diff --git a/flexure/figure_1.png b/flexure/figure_1.png new file mode 100644 index 0000000000000000000000000000000000000000..40a39a614a57817dcc1b1f5d765a5fe3d0d18f86 Binary files /dev/null and b/flexure/figure_1.png differ 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 +'''