LA BN T HNG HINEW EDITION

TRN ANH NGN

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LA BN T HNG HI

LI GII THIULa bn l mt dng c dng nh hng trn Tri t. N s dng mt kim nam chm c th t do quay theo t trng ca Tri t, t gip xc nh cc hng ng, Ty, Nam, Bc. Ngay t th k th 11, ngi Trung Hoa pht hin ra tnh cht ny ca nam chm v pht minh ra mt dng s khai ca la bn. V ngay lp tc, nhng nh hng hi nhn thy tm quan trng ca la bn trong vic dn tu trn bin, ni m vic xc nh phng hng l nhn t sng cn. Cui th k 12, chic la bn quen thuc vi nhng ngi thy th c pht minh ti chu u, v t y, la bn tr thnh mt biu tng gn lin vi nhng con tu vin dng, gn lin vi nhng ngi thuyn trng. Tuy nhin, nhng la bn trong thi k ny c cu to n gin bao gm mt bn st t ghp trn ci phao c t trong mt ci chu c nc. Cho n u th k 14, cu to ca la bn mi c thay i, hon chnh hn, v gn nh hn. Thi by gi ngi ta quan nim rng kim nam chm ca la bn ch ng hng Bc v Nam ca qu t. V nhng con thuyn bum bng g c trang b la bn, vi s ch hng ca n, rong rui khp cc i dng trn th gii. Cui th k 15, nhng ngi i bin pht hin ra kim nam chm khng phi ch ng hng Bc-Nam ca qu t m ch lch i mt gc no , ngi ta gi l lch a t. V vy, n th k 16, ngi ta bt u lm nhng cng tc xc nh lch a t v u th k 18 th xut hin nhng bn lch a t u tin. Cui th k 18, vi s pht trin ca ngnh ng tu v st, ngi ta pht hin ra rng di nh hng ca st trn tu th kim la bn ch lch i mt gc no so vi kinh tuyn a t. i lng ny thay i theo hng i ca tu v bin i khc nhau nhng con tu khc nhau. Gc lch ny ngi ta gi l lch ring la bn. V vy, la bn c th lm vic chnh xc tc l ch ng hng bc a t th phi tin hnh kh lch la bn. u th k 19, cc nh hng hi dn hon thnh vic kh lch la bn t bng vic thm vo mt s b phn trong cu to ca la bn t. Qua qu trnh pht trin v hon thin, la bn t trn tu bin dn hon chnh v mt cu to v cng tc kh lch la bn tr thnh mt nhim v ca ngi s quan hng hi. y l kt qu ca mt qu trnh dy cng nghin cu l thuyt la bn t vi s ng gp ca nhiu nh bc hc trn th gii nh l E.P Kolong, A.N Crulov, N.N Oglobilinaki, P.A Domogarov... Ngy nay, vi s pht trin ca khoa hc k thut, con ngi pht minh ra la bn con quay dng ch hng trn tu bin. Vi nguyn l hot ng hon ton khc vi la bn t, la bn con quay khng chu nh hng ca t trng do st trn tu gy TRN ANH NGN TRNG I HC GTVT TPHCM 2

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LA BN T HNG HI ra. Kh nng lm vic chnh xc ca la bn con quay v kh nng kt ni truy xut d liu vi mt s thit b in t khc nh my li t ng, GPS,... lm lu m i vai tr ca la bn t trn tu bin. Tuy nhin, la bn t c mt li th c bn m khng c la bn con quay no thay th c, l kh nng lm vic lin tc khng gin on v khng ph thuc ngun in trn tu, gip cho la bn t vn l trang b bt buc trn tu bin theo nh quy nh ca quc t. V vy, cho d c s tr gip ca cc trang thit b hin i, ngi s quan hng hi vn cn phi nm vng nhng kin thc v lch la bn t v thc hin c cng tc kh lch la bn. C nhiu phng php kh lch la bn c a ra, nhng ph bin Vit Nam v trn th gii l dng phng php Ery v xc nh lch bng chp tiu. V ti ny, th cng c nhiu thy, sinh vin v mt s s quan hng hi, nhng ngi am m v yu thch mn la bn t ny, nghin cu v bin dch cc ti liu nc ngoi. Vi mc ch l tm hiu v tng hp li kin thc ca nhng bc n anh i trc, ti liu ny s i su phn tch l thuyt lch la bn t v sau l gii thiu cng tc kh lch la bn t trn lung Si Gn- Vng Tu v ti ca Vng Tu.

TRN ANH NGN TRNG I HC GTVT TPHCM

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LA BN T HNG HI

MC LCPHN MT : C S L THUYT V T1.1 NHNG KHI NIM C BN V T: ....................................................................................................8 1.1.1 T TNH V NAM CHM: ............................................................................................................... 8 1.1.2 KHI NIM SC T, T KHI, NH LUT COULOMB V MMENT T:.............................. 9 1.1.3 T TRNG, CNG T TRNG V NG SC T: ..................................................11 1.2 CNG T TRNG CA MT THANH NAM CHM THNG:................................................. 13 a. Cng t trng ti mt im trn trc t: ..........................................................................................13 b.Cng t trng ti mt im trn ng trung trc ca thanh nam chm: ........................................14 c. Cng t trng ti mt im bt k trong t trng: ..........................................................................15 1.3 S TC DNG LN NHAU CA HAI THANH NAM CHM T TRONG T TRNG U: .......16 a. V tr Gay-lys-sc th nht: ......................................................................................................................18 b.V tr Gay-lys-sc th hai:.........................................................................................................................19 1.4 HIN TNG T HA: .......................................................................................................................... 19 1.4 VT LIU ST T, ST NON, ST GI: ............................................................................................. 22 1.5 QU TRNH KH T: ............................................................................................................................ 26

PHN HAI: A T TRNG, LCH A T, HOA A T2.1 A T TRNG.................................................................................................................................... 28 2.1.1 T trng ca Tri t: ......................................................................................................................28 2.1.2 Cc phn lc a t v s tc dng ca n: ..........................................................................................30 2.2 LCH A T: .................................................................................................................................. 31 2.3 HOA A T CU TO V CCH S DNG: .................................................................................. 32 2.4 BN CC YU T A T: ............................................................................................................ 34

PHN BA: LA BN T HNG HI, CU TO V NGUYN L LM VIC3.1 S LC LCH S LA BN T: ........................................................................................................... 37 3.2 PHN LOI LA BN T: ....................................................................................................................... 38 3.3 CU TO LA BN T HNG HI: ....................................................................................................... 40 3.3.1 Chn la bn:.......................................................................................................................................41 3.3.2 Chu la bn:.......................................................................................................................................42 3.3.3 Cc thanh nam chm v st non dng kh lch la bn t:...........................................................44 3.3.4 H thng quang hc hay h thng knh chiu vo bung li: ...............................................................46 3.3.5 Vng phng v: ................................................................................................................................48 3.4 NGUYN L LM VIC CA LA BN T: ......................................................................................... 49 3.5 CM NG A T V LCH LA BN: .......................................................................................... 50 3.6 MT S CH KHI S DNG LA BN T HNG HI: ................................................................... 52

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LA BN T HNG HI PHN BN: L LUN LCH RING LA BN4.1 KHI NIM T TRNG TU V LCH RING LA BN: ......................................................... 53 a. Khi nim t trng tu: ..........................................................................................................................53 b. T tnh vnh cu ca con tu: ...................................................................................................................53 c. T tnh cm ng ca con tu v tc dng ca n i vi la bn: ................................................................55 d. lch ring la bn:................................................................................................................................56 4.2 H PHNG TRNH POISSON: ............................................................................................................. 56 4.2.1 Khi nim h trc ta tu: ..............................................................................................................56 4.2.2 Phn tch lc tc dng ca a t trng theo h trc ta tu: ..........................................................57 4.2.3 Tc dng ca st thp trn tu i vi la bn: ......................................................................................58 a. Khi nim: ..........................................................................................................................................58 b. Tc dng ca st thp chiu dc i vi la bn: ....................................................................................59 c. Tc dng ca st non chiu ngang i vi la bn: .................................................................................60 d. Tc dng ca st non chiu thng ng i vi la bn: .........................................................................60 e. Tc dng ca st gi i vi la bn: .....................................................................................................61 4.2.4 Phng trnh Poisson: .........................................................................................................................61 4.3 H S ST NON V CCH BIU DIN CC H S ST NON: ........................................................ 62 4.3.1 Dng n st non biu th cc h s st non: ........................................................................................62 4.3.2 n st non biu th h s a - h s st non chiu dc sinh ra bi st non chiu dc ..............................63 4.3.3 n st non biu th h s b - h s st non chiu dc sinh ra bi st non chiu ngang:.........................64 4.3.4 n st non biu th h s c- h s st non chiu dc sinh ra bi st non chiu thng ng: ..................65 4.3.5 Bng tm tt s biu din cc h s st non bng cc n st non v du ca chng: ............................66 4.3.6 Phn tch tr s ca cc h s st non: ..................................................................................................67 4.4 CC LC LCH TC DNG LN LA BN: ( 4.4.1 Chng minh cc lc 4.4.2 Phn tch cc lc )...................68 : ............................................................68 : ..................................................................73

4.4.3 a gic lch: .................................................................................................................................75 4.5 LCH V CNG THC C BN CA LCH: ........................................................................ 75 4.5.1 Quan h gia lch sinh ra bi cc lc lch v hng tu i: ........................................................75 4.5.2 Cng thc c bn v lch: ..............................................................................................................81 4.5.3 Cng thc tnh cc h s gn ng ca cng thc lch: ...................................................................81 4.6 NGUYN L LCH TU NGHING: .............................................................................................. 82 4.6.1 S bin i ca sc t khi tu nghing v tc dng ca n i vi la bn: ............................................82 4.6.2 lch nghing ngang: ......................................................................................................................83 4.6.3 lch nghing dc ( nghing chi): ..................................................................................................87

PHN NM: MY O T LC - CC THIT B KH LCH LA BN T5.1 MY O T LC KOLONG: ................................................................................................................. 89

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LA BN T HNG HI5.1.1 Nguyn l cu to ca my Kolong: ....................................................................................................89 5.1.2. Cu to ca my o lc t Kolong: ....................................................................................................90 5.1.3 Kim tra v hiu chnh my Kolong: ...................................................................................................91 5.2 LA BN NGHING: ................................................................................................................................ 92 5.2.1 Cu to ca la bn nghing: ................................................................................................................92 5.2.2 Kim tra v iu chnh la bn nghing:................................................................................................92 5.3 PHNG PHP DNG MY KOLONG O LC BNG: .................................................................... 93 5.3.1 Phng php o lc H trn b:............................................................................................................93 5.3.2 Phng php o lc H: ......................................................................................................................94 5.4 PHNG PHP DNG MY KOLONG V LA BN NGHING O LC THNG NG: ........ 94 5.4.1 Phng php o lc Z trn b: ........................................................................................................94 5.4.2 Phng php hiu chnh lc Z trn tu: ..............................................................................................94 5.5 MT S DNG C KH LCH: ...................................................................................................... 95

PHN SU: CC PHNG PHP KH LCH LA BN T6.1 KHI NIM CA VIC KH LCH LA BN T: .......................................................................... 97 6.2. PHNG PHP KH LCH NA VNG: ..................................................................................... 97 6.2.1 PHNG PHP KH LCH NA VNG TRN BN HNG I T CHNH ( PHNG PHP ERY): ...............................................................................................................................................97 a. Nguyn l kh lc C b. Nguyn l kh lc B : ....................................................................................................................98 : ...................................................................................................................99

c. Mt s lu khi s dng phng php Ery kh lch na vng: ..................................................... 100 d. Phng php kh lch na vng gn ng: ................................................................................... 102 6.2.2 PHNG PHP KH LCH NA VNG TRN BN HNG I LA BN CHNH ( PHNG PHP KOLONG): ................................................................................................................. 103 a. c. Nguyn l kh lc B Nguyn l kh lc C .............................................................................................................. 103 .............................................................................................................. 106

c. Mt s lu trong vic s dng phng php Kolong kh lch na vng: ................................ 107 6.2.3 PHNG PHP DNG ST NON FLINDER KH LCH NA VNG PH THAY I THEO V :........................................................................................................................................... 108 6.3 PHNG PHP KH LCH GC PHN T VNG: ................................................................... 110 6.3.1 PHNG PHP KH LCH VNG DO LC D SINH RA: .......................................... 110 b. Nguyn l kh gn ng lc D H theo hng i t - Phng php ERY: ........................................ 112 c. Nguyn l kh gn ng lc D trn hai hng i la bn chnh vung gc vi nhau - Phng php Kolong:................................................................................................................................................. 114 6.3.2 PHNG PHP KH LCH VNG DO LC E H SINH RA: ......................................... 116 6.4 PHNG PHP KH LCH TU NGHING: .............................................................................. 118 6.4.1 KH LCH NGHING NGANG: ............................................................................................. 118 a. Nguyn l kh lch nghing ngang: .............................................................................................. 118 b. Cch kh lch nghing ngang: ...................................................................................................... 119

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LA BN T HNG HI6.4.2 KH LCH NGHING DC: ................................................................................................... 120

PHN BY: CNG TC HIU CHNH L BN T V LP BNG LCH CN LI7.1 CNG TC CHUN B TRC KHI HIU CHNH LA BN T: ...................................................... 121 7.2 TH T KH LCH TRONG CNG TC HIU CHNH LA BN: .............................................. 123 a. Th t kh lch trn tu mi: ............................................................................................................ 123 b. Th t kh lch trn tu c: .............................................................................................................. 124 7.3 CC PHNG PHP DN TU I THEO HNG I A T: ........................................................ 124 7.4 PHNG PHP O LCH LA BN KHI HIU CHNH: ............................................................... 126 a. Dng chp tiu hnh qut o lch: ................................................................................................. 126 b. Dng chp tiu n o lch: ......................................................................................................... 128 c. Dng mt mc tiu xa o lch: .................................................................................................. 129 d. Dng thin th o lch:................................................................................................................. 129 e. Dng phng php so snh hng i o lch: ............................................................................... 130 7.5 MT S VN CN CH KHI HIU CHNH LA BN: .............................................................. 131 7.6 CCH LP BNG LCH CN LI: ............................................................................................... 132 a. S cn thit phi lp bng lch cn li: .............................................................................................. 132 b. Cc bc tin hnh: ............................................................................................................................... 132 c. Cc phng php tnh ton cc h s gn ng A, B, C, D, E: ................................................................ 133 d. Tnh ton v lp bng lch: ............................................................................................................... 134

PHN TM: S DNG CHP TIU KH LCH LA BN T TRN LUNG SI GN VNG TU V CA VNG TU8.1 PHNG PHP KH LCH C S DNG: ................................................................................ 139 8.2 MT VI YU CU TRONG CNG TC KH LCH THC T V TRNG KH:...................... 139 8.3 S DNG CHP TIU KH LCH TRN LUNG SI GN VNG TU V CA VNG TU:............................................................................................................................................................. 140 8.3.1 Cng tc chun b: ............................................................................................................................ 140 8.3.2 Thng tin tuyn lung v cc chp tiu trong khu vc kh:................................................................ 140 8.3.3 Lc chn a im kh v cc chp tiu c s dng:...................................................................... 142 8.3.4 Lp s iu ng khu vc kh: (xem hnh 8.2) ............................................................................. 142 8.3.5 Cng tc kh s b trn lung Si Gn trc khi n khu vc th: .................................................... 142 8.3.6 Cng tc tin hnh kh: .................................................................................................................... 142

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LA BN T HNG HI PHN MT: C S L THUYT V T Nh chng ta bit, nguyn l lm vic ca la bn t l da trn s nh hng ca kim nam chm trong t trng tri t. Do vy, phn ny s cung cp nhng kin thc c bn nht lin quan n t v t trng. 1.1 NHNG KHI NIM C BN V T: 1.1.1 T TNH V NAM CHM: a. Khi nim: - T tnh l tnh cht ca cc vt c th ht c st thp. - St c t tnh gi l nam chm. Nam chm chia lm hai loi: nam chm t nhin v nam chm nhn to. Nu dng phng php nhn to lm thp v nhng hp kim tr thnh nam chm th gi l nam chm nhn to. Hnh dng ca nam chm nhn to c 3 loi: thanh di, hnh trn, hnh mng nga v hnh kim.

Hnh 1.1: Mt s loi nam chm b. Tnh cht ca nam chm: - gn hai u nam chm c t tnh mnh nht gi l t cc. ng ni hai t cc gi l trc t. B phn gia ca nam chm khng c t tnh gi l phn trung tnh. i vi nam chm hnh thanh di, v tr ca t cc cch hai u ca chng 1/12 chiu di ca thanh nam chm, i vi nam chm hnh kim th t cc ti u kim.

Hnh 1.2: V tr t cc trn thanh nam chm TRN ANH NGN TRNG I HC GTVT TPHCM 8

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LA BN T HNG HI Mt tnh cht rt quan trng ca nam chm lm c s ch to la bn l: nu mt kim nam chm c th quay t do, khi ng yn th s ch theo hng Bc Nam cho nn ta gi t cc ch hng Bc l cc Bc, biu th bng ch N( North), t cc ch hng Nam gi l cc Nam, biu th bng ch S( South). Trong thc t, ta gi cc Bc l cc dng hoc biu th bng du + v c sn mu ; cc Nam l cc m hoc biu th bng du - v c sn mu xanh. Nam chm c nhng c tnh sau: o Hai cc ng cc th y nhau, hai cc khc cc th ht nhau. Tng tc gia hai nam chm gi l tng tc t. o T cc khng th ct i c, bt k mt thanh nam chm no khi b ct thnh nhiu on nh, th mi on l mt thanh nam chm nh c cc cc bc v cc nam.

-

Hnh 1.3: Tng tc t gia hai nam chm Mt cu hi c t ra y l ti sao ch c st thp mi c th bin thnh nam chm? V ti sao li khng ct i t cc ca nam chm ra c? Hai vn ny s c cp r hn phn sau. 1.1.2 KHI NIM SC T, T KHI, NH LUT COULOMB V MMENT T: a. Sc t: - Lc ht v lc y nhau gia hai cc t gi l sc t, ta quy nh sc y gia hai cc cng tn l dng, v sc ht gia hai cc khc tn l m. TRN ANH NGN TRNG I HC GTVT TPHCM 9

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LA BN T HNG HI

(-)

(-)

(+)

(+)

(+)

(+)

Hnh 1.4:M t sc t

b. T khi ( hay t tch): - T khi l khi lng t biu th cng t cc, k hiu l m. Mi nam chm u c hai t khi hai u. Quy nh t khi ca cc bc l dng v ca cc nam l m c. Mment t: - Sc t tc dng ca hai cc ca mt nam chm ( ti mt im no trong khng gian) v t khi ca n u c du nghch nhau, tr s tuyt i bng nhau. Cho nn lc t do chng gy ra s lm suy yu ln nhau. Hai cc cng gn nhau, th s kh lc t gia chng cng ln. Dn n sc t ca mt thanh nam chm tc dng ti mt im no th s ph thuc vo t khi v khong cch gia hai cc ca nam chm. Do vy, tch s ca t khi ca nam chm vi khong cch gia hai cc gi l mment t. 2l - Theo hnh 1.4, l l mt na khong cch gia hai cc ca nam chm tc: (+m) M = 2ml (1-1) Trong h thng cm, gam, giy, n v ca moment t l cgsM. (-m) Hnh 1.5 : T khi v moment t 10

-

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LA BN T HNG HI d. nh lut Coulomb: - Qua th nghim Coulomb chng minh c rng: lc tc dng ca hai cc nam chm t l thun vi tch s ca t khi ca chng v t l nghch vi bnh phng khong cch gia hai t khi,tc l: (1-2) Trong : : l h s dn t, trong chn khng =1 th cng thc trn tr thnh: (1-3) Trong khng kh cho nn trong nhng vn thng thng ta c th dng cng thc trn tnh lc tc dng ca cc t cc trong khng kh.

1.1.3 T TRNG, CNG T TRNG V NG SC T: a. T trng: - Theo nh ngha tng qut th t trngl mi trng vt cht c bit sinh ra quanh ccin tch chuyn nghoc do s bin thin ca in trng hoc c ngun gc t cc mment lng cc t. - Trong phm vi nghin cu ca lun vn ny, chng ta ch cp n t trng xung quanh nam chm l khong khng gian b tc dng ca sc t nam chm. ( Ngun gc ca n cng bt ngun t chuyn ng ca cc ht in tch, y l cc ht electron trong nguyn t, s ni r hn trong phn t ho ).

Hnh 1.6: Hnh nh t trng xung quanh nam chm b. Cng t trng: - Cng t trng l sc t tc dng ln mt n v t khi dng ti mt im trong t trng. K hiu l H TRN ANH NGN TRNG I HC GTVT TPHCM 11

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LA BN T HNG HI Cng t trng H l mt i lng vecto. T cng thc ( 1-3) ta c cch tnh cng t trng ca mt t khi ti mt im bt k trong t trng: (1-4) Trong : m: l t khi, d l khong cch t t khi n v tr tnh H Trong h thng cgsM, n v ca cng t trng l Erstet k hiu Oe. Trong n v quc t, n v cng t trng c tnh l Ampermet ( A/M), trong 1A/M= Hng tc dng ca cng t trng biu th hng ca t trng. Nu trong phm vi no H c tr s v hng ging nhau th t trng trong phm vi gi l t trng u. Trong thc t hng hi cho php coi t trng Tri t khng gian tu chim ch l t trng u. iu ny lm n gin hn rt nhiu vic nghin cu la bn. Nu t cc c t khi m ti mt im trong t trng b tc dng bi mt sc t F th cng t trng ti im s l: (1-5) c. ng sc t: - Ni lin cc hng ca vecto cng t trng ca cc im trong t trng s to thnh ng cong hoc ng thng, ng y gi l ng sc t. Tip tuyn ti mt im no trn ng sc t trng vi phng t lc. - Trong t trng u, ng sc c dng ng thng, trong t trng khng u, ng sc c dng ng cong. - ng sc t ca nam chm i ra cc Bc v i vo cc Nam. - S lng ng sc t i qua mt n v din tch gi l mt ng sc t. Mt ng sc t cng cao th t trng cc mnh, v mt ng sc t hai u nam chm ln hn gia. - Hnh nh cc ng sc t gi l t ph.

-

-

Hnh 1.7: S dng mt st xc nh t ph ca mt thanh nam chm thng TRN ANH NGN TRNG I HC GTVT TPHCM 12

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LA BN T HNG HI Ch : - Trong t trng thanh nam chm t mt vt liu bng kim loi th ng sc t b bin dng. Chng t gip ta gii thch nhng khu vc c nhiu m qung kim loi c kh nng nhim t mnh s lm cho ng sc t ca t trng tri t bin mnh dn n hin tng nhiu lon t, thm ch sinh ra bo t gy tn tht nng cho cc thit b in, trm bin p in trn b cng nh cc thit b in trn tu - ng sc t khng xuyn qua hnh tr rng bng kim loi nn tu ngm khng t c la bn v y la bn t khng c kh nng nh hng. 1.2 CNG T TRNG CA MT THANH NAM CHM THNG: V cc thanh nam chm trong cu to ca la bn t hng hi v cc thanh nam chm kh lch u c dng thanh di v thng nn vic i su tm hiu tnh cht cng t trng ca thanh nm chm thng l cn thit. a. Cng t trng ti mt im trn trc t: - Nu t khi ca thanh nam chm NS l m, khong cch gia 2 cc l 2l, t khi tiim A l +1 n v, khong cch t A n trung tm ca thanh nam chm l OA=d v d>>l - Lc tc dng ca thanh +m nam chm i viim A l tngi s ca lc FN do H cc N tc dng v lc FS 1 do S tc dng. Hnh 1.8: Sc t tc dng ti1 im A trn trc t Theo nh lut Coulomb ta c:

-m

-

-

Gi H1 l cng t trng ti im A, ta c:

H1= FN + FS =

+

=

-

V theo gi thit ll. - Lc tc dng ca thanh nam chm i vi t khi ti B l tng hp lc ca lc H2 FN do cc Bc gy ra, v lc FS do cc Nam gy ra, hai lc ny c hng khc nhau nhng v ln th nh nhau, tc:

-

Gi H2 l cng t trng ca thanh nam chm ti im B, ta c H2 l hp lc Hnh 1.9: Cng t trng ti mt ca hai lc trn, tc: im nm trn ng trung trc ca thanh nam chm

H2 = FNcos + FScos = ( FN+FS)cos =Mt khc ta c: Cos = Suy ra H2 =

=rt b, nn c th b qua

V gi thit d>>l nn suy ra Cui cng ta c:

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LA BN T HNG HI

H2 =-

(1-7)

Vy vecto cng t trng H2 c phng song song vi trc dc thanh nam chm v c chiu hng v cc S. Nhn xt: So snh cng thc (1-6) v (1-7) ta nhn thy: nu A v B nm trn khong cch bng nhau i vi nam chm, th cng t trng ti mt im trn trc t s bng 2 ln cng t trng ti 1 im trn ng trung trc ca thanh nam chm. iu cho thy quan h t l thun gia cng t trng v mt ng sc t.

c. Cng t trng ti mt im bt k trong t trng: - t ti C l mt im bt k trong t trng mt t khi +1 n v. Gi khong cch t C n tm O thanh nam chm l d v d>>l. H2 C N N

Hc H1

-

-

S Hnh 1.10: Cng t trng ti mt im bt k trong t trng thanh nam Gi s thanhchm thng NS c moment t l M. Ta chiu vecto M ln nam chm hng OC v hng vung gc vi OC ta c hai vecto M1 v M2. Bng cch ta thay thanh nam chm NS bng 2 thanh nam chm NS v NS trn hng OC v hng vung gc vi OC. Trong , mt thanh NSc im C nm trn trc t, v mt thanh NSc im C nm trn ng trung trc. T hnh v, ta c: M1 = Msin v M2 = Mcos

S

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LA BN T HNG HI Gi H1 l cng t trng do thanh NS gy ra ti C, theo nhng chng minh trn ta c: H1 = Gi H2 l cng t trng ti im C do thanh nam chm NS gy ra, ta c: H2 = Nn cng t trng ti im C s l tng hp hai cng t trng trn, do vy: Hc = = Gi l gc hp bi Hc v H2 tac c: Tg = (1-9) = (1-8)

Ta nhn thy cng thc (1-6) v (1-7) chnh l dng thu gn ca ca cng thc (1-8) khi gc v gc . 1.3 S TC DNG LN NHAU CA HAI THANH NAM CHM T TRONG T TRNG U: - Trong qu trnh kh lch la bn t, ta s phi s dng cc thanh nam chm vnh cu hoc cc thanh st non, to ra lc tc dng nn kim nam chm ca la bn. V vy, phn ny s i su phn tch s tng tc gia cc thanh nam chm vi nhau khi t chng trong t trng u. Qua gip chng ta hiu phn no v c ch ca qu trnh kh. Phn tch lc tc dng ln kim nam chm trong t trng u: Nu kim nam chm NS c m men l 2ml, t trong t trng u c cng t trng H , th chng chu tc dng ca hai lc l +mH v -mH (Hnh 1.11).Cc lc +mH , mH to vi nhau thnh mt ngu lc vi cch tay n l NA, ta c: Hnh 1.11 16

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LA BN T HNG HI NA = 2lsin Di tc dng ca m men quay ny, kim nam chm s quay v nh hng dc theo hng ca vc t cng t trng . Gi tr m men quay k hiu l P c tnh theo cng thc: P = 2lmHsin (1-10) Gi s ti mt v tr no trong khng gian xung quanh kim nam chm ta t mtthanh nam chm thng N-S c nh , c m men t l M (hnh 1.12),

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Hnh 1.12 Cng t trng ca thanh nam chm N-S trng tm ca kim nam chm ta tnh c theo cng thc nghin cu 1.2 .

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y c hng vung gc vi ng OO1 v c hng song song vi OO1. Do vy lc tc dng ca thanh nam chm N-S ln kim nam chm c th tnh c l: mH1 v mH2, cc lc ny to ra nhng ngu lc v c tnh theo cng thc (1.9) l: 2lmH1cos( v 2lmH2sin ( Tnh tt c 3 m men lm quay kim nam chm v tng hp li, ta c: 2lmHsin - 2lmH1cos( Hay Hsin - H1cos ( - 2lmH2sin ( -H2sin ( =0 =0

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Thay gi tr H1 v H2 vo, ta c iu kin ton hc cn bng ca kim nam chm nh sau: TRN ANH NGN TRNG I HC GTVT TPHCM 17

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LA BN T HNG HI

Hsin -

(1-11)

Di y ta nghin cu 2 trng hp c bit v lc tc dng ln nhau ca kim namchm v thanh nam chm thng di tc dng ca t trng u H bao gm v tr Gay-lys-Sc thnht v th hai.

a. V tr Gay-lys-sc th nht: - Trc ca thanh nam chm nm vung gc vi hng t trng u H hay trng tm ca kim nam chm nm trn ng trc ca thanh nam chm. V tr ny tng ng vi v tr nam chm kh lch tu nghing trong thn la bn t. - Trong trng hp ny gc . Thay gi tr ny vo biu thc (1-10), ta c: Hsin Hay: (1-12)

Hnh 1.13 Cng thc (1.12) dng trong thc tin xc nh thnh phn nm ngang ca t trng tri t. xc nh H ta tin hnh nh sau : t mt thanh nam chm thng c m men t M , trong t trng tri t H . Trn khong cch d bit t mt kim nam chm v tr Gay-Lys-Sc th nht , o gc lch ca kim nam chm theo cng thc (1.11) ta tnh c H. Cng thc (1.12) cng c s dng tnh Mmen t ca thanh nam chm thng khi bit t trng H, khong cch d, gc lch . Tnh mmen t M t cng thc (1.12): M= (1-13)

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LA BN T HNG HI b. V tr Gay-lys-sc th hai: - Thanh nam chm t vung gc vi t trng H hay trng tm kim nam chm nm trn ng vung gc vi trc thanh nam chm v i qua trung im ca thanh . V tr ny tng ng vi v tr nam chm kh lch bn vng (hnh 1.14). - Trong trng hp ny thay , . Thay gi tr ny vo biu thc cn bng ca kim nam chm, ta c:

Suy ra: -

H=

(1-14)

Cng thc (1-14), thng c dng xc nh thnh phn t trng ca qu t v m men t ca thanh nam chm (lm tng t nh v tr Gay-lys- sc th nht)

Hnh 1.14

1.4 HIN TNG T HA: a. Hin tng t ha: - Theo nh ngha tng qut, th t ha l qu trnh thay i cc tnh cht t (cu trc t, mmen t...) ca vt cht di tc dng ca t trng ngoi. Khi c s dng nh mt ng t, t ha c ngha l lm thay i tnh cht t ca vt cht bng t trng ngoi. - Theo cch hiu trong lun vn ny th, t ha l qu trnh bin mt vt khng c t tnh thnh vt c t tnh. - Xt v mt hin tng, t ha l s thay i tnh cht t ca vt cht theo t trng ngoi, xt v mt bn cht, y l s thay i cc mmen t nguyn t. Khi t vo t trng ngoi, cc mmen t nguyn t c xu hng b quay i theo t trng ngoi dn n s thay i v tnh cht t.

Hnh 1.15:Cu trc t ca mng mng hp kimpermalloy (dy 20 nm) thay i trong qu trnh t ha (nh quan st bng knh hin vi Lorentz Philips CM20).

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LA BN T HNG HI b. t ha (t ): - nh gi kh nng b t ha ca vt liu, ngi ta dng khi nim t ha. Nh vy, t ha ( hay t ) l mt i lng vt l ni ln kh nng b t ha ca mt vt liu t, c xc nh bng tng mmen t nguyn t trn mt n v th tch, hoc mt n v khi lng. t ha c k hiu l M, ta c: (1-15) Trong : M: l t ha (A/m) N: l tng s lng moment t nguyn t V: l th tch vt liu m: l mment t nguyn t n: l mt moment t nguyn t trong mt n v th tch vt liu t. Ta nhn thy, t ha ch mi cp n kh nng ni ti ca vt liu t. Cha cp n vai tr ca t trng ngoi gy nn t ha. V vy cha th hin c ht bn cht ca hin tng t ha, v lm c iu ny, ngi ta dng mt i lng mi gi l h s t ha ( hay h s dn t hay cm t). -

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c. H s t ha ( hay cm t): - H s t ha ( hay cm t) l mt i lng vt l c trng cho kh nng t ha ca vt liu, hay ni ln kh nng phn ng ca vt liu di tc dng ca t trng ngoi. cm t th hin mi quan h gia t ha (l i lng ni ti) v t trng ngoi, nn thng mang nhiu ngha vt l gn vi cc tnh cht ni ti ca vt liu. H s t ha thng c k hiu l v c xc nh bng t s gia t ha (M) v cng t trng ngoi( H). (1-16) V M v H l hai i lng c cng th nguyn nn khng c th nguyn. l i lng

Tuy nhin trong k thut, ngi ta li quan tm n mt i lng khc cng c ngha tng t nh h s t ha. Gi l t thm.

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LA BN T HNG HI d. t thm: - t thm l mt i lng vt l c trng cho tnh thm ca t trng vo mt vt liu, hay ni ln kh nng phn ng ca vt liu di tc dng ca t trng ngoi. Khi nim t thm thng mang tnh cht k thut ca vt liu, ni ln quan h gia cm ng t (i lng sn sinh ngoi) v t trng ngoi. t thm thc cht ch ng k cc vt liu c trt t t (st t v feri t). t thm thng c k hiu l . - Mi quan h gia t thm v cm t: Cm ng t, B quan h vi t v cng t trng theo biu thc: B = 0(H + M) vi 0 l hng s t, hay c gi l t thm ca chn khng, c ln 0 = 4.10 7T.m / A Nh vy: B = 0(1 + ).H Suy ra: B=.H (1-17)

Nh vy, i lng t thm v cm t quan h vi nhau qua biu thc: = 0(1 + ) (1-18) t thm c cng ngha vi cm t, u ni ln kh nng phn ng ca cc vt liu di tc dng ca t trng ngoi.

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e. Phn loi vt liu t: - Ty theo s tc dng ca t trng ngoi v s hng ng ca vt liu t trong qu trnh t ha, ngi ta phn bit thnh cc loi vt liu t khc nhau: - Vt liu nghch t: ng vi 1 Qu trnh t ha cht thun t, cht c mmen t nguyn t nh v khng lin kt, xy ra n gin, cc mmen t nguyn t s quay theo t trng ngoi v to ra mt t trng ph dng (thng th hiu ng nghch t c hu). V th, qu trnh t ha ch n gin l s tng tuyn tnh ca t theo t trng ngoi v t bo ha khi t trng rt ln v nhit rt thp. Vt liu st t v cc vt liu c trt t t khc (phn st t, feri t): ng vi >>1 Trong cc vt liu ny, mmen t nguyn t ln v c lin kt vi nhau thng qua tng tc trao i nn qu trnh t ha tr nn rt phc tp. Qu trnh ny ph thuc vo nhiu yu t nh cu trc t, cu trc tinh th cng nh s ng nht ca vt liu. Cc qu trnh t ha lc ny l s thay i cu trc men t ( magnetic domain) ca cht, v dn n nhiu loi cht khc nhau, v d nh vt liu st t mm, vt liu st t cng...

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Hnh 1.16: S bin i ca cc men t trong vt liu st t khi b t ha

1.4 VT LIU ST T, ST NON, ST GI:V tu bin c ch to ch yu t st v cc hp kim ca st, m chng u l nhng vt liu st t, nn phn ny s i su phn tch c tnh t ha vt liu st t lm nn tng kin thc cho l lun lch la bn t c trnh by nhng phn sau.

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LA BN T HNG HI a. Vt liu st t: - St t l cc cht c t tnh mnh, hay kh nng hng ng mnh di tc dng ca t trng ngoi, m tiu biu l st (Fe), v tn gi "st t" c t cho nhm cc cht c tnh cht t ging vi st. Cc cht st t c hnh vi gn ging vi cc cht thun t c im hng ng thun theo t trng ngoi. - Cc cht st t c t thm rt ln (>>1), nn c kh nng t ha c bit. Kh nng ny c th c gii thch nh sau: - Vt th st t c cu to bi v s cc nam chm phn t ( hay cc moment t nguyn t). Nu cc nam chm phn t chuyn ng hn lon th lc tc dng gia chng trong trng hp tng qut bng khng v vt th khng c t tnh. Cc nam chm phn t tc dng tng h v gia chng v tr cn bng. - Nu ta em vt liu st t t vo trong mt t trng, di tc dng ca cc lc, cc nam chm phn t b nh hng theo hng xc nh, ngha l n b t ha. Sau khi tt c cc nam chm phn t nh hng theo t trng ngoi th n tnh trng bo ha t v khng c kh nng t ha hn na. - Nu ta trit tiu t trng t ha bn ngoi, th do lc tc dng tng h gia cc phn t li lm chng chuyn ng hn lon tr v tnh trng ban u. Nhng do hin tng nh hng song song ca cc nam chm phn t, mt khc lc tc dng tng h gia chng pht sinh khng hon ton ging nh ban u, do vy chng vn cn mt lng t d khi t trng bn ngoi b trit tiu, v chng c th tr thnh nam chm. ( xem hnh 1.16) - y cng l cch l gii cho s hnh thnh nam chm trong t nhin ( cc qung st b t ha bi t trng Tri t) v l nguyn l cho vic ch to nam chm nhn to, ng thi n cng gii thch s ht nhau gia thanh nam chm v vt liu st t ( nam chm t ha vt th st t tr thnh mt nam chm, nn xy ra lc tng tc gia 2 nam chm). - Cc cht st t (v d nh st (Fe), cban (Co), niken (Ni), gali (Gd)... l cc cht st t in hnh. Cc cht ny l cc cht vn c mmen t nguyn t ln (v d nh st l 2,2 B, Gd l 7 B...) v nh tng tc trao i gia cc mmen t ny, m chng nh hng song song vi nhau theo tng vng (gi l cc men t tnh). Mmen t trong mi vng gi l t t pht - c ngha l cc cht st t c t tnh ni ti ngay khi khng c t trng ngoi. y l cc ngun gc c bn to nn cc tnh cht ca cht st t. TRN ANH NGN TRNG I HC GTVT TPHCM

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LA BN T HNG HI b. Hin tng t tr, ng cong t tr v mt s tnh cht ca vt liu st t: - Hin tng t tr: L mt c trng d thy nht cht st t. Khi t ha mt khi cht st t cc mmen t s c xu hng sp xp trt t theo hng t trng ngoi do t ca mu tng dn n bo ha khi t trng ln (khi cc mmen t hon ton song song vi nhau). Khi ngt t trng hoc kh t theo chiu ngc li, do s lin kt gia cc mmen t v cc men t, cc mmen t khng lp tc b quay tr li trng thi hn n nh cc cht thun t m cn gi c t gi tr khc khng. Nu ta biu din qu trnh t ha vt liu st t thnh ng cong mi quan h gia t M v cng t trng H th ng cong o t s khng khp vi ng cong t ha ban u. V nu ta t ha v kh t theo mt chu trnh kn ca t trng ngoi, ta s c mt ng cong kn gi l ng cong t tr.

C

A

O

Hnh 1.17: ng cong t tr- c tnh quan trng nht ca st t Da vo ng cong t ha ban u, ta nhn thy on OA gn nh l ng thng, ngha l trong t trng yu, t gn nh l t l thun vi cng t trng ngoi. Khi tng H th M tng theo, n A th khng cn TRN ANH NGN TRNG I HC GTVT TPHCM 24

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LA BN T HNG HI tng na. A c gi l im bo ha. Sau nu tip tc tng H th ng t ha s tng gn nh theo hng bng. Ch : y l mt tnh cht quan trng cn phi ghi nh, c th pht biu li nh sau: trong t trng yu, st b t ha, th cng cm ng t ca n s t l thun vi lc t ha. Quan h ny l mt vn ch yu gii quyt lch la bn t.

ng cong t tr cng cung cp cho ta mt s tnh cht c bn ca vt liu st t, nh l: - T bo ha: L t t c trong trng thi bo ha t, c ngha l tt c cc mmen t nguyn t ca cht st t song song vi nhau. - T d: L gi tr t khi t trng ngoi c kh v 0. - Lc khng t ( lc gi t): L t trng ngoi cn thit kh mmen t ca vt mu v 0, hay l gi tr t i chiu. i khi lc khng t cn c gi ltrng o t. - Nhit Curie: L nhit m ti , cht b mt t tnh. di nhit Curie, cht trng thi st t, trn nhit Curie, cht s mang tnh cht ca cht thun t. Nhit Curie l mt tham s c trng cho cht st t. V d nh: Cht liu st t St Cban Niken Gadoli Dysproxium MnBi MnSb Nhit Curie (oK) 1043 1388 627 292,5 88 630 587

Hnh 1.18: Hnh nh cc men t ca mng CoIr chp ch Fresnel trn knh hin vi in t truyn qua.

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LA BN T HNG HI c. Phn loi vt liu st t: - C nhiu cch khc nhau phn chia cc vt liu st t, nhng cch thng dng nht ( v c s dng trong ti ny) vn l phn chia theo kh nng t ha v kh t ca vt liu. Theo cch phn chia ny s c 2 nhm vt liu st t chnh: - Vt liu t cng ( st t cng hay st gi):L cc vt liu st t kh t ha v kh kh t, chng c lc khng t ln, c s dng ch to cc thanh nam chm vnh cu, ng dng trong ch to vt liu ghi t.Cc vt liu t cng in hnh l Nd2Fe14B, Sm2Co5, FePt.. - Vt liu t mm (st t mm hay st non): L cc vt liu st t d t ha v d b kh t, chng c lc khng t nh, c ng dnghot ng trong t trng ngoi nh li bin th, nam chm in, li dn t, cm bin t trng... Cc vt liu t mm in hnh l st silic (FeSi), hp kim permalloy NiFe... Vt liu c t tnh non rt d b t ha nhng khi a ra ngoi t trng th mt i rt nhanh. V d nh st. c tnh t ha ca vt liu c t tnh gi th ngc li, tc l rt kh lm cho n t ha, nhng sau khi t ha th gi t rt lu. V d nh gang. Trong vt liu ng tu, u c st non v st gi, hiu chnh lch la bn t ta cng phi s dng st non, v st gi. Cho nn st non v st gi c lin quan cht ch n lch la bn t v ngi s quan hng hi cn nm vng nguyn l s dng chng cho vic kh lch la bn.

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1.5 QU TRNH KH T:Ngc vi qu trnh t ha l qu trnh kh t. Kh t l qu trnh lm trit tiu t tnh ca vt t, bng cch t vo mt t trng ngc ln, hoc lm tng nhit n trn nhit nh hng ca cht. o Kh t bng t trng: Kh t bng t trng l cch thng dng nht, bng cch t vo t trng ngc (vi chiu ca t d trong cht) bng vi gi tr lc khng t ca cht. Nu t trng ngc t vo tip tc tng, t ca cht s b o ngc, v ta c qu trnh o t. kh t hon ton, ngi ta khng dng t trng ngc mt chiu m dng t trng xoay chiu c bin gim dn (tt dn theo hm s m v i chiu), nh vy, t trng d trong vt TRN ANH NGN TRNG I HC GTVT TPHCM

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LA BN T HNG HI mu s b nh dn v o lin tc quay gi tr 0 v ngy cng tin ti gi tr 0. o Cc cch khc: C nhiu cc khc kh t, v d t nng vt t n trn nhit trt t t ca cht (nhit Curie vi cc cht st t, hay nhit Nel vi cc cht phn st t...), lc ny cc cht t trng thi c t ln s b mt t tnh v tr thnh cht thun t. Ngoi ra, s va p c hc v n mn ha hc cng l nhng cch kh i t tnh ca cht.

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LA BN T HNG HI PHN HAI: A T TRNG, LCH A T, HOA A T 2.1 A T TRNG 2.1.1 T trng ca Tri t: - Khi treo mt kim nam chm t do trn b mt Tri t bt k v tr no cng quan st thy mt u kim nam chm lun nh hng Bc-Nam. Th nghim trn chng t Tri t c t trng. - Ngi ta xem Tri t l mt nam chm khng l c bao bc bi cc ng sc t ni lin gia hai cc. Tuy nhin, cc cc nam chm ch nm gn cc cc a l ch khng trng ln nhau. Chng ta thng nhm ln trong vic xc nh tn cc cc a t, tht ra: o Cc Bc a t nm gn cc Bc a l li l cc Nam (S) ca t trng Tri t ( hay thanh nam chm Tri t), o Cc Nam a t nm gn cc Nam a l li l cc Bc (N) ca t trng Tri t ( hay thanh nam chm Tri t). - Nguyn nhn gy ra s nhm ln ny l do yu t lch s, u ca kim nam chm ch v hng bc nn thng gi l "cc bc" v u ch v pha nam gi l "cc nam", nhng thc cht v mt vt l hc th ngc li. - Mt ng thng tng tng ni hai cc t to thnh mt gc 11,3o so vi trc quay ca Tri t.

Hnh 2.1: T trng bao quanh Tri t

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LA BN T HNG HI Nhn vo m hnh t trng Tri t, ta nhn thy,at trng l mt t trng khng u. Tuy nhin, v phm vi qu rng, nn khi kh lch la bn ta c th xem trong phm vi xung quanh tu th a t trng l t trng u v rt yu. Cc t cc thng c v tr khng n nh v c th o ngc theo chu k. Theo kho st trong nm 2005, v tr ca hai cc a t c xc nh nh sau: o Cc Bc a t: c tnh 82.7N, 114.4W ( theo Cc kho st a cht Canada) o Cc Nam a t: c tnh 643148S, 1375136E, rt gn b bin Wilkes Land, Nam Cc. T trng lun bao quanh b mt Tri t, trn khng gian, trong lng t v c di nc bin u pht hin thy c t lc tc dng. T trng ca qu t c ngha rt ln trong cuc sng con ngi. Trong khng gian hng nghn km bao quanh mt t, t trng ca qu t l mi trng ngn cc tia bc x v t xuyn vo Tri t. Do , n bo v c cuc sng ca cc sinh vt trn mt t khi b hy dit do phng x v tr. Nghin cu t trng Tri t cho php chng ta khi qut nhng nt c bn xy dng b mt qu t, pht hin nhng va qung c ch, nghin cu cc hin tng pht sinh t mt tri v khng gian v tr. T trng ca Tri t cng c s dng nh hng trn mt t thng qua la bn, gip con ngi xc nh phng hng v i li trong rng, trn sa mc, v trn bin... Thm vo , t trng Tri t cng gip cho mt s loi ng vt xc nh c phng hng.

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Hnh 2.2: Mt tri khng ch em n nh sng v hi m m cn l mi him nguy ca con ngi. L do: mt tri lin tc phng ra cc ht giu nng lng - gi mt tri - vo v tr v v hng tri t. Trc khi cc ht c th chm vo hnh tinh ca chng ta th chng b mt tm chn ngn li, l t trng ca tri t.

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LA BN T HNG HI 2.1.2 Cc phn lc a t v s tc dng ca n: - Theo hnh 2.1, ta nhn thy cc ng sc t ca t trng Tri t i vo b mt Tri t nhng T gc khc nhau so vi mt phng chn tri. Cc gc ny gi l t nghing(angle of magnetic dip), k hiu l ( xem hnh 2.3). - Gi tr ca tng t 0 T o xch o t n 90 v pha cc cc a t. ng ni nhng im c cng t nghing gi l v t. - Xt 1 im A bt k trn b mt mt t, chu tc dng ca cng a t Hnh 2.3: Cc phn lc a t v t nghing trng, k hiu l T. Vc t cng a t trn ( ti mi im lun lun tip tuyn vi ng sc t. Nu ti im A ta treo mt kim nam chm th trc kim nam chm s theo hng ca vc t v lch vi mt phng nm ngang mt gc , tc l t nghing. o Nu u bc kim nam chm chi xung th gc mang du dng, o Nu u bc kim nam chm ngng ln th gc mang du m. Phn tch vc t cng a t trng hai thnh phn: o Thnh phn nm ngang: mt phng chn tri. thnh

song song vi

o Thnh phn thng ng: Thnh lp cng thc biu th mi quan h gia cc thnh phn lc nh sau: Hnh 2.4:Phn tch cc phn lc a t ( 2 -1)

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LA BN T HNG HI o Phn lc H ch hng Bc a t l mt s lun lun dng. N lm cho la bn ch c phng hng. Kinh tuyn i qua n gi l kinh tuyn a t, kinh tuyn a t c chn lm mc tnh hng i v phng v a t. o Qua cng thc trn ta thy nu im A xch o th =0, suy ra H=T=Hmax (khong 0.4 Oe), Z=0 chng t la bn hot ng vng xch o, gn xch o th kh nng nh hng l tt nht. Khi v cng tng th H cng gim, cc th =90o, suy ra H=0 chng t la bn khng c kh nng hot ng. o Phn lc thng ng Z khng c tc dng nh hng. Ta quy nh, hng ca Z ch xung l dng, v ch ln l m. Do , v bc a t th Z s dng, v nam a t th Z s m.

2.2 LCH A T: T khi ngi ta bit c cc cc a t ca Tri t khng trng vi cc cc a l, th hng ch ca kim la bn trong t trng Tri t s khng ng hng Bc tht m ch hng bc a t.

Hnh 2.5: S hnh thnh lch a t Gc hp gia kinh tuyn tht ( vng trn ln ni lin cc cc a l) v kinh tuyn t ( hng ca ng sc t) gi l lch a t ( cn gi l t thin hay variation). lch a t nhng ni khc nhau trn Tri t th bin i khc nhau. o Khi hng bc a t lch v pha ng ca hng bc tht ta gi l lch a t ng, ta quy c l lch a t dng v mang du +, o Khi hng bc a t lch v pha ty ca hng bc tht ta gi l lch a t ty, ta quy c l lch a t m v mang du -. TRN ANH NGN TRNG I HC GTVT TPHCM 31

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LA BN T HNG HI Nh ni trn, lch a t mang tnh a phng v bin i khng nhng theo v tr a l m cn theo thi gian. S bin i c 2 loi l bin i theo chu k v bin i khng theo chu k. o S bin i theo chu k: c ba loi l theo chu k ngy, nm v th k. Trong tr s bin i theo chu k ngy v nm l rt nh, trong hng hi c th b c, nhng tr s bin i theo chu k th k th tng i ln khng th b qua c. Tr s bin i theo th k ca lch a t cc ni u chia thnh lch theo nm v c ghi ch vng khc hoa la bn trn hi hiu chnh. o S bin i khng theo chu k: c nhiu Hnh 2.6: lch a t ng v ty nguyn nhn lm cho lch a t bin i khng theo chu k nh bo t, khu vc nhiu lon t... Bo t l hin tng t nhin pht sinh t, n c th lm cho trng thi ca a t thay i rt nhanh. Khu vc nhiu lon t l do qung st nam chm, tu b chm...lm cho t trng trong khu vc y bin i.

2.3 HOA A T CU TO V CCH S DNG: gip cho ngi i bin d dng xc nh c lch a t trn nhng vng bin khc nhau, phc v cho vic tnh ton phng v hoc hng i, ngi ta in cc thng s v s bin i lch a t trn hi thng qua cc hoa a t ( hay hoa la bn). Hoa a t l mt vng trn chia t 0o n 360o, trong vng trn ghi sn c gi tr lch a t, nm kho st v lng thay i hng nm. Trn nhng hi ca nhng nh xut bn khc nhau, th cu trc ca hoa a t c th c mt s khc bit.

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Hnh 2.7: Hoa a t trn hi Anh ( BA chart) TRN ANH NGN TRNG I HC GTVT TPHCM 32

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Cch s dng hoa a t: o Trn hi Vit Nam: hnh 2.8 bn l mt v d v hoa a t trn hi Vit Nam. Cch c nh sau: LT: 0o55w-1995 c ngha l lch a t kho st nm 1995 l d= 0o55 W, hng nm khng thay i. Hnh 2.8: Hoa a t trn VN Chart o Trn hi Anh: hnh 2.9 bn l mt v d hoa a t n gin trn BA chart. Cch c nh sau: Mag Var 2o05W 1990 (4W) c ngha l lch a t kho st ti vng bin ny nm 1990 l d=2o05w, thay i hng nm l 4W. Hnh 2.9: Hoa a t trn BA Chart

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Da vo hoa a t, ngi ta c th tnh lch a t ti mt thi im no theo cng thc sau: Vnm tnh = Vnm kho st ( nm tnh nm kho st) bin thin hng nm

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Trong cng thc tnh trn, nu lch ang tng th mang du +, nu lch ang gim th mang du -. Tng c ngha l kinh tuyn a t ngy cng lch xa kinh tuyn bc tht, cn gim th ngc li, kinh tuyn a t ngy cng di dch chuyn li gn kinh tuyn bc tht. Nu nh khng c s tc ng ca cc t trng khc th kim la bn t s ch hng bc a t ( tc l trng vi kinh tuyn a t).

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Phn trn cng ca Hoa a t l ch hng Bc tht ( trng vi vch 0o ca vng trn ngoi).

ng nh du hng Bc a t ( trng vi vch 0o ca vng trn bn trong ). y l hng m la bn s ch ( ging nh trong hi ).

lch a t c nh du tm Hoa a t. Trn ng nh du hng Bc a t. y, lch kho st nm 1999 l 12o30W.

bin thin hng nm ca lch a t. y, bin thin hng nm l 2W, ngha l lch thm 2 na v hng ty mi nm, tc lch a t ang tng.

Hnh 2.10: Gii thch mt hoa a t trn BA chart

2.4 BN CC YU T A T: lch a t, t nghing, phn lc bng, phn lc thng ng u l cc yu t a t. Trn bn , ni cc im c cng tr s, cng mt yu t thnh nhng ng ng tr, tc l ta c hnh cc yu t a t. ng ng tr lch a t gi l ng ng t thin, ng ng tr t nghing gi l ng ng t nghing. ng ng tr ca phn lc bng v phn lc thng ng gi l ng ng t lc bng v ng ng t lc thng ng. Nhng vng m t lc c bin thin t ngt s lm cho lch a t thay i ln, trn bn s c biu th bng cc ng m nt v ghi gi tr lch a t ( c khi gi tr ny ln n hng chc ). Khi tu hnh trnh qua nhng khu vc ny th ngi s quan hng hi phi ht sc lu nu s dng la bn t.

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Hnh 2.11: Bn lch a t trn Tri t n, 2010

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Hnh 2.12: Bn cc ng ng t nghing

Hnh 2.13: Bn cc ng ng t lc bng TRN ANH NGN TRNG I HC GTVT TPHCM 36

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LA BN T HNG HI PHN BA: LA BN T HNG HI, CU TO V NGUYN L LM VIC 3.1 S LC LCH S LA BN T: La bn t l mt thit b hng hi c tc dng dng ch hng i v xc nh v tr tu trn bin. Cn c vo tnh cht nh hng ca thnh phn nhy cm theo hng kinh tuyn t. Con ngi li dng tnh cht ny ch to la bn t u tin vo cui th k XII. La bn c cu to gm mt tm st t gn vo mt chic phao, c th vo trong mt chu nc. u th k XIV, cu to la bn t c thay i. Kim t ca la bn c gn vo mt chic phao. C phao v kim t c trn mt nh kim tr thng ng. Trn mt phao c gn thm mt vnh trn bng giy hoc bng ng, trn c chia hng theo tng ca v tng t 0 n 360. Ton b h thng kim t c th vo mt chu dung dch gm cn v nc ct. Cui th k XV, cc nh khoa hc hng hi pht hin ra kim la bn khng ch chnh xc theo hng bc, nam tht m ch lch i mt gc, gc c gi l lch a t. Cui th k XVIII cng vi s pht trin ca ngnh ng tu bng st thp. La bn t c trang b trn tu, cc nh hng hi pht hin ra la bn ch hng mang sai s ln. Nguyn nhn gy ra sai s la bn l do nh hng ca t trng st thp trn tu tc dng vo kim la bn lm kim la bn ch lch khi kinh tuyn t mt gc, gc ny gi l lch ring la bn. kh bt gc lch ny, ngi ta a thm cc thit b kh vo thn la bn. Hin nay trn cc tu hin i, ngoi la bn t trn tu cn c trang b thm nhiu thit b ch hng hin i khc nh: la bn con quay, h thng nh v ton cu GPS, h thng SATELLITE COMPASS, hot ng vi chnh xc cao, song iu khng lm gim vai tr ca la bn t trn tu bin. Do u im c bit l tin cy rt cao nn la bn t c cc nh hng hi gi l la bn chun. Nu thiu la bn chun trn tu, theo quy phm ca ng kim hng hi th tu khng in kin chy bin. Cng vi s pht trin ca ngnh hng hi, la bn t ngy cng pht trin khng ngng. La bn t truyn mt s ra i c s dng vo ngnh hng hi. N c tcdng truyn ch s hng i ca la bn ti my li t ng t ng iu khin tu. TRN ANH NGN TRNG I HC GTVT TPHCM 37

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c im ca la bn t trang b trn tu bin Vit Nam gm nhiu loi Nht, Lin X, c, Trung Quc v.v. V cu to la bn c bn ging nhau, cn cc thit b kh ty theo tng loi la bn, tng nc sn xut c b tr khc nhau.

Hnh 3.1: S dng la bn t trong chart works 3.2 PHN LOI LA BN T: a. La bn chun: Lp t l thin trn nc bung li dung ch hng i ca tu v o hng ngm ca mc tiu. V lp t trn nc bung li, t chu nh hng ca st thp trn tu, lch tng i nh nn gi l la bn chun.

Hnh 3.2: Mt la bn chun c lp t trn ng centre line trn o kh ( monkey island). TRN ANH NGN TRNG I HC GTVT TPHCM 38

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LA BN T HNG HI b. La bn li: c lp t trong bung li chuyn dng ch hng li. Hin nay c nhiu tu dng mt phn nh ca la bn con quay li, ng thi dng thit b phn chiu la bn chun t nc bung li (hnh 3.4) xung bung li i chiu vi la bn con quay. Do , la bn t dng li t xut hin trn tu bin ngy nay.

Hnh 3.3: La bn li v v s b tr ca n trong bung li

Hnh 3.4: S dng la bn chun trn nc bung li lm la bn i chiu trong bung li c. La bn t s c: c lp t gn tay li s c dng li khi s dng my li s c. Hin nay nhiu tu s dng mt la bn phn nh ca la bn con quay lm la bn s c. TRN ANH NGN TRNG I HC GTVT TPHCM 39

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LA BN T HNG HI d. La bn xung cu sinh: L mt loi la bn t nh trang b cho xung cu sinh c gi v c n du km theo, du trong n s dng c 10 ting ng h.

Hnh 3.5: Cc kiu la bn xung cu sinh 3.3 CU TO LA BN T HNG HI: nc ta hin nay cc phng tin vn ti trn bin cng nh cc tu khai thc c bin c nhp t rt nhiu nc. Trn cc con tu nh vy u c trang b la bn t hng hi, la bn ca mi nc c kt cu khng hon ton ging nhau. Song v mt nguyn l lm vic, vt liu ch to v l thuyt kh lch v c bn l ging nhau. Di y s m t cu to c bn nht ca mt la bn t hng hi. Trong c mt s khi nim lin quan n cc dng c v thit b dng cho vic kh lch la bn t s c ni s qua, cn tc dng ca chng nh th no s c phn tch r nhng phn sau.

Hnh 3.6: Mt la bn t hng hi hin i c s dng lm la bn chun trn cc tu bin ngy nay.

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LA BN T HNG HI Nguyn l chnh ca la bn t dng trong lnh vc hng hi ngy nay khng khc g vi la bn c xa. N bao gm mt kim t ha hoc mt t hp cc kim t ha vnh cu ( permanent magnetized needles) cho php quay trn trn mt phng chn tri. S vt tri ca cc la bn ngy nay l kt qu ca s hiu bit tt hn v quy lut ca t trng, m cc quy lut ny chi phi cch thc hot ng ca la bn v cng do cu trc ca la bn chnh xc hn. Phn di y s m t cc thnh phn chnh yu ca l bn theo tiu chun hi qun M.

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Hnh 3.7: Cu to v cc b phn ca chn la bn t hng hi - Mt la bn t hon chnh gm hai b phn chnh l: chn la bn v chu la bn. 3.3.1 Chn la bn: - Chn la bn dng chu la bn v cha cc thanh nam chm dng hiu chnh lch, c ch to bng loi vt liu phi t tnh. - Hai bn tri v phi ca chn c hai qu cu st non, t trn hai vai la bn, dng kh mt phn lch la bn, tm ca hai qu cu ny v kim nam chm trong la bn nm trn cng mt mt phng. (xem hnh 3.7) TRN ANH NGN TRNG I HC GTVT TPHCM 41

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LA BN T HNG HI Trn nh chn la bn c np la bn lm bng ng c ca pha trc v pha sau, bn trong c lp mt n du s dng phng khi hng n in. Bn trong ngay ng tm pha di chu la bn c mt ng ng thng ng , dng lp thanh nam chm ng kh lch nghing, trong c b phn iu chnh nng h thanh nam chm bng dy xch. ngay phi trc chn la bn c lp mt ng ng trong c lp mt thanh st non dng kh lch do ng khi v cc tr thng ng sinh ra gi l thanh st Flinder. Trong chn la bn c lp mt bng n in c b phn iu chnh sng v cng tc t bn ngoi. Phn pha di chn c ca, trong t gi gm nhiu l ngang t cc thanh nam chm kh lch.

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3.3.2 Chu la bn:

Hnh 3.8: Hnh dng bn ngoi ca chu la bn Ton b chu la bn c t trn mt gi chuyn ng t do gi cho la bn lun lun cn bng khi tu thuyn lc b. Chu v gi la bn cng c t trn chn la bn, trong cha tt c nhng g cn thit iu chnh lch v chiu sng cho la bn (xem hnh 3.8). Cu to bn trong chu la bn kh phc tp gm cc b phn nh sau: a khc ( a la bn), kim nam chm, qu ni bng ng, b trc, tr , chu, mt thy tinh y, b phn n hi, vt i trng... ( xem hnh 3.9). Di y s trnh by mt s b phn chnh ca chu la bn:

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Hnh 3.9: Cu to bn trong chu la bn A. Kim nam chm: Cc kim nam chm cng vi t trng Tri t to ra lc ch hng ca la bn. Nhng kiu gn y nht c hai nam chm song song vi nhau ( hoc c c mt h thng cc kim nam chm xp song song vi nhau nh la bn ca Nga), kiu c hn th c 4 nam chm. B. a la bn: hoc vnh nhm c dng hnh vng c gn lin vi cc nam chm v c chia t 0o n 360o theo chiu kim ng h, bt u ti im N ( bc) nh ta thy hnh 3.8.

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Hnh 3.10: Cc b phn chnh ca a la bn C. Thn chu la bn: bao gm ngng t kim nam chm, chu ng cht lng, vch ch hng la bn ( lubbersline). Chu la bn c lm kim loi khng TRN ANH NGN TRNG I HC GTVT TPHCM 43

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LA BN T HNG HI mang t tnh v nng duy tr hp l trng thi nm ngang khi tu nghing hoc to ra mt lc dc theo phng dy di h tr cho thit b ny. Chu la bn c lp t trn vng cc-ng cho php duy tr theo phng ngang ca n. Phng php lp t ny to ra s bo v thch hp t cc chn ng c hc. D. Dung dch la bn: Dung dch la bn dng gim nh hng ca trng lc, t gim nh hng ca ma st trn cht ngng ly phng v v cng gim nh hng chao o ca a la bn. Phng php lp t a la bn l c gng lm cho n gn vi phng nm ngang. Dung dch la bn trong nhng loi la bn gn y nht l mt loi du c bit gi l Varsol. N c s dng bi v nht ca n duy tr n nh hp l khi nhit gim. cc la bn c hn ngi ta dng dung dch cn lm dung dch la bn. E. a phao la bn: a phao la bn hay hp khng kh, c s dng gim hn na nh hng ca trng lng v v th gim ma st trn ngng phng v. S kt hp gia phao v dung dch la bn s gim c nh hng ca trng lng khong khong 97-98%. F. Mng xp gin n: Mng xp gin n cho php cho php chu la bn duy tr thch hp hn kh la bn gin n v nhit thay i.

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Hu ht cc la bn u bao gm cc b phn chnh ny, ch khc nhau v kch thc, chi tit v vic lp t. Tt c cc b phn ca la bn c lm bng kim loi khng mang t tnh, tr nam chm v dng c kh lch. 3.3.3 Cc thanh nam chm v st non dng kh lch la bn t: - Cc thanh nam chm vnh cu c dng kh lch bn vng v lch nghing, chng c ng trong hp g. Vt liu ch to nam chm kh l hp kim c bit, c lc khng t ln, khong vi trm Oe. Do n c tnh t hoa d cao v t thay i t tnh theo thi gian s dng. Tt c cc thanh kh u c sn hai mu, na u bc sn mu , cn na u nam sn mu en hoc trng. o Cc vt liu st t cng nh cc thanh kh lch bn vng, kh lchtu nghing v h thng kim t ca mt s la bn. Cc loi nam chm ny c ch to bng thp Vonfram, thp Crm, thp Coban v mt s hp kim c bit khc, cc cht ny c lc khng t ln ti 100 Oe. TRN ANH NGN TRNG I HC GTVT TPHCM

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LA BN T HNG HI o Ngi ta thng ch to cc thi nam chm c tit din trn hoc vung, kch thc tit din rt nh so vi chiu di ca chng , u bc sn mu , u nam sn mu en hoc trng. M men t ca thanh nam chm c th c ghi ngay trn thn thanh nam chm cng vi nm sn sut, s liu xut xng. Cc thanh nam chm kh lch c m men t rt ln c th t ti 35000 n v C.G.S.M ty theo tng nc sn xut, ty theo khong cch t thanh kh vi mt s la bn. o ch to nam chm c m men t ln ngi ta tin hnh ch to st t v cho t ha c bit. u tin ngi ta em ti bng cch nung chng ln 800c - 1200c (nung ti nhit no l ty thuc vo loi hp kim ch to thanh nam chm). Sau b nhanh chng ra ngoi khng kh hoc cho vo nc vo du (cho vo loi mi trng no ty loi hp kim). Sau khi ti xong, cc thanh nam chm c em lm n nh cu to bng cch luc chng trong nc si (100C) . Bng cch ny m bo n nh thnh phn hoa hc ca thanh nhanh hn so vi nhiu phng php khc. Mt gi luc thanh st t nh vy c tc dng bng thng ha ngoi khng kh bng my nm. o Sau khi n nh cu to ngi ta em t ha chng. t ha c chng, vi thp Vonfram v thp Crm, cng t trng t ha phi t ti 400 Oe n 500 Oe , cn thp Coban th phi t 1000 Oe n 1500 Oe. o Sau khi t ha xong ngi ta em nam chm i n nh t tnh, tc l loi tr cc t trng cc b ny sinh trong cc gi u tin. Mt khc n nh t tnh cn c tc dng lm cho thanh nam chm t nhy cm vi cc dao ng c hc v cc t trng bn ngoi, nh th cng c ngha l n nh c m men t ca thanh nam chm . o n nh t hay cn gi l gi t c ngi ta thc hin bng cch t thanh nam chm vo trong mt cun dy c dng in xoay chiu chy qua. Tn s dao ng ca dng in c chn tng ng vi cc pha dao ng in hoc dao ng c hc trn tu thng tc dng vo la bn. Sau khi cho dng in vo ngi ta dn dn gim dng in v 0. o Bng cch n nh nh vy cc thanh nam chm s c kh nng t nhy cm vi cc hin tng va p, rung ng. M men t ca chng gi c c nh khi bin dao ng nhit ti 30c v khi cng t trng ngoi thay i ti 2 Oe ng vi nam chm Vonfram v Crm , ti 3 Oe ng vi nam chm Coban - Crm. o Cc thanh nam chm vnh cu thng c bo v trong hp g c bit, cc nam chm cch nhau khng nh hn 5 cm , ty theo m men t ln hay nh. Cc lc cng tn khc pha trong hp g khng nn dnh cc thanh nam chm vi nhau v lm nh th khi tch chng ra s TRN ANH NGN TRNG I HC GTVT TPHCM 45

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LA BN T HNG HI khng m bo c c nh t tnh theo thi gian. trnh hin tng r ngi ta thng sn cc bc mu , cc nam mu xanh... khng nn nam chm ni c nhit cao, ni c t trng cng ln hn 3 Oe. Cc thanh nam chm khng c t gn cc vt bng st. Cc thanh st non dng kh lch phn t, n c ch to bng hp kim st t c lc khng t nh ch khong t 1 n 3 Oe hoc nh hn na. Cc thi v tm c ch to bng st non c lc khng t nh hn 1,5 Oe cn qu cu c ch to bng gang c lc khng t nh hn 3,5 Oe. chng r ngi ta c th em sn mu xanh, en.v.v...Ty theo yu cu lp t m trong thit b ton b c th bao gm thanh kh lch phn t tit din ch nht hay qu cu vi cc kch thc khc nhau.

3.3.4 H thng quang hc hay h thng knh chiu vo bung li: H thng quang hc bao gm n chiu sng, knh bo v hai thu knh, knh sy v gng phn chiu. Mt s b phn nm trong ng thp pha di. Thn la bn ngi ta t pha trn (bung hoa tiu), h thng ng quang hc v gng phn chiu c phn di chui qua mt boong thng i xung bung iu khin vo pha trc tay li. Nh th hin trn hnh 3.11 gng phn chiu, phn chiu nh sng t bng n qua mt s i ti gng. Do hnh nh mt s c th hin trong gng rt r rng , ngha l cc vch chia v cc s tng ng th hin r rng rt d quan st. H thng ng quang hc c hai phn, phn trn c nh phn di c th di chuyn ln xung c nh c phn di ng ny m ta c th iu chnh v tr ca gng sao cho ph hp vi tm quan st ca ngi iu khin tu. Ngoi ra phn pha di cn c th xoay theo chiu thng ng, gng phn chiu c th thay i c gc nghing . Khi nhit ngoi khng kh thp hn vi th h thng gng xut hin cc git nc lm m mt knh. khc phc hin tng ny ngi ta gn vo h thng gng mt b phn sy. N c t trong ng ca h thng gng. c th lm c vic ny ngi ta cho dng in chy qua mt mng mng

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dn in trong sut gn gia hai tm knh. Thay i cng dng in i qua bng cch iu chnh chit p ta c nhit sy cn thit.-

in cung cp cho la bn l dng xoay chiu ca li in tu, c in th 127 Vn v 220 Vn, cn ngun d phng l 24 . gim hiu in th dng in xoay chiu ngi ta dng bin p cn vi dng in mt chiu dng bin tr. c ca vo h thng quang hc v ni t cc thit b kh thn la bn ngi ta lm hai ca m.

Hnh 3.11. H thng quang hc ca la bn: 1. Mt s, 2. n chiu sng mt s, 3. Knh bo v, 4. thu knh pha trn, 5. thn la bn, 6. thu knh pha di, 7. tm knh sy, 8. ng ca h thng quang hc, 9. gng phn chiu.

Hnh 3.12: Hnh dng chung ca mt la bn bao gm c h thng quang hc: 1. Ci hm ng quang hc, 2. tay gt c kh nng h ng quang hc, 4. chit p, 5. ca m thn di, 6. phn ng c nh, 7. hp chit p, 8. cng tc chit p, 9. phn trn ca ng di ng, 10. Vng ai gi ng, 11. phn ng di, 12. gng phn chiu, 13. cu nh v gng. TRN ANH NGN TRNG I HC GTVT TPHCM

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LA BN T HNG HI

- Ngi ta dng mt vng phng v (azimuth circle), mt vng ngm ( bearing circle), hoc mt dng c tng t quan st phng v ca cc thin th. Vng phng v ( hnh 3.13) l mt thit b m cc phn chnh ca n gm: mt gng lm nh, c ni bng bn l, v mt lng knh chn c lp t trn vng i in vi gng. Hnh 3.13: Vng phng v Hnh 3.14: Cu to vng phng v: 1. Khung dy vch chun 2. Khung khe ngm 3. Cc khung knh mu 4. Hnh tr v cu gn my o t lc Kolonga 5. Gi vng phng v 6. Lng knh Gi gn ln chu la bn l mt vnh trn bng ng thau, c ly gn vo vnh ca chu, trn vnh ny c cc inh vt gn khung vch chun, khung khe ngm v lng knh c hai cht gn cu C-lng-ga. Khung vch chun c ch to hnh ch nht gia c mt dy vch chun dy vch chun v tr nm trong mt phang thng ng, dy vch chun c nh v v ko cng bng hai inh vt. ngoi khung vch chun c mt khung knh hoc tm kim loi bo v, n c th nng ln hoc h xung c. Ngoi ra n cn c mt ci gng phc v cho vic ly phng v cao ln hn 26. Khe ngm l b phn dng ngm qua gia mt s v dy vch chun ti mc tiu, khe ngm gip cho ngi quan st nhn mc tiu hoc thin th c d dng khi thi tit xu hoc ban m. ly s ch trn mt s c chnh xc v nhanh, pha di khe ngm c mt lng knh, lng knh c tc dng phng i s ch ca mt s v cho ta ngay s ch phng v. C khe ngm ln dy vch chun phi nm trong mt phang thng ng i qua trng tm ca thnh phn nhy cm, ngi ta gi l mt phng ngm. TRN ANH NGN TRNG I HC GTVT TPHCM 48

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B phn ngm C-lng-ga c ch to bng ng thau, n gm c mt ng hnh tr lng vo my C-lng-ga, ng hnh tr c gn vi cu, gn vo vng phng v bng 4 inh vt, tm ca ng hnh tr khi gn vo vng phng v phi nm trong mt phng ngm .

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Knh mu, pha trc khe ngm c gn 2 hoc 3 mu hnh trn, n c tc dng lc mu, lm gim cng tia sng khi ta quan st mt tri hoc cc thin th quan st, ty theo mc chi khc nhau m ta chn knh mu cho ph hp.

3.4 NGUYN L LM VIC CA LA BN T: Nh ta bit, thnh phn nhy cm ca la bn l kim t. Khi kim la bn c treo t do th trc kim ca n s nh hng dc theo vc t cng a t trng ( ) ca tri t v ch theo mt phang kinh tuyn t. Nhng kim t treo t do khng th s dng lm thnh phn nhy cm cho la bn t hng hi c, bi v khi t nghing ln ( v cao ) xc nh hng nm ngang theo kim nghing rt kh khn. V vy, trong cc la bn t hng hi ngi ta tm cch treo thnh phn nhy cm sao cho n ch t ng xoay trong mt phang nm ngang, hnh 111 th hin mt kim t c treo nh vy. Trc kim to vi thnh phn nm ngang ca t trng tri t, ngha l vi kinh tuyn t mt gc . T trng Tri t trong khng gian kim nam chm chim ch c th coi l t trng u. Vi iu kin ny theo cng thc (1-9), kim t chu tc dng ca mt m men quay P: P=2lmHsin y 2l l chiu di kim t v m l t khi mi u kim t. Bit 2ml = M l m men t ca kim nam chm, do : (3-1) P=MHsin Hnh 3.15: Kim t di tc dng ca t trng

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LA BN T HNG HI Di tc dng ca m men quay P, kim nam chm xoay v pha kinh tuyn t. Xong do c ma st im cho nn kim s n nh trn hng khc vi kinh tuyn t. Theo cng thc trn th kim t ch n nh khi tc sin , do vy P=0. M men P gi l m men quay ca kim la bn t. Trong thc t do iu kin thnh phn nhy cm cha l tng cho nn vn tn ti mt lc ma st lm trit tiu bi m men quay P. Tc l kim t s n nh v tr ng vi mt gc nh, gc ny gi l gc i, k hiu l . Vy lc ma st trit tiu bi lc P l Q Q = MHsin Xt nh nn c th vit Q = MH hay (3-2) .

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La bn no c gc i cng nh th la bn y cng tt. o Mun gim i' ta lm gim lc ma st Q im t gi tr nh nht. t c yu cu ny ngi ta gn kim t vo y mt chic phao kn nc bng nha hoc bng ng, sau th chng vo dung dch cn v nc ct. Ton b thnh phn nhy cm c trn mt kim tr. nh kim tr v ngi ta gn kim loi cng. Vi iu kin hot ng nh trn lc ma st t gi tr nh nht. o Mt khc gim gc i' ta tng mmen t ca kim nam chm, bng cch ngi ta ch to kim t khng phi l mt thanh nam chm m bng mt cp hay nhiu cp thanh nam chm t song song, cng cc, cng t lc, i xng qua trng tm kim la bn. H thng nam chm nh vy s m bo m men t ln nht. o Gi tr mmen quay p ca kim la bn cn ph thuc vo v . Khi tu xch o th H ln nht nn P cng ln nht, khi tu v cc th H = 0, nn m men quay P nh nht v c gc i ln nht, la bn nh hng rt km . o Gc i' ca la bn hin i cho php A + 15o C. 02 khi H = 0,05 Oe, nhit

3.5 CM NG A T V LCH LA BN: Tri t c xem nh mt kim nam chm khng l, nn st trn qu t u b t ha. Tu bin ngy ny hu ht c ch to bng st thp nn cng b t ha v mang t tnh.V lc a t c phn thnh hai phn lc: phn lc bng TRN ANH NGN TRNG I HC GTVT TPHCM 50

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LA BN T HNG HI H v phn lc thng ng Z, nn tc dng t ha ca n ln con tu c th xem nh l tc dng t ha ca hai phn lc a t H v Z. Do , khi chy tu trn nhng v v hng i khc nhau th trng thi t tnh ca con tu cng khc nhau.

Hnh 3.16: Trng thi t tnh ca con tu bin i theo hng i v v Trong thnh phn cu to nn con tu, cng c hai loi st non v st gi. Sau khi b a t trng t ha th st gi c t tnh vnh cu, st non th ty theo hng mi tu v v t khc nhau m c t tnh cm ng khc nhau. V th nn t trng ca tu l t trng tng hp ca hai lc t trng st non v st gi. Kim nam chm ca la bn nu ch b tc dng bi phn lc bng H ca a t trng th n c th ch ng hng Bc a t. Nhng v nh hng ca t trng tu, nn n c th lch i mt gc nht nh. Gc lch gia hng Bc la bn v hng Bc a t gi l lch ring la bn. K hiu l , ta c: o Nu hng Bc la bn lch v pha ng hng Bc a t th ta gi l lch ng hoc dng, o Nu hng Bc la bn lch v phi ty hng Bc a t th ta gi l lch ty hoc m. Nh vy ta c: Sai s la bn = lch a t + lch ring la bn (3-3)

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Hnh 3.17: S bin i ca hng i khi c sai s la bn

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LA BN T HNG HI 3.6 MT S CH KHI S DNG LA BN T HNG HI: a. Phng php kim tra chnh xc cng vic lp t la bn t: - Cc kim tra chnh xc ca cng vic lp t la bn t nh sau: o Cho tu chy trng thi cn bng, dng biu xch ngm vch chun la bn ( l vch c nh trn chu la bn biu th hng mi tu) xuyn qua ng trung tm ca ct cn cu pha trc, chng nm trn cng mt ng thng c ngha l la bn t chnh xc. o Nu chng khng nm trn cng mt ng thng th phi iu chnh bng cch tho vt c nh chn la bn, quay chn la bn qua li cho n khi ngm vch chun la bn v ng trung tm ca tu qua ct cn cu nm trn cng mt ng thng mi thi, sau xit cht vt c nh. o Trong trng hp ct cn cu ca tu l hnh ch mn hoc ch nhn th dng phng php s dng biu xch o gc mn ca ng trung tm hai chn ct cn cu. Nu gc mn ca hai chn ct bng nhau th la bn nm v tr chnh xc, nu khng, phi tin hnh hiu chnh. b. Cch th nhy ca la bn t: - Tu cp cu c nh, cc thit b trn tu v cc thit b c gii trn b gn tu cng khng hot ng, ghi li chnh xc hng i la bn trn vch chun ca la bn. - Dng mt thi nam chm nh a vo gn chu la bn ht kim nam chm la bn( a la bn) lch khi v tr cn bng ca n v pha tri hoc pha phi chng 2 n 30, sau a thi nam chm ra xa, quan st xem a la bn c tr v li v tr c khng, lch cho php khng qu 002, th c ngha l nhy ca la bn km, c th l b ca a c ma st ln. c. Cch kh bt kh trong chu la bn: - Bt kh trong chu la bn nh hng n chnh xc i vi hng i v phng v ca la bn, cho nn nu xut hin bt kh trong chu la bn cn phi kh b. - Cch lm n gin nh sau: t nghing chu la bn sao cho l thng chu la bn xoay ln trn, dng tuc-n-vt m np l, lc nh chu la bn cho bt kh trong chu thot ra l thng, sau thm nc vo cho y chu ri ng np l li. - Nu dung dch la bn l hn hp gia nc ct v cn,th trc khi cho thm dung dch vo, m bo dung dch khng b h, cn phi rt mt t dung dch c ra trn vi dung dch mi, nu sau khi trn m nc vn khng b vn trong khng b vn c, khng bin mu th l tt, v c th cho thm dung dch mi vo chu. PHN BN: TRN ANH NGN TRNG I HC GTVT TPHCM 52

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LA BN T HNG HI L LUN V LCH RING LA BN 4.1 KHI NIM T TRNG TU V LCH RING LA BN: a. Khi nim t trng tu: - Nu la bn t c trang b trn tu ng bng cc cht v t tnh ( hp kim nhm, nha, g...). Kim nam chm ca la bn lun ch ng kinh tuyn a t (Nd ), khng gy lch. Hin nay tt c cc tu chy bin u c ng bng st thp. St thp trn tu gm st t cng (st gi) v st t mm (st non). Cc cht st t trn tu b t ha bi t trng ca tri t to mt t trng tu. T trng tu ny lm thay i t trng ca tri t xung quanh con tu. Vy la bn t c t trn tu, di tc dng ca t trng tu lm kim la bn khng ch ng hng bc a t ( Nd ) m ch sang mt hng khc gi l bc la bn ( k hiu NL), ng i qua trc kim nam chm gi l kinh tuyn la bn ( hnh 3.17 ). Vy kinh tuyn la bn l giao tuyn ca mt phng nm ngang v mt phng thng ng i qua trc N -S ca kim la bn. Kinh tuyn la bn c chn lm mc tnh hng i la bn v phng v la bn.b. T tnh vnh cu ca con tu:

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Mt con tu ang ng mi hoc sa cha ln nm c nh trn mt hng trong t trng s mang t tnh vnh cu do p g, va chm,... Sau khi h thy ngun t tnh ny s b thay i v cui cng n s gi li c trng thi t tnh n nh nh l mt nam chm vnh cu ca con tu.

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Thc t mt con tu mang t tnh vnh cu khng c ngha l n khng th kt np thm t cm ng khi t n trong t trng ca Tri t. T cm ng sinh ra bt k mt thanh st non no - ph thuc vo tnh nng ca cng t trng, s sp xp ca st non, cng nh hnh dng v kch thc ca n t trong t trng. T tnh ny c th lm tng hoc gim t tnh vnh cu sn c trong tu. N ph thuc vo con tu nh hng nh th no trong t trng.Vi st mm hn n s b t ha d dng hn bi t trng Tri t v n cng s d mt t tnh hn khi ra khi t trng .

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Hnh 4.1: S bin i t trng vnh cu ca tu ng bng st thp trong qu trnh ng tu vi mi tu nhng hng khc nhau. T tnh ca con tu khc nhau trong cc cu trc ca n, iu ny c khuynh hng lm thay i t tnh ging nh to ra l do chy tu, do chn ng hoc do tui tc. Nhng n khng thay i tc th nh t trng cm ng, do n c gi l t trng vnh cu ph. Bt k lc no t tnh ny l mt phn ca t trng vnh cu v phi thng xuyn c kh, bi cc nam chm kh. y l nguyn nhn chnh gy ra lch la bn. Lc ny, t trng

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vnh cu s bao gm t trng vnh cu ph v t trng vnh cu hin ti ca con tu. Cui cng t tnh ca con tu l s kt hp gia t trng vnh cu, t trng ph v t trng cm ng.V th khi b va p, hn in, chn ng, thay i cng t trng... s lm thay i trng thi t v do kt qu ca vic kh t cng thay i.

Hnh 4.2: S thay i trng thi t ca con tu theo hng i v v c. T tnh cm ng ca con tu v tc dng ca n i vi la bn:

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T trng cm ng thay i theo ln ca t trng xung quanh, khi lng ca kim loi v s sp xp ca kim loi trong t trng. Do cng a t trng thay i trn b mt qu t nn t trng cm ng ca con tu s thay i theo v , hng mi tu v s nghing ca con tu.

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Vi mt con tu cn bng mi li, th t trng cm ng do n gy ra: nu khng c ch hng qua la bn th n s to ra mt lch m th ca n l mt ng cong lch bn vng. iu ny l ng, bi v ln v tnh phn cc ca t cm ng thng ng ch thay i theo v t v nghing ca con tu m khng thay i theo hng i ca con tu. Do , min l con tu cng v t th nh hng do s dao ng ca t cm ng thng ng i vi la bn cng tng t nh t tnh vnh cu i vi la bn.

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Trng hp cc thanh st non nm ngang, la bn, la bn cm, la bn con quay sp xp khng cn xng vi nhau v mt vt l cng to ra t tnh cm ng v TRN ANH NGN TRNG I HC GTVT TPHCM 55

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gy ra sai s A i vi la bn, hoc do cc sai s trong vic tnh ton phng v mt tri, thi gian quan st, gc nghing ca con tu cng to ra sai s thm vo sai s A la bn. Bn cht ln v tnh phn cc do hiu ng cm ng gy ra ph thuc s b tr, cu trc cn xng hay khng cn xng ca con tu, v tr lp t hp la bn, cng a t trng, v gc nghing ca con tu. d. lch ring la bn: lch ring la bn gc hp bi phn bc ca kinh tuyn a t v phn bc ca kinh tuyn la bn. 4.2 H PHNG TRNH POISSON: 4.2.1 Khi nim h trc ta tu: T th k 18, khi tu thuyn ng bng st thp pht trin. La bn t c trang b trn tu, cc nh hng hi pht hin ra la bn c lch rt ln. Nh bc hc Poisson ngi Php nghin cu v tm ra phng trnh biu th lc tc dng ca a t trng v t trng tu i vi la bn. Phng trnh y gi l Phng trnh Poisson. Phng trnh Poisson c xy dng trn h trc ta vung gc (hnh). Gc ta c t ti tm im ca la bn (n) trn tu vi 3 trc x, y, z c gi l h trc ta tu. o Trc x nm trng vi trc dc tu, hng v pha mi mang du dng (+), hng sau li ly du tr (-). o Trc y nm trng vi trc ngang tu, hng bn phi ly du cng (+), bn tri ly du tr (-), cng (+), hng ln trn ly du (-). Hnh 4.3: H trc ta tu o Trc z nm trng vi trc thng ng ca tu, hng xung di ly du

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Gi thit tm im la bn im (n) coi nh l mt n v dng t khi, nm trong t trng u ca Tri t phn tch lc tc dng khi tu v tr cn bng.

4.2.2 Phn tch lc tc dng ca a t trng theo h trc ta tu: Lc a t c tc dng trc tip v tc dng gin tip i i vi la bn: o Tc dng trc tip l do phn lc nm ngang H ca a t trng lun tc dng vo kim la bn lm u bc kim nam chm lun ch ng hng bc a t Nd. o Tc dng gin tip l lc a t lun t ha st thp trn tu to ra mt t trng mi tc dng vo kim la bn gy lch ring . tnh lc a t trn 3 trc tu, th cn phi phn tch theo h ta trc tu: o Trong ( hnh bn) cng a t trng T qua im n trung tm ca la bn c phn thnh phn lc thng ng Z v phn lc bng H, v H li c phn tch thnh phn lc X theo trc dc tu v phn lc Y theo trc ngang tu. o V hng mi tu c th biu th bng hng i a t HD, gc kp gia hng bc a t v mi tu tnh t 00 n 3600 theo chiu kim ng h, nn phn lc X v Y c th vit thnh hm s sin v cos ca hng i a t. du ca X v Y trn cc hng i khc nhau bin i ph hp vi yu cu v du ca trc ta , nn ta phi thm du + ng trc hm s cos, v du trc hm s sin. o Do , lc a t c th phn thnh cc phn lc:

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Suy ra:

(4-1)

Nh th lc a t c phn thnh 3 phn lc X, Y, Z, phn bit vi nhau, tc dng trc tip v gin tip i vi la bn. T cng thc trn ta thy: phn lc X v Y khng nhng bin i theo v a t m cn bin i theo hng i ca tu, phn lc Z ch bin i theo v a t.

Hnh 4.5: S thay i phn lc X v Y theo hng i a t 4.2.3 Tc dng ca st thp trn tu i vi la bn: a. Khi nim: St thp trn tu sau khi b t ha, sc t ca n tc dng vo la bn, sinh ra lch la bn. Nhng im c bn v st thp trn tu i vi la bn: o a t trng l mt t trng yu, lc tc dng ca st thp b t ha i vi la bn t l thun vi lc a t t ha st thp. TRN ANH NGN TRNG I HC GTVT TPHCM 58

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o Trng thi v v tr phn b ca st thp trn tu rt phc tp, v khng c quy lut, n gin ha vn t ha st thp, ta tng tng rng tt c st thp trnt tu l do v s thanh st thp di nm theo chiu dc, ngang v thng ng ca tu hp thnh. Nh th phn lc a t ch c th t ha st thp cng chiu vi n, ngha l: Phn lc X ch c th t ha st thp chiu dc, Phn lc Y ch c th t ha st thp chiu ngang, Phn lc Z ch c th t ha st thp chiu thng ng. Nh hnh 4.6, st thp chiu dc khi b t ha th ch cn xt tc dng t ha ca phn lc X i vi n, cn tc dng ca phn lc Y vung gc vi n th c th b qua. Di y ta s phn tch tc dng ln la bn ca 3 loi st thp: chiu dc, chiu ngang, v chiu thng ng. b. Tc dng ca st thp chiu dc i vi la bn: Tt c st non chiu dc u b phn lc X t ha. Sau khi b t ha th tc dng ca n i vi la bn t l thun vi phn lc a t X. Cho lX l lc tc dng ca st non chiu dc b t ha i vi la bn, trong l l h s st non chiu dc, do tnh t ha ca st non chiu dc, s lng st non chiu dc v v tr tng i ca n i vi la bn quyt nh. i vi mt chic tu nu nhng iu kin khng thay i th l c mt tr s c nh. Nu phn tch lc lX thnh phn lc aX, dX, gX theo 3 hng ca h trc ta tu ( hnh 4.7), th trong : o aX: lc dc sinh ra bi st non chiu dc, o dX: lc ngang sinh ra bi st non chiu dc, o gX: lc thng ng sinh ra bi st non chiu dc. Hnh 4.7 Hnh 4.6

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V 3 h s: a, d, g do l quyt nh c gi l nhng h s st non sinh ra bi st non chiu dc.

c. Tc dng ca st non chiu ngang i vi la bn: - Cng theo nguyn l trn, nhng st non chiu ngang sau khi b phn lc a t Y t ha, lc tc dng ca n i vi la bn cng t l thun vi lc Y, gi s bng mY, trong m gi l h s st non chiu ngang, n c nh ngha tng t nh h s st non chiu dc. - Nu phn lc mY c phn tch thnh 3 phn lc bY, eY v hY, trn 3 hng ca h trc ta tu (hnh 4.8), th trong : o bY: lc dc sinh ra bi st non chiu ngang. o eY: lc ngang sinh ra bi st non chiu ngang, o hY: lc thng ng sinh ra bi st non chiu ngang. - Trong : b, e, h do h s m quyt nh v c gi l nhng h s st non sinh Hnh 4.8 ra bi st non chiu ngang.

d. Tc dng ca st non chiu thng ng i vi la bn: - St non chiu thng ng sau khi b phn lc Z t ha cng c tc dng i vi la bn, gi s lc y la nZ, trong n c gi l h s st non chiu thng ng v cng c nh ngha nh trn. - Nu phn tch lc nZ thnh 3 phn lc cZ, fZ, kZ theo 3 hng ca h trc ta tu ( hnh 4.9), ta c: o cZ: lc dc sinh ra bi st non chiu thng ng. o fZ: lc ngang sinh ra bi st non chiu thng ng.

Hnh 4.9

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LA BN T HNG HI o kZ: lc thng ng sinh ra bi st non chiu thng ng. Trong : c, f, k do n quyt nh v c gi l nhng h s st non sinh ra bi st non chiu thng ng.

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e. Tc dng ca st gi i vi la bn: - Tu trong thi gian ng xng, hoc u ti mt ni trong thi gian di hoc g st, gia cng theo mt hng nht nh... th lm cho st gi trn tu c t tnh. T tnh y khng phi khng bin i, nhng n c th gi trong mt thi gian di, nn ta c th xem n l t tnh vnh cu. Sau khi st gi trn tu b t ha, ton b v tu ging nh mt nam chm vnh cu rt ln. - Lc tc dng ca t trng vnh cu do st gi to ra rt ln i vi la bn. Khi la bn v tr c nh th n khng bin i v tr s v hng tc dng. Hnh 4.10, lc Fp biu th lc tc dng ca st gi i vi la bn. - Phn tch lc Fp thnh 3 phn lc P, Q, R theo 3 hng ca h trc ta tu ( hnh 4.10), ta c: o P: lc dc sinh ra bi st gi, o Q: lc ngang sinh ra bi st gi, o R: lc thng ng sinh ra bi Hnh 4.10 st gi. - V st gi trn tu nhiu nn lc tc dng ca P, Q, R i vi la bn ln hn lc tc dng ca st non. 4.2.4 Phng trnh Poisson: - Theo kt qu phn tch trn, quy np tt c cc lc tc dng i vi la bn, ( hnh 4.11) ta c: o Lc tc dng i vi la bn trn trc X l : X, aX, bY, cZ, v P, o Lc tc dng i vi la bn trn trc Y l: Y, dX, eY, fZ v Q, o Lc tc dng i vi la bn trn trc Z l : Z, gX, hY, kZ

aX

Hnh 4.11 61

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LA BN T HNG HI v R. Gi X, Y, Z l hp lc tc dng i vi la bn trn 3 trc ta tu, ta c: H phng trnh: (4-2)

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Phng trnh ny ngi ta gi l phng trnh Poisson. Hnh 4.11, biu th cc lc tc dng i vi la bn theo phng trnh Poisson, khi tu trng thi cn bng. Lc Z khng gy ra lch nhng hp lc H ca X v Y c tc dng lm cho la bn ch hng bc, n lch phn lc bng ca a t H mt gc , chnh l lch ring ca la bn.

4.3 H S ST NON V CCH BIU DIN CC H S ST NON: 4.3.1 Dng n st non biu th cc h s st non: - Trong phng trnh Poisson ta c 9 h s st non biu th lc tc dng ca st non i vi la bn. d hiu ngha ca cc h s y, ta dng nhng n st non nhng v tr khc nhau xung quanh la bn, trc tip biu th cc h s st non, c th ha cc h s st non v dng c d dng trong thc t. - Nguyn tc ca vic dng n st non biu th cc h s st non l thay cc h s st non bng cc n st non sinh ra cng lc tc dng ln la bn. - Quan h v tr gia n st non v kim la bn c 3 trng hp, nh hnh 4.12: o La bn trn hng ca cc trc n st non, (a) o La bn trn hng thng gc ca mt u n st non, (b) o La bn trn ng trung trc ca n st non.(c) f

Hnh 4.12 vn tc dng ca n st non i vi la bn c n gin, ta tng tng rng n st non rt di, trong hai trng hp trn th ta ch xt lc tc dng ca u gn la bn m khng xt tc dng ca u xa la bn. Trong trng hp (c) th t cc hai u u c tc dng nh nhau i vi la bn. n gin trong qu trnh nghin cu ta t iu kin nh sau : o La bn c t trong mt phng ca tu. o T trng ni t la bn trn tu l t trng u, v tr kim la bn coi nh t mt n v t khi dng. TRN ANH NGN TRNG I HC GTVT TPHCM 62

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LA BN T HNG HI o Cc thi st t c biu din di dng s nam chm. o Tu nm v bc v i theo hng NW. Vi iu kin nh vy cc lc X , Y , z u c gi tr dng. Di y s phn tch cch biu th h s st non bng cc n st non.

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4.3.2 n st non biu th h s a - h s st non chiu dc sinh ra bi st non chiu dc - Trng hp 1: nh hnh 4.13 hai u ca n st non chiu dc cch u la bn. Sau khi n st non y b phn lc a t +X t ha, u v mi tu la cc N, u v li tu l cc S. V hai cc ca n cch u la bn nn hai cc ca n u c tc dng ln la bn. o Cc N ca n st non s tc dng mt lc y ln t aX0 bn. Nn a0 Nn a>0 Hnh 4.14 63

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LA BN T HNG HI st non theo hng i NW v chng minh trn hai hng i y c th dng chng biu th cho h s st non a dng v a m. Trn thc t bt c hng i no cng c th dng n st non biu th h s st non, n khng quan h n hng i ca tu. n st non chiu dc nh trong hnh 4.13, khi hng i ca tu thay i 3600, tuy du ca phn lc a t X c th thay i theo hng i nhng du ca ca n st non khng thay i, lun biu th h s a m. y l mt tnh cht quan trng trong vic biu th h s st non bng cc n st non m ta cn nm r.

-

-

aX0 Nn a0. Vy loi n st non ny biu th h s c dng.

cZ 0 Nn c0 Z>0 Nn c>0

Hnh 4.17 (a)

Hnh 4.17 (b) 65

TRN ANH NGN TRNG I HC GTVT TPHCM

66 -

LA BN T HNG HI Khi ta thay i v t Bc thnh Nam th nhng n st non biu th h s c vn gi nguyn tnh cht ca n.( hnh 4.18)

cZ >0 Z HW HE < HW Lc lch B B C C >0 < 0 0 Hng ca cc N ca thanh nam chm Hng mi tu Hng li tu Hng bn tri Hng bn phi

Khi kh lch nu khng c mc tiu hoc khng c la bn con quay so snh hng ngm th ch cn c my o t lc Kolong th cng c th dng phng php ny kh lch na vng, l u im ca phng php ny, nhng sau khi kh lch th khng th o c lch cn li, l khuyt im.

6.2.3 PHNG PHP DNG ST NON FLINDER KH LCH NA VNG PH THAY I THEO V : - Khi hiu chnh la bn ca tu vin dng ta dng nam chm vnh cu kh lch na vng do lc P v Q ca t trng vnh cu ca tu gy ra, nhng i vi lch do lc t trng cm ng ca tu cZ v fZ sinh ra, n bin i theo v t, nn phi dng st non Flinder kh. phn bit lch na vng do st gi gy ra gi l lch na vng chnh, cn lch do st non sinh ra gi l lch na vng ph. - Nguyn l c bn kh lc cZ: l dng lc cm ng, lc c1Z do st non Flinder sinh ra kh lc cm ng cZ do st non trn tu gy ra, nn c1Z v cZ phi c tr s bng nhau v nghch du, l l do ti sao st non Flinder phi t thng ng v cZ l lc tc dng theo chiu dc tu ca st non chiu thng ng. o Khi st non Flinder t trc la bn, theo quy tc xt du th biu th h s c1>0 c th kh h s st non ca tu c