def CoordsOrbScroll(theta, geo, shaveOn=True, just_involutes=False, Ndict={}):
from PDSim.scroll import scroll_geo
shaveDelta = None
if shaveOn == True:
shaveDelta = pi / 2
else:
shaveDelta = 1e-16
(xshave, yshave) = Shave(geo, theta, shaveDelta)
Nphi = Ndict.get('phi', 500)
Narc1 = Ndict.get('arc1', 100)
Nline = Ndict.get('line', 100)
Narc2 = Ndict.get('arc2', 100)
phi = np.linspace(geo.phi_ois, geo.phi_oie, Nphi)
(x_oi, y_oi) = scroll_geo.coords_inv(phi, geo, theta, flag="oi")
phi = np.linspace(geo.phi_oos, geo.phi_ooe - shaveDelta, Nphi)
(x_oo, y_oo) = scroll_geo.coords_inv(phi, geo, theta, flag="oo")
xarc1 = geo.xa_arc1 + geo.ra_arc1 * cos(
np.linspace(geo.t2_arc1, geo.t1_arc1, Narc1))
yarc1 = geo.ya_arc1 + geo.ra_arc1 * sin(
np.linspace(geo.t2_arc1, geo.t1_arc1, Narc1))
xline = np.linspace(geo.t1_line, geo.t2_line, Nline)
yline = geo.m_line * xline + geo.b_line
xarc2 = geo.xa_arc2 + geo.ra_arc2 * cos(
np.linspace(geo.t1_arc2, geo.t2_arc2, Narc2))
yarc2 = geo.ya_arc2 + geo.ra_arc2 * sin(
np.linspace(geo.t1_arc2, geo.t2_arc2, Narc2))
ro = geo.rb * (pi - geo.phi_fi0 + geo.phi_fo0)
om = geo.phi_fie - theta + 3.0 * pi / 2.0
xarc1_o = -xarc1 + ro * cos(om)
yarc1_o = -yarc1 + ro * sin(om)
xline_o = -xline + ro * cos(om)
yline_o = -yline + ro * sin(om)
xarc2_o = -xarc2 + ro * cos(om)
yarc2_o = -yarc2 + ro * sin(om)
if just_involutes:
x = np.r_[x_oo, x_oi[::-1]]
y = np.r_[y_oo, y_oi[::-1]]
else:
if shaveOn:
x = np.r_[x_oo, xshave, x_oi[::-1], xarc1_o, xline_o, xarc2_o]
y = np.r_[y_oo, yshave, y_oi[::-1], yarc1_o, yline_o, yarc2_o]
else:
x = np.r_[x_oo, x_oi[::-1], xarc1_o, xline_o, xarc2_o]
y = np.r_[y_oo, y_oi[::-1], yarc1_o, yline_o, yarc2_o]
#Output as a column vector
x = x.reshape(len(x), 1)
y = y.reshape(len(y), 1)
return x, y
def Shave(geo, theta, shaveDelta):
from PDSim.scroll import scroll_geo
phi = np.linspace(geo.phi_ooe - shaveDelta, geo.phi_ooe, 200)
(xo, yo) = scroll_geo.coords_inv(phi, geo, theta, "oo")
(xi, yi) = scroll_geo.coords_inv(phi, geo, theta, "oi")
z = (1 - 0.8 * (phi - (geo.phi_ooe - shaveDelta)) / (shaveDelta))
xnew = z * xo + (1 - z) * xi
ynew = z * yo + (1 - z) * yi
return (xnew, ynew)
def CoordsOrbScroll(theta,geo,shaveOn=True, just_involutes = False, Ndict = {}):
from PDSim.scroll import scroll_geo
shaveDelta=None
if shaveOn==True:
shaveDelta = pi/2
else:
shaveDelta = 1e-16
(xshave, yshave) = Shave(geo, theta, shaveDelta)
Nphi = Ndict.get('phi',500)
Narc1 = Ndict.get('arc1',100)
Nline = Ndict.get('line',100)
Narc2 = Ndict.get('arc2',100)
phi = np.linspace(geo.phi_ois, geo.phi_oie, Nphi)
(x_oi,y_oi) = scroll_geo.coords_inv(phi,geo,theta,flag="oi")
phi = np.linspace(geo.phi_oos, geo.phi_ooe - shaveDelta, Nphi)
(x_oo,y_oo) = scroll_geo.coords_inv(phi,geo,theta,flag="oo")
xarc1=geo.xa_arc1+geo.ra_arc1*cos(np.linspace(geo.t2_arc1,geo.t1_arc1,Narc1))
yarc1=geo.ya_arc1+geo.ra_arc1*sin(np.linspace(geo.t2_arc1,geo.t1_arc1,Narc1))
xline=np.linspace(geo.t1_line,geo.t2_line,Nline)
yline=geo.m_line*xline+geo.b_line
xarc2=geo.xa_arc2+geo.ra_arc2*cos(np.linspace(geo.t1_arc2,geo.t2_arc2,Narc2))
yarc2=geo.ya_arc2+geo.ra_arc2*sin(np.linspace(geo.t1_arc2,geo.t2_arc2,Narc2))
ro = geo.rb*(pi-geo.phi_fi0+geo.phi_fo0)
om = geo.phi_fie-theta+3.0*pi/2.0
xarc1_o=-xarc1+ro*cos(om)
yarc1_o=-yarc1+ro*sin(om)
xline_o=-xline+ro*cos(om)
yline_o=-yline+ro*sin(om)
xarc2_o=-xarc2+ro*cos(om)
yarc2_o=-yarc2+ro*sin(om)
if just_involutes:
x=np.r_[x_oo,x_oi[::-1]]
y=np.r_[y_oo,y_oi[::-1]]
else:
if shaveOn:
x=np.r_[x_oo,xshave,x_oi[::-1],xarc1_o,xline_o,xarc2_o]
y=np.r_[y_oo,yshave,y_oi[::-1],yarc1_o,yline_o,yarc2_o]
else:
x=np.r_[x_oo,x_oi[::-1],xarc1_o,xline_o,xarc2_o]
y=np.r_[y_oo,y_oi[::-1],yarc1_o,yline_o,yarc2_o]
#Output as a column vector
x=x.reshape(len(x),1)
y=y.reshape(len(y),1)
return x,y
def Shave(geo,theta,shaveDelta):
from PDSim.scroll import scroll_geo
phi=np.linspace(geo.phi_ooe-shaveDelta,geo.phi_ooe,200)
(xo,yo)=scroll_geo.coords_inv(phi,geo,theta,"oo")
(xi,yi)=scroll_geo.coords_inv(phi,geo,theta,"oi")
z=(1-0.8*(phi-(geo.phi_ooe-shaveDelta))/(shaveDelta))
xnew=z*xo+(1-z)*xi
ynew=z*yo+(1-z)*yi
return (xnew,ynew)
def plotScrollSet(theta,
geo=None,
axis=None,
fig=None,
lw=None,
OSColor=None,
show=False,
offsetScroll=False,
**kwargs):
"""
The function that plots the scroll sets
Arguments:
theta : float
Crank angle in radians in the range 0 to :math:`2\pi`
Returns:
OS : matplotlib polygon object for the orbiting scroll
Optional Parameters
============= =====================================================
Variable Description
============= =====================================================
fig figure to plot on : default, make new figure
axis axis to plot on : default pylab.gca()
geo geoVals class with geometric parameters
discOn plot the discharge port: True/[False]
OSColor color of orbiting scroll: default 'r'
lw line width : default 1.0
discCurves plot the discharge curves : True/[False]
shaveOn shave the end of orb. scroll : True/[False]
saveCoords save the coord. of the orb. scroll to file True/[False]
wallOn plot the outer wall : [True] /False
offsetScroll If true, scrolls are offset : True/[False]
============= =====================================================
"""
from PDSim.scroll import scroll_geo
if axis is None:
if fig is None:
fig = pylab.figure(figsize=(5, 5))
axis = fig.add_axes((0, 0, 1, 1))
if geo is None:
geo = geoVals(rb=0.003522,
phi_i0=0.19829,
phi_is=4.7,
phi_ie=15.5,
phi_o0=-1.1248,
phi_os=1.8,
phi_oe=15.5,
h=0.03289)
setDiscGeo(geo)
if OSColor is not None:
OSColor = kwargs['OSColor']
else:
OSColor = 'r'
if lw is None:
lw = 1.0
if offsetScroll:
#Turn off the conventional wall
kwargs['wallOn'] = False
#Turn off shaving of the orbiting scroll
kwargs['shaveOn'] = False
# # This is the part of the fixed scroll forming the extension for
# # the offset scroll pocket
# phi = np.linspace(geo.phi_fie, geo.phi_fie+geo.phi_ie_offset,1000)
# x,y = scroll_geo.coords_inv(phi, geo, 0.0, 'fi')
# axis.plot(x,y,'k')
# phi = np.linspace(geo.phi_ie,geo.phi_ie+1.02*pi,1000)
# x,y = coords_inv(phi,geo,theta,'oo')
# axis.plot(x,y,'r--')
# pitch (involute-involute distance for a given involute)
# for 2*pi radians or one rotation is equal to 2*pi*rb, subtract
# thickness of scroll to get diameter
# and divide by two to get radius of closing arc for offset region
r = (2 * pi * geo.rb - geo.t) / 2.0
xee, yee = scroll_geo.coords_inv(geo.phi_fie, geo, 0.0, 'fi')
xse, yse = scroll_geo.coords_inv(geo.phi_foe - 2 * pi, geo, 0.0, 'fo')
x0, y0 = (xee + xse) / 2, (yee + yse) / 2
beta = math.atan2(yee - y0, xee - x0)
t = np.linspace(beta, beta + pi, 1000)
x, y = x0 + r * np.cos(t), y0 + r * np.sin(t)
axis.plot(x, y, 'k', lw=lw)
axis.plot([x[0], x[-1]], [y[0], y[-1]], 'b-')
xarc1 = geo.xa_arc1 + geo.ra_arc1 * cos(
np.linspace(geo.t2_arc1, geo.t1_arc1, 100))
yarc1 = geo.ya_arc1 + geo.ra_arc1 * sin(
np.linspace(geo.t2_arc1, geo.t1_arc1, 100))
xline = np.linspace(geo.t1_line, geo.t2_line, 100)
yline = geo.m_line * xline + geo.b_line
xarc2 = geo.xa_arc2 + geo.ra_arc2 * cos(
np.linspace(geo.t1_arc2, geo.t2_arc2, 100))
yarc2 = geo.ya_arc2 + geo.ra_arc2 * sin(
np.linspace(geo.t1_arc2, geo.t2_arc2, 100))
##Fixed Scroll
phi = np.linspace(geo.phi_fis, geo.phi_fie, 500)
(x_fi, y_fi) = scroll_geo.coords_inv(phi, geo, theta, flag="fi")
phi = np.linspace(geo.phi_fos, geo.phi_foe, 500)
(x_fo, y_fo) = scroll_geo.coords_inv(phi, geo, theta, flag="fo")
## Discharge port
if 'discOn' in kwargs and kwargs['discOn'] == True:
t = np.linspace(0, 2 * pi, 100)
x = geo.disc_x0 + geo.disc_R * cos(t)
y = geo.disc_y0 + geo.disc_R * sin(t)
axis.plot(x, y, 'k--', lw=lw, zorder=0)
if 'discCurves' in kwargs and kwargs['discCurves'] == True:
(x_fis, y_fis) = coords_inv(geo.phi_os + pi, geo, theta, flag="fi")
(nx_fis, ny_fis) = coords_norm(geo.phi_os + pi, geo, theta, flag="fi")
x0 = x_fis - nx_fis * geo.ro
y0 = y_fis - ny_fis * geo.ro
axis.plot(x0, y0, 'o')
axis.plot(x_fis, y_fis, 's')
t = np.linspace(0, 2 * pi, 200)
axis.plot(x0 + geo.ro * cos(t), y0 + geo.ro * sin(t), '-')
axis.plot(geo.xa_arc1, geo.ya_arc1, '^')
axis.plot(geo.xa_arc1 + geo.ra_arc1 * cos(t),
geo.ya_arc1 + geo.ra_arc1 * sin(t), 'k--')
if 'wallOn' not in kwargs or kwargs['wallOn']:
## Outer Wall
(x_wall, y_wall) = circle(geo.x0_wall, geo.y0_wall, geo.r_wall, N=200)
axis.plot(x_wall, y_wall, 'k', lw=lw)
axis.set_xlim([min(x_wall) - 0.001, max(x_wall) + 0.001])
axis.set_ylim([min(y_wall) - 0.001, max(y_wall) + 0.001])
axis.plot(np.r_[xarc1, xline, xarc2],
np.r_[yarc1, yline, yarc2],
'k',
lw=lw)
axis.plot(x_fi, y_fi, 'k', lw=lw)
axis.plot(x_fo, y_fo, 'k', lw=lw)
axis.plot(np.r_[x_fo[-1], x_fi[-1]], np.r_[y_fo[-1], y_fi[-1]], 'k', lw=lw)
shaveOn = None
if 'shaveOn' in kwargs and kwargs['shaveOn'] == False:
shaveOn = False
else:
shaveOn = True
##Orbiting Scroll
(XOS, YOS) = CoordsOrbScroll(theta, geo, shaveOn)
xy = np.hstack((XOS, YOS))
OrbScroll = pyplot.Polygon(xy,
color=OSColor,
lw=lw,
fill=True,
closed=True,
ec='k')
axis.add_patch(OrbScroll)
axis.set_aspect(1.0)
axis.axis('off')
if 'saveCoords' in kwargs:
np.savetxt('xos.csv', XOS, delimiter=',')
np.savetxt('yos.csv', YOS, delimiter=',')
if show:
pylab.show()
return OrbScroll
def plotScrollSet(theta,geo = None,axis = None, fig = None, lw = None, OSColor = None, show = False, offsetScroll = False, **kwargs):
"""
The function that plots the scroll sets
Arguments:
theta : float
Crank angle in radians in the range 0 to :math:`2\pi`
Returns:
OS : matplotlib polygon object for the orbiting scroll
Optional Parameters
============= =====================================================
Variable Description
============= =====================================================
fig figure to plot on : default, make new figure
axis axis to plot on : default pylab.gca()
geo geoVals class with geometric parameters
discOn plot the discharge port: True/[False]
OSColor color of orbiting scroll: default 'r'
lw line width : default 1.0
discCurves plot the discharge curves : True/[False]
shaveOn shave the end of orb. scroll : True/[False]
saveCoords save the coord. of the orb. scroll to file True/[False]
wallOn plot the outer wall : [True] /False
offsetScroll If true, scrolls are offset : True/[False]
============= =====================================================
"""
from PDSim.scroll import scroll_geo
if axis is None:
if fig is None:
fig=pylab.figure(figsize=(5,5))
axis=fig.add_axes((0,0,1,1))
if geo is None:
geo=geoVals(rb=0.003522,phi_i0=0.19829,phi_is=4.7,phi_ie=15.5,phi_o0=-1.1248,phi_os=1.8,phi_oe=15.5,h=0.03289)
setDiscGeo(geo)
if OSColor is not None:
OSColor=kwargs['OSColor']
else:
OSColor='r'
if lw is None:
lw=1.0
if offsetScroll:
#Turn off the conventional wall
kwargs['wallOn'] = False
#Turn off shaving of the orbiting scroll
kwargs['shaveOn'] = False
# # This is the part of the fixed scroll forming the extension for
# # the offset scroll pocket
# phi = np.linspace(geo.phi_fie, geo.phi_fie+geo.phi_ie_offset,1000)
# x,y = scroll_geo.coords_inv(phi, geo, 0.0, 'fi')
# axis.plot(x,y,'k')
# phi = np.linspace(geo.phi_ie,geo.phi_ie+1.02*pi,1000)
# x,y = coords_inv(phi,geo,theta,'oo')
# axis.plot(x,y,'r--')
# pitch (involute-involute distance for a given involute)
# for 2*pi radians or one rotation is equal to 2*pi*rb, subtract
# thickness of scroll to get diameter
# and divide by two to get radius of closing arc for offset region
r = (2*pi*geo.rb-geo.t)/2.0
xee,yee = scroll_geo.coords_inv(geo.phi_fie,geo,0.0,'fi')
xse,yse = scroll_geo.coords_inv(geo.phi_foe-2*pi,geo,0.0,'fo')
x0,y0 = (xee+xse)/2,(yee+yse)/2
beta = math.atan2(yee-y0,xee-x0)
t = np.linspace(beta,beta+pi,1000)
x,y = x0+r*np.cos(t),y0+r*np.sin(t)
axis.plot(x,y,'k',lw=lw)
axis.plot([x[0],x[-1]],[y[0],y[-1]],'b-')
xarc1=geo.xa_arc1+geo.ra_arc1*cos(np.linspace(geo.t2_arc1,geo.t1_arc1,100))
yarc1=geo.ya_arc1+geo.ra_arc1*sin(np.linspace(geo.t2_arc1,geo.t1_arc1,100))
xline=np.linspace(geo.t1_line,geo.t2_line,100)
yline=geo.m_line*xline+geo.b_line
xarc2=geo.xa_arc2+geo.ra_arc2*cos(np.linspace(geo.t1_arc2,geo.t2_arc2,100))
yarc2=geo.ya_arc2+geo.ra_arc2*sin(np.linspace(geo.t1_arc2,geo.t2_arc2,100))
ro=geo.rb*(pi-geo.phi_fi0+geo.phi_fo0)
om=geo.phi_fie-theta+3.0*pi/2.0
xarc1_o=-xarc1+ro*cos(om)
yarc1_o=-yarc1+ro*sin(om)
xline_o=-xline+ro*cos(om)
yline_o=-yline+ro*sin(om)
xarc2_o=-xarc2+ro*cos(om)
yarc2_o=-yarc2+ro*sin(om)
##Fixed Scroll
phi=np.linspace(geo.phi_fis,geo.phi_fie,500)
(x_fi,y_fi)=scroll_geo.coords_inv(phi,geo,theta,flag="fi")
phi=np.linspace(geo.phi_fos,geo.phi_foe,500)
(x_fo,y_fo)=scroll_geo.coords_inv(phi,geo,theta,flag="fo")
## Discharge port
if 'discOn' in kwargs and kwargs['discOn']==True:
t=np.linspace(0,2*pi,100)
x=geo.disc_x0+geo.disc_R*cos(t)
y=geo.disc_y0+geo.disc_R*sin(t)
axis.plot(x,y,'k--',lw=lw,zorder=0)
if 'discCurves' in kwargs and kwargs['discCurves']==True:
(x_fis,y_fis)=coords_inv(geo.phi_os+pi,geo,theta,flag="fi")
(nx_fis,ny_fis)=coords_norm(geo.phi_os+pi,geo,theta,flag="fi")
x0=x_fis-nx_fis*geo.ro
y0=y_fis-ny_fis*geo.ro
axis.plot(x0,y0,'o')
axis.plot(x_fis,y_fis,'s')
t=np.linspace(0,2*pi,200)
axis.plot(x0+geo.ro*cos(t),y0+geo.ro*sin(t),'-')
axis.plot(geo.xa_arc1,geo.ya_arc1,'^')
axis.plot(geo.xa_arc1+geo.ra_arc1*cos(t),geo.ya_arc1+geo.ra_arc1*sin(t),'k--')
if 'wallOn' not in kwargs or kwargs['wallOn']:
## Outer Wall
(x_wall,y_wall)=circle(geo.x0_wall,geo.y0_wall,geo.r_wall,N=200)
axis.plot(x_wall,y_wall,'k',lw=lw)
axis.set_xlim([min(x_wall)-0.001,max(x_wall)+0.001])
axis.set_ylim([min(y_wall)-0.001,max(y_wall)+0.001])
axis.plot(np.r_[xarc1,xline,xarc2],np.r_[yarc1,yline,yarc2],'k',lw=lw)
axis.plot(x_fi,y_fi,'k',lw=lw)
axis.plot(x_fo,y_fo,'k',lw=lw)
axis.plot(np.r_[x_fo[-1],x_fi[-1]],np.r_[y_fo[-1],y_fi[-1]],'k',lw=lw)
shaveOn=None
if 'shaveOn' in kwargs and kwargs['shaveOn']==False:
shaveOn=False
else:
shaveOn=True
##Orbiting Scroll
(XOS,YOS)=CoordsOrbScroll(theta,geo,shaveOn)
xy=np.hstack((XOS,YOS))
OrbScroll=pyplot.Polygon(xy,color=OSColor,lw=lw,fill=True,closed=True,ec='k')
axis.add_patch(OrbScroll)
axis.set_aspect(1.0)
axis.axis('off')
if 'saveCoords' in kwargs:
np.savetxt('xos.csv',XOS,delimiter=',')
np.savetxt('yos.csv',YOS,delimiter=',')
if show:
pylab.show()
return OrbScroll