/
graphGeneratorWithDefault.py
148 lines (115 loc) · 4.98 KB
/
graphGeneratorWithDefault.py
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import numpy as np
import math
import matplotlib.pyplot as plt
import sympy
from IPython.display import display, clear_output
from sympy import *
import ipywidgets as widgets
#Symbols
km, ke = symbols('k_m k_e', constant=True, real=True, ) # Proportionality Constants (torque & emf)
Vo, Ve, Tm, Tf = symbols('V_o V_e T_m T_f', constant=True, real=True) # Supplied Voltage, Emf voltage, Motor Torque, Frictional Torque
I, rm, rb = symbols('I r_m r_b', constant=True, real=True) # Current, motor resistance, battery resistance
w = symbols('w', constant=True, real=True) # (omega) motor rotational speed
#More symbols
Tnet, rw, E= symbols('T_net r_w, E', constant=True, real=True) # net torque, wheel radius, Wheel efficiency
Iw, m = symbols('I_w m', constant=True, real=True) # Wheel inertia, robot mass
g = symbols('g', constant=True, real=True) # Gear ratio
# More Symbols
v = symbols('v', constant=True, real=True) # Robot velocity
# Motor Constant Symbols
Ts, Is, Io, wo, nm, Vm = symbols('T_s I_s I_o w_o nm V_m', constant=True, real=True) # Stall Torque, Stall Current, Free current, number of motors, nominal voltage
# Acceleration Definition
acelDef = Tnet / (rw*m/E + Iw/rw)
# Torque Definition
TorqueDef = km * (Vo - w*ke)/(rm + rb) - Tf
# Rotational Velocity Definition
wDef = v/(math.pi*rw )* 60 * g
vDef = solve(Eq(wDef, w), v)
# Motor Constant Definitions
KmDef = Ts / Is
KeDef = Vm / wo
RmDef = Vm / (Is * nm)
TfDef = Ts * Io * nm / Is
# Manipulations
workingAcel = simplify(acelDef.subs(Tnet, TorqueDef * g))
workingAcel2 = workingAcel.subs(w, wDef)
workingAcel3 = workingAcel2.subs([(km, KmDef), (ke, KeDef), (rm, RmDef), (Tf, TfDef)])
def graphRatio(distance_min, distance_max, mass,
motor_num, motor_type, free_speed, no_load_current, stall_torque, stall_current,
wheel_type, diameter, wheel_efficiency, inertia, intertia_drivetrain,
nominal_voltage, operating_voltage, batery_resistance,
minRatio, maxRatio,
):
# conversions
mass_lbs = mass
mass = mass / 2.20462 # lbs to kg
radius = (diameter / 2) * 0.0254 # inch to m
inertia += intertia_drivetrain
def aceleration(vel, gratio):
return FVAL*gratio + SVAL *gratio*gratio*vel
def timeAtRatio(targetDist, ratio):
assert(not ratio == 0)
t_acum = 0
x_acum = 0
v_acum = 0
dt= 0.0005
while x_acum < targetDist:
a = aceleration(v_acum, ratio)
v_acum += a*dt
x_acum += v_acum*dt
t_acum += dt
if a < 0:
print("Error, the gear ratio is too low")
return(0)
if t_acum > 10:
print('Error, the time is greater than 10 seconds')
return(0)
return t_acum
subList = [(Ts, stall_torque), (nm, motor_num), (Is, stall_current), (Io, no_load_current),
(Vm, nominal_voltage), (wo, free_speed), (rw, radius), (rb, batery_resistance),
(E, wheel_efficiency), (Vo, operating_voltage), (Iw, inertia), (m, mass)]
acelExp = workingAcel3.subs(subList)
if wheel_efficiency == 1:
wheelType = 'Tank Drive'
elif wheel_efficiency == 0.7:
wheelType = 'Mecanum Drive'
else:
wheelType = '' + 100 * wheel_efficiency + '% efficiency'
FCOMP, SCOMP = acelExp.expand().args
FVAL = float(FCOMP.subs(g, 1))
SVAL = float(SCOMP.subs([(g, 1), (v, 1)]))
progressBar = widgets.FloatProgress(min=minRatio, max=maxRatio, description='Calculating:')
display(progressBar)
def updateStatus(ratio):
progressBar.value = ratio
return None
fig = plt.figure()
ax = fig.add_subplot(111)
ratios = np.arange(minRatio, maxRatio, .1)
def computeForDist(distance, plotColor, first, last):
time = [updateStatus(x) or timeAtRatio(distance, x) for x in ratios]
minTime = min(time)
index = time.index(minTime)
minRatio = ratios[index]
label = 'Dist %.1fm, Min %.1f:1 @ %.3fs' %(distance, minRatio, minTime)
if first:
label = "<Model by Nicolas Eichenberger>\n" + label
if last:
label = label + "\n<Computed by GearRatioOptimizer>"
ax.plot(ratios, time, label=label, color=plotColor)
ax.plot(minRatio, minTime, '-o', color=plotColor)
if distance_min >= distance_max:
computeForDist(distance_min, 'blue', True, True)
else:
computeForDist(distance_max, 'red', True, False)
if distance_max - distance_min >= 0.3:
computeForDist((distance_max+distance_min)/2, 'green', False, False)
computeForDist(distance_min, 'blue', False, True)
ax.set_xlabel("Gear Reduction", fontsize=15)
ax.set_ylabel("Time", fontsize=18)
ax.legend(loc="best")
ax.set_title('%s | Mass = %.1f lbs | Dist = %.1f-%.1fm' %(wheelType, mass_lbs, distance_min, distance_max), fontsize=13)
ax.margins(0.1)
fig.tight_layout()
clear_output()
plt.show()