# MOST CHALLENGING PART OF VIBRATION MODELING

Introduction

Vibration is one of the most common aspects of life. Many natural phenomena, as well as man-made devices, involve periodic motion of some sort. Vibration is a mechanical phenomenon whereby oscillations occur about an equilibrium point. Vibration can be desirable for example, the motion of a tuning fork, the reed in a woodwind instrument or harmonica, o mobile phone or the cone of a loudspeaker. In many cases, however, vibration is undesirable, wasting energy and creating unwanted sound. For example, the vibration motions of engines, electric motors, or any mechanical device in operation are typically unwanted. Such vibrations could be caused by imbalances in the rotating parts, uneven friction or the meshing of gear teeth. Careful designs usually minimize unwanted vibration.

Vibration Control System

Structural vibration control system is to control the vibration of the structure under unbalanced forces by changing the stiffness, mass, damping and shape of the structure and providing a certain amount of passive or active reaction forces.

Vibration control system is classified as –

•     Passive Control system
•     Active Control system
•     Semi – Active Control system

The passive control system doesn’t require an external power source and being utilizes the structural motion to isolate the vibrations so that response of structure can be controlled. Active vibration control systems, also called active vibration isolation or active vibration cancellation, are isolation systems that dynamically react to incoming vibrations. That is, they sense incoming vibrations and react to them, rather than passively reducing their effect by virtue of their mechanical structure. The semi-active control system compromise between the passive and active control system. The structural motion is utilized to develop the control actions or forces through the adjustment of its mechanical properties.

Vibration Modeling

There are usually two different approaches to mathematical modeling: models made by equations describing the physics of relevant phenomena, - these may be defined as analytical models and empirical models, often called black box models.

In analytical model the equation approximating the behavior of the various parts of the system, along with the required approximations and simplifications, are written. Even if no real-world spring behaves exactly like the linear spring, producing a force proportional to the relative displacement, of its ends through a constant called stiffness and even if no device dissipating energy is a true linear damper, the dynamic of a mass-spring-damper system can be described, often to a very good approximation, by the usual ordinary differential equation (ODE).

The behavior of some systems, on the other hand, is so complex that writing equations to describe it starting from the physical and geometrical characteristics of their structure is forbiddingly difficult. Their behavior is studied experimentally and then a mathematical expression able to describe it is sought, identifying the various parameters from the experimental data. While each of the parameters m, c, and k included in the equation of motion of the mass–spring–damper system refers to one of the parts of the system and has a true physical meaning, the many coefficients appearing in empirical models usually have no direct physical meaning and refer to the system as a whole.

Once the model has been built and the equations of motion written, there is no difficulty in studying the response to any input, assuming the initial conditions are stated.

Vibration Modeling Considerations

Mechanics of vibration is not just a field for theoretical study. Design engineers had to deal with vibration for a long time, but recently the current tendencies of technology have made the dynamic analysis of machines and structures more important.

The following considerations the designer has to make for designing a vibration model –

• ·         The load conditions the designer has to take into account in the structural analysis of any member of a machine or a structure can be conventionally considered as static, quasi-static or dynamic.
• ·         All possible environmental effects (creep, corrosion, etc) must be taken into account.
• ·         If the deformations of the structure are consistent with the regular working of the machine.
• ·         Fatigue must generally be taken into account, and often the methods based on fracture mechanics must be applied.
• ·         Speed

Vibration Modeling Challenges

The computational predictions of the characteristics and the performance of a physical system are based on the construction of a mathematical model, constructed from a number of equations, whose behavior is similar to that of the physical system it replaces.

The complexity of the model depends on many factors that are the first challenge the analyst has to make. The model must be complex enough to allow a realistic simulation of the system’s characteristics of interest, but no more. The more complex the model, the more data it requires, and the more complicated are the solution and the interpretation of the results. Today it is possible to built very complex models, but overly complex models yield results from which it is difficult to extract useful insights into the behavior of the system.

It may require long computation time (and thus high costs) if the model is complex, or has characteristic that make numerical integration difficult, and it allows the effects of changes of the values of the parameters to be predicted only at the cost of a number of different simulations.

Another most challenging part is elimination of additional energy sources, isolate the system from external disturbances e.g. balancing, decrease of colliding bodies mass etc.

The damping is also an important parameter. It refers to mechanical dissipation which is exchanged to heat. It causes the decrease of general efficiency of machines and devices. In case when the undesirable vibrations cannot be eliminated via constructional or parameters changes the damping should be introduced. It a great challenge to maintain proper damping.

Conclusion

Vibration models are useful not only to the designer but also to the test engineer in interpreting the results of testing and performing all adjustments. The analyst has the duty not only of building, implementing and using the models correctly but also of updating and maintaining them. Before building the model, the analyst must be certain about what he wants to obtain from it.  In case of doing so, comes greater challenges. The analyst must be able to cope with these challenges.

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