A rotating machine, such as turbines or compressors, is vibrating and transmitting large forces to the ground. This vibration might be due to shock or unbalanced mass of the rotor. Considering the vibration in vertical direction only, the machine can be represented as a single degree of freedom system having mass M, stiffness K and damper B, subjected to a force, shown in Figure 1.
The harmonic force F is due to rotating unbalance when rotating at speed N (see Table 1).
Table 1: Data for the Mass, spring and damper of the machine and the rotational speed of the rotor.
|
Group #
|
Machine mass M (kg)
|
Spring constant K (N/m)
|
Damping constant B (N.s/m)
|
Rotational speed N (rpm)
|
Mass unbalance mf . e (kg.m)
|
|
1
|
100
|
8400000
|
3000
|
2760
|
2
|
|
2
|
150
|
8650000
|
3000
|
2290
|
2
|
|
3
|
200
|
9900000
|
3000
|
2120
|
2
|
|
4
|
250
|
8950000
|
3000
|
1800
|
2
|
|
5
|
300
|
9100000
|
5000
|
1660
|
2
|
|
6
|
350
|
9200000
|
5000
|
1550
|
2
|
|
7
|
400
|
9350000
|
5000
|
1460
|
2
|
|
8
|
450
|
9500000
|
5000
|
1385
|
2
|
|
9
|
500
|
9650000
|
5000
|
1325
|
2
|
|
10
|
550
|
9800000
|
5000
|
1275
|
2
|
A tuned mass damper device is to be mounted on the machine in order to reduce the dynamic response (the TMD has mass m, spring coefficient k and damping coefficient b. Two newly designs were proposed for the TMD devices, as shown in Figure 2.
Your task, as an engineer, is to evaluate the performance of each system in order to select the best configuration.