{
"cells": [
{
"cell_type": "markdown",
"metadata": {},
"source": [
"# Ch:27 Straight bevel gears"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"## exa 27-1 - Page 712"
]
},
{
"cell_type": "code",
"execution_count": 2,
"metadata": {
"collapsed": false
},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"Pt is 1061 N \n",
"\n",
"Ps is 386.18 N \n",
"\n",
"Pr is 345.41 N \n",
"\n",
"Pa is 172.71 N \n"
]
}
],
"source": [
"from math import sqrt, pi, atan, sin, tan, cos\n",
"from __future__ import division\n",
"P=8000#\n",
"N1=400#\n",
"N2=200#\n",
"i=N1/N2# #i=Zg/Zp=dg/dp\n",
"gamma1=atan(1/i)#\n",
"gamma2=90-gamma1#\n",
"rp=200#\n",
"R=rp/sin(gamma1)#\n",
"b=0.2*R#\n",
"rm1=rp-(b*sin(gamma1)/2)#\n",
"Pt=P*1000*60/(2*pi*N1*rm1)#\n",
"alpha=20*pi/180#\n",
"Ps=Pt*tan(alpha)#\n",
"Pr=Ps*cos(gamma1)#\n",
"Pa=Ps*sin(gamma1)#\n",
"print \"Pt is %0.0f N \"%(Pt)#\n",
"print \"\\nPs is %0.2f N \"%(Ps)#\n",
"print \"\\nPr is %0.2f N \"%(Pr)#\n",
"print \"\\nPa is %0.2f N \"%(Pa)#\n",
"\n",
"#The difference in the values is due to rounding-off of the values."
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"## exa 27-2 - Page 712"
]
},
{
"cell_type": "code",
"execution_count": 3,
"metadata": {
"collapsed": false
},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"Zpv is 22.88 \n",
"\n",
"Sb is 6653 N \n"
]
}
],
"source": [
"from math import sqrt, pi, atan, sin, tan, cos\n",
"alpha=20*pi/180#\n",
"Zp=20#\n",
"Zg=36#\n",
"m=4#\n",
"sigut=600#\n",
"b=25#\n",
"dp=m*Zp#\n",
"rp=dp/2#\n",
"dg=m*Zg#\n",
"rg=dg/2#\n",
"gamma1=atan(rp/rg)#\n",
"Zpv=Zp/cos(gamma1)#\n",
"Y=0.33+0.003*0.88#\n",
"sigb=sigut/3#\n",
"Sb=m*b*sigb*Y#\n",
"print \"Zpv is %0.2f \"%(Zpv)#\n",
"print \"\\nSb is %0.0f N \"%(Sb)#"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"## exa 27-3 - Page 712"
]
},
{
"cell_type": "code",
"execution_count": 4,
"metadata": {
"collapsed": false
},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"gamma1 is 33.7 deg \n",
"\n",
"gamma2 is 56.3 deg \n",
"\n",
"R is 162.25 mm \n",
"\n",
"FCA is 35.808 deg \n",
"\n",
"RCA is 31.04 deg \n"
]
}
],
"source": [
"from math import sqrt, pi, atan, sin, tan, cos,asin\n",
"m=6#\n",
"Zp=30#\n",
"Zg=45#\n",
"dp=m*Zp#\n",
"rp=dp/2#\n",
"dg=m*Zg#\n",
"rg=dg/2#\n",
"R=sqrt(rg**2+rp**2)#\n",
"gamma1=180/pi*asin(rp/R)#\n",
"gamma2=(90-gamma1)#\n",
"ha=6#\n",
"hf=1.25*ha#\n",
"phi=180/pi*atan(ha/R)#\n",
"beta=180/pi*atan(hf/R)#\n",
"#let Face Cone Angle be FCA\n",
"FCA=(gamma1+phi)#\n",
"#Let Root cone angle be RCA\n",
"RCA=(gamma1-beta)#\n",
"print \"gamma1 is %0.1f deg \"%(gamma1)#\n",
"print \"\\ngamma2 is %0.1f deg \"%(gamma2)#\n",
"print \"\\nR is %0.2f mm \"%(R)#\n",
"print \"\\nFCA is %0.3f deg \"%(FCA)#\n",
"print \"\\nRCA is %0.2f deg \"%(RCA)#"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"## exa 27-4 - Page 713"
]
},
{
"cell_type": "code",
"execution_count": 5,
"metadata": {
"collapsed": false
},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"Sw is 12142.4 N \n"
]
}
],
"source": [
"from math import sqrt, pi, atan, sin, tan, cos\n",
"alpha=20*pi/180#\n",
"Zp=25#\n",
"Zg=40#\n",
"m=5#\n",
"b=30#\n",
"BHN=400#\n",
"dp=m*Zp#\n",
"rp=dp/2#\n",
"dg=m*Zg#\n",
"rg=dg/2#\n",
"gamma1=atan(rp/rg)#\n",
"gamma1=180/pi*gamma1#\n",
"gamma2=(90-gamma1)#\n",
"a=cos(pi/180*gamma2)#\n",
"Zp1=Zp/cos(gamma1)#\n",
"Zg1=Zg/a#\n",
"Q=(2*Zg1)/(Zp1+Zg1)#\n",
"K=0.16*(BHN/100)**2#\n",
"Sw=0.75*b*dp*Q*K/cos(pi/180*gamma1)#\n",
"print \"Sw is %0.1f N \"%(Sw)#\n",
" \n",
" #The difference in the value of Sw is due to rounding-off of the value of Q."
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"## exa 27-5 - Page 713"
]
},
{
"cell_type": "code",
"execution_count": 6,
"metadata": {
"collapsed": false
},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"Sb is 4633 N \n",
"\n",
"Sw is 5438.0 N \n"
]
}
],
"source": [
"from math import sqrt, pi, atan, sin, tan, cos\n",
"Zp=20#\n",
"Zg=36#\n",
"m=4#\n",
"b=25#\n",
"BHN=360#\n",
"Np=750#\n",
"FOS=1.75#\n",
"dp=m*Zp#\n",
"rp=dp/2#\n",
"dg=m*Zg#\n",
"rg=dg/2#\n",
"gamma1=atan(dp/dg)#\n",
"gamma1=180/pi*gamma1#\n",
"gamma2=(90-gamma1)#\n",
"a=cos(pi/180*gamma2)#\n",
"Zp1=Zp/cos(pi/180*gamma1)#\n",
"Zg1=Zg/a#\n",
"Q=(2*Zg1)/(Zp1+Zg1)#\n",
"K=0.16*(BHN/100)**2#\n",
"R=sqrt(rp**2+rg**2)#\n",
"Y=0.33+0.003*0.86#\n",
"sigut=600#\n",
"sigb=sigut/3#\n",
"Sb=m*b*Y*sigb*(1-(b/R))#\n",
"Sw=0.75*b*dp*Q*K/cos(pi/180*gamma1)#\n",
"print \"Sb is %0.0f N \"%(Sb)#\n",
"print \"\\nSw is %0.1f N \"%(Sw)#\n",
"\n",
"#The answwer to Sb is calculated incorrectly in the book."
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"## exa 27-6 - Page 713"
]
},
{
"cell_type": "code",
"execution_count": 7,
"metadata": {
"collapsed": false
},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"m*Y is 2.613 mm**2 \n",
"\n",
"m is 6 mm \n"
]
}
],
"source": [
"from math import sqrt, pi, atan, sin, tan, cos\n",
"Dp=300#\n",
"rp=150#\n",
"#Let the angular velocity ratio be i\n",
"i=2/3#\n",
"rg=rp/i#\n",
"Dg=2*rg#\n",
"R=sqrt(rp**2+rg**2)#\n",
"P=15000#\n",
"N=300#\n",
"Cs=1.5#\n",
"FOS=2#\n",
"sigb=100#\n",
"gamma1=atan(Dp/Dg)#\n",
"gamma1=180/pi*gamma1#\n",
"gamma2=(90-gamma1)#\n",
"v=2*pi*N*rp/(60*1000)#\n",
"Cv=5.6/(5.6+sqrt(v))#\n",
"Pt=P/v#\n",
"Peff=Pt*Cs/Cv#\n",
"Sb=Peff*FOS#\n",
"b=R/4#\n",
"#let x=m*Y\n",
"x=Sb/(b*sigb*(1-(b/R)))#\n",
"m=6#\n",
"print \"m*Y is %0.3f mm**2 \"%(x)#\n",
"print \"\\nm is %0.0f mm \"%(m)#"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"## exa 27-7 - Page 714"
]
},
{
"cell_type": "code",
"execution_count": 8,
"metadata": {
"collapsed": false
},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"m is 4 mm \n",
"\n",
"BHN is 189 \n"
]
}
],
"source": [
"from math import sqrt, pi, atan, sin, tan, cos\n",
"Zp=24#\n",
"Zg=36#\n",
"N=1400#\n",
"P=11600#\n",
"Cs=1.4#\n",
"FOS=2#\n",
"sigut=600#\n",
"sigb=sigut/3#\n",
"gamma1=atan(Zp/Zg)#\n",
"gamma1=180/pi*gamma1#\n",
"gamma2=(90-gamma1)#\n",
"a=cos(pi/180*gamma2)#\n",
"Zp1=Zp/cos(pi/180*gamma1)#\n",
"Zg1=Zg/a#\n",
"Q=(2*Zg1)/(Zp1+Zg1)#\n",
"v=1.76#\n",
"Pt=P/v#\n",
"Cv=5.6/(5.6+sqrt(v))#\n",
"Peff=Pt*Cs/Cv#\n",
"x=Peff*FOS#\n",
"Y=0.352+(0.003*0.85)#\n",
"y=2*sigb*Y*(1-(6/21.63))#\n",
"m=sqrt(x/y)#\n",
"# Design is safe for m=4\n",
"m=4#\n",
"b=6*m#\n",
"dp=24*m#\n",
"rp=48#\n",
"dp=dp/cos(pi/180*gamma1)#\n",
"v=2*pi*N*rp/(60*1000)#\n",
"Cv=5.6/(5.6+sqrt(v))#\n",
"Sb=y*m**2#\n",
"#Sw=Sb#\n",
"K=Sb/(0.75*b*dp*Q)#\n",
"BHN=sqrt(K/0.16)*100#\n",
"print \"m is %0.0f mm \"%(m)#\n",
"print \"\\nBHN is %0.0f \"%(BHN)#\n",
" \n",
"#The answwer to BHN is calculated incorrectly in the book."
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"## exa 27-8 - Page 714"
]
},
{
"cell_type": "code",
"execution_count": 9,
"metadata": {
"collapsed": false
},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"m is 6 mm \n",
"\n",
"b is 36 mm \n",
"\n",
"R is 216 mm \n"
]
}
],
"source": [
"from math import sqrt, pi, atan, sin, tan, cos\n",
"Zp=40#\n",
"Zg=60#\n",
"P=3500#\n",
"N=600#\n",
"Cs=1.5#\n",
"sigb=55#\n",
"gamma1=atan(Zp/Zg)#\n",
"gamma1=180/pi*gamma1#\n",
"gamma2=(90-gamma1)#\n",
"a=cos(pi/180*gamma2)#\n",
"Zp1=Zp/cos(pi/180*gamma1)#\n",
"Zg1=Zg/a#\n",
"Q=(2*Zg1)/(Zp1+Zg1)#\n",
"# Design is safe for m=6\n",
"m=6#\n",
"b=6*m#\n",
"dp=Zp*m#\n",
"rp=dp/2#\n",
"dg=Zg*m#\n",
"rg=dg/2#\n",
"R=sqrt(rp**2+rg**2)#\n",
"print \"m is %0.0f mm \"%(m)#\n",
"print \"\\nb is %0.0f mm \"%(b)#\n",
"print \"\\nR is %0.0f mm \"%(R)#"
]
}
],
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