Magnetic dabaran Maxwell

Masanin kimiyyar lissafi dan kasar Ingila James Clark Maxwell, wanda ya rayu daga 1831-79, ya fi saninsa da tsara tsarin daidaita tsarin lantarki-da yin amfani da shi don hasashen samuwar igiyoyin lantarki. Duk da haka, wannan ba duka ba ne ga manyan nasarorin da ya samu. Maxwell ya kuma shiga cikin thermodynamics, incl. ya ba da ma’anar sanannen “aljani” da ke jagorantar motsin ƙwayoyin iskar gas, kuma ya samo wata dabara da ke kwatanta yadda ake rarraba saurinsu. Ya kuma yi nazarin nau'in launi kuma ya ƙirƙira na'ura mai sauƙi kuma mai ban sha'awa don nuna ɗaya daga cikin mafi mahimmancin dokokin yanayi - ka'idar kiyaye makamashi. Mu yi ƙoƙari mu san wannan na'urar da kyau.

Na'urar da aka ambata ana kiranta motar Maxwell ko pendulum. Za mu yi magana da nau'i biyu na shi. Maxwell zai fara ƙirƙira - bari mu kira shi classic, wanda babu maganadiso. Daga baya za mu tattauna da modified version, wanda ya fi ban mamaki. Ba wai kawai za mu iya amfani da zaɓuɓɓukan demo biyu ba, watau. gwaje-gwaje masu inganci, amma kuma don sanin tasirin su. Wannan girman ma'auni ne mai mahimmanci ga kowane inji da injin aiki.

Bari mu fara da sigar musamman ta dabaran Maxwell.

Lynx. daya. Sigar gargajiya ta dabaran Maxwell: 1 - sandar kwance, 2 - zare mai ƙarfi, 3 - axle, 4 - dabaran tare da babban lokacin inertia.

An nuna sigar gargajiya ta dabaran Maxwell a cikin siffa. fig. 1. Don yin shi, muna haɗa sanda mai ƙarfi a kwance - yana iya zama buroshin sanda da aka ɗaure a baya na kujera. Sa'an nan kuma kuna buƙatar shirya dabaran da ta dace kuma ku sanya shi marar motsi a kan wani bakin ciki na bakin ciki. Da kyau, diamita na da'irar ya kamata ya zama kusan 10-15 cm, kuma nauyin ya zama kusan 0,5 kg. Yana da mahimmanci cewa kusan dukkanin nauyin motar ya fadi a kan kewaye. A wasu kalmomi, dabaran yakamata ya kasance yana da cibiyar haske da baki mai nauyi. Don wannan dalili, zaku iya amfani da ƙaramin dabaran magana daga keken keke ko babban murfi na gwangwani daga gwangwani kuma ku ɗora su kewaye da kewaye tare da adadin da ya dace na juyawa na waya. Ana sanya dabaran ba motsi a kan siriri mai tsayin rabin tsayinsa. Axis yanki ne na bututun aluminum ko sanda tare da diamita na 8-10 mm. Hanya mafi sauƙi ita ce haƙa rami a cikin dabaran mai diamita na 0,1-0,2 mm ƙasa da diamita na axle, ko amfani da rami da ke akwai don sanya ƙafar a kan gatari. Don ingantacciyar hanyar haɗi tare da dabaran, ana iya shafan axle tare da manne a wurin tuntuɓar waɗannan abubuwan kafin dannawa.

A ɓangarorin biyu na da'irar, muna ɗaure sassa na zaren bakin ciki da ƙarfi mai tsayi 50-80 cm tsayi zuwa axis. tare da diamita, sanya zare ta cikin waɗannan ramukan da ɗaure shi. Muna ɗaure ragowar ƙarshen zaren zuwa sanda kuma don haka rataye da'irar. Yana da mahimmanci cewa axis na da'irar ya kasance a kwance a tsaye, kuma zaren suna tsaye kuma a ko'ina daga jirginsa. Don cikakkun bayanai, ya kamata a ƙara da cewa zaku iya siyan ƙaƙƙarfan dabarar Maxwell daga kamfanonin da ke siyar da kayan koyarwa ko kayan wasan yara na ilimi. A da, ana amfani da shi a kusan kowane dakin binciken kimiyyar lissafi na makaranta. 

Gwaje-gwaje na farko

Bari mu fara da halin da ake ciki lokacin da dabaran ya rataye a kan axis a kwance a matsayi mafi ƙasƙanci, watau. duka zaren duka ba su da rauni. Muna kama axle na dabaran tare da yatsunmu a ƙarshen duka kuma muna juya shi a hankali. Don haka, muna iska da zaren akan axis. Ya kamata ku kula da gaskiyar cewa jujjuyawar zaren na gaba suna da nisa - ɗaya kusa da ɗayan. Dole ne a ko da yaushe ya kasance a kwance. Lokacin da dabaran ta kusanci sandar, dakatar da iska kuma bari axle ya motsa cikin yardar kaina. Ƙarƙashin rinjayar nauyi, dabaran fara motsawa zuwa ƙasa kuma zaren suna kwance daga axle. Dabarar tana jujjuyawa a hankali da farko, sannan sauri da sauri. Lokacin da zaren ya cika cikakke, dabaran ta kai mafi ƙasƙanci, sannan wani abu mai ban mamaki ya faru. Juyawan dabaran na ci gaba da tafiya guda, kuma dabaran ta fara motsawa zuwa sama, kuma zaren sun raunata a kusa da kusurwoyinsa. Gudun dabaran a hankali yana raguwa kuma a ƙarshe ya zama daidai da sifili. Sai dabaran ya bayyana yana daidai da tsayin da yake kafin a fito dashi. Ana maimaita motsin sama da ƙasa sau da yawa. Duk da haka, bayan ƴan ko dozin irin waɗannan motsi, mun lura cewa tsayin da ƙafar ke tashi ya zama karami. A ƙarshe dabaran za ta tsaya a mafi ƙanƙanta matsayi. Kafin wannan, sau da yawa yana yiwuwa a lura da oscillations na axis na dabaran a cikin wata hanya madaidaiciya zuwa zaren, kamar yadda yake a cikin yanayin pendulum na jiki. Saboda haka, motsin Maxwell wani lokaci ana kiransa pendulum.

Lynx. daya. Babban sigogi na dabaran Maxwell: - nauyi, - radius dabaran, - radius axle, - nauyin dabaran tare da axle, - saurin madaidaiciya, ₀ - farkon tsawo.

Yanzu bari mu bayyana dalilin da yasa motar Maxwell ke yin hakan. Iskar zaren a kan gatari, ɗaga dabaran a tsayi ₀ kuma ku yi aiki da shi (fig. 2). A sakamakon haka, dabaran da ke cikin matsayi mafi girma yana da ƙarfin ƙarfin nauyi _pwanda aka bayyana ta hanyar dabara [1]:

ina gudun fadowa kyauta.

Yayin da zaren ya buɗe, tsayin yana raguwa, kuma tare da shi ƙarfin ƙarfin nauyi. Koyaya, dabaran yana ɗaukar sauri kuma ta haka yana samun kuzarin motsa jiki. _kwanda aka lissafta ta hanyar dabara [2]:

a ina ne lokacin inertia na dabaran, kuma shine saurin sa na kusurwa (= /). A cikin mafi ƙasƙanci matsayi na dabaran (₀ = 0) yuwuwar makamashi kuma daidai yake da sifili. Wannan makamashi, duk da haka, bai mutu ba, amma ya zama makamashin motsa jiki, wanda za'a iya rubuta shi bisa ga dabara [3]:

Yayin da dabaran ke motsawa sama, saurinsa yana raguwa, amma tsayin yana ƙaruwa, sannan makamashin motsa jiki ya zama ƙarfin kuzari. Wadannan canje-canje na iya ɗaukar kowane lokaci idan ba don juriya na motsi ba - juriya na iska, juriya da ke hade da iska na zaren, wanda ke buƙatar wasu aiki kuma ya sa motar ta rage gudu zuwa cikakkiyar tsayawa. Ƙarfin wutar lantarki ba ya dannawa, saboda aikin da aka yi wajen shawo kan juriya ga motsi yana haifar da karuwa a cikin makamashi na ciki na tsarin da kuma haɓakar yanayin zafi, wanda za'a iya gano shi tare da ma'aunin zafi da sanyio mai mahimmanci. Ana iya canza aikin injiniya zuwa makamashi na ciki ba tare da iyakancewa ba. Abin baƙin ciki shine, tsarin jujjuya yana ƙuntata ta hanyar ka'ida ta biyu na thermodynamics, don haka yuwuwar da kuzarin motsa jiki na dabaran ƙarshe yana raguwa. Ana iya ganin cewa motar Maxwell misali ne mai kyau don nuna canjin makamashi da kuma bayyana ka'idar halayensa.

inganci, yadda za a lissafta shi?

An ayyana ingancin kowane na'ura, na'ura, tsari ko tsari azaman rabon kuzarin da aka karɓa cikin tsari mai amfani. _u don isar da makamashi _d. Yawanci ana bayyana wannan ƙimar azaman kashi, don haka ana bayyana ingancin ta hanyar dabara [4]:

                                                        .

Ingancin abubuwa ko tsari koyaushe yana ƙasa da 100%, kodayake yana iya kuma yakamata ya kasance kusa da wannan ƙimar. Bari mu kwatanta wannan ma'anar da misali mai sauƙi.

Ƙarfin makamashi mai amfani na injin lantarki shine makamashin motsi na motsi. Domin irin wannan injin ya yi aiki, dole ne ya kasance da wutar lantarki, misali, daga baturi. Kamar yadda ka sani, wani ɓangare na makamashin shigar da wutar lantarki yana haifar da dumama iska, ko kuma ana buƙata don shawo kan ƙarfin juzu'i a cikin bearings. Saboda haka, makamashin motsa jiki mai amfani bai kai na shigar da wutar lantarki ba. Maimakon makamashi, ana iya musanya dabi'u na [4] a cikin dabara.

Kamar yadda muka kafa a baya, ƙafafun Maxwell yana da yuwuwar kuzarin nauyi kafin ya fara motsawa. _p. Bayan kammala zagaye ɗaya na motsi sama da ƙasa, ƙafar kuma tana da ƙarfin ƙarfin nauyi, amma a ƙananan tsayi. ₁don haka akwai karancin kuzari. Bari mu nuna wannan makamashi kamar _P1. Bisa ga dabara [4], ingancin dabararmu a matsayin mai canza makamashi za a iya bayyana shi ta hanyar dabara [5]:

Formula [1] yana nuna cewa yuwuwar kuzarin ya yi daidai da tsayi kai tsaye. Lokacin canza dabara [1] cikin dabara [5] da la'akari da madaidaitan alamomin tsayi da ₁, sai mu samu [6]:

Formula [6] yana sauƙaƙa ƙayyadaddun ingancin da'irar Maxwell - ya isa a auna madaidaicin tsayi da ƙididdige adadin su. Bayan zagaye ɗaya na motsi, tsayin daka na iya kasancewa kusa da juna sosai. Wannan na iya faruwa tare da dabaran da aka ƙera a hankali tare da babban lokacin inertia wanda aka ɗaga zuwa tsayi mai tsayi. Don haka dole ne ku ɗauki ma'auni tare da daidaito mai girma, wanda zai yi wahala a gida tare da mai mulki. Gaskiya ne, zaku iya maimaita ma'auni kuma ku lissafta matsakaici, amma zaku sami sakamakon da sauri bayan samun dabarar da ke la'akari da haɓaka bayan ƙarin motsi. Lokacin da muka maimaita hanyar da ta gabata don hawan keke, bayan haka dabaran za ta kai matsakaicin tsayinta _n, to, tsarin ingantaccen aiki zai kasance [7]:

tsawo _n bayan 'yan kadan ko dozin ko fiye da zagayowar motsi, ya sha bamban da haka ₀cewa zai kasance da sauƙin gani da aunawa. Ingantacciyar dabarar Maxwell, dangane da cikakkun bayanai na samarwa - girman, nauyi, nau'in da kauri na zaren, da sauransu - yawanci shine 50-96%. Ana samun ƙananan dabi'u don ƙafafu tare da ƙananan taro da radiyo da aka dakatar a kan zaren stiffer. Babu shakka, bayan isassun adadin zagayawa, dabaran tana tsayawa a mafi ƙanƙanta matsayi, watau. _n = 0. Mai karatu mai hankali, duk da haka, zai ce to, ingancin da aka ƙididdige ta hanyar dabara [7] daidai yake da 0. Matsalar ita ce a cikin ƙaddamar da dabara [7], da hankali mun ɗauki ƙarin zato mai sauƙi. A cewarsa, a kowace zagayowar motsi, dabarar tana rasa kaso iri daya na makamashin da take amfani da shi a halin yanzu kuma ingancinsa yana dawwama. A cikin yaren lissafi, mun ɗauka cewa tsayin da ya biyo baya yana haifar da ci gaba na geometric tare da ƙididdiga. A gaskiya ma, wannan bai kamata ya kasance ba har sai dabaran ta tsaya a ƙananan tsayi. Wannan yanayin misali ne na wani tsari na gaba ɗaya, bisa ga abin da duk hanyoyin da aka tsara, dokoki da ka'idodin jiki suna da iyakacin aiki, dangane da zato da sauƙaƙan da aka ɗauka a cikin tsarin su.

Sigar maganadisu

Lynx. daya. Maxwell's Magnetic dabaran: 1 - dabaran tare da babban lokacin rashin aiki, 2 - axis tare da maganadiso, 3 - jagorar karfe, 4 - mai haɗawa, 5 - sanda.

Yanzu za mu magance da Magnetic version na Maxwell dabaran - gini cikakkun bayanai da aka gabatar Shinkafa 3 da 4. Don haɗa shi, kuna buƙatar maganadisu neodymium na silinda guda biyu tare da diamita na 6-10 mm kuma tsayin 15-20 mm. Za mu yi dabaran axle daga bututun aluminum tare da diamita na ciki daidai da diamita na maganadiso. Ya kamata bangon bututu ya zama bakin ciki sosai

1 mm. Muna shigar da maganadisu a cikin bututu, sanya su a nesa na 1-2 mm daga iyakarsa, kuma mu manne su da manne epoxy, kamar Poxipol. Matsakaicin sandunan maganadisu ba kome. Muna rufe ƙarshen bututu tare da ƙananan fayafai na aluminum, wanda zai sa magnets ba a iya gani ba, kuma axis zai yi kama da sanda mai ƙarfi. Sharuɗɗan da za a cika ta hanyar dabaran da yadda za a shigar da shi iri ɗaya ne kamar da.

Don wannan sigar dabaran, kuma dole ne a yi jagororin ƙarfe daga sassa biyu da aka shigar a layi daya. Misali na tsawon jagororin da suka dace a cikin amfani mai amfani shine 50-70 cm. Abin da ake kira rufaffiyar bayanan martaba (rashin ciki) na sashin murabba'i, gefen wanda ke da tsayin 10-15 mm. Dole ne nisa tsakanin jagororin ya zama daidai da nisa na maganadisu da aka sanya akan axis. Ya kamata a shigar da ƙarshen jagororin a gefe ɗaya a cikin da'irar da'ira. Don ingantacciyar riƙon axis, ana iya danna guntun sandar ƙarfe a cikin jagororin da ke gaban fayil ɗin. Dole ne a haɗa ragowar ƙarshen raƙuman biyu zuwa mai haɗin sanda ta kowace hanya, misali, tare da kusoshi da kwayoyi. Godiya ga wannan, mun sami madaidaicin madaidaicin wanda za'a iya riƙe a hannunka ko haɗe zuwa tripod. Fitowar ɗayan kwafin da aka kera na nunin motsin maganadisu na Maxwell HOTO. daya.

Don kunna motsin maganadisu na Maxwell, sanya ƙarshen axle ɗinsa zuwa saman saman dogo kusa da mahaɗin. Rike jagororin ta hannun hannu, karkatar da su diagonal zuwa ƙullun zagaye. Sai dabaran ta fara birgima tare da jagororin, kamar a cikin jirgin sama mai karkata. Lokacin da aka kai ƙarshen jagororin, dabaran ba ta faɗi ba, amma tana birgima a kansu kuma

Lynx. daya. Ana nuna cikakkun bayanai na ƙirar magnetic wheel na Maxwell a sashin axial:

1 - dabaran tare da babban lokacin inertia, 2 - aluminum tube axle, 3 - cylindrical neodymium magnet, 4 - aluminum disk.

yana yin juyin halitta mai ban mamaki - yana mirgina saman saman jagororin. Ana maimaita sake zagayowar motsin da aka kwatanta sau da yawa, kamar sigar na gargajiya ta dabaran Maxwell. Za mu iya saita dogo a tsaye kuma dabaran za ta kasance daidai daidai. Tsayar da dabaran a kan saman jagorar yana yiwuwa saboda jawo hankalin axle tare da maɗaurin neodymium da ke ɓoye a ciki.

Idan, a cikin babban kusurwar sha'awar jagororin, dabaran tana zamewa tare da su, to, ƙarshen axis ya kamata a nannade shi da takarda mai laushi mai laushi kuma a liƙa tare da Butapren manne. Ta wannan hanyar, za mu ƙara juzu'in da ake buƙata don tabbatar da mirgina ba tare da zamewa ba. Lokacin da sigar maganadisu na dabaran Maxwell ta motsa, irin wannan canje-canje a cikin makamashin injina na faruwa, kamar yadda yake a cikin sigar gargajiya. Koyaya, asarar makamashi na iya ɗan ƙara girma saboda jujjuyawar jagororin. Don wannan sigar dabaran, za mu iya kuma tantance ingancin aiki kamar yadda aka bayyana a baya don sigar gargajiya. Zai zama mai ban sha'awa don kwatanta ƙimar da aka samu. Yana da sauƙi a yi la'akari da cewa jagororin ba dole ba ne su kasance madaidaiciya (za su iya zama, alal misali, wavy) sa'an nan kuma motsi na ƙafafun zai zama mafi ban sha'awa.

da kuma ajiyar makamashi

Gwaje-gwajen da aka yi tare da motar Maxwell sun ba mu damar zana sakamako da yawa. Mafi mahimmancin waɗannan shi ne cewa canjin makamashi yana da yawa a cikin yanayi. Kullum akwai abin da ake kira asarar makamashi, wanda shine ainihin sauye-sauye zuwa nau'ikan makamashi waɗanda ba su da amfani a gare mu a cikin wani yanayi. A saboda wannan dalili, ingancin injuna, na'urori da matakai koyaushe yana ƙasa da 100%. Shi ya sa ba zai yiwu a gina na'urar da, da zarar an saita ta, za ta ci gaba da tafiya har abada ba tare da samar da makamashi na waje da ake bukata don rufe asarar da aka yi ba. Abin takaici, a cikin karni na XNUMX, ba kowa ba ne ya san wannan. Abin da ya sa, daga lokaci zuwa lokaci, Ofishin Patent na Jamhuriyar Poland yana karɓar daftarin ƙirƙira na nau'in "Na'urar Universal don injin tuki", ta amfani da makamashin "marasa ƙarewa" na maganadiso (watakila ya faru a wasu ƙasashe ma). Tabbas, an ƙi irin waɗannan rahotanni. Ma'anar ita ce takaice: na'urar ba za ta yi aiki ba kuma ba ta dace da amfani da masana'antu ba (don haka bai dace da yanayin da ake bukata don samun takardar shaidar ba), saboda bai dace da ainihin ka'idar yanayi ba - ka'idar kiyaye makamashi.

Hoto 1. Bayyanar ɗaya daga cikin ƙafafun maganadisu na Maxwell.

Masu karatu na iya lura da wasu kwatance tsakanin dabaran Maxwell da shahararren abin wasan yara da ake kira yo-yo. A cikin yanayin yo-yo, asarar makamashi yana cika ta hanyar aikin mai amfani da abin wasan wasan yara, wanda ya ɗagawa kuma ya rage ƙarshen kirtani. Har ila yau, yana da mahimmanci a yanke cewa jikin da ke da babban lokacin rashin aiki yana da wuyar juyawa kuma yana da wuya a dakatar. Saboda haka, dabaran Maxwell a hankali yana ɗaukar gudu lokacin da yake motsawa kuma yana raguwa a hankali yayin da yake hawa. Hakanan ana maimaita hawan hawan sama da ƙasa na dogon lokaci kafin motar ta tsaya a ƙarshe. Duk wannan saboda an adana babban makamashin motsi a cikin irin wannan dabaran. Sabili da haka, ana yin la'akari da ayyukan don amfani da ƙafafu tare da babban lokacin rashin aiki kuma a baya an kawo su cikin sauri da sauri, a matsayin nau'i na "accumulator" na makamashi, wanda aka yi nufi, alal misali, don ƙarin motsi na motoci. A da, an yi amfani da ƙaƙƙarfan ƙaya daga cikin injinan tururi don samar da ƙarin jujjuyawa, kuma a yau su ma wani sashe ne na injunan konewa na cikin gida.