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_accounts_for_offset_centre_of_mass_in_mass_matrix(self):
# check mass matrix calculation when centre of mass is offset
# from proximal node.
b = RigidBody('body', mass=5.6, Xc=[1.2, 3.4, 5.4])
b.calc_mass()
# F = ma: a Z acceleration should produce a Z-force and X- and
# Y-moments.
F = -dot(b.mass_vv, [0, 0, 1, 0, 0, 0])
assert_array_equal(F, b.mass * array([0, 0, -1, -3.4, 1.2, 0]))
def test_accounts_for_offset_centre_of_mass_in_applied_force(self):
# check applied force due to gravity is correct
b = RigidBody("body", mass=5.6, Xc=[1.2, 3.4, 5.4])
s = System(gravity=9.81) # need a System to define gravity
s.add_leaf(b)
s.setup()
b.calc_mass()
b.calc_external_loading()
assert_array_equal(b.applied_forces, b.mass * 9.81 * array([0, 0, -1, -3.4, 1.2, 0]))
def test_accounts_for_offset_centre_of_mass_in_mass_matrix(self):
# check mass matrix calculation when centre of mass is offset
# from proximal node.
b = RigidBody("body", mass=5.6, Xc=[1.2, 3.4, 5.4])
b.calc_mass()
# F = ma: a Z acceleration should produce a Z-force and X- and
# Y-moments.
F = -dot(b.mass_vv, [0, 0, 1, 0, 0, 0])
assert_array_equal(F, b.mass * array([0, 0, -1, -3.4, 1.2, 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_interal_forces(self):
# NB minus sign because convention for applied_stress is that
# stiffness loads are positive.
b = RigidBody('body', 1)
# Constant loading
b.nodal_load = np.array([2, 3.1, 2.1])
b.calc_external_loading()
assert_array_equal(b.applied_forces, [2, 3.1, 2.1, 0, 0, 0])
assert_array_equal(b.applied_stress, [])
# Loading function
b.nodal_load = lambda element, t: np.ones(3)
b.calc_external_loading()
assert_array_equal(b.applied_forces, [1, 1, 1, 0, 0, 0])
assert_array_equal(b.applied_stress, [])
def build_structure(rigid_body_configs):
# Free joint represents the rigid-body motion of the platform
free_joint = FreeJoint('base')
for i, conf in enumerate(rigid_body_configs):
name = conf.get('name', 'body{}'.format(i))
conn = RigidConnection('conn-' + name, offset=conf['CoM'])
body = RigidBody(name,
mass=conf['mass'],
inertia=np.diag(conf['inertia']))
free_joint.add_leaf(conn)
conn.add_leaf(body)
system = System(free_joint)
return system
def test_accounts_for_offset_centre_of_mass_in_applied_force(self):
# check applied force due to gravity is correct
b = RigidBody('body', mass=5.6, Xc=[1.2, 3.4, 5.4])
s = System(gravity=9.81) # need a System to define gravity
s.add_leaf(b)
s.setup()
b.calc_mass()
b.calc_external_loading()
assert_array_equal(b.applied_forces,
b.mass * 9.81 * array([0, 0, -1, -3.4, 1.2, 0]))
def test_interal_forces(self):
# NB minus sign because convention for applied_stress is that
# stiffness loads are positive.
b = RigidBody("body", 1)
# Constant loading
b.nodal_load = np.array([2, 3.1, 2.1])
b.calc_external_loading()
assert_array_equal(b.applied_forces, [2, 3.1, 2.1, 0, 0, 0])
assert_array_equal(b.applied_stress, [])
# Loading function
b.nodal_load = lambda element, t: np.ones(3)
b.calc_external_loading()
assert_array_equal(b.applied_forces, [1, 1, 1, 0, 0, 0])
assert_array_equal(b.applied_stress, [])
def test_calculates_mass_and_inertia_in_global_coordinates(self):
# simple rigid body at origin: this just checks the mass and
# inertia carry directly through to element mass matrix
II = diag([4.2, 6.7, 11.7])
b = RigidBody('body', mass=4.3, inertia=II)
b.calc_mass()
assert_array_equal(b.mass_vv[:3, :3], 4.3 * eye(3))
assert_array_equal(b.mass_vv[:3, 3:], 0)
assert_array_equal(b.mass_vv[3:, :3], 0)
assert_array_equal(b.mass_vv[3:, 3:], II)
assert_array_equal(b.quad_forces, 0)
# now rotate node by 90 deg about z axis, swapping x & y. This
# confirms that the mass part doesn't change, but the inertia
# matrix is updated.
b.Rp = rotmat_z(pi / 2)
b.calc_mass()
assert_array_equal(b.mass_vv[:3, :3], 4.3 * eye(3))
assert_array_equal(b.mass_vv[:3, 3:], 0)
assert_array_equal(b.mass_vv[3:, :3], 0)
assert_array_almost_equal(b.mass_vv[3:, 3:], diag([6.7, 4.2, 11.7]))
assert_array_equal(b.quad_forces, 0)
def test_calculates_mass_and_inertia_in_global_coordinates(self):
# simple rigid body at origin: this just checks the mass and
# inertia carry directly through to element mass matrix
II = diag([4.2, 6.7, 11.7])
b = RigidBody("body", mass=4.3, inertia=II)
b.calc_mass()
assert_array_equal(b.mass_vv[:3, :3], 4.3 * eye(3))
assert_array_equal(b.mass_vv[:3, 3:], 0)
assert_array_equal(b.mass_vv[3:, :3], 0)
assert_array_equal(b.mass_vv[3:, 3:], II)
assert_array_equal(b.quad_forces, 0)
# now rotate node by 90 deg about z axis, swapping x & y. This
# confirms that the mass part doesn't change, but the inertia
# matrix is updated.
b.Rp = rotmat_z(pi / 2)
b.calc_mass()
assert_array_equal(b.mass_vv[:3, :3], 4.3 * eye(3))
assert_array_equal(b.mass_vv[:3, 3:], 0)
assert_array_equal(b.mass_vv[3:, :3], 0)
assert_array_almost_equal(b.mass_vv[3:, 3:], diag([6.7, 4.2, 11.7]))
assert_array_equal(b.quad_forces, 0)
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])
