Ufafanuzi: Harmonic ni nini?

Katika uchanganuzi wa mitetemo, harmonic ni frequency ambayo ni kuzidisha kwa namba kamili ya frequency ya msingi. Katika mashine zenye kuzunguka, frequency ya msingi kawaida ni kasi ya kuzunguka kwa mkingi, inajulikana kama harmonic ya 1 au 1×. The subsequent harmonics are integer multiples: 2× (twice shaft speed), 3× (three times), and so on. These frequencies are also called orders ya kasi ya operesheni, au harmonics zinazolingana kwa sababu zinajiratibu vizuri na kuzunguka kwa mkingi.

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.

Ufafanuzi wa Harmonic Frequency
fn = n × f1 = n × (RPM / 60)
where n = 1, 2, 3, 4… (harmonic order) and f₁ = shaft rotational frequency in Hz

Harmonics vs. Sub-Harmonics vs. Peak zisizolingana

Harmonics are integer multiples of shaft speed (2×, 3×, 4×…). Sub-harmonics are fractional multiples (½×, ⅓×, ¼×) and always indicate severe mechanical problems. Peak zisizolingana ni frequencies zisizohusiana na kasi ya mkingi — kama vile taajweza za kosa la kuzaa, frequencies za gear mesh, frequency ya mstari (50/60 Hz), au frequency za asili — na zinahitaji njia tofauti za kuchambua. Peak katika 3.57× RPM SI harmonic; pengine ni frequency ya kushindwa kwa kufa kwa mpigia.

Kwa nini Harmonics Zinaundwa?

Katika mfumo unaokamilika ulioelekezwa na nguvu yenye wimbi safi (kama vile rotor iliyokuwa na uwiano kamili, inayojaliwa vizuri katika mpigia kamili), tu harmonic ya 1× isingekuja. Mashine halisi kamwe sio kamili. Harmonics zinaonekana kila wakati wimbi la mitetemo linabadilika kutoka sine wimbi safi — kila wakati majibu ya mfumo ni non-linear au chaguo la nguvu yenyewe sio wa sinusoidali.

Hisabati: Nadharia ya Fourier

Nadharia ya Fourier inasema kwamba mawimbi yoyote ya kawaida — hakuna hali ipi — yanaweza kugawanywa katika jumla ya mawimbi ya sine katika masafa ya kimsingi na kuzidisha lake, kila moja ikiwa na amplitude na awamu mahususi. Algoriti ya FFT (Fast Fourier Transform) inayotumiwa na vichumi vya vibration inafanya mgawanyiko huu kwa kihisabati, kuweka wazi yaliyofichwa ya harmonic katika ishara.

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.

Utaratibu wa Kimwili Ambao Unazalisha Harmonics

  • Kumkata / kukataa wimbi: Wakati harakati ya shimoni inapingwa kwa kimwili (nyumba ya bearing, mawasiliano ya mkazo), wimbi linalosababishwa linakatamatwa, likitengeneza harmonics. Kumkata kwa nguvu zaidi kunazalisha harmonics zaidi.
  • Ugumu usio wa linganifu: 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: Mabano ya kawaida (boliti libwa, athari za kasoro la bearing) hutengeneza mawimbi mafupi ya muda mfupi ambayo yana harmonics nyingi sana — kama vile fimbo ya ngoma inazalisha sauti nyingi za juu.
  • Nguvu za kurudi isiyo na mstari: Wakati ugumu hubadilika na kuhamia (mabearing chini ya mlaji tofauti, kunyongeza nguvu za rubber), jibu kwa nguvu ya sinusoidali lina harmonics.
  • Msukumo wa parametri: Wakati mali ya mfumo inabadilika kwa kawaida katika masafa yanayohusiana na kasi ya shimoni, zinaweza kutengeneza harmonics na sub-harmonics ya masafa ya msukumo.
Kanuni Muhimu ya Utambuzi

Muundo wa harmonics ipi ipo, amplitudi zao za jamaa, na zipi zisizo na kitu inaonyesha mchambuzi ni utaratibu gani wa kimwili unazalisha kutokokuwa na mstari. Wachambuzi wenye tajriba wanatazama muundo kamili wa harmonic wa ghoshi — si tu kiwango chote cha vibration — kubaini utaratibu mahususi wa kasoro.

Muundo wa Kasoro wa Kina — Muundo wa Harmonics

1× Inayojulikana — Kutokwanza

Kilele cha 1× kinachojulikana na harmonics ndogo zaidi ya juu ni saini ya kawaida ya mass unbalance. Nguvu ya kutokwanza ni yenye asili ya sinusoidali (inaendelea na shimoni katika masafa ya 1×), kutengeneza kilele cha moja safi katika uwanja wa masafa.

Maelezo ya Utambuzi

  • Amplitude: Proportional to speed² (double speed → 4× amplitude) and proportional to unbalance mass
  • Phase: Imara, inayorudia, yenye thamani moja. Inabadilika kwa njia madhubuti na kuongezwa kwa uzani wa jaribio — huu ndio msingi wa zote taratibu za usawazishaji
  • Direction: Zaidi ya kimsingi radial; 1× axial ni chini isipokuwa rotor ina overhang kubwa
  • Confirmation: Jibu kwa uzani wa jaribio linathibitisha kutokuwa na uimbilifu. Ikiwa 1× haijibu kwa uzani wa jaribio, zingatiaje shimoni iliyoinama, eccentricity, au resonance
Si Kila Vibration ya 1× ni Kutokuwa na Uimbilifu

Hali kadhaa zinazalisha 1× ya juu ambayo HAIOZOWEZA kukamatwa kwa kutengeneza usawa: shimoni iliyoinama, eccentricity ya shimoni, electrical runout kwenye proximity probes, rotor bow kutokana na athari za joto, eccentricity ya coupling, na resonance amplification. Daima thibitisha chochote kabla ya kujaribu kutengeneza usawa.

2× Inatawala — Kukosa Unaendelea

Harmonic ya pili yenye nguvu, mara nyingi yenye amplitude inayolingana na au inayozidi kilele cha 1×, ni kiashiria kikuu cha kukosa unaendelea kwa shimoni. Kukosa unaendelea kulazimisha shimoni kwa njia isiyo na sinus wakati wa kila kuzunguka, na kusababisha distortion inayozaa 2× na wakati mwingine harmonics ya juu zaidi.

Kukosa Unaendelea kwa Angular dhidi ya Parallel

  • Kukosa unaendelea kwa angular: Shaft centerlines intersect at an angle at the coupling. Produces high 1× axial vibration. Phase across coupling shows ~180° shift in the axial direction.
  • Kukosa unaendelea kwa parallel (offset): 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: Katika matukio halisi, zote mbili kawaida zipo pamoja, na zinazalisha mchanganyiko wa signatures.

The 2×/1× Ratio as a Diagnostic Indicator

2×/1× Ratio Hali Inayowezekana Action
< 0.25 Kawaida; 2× iliyopo kwa kiwango cha chini katika mashine nyingi Hakuna hatua inayohitajika
0.25 – 0.50 Kukosa unaendelea kwa wastani kunaweza kuwezekanika; kawaida kwa aina baadhi za coupling Angalia unaendelea; linganisha na mstari wa msingi
0.50 – 1.00 Kukosa unaendelea kubwa kunajitokeza kuwezekanika Fanya uangalifu wa usambazaji wa laser wenye usahihi
> 1.00 Severe misalignment; 2× exceeds 1× Haraka — badilisha kwa kuangalia; kagua jambo la kuunganisha na mkazo wa kebo

Harmonic Nyingi — Uhalifu wa Mitambo

Msururu wa tajriba ya running speed harmonics (1×, 2×, 3×, 4×, 5×… to 10× or more) indicate kupungua kwa mitambo. Matatizo, kelele, na mzunguko wa kutenganisha/kuungana bila uwiano huleta upotoshaji mkubwa wa mawimbi ambayo unakamatia sehemu nyingi za harmonic.

Aina Tatu za Uhalifu

  • Aina A — Miundombinu: 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.
  • Aina B — Sehemu: 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).
  • Aina C — Kiti cha bearing: Impeller inayozunguka kwenye shimoni, jambo la kuunganisha linalozunguka, wazi nyingi wa bearing linaloruhusu rotor kuruka. Hutoa harmonic nyingi na kiwango cha kelele pana.
Sub-Harmonic: Kidole cha Uhalifu

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×.

Hali Nyingine Zinazobuza Harmonic

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.

Mashine ya Kupiga Mitikiso

Injini, kompresa, na mashine ya kupiga mitikiso huzalisha asili ya harmonic ya tajriba kwa sababu mwendo wa pistoni/crankshaft si wa sinusoidal kwa asili. Muundo wa harmonic unategemea idadi ya silinda, agizo la moto, na aina ya mtao (2-mtao vs. 4-mtao).

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.

Matatizo ya Umeme katika Motoki

Motoki ya AC huzalisha mitetemo kwa kuzidisha kwa kiwango cha mstari (50 au 60 Hz) huru ya kasi ya shimoni. Kawaida ni 2× kiwango cha mstari (100 Hz katika mifumo ya 50 Hz, 120 Hz katika mifumo ya 60 Hz). Hii SI harmonic ya kasi ya shimoni — ni harmonic ya kiwango cha mstari, ambayo ni muhimu kwa utofautishaji wa umeme kutokana na mitetemo ya mitambo. Ye power cut test ni muhimu: mitetemo ya umeme yanaanguka papo hapo wakati nguvu inarekebishwa, mitetemo ya mitambo hubaki wakati wa kuzorota.

Kasoro za ufa wa rotor hutoa upande kuzunguka 1× inayoandaliwa na kiwango cha kupita kwa nguvu (slip frequency × number of poles). These sidebands are very close to 1× (within 1–5 Hz), requiring high-resolution zoom FFT uchanganuzi kusuluhisha.

Mzunguko Usiotambati — Sio Harmonia Asili

Mzunguko kadhaa muhimu huelezewa mahali pengine kama harmonia lakini kwa kweli ni huru kwa kasi ya shimoni:

Frequency Type Formula Uhusiano na RPM Notes
Mzunguko wa kasoro wa bearing BPFO, BPFI, BSF, FTF Non-integer multiples (e.g. 3.57×, 5.43×) Always non-synchronous; depends on bearing geometry
Namba ya kugusiana kwa gesi GMF = #meno × RPM Nambari lakini mpangilio mwinuko zaidi Kwa kiufundi ni harmonia lakini inachambuliwa kando
Blade/vane pass BPF = #blades × RPM Kuzidisha nambari Kawaida; amplitude kupita kiasi inaonyesha tatizo
Line frequency FL = 50 au 60 Hz Sio mahusiano na RPM Umeme; hutoweka katika kukatwa kwa umeme
Mzunguko asilia fn = √(k/m)/2π Imara; sio mahusiano na RPM Mzunguko thabiti haijalishi mabadiliko ya kasi
Mzunguko wa ukanda fbelt = RPM×π×D/L Chini ya kitambatisho (< kasi ya shimoni) Belt frequency and its harmonics 2×, 3×, 4× BF

Mwongozo wa Uchambuzi — Jinsi ya Kutafsiri Mifumo ya Harmonia

Hatua 1: Tambua Msingi (1×)

Tafuta kilele cha 1× kinachofanana na kasi ya mzunguko wa shimoni. Thibitisha kutumia tachometer au chapa ya mfumo wa motor. Katika mashine zenye kasi inayoweza kubadilikayo, 1× lazima iidentifike kwa usahihi kwa kila kipimo.

Hatua ya 2: Orodhesha Kilele Kiote

Kwa kila kilele muhimu, bainisha: je, ni kizidisho halisi kamili cha 1× (harmonic halisi)? Kizidisho cha sehemu (sub-harmonic)? Haijakusudiwa kuwa jamaa na kasi ya shimoni (yasiyo ya synchronous)? Tumia vipengele vya cursor ya harmonic ya analyzer kwa ufanisi.

Hatua ya 3: Chunguza Mchoro wa Amplitude

  • Harmonic ipi inayotawala? → Inaonyesha kasoro mahususi
  • Harmonics ngapi zimewepo? → Zaidi = upotezaji kamili zaidi
  • Does 2× exceed 1×? → Likely misalignment
  • Je, sub-harmonics zimewepo? → Koleo, msuguano, au oil whirl
  • Je, amplitude inapungua na mpangilio (1/n decay)? → Kawaida kwa koleo

Hatua ya 4: Angalia Kuelekeza

  • Radial juu, axial chini: Kutokuwa na usawa au koleo
  • High axial: Unakamatia (hasa angular) au shimoni iliyobanwa
  • Radial inayoelekeza: Koleo la muundo (juu zaidi katika mwelekeo wa koleo)

Hatua ya 5: Elezea Kwa Wakati

  • Je, amplitudes ya harmonic zinaongezeka? → Kasoro inasambaa
  • Je, harmonics mpya zinakuja? → Utaratibu wa kasoro mpya unakuendeleza
  • Je, sauti ya uzuri inakwenda juu? → Mabingu ya kawaida au kushindwa kwa hatua ya mwisho

Hatua ya 6: Kuweka Nambari na Data ya Awamu

  • Unbalance: Awamu ya 1× ni imara na inaweza kurudiwa
  • Misalignment: 1× or 2× phase shows ~180° across coupling
  • Looseness: Awamu ni imara, inaweza kubadilika kwa nasibu kati ya vipimo

Katika mazoezi, hatua zote sita zinaweza kutekelezwa mahali pa kazi kwa chombo cha fuleni na chaneli mbili kama vile Balancet-1A: weka sensorer za kuongeza kasi, kamata spektri na 1× awamu wakati zamu inaendelea, na soma mzunguko wa harmonic moja kwa moja dhidi ya jedwali la tafakari hapo juu — kisha sahihisha kutokuwa na usawa wowote uliobaki bila kuondoa rotor.

Masomo ya Matukio — Uchambuzi wa Harmonic Uliotendekeza

Matukio 1: Motoka-Pampu — Je, ni Kutokuwa na Usawa au Kupotoka kwa Mstari?

Machine: Motoka ya 30 kW inaendesha pampu ya sentrifuji kwa RPM 2960 kupitia bidhaa yenye kubadilika. Vibration jumla: 6.2 mm/s kwenye tochi ya kuvuta la motoka.

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.

Matukio 2: Sherehe — Kwa Nini Balancing Haifanyi Kazi?

Machine: Sherehe ya sentrifuji kwa RPM 1480. Vibration: 8.5 mm/s. Jaribu la balancing lililopita lilipunguza 1× lakini vibration jumla ilibaki juu.

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: Ukaguzi ukaonyesha chumba cha kumfunga chombo 0.08 mm aliyefungama katika shimo la msaada. Nyumba iliyozuia na kumfunga mpya iliyowekwa. Baada ya kutengeneza: harmonic zote zilishuka hadi msingi. Jumla: 1.4 mm/s.

Matukio 3: Motoka ya Kusambaza — Umeme au Michakato?

Machine: Motoka ya induction ya pole 4, Hz 50 kwa RPM 1485 inaendesha kusambaza zamu. Vibration iliongezwa kutoka 2.0 hadi 5.5 mm/s kwa miezi 3.

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: Mkato wa umeme — kilele cha Hz 100 kilianguka hadi sifuri ndani ya mzunguko mmoja. Kando ya 1× zilipitia wakati wa kuteremka.

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: Motoka iletwa kwa kupinga upya. Kuthibitishwa: pau 2 za rotor iliyovunjwa + eccentricity ya stator kutoka sag ya msingi. Baada ya kupinga upya na kutengeneza: vibration 1.6 mm/s.

Vifaa vya Vibromera kwa Uchambuzi wa Harmonic

The Balancet-1A and Balancet-4 kuandaa kwa wakati halisi Uchambuzi wa spektri wa FFT with harmonic cursor tracking, enabling field identification of 1×, 2×, 3× patterns and fault diagnosis. The devices combine vibration analysis for diagnostics and precision kusawazisha kwa kusahihisha — kutambua tatizo na kulitengeneza kwa chombo kimoja.

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