diff --git a/flexure/figure_1.png b/flexure/figure_1.png
new file mode 100644
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diff --git a/flexure/flexure_stiffness.py b/flexure/flexure_stiffness.py
index 90870a667d16b7c4fc3b02a473814c48b4a487bd..9dea1f0cf5db2c2cd7a8ada1e764d78781273302 100644
--- a/flexure/flexure_stiffness.py
+++ b/flexure/flexure_stiffness.py
@@ -5,6 +5,8 @@ import argparse
from pyframe3dd.frame3dd import write_frame3dd_file, read_lowest_mode, read_frame3dd_displacements, compute_mass
from pyframe3dd.util import magnitudes, close
import subprocess
+import matplotlib.pyplot as plt
+plt.style.use('bmh')
def plot_connections(nodes,beamsets):
#for debug only, this is slow!
@@ -45,49 +47,61 @@ def clean_up_frame3dd(filename):
def build(args):
#return nodes,rods as numpy arrays
dxy = args.attach_radius/sqrt(2)
-
- if args.flexure_type == 'mirrored':
- nodes = args.l*array([[0,0,0],[0,1,0],[-1,1,0],[1,0,0],[1,-1,0]]) #one side of flexure plate
- beams = array([[0,1],[1,2],[0,3],[3,4]])
- nodes += array([dxy,dxy,0]) #offset by attachment radius
-
- elif args.flexure_type == 'cyclic':
- nodes = args.l*array([[0,0,0],[0,1,0],[-1,1,0]]) + array([dxy,dxy,0])
- beams = array([[0,1],[1,2],[3,4]])
- nodes = vstack((nodes, args.l*array([[1,1,0],[1,0,0]]) + array([dxy,-dxy,0])))
-
- nodes = vstack((nodes,array([[-n[0],-n[1],0] for n in nodes]))) #append reflection
- beams = vstack((beams, beams + 5))
+ nodes = array([[dxy,dxy,0],[-dxy,dxy,0],[-dxy,-dxy,0],[dxy,-dxy,0]])
+ solid_beams = array([ [0,1],[1,2],[2,3],[3,0],[0,2],[1,3] ])
z_os = array([0,0,.5*args.sep])
- nodes = vstack((nodes + z_os, nodes - z_os))
- beams = vstack((beams, beams + 10))
-
- solid_nodes = array([ [dxy,-dxy,.5*args.sep],[-dxy,dxy,.5*args.sep],[dxy,-dxy,-.5*args.sep],[-dxy,dxy,-.5*args.sep] ])
- nodes = vstack((nodes, solid_nodes))
- solid_beams = array([
- [0,5],[0,10],[5,15],[10,15],#[0,15],[5,10],
- [0,20],[0,21],[5,20],[5,21],[20,21],
- [10,22],[10,23],[15,22],[15,23],[22,23],
- [20,22],[21,23],#[20,23],[21,22],
- [0,22],[0,23],[5,22],[5,23],
- [10,20],[10,21],[15,20],[15,21]
- ])
- if args.flexure_type == 'cyclic':
- beams = vstack((beams, array([[4,20],[9,21],[14,22],[19,23]])))
-
+ nodes = vstack(( nodes+z_os, nodes-z_os ))
+ solid_beams = vstack((solid_beams, solid_beams + 4))
+ solid_beams = vstack((solid_beams, array([
+ [0,4],[1,5],[2,6],[3,7],
+ [0,5],[1,6],[2,7],[3,4],
+ [0,7],[1,4],[2,5],[3,6] ])))
+ #sensor nodes
nodes = vstack((nodes, array([ [args.sensor_radius,0,0],[0,args.sensor_radius,0],[-args.sensor_radius,0,0],[0,-args.sensor_radius,0] ])))
- solid_beams = vstack(( solid_beams, array([
- [24,0],[24,10],[24,20],[24,22],
- [25,0],[25,10],[25,21],[25,23],
- [26,5],[26,15],[26,21],[26,23],
- [27,5],[27,15],[27,20],[27,22]
- ])))
+ solid_beams = vstack((solid_beams, array([ [0,8],[3,8],[0,9],[1,9],[1,10],[2,10],[2,11],[3,11] ]) ))
+ solid_beams = vstack((solid_beams, array([ [4,8],[7,8],[4,9],[5,9],[5,10],[6,10],[6,11],[7,11] ]) ))
- return nodes, beams, solid_beams
+ if args.flexure_type == 'cyclic':
+ if args.chamfer > 0:
+ l = args.l; ch = args.chamfer
+ #chamfer the flexure
+ flexure_nodes = array([[0,l-ch,0],[-ch,l,0],[-l,l,0]]) + array([dxy,dxy,0])
+ flexure_nodes = vstack(( flexure_nodes, array([[l-ch,0,0],[l,ch,0],[l,l,0]]) + array([dxy,-dxy,0]) ))
+ #append reflection
+ flexure_nodes = vstack((flexure_nodes,array([[-n[0],-n[1],0] for n in flexure_nodes])))
+ flexure_beams = array([[0,12],[12,13],[13,14],[3,15],[15,16],[16,17],[2,18],[18,19],[19,20],[1,21],[21,22],[22,23]])
+ #append both plates
+ flexure_nodes = vstack(( flexure_nodes + z_os, flexure_nodes - z_os))
+ flexure_beams = vstack(( flexure_beams, array([[4,24],[24,25],[25,26],[7,27],[27,28],[28,29],[6,30],[30,31],[31,32],[5,33],[33,34],[34,35]]) ))
+ fixed_nodes = [14,17,20,23,26,29,32,35]
+ else:
+ flexure_nodes = args.l*array([[0,1,0],[-1,1,0]]) + array([dxy,dxy,0])
+ flexure_nodes = vstack(( flexure_nodes, args.l*array([[1,0,0],[1,1,0]]) + array([dxy,-dxy,0]) ))
+ #append reflection
+ flexure_nodes = vstack((flexure_nodes,array([[-n[0],-n[1],0] for n in flexure_nodes])))
+ flexure_beams = array([[0,12],[12,13],[3,14],[14,15],[2,16],[16,17],[1,18],[18,19]])
+ #append both plates
+ flexure_nodes = vstack(( flexure_nodes + z_os, flexure_nodes - z_os))
+ flexure_beams = vstack(( flexure_beams, array([[4,20],[20,21],[7,22],[22,23],[6,24],[24,25],[5,26],[26,27]]) ))
+ fixed_nodes = [13,15,17,19,21,23,25,27]
+ elif args.flexure_type == 'mirrored':
+ flexure_nodes = args.l*array([[0,1,0],[-1,1,0]]) + array([dxy,dxy,0])
+ flexure_nodes = vstack(( flexure_nodes, args.l*array([[1,0,0],[1,-1,0]]) + array([dxy,dxy,0]) ))
+ #append reflection
+ flexure_nodes = vstack((flexure_nodes,array([[-n[0],-n[1],0] for n in flexure_nodes])))
+ flexure_beams = array([[0,12],[12,13],[0,14],[14,15],[2,16],[16,17],[2,18],[18,19]])
+ #append both plates
+ flexure_nodes = vstack(( flexure_nodes + z_os, flexure_nodes - z_os))
+ flexure_beams = vstack(( flexure_beams, array([[4,20],[20,21],[4,22],[22,23],[6,24],[24,25],[6,26],[26,27]]) ))
+ fixed_nodes = [13,15,17,19,21,23,25,27]
+
+
+ nodes = vstack((nodes, flexure_nodes))
+ return nodes, flexure_beams, solid_beams, fixed_nodes
def run_simulation(args):
#set up simulation
- nodes,beams,solid_beams = build(args)
+ nodes,beams,solid_beams,fixed_nodes = build(args)
global_args = {
'n_modes':args.n_modes,'length_scaling':args.length_scaling,'exagerration':10,
'zoom_scale':2.,'node_radius':zeros(shape(nodes)[0]),
@@ -98,15 +112,14 @@ def run_simulation(args):
(beams,{'E':args.E,'nu':args.nu,'rho':args.rho,'cross_section':'rectangular','d2':args.w,'d1':args.t,'roll':0.,'loads':[],'beam_divisions':args.bd,'prestresses':[]}),
(solid_beams,{'E':10*args.E,'nu':args.nu,'rho':args.rho,'cross_section':'rectangular','d1':.003,'d2':.003,'roll':0.,'loads':[],'beam_divisions':1,'prestresses':[]})
]
- if args.flexure_type == 'mirrored':
- fixed_nodes = [2,4,7,9,12,14,17,19]
- elif args.flexure_type == 'cyclic':
- fixed_nodes = [2,3,7,8,12,13,17,18]
constraints = [{'node':node,'DOF':dof,'value':0} for dof in [0,1,2,3,4,5] for node in fixed_nodes]
- loaded_nodes = [0,5,10,15,20,21,22,23]
- sensor_nodes = [24,25,26,27]
+ #loaded_nodes = [0,5,10,15,20,21,22,23]
+ #sensor_nodes = [24,25,26,27]
+ loaded_nodes = range(8)
+ sensor_nodes = [8,9,10,11]
+
results = []
for force_dof in [0,1,2]:
@@ -125,7 +138,7 @@ def run_simulation(args):
loads = [{'node':n,'DOF':torque_dof,'value':torque_force if nodes[n][2]>0 else -torque_force} for n in loaded_nodes]
run_frame3dd(args,nodes,global_args,beam_sets,constraints,loads)
disps = read_frame3dd_displacements(global_args['frame3dd_filename'])
- moving_sensor_nodes = [24,26] if torque_dof==0 else [25,27]
+ moving_sensor_nodes = [8,10] if torque_dof==0 else [9,11]
#print disps[sensor_nodes]
#axis = (array([0,0,0]), array([0,-1,0]) if torque_dof==0 else array([1,0,0]) )
@@ -159,45 +172,9 @@ def run_simulation(args):
#todo: plot displacements vs. design parameters
return results
-def find_stability_threshold(args):
- #out loop of simulations to determine the buckling load
- lower = 0 #lower bound
- upper = 10*args.force_res #initial upper bound before bracketing
- bracketed=False
- #actually not necessary, but fun to have the unloaded frequency
- args.force = lower
- res = run_simulation(args)
- freqs = [res['fundamental_frequency']]
- forces = [args.force]
-
- i = 0
- while not bracketed:
- print lower,upper,bracketed,res['fundamental_frequency']
- args.force = upper
- res = run_simulation(args); i += 1
- if res['fundamental_frequency']<0:
- bracketed=True
- else:
- freqs.append(res['fundamental_frequency'])
- forces.append(args.force)
- lower = upper
- upper = 2*upper
- while (upper-lower > args.force_res):
- print lower,upper,bracketed
- args.force = .5*(upper+lower)
- res = run_simulation(args); i += 1
- if res['fundamental_frequency']>0:
- freqs.append(res['fundamental_frequency'])
- forces.append(args.force)
- lower = .5*(upper+lower)
- else:
- upper = .5*(upper+lower)
- return forces,freqs,res
-
-
if __name__ == '__main__':
parser = argparse.ArgumentParser()
- parser.add_argument('-M','--mode',choices=('simulate','search', 'visualize'), required=True)
+ parser.add_argument('-M','--mode',choices=('simulate','graph', 'visualize'), required=True)
parser.add_argument('-flexure_type','--flexure_type',choices=('cyclic','mirrored'), required=True)
parser.add_argument('-Q','--quiet',action='store_true',help='Whether to suppress frame3dd output')
parser.add_argument("-f","--force", type=double, default=.1, help="force to apply (N)")
@@ -208,8 +185,9 @@ if __name__ == '__main__':
parser.add_argument("-t","--t", type=double, default=.0023, help="thickness of flexure material (m)")
parser.add_argument("-l","--l", type=double, default=.0068, help="length of flexure segment (m)")
parser.add_argument("-attach_radius","--attach_radius", type=double, default=.0043, help="distance from z axis to flexure attachment (m)")
- parser.add_argument("-sep","--sep", type=double, default=.025, help="flexure plate z separation (m)")
+ parser.add_argument("-sep","--sep", type=double, default=.0185, help="flexure plate z separation (m)")
parser.add_argument("-sensor_radius","--sensor_radius", type=double, default=.012, help="distance from rotation axis to sensor (m)")
+ parser.add_argument("-chamfer","--chamfer", type=double, default=.001, help="chamfer length for flexure (m), zero for no chamfer")
parser.add_argument("-bd","--bd", type=int, default=1, help='how many divisions for each rod, useful in buckling analysis')
parser.add_argument("-E","--E", type=double, default=70e9, help="Young's Modulus of laminate")
@@ -220,21 +198,83 @@ if __name__ == '__main__':
parser.add_argument("-ls","--length_scaling", type=double, default=1., help="Scale factor to keep numbers commesurate")
args = parser.parse_args()
- if args.mode=='search':
- forces,freqs,last_res = find_stability_threshold(args)
- print "Fundamental frequency: %.3f Hz"%(freqs[-1])
- print "Critical force: %.3f N"%(forces[-1])
- print "Critical stress: %.3f MPa"%(last_res['stress']/1e6)
+ #if args.mode=='search':
+ # forces,freqs,last_res = find_stability_threshold(args)
+ # print "Fundamental frequency: %.3f Hz"%(freqs[-1])
+ # print "Critical force: %.3f N"%(forces[-1])
+ # print "Critical stress: %.3f MPa"%(last_res['stress']/1e6)
+ if args.mode == 'graph':
+ ws = linspace(.000, .9*args.l, 10)
+ res = {}
+ for wi in ws:
+ #args.w = wi
+ args.chamfer = wi
+ res[wi] = run_simulation(args)
+
+ X = [1e6*res[wi][0]['displacement'] for wi in ws]
+ Y = [1e6*res[wi][1]['displacement'] for wi in ws]
+ Z = [1e6*res[wi][2]['displacement'] for wi in ws]
+ rX = [1e6*res[wi][3]['displacement'] for wi in ws]
+ rY = [1e6*res[wi][4]['displacement'] for wi in ws]
+ rZ = [1e6*res[wi][5]['displacement'] for wi in ws]
+ print ws,X,Y,Z
+ plt.plot( 1e3*ws, X, label='X' )
+ plt.plot( 1e3*ws, Y, label='Y' )
+ plt.plot( 1e3*ws, Z, label='Z' )
+ plt.plot( 1e3*ws, rX, label='rX' )
+ plt.plot( 1e3*ws, rY, label='rY' )
+ plt.plot( 1e3*ws, rZ, label='rZ' )
+ plt.ylabel('displacement at sensor (microns)')
+ plt.xlabel('chamfer width (mm)')
+ plt.xlim([1e3*ws[0],1e3*ws[-1]])
+ plt.legend(loc='upper right')
+ plt.show()
elif args.mode=='simulate':
res = run_simulation(args)
print res
#print "Fundamental frequency: %.3f Hz"%res['fundamental_frequency']
#print "Stress: %.3f MPa"%(res['stress']/1e6)
elif args.mode=='visualize':
- nodes,rods,solid_beams = build(args)
+ nodes,rods,solid_beams,fixed_nodes = build(args)
plot_connections(nodes,[rods,solid_beams])
else:
assert(0) #should not be here
+'''
+def find_stability_threshold(args):
+ #out loop of simulations to determine the buckling load
+ lower = 0 #lower bound
+ upper = 10*args.force_res #initial upper bound before bracketing
+ bracketed=False
+ #actually not necessary, but fun to have the unloaded frequency
+ args.force = lower
+ res = run_simulation(args)
+ freqs = [res['fundamental_frequency']]
+ forces = [args.force]
+
+ i = 0
+ while not bracketed:
+ print lower,upper,bracketed,res['fundamental_frequency']
+ args.force = upper
+ res = run_simulation(args); i += 1
+ if res['fundamental_frequency']<0:
+ bracketed=True
+ else:
+ freqs.append(res['fundamental_frequency'])
+ forces.append(args.force)
+ lower = upper
+ upper = 2*upper
+ while (upper-lower > args.force_res):
+ print lower,upper,bracketed
+ args.force = .5*(upper+lower)
+ res = run_simulation(args); i += 1
+ if res['fundamental_frequency']>0:
+ freqs.append(res['fundamental_frequency'])
+ forces.append(args.force)
+ lower = .5*(upper+lower)
+ else:
+ upper = .5*(upper+lower)
+ return forces,freqs,res
+'''