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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
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5 `$ [/ w' j! c) \# F, | 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
9 B5 m/ x1 @* ?# Ht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
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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+ d; S. O: [! D6 X" @5 t5 c% C9 e
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 
* v b A- z+ o4 l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 ...
你那时做的齿形 是哪种齿形 是第几代的型线1 d% t4 M) M* O/ m
作者: shouce 时间: 2015-8-12 21:56
shouce 发表于 2015-5-26 20:04 & Y6 p' }1 J! d1 @7 J1 U
等下次有时间 我来解这个方程
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]);
5 }6 H# } F( I3 W$ n$ [* }! Baxis square/ p( O+ |- c6 n0 _! j
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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 ) t) F; g9 W" ^) g2 o% d
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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]);9 F2 d5 A& _" p
axis square
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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);$ Y' B6 M& @8 F8 N' J# K
Z = @(t) fzero(C(t),-1.361);
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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$ e, o6 v0 e% [
clear all;clc" g" o( K* r9 J* k$ s
format long X9 } M! A) c7 q5 @* k# y
global a
* P/ q( X7 \7 P9 T6 Ka_span=linspace(-0.06,0.06,200);
( q$ g# m# _3 y \n=length(a_span);
. p* I- Z0 K0 d4 G) J- Hx0=1e-9;
' L! w' \5 x1 y7 _) qoptions=optimset('Algorithm','trust-region-dogleg','TolFun',1e-12,'TolX',1e-12);
, z1 U7 L3 }5 E: ~% d4 B7 s7 [; ^6 afor i=1:n
3 b8 J6 K; F5 }( U- e2 D a=a_span(i);
0 o( t. k# o9 t+ s x(i)=fsolve(@nonl,x0,options);
) T% [7 i, P2 S7 J) j y(i)=nonl(x(i));
8 j6 D' T4 f( d. f* xend+ L3 A0 O& X' U2 m3 f6 p g7 h: E
a_span', x',y'
' q2 n7 c ~0 J$ ?3 _ kfunction f=nonl(x)7 e" ^0 M5 p8 E
global a: s7 s4 K- r5 m
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));
+ ^/ d/ j6 \! u3 ~) q' f
! x; b8 O2 \+ S: A, Q$ o运行结果 ans =
% c" P9 k8 S! W4 M: E } -0.060000000000000
$ G" }2 N% s8 B( x7 |% j -0.059396984924623+ G+ e8 s! z/ X
-0.058793969849246" q: d* D$ Y( ~
-0.058190954773869
# O5 `- o$ Y3 B6 Z ]- l -0.057587939698492
5 ]6 e# @4 X6 k! Q3 T" L, P | -0.056984924623116# x6 G7 t9 i1 _/ J
-0.0563819095477399 e! w5 ]. C+ M8 `& k
-0.055778894472362; O t3 }) r G$ Y
-0.0551758793969855 s8 A: M: K7 ]0 ?
-0.054572864321608
) G! c' P$ T) m& x0 W* z -0.053969849246231
- N' U2 L+ @1 ^" G+ _$ Q4 C -0.053366834170854# ^- H; ]! [1 ^+ y' h
-0.052763819095477
; p% V T S$ F4 F; F8 R -0.052160804020100
6 U" F. @5 g, ~: G -0.051557788944724
# {8 f) N& ?9 B -0.050954773869347
7 @/ W3 |9 Q: u" t# l% }, F( d -0.050351758793970
. K d, @. }! d8 g6 I0 M -0.0497487437185936 k. \; H5 x* e I& \! y; d9 B
-0.049145728643216& `* w) c2 ~8 G) {2 D
-0.048542713567839" p9 q! ^9 X6 X$ z3 l) X: r
-0.047939698492462
' y3 G0 l& k( B -0.047336683417085
+ b* D$ n& x5 c$ `& | -0.046733668341709" c" U: O9 _, t; ]( }
-0.046130653266332
6 v6 u4 C y# Y: H -0.045527638190955
9 `8 ~. D' g- M/ Z* g -0.044924623115578
+ Z( q8 z) f6 E -0.044321608040201
! E/ n+ n4 x) A -0.043718592964824
$ l% [* c( F* I: l8 C2 T -0.043115577889447
& c4 W+ t! q* O5 Z: s6 i( d, | -0.042512562814070
' N' X% k3 m5 e) h' y -0.041909547738693" I+ ]7 g+ P* c Z9 i
-0.041306532663317
5 s# z& M! @' D$ ? -0.040703517587940( g$ z0 W/ M6 R6 \6 _% A$ {( J
-0.040100502512563. {, E- A3 S) V' R8 A/ F a0 |
-0.039497487437186
Y5 p" W( ]. w& x. o. G! ^ -0.0388944723618098 @; M) R" l% E
-0.038291457286432% o+ V# a# @. T( }) d" x
-0.037688442211055) A7 {" v* C, |
-0.037085427135678" a# ^6 [/ [1 M
-0.036482412060302
) e- A2 l# J/ y9 ^8 h% F2 p -0.035879396984925
# ]6 g" _% k$ [, `0 B2 K -0.035276381909548
6 v0 ~! i8 L0 H! k( w" D -0.034673366834171' `; q+ Q8 }1 O( d- o
-0.034070351758794$ b$ _$ K9 o3 w7 R' q- E
-0.033467336683417* p" R) A4 s$ }3 b! P: [% f9 s" A
-0.032864321608040
& H6 v# Z& |7 ]) B h -0.032261306532663
* k. y$ O7 m1 a% W! E- n -0.031658291457286
6 h) R' F; j- j -0.0310552763819104 w2 z: Y+ k5 ~% S$ `9 |2 g- |
-0.030452261306533
: e- E3 y- Q# s! x4 r; K3 t -0.029849246231156
% ^- v4 B8 E& d# F& U1 L -0.029246231155779
) N3 C# h( l6 i9 ^ -0.028643216080402
: W y. Z% N5 Z- a -0.028040201005025
' D( M9 A+ l- e7 r# o& Q9 Z1 O* d -0.027437185929648! ~' H5 N0 `0 o: m/ L2 @
-0.0268341708542717 p# H% f3 ]* W
-0.026231155778894$ |' D. i( C, T8 N! i7 }
-0.025628140703518
, |$ n* y: E' Z9 w3 w+ s" _ -0.025025125628141
9 T, ?& F' Z# J -0.0244221105527644 D+ x( Y1 `) G% H' B
-0.0238190954773874 P, Q# r4 G! ]* m- t6 `5 [% K
-0.0232160804020109 u, D6 X1 J! K) S3 a
-0.0226130653266330 V% b% }% ^3 ?$ ^, O0 \" u" m' @- Z
-0.022010050251256
6 a* D! l3 b( |* f6 Z, @/ |% G -0.021407035175879
|# n" N4 A" i- N: B -0.020804020100503) H5 m* k s+ ^, y# n6 d- ] _
-0.020201005025126' Y% V: B, u$ p% B/ c
-0.019597989949749
4 } K* {5 J7 d3 Q -0.018994974874372
" M9 N# ^9 T. l5 s- f$ u* \3 K$ \ -0.018391959798995! c4 T* j, Z* m, y# o$ f
-0.017788944723618$ K9 X% o2 { I
-0.017185929648241
( ]+ ]+ J7 S4 w! L+ d, V% a% n8 q -0.016582914572864
' U, D" R) |* I; A% k4 m -0.0159798994974874 s# r, D: a& j+ M4 {. @, T
-0.015376884422111. Q- P* R" R, h/ G5 V
-0.014773869346734
5 S. B+ O9 {8 M! X+ G -0.014170854271357
8 N6 l5 X; n- {; `+ |' @ -0.0135678391959804 s7 E" v- l+ c5 j
-0.012964824120603
$ g p* ? P2 f! T- B6 q/ t: p, V -0.012361809045226
6 w& d' Z) Q, W# i( G -0.011758793969849
2 a/ K7 @3 ^: p) b& F% r -0.011155778894472% K7 K9 d4 B% R( i
-0.010552763819095/ e$ T( S* I, A2 H) |
-0.0099497487437195 q+ ^0 X8 g$ K# G( g v. z3 a
-0.009346733668342
& v) @% Y8 n/ G# Z6 K -0.008743718592965
% q3 m& E2 H# P -0.0081407035175885 k6 w; r5 P: u9 H
-0.007537688442211
5 C" X$ |4 r4 s( Q -0.006934673366834
* h8 E7 i; q2 Z: o% R5 Z0 ~7 J -0.006331658291457
) w: D% w0 e5 v& L( p6 G -0.005728643216080
7 X# V9 a# S4 B+ P( ?0 v -0.0051256281407048 d4 s9 _, |$ H7 Q$ S4 s
-0.004522613065327
% i! V; a0 V1 \9 n, U: s; F -0.003919597989950& u6 x( r+ |8 _5 N7 ]. h
-0.003316582914573
- A, k: }, e1 X( \# U) C -0.002713567839196' h- j x U! Z3 t9 Y. f
-0.002110552763819
* o4 d) V" t* \; W# z$ s; u+ o/ L -0.001507537688442! [; R- P0 g: f- ]
-0.000904522613065/ j! H) i" h2 E9 {3 Z7 C
-0.000301507537688
& v3 ~0 A6 r2 o& ]9 h 0.0003015075376880 D, Q. |: q2 I
0.000904522613065
/ X1 C$ s- n; X/ I9 k3 f; e* R 0.001507537688442$ _" q* Y0 t4 |: d
0.002110552763819
4 J" F1 ~! h1 K A# s( f 0.002713567839196/ ?$ }3 @2 }7 j" ?" N$ }/ h
0.003316582914573
' K/ t& ^4 t5 ]0 v: w) G 0.003919597989950& D7 ? ~% G- B) o3 [1 p
0.004522613065327
5 l" x0 G' p7 X( y7 `' C, f 0.005125628140704
3 H( b! r4 e+ b7 N0 J8 Z( A 0.0057286432160803 a6 d7 E0 L4 z @2 {
0.006331658291457& Y g, n0 \$ o/ M- R: E
0.0069346733668342 }/ B) Z- [) i2 j) g! A
0.007537688442211) H" u. H) X/ C4 ~ B' {
0.008140703517588
1 o: L! F1 y" l- F! a3 ` o, m 0.008743718592965
/ F1 W7 C9 {( F& | 0.009346733668342" C, [7 k2 _. T8 a; k
0.0099497487437196 r9 _& O5 r7 Q0 S4 ?
0.010552763819095
" p- e; G3 G! T/ `" J. J$ j8 b 0.011155778894472
. s. v( f$ {4 x( K) _$ o. P+ I 0.011758793969849
# b7 |( u; A2 a+ W; i- j* Z; ? 0.012361809045226
+ G p! O) z- e) A) p5 x 0.0129648241206031 q6 s0 l! W0 q
0.013567839195980
4 v& `" D' v, v/ z- c3 m0 V& N 0.014170854271357
6 ^6 [4 u; g4 Y5 q 0.014773869346734; o5 {) t* o: F; E# ?- p4 g
0.015376884422111
$ |% {$ ~& @3 ^, g e3 o 0.0159798994974875 }/ v* C, S; T- W/ j3 l7 C
0.016582914572864: y3 D P: o# ~1 b+ ^: K# G9 `
0.017185929648241
1 D% G( i( N; q8 {* R$ D( \; W 0.017788944723618
8 Q9 \. v- |8 X8 m2 t# x2 Q 0.018391959798995& L9 A% B1 w% E2 A
0.018994974874372
2 O$ k: i2 P/ [" O- R( o4 ~. v! r 0.019597989949749
/ [/ q4 W; `* v9 O2 A 0.0202010050251262 \0 m! x. S" l# z- v3 }1 Y
0.020804020100503# | @5 g) B- {7 E3 s3 J+ V/ k
0.0214070351758798 [% R6 z5 Z3 X' k! l
0.022010050251256
9 ?- M3 P' s5 j2 i' ?- Q# d 0.022613065326633
# q) f" g9 o8 |& v; \1 e 0.023216080402010
. N$ }7 Z, P9 U% A( l 0.023819095477387
; X6 T* l) G( h D/ v5 W, l4 b 0.024422110552764
" ~2 |0 S# H+ x5 g [- \ 0.025025125628141
/ E9 Z, N" Y8 p. Q+ E 0.025628140703518
6 W+ J* h8 I- `. D6 C 0.026231155778894
5 t7 L0 C5 t$ X) c 0.026834170854271; H/ m3 r3 V" m4 b
0.027437185929648% r @% ]: y- h/ y ^) ^' a
0.0280402010050256 \# A2 T1 ~: |( V" O7 r- B( M
0.028643216080402
* J9 ~1 D/ X3 p+ [ 0.0292462311557799 U' F7 }3 n. q* M
0.029849246231156* n4 A H0 h6 o% r; H+ _( B
0.030452261306533 k- B+ A3 P2 f2 a0 N `. }
0.031055276381910- t$ h; ^4 v' J7 v4 f
0.031658291457286
/ s8 X+ i" i; B, W' y I 0.032261306532663
* _7 L+ V# |7 r 0.032864321608040
$ I( x7 c; U; p5 J( `1 Z 0.033467336683417
6 k% y7 K7 C( o 0.034070351758794
% s7 P: y6 N9 O) n 0.034673366834171
0 A9 q7 @. l5 H: m 0.035276381909548+ N7 z7 I& d+ D5 r8 g: j
0.035879396984925 W3 P2 y G% ?4 \4 |
0.036482412060302+ ?' E, b$ U. r, z
0.0370854271356789 P9 k7 [) i3 a0 P
0.037688442211055
- A+ a% q+ [ k: c8 ] 0.038291457286432
8 D/ O& z! }" f 0.038894472361809
" a2 ]$ ~% p0 w. B& { 0.039497487437186
3 R0 {! b" c' w o/ e: g! m; z 0.040100502512563/ K2 F6 n5 N7 X0 @! N
0.040703517587940
' f9 N: X3 i2 j5 z 0.041306532663317
8 O! z+ P1 h1 E, D 0.041909547738693
1 V0 y5 @3 U s' H& W 0.042512562814070
# |$ @* l' u; r# C* l/ O 0.043115577889447- n+ B6 f! D W: Q5 h1 L* j; j% V, ]+ [
0.043718592964824* }* W& @1 O j, \" E' B
0.044321608040201
: ^& S' I) F( [5 M( R: A 0.044924623115578/ X7 ?: ?% p8 G @
0.045527638190955* b# j# r+ |. O. V0 c$ _& G$ p
0.046130653266332
( m1 I" y0 ~- S& y8 S 0.046733668341709
- L( [" l8 W& M% b 0.047336683417085
. v4 J5 n$ Y: f; M. L 0.047939698492462
. L9 y$ S0 W; e3 G; K% y9 r- ]0 g 0.0485427135678398 k( T" L# l( T" ~' F5 U
0.0491457286432163 `" N( R' \" I; {: @/ A
0.049748743718593) h+ n8 d+ O9 @) ~
0.050351758793970* ]5 k4 y2 b4 G# B
0.050954773869347 U0 k$ y) b* p# m
0.051557788944724
/ N+ {5 Y, {4 s/ E6 ? 0.052160804020101/ w& e6 S* j6 z0 D+ ^
0.052763819095477
. A) {6 p5 b$ ~ 0.053366834170854
8 i% H1 A& N" Q; V; |4 T 0.053969849246231
( J: l3 q0 u/ R# z1 A! c 0.054572864321608. }6 j# O# F& E2 y7 n; e. j
0.055175879396985
7 o; O# a" S* |& P/ E$ q! t/ p 0.055778894472362# o' K: u, s B1 v7 ?
0.056381909547739/ B7 P7 x) B5 C0 b
0.0569849246231160 p) t- k+ C1 g3 {* F' b/ F
0.0575879396984928 j3 Z7 S* ]" g1 U& U3 O: T
0.0581909547738697 R, Q2 H8 h s* x' \9 h
0.0587939698492465 J! B8 f, K+ I! R h/ M1 U8 ^. u
0.059396984924623
% @2 ]6 M/ Q! L' K3 n 0.060000000000000
! v- x0 d' M7 ?6 [# L9 ?" C* X- g$ n( d; }2 O
/ r( {% I, B' a0 i5 Fans =2 p( s8 S& E6 I4 L! I
F- _8 o/ n0 x- I9 J4 @' ^, F4 _ -1.033689540653716# N% M3 I7 R: s
-1.013619827890691
# N) ?: _5 h$ F9 S -0.994621366531083
+ ?3 {& k- d- v C7 e -0.976510534039504
( }! ]2 K3 Y- x -0.959151639002957
% m& y& P% S" T2 K1 d" j -0.942440908631668" Y0 [, z/ H& ]) O1 T
-0.926296779035772
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0.926296779035770, C: {8 [7 [' n a; ~+ C
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0.9765105340395024 ?6 K+ ^- ^: R! H- r3 p/ O
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$ W' x. U. g) ^' `2 J 1.013619827890692+ O3 e9 I. T" M% l* n
1.033689540653723" L) \$ K7 K6 j( X
x1 W5 _4 v$ Y5 J, x5 P+ X7 Y+ i
$ o5 h. _; ?* L, V( |" O8 f D6 J5 T6 d3 N( I0 p0 V2 I$ S
作者: shouce 时间: 2015-11-18 22:22
pacelife 发表于 2015-10-12 18:42
+ V* {* e& N, t. M3 F* r q楼主能否运用这些数据在生成三维图形
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" ^2 \) R+ ?, ` \0 P-2.129506122 249.824077 00 ~( P/ y1 R/ x& V* d$ A
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* Q! q$ V8 {5 ]0 r3 s" E0.236649334 249.9978355 0
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# m% G5 P. U" t. v0.552176899 249.9882131 0
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1.025444208 249.9593243 0
8 O3 N. U% ?/ z5 s8 ^8 |5 }1.183190233 249.9458317 0# j1 S+ ~/ R# U2 L1 ^
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1.971809995 249.8492486 0
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2.444864036 249.767835 0
( m9 ` F. p V- ^; o2.602524216 249.7367515 0
: v w- ?! Q! k. C; U2 F2.760170812 249.7036834 0: H4 \" Q, L: s; |/ v5 |' B
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3.233021227 249.5924912 0$ B1 X9 K- K5 @% O, ^6 h6 i9 z+ c
3.390605649 249.5514016 0
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! O2 W; h; f" r; D# w+ c4 U3.705721333 249.4631249 0
8 W8 D( K: p8 r# ~8 D# H3.863251097 249.4159162 0
3 ~8 W. a; R% A0 d5 r4.020761161 249.3666451 0' \& ]0 L( _& O8 h# H8 r, \7 C
4.178250801 249.3152993 0
* u1 p6 z( ~4 m& R- w6 W2 X7 o( N K4.335719306 249.2618659 0
+ Z+ ~, l$ w0 G! L+ n; z4.493165978 249.2063311 0
6 k' Z0 N: r; f# v% @4 H4.650590133 249.1486806 06 d/ f& X* a3 y& r. j+ C
4.807991099 249.0888994 06 t2 G7 |0 \% v0 u* N' M
4.965368224 249.0269718 0
% j7 O/ n* h$ T( g7 ]5 K+ u5.122720872 248.9628812 0# V8 l# u6 p, M; q- m' q
5.280048424 248.8966103 0
" l9 r+ [* L1 f3 Y* u5.437350282 248.828141 0. O$ _1 ^9 s% U5 m9 T& a
5.594625871 248.7574545 0
/ M" f0 B3 p4 I' U' _& f5.751874639 248.6845309 0
3 U9 y$ s* D+ p7 o; b2 v5.909096057 248.6093495 0
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6.223454876 248.4521256 0$ S# v9 _% q a, R) G
6.380591367 248.3700368 0
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6.694776495 248.1987818 0" v( d1 S7 O- ?) D
6.851824438 248.1095627 0
: m: d% D0 q& q' K# C; B; y7.008842241 248.0179119 0" z5 J3 D/ F7 O& f/ ^
7.16582967 247.9237998 00 [' r1 h+ y* d. L3 s# q
7.32278654 247.8271956 0
8 G S( J; f& |6 W* Z* j5 s& g7.479712721 247.7280668 0) f* j5 Q, K7 W2 q K9 P- g/ N
7.636608145 247.6263796 01 }( M2 q% U! e* ?& N7 C9 X
7.793472811 247.5220986 0
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8.107110216 247.3056047 0- V# W ]2 f ^$ w5 X; s
8.263883333 247.1933123 0
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8.577340022 246.9604227 0
/ ? _/ [! B( Y4 ^; _8.734024552 246.8397336 0
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9.047309269 246.5896193 0+ a$ G1 g' x1 `" C; x7 d) s
9.203911175 246.4600875 0& \1 K9 b, h4 T4 y/ `- o
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6 j2 l6 N1 M% C, e9.673568737 246.0528933 0/ i5 u- S1 [* @( ]! l/ g3 g- V
9.830076752 245.9107488 0; H, M$ f: K, r
9.986565496 245.7652821 0+ D, \5 T: y: w6 h: x& E
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7 w2 n* R# f9 ^* k6 D" W x10.92523646 244.818161 0
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/ A3 ~( w5 H/ c3 W11.55104095 244.1087796 0: h9 G1 c5 D- H/ u/ F
11.70754352 243.9205986 0$ c. }+ B& |. X% |- m4 R' a
11.86408148 243.7277924 01 {. v2 i F# z6 l& C8 j
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2 Y8 Z! R: e& @3 R n! |13.59207552 241.2422176 0
; ?/ {, i: v N7 p1 d13.75026839 240.9755931 05 m$ A* ?+ P1 ^, x- Y1 y# y
13.90879414 240.7004064 0
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3 c* v/ r. R8 g/ H14.54754137 239.500461 0. D+ E4 k% N2 ]& b, }* \
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/ A/ [. H, l6 } K8 j. j8 ~* x15.53387651 237.2748695 06 [' Y: C( v% S
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16.21413872 235.3358909 00 k7 g% \4 f' u# F
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% v+ `2 t" L& \6 S16.64807528 233.8066972 0: j' q$ _" x& v. r3 O5 w* Q2 \
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9 q( [9 N4 F* B! W+ b+ W+ I& [) `& h) B17.48757173 229.1142827 0
0 Z% d" Z& h9 h. a) j' g$ q! ?- K) L/ U" }( W3 ?
" f5 g( Z/ Y( n' R/ L1 o
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