def fun(cd,D,d,yx,θ,E,mo,Xs,Ys,F,ff1,canvas1,ff2,canvas2):
def a_ij(x,y,b,a):
f1 = lambda x, y: x + np.sqrt(x**2 + y**2)
return (x+b) * np.log(f1(y+a,x+b)/f1(y-a,x+b)) + \
(y+a) * np.log(f1(x+b,y+a)/f1(x-b,y+a)) + \
(x-b) * np.log(f1(y-a,x-b)/f1(y+a,x-b)) + \
(y-a) * np.log(f1(x-b,y-a)/f1(x+b,y-a))
#材料1
E_1 = E # MPa
mu_1 = mo
#材料2
E_2 = E# MPa
mu_2 = mo
k = ( (1 - mu_1**2)/E_1 + (1 - mu_2**2)/E_2) / np.pi
E_d = 1/(k*np.pi)
# x的界限
x1 = -(cd/2)
x2 = cd/2
x_yx = yx/2
y1 = -1
y2 = 1
# x方向网格数
x_grid_number = Xs
# y方向网格数
y_grid_number = Ys
# 网格大小
x_grid_size = (x2 - x1) / (2 * x_grid_number) # nuit:mm
y_grid_size = (y2 - y1) / (2 * y_grid_number) # nuit:mm
def influence_coefficient_matrix(x_number, y_number, x_size, y_size):
Matrix_mother = np.zeros([2 * x_number - 1, 2 * y_number - 1])
for i in range(2 * x_number - 1):
for j in range(2 * y_number - 1):
Matrix_mother[i, j] = a_ij(np.abs(i - x_number+1) * 2 * x_size, np.abs(j - y_number+1) * 2 * y_size, x_size, y_size)
n = 0
P = np.zeros([x_number*y_number, x_number * y_number])
for i in range(x_number):
for j in range(y_number):
t1 = Matrix_mother[(x_number-1-i):(x_number-1-i+x_number),(y_number-1-j):(y_number-1-j+y_number)]
P[n,:] = t1.reshape(1,-1)
n = n + 1
return P
P = influence_coefficient_matrix(x_grid_number, y_grid_number, x_grid_size, y_grid_size)
###
# 圆柱的表面坐标
D1=d
D2=D
theta=θ*(2*np.pi/360)
F_ext = F
R=(D1+D2)/4
xa = [x1 + (2*i + 1)* x_grid_size for i in range(x_grid_number)]
ya = [y1 + (2*i + 1)* y_grid_size for i in range(y_grid_number)]
#xx, yy = np.meshgrid(xa, ya)#, sparse=True)
#曲率半径
def Ri(x):
Di=(1-(x-x1)/(2*x2))*D1+(x-x1)/(2*x2)*D2
Ri=Di/(2*np.cos(theta))
return Ri
#对数曲线
def duishu(x_n):
ds = (F_ext/(np.pi*2*x_yx*E_d))*np.log(1/(1-(2*x_n/(2*x_yx))**2))
R_r = Ri(x_n) - ds
return R_r
z = np.zeros([x_grid_number, y_grid_number])
for i in range(x_grid_number):
for j in range(y_grid_number):
if np.logical_and(np.logical_and(xa[i] <x_yx, xa[i] >-x_yx), np.logical_and(ya[j]<y2, ya[j] > -y2)):
z[i,j] = np.sqrt(duishu(xa[i])**2 - ya[j]**2)
Ri_M=np.zeros(x_grid_number)
Ri_M.shape=x_grid_number,1
for i in range(x_grid_number):
Ri_M[i,0]=Ri(xa[i])
shape = z
#shape= np.zeros_like(z)
#shape = np.zeros([x_grid_number, y_grid_number])
#positon = np.logical_and(np.logical_and(xx < 1, xx > -1), np.logical_and(yy<1.5, yy > -1.5))
#shape[positon] = z[positon]
n=0
d_test = 0.003
# 确定位移下限
while True:
alpha = shape - Ri_M + d_test
b = alpha.reshape(1,-1)
# plt.plot(b[0,:])
for i in range(b.size):
if b[0,i] < 0:
b[0,i] = 0
c = np.linalg.solve(P,b.T/k)
F_calculate = 0
for i in range(c.shape[0]):
if(c[i,0]>0):
F_calculate += c[i,0] * 4 * x_grid_size * y_grid_size
#print(F_calculate)
if(F_ext < F_calculate):
d_test = 0.5 * d_test
else:
break
d_low = d_test
# 确定位移上限
d_test = 0.01
while True:
alpha = shape - Ri_M + d_test
b = alpha.reshape(1,-1)
b[b<0] = 0
# plt.plot(b[0,:])
c = np.linalg.solve(P, b.T/k)
c[c<0] = 0
F_calculate = (c * 4 * x_grid_size * y_grid_size).sum()
#print(F_calculate)
if(F_ext > F_calculate):
d_test = 2 * d_test
else:
break
d_up = d_test
d_test = 0.5 * (d_up + d_low)
while np.abs(d_up - d_low) > 1e-8:
alpha = shape - Ri_M + d_test
b = alpha.reshape(1,-1)
b[b<0] = 0
# plt.plot(b[0,:])
c = np.linalg.solve(P, b.T/k)
c[c<0] = 0
F_calculate = (c * 4 * x_grid_size * y_grid_size).sum()
#print(F_calculate)
if(F_ext > F_calculate):
d_low = d_test
d_test = 0.5 * (d_up + d_low)
else:
d_up = d_test
d_test = 0.5 * (d_up + d_low)
#print(d_low,d_up)
n = n+1
if(n>20000):
break
#
#d.max()
#
#a1 = (1 - mu_1**2)/E_1
#a2 = (1 - mu_2**2)/E_2
#
#np.sqrt(6 * F_ext * (1/(a1+a2))**2)/np.pi
Hz_s1 = 0.388 * (F_ext * (2*E_1*E_2/(E_1 + E_2))**2 / R**2)**(1/3)
#0.388 * (10000 * (2*E_1*E_2/(E_1 + E_2))**2)**(1/3)
#
#0.388 * (10000 * E_1**2)**(1/3)
#1.231 * (10000**2 / E_1**2)**(1/3)
#d_test
Hz_d1 = 1.231 * (F_ext**2 / E_1**2/R)**(1/3)
# =============================================================================
# print('赫兹接触应力 = %0.3f, \t 计算接触应力 = %0.3f ' % (Hz_s1, c.max()))
# print('赫兹接触深度 = %0.3f, \t 计算接触深度 = %0.3f ' % (Hz_d1, d_test))
# =============================================================================
#print('赫兹接触半径 = %0.3f' % r1)
qjbl.set_v('De',c.reshape(x_grid_number, y_grid_number))
###图1
ff1.clf()
a1 = ff1.add_subplot(111)
s1 = qjbl.get_v('De')[:,int((y_grid_number+1)/2)]
a1.plot(s1)
canvas1.show()
#text1.set('图1 - 最大接触应力分布图'+' F='+F_ext+'N')
###图2
ff2.clf()
a2 = ff2.gca(projection='3d')
x = np.arange(0, x_grid_number)
y = np.arange(0, y_grid_number)
X, Y = np.meshgrid(x, y)
Z = qjbl.get_v('De').T
# Plot the surface.
surf = a2.plot_surface(X, Y, Z, cmap=cm.coolwarm,
linewidth=0,)
ff2.colorbar(surf, shrink=0.5, aspect=10)
canvas2.show()
def func6(win,tl):
qjbl.set_v('Dd',0)
####绘图函数###################################################
def hui1():
f1.clf()
a1 = f1.add_subplot(111)
s1 = qjbl.get_v('Dd')[:,int((int(Ys.get())+1)/2)]
a1.plot(s1)
canvas1.show()
text1.set('图1 - 最大接触应力分布图'+' F='+F.get()+'N')
def hui2():
f2.clf()
a2 = f2.gca(projection='3d')
x = np.arange(0, int(Xs.get()))
y = np.arange(0, int(Ys.get()))
X, Y = np.meshgrid(x, y)
Z = qjbl.get_v('Dd').T
# Plot the surface.
surf = a2.plot_surface(X, Y, Z, cmap=cm.coolwarm,
linewidth=0,)
f2.colorbar(surf, shrink=0.5, aspect=10)
canvas2.show()
text2.set('图2 - 滚子接触应力三维分布图'+' F='+F.get()+'N')
#####################################################
########################################
# =============================================================================
# root2 = Tk()
# root2.title('滚子修形计算')
# =============================================================================
#tl = Toplevel()
#tl.title('圆锥直线型修形')
Fr = Frame(tl)
Fr.grid()
f1 = Frame(Fr)
f1.grid(row=0,column=0,sticky=N,pady=20,)
f1_1 = Frame(f1)
f1_1.grid(row=0,column=0,pady=2,padx=20,sticky=N+W)
ll = Label(f1_1,text='参数设置',font=('黑体',15))
ll.grid(row=0,column=0,padx=20,pady=2,sticky=W+N)
l1 = Label(f1_1,text='滚子长度 L',font=(10))
l1.grid(row=1,column=0,padx=20,pady=8,sticky=W)
cd = StringVar()
cd.set(20)
e1 = Entry(f1_1,textvariable=cd,)
e1.grid(row=1,column=1)
l1_1 = Label(f1_1,text='mm',font=(10))
l1_1.grid(row=1,column=2,pady=8,sticky=W)
l2 = Label(f1_1,text='有效长度 Lw',font=(10))
l2.grid(row=2,column=0,padx=20,pady=8,sticky=W)
yx = StringVar()
yx.set(18)
e2 = Entry(f1_1,textvariable=yx)
e2.grid(row=2,column=1)
l2_2 = Label(f1_1,text='mm',font=(10))
l2_2.grid(row=2,column=2,pady=8,sticky=W)
l3 = Label(f1_1,text='滚子半径 R',font=(10))
l3.grid(row=3,column=0,padx=20,pady=8,sticky=W)
R = StringVar()
R.set(16)
e3 = Entry(f1_1,textvariable=R)
e3.grid(row=3,column=1)
l3_3 = Label(f1_1,text='mm',font=(10))
l3_3.grid(row=3,column=2,pady=8,sticky=W)
l6 = Label(f1_1,text='弹性模量 E',font=(10))
l6.grid(row=6,column=0,padx=20,pady=8,sticky=W)
E = StringVar()
E.set(200000)
e6 = Entry(f1_1,textvariable=E)
e6.grid(row=6,column=1)
l6_6 = Label(f1_1,text='Mpa',font=(10))
l6_6.grid(row=6,column=2,pady=8,sticky=W)
l7 = Label(f1_1,text='泊松比 μ',font=(10))
l7.grid(row=7,column=0,padx=20,pady=8,sticky=W)
mo = StringVar()
mo.set(0.3)
e7 = Entry(f1_1,textvariable=mo)
e7.grid(row=7,column=1)
l8 = Label(f1_1,text='滚子轴向网格数 Xs',font=(10))
l8.grid(row=8,column=0,padx=20,pady=8,sticky=W)
Xs = StringVar()
Xs.set(60)
e8 = Entry(f1_1,textvariable=Xs)
e8.grid(row=8,column=1)
l9 = Label(f1_1,text='滚子径向网格数 Ys',font=(10))
l9.grid(row=9,column=0,padx=20,pady=8,sticky=W)
Ys = StringVar()
Ys.set(40)
e9 = Entry(f1_1,textvariable=Ys)
e9.grid(row=9,column=1)
l10 = Label(f1_1,text='施加载荷 F',font=(10))
l10.grid(row=10,column=0,padx=20,pady=8,sticky=W)
F = StringVar()
F.set(1000)
e10 = Entry(f1_1,textvariable=F)
e10.grid(row=10,column=1)
l10_10 = Label(f1_1,text='N',font=(10))
l10_10.grid(row=10,column=2,pady=8,sticky=W)
b = Button(f1_1,text='开始计算',command=lambda :yzds.fun(float(cd.get()),float(R.get()),float(yx.get()),float(E.get())
,float(mo.get()),int(Xs.get()),int(Ys.get()),float(F.get()),f1,canvas1,f2,canvas2),fg='red')
b.grid(row=11,column=0,columnspan=2,padx=30,pady=5,ipadx=25,)
f1_2 = Frame(Fr)
f1_2.grid(row=1,column=0,sticky=N+W,padx=20)
l9 = Label(f1_2,text='参数对应示意图',font=('黑体',15))
l9.grid(row=0,column=0,padx=20,pady=8,sticky=W)
c = Canvas(f1_2,bg='white',height=270,width=320)
c.grid(row=1,column=0,padx=20,pady=40)
img = PhotoImage(file = 'syt.gif')
c.create_image(0,0,anchor='nw',image=img)
######### 绘图 ###################################
f2_1 = Frame(Fr)
f2_1.grid(row=0,column=1,pady=20,sticky=W,padx=30)
lr = Label(f2_1,text='计算结果',font=('黑体',15))
lr.pack(anchor='w',pady=2)
# =============================================================================
# b1 = Button(f2_1,text='绘图1',command=hui1,fg='blue')
# b1.pack(anchor='w',ipadx=20)
# =============================================================================
text1=StringVar()
text1.set('图1 - 最大接触应力分布图')
lr_1 = Label(f2_1,textvariable=text1,font=(10))
lr_1.pack()
f1 = Figure(figsize=(7, 3), dpi=100)
canvas1 = FigureCanvasTkAgg(f1, master=f2_1)
canvas1.show()
canvas1.get_tk_widget().pack(pady=10,anchor='w')
#工具按钮
toolbar1 = NavigationToolbar2TkAgg(canvas1, f2_1)
toolbar1.update()
canvas1._tkcanvas.pack()
f2_2 = Frame(Fr)
f2_2.grid(row=1,column=1,pady=2,sticky=W,padx=30)
# =============================================================================
# b2 = Button(f2_2,text='绘图2',command=hui2,fg='blue')
# b2.pack(anchor='w',ipadx=20)
# =============================================================================
text2=StringVar()
text2.set('图2 - 滚子接触应力三维分布图')
lr_2 = Label(f2_2,textvariable=text2,font=(10))
lr_2.pack()
f2 = Figure(figsize=(7, 3), dpi=100)
canvas2 = FigureCanvasTkAgg(f2, master=f2_2)
canvas2.show()
canvas2.get_tk_widget().pack(pady=2,anchor='w')
#工具按钮
toolbar2 = NavigationToolbar2TkAgg(canvas2, f2_2)
toolbar2.update()
canvas2._tkcanvas.pack()
#############################################
win.mainloop()
