Dynamics of Machines - Part II - IFS.pdf
Dynamics of Machines - Part II - IFS.pdf Dynamics of Machines - Part II - IFS.pdf
1.11 Project 1 – Modal Analysis & Validation of Models GOAL – To get familiar with the dynamic interaction between machine and structure, the elaboration of mechanical and mathematical models for representing rotor-structure vibrations in 2D, implementation and vibration analysis using Matlab, visualization of natural frequencies and mode shapes. To test the accuracy of an analytical mathematical model proposed for describing the system dynamic behavior, i.e. natural frequencies and mode shapes. Remember, if the measured frequencies and mode shapes agree with those predicted by the analytical mathematical model, the model is verified and can be useful for design proposes and vibration predictions with some confidence. Otherwise, the analytical models are useless. (a) (b) Figure 38: Machine-structure dynamical interaction – (a) Offshore platform http : //www.oil−gas.uwa.edu.au/Troll−A−Graphics.htm; (b) Equivalent laboratory prototype composed of four concentrated masses attached to four flexible beams: 1- mass on the first floor, 2mass on the second floor, 3- mass on the third floor, 4- mass on the fourth floor, 5- motor-disk with unbalanced masses for simulating a rotating machine with unbalance problems, 6- acceleration sensor attached to the second mass, 7- acceleration sensor attached to the third mass, 8- magnetic actuator for simulating wave excitation, 9- magnetic actuator for simulating waves excitation. Figures 38(a) and (b) illustrate an offshore platform and an equivalent laboratory prototype, where the students can carry on measurements and vibration analyzes. The laboratory prototype is composed of four concentrated masses attached to four flexible beams. Elements 1,2,3 and 4 are the four masses connected by means of flexible beams. Element 5 is a motor-disk with a 66
changeable unbalanced mass for simulating rotating machines (for example compressors, turbines or pumps) with an unbalance problem. Elements 6 and 7 are two acceleration sensors attached to the second and third masses. Elements 8 and 9 are magnetic actuators built to apply forces with different dynamic characteristics (oscillatory, random, pulse etc.) to the structure (first floor). In that way it is possible to simulate the wave forces coming from the ocean by means of the magnetic actuators. The motor-disk with unbalanced masses is mounted at the top of the platform (fourth floor). The motor has variable angular velocity from 0 to 40 Hz (2400 rpm). Due to the unbalanced masses strong vibration amplitudes can be detected on the second and third floor of the platform. To represent the dynamical behavior of the system a mechanical model has to be created. Considering the range of frequencies between 0 and 40 Hz, all rotor-structure movements happen in a vertical plane (2D motion), and an appropriate mechanical model would be the one presented in figure 39(b). For the suggested mechanical model: (a) (b) Figure 39: Machine-structure dynamical interaction – (a) Laboratory prototype; (b) Mechanical model composed of four lumped masses attached to four flexible beams, an equivalent model of a 4 D.O.F. system for analyzing the linear vibrations of the platform in the horizontal direction due to the interaction with a machine and ocean waves. 1. MODELLING – The main information about the geometric properties of the structure presented in figure 39(b) is given below: 67
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- Page 33 and 34: ⎧ ⎫ ⎪⎨ ˙y1(t) ⎪⎬ ˙y
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1.11 Project 1 – Modal Analysis & Validation <strong>of</strong> Models<br />
GOAL – To get familiar with the dynamic interaction between machine and structure, the elaboration<br />
<strong>of</strong> mechanical and mathematical models for representing rotor-structure vibrations in<br />
2D, implementation and vibration analysis using Matlab, visualization <strong>of</strong> natural frequencies and<br />
mode shapes. To test the accuracy <strong>of</strong> an analytical mathematical model proposed for describing<br />
the system dynamic behavior, i.e. natural frequencies and mode shapes. Remember, if the measured<br />
frequencies and mode shapes agree with those predicted by the analytical mathematical<br />
model, the model is verified and can be useful for design proposes and vibration predictions with<br />
some confidence. Otherwise, the analytical models are useless.<br />
(a) (b)<br />
Figure 38: Machine-structure dynamical interaction – (a) Offshore platform http :<br />
//www.oil−gas.uwa.edu.au/Troll−A−Graphics.htm; (b) Equivalent laboratory prototype composed<br />
<strong>of</strong> four concentrated masses attached to four flexible beams: 1- mass on the first floor, 2mass<br />
on the second floor, 3- mass on the third floor, 4- mass on the fourth floor, 5- motor-disk<br />
with unbalanced masses for simulating a rotating machine with unbalance problems, 6- acceleration<br />
sensor attached to the second mass, 7- acceleration sensor attached to the third mass,<br />
8- magnetic actuator for simulating wave excitation, 9- magnetic actuator for simulating waves<br />
excitation.<br />
Figures 38(a) and (b) illustrate an <strong>of</strong>fshore platform and an equivalent laboratory prototype,<br />
where the students can carry on measurements and vibration analyzes. The laboratory prototype<br />
is composed <strong>of</strong> four concentrated masses attached to four flexible beams. Elements 1,2,3 and<br />
4 are the four masses connected by means <strong>of</strong> flexible beams. Element 5 is a motor-disk with a<br />
66
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