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
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
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
# 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
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
brun = pybladed.data.BladedRun(bladed_path)
thrust = brun.get('rotating hub Fx')
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 = 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)
import pybladed.data
brun = pybladed.data.BladedRun(bladed_path)
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 = ModalElement('el', modes, distal=True, damping_freqs=combined_freqs)
rna = RigidBody('rna',
109993,
np.diag([19406630, 19406630, 38813240]),
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)
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))
if False:
t, y1 = integ1.integrate(20, 0.05)
t, y2 = integ2.integrate(20, 0.05)
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))