Ta'rif: Garmonik nima?

Tebranish tahlilida, harmonic — bu asosiy chastotaning aniq butun son karrali bo'lgan chastota. Aylanuvchi mexanizmlarda asosiy chastota odatda val aylanish tezligi bo'lib, u 1-garmonik yoki 1×. The subsequent harmonics are integer multiples: 2× (twice shaft speed), 3× (three times), and so on. These frequencies are also called orders ishlash tezligidan, yoki sinxron garmoniklar chunki ular val aylanishi bilan aniq sinxronlashtirilgan.

For example, if a motor operates at 1,800 RPM (30 Hz), its harmonics appear at 60 Hz (2×), 90 Hz (3×), 120 Hz (4×), 150 Hz (5×), and so forth. The harmonic series is theoretically infinite, but in practice, amplitude decreases at higher orders and only the first several harmonics carry diagnostic information.

Garmonik chastota ta'rifi
fn = n × f1 = n × (RPM / 60)
where n = 1, 2, 3, 4… (harmonic order) and f₁ = shaft rotational frequency in Hz

Garmoniklar, quyi garmoniklar va sinxron bo'lmagan cho'qqilar

Harmonics are integer multiples of shaft speed (2×, 3×, 4×…). Sub-harmonics are fractional multiples (½×, ⅓×, ¼×) and always indicate severe mechanical problems. Sinxron bo'lmagan cho'qqilar — val tezligiga bog'liq bo'lmagan chastotalar, masalan podshipnik nosozlik chastotalariga, tishli uzatma mesh chastotalari, tarmoq chastotasi (50/60 Hz) yoki tabiiy chastotalar — va turli diagnostik yondashuvlarni talab qiladi. 3,57× RPM dagi cho'qqi garmonik EMAS; bu, ehtimol, podshipnik nosozligi chastotasidir.

Garmoniklar Nima Sababdan Hosil Bo'ladi?

To'liq chiziqli tizimda sof sinusoidal kuch ta'sirida (masalan, ideal muvozanatlashtirilgan, ideal tekislangan rotor ideal podshipniklarda) faqat 1× asosiy chastota namoyon bo'ladi. Haqiqiy mexanizmlar hech qachon mutlaqo chiziqli emas. Garmoniklar tebranish to'lqin shaklida sof sinusdan buzilish yuz berganda — tizim javobi non-linear yoki majburlash funksiyasining o'zi sinusoidal bo'lmagan hollarda paydo bo'ladi.

Matematik asos: Furye’ teoremasi

Furye’ teoremasi har qanday davriy to'lqin shakli — qanchalik murakkab bo'lmasin — asosiy chastota va uning butun sonli ko'paytmalarida sinusoidal to'lqinlar yig'indisiga ajratilishi mumkinligini, har biri o'ziga xos amplituda va fazaga ega ekanligini ta'kidlaydi. Tebranish analizatorlari tomonidan qo'llaniladigan FFT (Tez Furye Almashtirish) algoritmi ushbu ajratishni hisoblash yo'li bilan amalga oshiradi va signal garmonik tarkibini ochib beradi.

A pure sine wave has only a single frequency component. A square wave contains all odd harmonics (1×, 3×, 5×, 7×…) with amplitudes decreasing as 1/n. A sawtooth wave contains all harmonics with amplitudes decreasing as 1/n. The specific shape of the distortion determines which harmonics appear — this is what makes harmonic analysis so diagnostically powerful.

Garmoniklar Hosil Qiluvchi Fizik Mexanizmlar

  • To'lqin shaklining qirqilishi / kesilishi: Val harakati fizik jihatdan cheklanganda (podshipnik korpusi, ishqalanish kontakti), hosil bo'lgan to'lqin shakli qirqiladi va garmoniklar yuzaga keladi. Qirqilish qanchalik kuchli bo'lsa, garmoniklar shunchalik ko'p bo'ladi.
  • Assimetrik qattiqlik: If system stiffness differs between positive and negative halves of the vibration cycle (cracked shaft opening/closing, misalignment creating different tension/compression stiffness), even harmonics (2×, 4×, 6×) are generated.
  • Impact events: Davriy zarbalar (bo'sh murvat-gaykalar, podshipnik nuqsonli zarbalari) garmonik tarkibga juda boy bo'lgan o'tkir, qisqa muddatli to'lqin shakllarini hosil qiladi — xuddi barabanning tayoqchasi ko'plab yuqori tonlarni ishlab chiqarganidek.
  • Chiziqli bo'lmagan tiklash kuchlari: Qattiqlik ko'chish bilan o'zgarganda (o'zgaruvchan yuklanish ostidagi podshipniklar, bosqichli rezina tayanch muftalar), sinusoidal kuchga javob garmoniklar o'z ichiga oladi.
  • Parametrik qo'zg'alish: Tizim xossalari val tezligiga bog'liq chastotada davriy o'zgarganda, ular qo'zg'alish chastotasining garmoniklari va subgarmonikalarini hosil qilishi mumkin.
Asosiy Diagnostik Tamoyil

Qaysi garmoniklar mavjudligi, ularning nisbiy amplitudalari va qaysilari yo'qligi tahlilchiga qaysi fizik mexanizm chiziqli emaslikni keltirib chiqarayotganini aytib beradi. Tajribali tahlilchilar muayyan nosozlik mexanizmlarini aniqlash uchun faqat umumiy tebranish darajasini emas, balki spektrning to'liq garmonik tuzilishini ko'rib chiqadilar.

Nosozliklarning Batafsil Belgilari — Garmonik Naqshlar

1× Ustunlik — Muvozanatsizlik

Yuqori garmoniklar minimal bo'lganda 1× da ustun tepa — bu klassik belgi mass unbalance. Muvozanatsizlik kuchi o'z mohiyatiga ko'ra sinusoidal xarakterga ega (u val bilan birga 1× chastotada aylanadi) va chastota sohasida aniq bitta cho'qqi hosil qiladi.

Diagnostika tafsilotlari

  • Amplitude: Proportional to speed² (double speed → 4× amplitude) and proportional to unbalance mass
  • Phase: Barqaror, takrorlanadigan, bir qiymatli. Sinov og'irligi qo'shilishi bilan kutilganidek o'zgaradi — bu barcha balansirlash tartiblari
  • Direction: Asosan radial; 1× o'qli tebranish rotorda sezilarli konsol bo'lmasa past bo'ladi
  • Confirmation: Sinov og'irliklariga javob muvozanatsizlikni tasdiqlaydi. Agar 1× sinov og'irliklariga munosabat bildirmasa, egilgan val, ekssentrisite yoki rezonansni ko'rib chiqing
Barcha 1× Tebranish Muvozanatsizlik Emas

Bir qancha hollar balansirovka bilan bartaraf etib bo'lmaydigan yuqori 1× ni keltirib chiqaradi: egilgan val, val ekssentritsiteti, yaqinlik zondlarida elektr chiqishi, issiqlik ta'siridan vал egrilishi, muftaning ekssentritsiteti va resonance kuchaytirish. Balansirovka qilishga urinishdan oldin har doim tashxisni tasdiqlang.

2× Ustunligi — Noto'g'ri O'rnatish (Misalignment)

Kuchli 2-garmonik, ko'pincha 1× cho'qqisiga teng yoki undan oshib ketadigan amplituda bilan, valning noto'g'ri o'rnatilganligi (misalignment)ning asosiy ko'rsatkichi hisoblanadi. Noto'g'ri o'rnatish valni har bir aylanishda nosinusoidal yo'l bo'ylab harakatlanishga majbur qiladi, bu esa 2× va ba'zan yuqori garmonikalарни keltirib chiqaruvchi buzilishni hosil qiladi.

Burchakli va Parallel Noto'g'ri O'rnatish

  • Burchakli noto'g'ri o'rnatish: Shaft centerlines intersect at an angle at the coupling. Produces high 1× axial vibration. Phase across coupling shows ~180° shift in the axial direction.
  • Parallel (siljish) noto'g'ri o'rnatish: Shaft centerlines are parallel but offset. Produces high 2× radial vibration, often with 2× ≥ 1×. Severe cases generate 3× and 4×. Radial phase across coupling shows ~180° shift.
  • Combined: Amaliyotda ikkalasi odatda birga mavjud bo'lib, aralash diagnostik ko'rsatkichlar beradi.

The 2×/1× Ratio as a Diagnostic Indicator

2×/1× Ratio Ehtimoliy Holat Action
< 0.25 Odatiy; 2× aksariyat mashinalarda past darajada mavjud Hech qanday chora talab etilmaydi
0.25 – 0.50 Engil noto'g'ri o'rnatish mumkin; ba'zi muftа turlari uchun me'yoriy Tekislashni tekshiring; asosiy ko'rsatkichlar bilan solishtiring
0.50 – 1.00 Katta nosimmetrik o'rnatish (noto'g'ri tekislash) ehtimoli yuqori Lazerli aniq tekislashni amalga oshiring
> 1.00 Severe misalignment; 2× exceeds 1× Shoshilinch — tekislashni qayta bajaring; muftani va quvur zo'riqishini tekshiring

Ko'p garmonikalar — mexanik bo'shashlik

Ko'p sonli qator running speed harmonics (1×, 2×, 3×, 4×, 5×… to 10× or more) indicate mexanik bo'shashish. Zarbalar, taqillatishlar va chiziqli bo'lmagan kontakt/ajralish sikllari to'lqin shaklining kuchli buzilishini keltirib chiqaradi va bu ko'plab garmonik tashkil etuvchilarga parchalanadi.

Bo'shashlikning uch turi

  • A turi — Konstruktiv: Loose machine-to-foundation connection (soft foot, cracked base, loose anchor bolts). Produces directional 1× (higher in the loose direction). Key test: tighten/loosen individual bolts while monitoring 1× amplitude.
  • B turi — Komponent: Loose bearing liner in cap, loose cap on housing, excessive bearing clearance. Produces a family of harmonics, often with sub-harmonics (½×). Sub-harmonics are the key differentiator from misalignment (looseness, not misalignment, produces sub-harmonics).
  • S turi — Podshipnik o'rindig'i: Valda turbin g'ildiragining bo'shashishi, mufta vtulkasining bo'shashishi, rotorning sakrashiga yo'l qo'yadigan haddan tashqari podshipnik bo'shlig'i. Keng polosali shovqin sathining ko'tarilishi bilan birga ko'plab garmonikalar hosil qiladi.
Pastki garmonikalar: bo'shashlikning xarakterli belgisi

The presence of sub-harmonics (½×, ⅓×) is the most reliable differentiator between looseness and misalignment. Misalignment generates 2× and 3× but rarely produces sub-harmonics. Looseness (Types B and C) characteristically generates ½× because the rotor contacts one side of the bearing on one half-revolution and bounces to the other on the next — creating a pattern that repeats every two revolutions, hence ½×.

Garmonikalar hosil qiladigan boshqa holatlar

Bent Shaft

Produces both 1× and 2× vibration with high axial component. Unlike misalignment, a bent shaft shows 1× that cannot be corrected by balancing (geometric eccentricity, not mass distribution) and ~180° axial phase difference between shaft ends. The 2× comes from asymmetric stiffness as the bend opens and closes during rotation.

Qaytma harakat mexanizmlari

Dvigatellar, kompressorlar va qaytma harakat mexanizmlari o'z tabiatiga ko'ra boy garmonik spektr hosil qiladi, chunki piston/tirsakli val harakati asosan sinusoidal emas. Garmonik naqsh silindrlar soni, o't olish tartibi va takt turi (2 taktli va 4 taktli)ga bog'liq.

Rotor Rub

A partial rub (contact for a portion of each revolution) produces many high-order harmonics — sometimes to 10×, 20×, or more. A full annular rub (continuous 360° contact) generates dominant sub-harmonics (½×, ⅓×, ¼×) through reverse precession mechanisms.

Elektr motorlaridagi elektr muammolari

AC motorlar val tezligidan mustaqil ravishda tarmoq chastotasining (50 yoki 60 Gts) kattallariga mos tebranish hosil qiladi. Eng keng tarqalgani 2× tarmoq chastotasidir (50 Gts tizimlarda 100 Gts, 60 Gts tizimlarda 120 Gts). Bu val tezligining garmonikasi EMAS — bu tarmoq chastotasining garmonikasi bo'lib, elektr va mexanik tebranishni farqlashning asosiy kaliti hisoblanadi. power cut test hal qiluvchi ahamiyatga ega: elektr tebranishi quvvat uzilganda darhol to'xtaydi, mexanik tebranish esa inersiya bo'yicha to'xtash jarayonida davom etadi.

Rotor bar nuqsonlari qutb o'tish chastotasi oralig'ida 1× atrofida yon chastota komponentlarini hosil qiladi ("slip frequency × number of poles). These sidebands are very close to 1× (within 1–5 Hz), requiring high-resolution zoom FFT tahlil qilish uchun aniqlanadi.

Sinxron bo'lmagan chastotalar — haqiqiy garmonikalar emas

Bir necha muhim chastotalar ba'zida garmonikalar bilan adashtirilib yuboriladi, ammo ular aslida val tezligidan mustaqil:

Frequency Type Formula AYT bilan bog'liqligi Notes
Podshipnik nuqsoni chastotalari BPFO, BPFI, BSF, FTF Non-integer multiples (e.g. 3.57×, 5.43×) Always non-synchronous; depends on bearing geometry
Tishli juftlashma chastotasi GMF = #tish × AYT Butun son, lekin juda yuqori tartibli Texnik jihatdan garmonik, ammo alohida tahlil qilinadi
Parra/qanot o'tishi BPF = #parracha × AYD Butun son karrali Normal; haddan ortiq amplituda muammoni bildiradi
Line frequency FL = 50 yoki 60 Hz AYT bilan bog'liq emas Elektr tabiatli; quvvat uzilganda yo'qoladi
Tabiiy chastotalar fn = √(k/m)/2π Doimiy; AYT bilan bog'liq emas Tezlik o'zgarishidan qat'i nazar doimiy chastota
Tasma chastotalari fbelt = RPM×π×D/L Pastsinxron (< val tezligi) Belt frequency and its harmonics 2×, 3×, 4× BF

Tahlil qo'llanmasi — Garmonik naqshlarni qanday talqin qilish kerak

1-qadam: Asosiy chastotani (1×) aniqlash

Val aylanish tezligiga mos keladigan 1× cho'qqini toping. Tekshirish uchun tachometer yoki elektr motor plankasidan foydalaning. O'zgaruvchan tezlikli mashinalarda 1× har bir o'lchov uchun aniq aniqlanishi shart.

2-qadam: Barcha cho'qqilarni kataloglashtirish

Har bir muhim cho'qqi uchun aniqlang: u 1×ning aniq butun son kattaligimi (haqiqiy garmonik)? Kasr son kattaligimi (subgarmonik)? Val tezligi bilan bog'liq emasmi (nosinkron)? Samaradorlik uchun analizatorning garmonik kursor funksiyalaridan foydalaning.

3-qadam: Amplituda naqshini tekshirish

  • Qaysi garmonik ustunlik qiladi? → Muayyan nosozlikka ishora qiladi
  • Nechta garmonik mavjud? → Ko'proq = buzilish jiddiyligi yuqori
  • Does 2× exceed 1×? → Likely misalignment
  • Subgarmoniklar mavjudmi? → Bo'shashish, ishqalanish yoki oil whirl
  • Amplituda tartib bilan kamayib bormoqdami (1/n pasayish)? → Bo'shashish uchun xarakterli

4-qadam: Yo'nalishlilikni tekshirish

  • Yuqori radial, past o'qiy: Muvozanatsizlik yoki bo'shashish
  • High axial: Noto'g'ri tekislash (ayniqsa burchakli) yoki egilgan val
  • Yo'nalishli radial: Konstruktiv bo'shashish (bo'shashgan yo'nalishda yuqori)

5-qadam: Vaqt o'tishi bilan tendentsiyani kuzatish

  • Garmonik amplitudalar ortib bormoqdami? → Nosozlik rivojlanmoqda
  • Yangi garmoniklar paydo bo'lmoqdami? → Yangi nosozlik mexanizmi shakllanmoqda
  • Shovqin tubsatig'i oshmoqdami? → Umumiy eskirish yoki so'nggi bosqich ishdan chiqishi

6-qadam: Faza ma'lumotlari bilan bog'lash

  • Unbalance: 1× fazasi barqaror va takrorlanadigan
  • Misalignment: 1× or 2× phase shows ~180° across coupling
  • Looseness: Faza beqaror, o'lchashlar orasida tasodifiy siljishi mumkin

Amaliyotda barcha oltita bosqich qulay ko'chma ikki kanalli asbob yordamida, masalan, Balanset-1A: akselerometrlarni o'rnating, mashina ishlayotgan paytda spektr va 1× fazani qayd eting va garmonik naqshni bevosita yuqoridagi diagnostika jadvaliga solishtirib aniqlang — so'ngra rotorni chiqarmasdan qolgan muvozanatsizlikni bartaraf eting.

Amaliy misollar — Haqiqiy Garmonik Tahlil Holatlari

1-holat: Motor-Nasos — Muvozanatsizlikmi yoki Noto'g'ri o'qlanishmi?

Machine: Egiluvchan muftali 2960 RPM tezlikda markazdan qochma nasosni boshqaruvchi 30 kW motor. Umumiy tebranish: motor yurituvchi tomonidagi podshipnikda 6,2 mm/s.

Spectrum: 1× = 4.1 mm/s, 2× = 3.8 mm/s, 3× = 1.2 mm/s. The 2×/1× ratio = 0.93.

Direction: High radial 2× at both drive-end bearings. Axial 1× at coupling: motor = 2.8 mm/s, pump = 3.1 mm/s with 165° phase difference.

Diagnosis: Combined angular and parallel misalignment. The 2×/1× ratio approaching 1.0, high axial readings, and ~180° phase across coupling all confirm. NOT unbalance — even though 1× is elevated, the 2× pattern is the real story.

Action: Laser alignment performed. Post-alignment: 1× = 0.8 mm/s, 2× = 0.3 mm/s. Overall dropped to 1.1 mm/s — an 82% reduction.

2-holat: Ventilyator — Nega Muvozanatlash Natija Bermaydi?

Machine: 1480 RPM tezlikdagi markazdan qochma ventilyator. Tebranish: 8,5 mm/s. Oldingi muvozanatlash urinishi 1× ni kamaytirdi, ammo umumiy tebranish yuqori bo'lib qoldi.

Spectrum: 1× = 2.1 mm/s (low after balancing), ½× = 1.8 mm/s, 2× = 3.2 mm/s, 3× = 2.5 mm/s, 4× = 1.8 mm/s, 5× = 1.1 mm/s, 6× = 0.7 mm/s.

Diagnosis: Mechanical looseness (Type B). The harmonic family with ½× sub-harmonic is the signature. Balancing corrected 1× but couldn’t address the looseness-generated harmonics that dominate overall vibration.

Action: Tekshiruv shuni ko'rsatdiki, podshipnik korpusi poydevor teshigida 0,08 mm bo'sh edi. Korpus qayta yonildi va yangi podshipnik o'rnatildi. Ta'mirdan keyin: barcha garmonikalar bazaviy darajaga tushdi. Umumiy: 1,4 mm/s.

3-holat: Kompressor Motori — Elektrikmi yoki Mexanikmi?

Machine: Vintli kompressorni boshqaruvchi 4 qutbli, 50 Hz induksion motor, 1485 RPM tezlikda. Tebranish 3 oy ichida 2,0 dan 5,5 mm/s ga oshdi.

Spectrum: Dominant peak at 100 Hz (= 2FL). Also: 1× at 24.75 Hz = 1.2 mm/s, sidebands around 1× at ±1.0 Hz spacing.

Key Test: Quvvat o'chirildi — 100 Hz cho'qqisi bir aylana ichida nolga tushdi. 1× yon chastotalar to'xtash jarayonida davom etdi.

Diagnosis: Two problems: (1) Electrical — stator eccentricity causing 2FL. (2) Mechanical — 1× sidebands at ±1.0 Hz (= pole pass frequency for 4-pole motor with 1.0% slip) suggest developing rotor bar defect.

Action: Motor qayta o'ramga yuborildi. Tasdiqlandi: 2 ta singan rotor sterjenji + asos cho'kishidan kelib chiqqan stator eksentrisiteti. Qayta o'ram va yostiqcha qo'yishdan keyin: tebranish 1,6 mm/s.

Garmonik Tahlil uchun Vibromera Uskunalari

The Balanset-1A and Balanset-4 real vaqt rejimida taqdim etadi FFT spektral tahlil with harmonic cursor tracking, enabling field identification of 1×, 2×, 3× patterns and fault diagnosis. The devices combine vibration analysis for diagnostics and precision muvozanatlash tuzatish uchun — bitta asbob bilan muammoni aniqlash va bartaraf etish.

← Lug'at indeksiga qaytish