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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
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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
. k) e( m3 b: P) f+ c0 pt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 B( Y8 n( h! q+ H- `
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。現在忘光了。
作者: shouce 時間: 2015-5-26 22:09
seekfor 發表于 2015-5-26 20:27
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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 ...
4 P4 f+ X5 |( l7 z9 H M1 p你那時做的齒形 是哪種齒形 是第幾代的型線2 P) p7 ?/ E! M0 N/ V
作者: shouce 時間: 2015-8-12 21:56
shouce 發表于 2015-5-26 20:04
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等下次有時間 我來解這個方程
7 o* L2 S( W! F+ {0 v* y% ^0 R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]);3 z2 b+ W0 e+ Y+ `( B
axis 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
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- K2 k& {0 n+ [% u4 C Oezplot('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]);/ K+ ^$ T6 }8 z! Y+ t: y1 G5 G
axis square }( ?+ J$ ~0 M' ]( X E4 j
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& J0 L( y! B6 P' i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);. R( W& f* B W1 ?# I# N& Y
Z = @(t) fzero(C(t),-1.361);& g+ I2 q; V$ b
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_single12 f% O# Z8 i7 J8 Q, E d
clear all;clc
; b' ]5 Z; a- fformat long
3 x7 {4 i4 h1 |/ y" @0 g6 Hglobal a
. {' [( G! u/ |$ T: k P, ea_span=linspace(-0.06,0.06,200);# P# _/ p9 d8 B8 `6 [7 u
n=length(a_span);; ~* J; I! ~! Z1 t
x0=1e-9;7 ?* N) F2 f3 ]9 e3 @! r* g$ c) S: c
options=optimset('Algorithm','trust-region-dogleg','TolFun',1e-12,'TolX',1e-12);
) |' z7 z4 `$ kfor i=1:n5 ^$ f) Y. `1 ?& \, v" c% v8 Z
a=a_span(i);9 J3 B" m, [; @, n2 c0 l
x(i)=fsolve(@nonl,x0,options);* E! ^+ y, G9 i2 U) R: o w
y(i)=nonl(x(i));
! L e6 ]. m+ C' u: o, q5 wend
- b4 n$ Q5 Z+ U) U( \a_span', x',y'& [4 T u6 {# W x$ {
function f=nonl(x)6 B2 k9 C' U9 r' ^+ P+ o0 r6 d
global a
8 b$ j# |7 Y ~/ B; H3 Sf=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));8 {3 ?' J- `. A; ^4 q
/ G8 {& P! |% ]運行結果 ans =) e8 R" m( e* e
-0.060000000000000
& ?1 v8 D3 a6 Z0 T( Q3 U( r -0.059396984924623+ h! y7 q" h! P' f" x2 L- x, v7 U Q
-0.058793969849246! G+ {8 N3 J2 M6 e6 S0 i
-0.058190954773869- z9 I: b: R2 F Z) Y
-0.057587939698492
% u7 C7 ]& d4 K e" V -0.056984924623116- f1 i9 j2 W) m" Z
-0.0563819095477396 P9 O+ b3 ^! V, X
-0.055778894472362
" N- h6 j8 J Z/ e3 S( V* A; m -0.055175879396985
. P# j3 O3 ]: F# \( c) N -0.0545728643216087 n) W) E$ z. F9 V9 l: [
-0.053969849246231
5 _% K- t& ?+ Q* q0 z( `* p -0.053366834170854
- D4 D) ~5 l0 @! C( s5 U. h -0.052763819095477
2 s# ]% p/ u# B -0.052160804020100
3 ?1 K! q! c; \# A -0.051557788944724
6 Z1 M' V8 E& W s -0.0509547738693473 _& _% K3 ]5 U# @1 k7 ?
-0.050351758793970
( M% }* ?. L) W8 V6 Y* c1 w4 b! u -0.049748743718593
- G& y# u, B8 h4 J -0.0491457286432166 w% t. T. }9 y3 e' j! |: [1 S
-0.048542713567839
2 K5 f* c" i1 d: C6 C3 u4 ] -0.047939698492462
5 P: X# c: c, @7 z! G" E -0.0473366834170858 _: n2 A, g0 o6 N5 e% V, x; B
-0.046733668341709
0 [. r) l& K" S) }% I# a -0.0461306532663320 `6 u. r( J c. @- i: M. a1 b! k
-0.045527638190955
5 s C, c6 c$ I -0.0449246231155784 H9 i# N) B# C+ M0 y; k
-0.044321608040201% x* y) j% M8 Q( [$ G6 \2 R: [
-0.043718592964824: P: ~* @/ d" b0 u
-0.043115577889447. Q3 C, Z/ H* p' G2 e
-0.042512562814070# L3 w1 ]% Y0 ~2 L6 _
-0.041909547738693
& N% z7 u, E- G1 O( K) X B, t -0.041306532663317/ T5 W& Z m3 j9 \1 ?3 G% |
-0.0407035175879405 D( G& d+ k) J% J( `
-0.040100502512563
3 U \' [, L7 E# h2 X1 H' s -0.0394974874371865 o; X% |5 A" N5 E
-0.038894472361809( [7 N+ `" o' b
-0.038291457286432* G2 K; v6 Z# u& O
-0.0376884422110553 d! o9 @4 N$ Z0 k& `# J
-0.037085427135678
, w( Q& ~! j6 M# ]% r5 T$ { D -0.036482412060302/ ]' Q* H, T# H5 l' t# s' y9 E8 t
-0.035879396984925
( d# o, f, c& s+ a, f1 R -0.0352763819095481 |6 Q% n3 g* W3 ?
-0.034673366834171
* S; f/ n( I" v. t! n -0.034070351758794
/ j9 [: y/ |1 C7 [6 z1 W! V1 J -0.033467336683417$ @" E, p/ m7 w. d
-0.032864321608040
0 H/ Y" X% ?4 |9 I2 f! F, O/ N -0.0322613065326638 Z8 [1 U) T; i& D9 p
-0.031658291457286
7 Z) U5 I0 B3 t0 V' ~ -0.031055276381910' I+ e( Z% M, a, K B9 x
-0.030452261306533
! J6 K6 ~; F3 ?# Y5 ` -0.029849246231156
+ X* g- m3 Q+ d# e9 M4 s -0.029246231155779
, {& a" a. Q" j ~ -0.028643216080402; t+ _1 m" ~6 O% \& L' i
-0.028040201005025
4 I+ |4 }- u5 c! u, U6 |4 _ -0.0274371859296489 F _. m' c2 |, z4 A9 ^/ L: e
-0.026834170854271
T& U& [5 R( h: E/ N7 G2 M -0.026231155778894% g+ Q3 q" m4 k% ^/ S0 u
-0.025628140703518; V* y' A# E# s) j; X1 d/ o
-0.025025125628141
- r" t* w5 z) J2 T -0.024422110552764
7 U; {! M1 `; r$ o2 q -0.023819095477387
! H7 g7 @- x+ l( B4 L9 R0 u6 [2 S -0.023216080402010$ u* u! J* L Y+ y9 w
-0.0226130653266337 _$ @% ]* S- O
-0.022010050251256
: X1 y" `7 U/ a7 b8 x1 u) O( |* z -0.021407035175879
* D* v3 c" b; i: K* B3 Y -0.0208040201005032 N0 p+ h( w2 `/ q# a* P
-0.020201005025126
5 ]3 u. m$ W: p0 A5 d -0.019597989949749
, _$ P# f# d& U -0.018994974874372
9 a6 T3 ^3 C s5 w; S9 v* y0 e4 V -0.018391959798995
; c3 ^+ s* j6 Y9 K! Z- e -0.017788944723618
7 f* j# }9 w* D" A) n: b, I -0.0171859296482415 i/ @* ] U+ o- L
-0.016582914572864
! b8 f9 O |- ^- [ -0.015979899497487
) M# s. U ?5 R* H7 e; o* d- k -0.015376884422111
7 V' c: p- d; t -0.014773869346734
. c1 X$ \: n+ ] -0.0141708542713572 b. Y/ s! G" i) Z0 f4 a( [0 v* P6 H6 M
-0.013567839195980
# b# p7 i7 u$ L% l8 A -0.012964824120603
" V+ z* a/ d: Z4 k& b9 B0 w -0.012361809045226
9 f0 N* ~" [* Z+ ? -0.0117587939698497 i6 M8 x, W+ z @, m3 A
-0.011155778894472) m: _1 D N E
-0.010552763819095
( n" c A6 ]! Z1 \ -0.009949748743719( h- v9 i" F/ r
-0.009346733668342
: e" c$ [1 X' _3 v3 A -0.008743718592965! s7 K V; D. {0 C# {' P2 g
-0.008140703517588
# E# B6 x5 b1 X5 m: Z -0.007537688442211
/ T8 i, M. C& g6 S4 E5 h, [ -0.006934673366834
3 ^. q; i2 C. D8 {2 ` -0.006331658291457
1 ?. ] h; [ G! r& i -0.005728643216080
1 w/ F) c' f: @ -0.005125628140704
5 b7 X3 ]% p2 h- q0 r -0.0045226130653273 @* s/ G) x e: }2 [# z* S" I
-0.003919597989950
: |( ~" v5 t2 S9 t -0.003316582914573
# V# A# U" d2 v0 S, _4 M4 q -0.002713567839196) q8 n# _8 M8 T. o3 U
-0.002110552763819
1 a- w- `5 }% o* v -0.001507537688442& @ ?5 t: ]( ^
-0.000904522613065, Y+ Q! u; F( G
-0.0003015075376881 D: k" l+ [8 r h1 e8 T
0.000301507537688# M- Q/ K% W3 I/ \2 p# Z
0.000904522613065
: p2 H( A/ G @, g 0.001507537688442
) A" c4 x: |, I; z 0.002110552763819
" [- d5 r( S1 H5 |+ X 0.002713567839196
' V% r e8 o- ` 0.0033165829145730 h0 H: y& u) B" P
0.003919597989950, T: f/ [( Q9 j" u
0.0045226130653276 x; q: t- T5 N' @2 u
0.0051256281407047 a0 i3 E5 c( T+ S2 R4 u% w1 Y: y
0.005728643216080& d9 n5 u6 _+ r/ L& Z$ w2 o
0.006331658291457
1 x- ?+ E4 h6 Z/ G6 W. y 0.006934673366834
( A+ z7 Q7 U" d7 C3 s 0.007537688442211: G) @5 r7 {- k0 t- Y3 U; U. y
0.0081407035175881 r0 e, y! y) n
0.008743718592965' }+ q, N3 }& C& N
0.009346733668342
8 O4 d) z2 D- c# M- a. b: z 0.009949748743719
9 b, @- u, [) J$ d 0.0105527638190955 G+ J4 X0 |7 S% r2 v) _
0.011155778894472
5 {8 M* `; d% A, o. r 0.011758793969849) {. f2 t* ]1 V. ?/ }
0.012361809045226
# Y7 p% V3 g2 i6 ^ 0.012964824120603
) L# i& n6 ?8 ^& U 0.013567839195980: g: A e; U: t, j
0.0141708542713571 D9 B; h2 T& h- e
0.014773869346734. N P) c* q7 B5 m
0.015376884422111. `# S. w! L$ Y2 A
0.015979899497487( z- g) ?. p$ R3 N
0.016582914572864
" M* n1 x0 g2 u9 v$ F$ o/ a 0.0171859296482414 _6 @5 A. E8 w; v3 `% {" z1 x
0.017788944723618
0 h. N s% O2 e- d3 |( X7 R 0.018391959798995
9 R4 v8 \8 z$ W2 @1 Q 0.018994974874372
; c0 Y2 z( y/ d' F* V5 L! r 0.019597989949749
2 v, E( @! r' K# g- ^ 0.020201005025126# }" i2 P: R+ Z$ e, X, R' E" z! T
0.020804020100503: a& X& H4 K, M y i; @
0.021407035175879
7 q k& H+ c2 B! N6 R2 C. E. c 0.022010050251256
! s* M( v! O8 R' O 0.022613065326633
* B8 `% F$ G2 ? 0.023216080402010( _" S- [ W2 [! k* a9 u
0.0238190954773874 T5 \1 r/ I# k! ?9 O9 R# l
0.024422110552764
* L2 @% U2 N7 i# O: k5 @. G2 M 0.025025125628141
6 h( |( u6 i4 @+ M 0.025628140703518
( @& m6 d! f1 \. P! f+ T 0.026231155778894
0 [* ^: M9 u( n: @4 q. ? 0.026834170854271
; I+ H! ^0 n& r6 E1 @0 J) Q5 X# Q1 e 0.027437185929648" ?* h# G7 j1 @8 ]
0.0280402010050250 k0 X: H9 i0 P5 O+ t
0.028643216080402* \" {+ P- M3 P; L, I0 W5 S6 z5 q
0.029246231155779( b0 n4 O+ T# o) A1 L0 `$ X( `
0.0298492462311562 c" G9 ^ S" ?/ x% F+ Z
0.0304522613065336 G: C- v( U2 T
0.031055276381910
0 {6 A2 E6 s- G6 Q 0.0316582914572862 B( |- ?" d3 i% i- ]# F
0.0322613065326632 R4 ^6 V* D& t
0.0328643216080404 }0 r. [5 [& U, l D# e
0.033467336683417
+ q6 Y* m* o5 z6 c) X8 [ 0.034070351758794
$ Y! B1 ~& U- l, @& H" d 0.034673366834171! X5 ]; y \; d8 d4 l& z& y9 S% G
0.0352763819095489 ^! C( ?4 [5 H6 Q5 T2 M: Z
0.035879396984925, ?* O \# c) p" I
0.036482412060302
9 o( ]3 D; a* o/ p# M" x 0.037085427135678" G* h" `4 T% ]3 B# s& Z, u, Z
0.037688442211055 d% C1 q/ e0 J) O1 y
0.038291457286432
0 D4 V' s9 J8 a3 f8 ~5 h" P2 O 0.038894472361809
+ ]* O' f2 ]/ m( q7 e* E 0.0394974874371867 ]; p, z) }3 r7 @
0.0401005025125633 q5 k% b, e d6 B2 ^
0.040703517587940
+ J) H8 o4 E# j% u% }+ n 0.041306532663317
8 A9 t2 |- d& w& q0 }! Q. }9 l 0.041909547738693$ N+ z. C# }* H7 ^1 P2 M; d
0.042512562814070% N! E& f# |0 @
0.043115577889447
/ o2 @! d3 Y1 S 0.0437185929648246 J. l& A/ T9 ] y3 @$ Q' n
0.0443216080402013 f2 c8 [# B/ {+ `! M
0.044924623115578
1 ^- `. p& S+ e& Q3 N. d$ e 0.045527638190955
& ]" \! B% _" z- M 0.046130653266332
8 V$ m2 B9 k& l8 f 0.046733668341709$ U+ K5 _. A1 I: i
0.047336683417085
2 j2 z, c( Z6 e& i7 g& r 0.047939698492462) V! [$ i( m7 D/ w1 [+ d
0.048542713567839
" j; t/ T( y- v6 { 0.0491457286432163 v; T7 i8 g9 Q7 T- v2 P. K6 Y
0.049748743718593
2 z7 P3 |( F+ w& T. L 0.0503517587939705 C, S0 \8 G2 i% P. r+ \
0.050954773869347 N9 P& A; l! I% f
0.0515577889447247 ^7 z6 T2 e+ K; Z2 Z
0.052160804020101
1 j) ]5 z* }* a 0.0527638190954777 Q R4 @* K: v* E8 \" N; g
0.053366834170854
/ n# ~1 o' f5 l' m2 Z7 o# u 0.0539698492462313 [* p" g0 ?3 y- {( ]
0.054572864321608# T8 H6 |$ [. \' G- S4 w# u: l
0.055175879396985! x' z t/ A; [- P7 a. U
0.055778894472362
6 H3 [' W- p9 U. \( q; ~# k 0.056381909547739 Z* V1 U7 ]' L0 M& E
0.056984924623116- `7 [" M, @) } E, L
0.057587939698492
2 c2 S8 W! q7 {/ v: \9 @% S+ U) S. C 0.058190954773869( v ~$ F4 L7 O
0.058793969849246
& f( k& `. I4 B! n1 ^- ^: T7 Z 0.059396984924623
% A& I8 x& Y8 k 0.060000000000000
* E U0 {* O! s* {3 [- r- h& m4 e5 |6 G. {5 v4 B
% z& D, z% Y, V& c' ]# i/ @) W! \; k5 Hans =4 l7 |! {! o7 M+ ]1 \+ w1 X5 l
/ Y7 h& r0 y/ r6 O0 h- K) {
-1.033689540653716
1 @2 M+ M0 [! s& T) B6 c+ x5 i -1.013619827890691. h$ x1 Q/ Q/ G
-0.994621366531083
9 x8 f$ q9 t6 `. b$ K0 x -0.976510534039504. s& a) j6 x z0 x: [4 p' r
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6 k5 v) ` c+ V9 G9 V 0.436006253471471% E1 Q3 |1 c% [8 Q
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; P, y* ~6 C2 T& y$ B" G* z; I 0.454760601275070' ]) v7 s% k: @: _+ N
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0.4929000140898360 {( [) p! @1 Y0 |5 G( V$ C
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0.522120649763840
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" \) H' b" |6 T L 0.690158586205831
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0.713114466033284
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1 C5 |8 D3 X* x" T& M 0.7608630174676032 A2 t! u$ m7 T: s- C
0.7732370280687440 v# L K [3 D* Y- m! _" T1 C, @
0.785808117918194
5 D0 C. H- l/ U {& l0 a5 l 0.798589541746277; `/ i# N5 M8 v+ R4 Q
0.811596057546417
* ]5 D. P+ b' V 0.824844183890336
6 t- S" C2 f7 T2 | 0.838352517460555
; A7 I2 L; |; v$ Y/ ` 0.852142129100673
( l+ E5 v# X! b& V6 T$ @# m( N 0.8662370636710581 F& _' s; b8 Z
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0.895457976752096* w2 Y0 v2 V1 w4 B
0.9106536943112828 T4 r0 P: m9 J5 x6 m1 F
0.926296779035770$ }. v* I2 M/ y1 ?
0.942440908631660' A$ Q2 _5 {, o8 h$ V
0.959151639002953
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0.994621366531092
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( Z/ V' I0 {! S; r6 g% y 1.0336895406537230 {. P9 p! F* A/ W2 o
- y1 Z* H8 B& u$ K9 `; ~4 R% j+ S% V) t* X2 c: Q
; d0 {( y* Z& H2 |: R1 ?
作者: shouce 時間: 2015-11-18 22:22
pacelife 發表于 2015-10-12 18:42
8 g4 U+ Z: w4 H7 n# n( f
樓主能否運用這些數據在生成三維圖形
' o0 ?8 n$ Y& Y( U2 ~0 l3 `-17.48757173 229.1142827 0
/ ^# D# i/ I7 M, T8 b: R-17.39586705 229.8949441 0
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" B5 V7 o4 p" S( N& B- @( g7 x8 v-8.263883333 247.1933123 00 P6 Z0 j9 B- \* ^; M) Q
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" |. S7 P5 ^$ `: @7 K( Y( k-7.636608145 247.6263796 01 |1 y7 Q* x% ^& C
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: y* r; P8 A. V-6.537698696 248.2855975 0
' s8 c3 d6 i' i& k: Q-6.380591367 248.3700368 0
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-2.602524216 249.7367515 0- u/ K& c, B5 M. a: i
-2.444864036 249.767835 0
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" l' I* T. o' @7 F6 z6 u' H/ ~0 I0.709936708 249.9805126 0
3 ~$ W* u: i- V. s, w0.867692756 249.9708837 0
8 P. K' _2 C4 ?, T$ d& p1 Z1.025444208 249.9593243 0$ k; l5 L% Q" q7 z/ R4 x/ V3 m9 ?
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1.340930002 249.9304029 06 q$ v1 a( [7 u6 n
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2 o8 V# T7 H; N) I5 M( K& T1.814103503 249.8724619 0
" }3 I/ ?6 n4 p6 ^2 R( v3 c1.971809995 249.8492486 0
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3.390605649 249.5514016 0: t) g1 P: R9 `3 v/ u
3.548172602 249.508283 0
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3.863251097 249.4159162 0
3 w) h0 P( Z' t. B: k4.020761161 249.3666451 0
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4.335719306 249.2618659 0
3 K" g3 {5 u/ U* {6 W9 B- a4.493165978 249.2063311 09 _# n8 g: _( P& m" S
4.650590133 249.1486806 0
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8 T! P \* H( @# O o) w- y4.965368224 249.0269718 06 \" }3 c3 V! u* y2 A8 ]* Y: A* `
5.122720872 248.9628812 0
" n; x# M1 w$ E+ z: u5.280048424 248.8966103 09 \) Q9 X! v* V& { V
5.437350282 248.828141 0
. h: n8 G2 K& ?5.594625871 248.7574545 0# C' l0 Q6 ^# s4 b9 u
5.751874639 248.6845309 0) u: K* V/ h* H7 H' \0 n+ x F6 Q
5.909096057 248.6093495 0% f, n: ~8 L& D7 x1 {3 b, `
6.066289626 248.5318886 0: N- r U# }3 Z* [5 d
6.223454876 248.4521256 09 A0 ?* z7 i4 h. w0 i
6.380591367 248.3700368 0- q4 e# W5 i5 X
6.537698696 248.2855975 0
[5 x9 u P" R# a( n8 I4 d( G6.694776495 248.1987818 0
6 ~) ~+ `. N' F% X) b- u6.851824438 248.1095627 0 D9 t' C. q' H. {8 E
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9 E8 X' R* w k7.16582967 247.9237998 0
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* @+ O0 @) W) Z% \$ _7.479712721 247.7280668 0; Y9 z, d- l, `7 U
7.636608145 247.6263796 0/ f2 t( R- }% W# F8 ]
7.793472811 247.5220986 0
$ x/ Y+ L, N2 M, M: h0 T% K7.950306785 247.4151866 05 K8 s! D3 W+ w( \# C: @: H) l
8.107110216 247.3056047 0
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8.42062646 247.0782666 03 V1 _$ A0 R. A" i' j4 a6 q
8.577340022 246.9604227 01 ] m# ?+ \ f! v; A6 s- L
8.734024552 246.8397336 0' R1 z+ q. Z+ o, L! X4 n
8.890680706 246.7161497 0& Q; S/ l1 R- q* a0 ~' b8 f
9.047309269 246.5896193 0$ C, Y6 f( o; v& |
9.203911175 246.4600875 0
9 y6 u9 l/ k* u. h9.360487512 246.3274969 01 E! d4 F( y, y( g6 Z/ F: T; h
9.517039547 246.1917868 0' B8 V9 x5 `: E. x$ Q. z" }
9.673568737 246.0528933 0
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10.14303713 245.6164179 0
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3 L; F2 i \4 m10.45593921 245.3081723 01 K# A; s* U) a+ n+ U* @
10.61237554 245.1486165 0
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11.55104095 244.1087796 0
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11.86408148 243.7277924 0
# H# |/ q" J7 ~% n& f- Y! A: u9 Z12.02066392 243.5301959 0
$ U) E7 [7 b1 \( E8 q12.17730112 243.3276304 07 O* T; T; P) m. j5 Y' z0 U/ D
12.33400471 243.1199023 0* ], w* b( X9 P3 n. U
12.49078787 242.9068011 0
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12.80465505 242.4635397 0
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13.11905015 241.9957329 0
; \4 }9 I8 r0 J7 }6 c7 _; {! R) P13.27650414 241.7518437 0
' W/ E1 I$ k* I% E. D% k) V3 t# J2 O: f13.43416766 241.5008112 0
- O9 n& s( t( E/ m/ U* d13.59207552 241.2422176 0
7 c2 N I% s1 Y/ l, u) D. Y13.75026839 240.9755931 0
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14.06770943 240.4160523 03 T/ b, S+ x9 z; y
14.22708188 240.1218359 0
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14.54754137 239.500461 0% [! R1 u, j* |" E( n/ `
14.70884907 239.1712469 02 S' X7 V# X8 G# A2 Z6 s
14.87106763 238.827974 0
2 ]6 ?- S; g" |+ w W' {, j15.03438904 238.4690147 0/ N) P6 }* i3 v4 U: r9 r
15.19906081 238.0923492 0/ O0 H: L2 p @. e
15.36540928 237.6954146 0$ G2 M8 d/ Y! X9 g
15.53387651 237.2748695 00 N* w. E) t5 T5 i/ D
15.70508222 236.8262052 0
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16.21413872 235.3358909 0
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16.64807528 233.8066972 0
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17.00517067 232.2506108 0
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