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Vibration and Shock Isolation (tansmissibility

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    Vibration and Shock Isolation (tansmissibility

    Vibration and Shock Isolation


    The principles involved in both vibration and shock isolation are similar. However,
    differences exist due to the steady state nature of vibration and the transient
    nature of shock.
    This paper discusses the basic properties of vibration and shock isolators, the
    requirements for designing successful isolation systems and offers practical
    examples using these principles.



    .
    the pdf paper to learn

    http://www.zshare.net/download/37590971930361/

  2. [2]
    tafatneb_dichar
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    the seconde very good paper to learn



    http://www.herzan.com/herz3.htm

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    Vibrations Transmitted to Floor: Transmissibility

    It is often necessary to try to isolate:
    1. the force developed in a machine from being transmitted to the founda-
    tions, or
    2. the motion developed in some surrounding framework (possibly the °oor)
    from being transmitted to a delicate instrument or machine.
    In each case, the e±ciency of any suitable arrangement (often known as an
    isolator) is called the transmissibility (TR) and is the ratio of output to input
    (force, or displacement). Isolators are often made of visco-elastic materials
    which have both sti®ness and damping characteristics






    From the graph, it follows that for the isolator to be e®ective:
    1. ¯ should have a large value, i.e. !n should be small, which means that k
    should be small - soft spring.
    2. ³ should be small, i.e. damping should be light.
    But, beware of large static de°ections and excessive vibration amplitudes when
    powering up and down through resonance

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  5. [5]
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    Performance

    Based on field testing and user evaluations, the Minus K 1/2-Hz vibration isolation platforms and workstations perform about 10 to 100 times better than high-performance air tables depending on the vibration isolation frequencies. They also perform better than active or electronic-cancellation systems.

    The transmissibility curves, which compare top-performing air tables with the typical Minus K 1/2-Hz performance, are shown below. Minus K isolators (adjusted to 1/2 Hz) achieve 93% isolation efficiency at 2 Hz, 99% at 5 Hz, and 99.7% at 10 Hz. Isolation performance closely follows that of an ideal undamped single DOF system up to about 10 Hz and reaches a floor in the transmissibility curve with some resonances at the higher frequencies.

    The Minus K curve below is typical for any Minus K 1/2-Hz system, horizontal or vertical. Measured transmissibility curves for some Minus K bench top products are also shown below.


    Transmissibility test procedure:

    The transmissibility curves provided by Minus K Technology are generated using a Stanford Research Instruments SR785 Dynamic Signal Analyzer. The output source of the SR785 is set to generate a swept sine signal. This signal is fed into a Labworks PA-138 power amplifier. The amplifier drives a Labworks ET-126 electrodynamic shaker. The shaker is mounted in a heavily reinforced frame that also supports a 650BM-1 isolator. This support isolator has been adjusted to about 2.75 Hz. It has also been modified to work only in the vertical direction. This isolator supports a heavy top plate and whatever ballast weight is needed to bring the total payload including the test isolator up to around 650 pounds.

    Transmissibility as it applies to our isolators is a ratio of the output signal on the top plate divided by the input signal that the base of the isolator sees. One can also think of it as the ratio of what gets through the isolator divided by what is present on the isolator support. Two similar accelerometers are used to acquire the input and output signals. The input accelerometer is attached to the heavy top plate on the 650BM-1 support isolator. The test isolator rests on the heavy top plate as well. This way the accelerometer measures the vibrations that are fed to the isolator. The output accelerometer is placed on top of the properly loaded test isolator top plate. Both accelerometers are held in place with a thin layer of seismic wax. This works quite well, providing a secure, yet easy to undo bond for measurement.

    The SR785 acquires both sets of data, calculates their ratio and displays the ratio as transmissibility..

    The horizontal transmissibility was acquired in much the same way. The differences were that the support isolator was allowed to move horizontally. The electrodynamic shaker was mounted horizontally. The accelerometers were mounted on their sides, which allowed the ratio of horizontal data to be calculated and displayed as horizontal transmissibility.
    BM-1:

    The curve below shows the typical vertical 1/2 Hz performance of the BM-1. It offers 10-100 times better performance than typical high-performance air tables.


    BM-4:

    The curve below shows the typical vertical 1/2 Hz performance of the BM-4. It offers 10-100 times better performance than typical high-performance air tables.

    BM-6:


    The curves below demonstrate the better-than-air performance that the BM-6 delivers. Vertically, the BM-6 offers a resonant frequency that is comparable to or better than most air tables. Horizontally, the BM-6 offers much better performance than typical air tables, which can have horizontal frequencies as high as 4-5 Hz.




    BM-8:

    The curve below demonstrates the vertical 1/2 Hz performance of the BM-8. The BM-8 delivers the high performance of our larger isolators in a package only 4.6 inches tall. The horizontal performance of the BM-8 is the same as that of the BM-6.




    BM-10:

    The curve below shows the vertical 1/2 Hz performance of the BM-10. It offers 10-100 times better performance than an air table in a package many times smaller. The horizontal isolation performance of the BM-10 is the same as that of the BM-6.


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  6. [6]
    tafatneb_dichar
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    very good article to learn

    http://www.zshare.net/download/37602847c87718

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  7. [7]
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    General abutment input

    We may represent a general force input by xo(t) as shown in the diagram. Using Newton II and a free body diagram we obtain the equation of motion as,
    The solution of this equation consists of two parts, the complimentary function (a transient component) and the particular integral [the response to xo(t)].
    A typical excitation and response are shown above. There are various mathematical methods available for solving x(t) for particular examples of xo(t). It is also possible to use numerical methods and an example program has been written using the Runge-Kutta method.

    Sinusoidal input: abutment
    The equation of motion when the abutment input xo(t) is Xosinwt is
    Typical motion resulting from such an exciting force is shown below.
    However if c>0 the motion will after some time settle down to be sinusoidal as shown below.


    Transmissibility

    Transmissibility is defined in two ways. For one degree of freedom vibration both definitions result in the same equation.
    Transmissibility for steady state abutment excitation refers to the ratio of the amplitude of vibration of the mass (X) divided by the excitation amplitude Xo. This has been shown to be
    The other use of transmissibility is when a sinusoidal force is applied to the mass and the force transmitted to the abutment is of interest. The ratio of the amplitude of the force transmitted to the abutment (FT) to the amplitude of the exciting force F is also called the transmissibility. It can be shown that this ratio is the same as that shown above,
    These results may be presented in graphical form. The abutment excitation results apply to force transmissibility.

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  8. [8]
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    Sinusoidal Abutment Excitation

    Sinusoidal Force Excitation

    NOTES:





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    Steady state: abutment
    The equation of motion with a sinusoidal excitation force is
    Typical steady state motion is as shown below.
    The steady state solution for x(t) can be shown to be

    X is the displacement amplitude and f is the phase angle between the displacement and the input.
    It is common to non-dimensionalise these equations so that
    These equations may be presented in graphical form,


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