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標題: 螺桿轉子刀具設計 數學模型 [打印本頁]
作者: shouce 時間: 2015-5-26 19:44
標題: 螺桿轉子刀具設計 數學模型
本帖最后由 shouce 于 2015-5-26 19:49 編輯 " b3 f" J# Q5 L& W5 n. d
4 V1 x6 `; y. ~4 i( ?# h1 } ] 螺桿轉子刀具設計
設中心距 100mm 陰陽轉子齒數比為6:4 型線為原始單邊對稱型線 齒高半徑為0.25*100=25mm 如下圖1所示
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陰轉子型線方程為: x=60-25*cos(t)
y=25*sin(t) 形狀如圖2
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t的范圍【-1.361,1.361】弧度表示
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螺旋角為45度 螺桿旋向為左旋 陰轉子的扭轉角為5.235弧度 則陰轉子的導程:T=2*pi*12/10*100*tan45=376.991
P=T/(2*pi)=59.9999
要求轉子刀具 先要解下面的方程 如圖3
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式中AC為砂輪直徑 設為500mm Ψ是螺旋角為45度
現需要求150對 (t,τ) 意思是已知一個t 求一個τ 使得上面的方程成立。 又t的范圍為【-1.361,1.361】 在這個區間等間距取150個t 則對應有150個τ值 τ 范圍為【0, 5.235】 整理后方程為:
11679999.7*sin(A1)-1679997.5*cos(B1)*sin(A1)-1499997.5*sin(B1)*cos(A1)-75000*sin(A1)^3-179999.4000005*B1*cos(B1)*cos(A1)+179999.4000005*B1*sin(B1)*sin(A1)+75000*cos(B1)*cos(A1)*sin(A1)=0
注A1表示t B1表示τ
解出這個方程后 將(t,τ)代入轉子螺旋齒面方程 得到齒面的坐標點 再轉換到刀具坐標系中 得到刀具回轉面坐標 最后轉換為刀具的形狀。
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作者: shouce 時間: 2015-5-26 20:04
等下次有時間 我來解這個方程7 D( E& `8 l6 _( c$ d
作者: seekfor 時間: 2015-5-26 20:27
讓我想起大學畢業設計是雙螺桿壓縮機齒形加工刀具設計了,端面方程,齒面方程,接觸方程,中心距安裝角,各種算;可惜matlab沒學好,求解程序是老師帶的研究生幫忙編制的。這東西真的是純粹數學計算?,F在忘光了。
作者: shouce 時間: 2015-5-26 22:09
seekfor 發表于 2015-5-26 20:27 
0 u, l' S( e) A: i7 R( `讓我想起大學畢業設計是雙螺桿壓縮機齒形加工刀具設計了,端面方程,齒面方程,接觸方程,中心距安裝角,各 ...
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你那時做的齒形 是哪種齒形 是第幾代的型線% V+ u, I7 u) d; Q
作者: shouce 時間: 2015-8-12 21:56
shouce 發表于 2015-5-26 20:04 
* U1 ?6 T4 n( x' q等下次有時間 我來解這個方程
$ _3 ]& q0 h7 E# [; ?- S盡信書 不如無書 自己動手計算 才發現教材的錯誤
作者: shouce 時間: 2015-10-6 21:14
ezplot('1/2*(285+60)*3000*sin(t)-1/2*(25*sin(t)*sin(z)+(60-25*cos(t))*cos(z))*3000*sin(t)+60^2*25*sin(t)*z*sin(z)-60^2*25*cos(t)*z*cos(z)-60*285*(25*cos(t)*sin(z)+25*sin(t)*cos(z))=0',[-1.361 1.361 -5 5]);
) q3 R! c3 g q, d; U0 k! Waxis square
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作者: shouce 時間: 2015-10-6 21:14
本帖最后由 shouce 于 2015-10-6 21:16 編輯 # d& h, k2 y" D* j, d" Z3 m8 R
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ezplot('1/2*(285+60)*3000*sin(t)-1/2*(25*sin(t)*sin(z)+(60-25*cos(t))*cos(z))*3000*sin(t)+60^2*25*sin(t)*z*sin(z)-60^2*25*cos(t)*z*cos(z)-60*285*(25*cos(t)*sin(z)+25*sin(t)*cos(z))=0',[-1.361 1.361 -5 5]);, E8 v. K, d) ?! m3 M" Y
axis square) E8 @) a) S9 G( F: f
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M- B6 b. r# B0 B: k$ H8 p
. H2 R3 I3 o1 ~方程快速解法 :A= @(t,z) 1/2*(285+60)*3000*sin(t)-1/2*(25*sin(t)*sin(z)+(60-25*cos(t))*cos(z))*3000*sin(t);B = @(t,z) 60^2*25*sin(t)*z*sin(z)-60^2*25*cos(t)*z*cos(z)-60*285*(25*cos(t)*sin(z)+25*sin(t)*cos(z));C = @(t) @(z) A(t,z)+B(t,z);
+ C1 s6 _5 O$ e8 `$ K7 M( c) cZ = @(t) fzero(C(t),-1.361);
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作者: 木子12 時間: 2015-10-12 13:55
本科課程設計,計算一大堆,但大多都是用書上的公式
作者: pacelife 時間: 2015-10-12 18:42
樓主能否運用這些數據在生成三維圖形
作者: 小楊123589 時間: 2015-10-15 19:47
螺桿馬達的線型和這個一樣么
作者: shouce 時間: 2015-11-17 22:57
function solve_nonl_single16 r: ~& k4 F" @
clear all;clc
: S0 z3 j s6 L1 z# w( Mformat long" Z: X x0 a2 t' ?/ H
global a
1 |) X) Y$ w6 w: A* va_span=linspace(-0.06,0.06,200);, Y, C% d- T8 W w4 _1 p5 A( N1 v
n=length(a_span);% a \, J% D9 [4 k, e
x0=1e-9;* E" z0 `& x4 L7 h/ t4 o7 ?
options=optimset('Algorithm','trust-region-dogleg','TolFun',1e-12,'TolX',1e-12);: A+ L! v3 v6 `! d4 t
for i=1:n
: y5 l3 M1 @" C7 c; U' z a=a_span(i);
# X T$ Q; g8 {2 D x(i)=fsolve(@nonl,x0,options);
0 ?' x# J6 n1 ]$ M y(i)=nonl(x(i));
1 a: C# R5 ]$ t' kend6 [2 I7 V2 s. O: q- ]
a_span', x',y'2 y" Q6 S/ U7 ~. x$ p# A
function f=nonl(x); Q# P2 L( r2 p. T
global a: i& r% p. L# D; X& d4 p
f=1/2*(285+60)*3000*sin(x)-1/2*(25*sin(x)*sin(a)+(60-25*cos(x))*cos(a))*3000*sin(x)+60^2*25*sin(x)*a*sin(a)-60^2*25*cos(x)*a*cos(a)-60*285*(25*cos(x)*sin(a)+25*sin(x)*cos(a));
0 Z: \ P; M$ U: s7 J
$ Y4 j. u r$ L: C& ?運行結果 ans =
! \) g' U( D4 c' d1 `, U -0.060000000000000
! d. X$ ~5 q( d/ t* b -0.059396984924623+ m `% t0 M; ?: p8 }
-0.058793969849246% o/ B4 R0 f, y6 c
-0.058190954773869
3 p4 A( m; j2 B- r) G3 N2 Y -0.057587939698492
P* U) X" O8 D -0.056984924623116- t- m+ u1 @& ?1 Z6 E
-0.056381909547739
& d5 W& n- b- p$ i; h -0.055778894472362
% l. t& x, {& t* b# M9 [ -0.055175879396985
- G- r" ?2 w F: o I -0.054572864321608
8 S4 C% Q; {$ V7 b3 \9 Y% ^8 l -0.053969849246231& V! k3 j% W; N/ J. b
-0.053366834170854, P; _. s# W$ x z4 }1 A: W
-0.052763819095477+ z/ X% H6 p/ n% z
-0.052160804020100* j; ]( @+ ~! G
-0.0515577889447246 S: c5 l6 V2 ]) c3 f2 \; q' W
-0.0509547738693470 Y# V& e2 o" r- p6 P3 I" ~+ k
-0.0503517587939707 M4 x: Y4 D6 l& U
-0.049748743718593
! Z& O4 w. o2 Z( K -0.049145728643216 K6 q! |' Q( [% Y/ P
-0.0485427135678397 }3 F0 g3 m( k. J1 k6 R. ^+ x
-0.0479396984924623 L9 H2 F2 H. Q9 ^$ b3 o
-0.047336683417085
( z" W. p$ l2 e6 q -0.046733668341709
. d% e* @$ T: t0 K -0.046130653266332
! P" k9 e" C( j9 U- p5 L -0.045527638190955
# V9 y$ h2 I8 E; b! A -0.044924623115578
5 G" n) O( T* Y -0.0443216080402015 x& I6 k' U0 C9 N& ]2 L
-0.0437185929648243 w& {, u( k. W @
-0.043115577889447* I; o/ o8 H' b) ?6 u
-0.042512562814070% A7 _7 }7 i8 u8 ~2 s, x& R* r
-0.041909547738693
" R- w+ d, |; s2 ?' N$ X/ A -0.041306532663317, f X, Y* T: r7 I1 O
-0.040703517587940* R; n) H5 i3 e: e
-0.040100502512563% `& u O! R4 o7 u
-0.039497487437186: h7 k8 k2 l: T9 Z s. y4 a
-0.038894472361809. Z* Y! R( C9 [+ ]7 R( n
-0.038291457286432- r0 h' Q# J# P2 y
-0.037688442211055
1 V8 S' |$ T% F4 y5 I' x -0.0370854271356785 d7 y6 ]# h1 c5 Q) R
-0.036482412060302
- Y/ {$ Z1 U6 m% P/ G' ^# ~, ? -0.035879396984925
) o5 L! M8 \2 i( g4 R7 E0 c -0.035276381909548/ E& B9 P- i! H: r
-0.034673366834171/ p& c: y) ], L+ G! R1 Y
-0.034070351758794/ U+ h3 T5 R+ D6 Q8 O7 @' E
-0.033467336683417
9 Y' Z- W0 O' @4 {2 a4 v0 P- K1 ? -0.032864321608040& U' H- i7 ?6 k/ ~. x+ ~" H
-0.032261306532663
! y y% ^- x! R$ A+ H% f/ y -0.031658291457286- K2 \) q; B5 _7 b9 F2 b
-0.031055276381910# w. m- A/ v1 o6 M
-0.030452261306533
9 x7 W, |( Y: Y% Q- M. V: j0 ]0 S3 Y -0.029849246231156
N" B- J4 H/ m% @ z9 z -0.029246231155779% P( f( p4 l6 d
-0.028643216080402
+ h0 }' {& k) |8 _ v* c -0.0280402010050255 c8 Q; u" z3 I! h1 h9 I
-0.0274371859296489 J3 W- z) g4 ~. R1 J$ V
-0.026834170854271
0 u& s$ e2 S1 }! [8 \ -0.026231155778894
H! @5 E& ~' X -0.025628140703518 ^# Z. R l, `4 l
-0.025025125628141% [+ N/ t, ?7 ?9 E1 r
-0.0244221105527648 s; t5 V3 z+ F% |1 n9 r2 C' c5 }
-0.023819095477387
" R9 l0 S7 Q. [2 k -0.023216080402010; W* o. _0 @. O/ R, C
-0.0226130653266333 V; H9 Y: u! K9 ~' X; n$ N
-0.022010050251256! w& z" J3 Y6 o
-0.0214070351758799 ?, @6 l! C8 J" F0 C
-0.020804020100503) H: s) Z; g& k3 y' \/ ~) J( d
-0.020201005025126% n9 V% s# C$ P9 ^+ W4 O
-0.019597989949749
: S+ }/ A2 B2 E -0.018994974874372
6 U' P1 t9 ]; Y) y. G, g. h* _ Y -0.0183919597989953 q4 R$ a4 b0 J; G& U
-0.017788944723618
6 ^, ^4 Q+ O5 j, b9 g/ { -0.017185929648241
& f y# n7 B6 ^& q1 l- x" X -0.016582914572864
+ n q o; m+ c4 D# k; r* S -0.015979899497487
Y2 V! t- P. w8 A( ]2 e -0.015376884422111$ q( ]# |, [6 F5 l. b
-0.014773869346734/ a$ `: J0 {, |/ M1 e
-0.014170854271357/ [7 E+ U8 G, w, U* }) u
-0.013567839195980$ L d; o0 s8 s( q8 P- R
-0.0129648241206030 t4 V' P M5 j9 Q. i- U
-0.012361809045226
$ v0 s5 z: {4 N/ h+ d% F -0.011758793969849) U+ Q6 l6 X' i. t8 g
-0.011155778894472
+ l" S9 B3 Z1 f) }% ` -0.010552763819095
" x, O# t7 M9 y$ [+ B& J( I -0.009949748743719
) g/ t1 p; l4 a8 e -0.009346733668342
7 s% [: |1 ~( Z1 _) w -0.008743718592965
# @; B5 ~8 G- r -0.008140703517588! j7 j6 o( U/ [; G# i2 x
-0.007537688442211% s4 l) N- d8 U( S
-0.0069346733668345 W* ~. Q' ^3 O) W) y
-0.006331658291457
/ f2 O) l1 K+ {8 [/ {1 }- e* p1 s -0.005728643216080
) {; K0 B) G8 k* ^ -0.005125628140704$ D% ]6 y- q1 D% m4 V4 e
-0.004522613065327
8 w- }& p( ?/ |6 k6 z -0.003919597989950
% k c( w2 J0 u2 s' }% C -0.0033165829145730 u2 V+ P* Y. n! o* ]. ^
-0.002713567839196; i& b3 [. |0 n$ Y- C" i
-0.002110552763819
8 _$ u- Y; _3 B& E -0.0015075376884422 s i& O5 `( A7 r4 A3 u5 @/ ], u
-0.000904522613065
8 |( I+ B. F5 s7 u9 N1 q( G$ T -0.000301507537688$ Y- A" Z+ S& q( y& y: P
0.000301507537688
, x# S [# [3 J" _2 t$ \! N+ y 0.000904522613065
1 }$ ]0 @: ]% K$ R/ u, f5 E 0.001507537688442
* C" O! l6 {9 o6 ` 0.002110552763819
) v# [% ?4 I! ^- U L [ 0.002713567839196: O: `' ?4 Q* C' [- q
0.003316582914573, o6 @/ X3 W' B$ `" z! X! c5 y
0.003919597989950
0 s- L1 A% Q" d 0.004522613065327
1 w* }# a" [; x) l, @$ x/ n4 e! M; L 0.005125628140704 J& T% \: t- t6 J8 [% F
0.005728643216080
" G, `- J4 ?7 I 0.006331658291457
" \! d7 R4 i+ J2 x* R 0.006934673366834) x$ E9 x$ Y3 y. l7 C
0.0075376884422118 j e6 I0 D5 N0 S
0.008140703517588/ M7 e9 ]/ u7 G3 X% W9 }# Z
0.008743718592965 d. E/ O/ s- y, ~8 A y) K
0.009346733668342$ L9 m1 B5 B( m2 J2 W7 c4 P
0.009949748743719" R; l4 p( d( g' e$ v9 w
0.010552763819095
' e; w: {. v3 R1 p% ~0 [ 0.011155778894472
; h) ]+ H* z6 G6 L0 x 0.011758793969849
c) Y' f, V! S7 j* M 0.012361809045226
& o6 O( F6 ~- _/ Y! S 0.0129648241206035 ^) k& V0 Z6 Z1 }
0.013567839195980
4 h& O) ^' D9 {( d 0.014170854271357
1 p( F9 j- q; f' m# v! W( R5 D 0.014773869346734* A2 ~+ n X) A- F% f
0.015376884422111
* q" {- g, P K4 P8 T0 J 0.015979899497487) \5 M; E3 n3 X$ f
0.016582914572864& P- `, g D- m& d! p/ b3 Z4 B+ z; k
0.0171859296482417 p) e e- n' K$ y( I7 W6 H
0.017788944723618% z; z/ _. [* g( a
0.018391959798995
; t- q* ~! z- c7 U* n 0.018994974874372
& M3 o9 y+ w9 |& f! E& E @ 0.019597989949749
/ S2 g- k4 o2 F% b+ F: G# M3 Y- a 0.020201005025126
% A1 B- c- T$ m! X, b 0.020804020100503
/ R. ~/ A3 v# {" b; ^0 g2 M 0.0214070351758798 C3 T* N1 t2 [; e
0.022010050251256
6 ~; P, B. J% i+ R6 L' O 0.0226130653266331 v4 X/ O7 A% u: _7 { L2 R
0.023216080402010) ?# a: E8 A9 u* a6 y3 V
0.023819095477387
/ K Q i! {* t/ }9 A, f 0.024422110552764
2 W' n8 \( C4 p( g 0.025025125628141! |7 J! \! |3 k! H! C. p; t+ l
0.025628140703518
3 O* A" W/ e4 L, Z6 @9 Z 0.0262311557788943 ]! q+ }+ v2 ]1 N9 I5 w" M% h% U
0.026834170854271
* _3 v$ v( T. r& o' I8 ?; R 0.027437185929648
3 M# B2 T: |8 c 0.028040201005025
! L$ L, q6 M8 w7 w% e0 L 0.028643216080402
0 p" Q5 B" _' y+ d* k 0.029246231155779; s8 `. c/ [: a! ~ A4 s& u
0.029849246231156( w- o6 W1 ] W v. ^
0.0304522613065337 o' m! A. Q1 i6 i
0.031055276381910
# K3 K7 P) w+ x/ y- D/ k$ u9 o 0.0316582914572868 `8 x# h% U) ~. w
0.0322613065326636 n+ O8 _' c0 M
0.032864321608040# t3 F3 n; |# A
0.033467336683417# u# Z' a- U) N* [- B9 I( W9 m: s
0.0340703517587949 c+ J$ K4 Q- Y4 [* J
0.0346733668341711 h5 e3 G4 t& C k$ J; k7 g% ]
0.0352763819095480 u, a- c6 a2 Y4 |) F* ^1 D% F7 V4 O- i
0.035879396984925: q# `/ c# `* K4 p; Z
0.0364824120603025 [, F3 Z1 f& r. J' Y
0.0370854271356786 E0 _5 h& t5 b0 n9 |1 K* W
0.037688442211055: r& B3 |: ]# N( O9 `3 g5 g
0.0382914572864324 ~2 w! J* F' K. L( U- ]
0.038894472361809* m& b( m- O* D+ j/ Y
0.0394974874371867 e1 q& K4 J. O- ^" Z6 |
0.040100502512563
2 \) `; n: x; w 0.040703517587940
9 Y) h7 q7 F' Y' G2 @& A2 [! b/ W' Q1 } 0.041306532663317
) c% g( X* F: W9 a" `1 h1 ? 0.0419095477386934 h/ T( G: D' N& ?2 D' \7 S" l
0.042512562814070
: T2 c. m" e( ~6 B N4 R3 b 0.043115577889447; B9 m. n4 |0 {- s
0.043718592964824
' h7 R$ ?1 p$ J0 m4 e$ p/ J+ g 0.044321608040201
3 T8 y7 a" T3 I' a5 ] _ 0.044924623115578
1 x8 T. j: S7 a. B2 P" A: M 0.045527638190955/ e& ~, Q, m/ q+ |& q6 s
0.046130653266332* l* O j* l# ~' w O. M
0.046733668341709- |9 a9 j, T. S
0.047336683417085
* N& i% T! K) L9 m; x 0.0479396984924629 [/ C( ~3 p% L
0.048542713567839$ ~1 a% o' M, ~$ N: n) n# O
0.049145728643216" R3 a) `; k' b t. _% A- a4 k
0.049748743718593 O: a7 e, {$ a; l/ K- J, c
0.0503517587939702 U5 `( T$ E+ j: |
0.050954773869347! a3 _. S1 p6 Q5 v. K; E
0.051557788944724
1 s; x/ m9 O; N: I5 ?% {: L 0.052160804020101
+ j+ V9 ]: Z! I0 P, \ 0.052763819095477
4 g0 H% ~( `3 W/ G' ~ 0.053366834170854
4 e, m2 }% v7 U 0.0539698492462318 M' h7 k- w& D, K; {5 S
0.054572864321608
6 F. O; ]0 y; i4 U9 [ 0.055175879396985
. s9 w8 R4 }. q 0.055778894472362# L. r4 s4 R% |% G [
0.056381909547739
: S* C4 o8 I7 r- a) K 0.0569849246231162 P4 c9 k8 u) o
0.057587939698492
1 ^! k* R9 q7 d 0.058190954773869; J9 O9 A; c0 ^4 { D+ f! }+ D. e
0.058793969849246, e: M9 a; Y v) x: [
0.059396984924623
7 p' M" d7 t6 m' X, V 0.0600000000000005 ?" }! s9 g/ Y9 k8 d7 {; A
7 E4 B4 q+ K- O- _. J5 ?, k
) I6 O b2 |1 p6 R$ p( Q
ans =
& x; @% {. ^- A: `
8 L' @( O: l: p, P2 X7 W+ F -1.033689540653716
2 B8 u2 o+ a2 T8 \3 A2 c -1.013619827890691% |7 q& E9 K1 |% j$ |8 n/ K i
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! Z& g9 B* Q% X, Y- | 0.4642137525352636 }' m( Z* j6 }( d6 R
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' z# H( R( ?9 E0 v! O 0.748674124097121- }( M( b5 L" Z) N8 l; \
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9 ]8 c; Q: Z0 |- m% M 0.811596057546417, A* h9 Y o% H2 T: g
0.824844183890336; d7 a% Z. a" M5 |1 Z4 ~
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, d1 c7 B; L+ x8 O0 o% ~ 0.852142129100673
$ Q7 H7 y Y: c, S5 t& C! c! U+ d) Q 0.8662370636710580 e. M }7 Q" r7 f7 d. ^
0.880664979264975
x) V1 [' W+ `8 L: z4 J 0.895457976752096
7 X, R, V) t1 d6 r# D, o2 k 0.910653694311282
& m, v5 q# F& u4 ` 0.926296779035770: R4 [+ @! I' | a9 ]' x: T
0.942440908631660
& j. ]2 U9 p5 t, h 0.959151639002953
' p9 V& E" g: C9 Y( a 0.976510534039502# Q+ Y" [) i1 J0 N8 D- b
0.994621366531092" b' N2 ^8 s* L7 \
1.0136198278906921 A0 b: C& p" z
1.0336895406537232 U' x( g# _2 X* T. Y- v) q) v* Z
, Z Z: i7 Y i* H
5 f5 s3 r9 `& L; w6 G2 q0 P; d% q
' h9 W) E/ {+ R: s
作者: shouce 時間: 2015-11-18 22:22
pacelife 發表于 2015-10-12 18:42 
4 R; n# Z$ W6 E/ ?* L* j樓主能否運用這些數據在生成三維圖形
- k: b6 {1 ~* P- \6 O( ?. O-17.48757173 229.1142827 0; U8 s6 a x: {2 q* d" n
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Y& D+ ~, X% H. D* Y-17.28495351 230.6801339 0 ]7 t u! `0 f
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4 T7 |' C; [& l& a5 H/ {" N-13.11905015 241.9957329 0" O! F# I1 f" w& |) S9 q
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& B, n- ~4 Q/ Q8 j4 T' N6 { ~-10.76880664 244.9853133 09 S' [3 b4 M3 h" I+ n6 O7 d
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! W/ v" j w8 W; c2 K-8.734024552 246.8397336 01 D' L! @( i; @1 }) W# t
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; G, K% ], X5 g( L2 a. l/ P-8.42062646 247.0782666 01 T6 F4 ?- b& p( p" Z; Z; c ~3 l
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, i/ P2 D( R9 K% V/ ]: n-7.793472811 247.5220986 0
6 O. C' ^& s! Y-7.636608145 247.6263796 0) {5 i" A+ [) N9 j- ^( t0 j
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. p8 O2 K& }: N5 o4 p-7.32278654 247.8271956 07 m+ k# Z$ Y* B7 w3 `! d
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9 ~6 N. F- z6 I# e7 |-7.008842241 248.0179119 0 z# C+ A: e( U3 W: x7 V
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! b. C; t) z/ d W3 x j+ b-6.066289626 248.5318886 0
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* G) T" g) h# F9 w9 H% ?' ?/ `-5.280048424 248.8966103 0
1 W% ~2 \% a+ g* ~) Z-5.122720872 248.9628812 0
9 W& x$ f1 }2 E# G. R) E-4.965368224 249.0269718 0
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6 t+ f4 i- T, C; G g$ ~8 H! w( X, j-4.335719306 249.2618659 08 R- ^! L$ [- [7 N
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. | Z w4 K/ t( W8 A S7 F-3.863251097 249.4159162 00 y% r+ _" j$ [" W' y l
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' |! l7 t k6 T# _$ _, u4 ~2 L% j-3.548172602 249.508283 0
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-2.917803035 249.668623 0/ ?0 x8 c1 c g* C, A
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6 q, q( r R8 n8 U, N" G+ L% i, B-1.340930002 249.9304029 0; Y! _! o! \) O
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7 L7 j" O7 f9 l' \0.078883251 249.9997595 0
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, X1 k: {- W6 y. j1 b0.867692756 249.9708837 0
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1.340930002 249.9304029 00 b" U( Y, d4 P% V) g: n; w
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1.814103503 249.8724619 0
7 Y" c* ?+ {% O* I* a1.971809995 249.8492486 0/ F/ @2 A8 i, C: m2 I
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2.287191071 249.7969412 0 A5 _' W0 u0 U; p4 R
2.444864036 249.767835 02 l; K4 Y3 s- i* a' U. X
2.602524216 249.7367515 0
8 X* h* y6 C2 m# V* R2.760170812 249.7036834 0
V9 m, A/ s. k2.917803035 249.668623 0% G. B5 I" D. `& d' h2 c8 f; ^9 N, t
3.075420099 249.6315619 0
' a0 }' M! G+ i) R3.233021227 249.5924912 02 _+ _% ^, v O) A
3.390605649 249.5514016 0
' c6 t; M3 D8 E+ E; B% G R! b3.548172602 249.508283 0/ A2 V- F. T8 a- X$ T
3.705721333 249.4631249 0
* ^4 c, [" t9 D4 e5 \3.863251097 249.4159162 09 i4 T B- }3 k# _ N- z s
4.020761161 249.3666451 0- V8 S. r- ?! G. h4 l
4.178250801 249.3152993 0$ f1 C" @' N5 r4 k& Z
4.335719306 249.2618659 0: `7 P9 g0 N8 E7 ~) e# Q
4.493165978 249.2063311 0
" m8 Z5 m0 G, P$ v% t4.650590133 249.1486806 0* x2 \- o# D2 Q3 a
4.807991099 249.0888994 01 D5 R' z" `' W; U* g9 l/ F
4.965368224 249.0269718 0
' v8 }, d \& G: C/ v1 |+ H/ x5.122720872 248.9628812 0! b) N( S9 J- W) C1 e# G6 e: j
5.280048424 248.8966103 0- O) ~$ D% u D- Q
5.437350282 248.828141 0
- `9 I0 h4 a7 A$ d" ~5.594625871 248.7574545 0
* Z0 e7 I& z8 w$ @# g- c5.751874639 248.6845309 0
) o3 k8 n1 {* @! n; t' E5.909096057 248.6093495 0
2 C$ J. Y. Y# Y1 [6.066289626 248.5318886 0
7 v* @- J! {! f/ m4 B% \( S6.223454876 248.4521256 0
2 \0 V, T2 F7 T v; c. ^6.380591367 248.3700368 0
P# s# @7 \0 c, C/ K0 a) k6.537698696 248.2855975 06 ~( r% J4 I6 X0 I
6.694776495 248.1987818 0
9 H* m+ u/ N$ O3 o6.851824438 248.1095627 08 g& v K3 |& D+ R6 @
7.008842241 248.0179119 0
! u! N+ t: }) R9 \+ R! Y7.16582967 247.9237998 02 l9 Q, Z+ {# S: e0 d
7.32278654 247.8271956 05 v( [6 X* C6 n; v1 F1 |* T: U
7.479712721 247.7280668 0
, P. u; i+ C# }9 A$ ~, l4 _3 y7.636608145 247.6263796 0& m; I" D4 T% @5 \" j
7.793472811 247.5220986 08 j1 V) {7 A9 O- C+ X, x
7.950306785 247.4151866 0
2 ~% V8 [, K5 _0 p% J4 Q8.107110216 247.3056047 03 o X7 N& t1 n
8.263883333 247.1933123 00 j9 Y: Z R. h3 i0 S& r' p
8.42062646 247.0782666 0# `% Y1 N d J& }) v2 ?
8.577340022 246.9604227 0# b! C: ^ L1 K2 [1 f- \
8.734024552 246.8397336 0/ M( _5 w, N1 w1 n$ n9 f! L
8.890680706 246.7161497 0
$ s) _" t! K( [8 Q6 \9.047309269 246.5896193 07 a( _. Y, r# ~
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9.360487512 246.3274969 0
) _5 D( a1 N6 P8 ^! u! z8 G9.517039547 246.1917868 0' T+ `4 k, V) x. K
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9.830076752 245.9107488 01 e/ P- J& u$ t
9.986565496 245.7652821 0+ \2 U6 g0 \9 [* }
10.14303713 245.6164179 0
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10.45593921 245.3081723 0. T/ I N! R c
10.61237554 245.1486165 01 M5 V/ V' k, L% U% B' i: S
10.76880664 244.9853133 05 `# b0 f: y/ }- a
10.92523646 244.818161 0$ x" g8 K4 Q" l0 s( f
11.08166946 244.6470513 0
( e% Q, |/ `$ X; T' L2 r7 O11.23811067 244.4718685 0
+ b4 A7 [; Z' `! g" B& z- B11.39456571 244.2924888 0
) X s/ v- i( z8 ^2 W y4 R11.55104095 244.1087796 0# K$ I3 k8 g/ [ x" {
11.70754352 243.9205986 0
$ {, g+ T; H0 z5 i7 a5 H& U11.86408148 243.7277924 0
W$ L8 Y' U4 k* n12.02066392 243.5301959 0
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9 E$ |: T. Z+ H$ u& H8 Q* A12.33400471 243.1199023 0
: A1 E9 c/ i$ u4 a12.49078787 242.9068011 0
& T/ d! ?! ]9 G U2 q12.64766561 242.6880972 0
1 z! W+ D, o3 F12.80465505 242.4635397 0; T6 {2 ~: K( _& Z7 t
12.96177574 242.2328529 0. z' h9 V0 z9 W) L9 D
13.11905015 241.9957329 0' B( G3 j; R+ k: P) X8 P6 s9 Z' Z
13.27650414 241.7518437 0/ t- n3 S/ y. I+ v" p( Q6 Q
13.43416766 241.5008112 0 d7 D2 i9 ~& R) N; k3 r: P
13.59207552 241.2422176 0/ n8 I' {# [ j( }
13.75026839 240.9755931 0
5 f' ]9 ^/ o4 |3 @% M% ]13.90879414 240.7004064 0) l' q" y2 p* n: ]! E5 J$ w: _
14.06770943 240.4160523 0
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14.38699287 239.8169526 0
* }6 _9 \ w+ J I; O/ d+ j: L14.54754137 239.500461 0
; {) }6 ?5 C0 a14.70884907 239.1712469 0
3 F, l. {# R! t14.87106763 238.827974 0$ T, o3 T/ L) D4 b1 E, s
15.03438904 238.4690147 0# p! J' B3 E5 ~1 e, `7 E
15.19906081 238.0923492 0! T" C1 p( \+ @( }+ b7 A$ a
15.36540928 237.6954146 0& o" M" [, B) w; U3 J
15.53387651 237.2748695 0: _5 U& v+ X0 u/ j' U6 Y& i1 L/ a% k
15.70508222 236.8262052 0
6 R3 L# K% L6 E$ j$ G5 c% v# X15.96864056 236.0872311 07 s) |2 R+ v7 _; o9 Q, z
16.21413872 235.3358909 04 W% o F) ]. P# m! t! Y
16.44066252 234.5753164 0
0 W7 `* a) _) Y5 R7 _! R16.64807528 233.8066972 0
( ~: j6 k5 ` y* K" ?. O16.83627004 233.0313194 0
0 Y: M) x/ A$ ?17.00517067 232.2506108 0
( D5 i: p0 c0 z, I a17.15473398 231.4662174 05 j$ x% A9 q5 R# p: @( }
17.28495351 230.6801339 0/ V5 {+ z9 j3 ^7 N. h/ [
17.39586705 229.8949441 0. p/ O. T& ? S% Z/ w
17.48757173 229.1142827 07 A& D5 P D" k! x- U1 x
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