def test_distal_forces_cause_acceleration(self): j = FreeJoint('joint') b = RigidBody('body', mass=3, inertia=np.diag([7, 7, 7])) s = System() s.add_leaf(j) j.add_leaf(b) s.setup() # Constant loading j.distal_forces = np.array([2, 0, 0, 0, 0, 0]) s.update_kinematics() s.update_matrices() s.solve_accelerations() s.update_kinematics() assert_array_equal(j.ad, [2. / 3, 0, 0, 0, 0, 0])
class TestReactionForcesForCentrifugalForce(unittest.TestCase): """ System ------ A rigid body with offset mass, attached to a spinning hinge. Tests ----- Check centrifugal force reaction on hinge is in correct direction. """ mass = 5.0 # kg offset = 3.2 # m def setUp(self): # Rigid body with offset centre of mass self.body = RigidBody("body", self.mass, Xc=[self.offset, 0, 0]) # Hinge with axis along Z axis self.hinge = Hinge("hinge", [0, 0, 1]) # Build system self.system = System() self.system.add_leaf(self.hinge) self.hinge.add_leaf(self.body) self.system.setup() self.system.update_kinematics() # Set up nodal values initially self.system.update_matrices() def test_reactions(self): # Set angular acceleration w = 5.21 # rad/s self.hinge.vstrain[0] = w self.system.update_kinematics() # Update nodal values based on DOFs self.system.update_matrices() self.system.solve_reactions() # Solve reactions incl d'Alembert # Some parameters L = self.offset m = self.mass # Check reactions at beam root Pg = self.system.joint_reactions["ground"] P0 = self.system.joint_reactions["node-0"] Fx_expected = -m * L * w ** 2 assert_aae(P0, [Fx_expected, 0, 0, 0, 0, 0]) assert_aae(Pg, P0)
class TestReactionForcesForCentrifugalForce(unittest.TestCase): """ System ------ A rigid body with offset mass, attached to a spinning hinge. Tests ----- Check centrifugal force reaction on hinge is in correct direction. """ mass = 5.0 # kg offset = 3.2 # m def setUp(self): # Rigid body with offset centre of mass self.body = RigidBody('body', self.mass, Xc=[self.offset, 0, 0]) # Hinge with axis along Z axis self.hinge = Hinge('hinge', [0, 0, 1]) # Build system self.system = System() self.system.add_leaf(self.hinge) self.hinge.add_leaf(self.body) self.system.setup() self.system.update_kinematics() # Set up nodal values initially self.system.update_matrices() def test_reactions(self): # Set angular acceleration w = 5.21 # rad/s self.hinge.vstrain[0] = w self.system.update_kinematics() # Update nodal values based on DOFs self.system.update_matrices() self.system.solve_reactions() # Solve reactions incl d'Alembert # Some parameters L = self.offset m = self.mass # Check reactions at beam root Pg = self.system.joint_reactions['ground'] P0 = self.system.joint_reactions['node-0'] Fx_expected = -m * L * w**2 assert_aae(P0, [Fx_expected, 0, 0, 0, 0, 0]) assert_aae(Pg, P0)
class hinged_beam_tests(unittest.TestCase): density = 5.0 length = 20.0 force = 34.2 # N/m hinge_torque = 0.0 free_beam = False def setUp(self): # FE model for beam x = linspace(0, self.length, 20) fe = BeamFE(x, density=self.density, EA=0, EIy=1, EIz=0) fe.set_boundary_conditions('C', 'F') self.beam = ModalElementFromFE('beam', fe, 0) # Set loading - in negative Z direction load = np.zeros((len(x), 3)) load[:, 2] = -self.force self.beam.loading = load # Hinge with axis along Y axis self.hinge = Hinge('hinge', [0, 1, 0]) self.hinge.internal_torque = self.hinge_torque # Build system self.system = System() self.system.add_leaf(self.hinge) self.hinge.add_leaf(self.beam) self.system.setup() if not self.free_beam: # Prescribe hinge to be fixed self.system.prescribe(self.hinge) # Initial calculations self.recalc() def recalc(self): self.system.update_kinematics() # Set up nodal values initially self.system.update_matrices() self.system.solve_accelerations() # Calculate accelerations of DOFs self.system.update_kinematics() # Update nodal values based on DOFs self.system.update_matrices() self.system.solve_reactions() # Solve reactions incl d'Alembert
def test_find_equilibrium(self): g = 9.81 m = 23.1 k = 45.2 s = System(gravity=g) slider = PrismaticJoint('slider', [0, 0, 1]) slider.stiffness = k body = RigidBody('body', mass=m) s.add_leaf(slider) slider.add_leaf(body) s.setup() # Initially position should be zero and acceleration nonzero s.solve_accelerations() assert_aae(slider.xstrain, 0) assert_aae(slider.astrain, -g) # At equilibrium, position should be nozero and force on body zero s.find_equilibrium() s.update_matrices() # recalculate stiffness force s.solve_accelerations() assert_aae(slider.xstrain, -m * g / k) assert_aae(slider.astrain, 0)
class TestReactionForcesWithRotatedBeam(unittest.TestCase): """Intended to check the transformation from blade loading to rotor loading in a wind turbine rotor: the loads are applied to the beam in the local rotated coordinate system, check they work through to the ground reactions correctly. """ force = 24.1 length = 4.3 root_length = 0.0 def setUp(self): # FE model for beam - no modes, i.e. rigid self.x = x = linspace(0, self.length, 20) fe = BeamFE(x, density=2, EA=0, EIy=0, EIz=0) # Build the elements self.shaft = Hinge('shaft', [1, 0, 0]) self.roots = [] self.blades = [] self.pitch_bearings = [] for ib in range(1): R = rotations(('x', ib * 2 * pi / 3), ('y', -pi / 2)) root_offset = dot(R, [self.root_length, 0, 0]) root = RigidConnection('root%d' % (ib + 1), root_offset, R) bearing = Hinge('pitch%d' % (ib + 1), [1, 0, 0]) blade = ModalElementFromFE('blade%d' % (ib + 1), fe, 0) self.shaft.add_leaf(root) root.add_leaf(bearing) bearing.add_leaf(blade) self.roots.append(root) self.blades.append(blade) self.pitch_bearings.append(bearing) # Build system self.system = System() self.system.add_leaf(self.shaft) self.system.setup() self.system.update_kinematics() # Set up nodal values initially self.system.update_matrices() def test_reactions(self): # Some parameters L = self.length F = self.length * self.force # Set loading - in local z direction load = np.zeros((len(self.x), 3)) load[:, 2] = self.force self.blades[0].loading = load self.system.update_kinematics() self.system.update_matrices() self.system.solve_reactions() # Check reactions at ground (0, 0, 0) P = -self.system.joint_reactions['ground'] F_expected = [-F, 0, 0] M_expected = [0, -F * (L + self.root_length) / 2, 0] assert_aae(P, np.r_[F_expected, M_expected]) # Reactions on other side of hinge P2 = -self.system.joint_reactions['node-0'] assert_aae(P, P2) # Now set pitch angle to 45deg # NB: hinge rotation is opposite to wind turbine pitch convention self.pitch_bearings[0].xstrain[0] = -pi / 4 self.system.update_kinematics() self.system.update_matrices() self.system.solve_reactions() # Check reactions at ground (0, 0, 0) P = -self.system.joint_reactions['ground'] F_expected = [-F / sqrt(2), F / sqrt(2), 0] M_expected = [-F / sqrt(2) * L / 2, -F / sqrt(2) * L / 2, 0] assert_aae(P, np.r_[F_expected, M_expected]) # Reactions on other side of hinge P2 = -self.system.joint_reactions['node-0'] assert_aae(P, P2)
class TestReactionForcesWithRotatedBeam(unittest.TestCase): """Intended to check the transformation from blade loading to rotor loading in a wind turbine rotor: the loads are applied to the beam in the local rotated coordinate system, check they work through to the ground reactions correctly. """ force = 24.1 length = 4.3 root_length = 0.0 def setUp(self): # FE model for beam - no modes, i.e. rigid self.x = x = linspace(0, self.length, 20) fe = BeamFE(x, density=2, EA=0, EIy=0, EIz=0) # Build the elements self.shaft = Hinge('shaft', [1, 0, 0]) self.roots = [] self.blades = [] self.pitch_bearings = [] for ib in range(1): R = rotations(('x', ib*2*pi/3), ('y', -pi/2)) root_offset = dot(R, [self.root_length, 0, 0]) root = RigidConnection('root%d' % (ib+1), root_offset, R) bearing = Hinge('pitch%d' % (ib+1), [1, 0, 0]) blade = ModalElementFromFE('blade%d' % (ib+1), fe, 0) self.shaft.add_leaf(root) root.add_leaf(bearing) bearing.add_leaf(blade) self.roots.append(root) self.blades.append(blade) self.pitch_bearings.append(bearing) # Build system self.system = System() self.system.add_leaf(self.shaft) self.system.setup() self.system.update_kinematics() # Set up nodal values initially self.system.update_matrices() def test_reactions(self): # Some parameters L = self.length F = self.length * self.force # Set loading - in local z direction load = np.zeros((len(self.x), 3)) load[:, 2] = self.force self.blades[0].loading = load self.system.update_kinematics() self.system.update_matrices() self.system.solve_reactions() # Check reactions at ground (0, 0, 0) P = -self.system.joint_reactions['ground'] F_expected = [-F, 0, 0] M_expected = [0, -F*(L+self.root_length)/2, 0] assert_aae(P, np.r_[F_expected, M_expected]) # Reactions on other side of hinge P2 = -self.system.joint_reactions['node-0'] assert_aae(P, P2) # Now set pitch angle to 45deg # NB: hinge rotation is opposite to wind turbine pitch convention self.pitch_bearings[0].xstrain[0] = -pi / 4 self.system.update_kinematics() self.system.update_matrices() self.system.solve_reactions() # Check reactions at ground (0, 0, 0) P = -self.system.joint_reactions['ground'] F_expected = [-F/sqrt(2), F/sqrt(2), 0] M_expected = [-F/sqrt(2)*L/2, -F/sqrt(2)*L/2, 0] assert_aae(P, np.r_[F_expected, M_expected]) # Reactions on other side of hinge P2 = -self.system.joint_reactions['node-0'] assert_aae(P, P2)