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标题: 螺杆转子刀具设计 数学模型 [打印本页]
作者: shouce 时间: 2015-5-26 19:44
标题: 螺杆转子刀具设计 数学模型
本帖最后由 shouce 于 2015-5-26 19:49 编辑 . l1 A" Q" L' @8 S
& ?1 r5 `% g5 o% w9 o8 H 螺杆转子刀具设计
设中心距 100mm 阴阳转子齿数比为6:4 型线为原始单边对称型线 齿高半径为0.25*100=25mm 如下图1所示
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阴转子型线方程为: x=60-25*cos(t)
y=25*sin(t) 形状如图2
% u7 t% A* f! k7 e
t的范围【-1.361,1.361】弧度表示
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螺旋角为45度 螺杆旋向为左旋 阴转子的扭转角为5.235弧度 则阴转子的导程:T=2*pi*12/10*100*tan45=376.991
P=T/(2*pi)=59.9999
要求转子刀具 先要解下面的方程 如图3
3 }4 x0 ^ f! |1 a- Q5 A式中AC为砂轮直径 设为500mm Ψ是螺旋角为45度
现需要求150对 (t,τ) 意思是已知一个t 求一个τ 使得上面的方程成立。 又t的范围为【-1.361,1.361】 在这个区间等间距取150个t 则对应有150个τ值 τ 范围为【0, 5.235】 整理后方程为:
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
解出这个方程后 将(t,τ)代入转子螺旋齿面方程 得到齿面的坐标点 再转换到刀具坐标系中 得到刀具回转面坐标 最后转换为刀具的形状。
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作者: shouce 时间: 2015-5-26 20:04
等下次有时间 我来解这个方程: a, C/ v0 M$ `2 z! u
作者: seekfor 时间: 2015-5-26 20:27
让我想起大学毕业设计是双螺杆压缩机齿形加工刀具设计了,端面方程,齿面方程,接触方程,中心距安装角,各种算;可惜matlab没学好,求解程序是老师带的研究生帮忙编制的。这东西真的是纯粹数学计算。现在忘光了。
作者: shouce 时间: 2015-5-26 22:09
seekfor 发表于 2015-5-26 20:27 5 Y9 N7 H: j; |* D
让我想起大学毕业设计是双螺杆压缩机齿形加工刀具设计了,端面方程,齿面方程,接触方程,中心距安装角,各 ...
0 V" p6 C& r% q你那时做的齿形 是哪种齿形 是第几代的型线$ Q0 N3 L N7 b2 s1 ]
作者: shouce 时间: 2015-8-12 21:56
shouce 发表于 2015-5-26 20:04
. O; H$ y) V0 H( v9 k, _等下次有时间 我来解这个方程
+ Z- t1 D: z a/ e; d0 J尽信书 不如无书 自己动手计算 才发现教材的错误
作者: shouce 时间: 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]);6 c9 D" i8 w+ w- o) }- N1 z: C
axis square
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5 Z9 w) `) D1 x3 {2 _7 P! E$ `5 A& t0 p, l8 t# R
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作者: shouce 时间: 2015-10-6 21:14
本帖最后由 shouce 于 2015-10-6 21:16 编辑 - `" b1 v. N+ h& `- G3 _- [
6 w, o( U; \' rezplot('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]);' A& z+ V0 z0 \* C
axis square" u, N z, @3 t/ C0 g
2 i+ E0 u: L7 v3 g5 z. u( K9 ?/ H4 D2 m* i% U
6 n0 D- Q* w; Q3 Q
, G' {+ [6 v/ ^- Y
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);
7 K- T$ d" l9 v. b/ AZ = @(t) fzero(C(t),-1.361);5 u" u9 K1 h& n" u! j. z& s# g/ V
作者: 木子12 时间: 2015-10-12 13:55
本科课程设计,计算一大堆,但大多都是用书上的公式
作者: pacelife 时间: 2015-10-12 18:42
楼主能否运用这些数据在生成三维图形
作者: 小杨123589 时间: 2015-10-15 19:47
螺杆马达的线型和这个一样么
作者: shouce 时间: 2015-11-17 22:57
function solve_nonl_single1- Z; k" m/ ]: W: _ P' O. M
clear all;clc- O: ^+ P- ^( s
format long! m N+ n n% S4 D" c& F
global a. W( M$ L7 Q: W2 c( b; w+ x9 w3 V
a_span=linspace(-0.06,0.06,200);
; r4 @1 |3 ]7 X \; F4 An=length(a_span);; v/ d" c) C1 B
x0=1e-9;* G0 |3 `- ^; g- N+ G
options=optimset('Algorithm','trust-region-dogleg','TolFun',1e-12,'TolX',1e-12);
0 B8 C3 N2 v5 f% {for i=1:n
2 o+ x# ?) n) R! q a=a_span(i);
* U7 Y8 P6 i" ]7 X$ I5 |' |3 a. S x(i)=fsolve(@nonl,x0,options);4 e$ N5 |( x6 t9 |9 O
y(i)=nonl(x(i));0 l9 H& h* O7 \5 n
end
) l' J% W: A5 ^( D9 E$ N6 Ra_span', x',y'$ h9 A" f# ]0 ^( Y9 l
function f=nonl(x)
, A! O2 f3 z6 t$ ]* H7 Cglobal a
* @- P! Y6 M' M$ s3 pf=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));) Z) r1 \& y! ^7 m' a* F4 k+ K
& B1 b& A1 s6 Y4 v
运行结果 ans =( ^& p' l6 @, U% P: V
-0.060000000000000
$ o7 f% f+ ^: ?- B; f) o, t; @ -0.059396984924623
" c% h& e: d+ `5 G' x -0.058793969849246
- Z8 V7 `- M. d -0.0581909547738691 O! o! F$ l. _' N2 A) P% C& V+ t
-0.057587939698492$ G" o) f8 `% ^: e* {* {" L2 h2 o
-0.056984924623116
2 _& w, L/ k# z" R6 u -0.0563819095477396 q' r# R9 A' D8 z* i
-0.055778894472362
7 e+ e0 o& s" r0 w9 E! x6 f& E. v -0.055175879396985& r& P" ?2 {6 A- E
-0.054572864321608
% S* J/ F' O5 I5 _. {5 s+ i% B -0.053969849246231( @6 K* ]2 }0 g7 B; i& O' R: O
-0.053366834170854
3 ]1 \' _, x9 u8 p -0.052763819095477
8 V' e* ~+ S4 u$ f -0.052160804020100
7 w4 F/ q" u+ z6 N2 F/ u -0.051557788944724
7 U- w& C$ _" f -0.0509547738693470 o" ]) N1 u/ m, F+ {& [; D
-0.050351758793970& ]" P7 A. h6 N; v
-0.049748743718593- z# Z. e7 a; Q7 m3 R, k. ^
-0.049145728643216
6 C% i, y' m3 E& I. W1 E -0.048542713567839
1 B, ?- D# M, A6 B- t2 [# ~ -0.047939698492462
+ V' f# U" Q; X5 v @ -0.047336683417085
5 k9 }' Q, O2 [ -0.046733668341709 c0 P. {7 H; Q+ t
-0.046130653266332
, n: H. E0 |: B( R -0.0455276381909556 l) x& ~6 ^1 n! g
-0.0449246231155786 A- N* y6 H9 B6 ], ^" a2 _
-0.044321608040201- ?) N6 s5 I! m9 y% f
-0.043718592964824
' u7 U1 g7 Y, L3 }+ p" |4 f -0.043115577889447
; M; e8 `: |+ K- [( g, j K. b+ t -0.042512562814070
6 H! R4 @) ? r" U6 N -0.041909547738693
5 y: X' ]8 R+ `6 Q# ?8 C -0.041306532663317
& o( g1 n; Y' y# | -0.040703517587940. K+ X4 T( p* d
-0.040100502512563
3 r9 f8 |( i9 _) @7 b; s; k3 F -0.039497487437186" O+ Z1 a& k; z! w( \" g
-0.0388944723618093 b0 ?- `. v( m/ `; b3 H" j! R% I
-0.0382914572864325 @+ n- o/ f5 Q
-0.037688442211055
U5 J! \& ?) B' s, s+ | L4 @ -0.037085427135678
& k) s# w9 H) S/ T -0.036482412060302, M8 e, F0 [2 x' f5 C9 }; e. J) _
-0.035879396984925) ^' T% W1 O6 g/ X- B, u( m
-0.035276381909548
. t1 n* D4 |: ^/ `! k6 n -0.0346733668341715 | Q, P% c5 C) S, d A. a# y
-0.034070351758794
; B5 r5 u, \2 p; ?% o -0.033467336683417) @, _8 c1 w3 V7 ~1 u& S
-0.032864321608040
5 Q; [- u4 ?1 X -0.032261306532663( ~0 P" C# n1 W4 ^! [( F0 @
-0.031658291457286
3 j9 i+ a$ F0 Z0 q- y2 a0 R8 E -0.031055276381910. e5 }# N* }$ ?% k" U0 c
-0.0304522613065330 R0 u( I5 Y& d
-0.029849246231156( a1 l8 M% v6 g. R% j& c
-0.029246231155779
1 o t: f# B/ S! x! c, C P8 Y -0.028643216080402
) ? V& c V7 a -0.028040201005025; x4 ?! Y4 L0 I6 b
-0.0274371859296482 g: A7 [% L e: H3 q
-0.0268341708542715 ~) T+ Q% B& p- o
-0.0262311557788948 T' m, l! c2 f9 W; X' _
-0.025628140703518: Y' i/ @9 h- j; z( t0 t
-0.025025125628141
6 }2 G' o3 X, C# Y9 R1 z [ -0.024422110552764" \+ l# ^; `5 y5 ?0 o3 {
-0.0238190954773871 u- O( ^- R; L' k+ L) |6 f1 l
-0.023216080402010
8 A n- s o: Y- x8 N -0.022613065326633
% a1 |- B$ j; q4 g; v -0.022010050251256+ X& e5 `$ G7 t% s' j. r1 P
-0.021407035175879
/ Q: |% c2 I4 g+ V -0.020804020100503) W0 Q7 A4 p& m7 [, F
-0.020201005025126
, G9 ^0 l1 ?- i5 W. j -0.019597989949749
8 L# A! Z9 }' c" w# [ -0.018994974874372& q! j& p* }$ Q! `! S; F
-0.018391959798995- C+ a. E, x R- z$ }
-0.017788944723618* p4 I( k/ A/ P, g8 O6 w; }
-0.017185929648241
7 Y* ~1 {+ K% z) B$ M, S -0.016582914572864
" I5 r) \' ^7 X# ?" H% C -0.015979899497487
; G% ~5 F6 f# w7 b+ q8 V -0.015376884422111" @. ?: }4 z# z; H
-0.014773869346734& d7 @) H2 d( s: U3 P1 z# f
-0.014170854271357
% e4 k0 j8 a) F5 M) I -0.013567839195980
+ B. h& L3 |+ p2 j" n9 c -0.012964824120603
$ X; e" g7 ?2 ?+ _ -0.012361809045226; Q& |1 {% C4 z3 U0 W
-0.011758793969849( s$ P/ ^( H9 b" B, D
-0.011155778894472
* Z6 n7 \2 @5 J/ I8 P3 z -0.010552763819095
4 _2 S9 b0 M6 ^9 K -0.009949748743719
5 r$ V6 E8 H$ h7 R8 o -0.009346733668342
; d" w; x* R9 {5 p8 | -0.008743718592965
. l5 }+ J& s$ z# p; c- Y -0.0081407035175881 v" z& W# e8 \1 r4 ]" @8 K, x
-0.0075376884422116 G/ f7 q& W, C- S
-0.006934673366834 ]- }7 L5 k# I: F% F9 [5 U; W3 r
-0.0063316582914570 K6 e8 W- e6 H5 W; ?
-0.005728643216080
" q1 G D/ y( N2 c" Q- j -0.005125628140704
1 j/ Q- `- g/ \$ C! t4 \& }- Q -0.004522613065327
7 D1 C" f& ]6 f: T: I8 g -0.0039195979899508 `6 b1 Y, d! S
-0.003316582914573. n% r$ W1 P3 K) b' [) k. m
-0.002713567839196
+ y/ i1 ~' U2 ?, E { n -0.002110552763819
6 Q+ X0 }: L2 a6 q -0.001507537688442
$ m- s+ H a l8 W% l4 e6 w -0.000904522613065. ?/ Y) N3 |! y, K/ d
-0.0003015075376889 [) G2 H% w& u6 {. a( s+ N' e
0.000301507537688
7 B* N# G. r. }6 i 0.000904522613065
) @& r% @ p. y1 a 0.001507537688442
! V; g" v+ g0 H2 M B4 y& R 0.002110552763819
' C/ j" ~7 E$ [) w 0.0027135678391962 t% O1 [' e9 U0 M& g, e+ V
0.0033165829145736 k- Z3 M4 t7 [9 P3 u. n
0.003919597989950% x1 T2 @+ G. B) {- F W
0.004522613065327
4 b* L- _6 n8 G4 r6 V% R( | 0.005125628140704
. z7 G6 `5 u: R% \6 A/ Z. ? 0.005728643216080
2 n( N" x: d- [ 0.0063316582914574 V$ j2 r9 e5 A/ \8 b, J
0.006934673366834
- h- P! w6 @: S' Y 0.0075376884422117 S8 |# j% U( C3 @; ?! o
0.0081407035175880 I: ?1 v, l2 X3 y& }
0.008743718592965! A8 k5 B9 p. m- [3 K- L) C: j; F
0.009346733668342. ~9 B, E5 C' }9 a: s/ E
0.009949748743719
* P+ W; @- ~* b: F( s4 C 0.010552763819095" K3 k9 _- _/ i; R7 {
0.011155778894472
( p. r2 W% m) u. O 0.011758793969849" b3 K0 I2 `8 ?" \1 ]
0.0123618090452267 `0 o2 [5 m/ o. S( I
0.012964824120603
4 C9 V$ H( \9 L5 i2 U, ~5 S# U 0.013567839195980% \# o+ L: ~# p2 r4 L l
0.014170854271357
+ n0 y6 f+ y/ D$ V4 L3 E8 S! q 0.014773869346734
^. ^# H9 m& F1 G. w* B Y 0.015376884422111# N9 m' G/ g _, e1 s w
0.0159798994974879 Y# \5 @; `1 S+ R8 a B( i1 ^3 Z+ D) |
0.016582914572864
5 W- W4 n+ @4 N" x1 h 0.017185929648241
6 | E t" S$ c$ H6 o 0.017788944723618
8 \" `$ l$ m t4 i 0.018391959798995
- P! u0 _4 a* A; j4 m 0.018994974874372
% k$ G3 R0 _" q3 {4 X% y$ q2 q 0.019597989949749. e) m9 D/ q, p! E
0.020201005025126% I/ f3 l0 f! I9 ^; J [' Z& ~
0.020804020100503
9 t3 R- \; y: Q6 ]4 a. h3 O$ s 0.0214070351758794 d- ^$ U" e: {( S) M6 U+ p
0.022010050251256
2 a6 [1 j7 c# S8 r* T5 \; v 0.022613065326633( K+ W% @2 c3 }$ s) z: J) K
0.023216080402010
1 \/ b1 ^: D6 N" p1 I: y 0.023819095477387
9 G; g3 ]/ @4 W0 b2 l1 F 0.024422110552764
0 N8 a, m: e9 U4 V/ E2 z0 i 0.0250251256281418 G1 K% e4 _. u+ }. L( b' {5 W0 }6 U
0.0256281407035183 s, `9 `, X; c. w4 l0 Z
0.026231155778894
8 i$ n: ]. B% ] 0.026834170854271
% R/ J1 h, M6 x9 B1 [ 0.027437185929648
6 L3 |" \ q" k3 P7 d7 u \# {7 @ 0.0280402010050255 \( ~) x- L1 T
0.028643216080402
4 B' v( H# Q3 X6 F 0.029246231155779
! J5 \/ a$ X" E0 W/ o% I 0.0298492462311567 `! [9 c- A- A" p& M( S6 I
0.030452261306533. g7 `8 _9 q! G6 A
0.031055276381910
2 |. |( ^: b/ B/ D# l- Z 0.031658291457286
; T# Q8 x" k3 x 0.0322613065326632 Z! C. W5 p* u
0.032864321608040
9 Z/ h% u& G; B! Y7 q( a0 D 0.033467336683417" [. _, o$ W. B) }0 r
0.034070351758794
} j5 E) h1 v) `) V" m 0.0346733668341713 M& t) |9 W1 ^, G2 i+ {
0.035276381909548' E0 \, [9 R8 R1 w v) C& ^
0.035879396984925
~' i/ f4 ^ Z( @) X 0.036482412060302+ T1 S; R, b- A2 Z" ^/ p. J: u- S
0.037085427135678
4 g$ d- Y* V( q4 l$ s/ s 0.037688442211055% ] I: Z; b& j+ n
0.038291457286432. y9 } L3 [. i
0.038894472361809! F* Q: d& W" u5 [! k( V
0.039497487437186
8 m+ x. u+ ?6 f9 N- K 0.040100502512563
, t8 C$ r k3 z) M 0.0407035175879404 p; C! c$ {- Y; g5 s/ O
0.041306532663317. S, |) n9 I1 b8 `# }
0.041909547738693
; L: ~3 L7 R) m. D 0.0425125628140708 G+ `# e9 @9 f7 C- N
0.043115577889447
$ c4 r- N. N3 D4 @ 0.043718592964824
/ P) f2 Y9 Q' h; g& b T4 b9 {, j+ x 0.044321608040201" z4 A" o( O$ |* ~
0.044924623115578" [% N0 b) V" X- A
0.045527638190955% i% X0 f: n& u
0.0461306532663326 a1 C$ ~8 a4 h, t7 U/ b
0.046733668341709
6 W7 ~. w: ^- c# q' i 0.0473366834170859 S. I: L: p+ e9 j# U
0.047939698492462! x% \! R) A4 @) m y. {0 `
0.048542713567839* ^ i/ q7 Q. @% W7 p4 O
0.049145728643216; w& b3 I2 p" g; x
0.0497487437185930 |) x! R9 _/ f$ P* F
0.050351758793970
# Q6 p, e' J0 ` o+ s! u 0.050954773869347
* f% o6 U$ E4 P! X: p! H7 ?1 z# M# ` 0.051557788944724: ~' y$ t U$ a& n& B
0.052160804020101( }/ }3 ? I8 w* n0 c
0.052763819095477
- w2 J: d7 Z% A& }2 p 0.053366834170854
1 Y/ D N4 A% L' F: ? 0.053969849246231
/ r8 W M1 K* n7 L6 M6 N 0.054572864321608/ e; ?8 _3 e: g2 D- N
0.055175879396985+ |& I5 j2 u5 l! M
0.055778894472362
: X- c6 u4 R* F6 l7 p! I# p5 B 0.056381909547739
' L0 `' E$ `% c 0.056984924623116
1 [& b2 z% L# Z2 Y8 [: s! | 0.057587939698492
2 a5 q+ Q+ P3 N6 q5 S 0.0581909547738690 ^( r# a9 V" m3 I7 o' P$ c
0.058793969849246" Z$ D0 Y8 o' A
0.059396984924623
0 d& Z2 e6 f1 p+ Z: U! t. w 0.060000000000000
* x j: z) c: z! J0 N5 r7 g8 g2 d. y6 ^ A: B7 F j
% O* p8 d2 {: U7 t" J; L$ a! Y
ans =1 ^* ^+ p, j+ Y& w9 r4 B
/ H( x& j6 L: ]
-1.033689540653716" I2 R) d0 V4 ?% R( v
-1.013619827890691
+ I! a1 o1 Z5 M1 r -0.9946213665310832 x, B- X) `. U( w( p
-0.976510534039504" o5 z4 V% B/ K
-0.959151639002957
8 |( m8 f8 W( K3 q4 V3 o6 X -0.942440908631668
; V/ d; b2 B- N, o$ j3 ~# N: o# B+ k -0.926296779035772 E5 X, f4 Q4 a3 v
-0.910653694311287
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0.976510534039502- P6 l" }# K5 d) R
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1.033689540653723& T$ S# u: T. F' L. C2 s* l0 r
+ V: c) l) w3 ]) Y6 J9 s0 A- l+ |7 @( ]7 [
! K# i3 d5 V o) a. b/ O" X
作者: shouce 时间: 2015-11-18 22:22
pacelife 发表于 2015-10-12 18:42
& Z: Q- Z/ ~) E楼主能否运用这些数据在生成三维图形
' O( k8 |) g% ~0 U3 N
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-1.498662686 249.9130344 0: C; S/ \1 Y: e
-1.340930002 249.9304029 0+ q- u# o4 S! M* E8 L
-1.183190233 249.9458317 0
9 w5 x. \6 a. C+ J" Q-1.025444208 249.9593243 0
( }8 X5 P6 H4 o9 P! l-0.867692756 249.9708837 03 U- h2 b! E' A& G1 l# `
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! @5 Z U: V$ g/ F& e" g$ M- D-0.552176899 249.9882131 0" b: t0 b4 S- n6 V8 d
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# `) U* n5 |# R2 a! w/ x-0.236649334 249.9978355 0+ p+ E/ O4 p* A
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0.078883251 249.9997595 0
4 }2 Y; Z1 N% w% _2 V9 Z) O: {0.236649334 249.9978355 0
" d% X* U) u6 F0.394414162 249.9939869 0
2 C& R+ B" F5 e% J- J6 h! Y, O. d: G0.552176899 249.9882131 0* W( }! Y8 k# h1 P2 K, a; a* E
0.709936708 249.9805126 01 u" E4 |! P% R
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1.183190233 249.9458317 0
& k: Y4 R' ~9 g! Y" Z1.340930002 249.9304029 0' W8 U- ?8 {" F+ A
1.498662686 249.9130344 0+ Z5 v( f: W4 [2 o- K( n
1.65638746 249.8937222 0: Q( b, ?, t2 F6 P
1.814103503 249.8724619 0
; b! k1 J& t5 K* X: c% u1.971809995 249.8492486 0
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2.287191071 249.7969412 0) L& U! F) B o, C6 k, L* B
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. c* ^4 P0 ?: O- w; x5 A3.233021227 249.5924912 0, I8 @8 H& y: C* e) w* g
3.390605649 249.5514016 04 Q2 c- ]" w+ q6 N; [% z* N$ b
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Q1 G9 _5 s: n7 e& v# U9 y6 Z3.705721333 249.4631249 0: \7 X; |! x1 [
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/ e. l4 E* L+ }7 M- o0 g# L4 V6 g4.020761161 249.3666451 0
& [; v9 i% b0 T$ q) `4.178250801 249.3152993 0
+ l1 e( ~" x4 @- T6 Q8 N4.335719306 249.2618659 0
% D, f& U. c5 r$ ?3 y. F4.493165978 249.2063311 0
% @' L8 {2 N( \0 X. ~4.650590133 249.1486806 0
6 l" m* k9 z B V% V3 v1 c% {7 Q4.807991099 249.0888994 0
, x8 v5 s: H0 y8 C$ c2 u3 d Y, H4.965368224 249.0269718 0
' D3 d0 }; C4 m* s- w6 d5.122720872 248.9628812 0
* F( Y u1 o% `/ H0 D; s; y+ r5.280048424 248.8966103 0) f. F( c5 j; O
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8 Y$ Z7 _5 `2 R0 k, q9 Q: w5.751874639 248.6845309 0; D( |1 n+ k1 h# n
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8 W4 q' p. c$ F: m2 c& l6.066289626 248.5318886 0- n0 n9 _4 Y; [% \
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6 D2 m/ H$ q+ X5 w4 ?4 Y# d% H; o6.380591367 248.3700368 01 ?8 ` J# f/ ^ O) f/ K
6.537698696 248.2855975 0, I: s* W0 V. o) a0 W3 E
6.694776495 248.1987818 01 n' u) J3 I: X8 @2 e% w) c
6.851824438 248.1095627 0
/ G: p) W; c# _0 n# p7.008842241 248.0179119 0/ d @: M9 ^" H( w
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' G% U9 ^. N0 X- w+ f# k6 ]3 C7.32278654 247.8271956 0+ z: M$ i6 s$ J& K |6 p
7.479712721 247.7280668 0
' O p! o3 V5 R+ N) \7.636608145 247.6263796 0
, S7 h5 M7 p# A; |8 }' @1 i7.793472811 247.5220986 0
# Y3 z% |+ I$ c2 ^. G1 X; z- j7.950306785 247.4151866 0
T' |2 |: g3 H; h' ^+ h- m8.107110216 247.3056047 0
! c+ z) _. ^# i% X% I+ d2 A7 J) E1 j i+ D8.263883333 247.1933123 0
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4 B5 c1 V' u4 H$ u8.577340022 246.9604227 0
5 l& S9 I! k7 N8.734024552 246.8397336 0
4 @3 l( n3 n8 r* T; ~# \8.890680706 246.7161497 0
4 D2 p @1 R; H- l9.047309269 246.5896193 0) u! R1 Q! e# L, z ]0 s% P
9.203911175 246.4600875 01 e: V* ^7 W' ^7 k) }( M$ e" r) F+ e
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" G3 J3 D0 F1 Y6 ~# ~# E9.517039547 246.1917868 0
Q2 k) k7 M! d0 f- |9.673568737 246.0528933 0: ]" s9 D# O6 K8 w z
9.830076752 245.9107488 0 a0 H- K' P5 i6 c
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7 E. x* T4 a$ U, w0 b10.14303713 245.6164179 0
& _* U; P3 Z* g2 U$ `! O10.29949411 245.4640761 0, j J+ D- E4 Z% b9 G( P) b* L
10.45593921 245.3081723 0
% ?' C! A/ C/ y3 j10.61237554 245.1486165 0
# n0 ]9 s/ K7 n4 L7 o2 Z" l' x10.76880664 244.9853133 0( M1 |0 @) E; Q* ` h$ w
10.92523646 244.818161 0
, K$ R' A7 Q' X8 Q) I, z; X11.08166946 244.6470513 0/ x6 n9 T2 L2 I, x5 B! K& K1 w
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$ b9 b3 s6 t S11.39456571 244.2924888 0
5 j& ]: J* F& [2 }11.55104095 244.1087796 0% C! m7 W. p' M9 a; B8 v; B
11.70754352 243.9205986 03 F& J9 T1 |; a2 t
11.86408148 243.7277924 05 _' l# P: z6 f$ i2 E0 _3 D3 f
12.02066392 243.5301959 0! g/ G, ?4 L+ O5 F z, I4 ?
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% q* Z3 E L: P' [12.49078787 242.9068011 0
) J" d+ t" {& Q( y12.64766561 242.6880972 0) K. ~4 I% G( X* |2 |# Z1 x
12.80465505 242.4635397 0
V9 T! _/ O$ j. D7 o' v- P+ |12.96177574 242.2328529 0" J8 u# R5 Q3 N9 _) q- l
13.11905015 241.9957329 0
- b2 P6 O+ Z' h+ {13.27650414 241.7518437 0
2 W& m2 ]3 V4 E+ a13.43416766 241.5008112 0* T% o4 O/ L9 b( h; r
13.59207552 241.2422176 03 s8 K' n& R( Z; U+ o" t
13.75026839 240.9755931 0" I, G. q% s" j4 |, j6 z
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7 F: `6 M/ R% ~$ r c14.38699287 239.8169526 0
. L* @0 @, E, C* L1 X5 |: r, Y14.54754137 239.500461 0
8 ]) Y( X5 {. ?$ b9 s! H8 T7 O14.70884907 239.1712469 0( [! S; x5 I. I
14.87106763 238.827974 0& A0 k$ i. V N! c& S
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0 O8 F! i" O4 n O3 i8 [15.19906081 238.0923492 0. R) u# r- q# |0 O( R, Y
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o3 K) B. B h; e* S15.70508222 236.8262052 0) g3 K* R% j9 i
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16.21413872 235.3358909 0' g2 C' x& T5 q+ ?5 Z& B* g: `" D- i
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( C8 y3 s# T/ x; T& ^17.00517067 232.2506108 0! M3 i- l' D' F! L
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" J! ^ X& j* |2 z/ W$ Y& U17.28495351 230.6801339 0* Z4 C7 v7 e" {' O
17.39586705 229.8949441 02 S6 @! ^/ l [2 W; a
17.48757173 229.1142827 0+ X6 C/ `2 C e" E. u* y
/ t+ s" T9 K- q( j# M5 }7 }7 z+ o. ~' [8 ]9 s
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