Teburin Abubuwan Ciki
- 1. Gabatarwa
- 2. Yaƙin Pancreas na Jami'ar Zachary
- 3. Bayanin Tsarin Tumbin Doki
- 4. Layer na Tushe – Mathematica
- 5. Layer na Tsakiya
- 6. Layer na Sama – Nunin 3D na Tambarin
- 7. Haɗa Layers da Fitar da STL
- 8. Tsarin Bugu na 3D da La'akari da Kayan Abu
- 9. Bayanan Fasaha da Tsarin Lissafi
- 10. Sakamakon Gwaji da Rubuce-rubucen Gani
- 11. Tsarin Bincike: Nazarin Harka na Tambarin Yaƙin Pancreas
- 12. Aikace-aikace da Hanyoyi na Gaba
- 13. Bincike na Asali da Sharhin Masana
- 14. Manazarta
1. Gabatarwa
Wannan takarda ta bayyana wani aiki don kera bugu 3D na tumbin doki wanda ya haɗa da tambari. Hanyoyin sun haɗa da sarrafa hoton tambarin ta hanyar rubutun Mathematica don ƙirƙirar fayil ɗin STL, wanda sai mai bugu 3D yake amfani da shi. Ana ɗaukan mai karatu ya san tushen abubuwan bugu 3D. Aikin yana nuna hanyar aiki mai amfani don haɗa hotuna 2D cikin abubuwan da aka buga 3D.
2. Yaƙin Pancreas na Jami'ar Zachary
JDRF (a da Gidauniyar Bincike kan Ciwon Suga na Yara) babbar ƙungiyar agaji ce da ta sadaukar da kanta don hana, magance, da warkar da ciwon suga na nau'in 1 (T1D). T1D yana faruwa ne lokacin da tsarin garkuwar jiki ya lalata ƙwayoyin beta masu samar da insulin a cikin pancreas. Kimanin Amurkawa miliyan 1.25 ne ke da T1D. Iyalin marubucin suna tara kuɗi don JDRF ta hanyar tara kuɗi na "JDRF One Walk". Sunan ƙungiyar shine "Yaƙin Pancreas na Jami'ar Zachary", kuma John da Xavier Golden ne suka tsara tambarin (duba Hoto 1). Tumbin dokin da aka ƙirƙira a cikin wannan aikin yana ɗauke da wannan tambarin.
3. Bayanin Tsarin Tumbin Doki
Ana gina tumbin dokin ta amfani da Mathematica ta hanyar haɗa sassa uku: layer na tushe mai haruffa "ZUFP", layer na tsakiya mai sauƙi, da layer na sama wanda shine nunin 3D na tambarin Yaƙin Pancreas. Kowane layer yana da iyaka da da'irar $x^2 + (y+10)^2 = 4900$ kuma ya haɗa da rami don maɗauri wanda aka ayyana ta $x^2 + (y+64)^2 \leq 49$. Axis y mai inganci yana nuna ƙasa saboda yadda Mathematica ke adana bayanan hoto. Bayan haɗa layers ta amfani da umarnin Show na Mathematica, ana fitar da sakamakon azaman fayil ɗin STL don bugu 3D.
4. Layer na Tushe – Mathematica
An ayyana layer na tushe don $0 \leq z \leq 6$. Ƙirƙirar ta fara ne da loda fayil ɗin JPEG na haruffan "ZUFP" da aka juye cikin Mathematica ta amfani da lambar da Melissa Sherman-Bennett da Sylvanna Krawczyk suka yi. Lambar tana shigo da hoton, ta canza shi zuwa launin toka, kuma ta sarrafa matrix ɗin bayanan. Umurnai masu mahimmanci sune:
ClearAll["Global‘*"]
DataBase = Import["C:\\data\\3d\\ZUFP\\ZUFP-letters-flip.jpg"];
SizeBase = Import["C:\\data\\3d\\ZUFP\\ZUFP-letters-flip.jpg", "ImageSize"];
GrayBase = ColorConvert[Image[DataBase, "Real"], "Grayscale"];Ana amfani da ƙimar launin toka (0 zuwa 1) don tantance tsayin layer na tushe a kowane pixel.
5. Layer na Tsakiya
Layer na tsakiya shine mai sarrafa silinda mai sauƙi wanda ke ba da tallafi na tsari tsakanin layer na tushe da na sama. An ayyana girmansa ta hanyar da'irar iyaka da ƙuntatawa na rami iri ɗaya. Tsayin wannan layer yawanci ana saita shi zuwa 'yan millimeters don ƙirƙirar rabuwa da ake iya gani tsakanin rubutun tushe da tambarin sama.
6. Layer na Sama – Nunin 3D na Tambarin
Ana ƙirƙirar layer na sama ta hanyar sarrafa hoton tambarin Yaƙin Pancreas ta hanyar rubutun Mathematica mai kama da shi. Ana tsara ƙimar launin toka na tambarin zuwa tsayi, suna ƙirƙirar taimako 3D. Ƙuntatawa na da'irar iyaka da rami iri ɗaya suna aiki. An daidaita tambarin ta yadda zai bayyana daidai lokacin da aka kalli tumbin dokin daga gaba.
7. Haɗa Layers da Fitar da STL
Ana haɗa layers uku ta amfani da umarnin Show na Mathematica. Ana fitar da samfurin 3D da aka haɗa azaman fayil ɗin STL ta amfani da umarnin Export. Fayil ɗin STL yawanci yana da girma (sama da 20 MB) kuma ya kamata a adana shi a gida don guje wa jinkirin hanyar sadarwa. Ana sikelin samfurin a cikin software ɗin bugu zuwa diamita na 50 mm don tumbin doki, ko ƙarami don 'yan kunne ko kayan ado.
8. Tsarin Bugu na 3D da La'akari da Kayan Abu
Ana buga tumbin dokin ta amfani da filament masu launi daban-daban guda uku. Marubucin yana amfani da bugu mai filament guda ɗaya (Makerbot Replicator 2) kuma yana dakatar da bugu a lokutan da suka dace don canza filament. Ana ba da shawarar filament na Hatchbox daga Amazon. Tsarin bugu yana buƙatar lokaci mai kyau don tabbatar da mannewar layer da canza launi daidai.
9. Bayanan Fasaha da Tsarin Lissafi
Da'irar iyaka ita ce $x^2 + (y+10)^2 = 4900$, wanda ke ba da radius na raka'a 70. Ramin maɗauri an ayyana shi ta $x^2 + (y+64)^2 \leq 49$, tare da radius na raka'a 7. Ana tsara ƙimar launin toka daga hotunan JPEG zuwa tsayi a cikin axis z. Don layer na tushe, tsayin $h(x,y)$ ana bayar da shi ta $h(x,y) = 6 \times (1 - g(x,y))$, inda $g(x,y)$ shine ƙimar launin toka (0 don baƙi, 1 don fari). Wannan yana ƙirƙirar haruffa masu tasowa inda hoton yake duhu.
10. Sakamakon Gwaji da Rubuce-rubucen Gani
Hoto 1 a cikin takarda ta asali yana nuna halin Yaƙin Pancreas, hoton tambarin na asali, da tumbin dokin da aka buga 3D daga gaba da baya. Tumbin dokin ya sake samar da tambarin da kyau tare da cikakkun bayanai. Tsarin bugu mai launi da yawa yana haifar da abu mai ban sha'awa na gani tare da layers daban-daban. Marubucin ya ba da rahoton cewa sikelin samfurin zuwa diamita 50 mm yana aiki da kyau don tumbin doki, kuma ƙananan sikeli sun dace da 'yan kunne ko alamomin jaka.
11. Tsarin Bincike: Nazarin Harka na Tambarin Yaƙin Pancreas
Wannan nazarin harka yana nuna hanyar aiki don canza tambarin 2D zuwa tumbin doki da aka buga 3D. Tsarin ya haɗa da: (1) samun hoto da sarrafa shi, (2) canza launin toka da tsara tsayi, (3) ayyana layer da haɗawa, (4) fitar da STL, da (5) bugu 3D tare da damar kayan abu da yawa. Ana iya amfani da tsarin iri ɗaya ga kowane tambari ko hoto, yana mai da shi kayan aiki mai amfani don ayyukan bugu 3D na musamman.
12. Aikace-aikace da Hanyoyi na Gaba
Hanyoyin da aka bayyana a cikin wannan takarda za a iya faɗaɗa su zuwa wasu aikace-aikace, kamar ƙirƙirar kayan ado na musamman, abubuwan talla, ko samfuran ilimi. Ayyuka na gaba na iya bincika tsara launi ta atomatik, haɗawa da bugu masu fitar da biyu, da inganta girman fayil ɗin STL. Amfani da Mathematica don bugu 3D yana buɗe damar yin amfani da siffofi na lissafi masu rikitarwa da ƙira da bayanai suka jagoranta.
13. Bincike na Asali da Sharhin Masana
Mahimman Bayani: Wannan takarda tana gabatar da hanyar aiki mai amfani, mai sakewa don canza tambari 2D zuwa tumbin doki da aka buga 3D ta amfani da Mathematica, tana haɗa sarrafa hoto da masana'antar ƙara. Sabon abu shine amfani da tsara tsayi na launin toka don ƙirƙirar tsarin taimako, wanda shine dabara mai sauƙi amma ingantacciya don keɓance bugu 3D.
Tsarin Hankali: Takardar tana bin tsari mai layi, mataki-mataki: daga motsawar matsala (tara kuɗi na JDRF) zuwa aiwatar da fasaha (lambar Mathematica, tsarin layer) zuwa aiwatarwa a aikace (bugu 3D, canza filament). Kowane sashe yana gina kan na baya a hankali, yana mai da shi mai sauƙin fahimta ga masu karatu da ke da ilimin bugu 3D na asali.
Ƙarfi da Rashi: Ƙarfin wannan aikin yana cikin bayyanarsa da sakewarsa. Sassa na lambar da ƙuntatawa na geometric an rubuta su da kyau, suna ba da damar wasu su maimaita tsarin. Duk da haka, takardar ba ta da kimanta ƙididdiga na ingancin bugu, kamar daidaiton girma ko ƙarewar saman. Hakanan ba ta kwatanta hanyar tushen Mathematica da wasu hanyoyin (misali, amfani da Blender ko OpenSCAD). Dogaro da bugu mai filament guda ɗaya tare da canza filament da hannu shine iyakancewa ga haɓaka.
Bayani Masu Amfani: Ga masu aiki, wannan hanyar aiki tana da amfani nan take don ƙirƙirar tumbin doki na musamman, maɓallan maɓalli, ko baji. Don inganta inganci, yi la'akari da amfani da bugu masu fitar da biyu ko masu canza filament ta atomatik. Ga masu bincike, ana iya faɗaɗa dabarar tsara tsayi na launin toka don haɗa bayanan launi ko ayyukan tsayi marasa layi. Takardar kuma tana nuna yuwuwar Mathematica azaman kayan aiki don bugu 3D, wanda ba a bincika sosai ba idan aka kwatanta da software na CAD. Ayyuka na gaba yakamata su mayar da hankali kan sarrafa tsarin bugu mai launi da yawa ta atomatik da kimanta kaddarorin injiniyan abubuwan da aka samu.
14. Manazarta
- Aboufadel, E. (2015). 3D Printing A Pendant with A Logo. arXiv:1507.03102v1 [math.HO].
- Sherman-Bennett, M., & Krawczyk, S. (2013). Primer on 3D Printing with Mathematica. REU Program, Grand Valley State University.
- JDRF. (n.d.). Type 1 Diabetes Research. An dawo daga https://www.jdrf.org/
- MakerBot Industries. (2013). MakerBot Replicator 2 User Manual.
- Hatchbox. (n.d.). PLA Filament Specifications. An dawo daga https://www.hatchbox3d.com/