Vektor kalkulyatori
Vektor kalkulyatori
Vector A
Vector B
Operation
Bu kalkulyator nima uchun mo'ljallangan?
Bu kalkulyator qutb koordinatalari (modul va burchak) yordamida vektor amallarini bajaradi. U rotor muvozanatlash ilovalari uchun mo'ljallangan bo'lib, bunda muvozanatsizlik muayyan burchak holatidagi massa sifatida o'lchanadi. Kalkulyator bir nechta muvozanatsizlik o'lchov natijalarini birlashtirish, tuzatish og'irligini o'rnatish joyini aniqlash va koordinata sistemalari o'rtasida o'tkazish imkonini beradi.
Input format
Har bir vektor ikkita qiymat bilan aniqlanadi: massa (gramm yoki shartli birliklarda) va burchak (0 dan 360 gradusgacha). 0° boshlang'ich burchak yuqoriga yo'nalgan (soat 12 holati), burchaklar soat yo'nalishi bo'yicha ortib boradi. Bu ko'pchilik muvozanatlash asboblarida qo'llaniladigan konvensiyaga mos keladi, bunda faza nishoni odatda rotorning yuqori qismida belgilanadi.
Operations
- Addition (+) — Ikkita vektorni bitta natijaviy vektorga birlashtiradi. Bir nechta manbadan umumiy muvozanatsizlikni topish yoki ikkita tuzatish og'irligini bittaga birlashtirish kerak bo'lganda foydalaning.
- Ayirish (−) — Ikki vektor o'rtasidagi farqni (A minus B) hisoblaydi. Tuzatishdan keyin qoldiq muvozanatsizlikni aniqlash uchun qulay.
- Opposite (±180°) — A vektorining burchagiga 180° qo'shadi. Bu tuzatish og'irligini o'rnatish kerak bo'lgan holatni beradi.
- Scale (k×) — Massani k koeffitsientiga ko'paytiradi. Boshqa o'rnatish radiusiga tuzatish massasini qayta hisoblashda zarur: m2 = m1 × (r1 / r2).
- Dekart (X, Y) — Converts polar coordinates to Cartesian: X = m × cos(angle), Y = m × sin(angle).
Odatiy qo'llanish sohalari
- Bir tekislikda muvozanatlash: Muvozanatsizlikni o'lchang, tuzatish burchagini topish uchun Opposite funksiyasidan foydalaning, og'irlikni o'rnating va natijani tekshiring.
- Og'irliklarni birlashtirish: Qo'yilgan ikkita tuzatish og'irligini Qo'shish funksiyasi yordamida bitta ekvivalent og'irlik bilan almashtiring.
- Radiusni o'zgartirish: Tuzatish og'irligini boshqa radiusga ko'chirishda massani qayta hisoblash uchun Shkala funksiyasidan foydalaning.
- Split weights: Aniq burchakka kirish imkoni bo'lmasa, tuzatish massasini ikkita qo'shni qanotchaga taqsimlang.
1-misol: Tuzatish og'irligining o'rnini aniqlash
Balanslovchi asbob quyidagi muvozanatsizlikni ko'rsatmoqda: 72° burchakda 15 gramm.
Enter Vector A: Mass = 15, Angle = 72
Select Opposite (±180°) va Hisoblash tugmasini bosing.
Result: 252° burchakda 15 gramm
Muvozanatsizlikni kompensatsiya qilish uchun 252° holatiga 15 gramm tuzatish og'irligini o'rnating.
Enter Vector A: Mass = 15, Angle = 72
Select Opposite (±180°) va Hisoblash tugmasini bosing.
Result: 252° burchakda 15 gramm
Muvozanatsizlikni kompensatsiya qilish uchun 252° holatiga 15 gramm tuzatish og'irligini o'rnating.
2-misol: Ikkita og'irlikni bittaga birlashtirish
Bir necha balanslash iteratsiyasidan so'ng rotorga ikkita tuzatish og'irligi o'rnatilgan:
5 grams at 30° and 8 grams at 75°.
Ularni bitta og'irlik bilan almashtirishni xohlaysiz.
Enter Vector A: Mass = 5, Angle = 30
Enter Vector B: Mass = 8, Angle = 75
Select Addition (+) va Hisoblash tugmasini bosing.
Result: 57,9° burchakda 12,05 gramm
Ikkala og'irlikni ham olib tashlang va taxminan 58° holatiga bitta 12 gramm og'irlik o'rnating. Bu bitta og'irlik dastlabki ikkita og'irlikning birgalikdagi balanslash effektini ta'minlaydi.
Enter Vector A: Mass = 5, Angle = 30
Enter Vector B: Mass = 8, Angle = 75
Select Addition (+) va Hisoblash tugmasini bosing.
Result: 57,9° burchakda 12,05 gramm
Ikkala og'irlikni ham olib tashlang va taxminan 58° holatiga bitta 12 gramm og'irlik o'rnating. Bu bitta og'irlik dastlabki ikkita og'irlikning birgalikdagi balanslash effektini ta'minlaydi.
3-misol: Tuzatish radiusini o'zgartirish
Balanslash tizimi quyidagi tuzatishni hisobladi: 20 grams radius uchun 100 mm.
Biroq, og'irlikni quyidagi radiusga o'rnatishingiz kerak: 80 mm joy cheklovlari tufayli.
Since the balancing effect depends on the product of mass and radius (m × r = const), you need to recalculate: k = 100 / 80 = 1.25
Enter Vector A: Mass = 20, Angle = (your correction angle)
k = 1,25 ko'paytirgichini o'rnating
Select Scale (k×) va Hisoblash tugmasini bosing.
Result: 25 grams bir xil burchakda
80 mm kichikroq radiusda xuddi shu tuzatishga erishish uchun 20 gramm o'rniga 25 gramm kerak bo'ladi.
Since the balancing effect depends on the product of mass and radius (m × r = const), you need to recalculate: k = 100 / 80 = 1.25
Enter Vector A: Mass = 20, Angle = (your correction angle)
k = 1,25 ko'paytirgichini o'rnating
Select Scale (k×) va Hisoblash tugmasini bosing.
Result: 25 grams bir xil burchakda
80 mm kichikroq radiusda xuddi shu tuzatishga erishish uchun 20 gramm o'rniga 25 gramm kerak bo'ladi.
4-misol: Og'irlikni ikki palla o'rtasida taqsimlash
Talab qilinadigan tuzatish 110° burchakda 10 gramm, ammo og'irliklarni faqat ventilator pallalariga biriktirish mumkin, ular 90° and 126° (5 ta palla, 36° oralig'ida) joylashgan.
The correction angle 110° lies between these two blades. To find how much weight goes on each blade, use the exact trigonometric split (a simple proportional split of the mass by angle is only an approximation and under-corrects the balance mass by several percent):
Angular distance to the blade at 90°: α = 110° − 90° = 20°
Angular distance to the blade at 126°: β = 126° − 110° = 16°
Angle between the blades: α + β = 36°
Weight on 90° blade: 10 × sin(16°) / sin(36°) = 4.69 g
Weight on 126° blade: 10 × sin(20°) / sin(36°) = 5.82 g
Tekshirish uchun qo'shish usulidan foydalaning:
Vector A: Mass = 4.69, Angle = 90
Vector B: Mass = 5.82, Angle = 126
Result: 110° burchakda 10 gramm — dastlabki talabga mos keladi.
The correction angle 110° lies between these two blades. To find how much weight goes on each blade, use the exact trigonometric split (a simple proportional split of the mass by angle is only an approximation and under-corrects the balance mass by several percent):
Angular distance to the blade at 90°: α = 110° − 90° = 20°
Angular distance to the blade at 126°: β = 126° − 110° = 16°
Angle between the blades: α + β = 36°
Weight on 90° blade: 10 × sin(16°) / sin(36°) = 4.69 g
Weight on 126° blade: 10 × sin(20°) / sin(36°) = 5.82 g
Tekshirish uchun qo'shish usulidan foydalaning:
Vector A: Mass = 4.69, Angle = 90
Vector B: Mass = 5.82, Angle = 126
Result: 110° burchakda 10 gramm — dastlabki talabga mos keladi.
Formulas
Polar to Cartesian: X = m × cos(a), Y = m × sin(a)Cartesian to Polar: m = sqrt(X² + Y²), a = atan2(Y, X)
Radius bo'yicha tuzatish: m2 = m1 × (r1 / r2)
Split weights (exact): m1 = M × sin(β) / sin(α + β), m2 = M × sin(α) / sin(α + β), where α is the angular distance from the correction angle to blade 1 and β is the angular distance to blade 2
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