearing.add_leaf(root1)
self.bearing.add_leaf(root2)
self.bearing.add_leaf(root3)
root1.add_leaf(self.flap1)
root2.add_leaf(self.flap2)
root3.add_leaf(self.flap3)
self.flap1.add_leaf(self.blade1)
self.flap2.add_leaf(self.blade2)
self.flap3.add_leaf(self.blade3)
self.system = System(self.base)
# Prescribed DOF accelerations - constant rotor speed
self.base_motion = None
self.base_motion_amp = 0
self.system.prescribe(self.bearing, vel=0)
self.system.prescribe(self.base, vel=0)
# setup integrator
self.integ = Integrator(self.system, ('pos','vel','acc'))
self.integ.add_output(dynamics.LoadOutput(self.base.iprox))
self.integ.add_output(dynamics.LoadOutput(self.towerlink.iprox))
self.integ.add_output(dynamics.LoadOutput(self.bearing.iprox, local=True))
self.integ.add_output(dynamics.LoadOutput(self.bearing.idist[0], local=True))
for b in (self.blade1, self.blade2, self.blade3):
self.integ.add_output(dynamics.LoadOutput(b.iprox, local=True))
for b in (self.blade1, self.blade2, self.blade3):
self.integ.add_output(dynamics.NodeOutput(b.iprox, local=True, deriv=2))
def set_base_motion(self, dof, w, amp):
self.base_motion = dof
self.base_motion_amp = amp
self.system.prescribe(self.base, part=dof,
vel=lambda t: -w *amp*np.sin(w*t),
acc=lambda t: -w**2*amp*np.cos(w*t))
def set_initial_conditions(self, qm0=None, az0=None, rotor_speed=None):
# initial conditions
if qm0 is not None: # initial hinge angle
self.system.q[self.flap1.istrain][0] = qm0
self.system.q[self.flap2.istrain][0] = qm0
self.system.q[self.flap3.istrain][0] = qm0
if az0 is not None:
self.system.q[self.bearing.istrain][0] = az0
if self.base_motion is not None:
self.system.q[self.base.istrain][self.base_motion] = self.base_motion_amp
if rotor_speed is not None:
self.system.prescribe(self.bearing, vel=rotor_speed)
def simulate(self, qm0=None, az0=0.0, rotor_speed=10.0, t1=None,
dt=0.01, t0=0.0, init=False):
# reset
self.system.q [:] = 0.0
self.system.qd[:] = 0.0
self.set_initial_conditions(qm0, az0, rotor_speed)
if t1 is None:
t1 = 4*pi/rotor_speed if (rotor_speed != 0.0) else 2
if init:
self.system.find_equilibrium()
# simulate
t,y = self.integ.integrate(t1, dt, t0)
#for i,lab in enumerate(self.integ.labels):
# print "%2d %s" % (i,lab)
#return self.t, self.y
# Build results structure
results = FlappedTurbineResults(t, y)
return results
def lin(self, qm0=None, az0=None, rotor_speed=None, init=False):
# reset
self.system.q [:] = 0.0
self.system.qd[:] = 0.0
self.set_initial_conditions(qm0, az0, rotor_speed)
if init:
self.system.find_equilibrium()
# need initial amplitudes for linearisation point
if qm0 is None:
qm0 = self.system.q[self.blade1.istrain]
linsys = linearisation.LinearisedSystem(self.system, np.tile(qm0, 3))
return linsys
def ani(self, results, x=0, y=1):
H = self.tower.hubheight + self.blade.radii[-1]
limits = [(-H,H), (-H,H), (-5,H+5)]
return dynvis.anim(self.system, results.t, results.strains.as_matrix(),
(x, y), limits[x], limits[y])
b1 = EulerBeam('b1',blade_length, 250, 1000e6, EIy, EIz, 200e6)
b2 = EulerBeam('b2',blade_length, 250, 1000e6, EIy, EIz, 200e6)
b3 = EulerBeam('b3',blade_length, 250, 1000e6, EIy, EIz, 200e6)
tower.damping = 0.05
foundation.add_leaf(tower)
tower.add_leaf(nacelle)
nacelle.add_leaf(bearing)
bearing.add_leaf(hb1)
bearing.add_leaf(hb2)
bearing.add_leaf(hb3)
hb1.add_leaf(b1)
hb2.add_leaf(b2)
hb3.add_leaf(b3)
system = System(foundation)
def thrust(xp, xd, xstrain, vp, vd, vstrain):
f = zeros(NQD * 2)
f[6] = -70000
return f
def test1():
# Initial conditions
system.qd[bearing.istrain[0]] = -10 * pi/180
# Prescribed DOFs
#system.prescribe(foundation.istrain, 0.0)
system.prescribe(tower.istrain, 0.0)
system.prescribe(bearing.istrain, 0.0)
system.prescribe(b1.istrain, 0.0)
bladed_defl = np.c_[brun.get("Nacelle fore-aft displacement"), brun.get("Nacelle nod angle")]
# loading = PointLoading(blade, wind_table, None)
thrust_time = [0, 1, 2, 10]
thrust_force = [0, 0, 10e3, 10e3]
thrust = np.c_[thrust_force, np.zeros((4, 2))].T
loadfunc = scipy.interpolate.interp1d(thrust_time, thrust)
# Modal element
base = RigidConnection("base", rotation=rotmat_y(-np.pi / 2))
el = DistalModalElement("el", modes, distal=True, damping_freqs=modes2.freqs)
# el = ModalElement('el', modes, distal=True, damping_freqs=modes2.freqs)
rna = RigidBody("rna", 24000, np.diag([6400003, 6400003, 4266667]), nodal_load=loadfunc)
base.add_leaf(el)
el.add_leaf(rna)
system = System(base)
system.prescribe(el, vel=0, part=[0, 3])
integ = Integrator(system)
integ.add_output(el.output_deflections())
integ.add_output(el.output_rotations())
integ.add_output(dynamics.LoadOutput(rna.iprox))
linsys = LinearisedSystem(system)
def ani_xy(s, t, y):
return dynvis.anim(s, t, y, (0, 1), (-5, 45), (-5, 5), velocities=False)
def __init__(self, bladed_file, root_length=0):
# Load modes but use a simple flapped blade
print "Loading modes from '%s'..." % bladed_file
self.blade = Blade(bladed_file)
self.tower = Tower(bladed_file)
self.modes = self.blade.modal_rep()
# Calculate equivalent blade properties
I1 = self.modes.I0[0]
I2 = self.modes.J0[0,0]
print I1, I2
wflap = self.modes.freqs[0]
bmass = self.modes.mass
inertia = self.modes.inertia_tensor(np.zeros(len(self.modes.freqs)))
Xc = [I1 / bmass, 0, 0]
kflap = I2 * wflap**2
Ry = rotmat_y(-pi/2)
Rhb1 = rotmat_x(0 * 2*pi/3)
Rhb2 = rotmat_x(1 * 2*pi/3)
Rhb3 = rotmat_x(2 * 2*pi/3)
self.base = FreeJoint('base')
self.towerlink = RigidConnection('tower', [0,0,self.tower.hubheight])
self.bearing = Hinge('bearing', [1,0,0])
root1 = RigidConnection('root1', root_length*np.dot(Rhb1,[0,0,1]), dot(Rhb1,Ry))
root2 = RigidConnection('root2', root_length*np.dot(Rhb2,[0,0,1]), dot(Rhb2,Ry))
root3 = RigidConnection('root3', root_length*np.dot(Rhb3,[0,0,1]), dot(Rhb3,Ry))
self.flap1 = Hinge('flap1', [0,1,0])
self.flap2 = Hinge('flap2', [0,1,0])
self.flap3 = Hinge('flap3', [0,1,0])
self.blade1 = RigidBody('blade1', bmass, inertia, Xc)
self.blade2 = RigidBody('blade2', bmass, inertia, Xc)
self.blade3 = RigidBody('blade3', bmass, inertia, Xc)
self.flap1.stiffness = self.flap2.stiffness = self.flap3.stiffness = kflap
self.base.add_leaf(self.towerlink)
self.towerlink.add_leaf(self.bearing)
self.bearing.add_leaf(root1)
self.bearing.add_leaf(root2)
self.bearing.add_leaf(root3)
root1.add_leaf(self.flap1)
root2.add_leaf(self.flap2)
root3.add_leaf(self.flap3)
self.flap1.add_leaf(self.blade1)
self.flap2.add_leaf(self.blade2)
self.flap3.add_leaf(self.blade3)
self.system = System(self.base)
# Prescribed DOF accelerations - constant rotor speed
self.base_motion = None
self.base_motion_amp = 0
self.system.prescribe(self.bearing, vel=0)
self.system.prescribe(self.base, vel=0)
# setup integrator
self.integ = Integrator(self.system, ('pos','vel','acc'))
self.integ.add_output(dynamics.LoadOutput(self.base.iprox))
self.integ.add_output(dynamics.LoadOutput(self.towerlink.iprox))
self.integ.add_output(dynamics.LoadOutput(self.bearing.iprox, local=True))
self.integ.add_output(dynamics.LoadOutput(self.bearing.idist[0], local=True))
for b in (self.blade1, self.blade2, self.blade3):
self.integ.add_output(dynamics.LoadOutput(b.iprox, local=True))
for b in (self.blade1, self.blade2, self.blade3):
self.integ.add_output(dynamics.NodeOutput(b.iprox, local=True, deriv=2))
class Turbine(object):
def __init__(self, bladed_file, root_length=0, rigid=False):
# Modal element using data from Bladed model
print "Loading modes from '%s'..." % bladed_file
self.blade = Blade(bladed_file)
self.tower = Tower(bladed_file)
self.modes = self.blade.modal_rep()
Ry = rotmat_y(-pi/2)
Rhb1 = rotmat_x(0 * 2*pi/3)
Rhb2 = rotmat_x(1 * 2*pi/3)
Rhb3 = rotmat_x(2 * 2*pi/3)
self.base = FreeJoint('base')
self.towerlink = RigidConnection('tower', [0,0,self.tower.hubheight])
self.bearing = Hinge('bearing', [1,0,0])
root1 = RigidConnection('root1', root_length*np.dot(Rhb1,[0,0,1]), dot(Rhb1,Ry))
root2 = RigidConnection('root2', root_length*np.dot(Rhb2,[0,0,1]), dot(Rhb2,Ry))
root3 = RigidConnection('root3', root_length*np.dot(Rhb3,[0,0,1]), dot(Rhb3,Ry))
self.blade1 = ModalElement('blade1', self.modes)
self.blade2 = ModalElement('blade2', self.modes)
self.blade3 = ModalElement('blade3', self.modes)
self.base.add_leaf(self.towerlink)
self.towerlink.add_leaf(self.bearing)
self.bearing.add_leaf(root1)
self.bearing.add_leaf(root2)
self.bearing.add_leaf(root3)
root1.add_leaf(self.blade1)
root2.add_leaf(self.blade2)
root3.add_leaf(self.blade3)
self.system = System(self.base)
# Prescribed DOF accelerations - constant rotor speed
self.base_motion = None
self.base_motion_amp = 0
self.system.prescribe(self.bearing, vel=0)
self.system.prescribe(self.base, vel=0)
if rigid:
for b in (self.blade1, self.blade2, self.blade3):
self.system.prescribe(b, vel=0)
# setup integrator
self.integ = Integrator(self.system, ('pos','vel','acc'))
self.integ.add_output(dynamics.LoadOutput(self.base.iprox))
self.integ.add_output(dynamics.LoadOutput(self.towerlink.iprox))
self.integ.add_output(dynamics.LoadOutput(self.bearing.iprox, local=True))
self.integ.add_output(dynamics.LoadOutput(self.bearing.idist[0], local=True))
for b in (self.blade1, self.blade2, self.blade3):
self.integ.add_output(dynamics.LoadOutput(b.iprox, local=True))
for b in (self.blade1, self.blade2, self.blade3):
self.integ.add_output(b.output_deflections())
for b in (self.blade1, self.blade2, self.blade3):
self.integ.add_output(b.output_positions())
for b in (self.blade1, self.blade2, self.blade3):
self.integ.add_output(dynamics.NodeOutput(b.iprox, local=True, deriv=2))
def set_base_motion(self, dof, w, amp):
self.base_motion = dof
self.base_motion_amp = amp
self.system.prescribe(self.base, part=dof,
vel=lambda t: -w *amp*np.sin(w*t),
acc=lambda t: -w**2*amp*np.cos(w*t))
def set_initial_conditions(self, qm0=None, az0=None, rotor_speed=None):
# initial conditions
if qm0 is not None: # initial modal amplitudes
self.system.q[self.blade1.istrain] = qm0
self.system.q[self.blade2.istrain] = qm0
self.system.q[self.blade3.istrain] = qm0
if az0 is not None:
self.system.q[self.bearing.istrain][0] = az0
if self.base_motion is not None:
self.system.q[self.base.istrain][self.base_motion] = self.base_motion_amp
if rotor_speed is not None:
self.system.prescribe(self.bearing, vel=rotor_speed)
def simulate(self, qm0=None, az0=0.0, rotor_speed=10.0, t1=None,
dt=0.01, t0=0.0, init=False):
# reset
self.system.q [:] = 0.0
self.system.qd[:] = 0.0
self.set_initial_conditions(qm0, az0, rotor_speed)
if t1 is None:
t1 = 4*pi/rotor_speed if (rotor_speed != 0.0) else 2
if init:
self.system.find_equilibrium()
# simulate
t,y = self.integ.integrate(t1, dt, t0)
#for i,lab in enumerate(self.integ.labels):
# print "%2d %s" % (i,lab)
#return self.t, self.y
# Build results structure
results = TurbineResults(t, y, self.modes.mode_names)
return results
def lin(self, qm0=None, az0=None, rotor_speed=None, init=False):
# reset
self.system.q [:] = 0.0
self.system.qd[:] = 0.0
self.set_initial_conditions(qm0, az0, rotor_speed)
if init:
self.system.find_equilibrium()
# need initial amplitudes for linearisation point
if qm0 is None:
qm0 = self.system.q[self.blade1.istrain]
linsys = linearisation.LinearisedSystem(self.system, np.tile(qm0, 3))
return linsys
def ani(self, results, x=0, y=1):
H = self.tower.hubheight + self.blade.radii[-1]
limits = [(-H,H), (-H,H), (-5,H+5)]
return dynvis.anim(self.system, results.t, results.strains.as_matrix(),
(x, y), limits[x], limits[y])
def __init__(self, bladed_file, root_length=0, rigid=False):
# Modal element using data from Bladed model
print "Loading modes from '%s'..." % bladed_file
self.blade = Blade(bladed_file)
self.tower = Tower(bladed_file)
self.modes = self.blade.modal_rep()
Ry = rotmat_y(-pi / 2)
Rhb1 = rotmat_x(0 * 2 * pi / 3)
Rhb2 = rotmat_x(1 * 2 * pi / 3)
Rhb3 = rotmat_x(2 * 2 * pi / 3)
self.base = FreeJoint('base')
self.towerlink = RigidConnection('tower', [0, 0, self.tower.hubheight])
self.bearing = Hinge('bearing', [1, 0, 0])
root1 = RigidConnection('root1', root_length * np.dot(Rhb1, [0, 0, 1]),
dot(Rhb1, Ry))
root2 = RigidConnection('root2', root_length * np.dot(Rhb2, [0, 0, 1]),
dot(Rhb2, Ry))
root3 = RigidConnection('root3', root_length * np.dot(Rhb3, [0, 0, 1]),
dot(Rhb3, Ry))
self.blade1 = ModalElement('blade1', self.modes)
self.blade2 = ModalElement('blade2', self.modes)
self.blade3 = ModalElement('blade3', self.modes)
self.base.add_leaf(self.towerlink)
self.towerlink.add_leaf(self.bearing)
self.bearing.add_leaf(root1)
self.bearing.add_leaf(root2)
self.bearing.add_leaf(root3)
root1.add_leaf(self.blade1)
root2.add_leaf(self.blade2)
root3.add_leaf(self.blade3)
self.system = System(self.base)
# Prescribed DOF accelerations - constant rotor speed
self.base_motion = None
self.base_motion_amp = 0
self.system.prescribe(self.bearing, vel=0)
self.system.prescribe(self.base, vel=0)
if rigid:
for b in (self.blade1, self.blade2, self.blade3):
self.system.prescribe(b, vel=0)
# setup integrator
self.integ = Integrator(self.system, ('pos', 'vel', 'acc'))
self.integ.add_output(dynamics.LoadOutput(self.base.iprox))
self.integ.add_output(dynamics.LoadOutput(self.towerlink.iprox))
self.integ.add_output(
dynamics.LoadOutput(self.bearing.iprox, local=True))
self.integ.add_output(
dynamics.LoadOutput(self.bearing.idist[0], local=True))
for b in (self.blade1, self.blade2, self.blade3):
self.integ.add_output(dynamics.LoadOutput(b.iprox, local=True))
for b in (self.blade1, self.blade2, self.blade3):
self.integ.add_output(b.output_deflections())
for b in (self.blade1, self.blade2, self.blade3):
self.integ.add_output(b.output_positions())
for b in (self.blade1, self.blade2, self.blade3):
self.integ.add_output(
dynamics.NodeOutput(b.iprox, local=True, deriv=2))
