Calculate the amplitude of force transmitted:

A machine contains weight 650 kg operates at 1500 rpm. This has an unbalance 0.1 kg m. The damping in the isolators is specified by damping factor J = 0.1. Measure stiffness of isolators so that the transmissibility is less than or equal to 0.15. Calculate the amplitude of force transmitted.

Solution

It is given that

Mass of machine = 650 kg

 Speed = 1500 rpm

 Unbalance = 0.1 kg m

ζ = 0.1

ε = 0.15

0.0225 {(1 - 2r ²  + r ⁴ ) + 0.04 r ² } = 1 + 0.04 r ²

or            r ⁴  - 3.74 r ²  - 43.4 = 0

It gives the following,

r = 2.95

∴ ω/ ω_n  = 2.95

ω= (2π× 1500) /60= 157.1 r/s

ω _n =   ω/2.95 = 157.1 /2.95= 53.25 r/s

∴   

or            k = 650 × (53.25)²  = 1843409 N/m

= 1.84 mN/m

Unbalance = 0.1 kg m

Unbalanced force = 0.1 × (157.1)² = 2468 N

Force transmitted to the ground

= 2468 × 1.5 = 370.2 N