BITS PilaniPilani Campus

Jitendra S Rathore

Department of Mechanical Engineering

Balancing of Reciprocating masses

Unbalance

Rotating Unbalance Reciprocating Unbalance

Single plane

Primary force

& couple

Secondary

force & couple

Different plane

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

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

rB

A

C

D

O

Complete Balancing for single cylinder engine:

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

Single cylinder engines:

Partial balancing

Multi cylinder engines:

Passive balancing i.e. changing the firing order

Active balancing

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.

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.

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.

Answers

Correction weight radii: eA = eB = 0.1905 m

mA = 2.55 kg, mB = 1.896 kg

A = 221.15, B = 43.09