기어 설계 참고 사항

Ref : http://blog.daum.net/gear-root/44

기어 정밀도 등급별 비교표 (대략)

USA, FR, RU, UK 등은 생략

Nation	Standard
ISO	ISO 1328:1975	0	1	2	3	4	5	6	7	8	9	10	11	12
KR	KS B ISO 1328-1.2:2005	0	1	2	3	4	5	6	7	8	9	10	11	12
JP	JIS B 1702-1.2:1998	0	1	2	3	4	5	6	7	8	9	10	11	12
DE	DIN 3962.3:1959		1	2	3	4	5	6	7	8	9	10	11	12
KR(old)	KS B 1405-85:1971					0	1	2	3	4	5	6	7	8
JP(old)	KS B 1702:1976					0	1	2	3	4	5	6	7	8

가공방법에 따른 정밀도 등급 한계 (대략)

기계 상태가 좋고, 뛰어난 숙련공이 작업하고, 품질검수를 제대로 할 경우에는, 아래의 도달 한계등급보다 1등급 더 높은 등급까지 기대 가능

가공방법	도달 한계 등급(KS B ISO 1328-1.2:2005)
CNC (초경 CBN날로 마무리)	6
연삭(Grind) 마무리	4
쉐이빙(Shave) 마무리	7
랙커터(Rack Cutter) 셰이퍼(Shaper) 가공	8
디스크 커터(Disc Cutter) 셰이퍼(Shaper) 가공	9
AA급 호브(Hob)	8
A급 호브(Hob)	9
B급 호브(Hob)	10
사출성형	10

용도별 정밀도 등급 기준

Ref : http://blog.daum.net/_blog/BlogTypeView.do?blogid=05KgA&articleno=16050627&_bloghome_menu=recenttext

등급(KS B ISO 1328-1.2:2005)	용도	가공방법
2	기준 원기용 마스터 기어	형상 연마
3	검사 부서의 마스터 기어	형상 연마 및 창성 연마
4	공장의 마스터 기어	형상 연마 및 창성 연마
4	측정기기의 매커니즘	형상 연마 및 창성 연마
4	초고속 회전, 극한 하중	형상 연마 및 창성 연마
5	산업용 로봇 정밀급 감속기	형상 연마 및 창성 연마
5,6	공작기계	형상 연마 및 창성 연마
5,6	항공기용 터빈 기어	형상 연마 및 창성 연마
5,6	측정기기의 구동	형상 연마 및 창성 연마
6,7	자동차 변속기의 최고속 부위	호브,셰이퍼,쉐이빙후 경화하고, 이후 연마
8,9	자동차 변속기의 중저속 부위	호브,셰이퍼,쉐이빙후 경화 (연마 생략)
8,9	철도차량	호브,셰이퍼,쉐이빙후 경화 (연마 생략)
8,9	공구	호브,셰이퍼,쉐이빙후 경화 (연마 생략)
8,9	사무기기	호브,셰이퍼,쉐이빙후 경화 (연마 생략)
9	산업용 로봇의 감속기 입력기어	호브,셰이퍼,쉐이빙후 경화 (연마 생략)
10	일반기계(일반 변속기, 호이스트 등)	인발, 소결, 사출성형
11,12	일반 농업용 장비



In [30]:

    
#########################################################################
# FGPG (Fine_Gear_Profile_Generator) V13
# 20200319
# by Dongho Kim  from Korea
# dymaxion.kim@gmail.com
# http://dymaxionkim.blogspot.kr/
#########################################################################
## Ref.
# http://tro.kr/29
# http://en.wikipedia.org/wiki/Coordinate_rotations_and_reflections
# http://dip28p.web.fc2.com/
#########################################################################
## History
# 20141114 V0.44 : SageMath Version
# 20150519 V0.1 : Trying to Conversion for Julia, Trying Interact Macro
# 20150519 V0.2 : Studying about Lack
# 20150527 V01 : Plotting Whole Gear at first
# 20150527 V02 : Trying Interact Macro
# 20150527 V03 : Debug V01
# 20150527 V04 : Adding Annotations, Saving Profile Data File, ...
# 20150527 V05 : Adding More Error Checks, Making geo File
# 20150528 V06 : Debug Making geo File
# 20150528 V07 : Align vertically Gear, Add Shaft
# 20150528 V08 : Modifying Sequences, Debug Making geo File, Make new Figure, Make svg Pictures, Save scr File, Modify Annotations
# 20150530 V09 : Modifying Shaft, Internal-External Condition, geo File
# 20150531 V10 : Adding version Variable
# 20150602 V11 : Making case.sif, case.bat, case.sh files
# 20161022 V12 : Conversion for Julia V0.5
# 20181127 V13 : Conversion for Julia V1.0
# 20200319 V14 : Add Some KS Standard Results
# 20200718 V15 : Change from CSV.read() to CSV.file()
#########################################################################
## Todo
# Write Theory Doc
# Write User Manual
# Write Some Actual Examples
# Tip Relief to Modifying Tooth Profile
# Profile Repairing in Undercut Condition
# Change Result File Name based in Time
# Build to Standalone Executable

using CSV
using DataFrames
using PyPlot
PyPlot.svg(true)

############################
# Parameters
version = "v15"
m = 1  # Module
z = 20  # Teeth Number
alpha_0_deg = 20  # Pressure Angle [Deg]
x = 0.2  # Offset Factor
b = 0  # Backlash Factor
a = 1.0  # Addendum of Tooth
d = 1.2  # Dedendum of Tooth
c = 0.3  # Radius Factor of Edge Round of Hob
e = 0.2  # Radius Factor of Edge Round of Tooth
# Center of Gear
x_0 = 0
y_0 = 0
# Segmentation Points Numbers for each curves
seg_circle = 360
seg_involute = 50
seg_edge_r = 4
seg_root_r = 20
seg_center = 2
seg_outter = 4
seg_root = 4


############################
# Input Parameters from input4fgpg.csv file
input4fgpg = DataFrame!(CSV.File("input4fgpg.csv"))

m = Float64(input4fgpg[1,3])
z = Int(input4fgpg[2,3])
alpha_0_deg = Float64(input4fgpg[3,3])
alpha_0 = alpha_0_deg*2*pi/360
x = Float64(input4fgpg[4,3])
b = Float64(input4fgpg[5,3])
a = Float64(input4fgpg[6,3])
d = Float64(input4fgpg[7,3])
c = Float64(input4fgpg[8,3])
e = Float64(input4fgpg[9,3])
x_0 = Float64(input4fgpg[10,3])
y_0 = Float64(input4fgpg[11,3])
seg_circle = Int(input4fgpg[12,3])
seg_involute = Int(input4fgpg[13,3])
seg_edge_r = Int(input4fgpg[14,3])
seg_root_r = Int(input4fgpg[15,3])
seg_center = Int(input4fgpg[16,3])
seg_outter = Int(input4fgpg[17,3])
seg_root = Int(input4fgpg[18,3])


############################
# Involute Curve
# alpha_m = Center Line's Slope [Rad]
alpha_m = pi/z
# alpha_is = Start Angle for Involute Curve
alpha_is = alpha_0 + pi/(2*z) + b/(z*cos.(alpha_0)) - (1+2*x/z)*sin.(alpha_0)/cos.(alpha_0)
# theta_is = Minimum Range of Parameter to Draw Involute Curve
theta_is = sin.(alpha_0)/cos.(alpha_0) + 2*(c*(1-sin.(alpha_0))+x-d)/(z*cos.(alpha_0)*sin.(alpha_0))
# theta_ie = Maximum Range of Parameter to Draw Involute Curve
theta_ie = 2*e/(z*cos.(alpha_0)) + sqrt.( ((z+2*(x+a-e))/(z*cos.(alpha_0)))^2 - 1 )
# Condition of theta_ie
if alpha_m<alpha_is+theta_ie-atan.(theta_ie)
    # theta_ie를 뉴튼라프슨법으로 수치해석하여 근사해를 다시 구해서 작도에 적용해야 함 (아직 미구현)
end
# Condition of Undercut
if theta_is<0 && (z/2)*sin.(alpha_0)^2<d-x-c*(1-sin.(alpha_0))
    # 언더컷 발생한 경우이므로, theta_ie, theta_te를 비선형 연립방정식 반복해법으로 다시 구해야 함 (아직 미구현)
end
THETA1 = range(theta_is,stop=theta_ie,length=seg_involute) 
X1 = ones(length(THETA1))
Y1 = X1
X1 = x_0 .+ (1 ./2).*m.*z.*cos.(alpha_0).*sqrt.(1 .+THETA1.^2).*cos.(alpha_is .+THETA1 .-atan.(THETA1))
Y1 = y_0 .+ (1 ./2).*m.*z.*cos.(alpha_0).*sqrt.(1 .+THETA1.^2).*sin.(alpha_is .+THETA1 .-atan.(THETA1))
#plot(X1,Y1,color="red",linestyle="-")


############################
# Edge Round Curve of Tooth
# alpha_e = Angle between Tooth's Center & End Point of Tooth
alpha_e = alpha_is + theta_ie - atan.(sqrt.( ( (z .+2*(x+a-e))/(z*cos.(alpha_0)) )^2 - 1 ))
# modify "e"
if alpha_e>alpha_m && alpha_m>alpha_is+theta_ie-atan.(theta_ie)
    e = (z/2)*cos.(alpha_0)*( theta_ie - sqrt.( (1/cos.(alpha_is+theta_ie-alpha_m))^2-1 ) )
end
# x_e, y_e = Location of Tooth's End Point
x_e = x_0 + m*((z/2)+x+a)*cos.(alpha_e)
y_e = y_0 + m*((z/2)+x+a)*sin.(alpha_e)
# x_e0, y_e0 = Location of Edge Round Center
x_e0 = m*(z/2+x+a-e)*cos.(alpha_e) + x_0
y_e0 = m*(z/2+x+a-e)*sin.(alpha_e) + y_0
# Parameter Range of Edge Round
theta3_min = atan.((Y1[length(Y1)]-y_e0)/(X1[length(X1)]-x_e0))
theta3_max = atan.((y_e-y_e0)/(x_e-x_e0))
THETA3 = range(theta3_min,stop=theta3_max,length=seg_edge_r) 
X3 = m*e*cos.(THETA3) .+ x_e0
Y3 = m*e*sin.(THETA3) .+ y_e0
#plot(X3,Y3,color="green",linestyle="-")


############################
# Root Round Curve of Tooth
# Condition Check
# alpha_ts = Start Angle of Root Round Curve
# THETA_s = Substitution Variable to plot Root Round Curve
alpha_ts = (2*(c*(1-sin.(alpha_0))-d)*sin.(alpha_0)+b)/(z*cos.(alpha_0)) - 2*c*cos.(alpha_0)/z + pi/(2*z)
theta_te = 2*c*cos.(alpha_0)/z - 2*(d-x-c*(1-sin.(alpha_0)))*cos.(alpha_0)/(z*sin.(alpha_0))
THETA_t  = range(0,stop=theta_te,length=seg_root_r) 
if c!=0 && (d-x-c)==0
    # mc를 반지름으로 하는 원호를 그려서 대체하게 됨
    THETA_s = (pi/2)*ones(length(THETA_t))
    elseif c==0 && (d-x-c)==0
    # 루트커브 작도 생략하고, (x_is,y_is) 점을 대칭으로 이뿌리호를 그려서 대체하게 됨
    elseif (d-x-c)!=0
    THETA_s = atan.((m*z*THETA_t/2)/(m*d-m*x-m*c))
end
X_t = x_0 .+ m*( (z/2+x-d+c).*cos.(THETA_t.+alpha_ts) .+ (z/2)*THETA_t.*sin.(THETA_t.+alpha_ts) - c.*cos.(THETA_s.+THETA_t.+alpha_ts) )
Y_t = y_0 .+ m*( (z/2+x-d+c).*sin.(THETA_t.+alpha_ts) .- (z/2)*THETA_t.*cos.(THETA_t.+alpha_ts) - c.*sin.(THETA_s.+THETA_t.+alpha_ts) )
#plot(X_t,Y_t,color="green",linestyle="-")


############################
# Outter Arc
#alpha_em = 2*alpha_m-alpha_e
#x_em = x_0 + m*(z/2+x+a)*cos.(alpha_em)
#y_em = y_0 + m*(z/2+x+a)*cos.(alpha_em)
THETA6  = range(alpha_e,stop=alpha_m,length=seg_outter) 
X6 = m*(z/2+a+x)*cos.(THETA6) .+x_0
Y6 = m*(z/2+a+x)*sin.(THETA6) .+y_0
#plot(X6,Y6,color="red",linestyle="-")


############################
# Root Arc
#x_rm = x_0 + m*(z/2+x-d)*cos.(alpha_ts)
#y_rm = y_0 - m*(z/2+x-d)*sin.(alpha_ts)
THETA7  = range(0,stop=alpha_ts,length=seg_root) 
X7 = m*(z/2-d+x)*cos.(THETA7) .+x_0
Y7 = m*(z/2-d+x)*sin.(THETA7) .+y_0
#plot(X7,Y7,color="red",linestyle="-")


############################
# Combine Curves
# Not using Root Round Curve (X_t,Y_t)
if c==0 && (d-x-c)==0
    Xc = X7[1:length(X7)-1]
    Yc = Y7[1:length(Y7)-1]
else
    Xc = [ X7[1:length(X7)-1]; X_t[1:length(X_t)-1] ]
    Yc = [ Y7[1:length(Y7)-1]; Y_t[1:length(Y_t)-1] ]
end
# Not using Edge Round Curve (X3,Y3)
if e==0 || alpha_m==alpha_is+theta_ie-atan.(theta_ie)
    Xc = [ Xc; X1[1:length(X1)-1] ]
    Yc = [ Yc; Y1[1:length(Y1)-1] ]
else
    Xc = [ Xc; X1[1:length(X1)-1]; X3[1:length(X3)-1] ]
    Yc = [ Yc; Y1[1:length(Y1)-1]; Y3[1:length(Y3)-1] ]
end
# Not using Outter Arc (X6,Y6)
if alpha_e == alpha_m || alpha_m==alpha_is+theta_ie-atan.(theta_ie)
    Xc = Xc
    Yc = Yc
else
    Xc = [ Xc; X6[1:length(X6)-1] ]
    Yc = [ Yc; Y6[1:length(Y6)-1] ]
end
#Xc = [ X7[1:length(X7)-1]; X_t[1:length(X_t)-1]; X1[1:length(X1)-1]; X3[1:length(X3)-1]; X6[1:length(X6)-1]]
#Yc = [ Y7[1:length(Y7)-1]; Y_t[1:length(Y_t)-1]; Y1[1:length(Y1)-1]; Y3[1:length(Y3)-1]; Y6[1:length(Y6)-1]]
#plot(Xc,Yc,color="black",linestyle="-",linewidth=2)


############################
# Make Whole One Tooth
Xc2 = Xc[2:length(Xc)]
Yc2 = Yc[2:length(Yc)]
# Reflect Transform
Xcc = cos.(2*alpha_m)*(Xc2 .-x_0) .+ sin.(2*alpha_m)*(Yc2 .-y_0)
Ycc = sin.(2*alpha_m)*(Xc2 .-x_0) .- cos.(2*alpha_m)*(Yc2 .-y_0)
# Location Transform to (x_0,y_0)
Xcc = Xcc .+ x_0
Ycc = Ycc .+ y_0
# Invert
Xcc = Xcc[length(Xcc):-1:1]
Ycc = Ycc[length(Ycc):-1:1]
# Combine
Xcc = [Xc; Xcc]
Ycc = [Yc; Ycc]
#plot(Xcc,Ycc,color="black",linestyle="-",linewidth=2)


############################
# Align to Top
align_angle = pi/2-pi/z
X_align = Xcc
Y_align = Ycc
# Rotate
X_align = cos.(align_angle)*(Xcc .-x_0) .- sin.(align_angle)*(Ycc .-y_0)
Y_align = sin.(align_angle)*(Xcc .-x_0) .+ cos.(align_angle)*(Ycc .-y_0)
# Location Transform to (x_0,y_0)
X_align = X_align .+ x_0
Y_align = Y_align .+ y_0
#plot(X_align,Y_align,color="black",linestyle="-",linewidth=2)


############################
# Make Whole Gear
p_angle = 2*pi/z
Xccc = X_align
Yccc = Y_align
Xtemp = X_align[2:length(X_align)]
Ytemp = Y_align[2:length(Y_align)]
for i = 1:z-1
    # Rotate
    Xtemp = cos.(p_angle*i).*(X_align[2:length(X_align)] .- x_0) .- sin.(p_angle*i).*(Y_align[2:length(Y_align)] .- y_0)
    Ytemp = sin.(p_angle*i).*(X_align[2:length(X_align)] .- x_0) .+ cos.(p_angle*i).*(Y_align[2:length(Y_align)] .- y_0)
    # Location Transform to (x_0,y_0)
    Xtemp = Xtemp .+ x_0
    Ytemp = Ytemp .+ y_0
    Xccc = [Xccc; Xtemp]
    Yccc = [Yccc; Ytemp]
end


############################
# Plot Figure
f=figure(figsize=(10,10))
grid("on")
title("FGPG (Fine_Gear_Profile_Generator) $version \n by Dymaxion.Kim")
axis("equal")


############################
# Base, Pitch, Offset, Outter, Root Circle
THETA0 = range(0.0,stop=2*pi,length=seg_circle) 
# Base Circle
base_dia = m*z*cos.(alpha_0)
X_base = base_dia/2*sin.(THETA0) .+ x_0
Y_base = base_dia/2*cos.(THETA0) .+ y_0
plot(X_base, Y_base, color="cyan", linestyle="--")
# Pitch Circle
pitch_dia = m*z
X_pitch = pitch_dia/2*sin.(THETA0) .+ x_0
Y_pitch = pitch_dia/2*cos.(THETA0) .+ y_0
plot(X_pitch, Y_pitch, color="magenta", linestyle="--")
# Offset Circle
offset_dia = 2*m*(z/2+x)
X_offset = (offset_dia/2)*sin.(THETA0) .+ x_0
Y_offset = (offset_dia/2)*cos.(THETA0) .+ y_0
plot(X_offset, Y_offset, color="red", linestyle="--")
# Outter Circle
outter_dia = 2*m*(z/2+x+a)
X_out = (outter_dia/2)*sin.(THETA0) .+ x_0
Y_out = (outter_dia/2)*cos.(THETA0) .+ y_0
plot(X_out, Y_out, color="brown", linestyle="--")
# Root Circle
root_dia = 2*m*(z/2+x-d)
X_root = (root_dia/2)*sin.(THETA0) .+ x_0
Y_root = (root_dia/2)*cos.(THETA0) .+ y_0
plot(X_root, Y_root, color="grey", linestyle="--")


############################
# Center Line of Tooth
X_m = range(x_0,stop=(m*(z/2+a+x))*cos.(alpha_m)+x_0,length=seg_center) 
Y_m = (X_m .- x_0).*tan.(alpha_m) .+ y_0
plot(X_m,Y_m,color="orange",linestyle="--")


############################
# Shaft
THETA8 = range(0,stop=2*pi,length=seg_circle) 
if a<d  # Outternal Gear
    d_shaft = m*(z+x-d)-m*(4*(a+d))
    elseif a>d  # Internal Gear
    d_shaft = m*(z+x+a)+m*(4*(a+d))
    elseif a==d  # No correct
    #d_shaft = m*(z+x-d)-m*(2*(a+d))
    d_shaft = 0
end
X_shaft = (d_shaft/2)*sin.(THETA8) .+ x_0
Y_shaft = (d_shaft/2)*cos.(THETA8) .+ y_0
plot(X_shaft, Y_shaft, color="black", linestyle="-", linewidth=2)


############################
# Plot Whole Gear
plot(Xccc,Yccc,color="black",linestyle="-",linewidth=2)
char_scale = 0.03*m*z
annotate(["Module = $m mm"],xy=(x_0,y_0+5*char_scale),ha="center",va="center",color="black",fontsize="x-small")
annotate(["Teeth Number = $z ea"],xy=(x_0,y_0+4*char_scale),ha="center",va="center",color="black",fontsize="x-small")
annotate(["Pressure Angle = $alpha_0_deg DEG"],xy=(x_0,y_0+3*char_scale),ha="center",va="center",color="black",fontsize="x-small")
annotate(["Offset Factor = $x"],xy=(x_0,y_0+2*char_scale),ha="center",va="center",color="black",fontsize="x-small")
annotate(["Backlash Factor = $b"],xy=(x_0,y_0+1*char_scale),ha="center",va="center",color="black",fontsize="x-small")
annotate(["Addendum Factor = $a"],xy=(x_0,y_0+0*char_scale),ha="center",va="center",color="black",fontsize="x-small")
annotate(["Dedendum Factor = $d"],xy=(x_0,y_0-1*char_scale),ha="center",va="center",color="black",fontsize="x-small")
annotate(["Radius Factor of Edge Round of Hob = $c"],xy=(x_0,y_0-2*char_scale),ha="center",va="center",color="black",fontsize="x-small")
annotate(["Radius Factor of Edge Round of Tooth = $e"],xy=(x_0,y_0-3*char_scale),ha="center",va="center",color="black",fontsize="x-small")
annotate(["Center Position [mm] = ($x_0,$y_0)"],xy=(x_0,y_0-4*char_scale),ha="center",va="center",color="black",fontsize="x-small")
legend(["Base Circle Dia = $base_dia", "Pitch Circle Dia = $pitch_dia", "Offset Circle Dia = $offset_dia",
    "Outter Circle Dia = $outter_dia", "Root Circle Dia = $root_dia", "Center Line"], loc="lower left", fontsize="x-small")
savefig("case01.svg")


############################
# Figuer 2
f2=figure(figsize=(10,10))
grid("on")
title("FGPG (Fine_Gear_Profile_Generator) $version \n by Dymaxion.Kim")
axis("equal")


############################
# Base, Pitch, Offset, Outter, Root Circle 2
THETA9 = range(atan.(X_align[length(X_align)]/Y_align[length(Y_align)]),stop=atan.(X_align[1]/Y_align[1]),length=Int(seg_circle/10)) 
# Base Circle
X_base9 = base_dia/2*sin.(THETA9) .+ x_0
Y_base9 = base_dia/2*cos.(THETA9) .+ y_0
plot(X_base9, Y_base9, color="cyan", linestyle="--")
# Pitch Circle
X_pitch9 = pitch_dia/2*sin.(THETA9) .+ x_0
Y_pitch9 = pitch_dia/2*cos.(THETA9) .+ y_0
plot(X_pitch9, Y_pitch9, color="magenta", linestyle="--")
# Offset Circle
X_offset9 = (offset_dia/2)*sin.(THETA9) .+ x_0
Y_offset9 = (offset_dia/2)*cos.(THETA9) .+ y_0
plot(X_offset9, Y_offset9, color="red", linestyle="--")
# Outter Circle
X_out9 = (outter_dia/2)*sin.(THETA9) .+ x_0
Y_out9 = (outter_dia/2)*cos.(THETA9) .+ y_0
plot(X_out9, Y_out9, color="brown", linestyle="--")
# Root Circle
X_root9 = (root_dia/2)*sin.(THETA9) .+ x_0
Y_root9 = (root_dia/2)*cos.(THETA9) .+ y_0
plot(X_root9, Y_root9, color="grey", linestyle="--")


############################
# Plot only One Tooth
plot(X_align,Y_align,color="black",linestyle="-",linewidth=1)
plot(X_align,Y_align,"b.")
base_radius = base_dia/2
pitch_radius = pitch_dia/2
offset_radius = offset_dia/2
outter_radius = outter_dia/2
root_radius = root_dia/2
xmm = x*m
emm = e*m
bmm = b*m
cmm = c*m
annotate(["Base Radius = $base_radius mm"],xy=(0,base_dia/2),ha="center",va="bottom",color="cyan",fontsize="x-small")
annotate(["Pitch Radius = $pitch_radius mm"],xy=(0,pitch_dia/2),ha="left",va="bottom",color="magenta",fontsize="x-small")
annotate(["Offset Radius = $offset_radius mm"],xy=(0,offset_dia/2),ha="right",va="bottom",color="red",fontsize="x-small")
annotate(["Outter Radius = $outter_radius mm"],xy=(0,outter_dia/2),ha="right",va="bottom",color="brown",fontsize="x-small")
annotate(["Root Radius = $root_radius mm"],xy=(0,root_dia/2),ha="center",va="bottom",color="grey",fontsize="x-small")
annotate(["Offset = $xmm mm"],xy=(0,offset_dia/2),ha="right",va="top",color="red",fontsize="x-small")
annotate(["Radius of Hob Edge = $cmm mm"],
        xy=(X_align[seg_root+Int(seg_root_r/2)],Y_align[seg_root+Int(seg_root_r/2)]),
        ha="right",va="top",color="blue",fontsize="x-small")
annotate(["Radius of Edge = $emm mm"],
        xy=(X_align[seg_root+seg_root_r+seg_involute],Y_align[seg_root+seg_root_r+seg_involute]),
        ha="left",va="bottom",color="blue",fontsize="x-small")
annotate(["Backlash = $bmm mm"],
        xy=(X_align[seg_root+seg_root_r+Int(seg_involute/2)],Y_align[seg_root+seg_root_r+Int(seg_involute/2)]),
        ha="left",va="bottom",color="blue",fontsize="x-small")
amm = a*m
dmm = d*m
hmm = amm+dmm
tmm = 2*X_align[seg_root+seg_root_r]
#temm = 2*X_align[seg_root+seg_root_r+seg_involute+Int(seg_edge_r/2)]
temm = 2*X_align[seg_root+seg_root_r+seg_involute]
annotate(["Addendum = $amm mm"],xy=(X_out9[1],Y_out9[1]),ha="left",va="top",color="black",fontsize="x-small")
annotate(["Dedendum = $dmm mm"],xy=(X_root9[1],Y_root9[1]),ha="left",va="top",color="black",fontsize="x-small")
annotate(["Tooth Height = $hmm mm"],xy=(X_offset9[1],Y_offset9[1]),ha="left",va="top",color="black",fontsize="x-small")
annotate(["Approx Tooth Thickness = $tmm mm"],xy=(0,base_dia/2),ha="center",va="top",color="black",fontsize="x-small")
annotate(["Approx Tooth End Thickness = $temm mm"],xy=(0,outter_dia/2),ha="center",va="top",color="black",fontsize="x-small")

savefig("case02.svg")


############################
# Save case.geo
fileout = open("case.geo", "w")
println(fileout, "cl__1 = 1;")
num_Point_gear = length(Xccc)
num_Line_gear = num_Point_gear-1
num_Point_shaft = num_Point_gear + length(X_shaft) -1
num_Line_shaft = num_Point_shaft-1
for i=1:num_Point_gear
    println(fileout, "Point(",i,") = {",Xccc[i],", ",Yccc[i],", ",0,", ","cl__1};")
end
for i=num_Point_gear+1:num_Point_shaft
    println(fileout, "Point(",i,") = {",X_shaft[i-num_Point_gear],", ",Y_shaft[i-num_Point_gear],", ",0,", ","cl__1};")
end
for j=1:num_Line_gear
    println(fileout, "Line(",j,") = {",j,", ",j+1,"};")
end
println(fileout, "Line(",num_Line_gear+1,") = {",num_Line_gear+1,", ",1,"};")
for j=num_Line_gear+2:num_Line_shaft
    println(fileout, "Line(",j,") = {",j,", ",j+1,"};")
end
println(fileout, "Line(",num_Line_shaft+1,") = {",num_Line_shaft+1,", ",num_Line_gear+2,"};")
# Combine
#array_LineLoop = [1:num_Line_shaft+1]
array_LineLoop = Array{Int}(range(1,stop=num_Line_shaft+1,length=num_Line_shaft+1))
array_LineLoop[num_Line_gear+2:num_Line_shaft+1] = -array_LineLoop[num_Line_gear+2:num_Line_shaft+1]
array_LineLoop = string(array_LineLoop)
array_LineLoop = array_LineLoop[2:length(array_LineLoop)-1]
println(fileout, "Line Loop(",num_Line_shaft+3,") = {",array_LineLoop,"};")
println(fileout, "Plane Surface(",num_Line_shaft+3,") = {",num_Line_shaft+3,"};")
#Physical Line(13) = {8, 9};
#Physical Surface(14) = {11};
array_PhysicalLine = [num_Line_gear+2:num_Line_shaft+1]
array_PhysicalLine = string(array_PhysicalLine)
array_PhysicalLine = array_PhysicalLine[2:length(array_PhysicalLine)-1]
#println(fileout, "Physical Line(",num_Line_shaft+4,") = {",array_PhysicalLine,"};")
# Position for Normal Force
#position_NormalForce = (length(Xcc)-1) - (seg_root+seg_root_r-2) - (seg_involute-3)
#println(fileout, "Physical Line(",num_Line_shaft+5,") = {",position_NormalForce,"};")
# Fixed
#println(fileout, "Physical Surface(",num_Line_shaft+6,") = {",num_Line_shaft+3,"};")
println(fileout, "Mesh.ElementOrder = 2;")
println(fileout, "Mesh.RecombineAll = 1;")
close(fileout)


############################
# Save case01.scr (Total)
fileout = open("case01.scr", "w")
println(fileout, "spline")
for i=1:num_Point_gear
    println(fileout, Xccc[i],",",Yccc[i],",0")
end
println(fileout, Xccc[1],",",Yccc[1],",0")
println(fileout, "  ")
println(fileout, "circle")
println(fileout, x_0,",",y_0)
println(fileout, d_shaft/2)
close(fileout)

############################
# Save case02.scr (Single tooth)
fileout = open("case02.scr", "w")
println(fileout, "spline")
for i=1:length(X_align)
    println(fileout, X_align[i],",",Y_align[i],",0")
end
println(fileout, -X_align[1],",",Y_align[1])
println(fileout, "  ")
println(fileout, "circle")
println(fileout, x_0,",",y_0)
println(fileout, (outter_dia/2)+m)
println(fileout, "line")
println(fileout, x_0,",",y_0)
println(fileout, x_0,",",(outter_dia/2)+m)
println(fileout, "")
println(fileout, "array")
println(fileout, "L")
println(fileout, "")
println(fileout, "P")
println(fileout, x_0,",",y_0)
println(fileout, Int(z*2))
println(fileout, "360")
println(fileout, "Y")
close(fileout)

기어 등급에 따른 오차 허용값 산출

KS B ISO 1328-1:2005, 원통 기어 - 정밀도 등급 제1부 : 기어의 이에 관한 오차의 정의 및 허용값



In [31]:

    
## 원하는 정밀도 등급 (0~12급, 계산공식은 5급 기준이고, 이웃 등급과는 sqrt(2) 곱하기 만큼씩 차이가 남)
KS = 5;
KS = Int(input4fgpg[21,3]);

## 구표준 KS B 1405-85 : 1971 정밀도 등급
KS_old = KS-4;
if KS_old<0; KS_old=0; end

## 기준원 지름 (d) 기하평균
KS_d = 0.0;
if pitch_dia <= 5.0;     KS_d = sqrt(0.0+5.0);
    elseif pitch_dia <= 20.0;    KS_d = sqrt(5.0+20.0);
    elseif pitch_dia <= 50.0;    KS_d = sqrt(20.0+50.0);
    elseif pitch_dia <= 125.0;    KS_d = sqrt(50.0+125.0);
    elseif pitch_dia <= 280.0;    KS_d = sqrt(125.0+280.0);
    elseif pitch_dia <= 560.0;    KS_d = sqrt(280.0+560);
    elseif pitch_dia <= 1000.0;    KS_d = sqrt(560.0+1000.0);
    elseif pitch_dia <= 1600.0;    KS_d = sqrt(1000.0+1600.0);
    elseif pitch_dia <= 2500.0;    KS_d = sqrt(1600.0+2500.0);
    elseif pitch_dia <= 4000.0;    KS_d = sqrt(2500.0+4000.0);
    elseif pitch_dia <= 6000.0;    KS_d = sqrt(4000.0+6000.0);
    elseif pitch_dia <= 8000.0;    KS_d = sqrt(6000.0+8000.0);
    elseif pitch_dia <= 10000.0;    KS_d = sqrt(8000.0+10000.0);
end

## 모듈(치직각 모듈;정면모듈) (m) 기하평균
KS_m = 0.0;
if m <= 0.5;    KS_m = sqrt(0.0+0.5);
    elseif m <= 2.0;    KS_m = sqrt(0.5+2.0);
    elseif m <= 3.5;    KS_m = sqrt(2.0+3.5);
    elseif m <= 6.0;    KS_m = sqrt(3.5+6.0);
    elseif m <= 10.0;    KS_m = sqrt(6.0+10.0);
    elseif m <= 16.0;    KS_m = sqrt(10.0+16.0);
    elseif m <= 25.0;    KS_m = sqrt(16.0+25.0);
    elseif m <= 40.0;    KS_m = sqrt(25.0+40.0);
    elseif m <= 70.0;    KS_m = sqrt(40.0+70.0);
end

## 치폭 (b) 기하평균 (헬리컬 기어일 경우)
temp_b = 10.0;
temp_b = Float64(input4fgpg[19,3]);
KS_b = 10.0;
if temp_b <= 4.0;    KS_m = sqrt(0.0+4.0);
    elseif temp_b <= 10.0;    KS_m = sqrt(4.0+10.0);
    elseif temp_b <= 20.0;    KS_m = sqrt(10.0+20.0);
    elseif temp_b <= 40.0;    KS_m = sqrt(20.0+40.0);
    elseif temp_b <= 80.0;    KS_m = sqrt(40.0+80.0);
    elseif temp_b <= 160.0;    KS_m = sqrt(80.0+160.0);
    elseif temp_b <= 250.0;    KS_m = sqrt(160.0+250.0);
    elseif temp_b <= 400.0;    KS_m = sqrt(250.0+400.0);
    elseif temp_b <= 650.0;    KS_m = sqrt(400.0+650.0);
    elseif temp_b <= 1000.0;    KS_m = sqrt(650.0+1000.0);
end

## 연속 피치수 (k)
## 일반적으로, 2보다 크고, 기어이빨개수(z)의 1/8 보다 작은 정수 값을 선택하여, 직접 입력해 줄 것.
KS_k = 0;
KS_k = Int(input4fgpg[20,3]);


############################
# 오차 계산

## 단일피치오차 (f_pt)
f_pt = 0.0;
f_pt = 0.3*(KS_m+0.4*sqrt(KS_d))+4.0;

## 부분 누적 피치 오차 (F_pk)
F_pk = 0.0;
F_pk = f_pt+1.6*sqrt((KS_k-1.0)*KS_m);

## 누적 피치 오차 (F_p)
F_p = 0.0;
F_p = 0.3*KS_m+1.25*sqrt(KS_d)+7.0;

## 전 치형 오차 (F_alpha)
F_alpha = 0.0;
F_alpha = 3.2*sqrt(KS_m)+0.22*sqrt(KS_d)+0.7;

## 전 잇줄 오차 (F_beta) - 헬리컬 기어에만 해당
F_beta = 0.0;
F_beta = 0.1*sqrt(KS_d)+0.63*sqrt(KS_b)+4.2;


############################
# 등급별로 오차값 산출
i = 0;
KS_factor = 0.0;
if KS==0;    i=(-5);
    elseif KS==1;    i=(-4);
    elseif KS==2;    i=(-3);
    elseif KS==3;    i=(-2);
    elseif KS==4;    i=(-1);
    elseif KS==5;    i=0;
    elseif KS==6;    i=1;
    elseif KS==7;    i=2;
    elseif KS==8;    i=3;
    elseif KS==9;    i=4;
    elseif KS==10;    i=5;
    elseif KS==11;    i=6;
    elseif KS==12;    i=7;
end
KS_factor = sqrt(2.0)^i;

 
f_pt = f_pt*KS_factor;
F_pk = F_pk*KS_factor;
F_p = F_p*KS_factor;
F_alpha = F_alpha*KS_factor;
F_beta = F_beta*KS_factor;

############################
# 수치의 맺음법
if f_pt > 5.0
    f_pt = floor(Int64, f_pt);
    else
    f_pt = floor(Int64,10*f_pt)/10;
end
if F_pk > 5.0
    F_pk = floor(Int64, F_pk);
    else
    F_pk = floor(Int64,10*F_pk)/10;
end
if F_p > 5.0
    F_p = floor(Int64, F_p);
    else
    F_p = floor(Int64,10*F_p)/10;
end
if F_alpha > 5.0
    F_alpha = floor(Int64, F_alpha);
    else
    F_alpha = floor(Int64,10*F_alpha)/10;
end
if F_beta > 5.0
    F_beta = floor(Int64, F_beta);
    else
    F_beta = floor(Int64,10*F_beta)/10;
end

############################
# 결과값 확인
println("정밀도 등급 : ",KS," (구표준 ",KS_old,", KS B 1405-85:1971)")
println("단일피치오차 (f_pt) : ±",f_pt,"um")
println("부분 누적 피치 오차 (F_pk) : ",F_pk,"um (연속피치수 k=",KS_k,")")
println("누적 피치 오차 (F_p) : ",F_p,"um")
println("전 치형 오차 (F_alpha) : ",F_alpha,"um")
#println("전 잇줄 오차 (F_beta) : ",F_beta,"um (헬리컬기어일 경우. 치폭 (b) : ",temp_b,"mm)")









    



정밀도 등급 : 9 (구표준 5, KS B 1405-85:1971)
단일피치오차 (f_pt) : ±21um
부분 누적 피치 오차 (F_pk) : 33um (연속피치수 k=2)
누적 피치 오차 (F_p) : 43um
전 치형 오차 (F_alpha) : 29um

기어 등급에 따른 백래시(Backlash) 산출

KS B 1411:2016, 스퍼 기어 및 헬리컬 기어의 백래시



In [32]:

    
# Read Backlash Data
using ExcelReaders
KS_Backlash = readxl("KSB1411_Backlash_Data.xlsx", join([string(KS_old),"!C2:M41"]))

# Focus on Module (m)
i = 0;
if m<=0.5; i=1;
    elseif m<=1.0; i=3;
    elseif m<=1.5; i=5;
    elseif m<=2.0; i=7;
    elseif m<=2.5; i=9;
    elseif m<=3.0; i=11;
    elseif m<=3.5; i=13;
    elseif m<=4.0; i=15;
    elseif m<=5.0; i=17;
    elseif m<=6.0; i=19;
    elseif m<=7.0; i=21;
    elseif m<=8.0; i=23;
    elseif m<=10.0; i=25;
    elseif m<=12.0; i=27;
    elseif m<=14.0; i=29;
    elseif m<=16.0; i=31;
    elseif m<=18.0; i=33;
    elseif m<=20.0; i=35;
    elseif m<=22.0; i=37;
    elseif m<=25.0; i=39;
end
KS_Backlash = KS_Backlash[i:(i+1),:,];

# Focus on Pitch Diameter (pitch_dia)
if pitch_dia<1.5; println("Too small pitch_dia");
    elseif pitch_dia<=3.0; i=1;
    elseif pitch_dia<=6.0; i=2;
    elseif pitch_dia<=12.0; i=3;
    elseif pitch_dia<=25.0; i=4;
    elseif pitch_dia<=50.0; i=5;
    elseif pitch_dia<=100.0; i=6;
    elseif pitch_dia<=200.0; i=7;
    elseif pitch_dia<=400.0; i=8;
    elseif pitch_dia<=800.0; i=9;
    elseif pitch_dia<=1600.0; i=10;
    elseif pitch_dia<=3200.0; i=11;
end
KS_Backlash = KS_Backlash[:,i];
KS_Backlash[1] = parse(Float64,KS_Backlash[1]);
KS_Backlash[2] = parse(Float64,KS_Backlash[2]);

println("Minimum Backlash : ",KS_Backlash[1],"um")
println("Average Backlash : ",(KS_Backlash[1]+KS_Backlash[2])/2.0,"um (Factor ",(((KS_Backlash[1]+KS_Backlash[2])/2.0)/1000.0)/m,")")
println("Maximum Backlash : ",KS_Backlash[2],"um")









    



Minimum Backlash : 35.0um
Average Backlash : 92.5um (Factor 0.0925)
Maximum Backlash : 150.0um

걸치기 이두께 치수 산출

KS B 1406:1990, 스퍼기어 및 헬리컬기어의 측정 방법



In [33]:

    
if z>=6 && z<=17;    KS_Zm=2;
    elseif z<=26;    KS_Zm=3;
    elseif z<=35;    KS_Zm=4;
    elseif z<=44;    KS_Zm=5;
    elseif z<=53;    KS_Zm=6;
    elseif z<=62;    KS_Zm=7;
    elseif z<=71;    KS_Zm=8;
    elseif z<=80;    KS_Zm=9;
    elseif z<=89;    KS_Zm=10;
    elseif z<=98;    KS_Zm=11;
    elseif z<=197;    KS_Zm=12;
    elseif z<=116;    KS_Zm=13;
    elseif z<=125;    KS_Zm=14;
    elseif z<=134;    KS_Zm=15;
    elseif z<=143;    KS_Zm=16;
    elseif z<=150;    KS_Zm=17;
    else println("기어의 잇수(z)가 규정범위를 벗어남.")
end

#KS_Zm = KS_k;
KS_omega = 0.0;
KS_omega = m*cos(alpha_0)*(pi*(KS_Zm-0.5)+z*(tan(alpha_0)-alpha_0))+2.0*x*m*sin(alpha_0);
KS_omega = floor(Int64,KS_omega*10000.0)/10000.0;

## Backlash
# Ref : http://m.blog.daum.net/again114/37
KS_omega_Backlash_Min = -(KS_Backlash[1]*cos(alpha_0))/1000.0;
KS_omega_Backlash_Min = floor(Int64,KS_omega_Backlash_Min*10000.0)/10000.0;
KS_omega_Backlash_Max = -(KS_Backlash[2]*cos(alpha_0))/1000.0;
KS_omega_Backlash_Max = floor(Int64,KS_omega_Backlash_Max*10000.0)/10000.0;

println("걸치기 잇수 (Zm) : ",KS_Zm,"ea")
println("걸치기 이두께 (omega) : ",KS_omega,"mm (",KS_omega_Backlash_Min,", ",KS_omega_Backlash_Max,")")









    



걸치기 잇수 (Zm) : 2ea
걸치기 이두께 (omega) : 4.9803mm (-0.0329, -0.141)

기어 요목표 출력



In [34]:

    
##############################################################################################
## Save case_spec.csv
fileout = open("case_spec.csv", "w")
if alpha_0_deg==20
    println(fileout, "치형, ","표준")
    else println(fileout, "치형, ","비표준")
end
println(fileout, "모듈, ",m,"mm")
println(fileout, "압력각, ",alpha_0_deg,"deg")
println(fileout, "잇수, ",z,"ea")
println(fileout, "기준 피치원 지름, ",pitch_dia,"mm")
println(fileout, "전위량(Factor), ",x)
println(fileout, "전체 이높이, ",a+d,"mm")
println(fileout, "걸치기 이두께"," (걸치기 잇수 ",KS_Zm,"), ",KS_omega,"mm (",KS_omega_Backlash_Min,"/",KS_omega_Backlash_Max,")")
println(fileout, "정밀도 (KS B ISO 1328-1:2005), ",KS,"급  / 구표준(KS B 1405-85:1971) : ",KS_old,"급")
println(fileout, "백래시(단일기어), ",KS_Backlash[1],"~",KS_Backlash[2],"um")
close(fileout)

println("Finish!")









    



Finish!



In [ ]: