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
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, 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, 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
print "Loading modes from '%s'..." % path_damped 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_[
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(), \
# Load Bladed data for comparison import pybladed.data 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)
# Load Bladed data for comparison 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)
print "Loading blade from '%s'..." % bladed_path blade = Blade(bladed_path+'.$pj') modes = blade.modal_rep() # Blade loading wind_table = np.array([ [0, 1, 2, 10], # time [0, 0, 20, 20], # x [0, 0, 0, 0 ], # y [0, 0, 0, 0 ], # z ]) loading = BladeLoading(blade, wind_table, None) # Modal element base = RigidConnection('base', rotation=rotmat_y(-np.pi/2)) el = ModalElement('el', modes, loading) base.add_leaf(el) system = System(base) integ = Integrator(system) integ.add_output(el.output_deflections(stations=[8,16])) integ.add_output(dynamics.CustomOutput( lambda s: el._get_loading()[8,:], 'loading')) integ.add_output(dynamics.CustomOutput( lambda s: el.loading.relspeed, 'relspeed')) # Load Bladed data for comparison import pybladed.data brun = pybladed.data.BladedRun(bladed_path) bladed_defl = np.c_[ brun.get('blade 1 x-deflection;1'),
from blade import Tower # 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))
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))