class Gyroscope(object): def __init__(self, length, radius, mass, spin, endmass): self.length = length self.radius = radius self.mass = mass self.spin = spin self.endmass = endmass Jz = radius**2 / 2 Jxy = (3*radius**2 + length**2) / 12 inertia = mass * np.diag([Jxy, Jxy, Jz]) self.bearing = Hinge('bearing', [0,0,1]) 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.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 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 ani(self, vs=1): l = self.length * 1.1 return dynvis.anim(self.system, self.t, self.y, (0,vs), (-l,l), (-l,l), velocities=False)
class Gyroscope(object): 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 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 elevation 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)) # 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 ani(self, vs=1): l = self.length * 1.1 return dynvis.anim(self.system, self.t, self.y, (0, vs), (-l, l), (-l, l), velocities=False)
class Gyroscope(object): 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 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 elevation 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)) # 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 ani(self, vs=1): l = self.length * 1.1 return dynvis.anim(self.system, self.t, self.y, (0,vs), (-l,l), (-l,l), velocities=False)
class Rotor(object): 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.blade = Blade(mode_source_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.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, 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 simulate(self, qm0=None, spin=10.0, t1=1.5, dt=0.01): # reset self.system.q[:] = 0.0 self.system.qd[:] = 0.0 # initial conditions if qm0 is not None: # initial modal amplitudes self.system.q[self.blade1.istrain] = qm0 self.system.q[self.blade2.istrain] = qm0 self.system.q[self.blade3.istrain] = qm0 self.system.qd[self.bearing.istrain][0] = spin # simulate 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 lin(self, qm0=None, spin=10.0): # reset self.system.q[:] = 0.0 self.system.qd[:] = 0.0 # initial conditions if qm0 is not None: # initial modal amplitudes self.system.q[self.blade1.istrain] = qm0 self.system.q[self.blade2.istrain] = qm0 self.system.q[self.blade3.istrain] = qm0 else: qm0 = np.zeros(self.blade1._nstrain * 3) self.system.prescribe(self.bearing, vel=spin, acc=0.0) self.system.qd[self.bearing.istrain][0] = spin linsys = linearisation.LinearisedSystem(self.system, qm0) return linsys def ani(self, t=None, y=None, planview=True): if t is None: t = self.t if y is None: y = self.y l = 40 if planview: return dynvis.anim(self.system, t, y, (1, 2), (-l, l), (-l, l)) else: return dynvis.anim(self.system, t, y, (0, 1), (-l, l), (-5, 5))
class Rotor(object): 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.blade = Blade(mode_source_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.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, 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 simulate(self, qm0=None, spin=10.0, t1=1.5, dt=0.01): # reset self.system.q [:] = 0.0 self.system.qd[:] = 0.0 # initial conditions if qm0 is not None: # initial modal amplitudes self.system.q[self.blade1.istrain] = qm0 self.system.q[self.blade2.istrain] = qm0 self.system.q[self.blade3.istrain] = qm0 self.system.qd[self.bearing.istrain][0] = spin # simulate 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 lin(self, qm0=None, spin=10.0): # reset self.system.q [:] = 0.0 self.system.qd[:] = 0.0 # initial conditions if qm0 is not None: # initial modal amplitudes self.system.q[self.blade1.istrain] = qm0 self.system.q[self.blade2.istrain] = qm0 self.system.q[self.blade3.istrain] = qm0 else: qm0 = np.zeros(self.blade1._nstrain * 3) self.system.prescribe(self.bearing, vel=spin, acc=0.0) self.system.qd[self.bearing.istrain][0] = spin linsys = linearisation.LinearisedSystem(self.system, qm0) return linsys def ani(self, t=None, y=None, planview=True): if t is None: t = self.t if y is None: y = self.y l = 40 if planview: return dynvis.anim(self.system, t, y, (1,2), (-l,l), (-l,l)) else: return dynvis.anim(self.system, t, y, (0,1), (-l,l), (-5,5))
class Turbine(object): 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() #self.tmodes = self.tower.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)) 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)) @property def mass(self): """Total mass of turbine""" return self.tower.total_mass + self.modes.mass * 3 @property def inertia(self): """Total rotational inertia of turbine about base""" inertia = self.tower.total_inertia inertia[(0,1),(0,1)] = self.modes.mass * 3 * self.tower.hubheight return inertia # XXX neglecting rotor rotational inertia def set_base_motion(self, dof, w, amp): self.base_motion = dof self.base_motion_amp = amp self.system.prescribe(self.base, part=dof, vel=lambda t: -w *amp*np.sin(w*t), acc=lambda t: -w**2*amp*np.cos(w*t)) def set_initial_conditions(self, qm0=None, az0=None, rotor_speed=None): # initial conditions if qm0 is not None: # initial modal amplitudes self.system.q[self.blade1.istrain] = qm0 self.system.q[self.blade2.istrain] = qm0 self.system.q[self.blade3.istrain] = qm0 if az0 is not None: self.system.q[self.bearing.istrain][0] = az0 if self.base_motion is not None: self.system.q[self.base.istrain][self.base_motion] = self.base_motion_amp if rotor_speed is not None: self.system.prescribe(self.bearing, vel=rotor_speed) def simulate(self, qm0=None, az0=0.0, rotor_speed=10.0, t1=None, dt=0.01, t0=0.0, init=False): # reset self.system.q [:] = 0.0 self.system.qd[:] = 0.0 self.set_initial_conditions(qm0, az0, rotor_speed) if t1 is None: t1 = 4*pi/rotor_speed if (rotor_speed != 0.0) else 2 if init: self.system.find_equilibrium() # simulate self.t,self.y = self.integ.integrate(t1, dt, t0) for i,lab in enumerate(self.integ.labels()): print "%2d %s" % (i,lab) return self.t, self.y def lin(self, qm0=None, az0=None, rotor_speed=None, init=False): # reset self.system.q [:] = 0.0 self.system.qd[:] = 0.0 self.set_initial_conditions(qm0, az0, rotor_speed) if init: self.system.find_equilibrium() linsys = linearisation.LinearisedSystem(self.system) return linsys def ani(self, vs=(0,1), t=None, y=None): if t is None: t = self.t if y is None: y = self.y limits = [(-10,10), (-42,42), (-5,110)] return dynvis.anim(self.system, t, y, vs, limits[vs[0]], limits[vs[1]])
class Gyroscope(object): def __init__(self, length, radius, mass, spin, endmass): self.length = length self.radius = radius self.mass = mass self.spin = spin self.endmass = endmass Jz = radius**2 / 2 Jxy = (3 * radius**2 + length**2) / 12 inertia = mass * np.diag([Jxy, Jxy, Jz]) self.bearing = Hinge('bearing', [0, 0, 1]) 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.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 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 ani(self, vs=1): l = self.length * 1.1 return dynvis.anim(self.system, self.t, self.y, (0, vs), (-l, l), (-l, l), velocities=False)