def test_rotmats(self):
assert_array_equal(rotmat_x(0), eye(3))
assert_array_equal(rotmat_y(0), eye(3))
assert_array_equal(rotmat_z(0), eye(3))
# Rotate 45 deg about each axis
assert_aae(dot(rotmat_x(pi / 4), [1, 1, 1]), [1, 0, sqrt(2)])
assert_aae(dot(rotmat_y(pi / 4), [1, 1, 1]), [sqrt(2), 1, 0])
assert_aae(dot(rotmat_z(pi / 4), [1, 1, 1]), [0, sqrt(2), 1])
def test_rotmats(self):
assert_array_equal(rotmat_x(0), eye(3))
assert_array_equal(rotmat_y(0), eye(3))
assert_array_equal(rotmat_z(0), eye(3))
# Rotate 45 deg about each axis
assert_aae(dot(rotmat_x(pi / 4), [1, 1, 1]), [1, 0, sqrt(2)])
assert_aae(dot(rotmat_y(pi / 4), [1, 1, 1]), [sqrt(2), 1, 0])
assert_aae(dot(rotmat_z(pi / 4), [1, 1, 1]), [0, sqrt(2), 1])
def test_element_mass_when_rotated_and_offset(self):
Rp = dot(rotmat_y(pi / 5), dot(rotmat_z(-pi / 7),
rotmat_x(3 * pi / 4)))
self.element.rp[:] = [304.3, 12.3, -402.0]
self.element.Rp[:, :] = Rp
self.element.calc_mass()
# Expected values: rod along x axis
m = self.density * self.length
Iy = m * self.length**2 / 3
expected_mass = m * eye(3)
expected_inertia = diag([0, Iy, Iy])
expected_offdiag = zeros((3, 3))
# Y accel -> positive moment about Z
# Z accel -> negative moment about Y
expected_offdiag[2, 1] = m * self.length / 2
expected_offdiag[1, 2] = -m * self.length / 2
transform = lambda A: dot(Rp, dot(A, Rp.T))
assert_aae(expected_mass, transform(expected_mass))
elmass = self.element.mass_vv
assert_aae(elmass[:3, :3], transform(expected_mass))
assert_aae(elmass[3:, 3:], transform(expected_inertia))
assert_aae(elmass[3:, :3], transform(expected_offdiag))
assert_aae(elmass[:3, 3:], transform(expected_offdiag).T)
def test_has_gyroscopic_forces_when_spinning(self):
# When the body is spinning, a torque should cause a
# perpendicular acceleration
# Set up rigid body spinning about x axis, and precessing about z axis
precession = 0.1
spin = 27.3
A = 2.4 # perpendicular inertia
C = 5.7 # polar inertia
b = RigidBody('body', mass=7.04, inertia=diag([A, A, C]))
b.Rp[:, :] = rotmat_y(pi / 2)
b.vp[3:] = [spin, 0, precession]
update_skewmat(b.wps, b.vp[3:])
b.calc_mass()
# Expect moment of momentum to be [C*spin, 0, A*precession] in global
Jp = dot(b.Rp, dot(b.inertia, b.Rp.T))
hp = dot(Jp, b.vp[3:])
assert_array_almost_equal(hp, [C * spin, 0, A * precession])
# Expect the torque to be (precession * spin_speed) * (C - A)
# about the y axis
expected_Q2 = spin * precession * (C - A)
assert_array_almost_equal(b.quad_forces, [0, 0, 0, 0, expected_Q2, 0])
def test_has_gyroscopic_forces_when_spinning(self):
# When the body is spinning, a torque should cause a
# perpendicular acceleration
# Set up rigid body spinning about x axis, and precessing about z axis
precession = 0.1
spin = 27.3
A = 2.4 # perpendicular inertia
C = 5.7 # polar inertia
b = RigidBody("body", mass=7.04, inertia=diag([A, A, C]))
b.Rp[:, :] = rotmat_y(pi / 2)
b.vp[3:] = [spin, 0, precession]
update_skewmat(b.wps, b.vp[3:])
b.calc_mass()
# Expect moment of momentum to be [C*spin, 0, A*precession] in global
Jp = dot(b.Rp, dot(b.inertia, b.Rp.T))
hp = dot(Jp, b.vp[3:])
assert_array_almost_equal(hp, [C * spin, 0, A * precession])
# Expect the torque to be (precession * spin_speed) * (C - A)
# about the y axis
expected_Q2 = spin * precession * (C - A)
assert_array_almost_equal(b.quad_forces, [0, 0, 0, 0, expected_Q2, 0])
def test_element_mass_when_rotated_and_offset(self):
Rp = dot(rotmat_y(pi/5), dot(rotmat_z(-pi/7), rotmat_x(3*pi/4)))
self.element.rp[:] = [304.3, 12.3, -402.0]
self.element.Rp[:, :] = Rp
self.element.calc_mass()
# Expected values: rod along x axis
m = self.density * self.length
Iy = m * self.length**2 / 3
expected_mass = m * eye(3)
expected_inertia = diag([0, Iy, Iy])
expected_offdiag = zeros((3, 3))
# Y accel -> positive moment about Z
# Z accel -> negative moment about Y
expected_offdiag[2, 1] = m * self.length / 2
expected_offdiag[1, 2] = -m * self.length / 2
transform = lambda A: dot(Rp, dot(A, Rp.T))
assert_aae(expected_mass, transform(expected_mass))
elmass = self.element.mass_vv
assert_aae(elmass[:3, :3], transform(expected_mass))
assert_aae(elmass[3:, 3:], transform(expected_inertia))
assert_aae(elmass[3:, :3], transform(expected_offdiag))
assert_aae(elmass[:3, 3:], transform(expected_offdiag).T)
def __init__(self, structure_config):
s = structure_config
#### Load details of flexible elements ####
if "definition" in s["tower"]:
if "mass" in s["tower"]:
raise ValueError("Both tower definition and explicit mass!")
self.tower_definition = Tower(s["tower"]["definition"])
assert np.all(self.tower_definition.stn_pos[:, :2] == 0) # vert.
z_tower = self.tower_definition.stn_pos[:, 2]
self.tower_modes = ModesFromScratch(
z_tower - z_tower[0],
self.tower_definition.density,
1,
self.tower_definition.EIy,
self.tower_definition.EIz,
)
else:
self.tower_definition = None
self.tower_modes = None
if "blade" in s:
self.blade_modes = load_modes_from_Bladed(s["blade"]["definition"])
else:
self.blade_modes = None
#### Create the elements ####
# Free joint represents the rigid-body motion of the platform
free_joint = FreeJoint("base")
# This is the rigid-body mass of the platform structure
conn_platform = RigidConnection("conn-platform", offset=s["platform"]["CoM"])
platform = RigidBody("platform", mass=s["platform"]["mass"], inertia=np.diag(s["platform"]["inertia"]))
free_joint.add_leaf(conn_platform)
conn_platform.add_leaf(platform)
# Make a rigid body to represent the added mass
# (approximate to zero frequency)
# XXX this is skipping the coupling matrix
# A = whales_model.A(0)
# added_mass = RigidBody('added-mass', mass=np.diag(A[:3, :3]),
# inertia=A[3:, 3:])
# Flexible tower or equivalent rigid body
if self.tower_modes:
# move base of tower 10m up, and rotate so tower x-axis is vertical
conn_tower = RigidConnection("conn-tower", offset=[0, 0, z_tower[0]], rotation=rotmat_y(-pi / 2))
tower = DistalModalElementFromScratch("tower", self.tower_modes, s["tower"]["number of normal modes"])
else:
# move tower to COG
conn_tower = RigidConnection("conn-tower", offset=s["tower"]["CoM"])
tower = RigidBody("tower", s["tower"]["mass"], np.diag(s["tower"]["inertia"]))
free_joint.add_leaf(conn_tower)
conn_tower.add_leaf(tower)
# The nacelle -- rigid body
# rotate back so nacelle inertia is aligned with global coordinates
if self.tower_modes:
nacoff = s["nacelle"]["offset from tower top"]
conn_nacelle = RigidConnection(
"conn-nacelle", offset=dot(rotmat_y(pi / 2), nacoff), rotation=rotmat_y(pi / 2)
)
tower.add_leaf(conn_nacelle)
else:
conn_nacelle = RigidConnection("conn-nacelle", offset=np.array([0, 0, s["nacelle"]["height"]]))
free_joint.add_leaf(conn_nacelle)
nacelle = RigidBody(
"nacelle", mass=s["nacelle"]["mass"], inertia=np.diag(s["nacelle"].get("inertia", np.zeros(3)))
)
conn_nacelle.add_leaf(nacelle)
# The rotor hub -- currently just connections (no mass)
# rotate so rotor centre is aligned with global coordinates
if self.tower_modes:
rotoff = s["rotor"]["offset from tower top"]
conn_rotor = RigidConnection("conn-rotor", offset=dot(rotmat_y(pi / 2), rotoff), rotation=rotmat_y(pi / 2))
tower.add_leaf(conn_rotor)
else:
conn_rotor = RigidConnection("conn-rotor", offset=np.array([0, 0, s["nacelle"]["height"]]))
free_joint.add_leaf(conn_rotor)
# The drive shaft rotation (rotation about x)
shaft = Hinge("shaft", [1, 0, 0])
conn_rotor.add_leaf(shaft)
# The blades
if self.blade_modes:
rtlen = s["rotor"]["root length"]
Ryx = dot(rotmat_y(-pi / 2), rotmat_x(-pi / 2)) # align blade modes
for i in range(3):
R = rotmat_x(i * 2 * pi / 3)
root = RigidConnection("root%d" % (i + 1), offset=dot(R, [0, 0, rtlen]), rotation=dot(R, Ryx))
blade = ModalElement("blade%d" % (i + 1), self.blade_modes)
shaft.add_leaf(root)
root.add_leaf(blade)
else:
rotor = RigidBody("rotor", s["rotor"]["mass"], np.diag(s["rotor"]["inertia"]))
shaft.add_leaf(rotor)
# Build system
self.system = System(free_joint)
# Constrain missing DOFs -- tower torsion & extension not complete
if self.tower_modes:
self.system.prescribe(tower, vel=0, part=[0, 3])
def __init__(self, structure_config):
s = structure_config
#### Load details of flexible elements ####
if 'definition' in s['tower']:
if 'mass' in s['tower']:
raise ValueError("Both tower definition and explicit mass!")
self.tower_definition = Tower(s['tower']['definition'])
assert np.all(self.tower_definition.stn_pos[:, :2] == 0) # vert.
z_tower = self.tower_definition.stn_pos[:, 2]
self.tower_modes = ModesFromScratch(
z_tower - z_tower[0],
self.tower_definition.density, 1,
self.tower_definition.EIy, self.tower_definition.EIz)
else:
self.tower_definition = None
self.tower_modes = None
if 'blade' in s:
self.blade_modes = load_modes_from_Bladed(s['blade']['definition'])
else:
self.blade_modes = None
#### Create the elements ####
# Free joint represents the rigid-body motion of the platform
free_joint = FreeJoint('base')
# This is the rigid-body mass of the platform structure
conn_platform = RigidConnection('conn-platform',
offset=s['platform']['CoM'])
platform = RigidBody('platform',
mass=s['platform']['mass'],
inertia=np.diag(s['platform']['inertia']))
free_joint.add_leaf(conn_platform)
conn_platform.add_leaf(platform)
# Make a rigid body to represent the added mass
# (approximate to zero frequency)
# XXX this is skipping the coupling matrix
#A = whales_model.A(0)
# added_mass = RigidBody('added-mass', mass=np.diag(A[:3, :3]),
# inertia=A[3:, 3:])
# Flexible tower or equivalent rigid body
if self.tower_modes:
# move base of tower 10m up, and rotate so tower x-axis is vertical
conn_tower = RigidConnection(
'conn-tower', offset=[0, 0, z_tower[0]],
rotation=rotmat_y(-pi/2))
tower = DistalModalElementFromScratch(
'tower', self.tower_modes,
s['tower']['number of normal modes'])
else:
# move tower to COG
conn_tower = RigidConnection(
'conn-tower', offset=s['tower']['CoM'])
tower = RigidBody('tower', s['tower']['mass'],
np.diag(s['tower']['inertia']))
free_joint.add_leaf(conn_tower)
conn_tower.add_leaf(tower)
# The nacelle -- rigid body
# rotate back so nacelle inertia is aligned with global coordinates
if self.tower_modes:
nacoff = s['nacelle']['offset from tower top']
conn_nacelle = RigidConnection('conn-nacelle',
offset=dot(rotmat_y(pi/2), nacoff),
rotation=rotmat_y(pi/2))
tower.add_leaf(conn_nacelle)
else:
conn_nacelle = RigidConnection(
'conn-nacelle',
offset=np.array([0, 0, s['nacelle']['height']]))
free_joint.add_leaf(conn_nacelle)
nacelle = RigidBody(
'nacelle',
mass=s['nacelle']['mass'],
inertia=np.diag(s['nacelle'].get('inertia', np.zeros(3))))
conn_nacelle.add_leaf(nacelle)
# The rotor hub -- currently just connections (no mass)
# rotate so rotor centre is aligned with global coordinates
if self.tower_modes:
rotoff = s['rotor']['offset from tower top']
conn_rotor = RigidConnection('conn-rotor',
offset=dot(rotmat_y(pi/2), rotoff),
rotation=rotmat_y(pi/2))
tower.add_leaf(conn_rotor)
else:
conn_rotor = RigidConnection(
'conn-rotor',
offset=np.array([0, 0, s['nacelle']['height']]))
free_joint.add_leaf(conn_rotor)
# The drive shaft rotation (rotation about x)
shaft = Hinge('shaft', [1, 0, 0])
conn_rotor.add_leaf(shaft)
# The blades
if self.blade_modes:
rtlen = s['rotor']['root length']
Ryx = dot(rotmat_y(-pi/2), rotmat_x(-pi/2)) # align blade modes
for i in range(3):
R = rotmat_x(i*2*pi/3)
root = RigidConnection('root%d' % (i+1),
offset=dot(R, [0, 0, rtlen]),
rotation=dot(R, Ryx))
blade = ModalElement('blade%d' % (i+1), self.blade_modes)
shaft.add_leaf(root)
root.add_leaf(blade)
else:
rotor = RigidBody('rotor', s['rotor']['mass'],
np.diag(s['rotor']['inertia']))
shaft.add_leaf(rotor)
# Build system
self.system = System(free_joint)
# Constrain missing DOFs -- tower torsion & extension not complete
if self.tower_modes:
self.system.prescribe(tower, vel=0, part=[0, 3])
