balancing 27th
DESCRIPTION
balancingTRANSCRIPT
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BITS PilaniPilani Campus
Jitendra S Rathore
Department of Mechanical Engineering
Balancing of Reciprocating masses
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Unbalance
Rotating Unbalance Reciprocating Unbalance
Single plane
Primary force
& couple
Secondary
force & couple
Different plane
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Reciprocating Unbalance When a machine has accelerating parts, the resultants of inertia
forces and moments of all such accelerating parts represents
the forces and moments transmitted to the frame or foundation.
NQ sin
xmpAQreccos RTxQ )sin(
sinQRV
cosQRH
)2cos
(cos2
nrwmxmRpAF
recrecHx
0 NRF
Vy
0RZ
TNxM
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I.C. Engines
Where: mrecr2cos is Primary force and
mrec/(4n) r(2)2(cos 2t) is Secondary force
The magnitude of secondary force 1/4n times andfrequency is 2 times as compared to the primary forceand hence required to balance in high speed engine.
)2cos
(cos2
nrwmF recx
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rB
A
C
D
O
Complete Balancing for single cylinder engine:
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Partial balancing for primary force:
Primary force is the component (in the direction of stroke) of
fictitious mass equivalent to reciprocating mass placed at
crank radius r
mrec 2 r
R
mrec 2 r cos
r
B
B 2 b
b
B 2 b sin
B 2 b cos
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Single cylinder engines:
Partial balancing
Multi cylinder engines:
Passive balancing i.e. changing the firing order
Active balancing
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The following data refer to single cylinder engine:
Speed =240 rpm
Stroke = 30 cm
Mass of reciprocating parts = 50 kg
Mass of revolving parts at 15 cm radius = 37 kg
If 2/3 of the reciprocating parts and all the revolving parts are to
be balanced, find
(a) The balancing weight required at a radius of 40 cm , and
(b) The residual unbalanced force when crank has rotated 60 degree
from top dead centre.
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A marine oil engine has four cylinders with cranks at angular
displacement of 90 degree. The speed of the engine is 90 rpm
and the mass of the reciprocating parts for each cylinder is 900
kg. Each crank is 45 cm long. The outer cranks are 3m apart.
The inner cranks are 1.2m apart and are placed symmetrically
between the outer cranks. Find the firing order of the cylinder
for the best primary balancing of reciprocating masses.
Determine the maximum unbalanced primary couple for the
best arrangement.
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A wheel and tire assembly has been run at 100 rpm on a dynamic balancing machine
as shown in Fig Q. The force measured at the left bearing had a peak of 22.24 N at a
phase angle of 45 with respect to zero reference angle on the tire. The forcemeasured at the right bearing had a peak of 8.9 N at a phase angle (-) 120 withrespect to the reference zero on the tire.
The centre distance between the two bearings on the machine is 254 mm. The left
edge of the wheel rim is 101.6 mm from the centerline of the closest bearing. The
wheel is 177.8 mm wide at the rim. Calculate the size and location with respect to the
tire zero reference angle, of balance weights needed on each side of the rim to
dynamically balance the tire assembly. The wheel rim diameter is 381 mm.
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Answers
Correction weight radii: eA = eB = 0.1905 m
mA = 2.55 kg, mB = 1.896 kg
A = 221.15, B = 43.09