Question

A 100 [kg] reciprocating internal combustion engine is fitted to a thin, massless beam using a vibrations damper. It is known that a machine with a rotating unbalance experiences a frequency squared harmonic excitation. The magnitude of the rotating unbalance is A = m,e = 0.3 [kg. m). 1. Calculate the nondimensional function for the state that has a steady state amplitude of 10 [mm] at a 90 [rad/s] speed. 2- Determine the frequency ratio, natural frequency, and the beams equivalent stiffness for the rotating machines unbalance. Knowing that the value of the damping ratio is ? = 0.2. 3. Furthermore, find the magnification factor and the damping coefficient used in the damper. 10.1 0.2 0.3 0.4 On the opposite side of the assembly the internal combustion engine is linked to a 90 [kg] electric motor using a coupling. The electric motor operates at a frequency of 60 [HZ] and is mounted on an elastic foundation that has a stiffness of 8106 [N/m] that also has a vibration damper. The phase difference between excitation and the steady state response is 21° 4- What is the damping ratio of the system and what is the used damping coefficient? 5. Write a paragraph which will be added to a technical report which mentions your analysis and recommendation for the studied case for a private contractor.

Answer 1

For the given value of A, the unbalance force is calculated for ω = 90 rad/s. The Non dimensional function in terms of ω is derived. The stiffness of beam, natural frequency and the frequency ratio is calculated afterwards. For the given value of ζ=0.2, the damping coefficient is calculated. The magnification factor is obtained at ω=90 rad/s.

For the second part, using the given data and relating it to the given phase difference, the damping ratio ζ can be obtained. The damping ratio has to be less than 1 but it is coming more than 1. There might be some thing wrong in data given in the problem. Once damping ratio is known, the damping coefficient can be obtained.