def test_I_rim_only():
'Check that wheel inertia returns rim inertia if no spoke density is given'
w = BicycleWheel()
w.hub = Hub(diameter=0.050, width=0.05)
w.rim = Rim(radius=0.3,
area=100e-6,
I_lat=200. / 69e9,
I_rad=100. / 69e9,
J_tor=25. / 26e9,
I_warp=0.0,
young_mod=69e9,
shear_mod=26e9,
density=1.)
w.lace_cross(n_spokes=36,
n_cross=3,
diameter=1.8e-3,
young_mod=210e9,
offset=0.)
# Should return a warning that some spoke densities are not specified
with pytest.warns(UserWarning):
I_wheel = w.calc_rot_inertia()
assert np.allclose(I_wheel, (2 * np.pi * 0.3 * 100e-6) * 0.3**2)
def test_I_spokes_only():
'Check that spoke inertias are correctly calculated'
w = BicycleWheel()
w.hub = Hub(diameter=0.050, width=0.05)
w.rim = Rim(radius=0.3,
area=100e-6,
I_lat=200. / 69e9,
I_rad=100. / 69e9,
J_tor=25. / 26e9,
I_warp=0.0,
young_mod=69e9,
shear_mod=26e9)
w.lace_radial(n_spokes=36,
diameter=1.8e-3,
young_mod=210e9,
offset=0.,
density=1.0)
# Calculate inertia of a single spoke
m_spk = np.hypot(0.3 - 0.025, 0.025) * np.pi / 4 * (1.8e-3)**2 * 1.0
I_spk = m_spk * (0.3 - 0.025)**2 / 12. + m_spk * (0.5 * (0.025 + 0.3))**2
# Should return a warning that the rim density is not specified
with pytest.warns(UserWarning):
I_wheel = w.calc_rot_inertia()
assert np.allclose(I_wheel, 36. * I_spk)
def wheel_from_row(self, j):
'Create a BicycleWheel object from a job row'
# Try to un-pickle wheel object
if 'wheel_pickle' in j:
with open(self.out_dir + '/' + j['wheel_pickle'], 'rb') as p:
w = pickle.load(p)
else:
w = BicycleWheel()
w.hub = Hub(diam1=j['hub_diam1'], width1=j['hub_width1'])
w.rim = Rim(radius=j['rim_radius'],
area=j['rim_area'],
I11=j['rim_I11'],
I22=j['rim_I22'],
I33=j['rim_I33'],
Iw=j['rim_Iw'],
young_mod=j['rim_young_mod'],
shear_mod=j['rim_shear_mod'])
w.lace_radial(n_spokes=int(j['spk_num']),
diameter=j['spk_diameter'],
young_mod=j['spk_young_mod'])
if 'spk_paired' in j.keys() and j['spk_paired']:
w = convert_to_paired(w)
return w
def wheel_from_name(name):
'Generate a wheel from a standard template'
df = pd.read_csv('../data/wheel_properties.csv', index_col=0)
# Find requested wheel
if name in df:
p = df[name]
w = BicycleWheel()
w.hub = Hub(diam1=float(p['hub_diameter']) / 1000.,
width1=float(p['hub_width']) / 2000.)
w.rim = Rim(
radius=float(p['rim_radius']) / 1000.,
area=float(p['rim_area']) / 1e6,
I11=float(p['rim_GJ']) / (float(p['rim_shear_mod']) * 1e9),
I22=float(p['rim_EI2']) / (float(p['rim_young_mod']) * 1e9),
I33=float(p['rim_EI1']) / (float(p['rim_young_mod']) * 1e9),
Iw=0.0,
young_mod=float(p['rim_young_mod']) * 1e9,
shear_mod=float(p['rim_shear_mod']) * 1e9)
if p['spk_pattern'] == 'radial':
w.lace_radial(n_spokes=int(p['spk_num']),
diameter=float(p['spk_diameter']) / 1000.,
young_mod=float(p['spk_young_mod']) * 1e9,
offset=float(p['spk_offset']) / 1000.)
else:
raise KeyError('Spoke pattern {0:s} is not defined.'.format(
p['spk_pattern']))
return w
else:
raise KeyError('Wheel template {0:s} is not defined.'.format(name))
def _build_wheel():
w = BicycleWheel()
w.hub = Hub(diameter=0.050, width=0.05)
w.rim = Rim(radius=0.3,
area=100e-6,
I_lat=200. / 69e9,
I_rad=100. / 69e9,
J_tor=25. / 26e9,
I_warp=0.0,
young_mod=69e9,
shear_mod=26e9)
return w
def create_wheel_from_lm(l, mu):
"""Create a wheel with arbitrary values of lambda and mu.
Since the reverse problem of generating a wheel with a specified lambda
and mu is not unique, some constraints must be applied:
- wheel dimensions are R=300m, d_hub=50mm, w_hub=25mm
- radial spokes, E=200 GPa
- number and diameter of spokes are chosen to ensure that Pn_lat = 2
"""
wheel = BicycleWheel()
wheel.hub = Hub(diam1=0.05, width1=0.025)
wheel.rim = Rim(radius=0.3,
area=100e-6,
I11=1000e-12 * (69. / 26.) * mu,
I22=1000e-12,
I33=1000e-12,
Iw=0.0e-12,
young_mod=69.0e9,
shear_mod=26.0e9)
alpha = np.arctan(wheel.hub.width1 /
(wheel.rim.radius - wheel.hub.diam1 / 2))
ls = np.sqrt(wheel.hub.width1**2 +
(wheel.rim.radius - wheel.hub.diam1 / 2)**2)
# Calculate n_s by requiring that Pn_lat = 2.0 and round up to next even
n_s = 1.5 * (8 * np.pi / np.power(4, 0.25)) * np.power(
l * (mu + 1) / mu, 0.25)
n_s = 2 * int(np.ceil(n_s / 2))
# Calculate spoke diameter based on requirement on lambda
k_uu = l * wheel.rim.young_mod * wheel.rim.I22 / (wheel.rim.radius**4)
A_s = 2 * np.pi * wheel.rim.radius * ls * k_uu / (n_s * 200e9 *
np.sin(alpha)**2)
d_s = np.sqrt(4 * A_s / np.pi)
# Create spokes
wheel.lace_radial(n_spokes=n_s, diameter=d_s, young_mod=200e9)
return wheel
def _build_wheel(n_cross=0):
w = BicycleWheel()
w.hub = Hub(diameter=0.050, width=0.05)
w.rim = Rim(radius=0.3,
area=100e-6,
I_lat=200. / 69e9,
I_rad=100. / 69e9,
J_tor=25. / 26e9,
I_warp=0.0,
young_mod=69e9,
shear_mod=26e9)
w.lace_cross(n_spokes=36,
n_cross=n_cross,
diameter=1.8e-3,
young_mod=210e9,
offset=0.)
return w
def test_I_wheel_less_than_max():
'Check that rotational inertia is less than theoretical maximum'
w = BicycleWheel()
w.hub = Hub(diameter=0.050, width=0.05)
w.rim = Rim(radius=0.3,
area=100e-6,
J_tor=25. / 26e9,
I_lat=200. / 69e9,
I_rad=100. / 69e9,
I_warp=0.0,
young_mod=69e9,
shear_mod=26e9,
density=1.0)
w.lace_radial(n_spokes=36,
diameter=1.8e-3,
young_mod=210e9,
offset=0.,
density=1.0)
I_wheel = w.calc_rot_inertia()
assert I_wheel < w.calc_mass() * w.rim.radius**2
def build_wheel_from_UI():
'Create a BicycleWheel object from UI inputs'
w = BicycleWheel()
# Hub
w.hub = Hub(diameter=float(hub_diam.value)/1000.,
width_nds=np.abs(float(hub_width.value[0]))/1000.,
width_ds=np.abs(float(hub_width.value[1]))/1000.)
# Rim
r_matl = list(RIM_MATLS)[rim_matl.active]
radius = RIM_SIZES[rim_size.value]['radius']
density = RIM_MATLS[r_matl]['density']
mass = float(rim_mass.value) / 1000.
area = mass / (2*np.pi*radius*density)
rim_young_mod = RIM_MATLS[r_matl]['young_mod']
rim_shear_mod = RIM_MATLS[r_matl]['shear_mod']
w.rim = Rim(radius=radius,
area=area,
I11=float(rim_GJ.value) / rim_shear_mod,
I22=float(rim_EI2.value) / rim_young_mod,
I33=float(rim_EI1.value) / rim_young_mod, Iw=0.0,
young_mod=rim_young_mod, shear_mod=rim_shear_mod)
# Drive-side
if spk_pat_ds.value == 'Radial':
n_cross_ds = 0
elif spk_pat_ds.value.endswith('-cross'):
n_cross_ds = int(spk_pat_ds.value[0])
else:
raise ValueError('Undefined drive-side spoke pattern: {:s}'.format(spk_pat_ds.value))
s_matl_ds = list(SPK_MATLS)[spk_matl_ds.active]
w.lace_cross_ds(n_spokes=int(spk_num.value)//2,
n_cross=n_cross_ds,
diameter=float(spk_diam_ds.value)/1000.,
young_mod=SPK_MATLS[s_matl_ds]['young_mod'],
offset=0.) # Implement this later
# Non-drive-side
if spk_pat_nds.value == 'Radial':
n_cross_nds = 0
elif spk_pat_nds.value.endswith('-cross'):
n_cross_nds = int(spk_pat_nds.value[0])
else:
raise ValueError('Undefined drive-side spoke pattern: {:s}'.format(spk_pat_nds.value))
s_matl_nds = list(SPK_MATLS)[spk_matl_nds.active]
w.lace_cross_nds(n_spokes=int(spk_num.value)//2,
n_cross=n_cross_nds,
diameter=float(spk_diam_nds.value)/1000.,
young_mod=SPK_MATLS[s_matl_nds]['young_mod'],
offset=0.) # Implement this later
if (spk_pat_ds.value == 'Radial' and spk_pat_nds.value == 'Radial'
and float(spk_T_ds.value) == 0.):
# Apply a vanishingly small tension to make stiffness matrix invertable
w.apply_tension(T_avg=w.spokes[0].EA*1e-6)
else:
w.apply_tension(T_right=9.81*float(spk_T_ds.value))
return w
from bikewheelcalc import BicycleWheel, Rim, Hub, ModeMatrix
import matplotlib.pyplot as plt
import numpy as np
# Create an example wheel and rim
wheel = BicycleWheel()
wheel.hub = Hub(width=0.05, diameter=0.05)
wheel.rim = Rim(radius=0.3,
area=100e-6,
I_lat=200. / 69e9,
I_rad=100. / 69e9,
J_tor=25. / 26e9,
I_warp=0.0,
young_mod=69e9,
shear_mod=26e9)
wheel.lace_cross(n_spokes=36, n_cross=3, diameter=2.0e-3, young_mod=210e9)
# Create a ModeMatrix model with 24 modes
mm = ModeMatrix(wheel, N=24)
# Create a 500 Newton pointing radially inwards at theta=0
F_ext = mm.F_ext(0., np.array([0., 500., 0., 0.]))
# Calculate stiffness matrix
K = mm.K_rim(tension=False) + mm.K_spk(smeared_spokes=False, tension=False)
# Solve for the mode coefficients
dm = np.linalg.solve(K, F_ext)
# Get radial deflection
theta = np.linspace(-np.pi, np.pi, 100)