Hunting Tooth chastotasini tushunish
Hunting tooth chastotasi (HTF — assambley fazasi chastotasi yoki eng katta umumiy bo'luvchi chastota deb ham ataladi) — bu past chastotali vibration tishli juftlikdagi komponent bo'lib, u same individual tooth on the pinion comes back into contact with the same individual tooth on the gear. It is governed by the least common multiple (LCM) of the two tooth counts and is normally a very low frequency — well below shaft speed — that appears as a slow, periodic amplitude modulation of the tishli ilashish chastotasi (GMF) and its sidebands.
HTF diagnostik jihatdan muhim, chunki bu tezlikdagi tebranish muayyan alohida tishlardagi — yorilgan tish, lokal yemirilish yoki ekssentrik montaj kabi — muammolarni ko'rsatadi, tishli uzatmaning umumiy holatini emas. Shuning uchun HTF yon chastotalarini aniqlash analizatorg aynan qaysi tishli g'ildirak, hatto qaysi tish nuqson manbai ekanligini aniqlashga imkon beradi, bu esa gear defect diagnosis.
1. Ta'rif va fizik ma'no
Ikki tishli g'ildirak birgalikda ishlayotganda, berilgan shaxtercha tishi g'ildirakning tishlarini ketma-ket — aylanmadan aylanmaga — ilashadi. U birinchi ilashgan tishga qaytib kelishi yoki kelmayotganligi — va qanchalik tez — ikki tish sonining arifmetik munosabatiga bog'liq. Hunting tooth chastotasi shunchaki shu qaytish tezligidir. Past HTF muayyan tish jufti juda kam uchrashadigan degani; yuqori HTF bir nechta juft doim takror-takror ishlaydigan degani.
Buning qarama-qarshi yo'nalishda ikki oqibati bor. Yeyilish nuqtai nazaridan past HTF yaxshi: zarar va ishlab chiqarish xatolari barcha tishlarga tarqaladi. Diagnostika nuqtai nazaridan esa xuddi shu past HTF bitta shikastlangan tishning tebranish izini aniqlash oson bo'lgan toza, bir aylanma tadbir sifatida jamlaydi. Bu sonni tushunish ikki hikoyani bir vaqtda o'qish imkonini beradi.
2. Matematik asosi
The formula
HTF = GMF / LCM(N₁, N₂) = GMF × GCD(N₁, N₂) / (N₁ × N₂)
- N₁ = number of teeth on the pinion
- N₂ = tishli g'ildiraqdagi tishlar soni
- GMF = gear mesh frequency = N₁ × pinion speed (Hz) = N₂ × gear speed (Hz)
- LCM = the least common multiple of N₁ and N₂ (equal to N₁ × N₂ / GCD, where GCD is the greatest common divisor)
HTF modulatsiyalaydigan GMF o'zi N × val aylanish tezligiga teng (istalgan tishli g'ildirak uchun); u holda tishli ilashish chastotasi kalkulyatori GMF va uning yon chastotalar oilasini bevosita hisoblaydi, tishli uzatma nisbati kalkulyatori esa formulani qo'llashdan oldin zarur bo'lgan kirish/chiqish tezligi munosabatini hisoblaydi.
1-misol: hunting-tooth juftligi
- Pinion: 1800 RPM da 23 ta tish
- Gear: 67 teeth
- GCD(23, 67): 1 — both are prime, so they share no common factor; LCM(23, 67) = 23 × 67 = 1541
- GMF: 23 × (1800 / 60) = 690 Hz
- HTF = 690 / 1541 ≈ 0.45 Hz — the same tooth pair meets only about once every 2.2 seconds, far below the 30 Hz pinion shaft speed
- Meaning: naqsh takrorlanishidan oldin har bir pinion tishi har bir tishli g'ildirak tishi bilan tutashadi
- Result: optimal eskirish taqsimotiga ega haqiqiy ov-tishli uzatma juftligi
2-misol: ov-tishsiz juftlik
- Pinion: 1800 RPM da 20 ta tish
- Gear: 60 teeth
- GCD(20, 60): 20; LCM(20, 60) = 60
- GMF: 20 × (1800 / 60) = 600 Hz
- HTF = 600 / 60 = 10 Hz — equal to the output (gear) shaft speed
- Meaning: only 20 distinct tooth pairs exist, and each pair re-meshes ten times every second
- Result: bir xil tishlarda kontsentrlashgan eskirish naqshi
3-misol: oraliq holat
- Pinion: 3600 RPM da 18 ta tish
- Gear: 54 teeth
- GCD(18, 54): 18; LCM(18, 54) = 54
- GMF: 18 × (3600 / 60) = 1080 Hz
- HTF = 1080 / 54 = 20 Hz
- Pattern: only 18 distinct tooth-contact pairs exist, each repeating 20 times per second
3. Ov-tishli va ov-tishsiz tishli uzatma to'plamlari
Ov-tishli konstruktsiya (EKUB = 1)
Tishlar soni o'zaro tub (umumiy bo'luvchilari yo'q) bo'lganda erishiladi:
- Advantages:
- Har bir pinion tishi oxir-oqibat barcha tishli g'ildirak tishlari bilan tutashadi.
- Eskirish barcha tishlar bo'ylab bir xil taqsimlanadi.
- Ishlab chiqarish xatoliklari kuchaytirilmasdan o'rtalashtiriladi.
- Tishli uzatmaning uzoq muddati.
- Ko'pchilik ilovalar uchun afzal ko'riladi.
- Disadvantages:
- A defect involving one specific tooth pair repeats only at the very low HTF (a small fraction of shaft speed), so long time records are needed to resolve it. A single damaged tooth still impacts once per revolution of its own shaft.
- Yanada aniqroq ishlab chiqarishni talab qilishi mumkin.
Non-hunting konstruksiya (EKB > 1)
Tish sonlari umumiy bo'luvchilarga ega bo'lganda yuzaga keladi:
- Advantages:
- Tish sonini tanlash oddiyroq.
- Standart, tayyor reduktor o'lchamlaridan foydalanish imkonini beradi.
- Disadvantages:
- Bir xil tishlar qayta-qayta tutashadi (faqat EKB ta noyob juft mavjud).
- Eyilish o'sha bir xil tish juftlarida to'planadi.
- Muayyan tishlardagi ishlab chiqarish xatoliklari har tsiklda takrorlanadi.
- Odatda reduktor xizmat muddati qisqaroq bo'ladi.
- Sifatli reduktor konstruksiyasida odatda bunday holdan qochiladi.
4. Tebranish tasviri
HTF in the spectrum and waveform
HTF rarely appears as a strong standalone peak, and it is usually far too low to be resolved as sideband spacing. Sidebands around the mesh frequency in the tebranish spektri are spaced at the shaft speeds of the two gears; HTF itself shows up as a slow, periodic amplitude modulation (a beat) of the mesh vibration:
- Central peak: GMF (tishli g'ildirak tutashuv chastotasi).
- Sidebands: GMF ± 1×, 2×, 3× the shaft speed of the gear carrying a localised defect.
- HTF signature: a slow beat in the time waveform — the overall vibration level swells and fades at the HTF rate (typically a fraction of a hertz to a few hertz).
- Interpretation: modulation repeating at HTF points to a fault involving a particular tooth pair, such as a damaged pinion tooth periodically striking a damaged gear tooth; the modulation depth reflects the severity of the localised defect.
Bu yon chastotalar yuqori tutashuv chastotasi atrofida to'planadigan va zich bo'lishi mumkin bo'lganligi sababli, ularni aniqlashga yordam beradigan ikki usul mavjud. Kepstrum tahlili muntazam joylashgan yon chastotalar guruhini bitta kvefrensi chizig'iga jamlaydi, bu esa masofa o'qishni osonlashtiradi, va konvert tahlili modulyatsiyalangan tishlanma signalidan shikastlangan tishning har aylanmadagi ta'sirini tiklaydi.
Diagnostika naqshlari
Bitta shikastlangan tish: strong sidebands around GMF spaced at the shaft speed of the gear carrying the damaged tooth; one impact per revolution of that gear; the time waveform aniq davriy impulsni ko'rsatadi.
Tishli g'ildirak ekssentrisiteti: shaft-speed sidebands arising from runout or eccentric mounting; tooth-engagement depth varies once per revolution, amplitude-modulating the GMF; usually correctable by remounting or runout compensation (see eccentricity).
Damage on both gears (tooth-pair fault): when a damaged pinion tooth periodically meets a damaged gear tooth, the vibration swells and fades at the low HTF rate — a slow beat superimposed on the mesh vibration; may require gear replacement, or acceptance if it falls within tolerance.
5. Amaliy diagnostika
Nuqsonli tishli g'ildirakni aniqlash
Nuqson qaysi elementda — kichik tishli g'ildirakda yoki asosiy tishli g'ildirakda ekanligini aniqlash uchun:
- Ikkala val tezligini hisoblang: kirish va chiqish aylanish tezligi (RPM).
- Yon chastota komponentlari oralig'ini o'lchang tebranish spektridan.
- Agar oraliq = kirish vali chastotasi bo'lsa → nuqson kichik tishli g'ildirakda joylashgan.
- Agar oraliq = chiqish vali chastotasi bo'lsa → nuqson asosiy tishli g'ildirakda joylashgan.
- Xulosa: yon chastota oralig'i qaysi val — va shuning uchun qaysi tishli g'ildirak — muammoli ekanligini aniqlaydi.
Bu aynan ko'chma ikki kanalli analizator mos keladigan o'lchov turidir. Optik taxometr ma'lumotlarni val burchagiga sinxronlab, Balanset-1A tishli quti korpusida spektr va vaqt to'lqin shaklini qayd etadi, shunda yon chastota oralig'ini ma'lum kirish va chiqish aylanish tezliklari bilan solishtirish mumkin, hamda yoriq tishning aylanma impuls belgisi to'lqin shaklida tasdiqlanadi — bularning barchasi mashina ishlayotgan holatda, qopqoqni ochmasdan amalga oshiriladi. A garmonik chastota kalkulyatori keyin o'lchangan AYD (aylanish/daqiqa) qiymatini izlash kerak bo'lgan aniq Gts qiymatlariga aylantiradi.
Og'irlik darajasini baholash
- Yon chastota amplitudasi: yuqoriroq amplitudalar yanada og'ir mahalliy nuqsonni bildiradi.
- Yon chastotalar soni: ko'proq yon chastotalar (yuqori tartiblar) holatning yomonroqligini ko'rsatadi.
- Time waveform: aniq davriy impuls alohida tishning zarbasini tasdiqlaydi.
- GMCh bilan solishtirish: GMCh amplitudasining ~25% dan yuqori yon chastotalar muhim nuqsonni bildiradi — foydali defect-severity threshold.
6. Konstruktiv mulohazalar
Tish sonini tanlash
- Tub sonlardan foydalaning GUB = 1 bo'lishini ta'minlash uchun imkon qadar ("hunting-tooth" konstruksiyasi).
- Umumiy bo'luvchilardan qoching — 20:60 (GUB = 20) kabi juftliklardan uzoq bo'ling.
- Yaxshi juftlik misollari: 17:51, 19:57, 23:69 (barcha EKUB = 1).
- Trade-off: cheklov mavjud bo'lgan tishli uzatmalar nisbatlarini biroz cheklashi mumkin.
Non-hunting usul qabul qilinishi mumkin bo'lgan holatlarda
- Eskirish muhim bo'lmagan past yuklamali ilovalar.
- Aniq uzatma nisbati majburiy bo'lgan standart tishli uzatmalar to'plamlari.
- Eskirishni taqsimlash kamroq ahamiyatga ega bo'lgan qisqa muddatli ilovalar.
- Ishlab chiqarish afzalliklari eskirish kamchiligidan ustun keladigan holatlarda.
7. Boshqa tishli uzatma chastotalari bilan munosabat
Reduktoridagi chastota ierarxiyasi
- Shaft speeds: 1× for input and output — the lowest rotational frequencies.
- HTF: normally the lowest frequency of all — a small fraction of shaft speed in a hunting design (GCD = 1), and never higher than the slower shaft speed even in a non-hunting one.
- GMF: tishlar soni × val aylanish tezligi — eng yuqori asosiy chastota.
- GMF harmonics: 2×GMF, 3×GMF and so on, arising from mesh non-linearities and backlash.
Yon chastotalarni tahlil qilish strategiyasi
- Val tezligi oralig'idagi yon chastotalar → ekssentrik tishli uzatma yoki alohida tish nuqsoni.
- Slow amplitude modulation (beating) at the HTF rate → a repeating tooth-pair issue, such as matched damage on both gears.
- Aniq yon chastotalar yo'q → umumiy taqsimlangan gear wear, yoki shunchaki sog'lom tishli uzatma.
Hunting tish chastotasi tishli uzatma dinamikasining nozik bir qirrasi bo'lsa-da, kuchli diagnostik ma'lumot beradi. HTF hisoblashini tushunish va HTF yon chastotalarini aniqlash tahlilchiga qaysi tishli uzatmada nuqson borligini va muammo bitta shikastlangan tishda yoki kengroq tarqalgan holatda ekanligini aniq belgilash imkonini beradi — bu reduktor nosozliklarini bartaraf etishda maqsadli va ishonchli texnik xizmat ko'rsatish qarorlarini qabul qilishga yo'l ko'rsatadi.
