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 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 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 __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, 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())
def init(self, rotspeed, ip0, oop0):
# reset
self.system.q[:] = 0.0
self.system.qd[:] = 0.0
# initial conditions
self.system.qd[self.beam.istrain] = [ip0, oop0] # initial OOP angle
# prescribed values
self.system.prescribe(self.bearing.istrain, vel=rotspeed,
acc=0.0) # constant rotational speed
# setup integrator
self.integ = Integrator(self.system, ('pos', 'vel'))
self.integ.add_output(dynamics.LoadOutput(self.beam.iprox, local=True))
# 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 ani_yz(s, t, y):
return dynvis.anim(s,
t,
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 p():
fig = plt.figure()
ax = fig.add_subplot(311)
ax.plot(t, y2[3][:, 2], 'b-', label='With end mass')
ax.plot(t, y1[1][:, 2], 'k--', label='Just beam')
ax.set_ylabel('Z tip defl')
ax = fig.add_subplot(312)
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 __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))