Vibration Analysis

**Category : **Railways

**Vibration Analysis**

- Vibration is a mechanical phenomenon whereby oscillations occur about an equilibrium point. The oscillations may be periodic such as the motion of a pendulum or random such as the movement of a tire on a gravel road.
- Vibration is occasionally "desirable". For example, the motion of a tuning fork, the reed in a woodwind instrument or harmonica, or mobile phones or the cone of a loudspeaker is desirable vibration, necessary for the correct functioning of the various devices.
- More often, vibration is undesirable, wasting energy and creating unwanted sound - noise. For example, the vibrational motions of engines, electric motors, or any mechanical device in operation are typically unwanted.
- Such vibrations can be caused by imbalances in the rotating parts, uneven friction, the meshing of gear teeth, etc. Careful designs usually minimize unwanted vibrations.
- The study of sound and vibration are closely related. Sound, or "pressure waves", are generated by vibrating structures, these pressure waves can also induce the vibration of structures hence, when trying to reduce noise it is often a problem in trying to reduce vibration.
- Free vibration occurs when a mechanical system is set off with an initial input and then allowed to vibrate freely. Examples of this type of vibration are pulling a child back on a swing and then letting go or hitting a tuning fork and letting it ring.
- The mechanical system will then vibrate at one or more of its "natural frequency" and damp down to zero.
- Forced vibration is when a time-varying disturbance is applied to a mechanical system. The disturbance can be a periodic, steady-state input, a transient input, or a random input.
- The periodic input can be a harmonic or a non-harmonic disturbance. Examples of these types of vibration include a shaking washing machine due to an imbalance, transportation vibration or the vibration of a building during an earthquake.
- For linear systems, the frequency of the steady-state vibration response resulting from the application of a periodic, harmonic input is equal to the frequency of the applied force or motion, with the response magnitude being dependent on the actual mechanical system.
- Vibration testing is accomplished by introducing a forcing function into a structure, usually with some type of shaker. Alternately, a DUT (device under test) is attached to the "table" of a shaker. Vibration testing is performed to examine the response of a device under test (DUT) to a defined vibration environment.
- The measured response may be fatigue life, resonant frequencies or squeak and rattle sound output (NVH). Squeak and rattle testing is performed with a special type of quiet shaker that produces very low sound levels while under operation.
- For relatively low frequency forcing, servo hydraulic (electrohydraulic) shakers are used. For higher frequencies, electro dynamic shakers are used. Generally, one or more "input" or "control" points located on the DUT-side of a fixture is kept at a specified acceleration.
- Other "response" points experience maximum vibration level (resonance) or minimum vibration level (anti-resonance). It is often desirable to achieve anti-resonance in order to keep a system from becoming too noisy, or to reduce strain on certain parts of a system due to vibration modes caused by specific frequencies of vibration.
- The most common types of vibration testing services conducted by vibration test labs are Sinusoidal and Random. Sine (one-frequency-at-a-time) tests are performed to survey the structural response of the device under test (DUT).
- A random (all frequencies at once) test is generally considered to more closely replicate a real world environment, such as road inputs to a moving automobile.
- Most vibration testing is conducted in a 'single DUT axis' at a time, even though most real-world vibration occurs in various axes simultaneously. MIL-STD-810G, released in late 2008, Test Method 527, calls for multiple exciter testing.
- The vibration test fixture which is used to attach the DUT to the shaker table must be designed for the frequency range of the vibration test spectrum.
- Generally for smaller fixtures and lower frequency ranges, the designer targets a fixture design which is free of resonances in the test frequency range.
- This becomes more difficult as the DUT gets larger and as the test frequency increases, and in these cases multi-point control strategies can be employed to mitigate some of the resonances which may be present in the future.
- Devices specifically designed to trace or record vibrations are called vibroscopes.
- The fundamentals of vibration analysis can be understood by studying the simple mass-spring-damper model. Indeed, even a complex structure such as an automobile body can be modeled as a "summation" of simple mass-spring-damper models.
- The mass-spring-damper model is an example of a simple harmonic oscillator. The mathematics used to describe its behavior is identical to other simple harmonic oscillators such as the RLC circuit.
- To start the investigation of the mass-spring-damper assume the damping is negligible and that there is no external force applied to the mass The force applied to the mass by the spring is proportional to the amount the spring is stretched "
*x*" (we will assume the spring is already compressed due to the weight of the mass). - The proportionality constant, k, is the stiffness of the spring and has units of force/distance.
- Vibrational motion could be understood in terms of conservation of energy. In the above example the spring has been extended by a value of x and therefore some potential energy \[({\scriptstyle{}^{1}/{}_{2}}k{{x}^{2}})\] is stored in the spring.
- Once released, the spring tends to return to its un- stretched state (which is the minimum potential energy state) and in the process accelerates the mass. At the point where the spring has reached its un-stretched state all the potential energy that we supplied by stretching it has been transformed into kinetic energy\[({\scriptstyle{}^{1}/{}_{2}}m{{v}^{2}})\].
- The mass then begins to decelerate because it is now compressing the spring and in the process transferring the kinetic energy back to its potential. Thus oscillation of the spring amounts to the transferring back and forth of the kinetic energy into potential energy.
- In this simple model the mass will continue to oscillate forever at the same magnitude, but in a real system there is always damping that dissipates the energy, eventually bringing it to rest.
- The following are some other points in regards to the forced vibration shown in the frequency response plots.
- At a given frequency ratio, the amplitude of the vibration, X, is directly proportional to the amplitude of the force \[{{F}_{0}}\] (e.g. if you double the force, the vibration doubles)
- With little or no damping, the vibration is in phase with the forcing frequency when the frequency ratio r < 1 and 180 degrees out of phase when the frequency

Whatever the damping is, the vibration is 90 degrees out of phase with the forcing frequency when the frequency ratio r =1, which is very helpful when it comes to determining the natural frequency of the system.

- Resonance is simple to understand if the spring and mass are viewed as energy storage elements –with the mass storing kinetic energy and the spring storing potential energy.
- In other words, if energy is to be efficiently pumped into both the mass and spring the energy source needs to feed the energy in at a rate equal to the natural frequency.
- Applying a force to the mass and spring is similar to pushing a child on swing, a push is needed at the correct moment to make the swing get higher and higher.
- As in the case of the swing, the force applied does not necessarily have to be high to get large motion; the pushes just need to keep adding energy into the system
- The damper, instead of storing energy, dissipates energy. Since the damping force is proportional to the velocity, the more the motion, the more the damper dissipates the energy. Therefore a point will come when the energy dissipated by the damper will equal the energy being fed in by the force.
- At this point, the system has reached its maximum amplitude and will continue to vibrate at this level as long as the force applied stays the same. If no damping exists, there is nothing to dissipate the energy and therefore theoretically the motion will continue to grow on into infinity
- The Fourier transform of the square wave generates a frequency spectrum that presents the magnitude of the harmonics that make up the square wave (the phase is therefore is also generated but is typically of less concern and therefore is often not plotted).
- The Fourier transform can also be used to analyze non periodic functions such as transients and random functions. The Fourier transform is almost always computed using the Fast Fourier Transform (FFT) computer algorithm in combination with a window function.

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