{
"cells": [
{
"cell_type": "markdown",
"metadata": {},
"source": [
"# Ch:14 Keys and couplings"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"## exa 14-1 - Page 401"
]
},
{
"cell_type": "code",
"execution_count": 2,
"metadata": {
"collapsed": false
},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
" FOS1 is 4.376 \n",
"\n",
" FOS2 is 4.85 \n"
]
}
],
"source": [
"from math import sqrt, pi, atan, acos, cos\n",
"d=40#\n",
"r=d/2#\n",
"P=6*10**3#\n",
"N=350#\n",
"sigyt=380#\n",
"A=pi*12**2/2#\n",
"theta=pi-(2*atan(4/12))#\n",
"alpha=180-(theta*pi/180)#\n",
"l=2*12*cos(19.5*pi/180)#\n",
"A1=l*4/2#\n",
"Abcd=(A*141/180)-A1#\n",
"A2=A-Abcd#\n",
"A3=8*l#\n",
"w=2*pi*N/60#\n",
"T=P/w#\n",
"Pt=T*10**3/r#\n",
"sigb=Pt/A2#\n",
"#Let shear stress developed in key Tk\n",
"Tk=Pt/A3#\n",
"FOS1=sigyt/sigb#\n",
"FOS2=0.577*sigyt/Tk#\n",
"print \" FOS1 is %0.3f \"%(FOS1)#\n",
"print \"\\n FOS2 is %0.2f \"%(FOS2)#"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"## exa 14-2 - Page 401"
]
},
{
"cell_type": "code",
"execution_count": 3,
"metadata": {
"collapsed": false
},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
" Ts is 3.39 N/mm**2 \n",
"\n",
" Th is 2.98 N/mm**2 \n"
]
}
],
"source": [
"from math import sqrt, pi\n",
"n=12#\n",
"phi=360*pi/(180*12*2)#\n",
"R1=45/2#\n",
"R2=50/2#\n",
"l=60#\n",
"Rm=(R1+R2)/2#\n",
"p=6.5#\n",
"Pn=(R2-R1)*l*p#\n",
"T=Pn*Rm#\n",
"T=T*n#\n",
"N=400#\n",
"w=2*pi*N/60#\n",
"P=T*w#\n",
"A=(pi*R1*l)/n#\n",
"Ts=Pn/A#\n",
"Ah=(pi*R2*l)/n#\n",
"Th=Pn/Ah#\n",
"print \" Ts is %0.2f N/mm**2 \"%(Ts)#\n",
"print \"\\n Th is %0.2f N/mm**2 \"%(Th)#"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"## exa 14-3 - Page 402"
]
},
{
"cell_type": "code",
"execution_count": 4,
"metadata": {
"collapsed": false
},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
" l1 is 17 mm \n",
"\n",
" l2 is 19.85 mm \n"
]
}
],
"source": [
"from math import sqrt, pi\n",
"N=360#\n",
"w=2*pi*N/60#\n",
"sigyt=380#\n",
"r=25#\n",
"P=40*10**3#\n",
"FOS=3#\n",
"T=P/w#\n",
"Pt=T*10**3/(2*r)#\n",
"siga=380/3#\n",
"Ta=0.577*380/3#\n",
"l1=Pt/(sqrt(2)*12*Ta)#\n",
"l2=Pt*sqrt(2)/(siga*12)#\n",
"print \" l1 is %0.0f mm \"%(l1)#\n",
"print \"\\n l2 is %0.2f mm \"%(l2)#"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"## exa 14-4 - Page 403"
]
},
{
"cell_type": "code",
"execution_count": 5,
"metadata": {
"collapsed": false
},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
" d is 40 mm \n",
"\n",
" Tsh is 3.13 MPa \n",
"\n",
" b is 7 mm \n",
"\n",
" t is 7 mm \n"
]
}
],
"source": [
"from math import sqrt, pi\n",
"N=300#\n",
"w=2*pi*N/60#\n",
"P=12*10**3#\n",
"Ks=1.25#\n",
"Pd=P*Ks#\n",
"T=Pd/w#\n",
"Tas=50#\n",
"d=16*T*10**3/(pi*Tas)#\n",
"d=d**(1/3)#\n",
"d=40#\n",
"Ts=10#\n",
"d1=(2*d)+13#\n",
"x=(d1**4-d**4)/d1#\n",
"#Let the shear stress in the key be Tsh\n",
"Tsh=T*10**3*16/(pi*x)#\n",
"l=3.5*d#\n",
"Ft=T*2*10**3/d#\n",
"l1=70#\n",
"sigak=50#\n",
"b=Ft/(l1*sigak)#\n",
"t=2*Ft/(100*l1)#\n",
"print \" d is %0.0f mm \"%(d)#\n",
"print \"\\n Tsh is %0.2f MPa \"%(Tsh)#\n",
"print \"\\n b is %0.0f mm \"%(b)#\n",
"print \"\\n t is %0.0f mm \"%(t)#"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"## exa 14-5 - Page 403"
]
},
{
"cell_type": "code",
"execution_count": 6,
"metadata": {
"collapsed": false
},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
" d is 60 mm \n",
"\n",
" b is 13.6 mm \n",
"\n",
" t is 12 mm \n",
"\n",
" dr is 27.822 mm \n"
]
}
],
"source": [
"from math import sqrt, pi\n",
"P=36*10**3#\n",
"N=200#\n",
"w=2*pi*N/60#\n",
"T=P/w#\n",
"Tas=45#\n",
"d=16*T*10**3/(pi*Tas)#\n",
"d=d**(1/3)#\n",
"d=60#\n",
"d1=(2*d)+13#\n",
"l=3.5*d#\n",
"Ftk=T*2/d#\n",
"lk=l/2#\n",
"Tak=40#\n",
"sigack=90#\n",
"b=Ftk*10**3/(lk*Tak)#\n",
"t=2*Ftk*10**3/(sigack*lk)#\n",
"n=4#\n",
"sigatb=60#\n",
"u=0.25#\n",
"dr=16*T*10**3/(u*pi**2*sigatb*n*d)#\n",
"dr=sqrt(dr)#\n",
"print \" d is %0.0f mm \"%(d)#\n",
"print \"\\n b is %0.1f mm \"%(b)#\n",
"print \"\\n t is %0.0f mm \"%(t)#\n",
"print \"\\n dr is %0.3f mm \"%(dr)#"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"## exa 14-6 - Page 404"
]
},
{
"cell_type": "code",
"execution_count": 7,
"metadata": {
"collapsed": false
},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
" d is 32 mm \n",
"\n",
" b is 7 mm \n",
"\n",
" t is 8 mm \n",
"\n",
" db is 5.96 mm \n",
"\n",
" db1 is 6.15 mm \n"
]
}
],
"source": [
"from math import sqrt, pi\n",
"P=16*10**3#\n",
"N=1000#\n",
"w=2*pi*N/60#\n",
"T=P/w#\n",
"Ks=1.4#\n",
"Td=T*Ks#\n",
"Tas=40#\n",
"d=16*T*10**3/(pi*Tas)#\n",
"d=d**(1/3)#\n",
"d=32#\n",
"d1=2*d#\n",
"l=1.5*d#\n",
"ds=1.5*d#\n",
"Tak=40#\n",
"sigack=70#\n",
"Ftk=Td*2/d#\n",
"b=Ftk*10**3/(l*Tak)#\n",
"t=2*Ftk*10**3/(sigack*l)#\n",
"Taf=10#\n",
"tf=Td*10**3*2/(pi*Taf*d1**2)#\n",
"Ftb=Td*10**3/(1.5*d*4)#\n",
"Tab=40#\n",
"db=sqrt(Ftb*4/(Tab*pi))#\n",
"D=4*d#\n",
"trp=d/6#\n",
"Ftb1=Td*10**3/(45*4)#\n",
"db1=sqrt(Ftb1*4/(Tab*pi))#\n",
"print \" d is %0.0f mm \"%(d)#\n",
"print \"\\n b is %0.0f mm \"%(b)#\n",
"print \"\\n t is %0.0f mm \"%(t)#\n",
"print \"\\n db is %0.2f mm \"%(db)#\n",
"print \"\\n db1 is %0.2f mm \"%(db1)#\n",
" \n",
"#The answer to Key thickness 't' is calculated incorrectly in the book."
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"## exa 14-7 - Page 404"
]
},
{
"cell_type": "code",
"execution_count": 8,
"metadata": {
"collapsed": false
},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
" sigmax is 36.77 MPa \n",
"\n",
" b is 9 mm \n",
"\n",
" t is 6 mm \n",
"\n",
" Lf is 36 mm \n",
"\n",
" Do is 180 mm \n"
]
}
],
"source": [
"from math import sqrt, pi\n",
"P=30*10**3#\n",
"N=1440#\n",
"w=2*pi*N/60#\n",
"T=P/w#\n",
"d=36#\n",
"d1=30#\n",
"d2=2*d#\n",
"d3=d1*2#\n",
"l=1.5*d#\n",
"Dp=3.5*d#\n",
"n=6#\n",
"Ft=(2*T)/(Dp*n)#\n",
"p=0.5#\n",
"A=Ft/p#\n",
"Lf=d#\n",
"dp=A/Lf#\n",
"M=Ft*10**3*(5+(Lf/2))#\n",
"db=(32*M/(pi*40))**(1/3)#\n",
"db=15#\n",
"T=(4*526)/(pi*db**2)#\n",
"sigb=32*M/(pi*db**3)#\n",
"sigmax=(sigb/2)+sqrt(((sigb/2)**2)+(T**2))#\n",
"b=d/4#\n",
"t=6#\n",
"Lf=36#\n",
"La=10#\n",
"Do=126+30+(2*(5+1))+(2*6)#\n",
"print \" sigmax is %0.2f MPa \"%(sigmax)#\n",
"print \"\\n b is %0.0f mm \"%(b)#\n",
"print \"\\n t is %0.0f mm \"%(t)#\n",
"print \"\\n Lf is %0.0f mm \"%(Lf)#\n",
"print \"\\n Do is %0.0f mm \"%(Do)#"
]
}
],
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