Question

A CPVA is attached to the crankshaft driven by a three-cylinder four-stroke engine which produces a maximum primary torque oscillation of magnitude T0 = 30 Nm. The circular path of the absorber is centered at a point R = 5 cm from the center of crankshaft rotation. Find the desired radius and mass of the absorber if the absorber is to not exceed an angular deflection amplitude of 30 degrees when the engine is running at 750 rpm.

Answer 1

Here Torque is given 10Nm and R = 5cm

According the formula

T = R X F ................(1)

T = RF sin(theta) ...................(2)

30 = 5 F sin30

F = 60 N

Now calculate omega

1 rad/sec = 9.5493 rpm

theefore

= 9.5493 *750 = 7161 rad/sec

According Newton 3rd Law, magnitude has to take here

Fa = Fr (Fa = absorber, Fr = Rotation )

M(w0^2-)/(theta) = Fr

M/(theta) = Fr/wo^2 (M/(theta) = Mass absorber angular deflecation of 30, Wo = angluar velcocity during absorber, Fr = Cranshaft rotation )

M/(theta) = 60 / (7161^2 ) = 11.71 * 10^-7 kg/rad

Find desired radius

Ar = Rr w^2 ( Ar = accleration, Rr = Radius, w = angular velocity)

Fr/Mr = Rr * w^2

Rr = 60/11.71 * 10^-7 * 5.12 * 10^7 = 60/ 59.95 ( 59.9 ~ 60)

Rr = 1 cm

Answer 2

omega calculation incorrect, rest of calculation suspect