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Belt drive formula summary

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Belt drive formula summary

1. 1. BELT DRIVETerm & symbolNisbah halaju (velocity ratio) – nSudut lekapan (angle of contact) – θJarak antara pemacu & penurut (distance between driver & driven) – xTegangan tali sawat (belt tension) – F (sometimes T)Kesan empar terhadap tegangan talisawat (centrifugal effect on belt tension) – FcKuasa terhantar (power transmitted) – PSpeed ratio + tension, F1drivend2 driverVelocity ratio; nN2 d1 N1 slack, F2Assuming no slip + v1 = 2 v but v = rω r1ω r 2ω 1 = 2 and d=2r d1 d2 ω = 1 ω2 2 2 ω2 d1 = ω1 d 2Therefore; halajudriven N2 ω2 d1 n= = = = halajudriver N1 ω1 d2
2. 2. Angle of contact For open drive: α α Mdriven driver α N1, r1N2, r2 O2 x θ O1 α α Note: always measure angle of contact from smaller pulley O 2M r 2 −r1 sin α = = O 2O1 x π θ = (180 −2α)( ) , in radian 180 For cross drive: M α E αdriven α driver O2 θN2, r2 O1 N1, r1 α α O2M O 2 E +ME r 2 +r1 sin α = = = O 2O1 O 2 +O1 x π θ = (180 +2α)( ) , in radian 180 Belt tension
3. 3. F 2 < 1 < max F F F1 - belt tension at tension side (N) F2 - belt tenson at slack side (N) Fmax – max belt tension before fail For flat belt [flat belt, inelastic, friction theory] F1 − Fc µθ F 2 − Fc e = F1 - belt tension at tension side (N) F2 - belt tenson at slack side (N) Fc – tension due to centrifugal effect (N) μ – coefficient of friction between belt & pulley θ – angle of contact (rad) cross-section view side view F1 F2 beltfriction pulley + For V belt [flat belt, inelastic, friction theory] Fc F1 − Fc  µθ    F1 − Fc ( µθ csc β ) = e sin β  F 2 − Fc e   or = F 2 − Fc F1 - belt tension at tension side (N) F2 - belt tenson at slack side (N) Fc – tension due to centrifugal effect (N) μ – coefficient of friction between belt & pulley θ – angle of contact (rad) belt pulley friction angle = 2β
4. 4. Where: Fc =mv 2 and ρ m = A m – weight per unit length (kg/m) v – velocity (m/s) ρ – belt material density (kg/m) belt initial tension F1 + F 2 + 2 Fc Fo = 2 Power transmission P = 1 − 2) v (F F P = ω T and T = 1 − 2) r (F F Belt creep (only for elastic belt) + tension, F1 driven Velocity, v1Velocity, v2 driver d2 N2 d1 When creep occur: N1 slack, F2 v2 ≠ 1 v + v2 F1 −F 2 =1 −( ) v1 AE Thus, power: P = 1 − 2)v 2 (F F (use v2 for calculation) A – cross-sectional area of belt (m2) E – belt material modulus of elasticity (N/m2)