Relationship Between Vibration Transmission, Disturbing Frequency And Deflection

Figure 1.11


Example 1 — Mounting Method And Part Selection

It is important that anti-vibration mountings are loaded in the correct manner in order to provide the required isolation. This is illustrated in the following typical example (fig 1.12) in which a motor, bellhousing and pump, each of known mass, require isolation. The overall centre of gravity must first be located for the set-up shown.

Figure 1.12

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In order to find the overall centre of gravity of the set-up, which is required to determine mounting positions, it is necessary to take moments.

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Figure 1.13

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The standard motor fixing positions are shown in figure 1.13. It may initially be considered that GMT anti-vibration mountings can be located in these positions. However, this is unsuitable in this case as it can be seen that the overall centre of gravity acts to the left of these fixing positions and so anti-vibration mountings would be unevenly loaded and more seriously, the outermost mountings would be subject to tension which is not recommended. Therefore, it is necessary to rigidly support (i.e. bolt solid to solid) the set-up to a subframe which will then provide positions for the anti-vibration mountings to be installed as shown in figure 1.14.

Figure 1.14

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In this way, equal loading of the mountings is achieved whilst ensuring they are subjected to only compressive forces. It is now necessary to select suitable mountings to adequately isolate the machine as follows:-

For this example, the running speed of the motor is 1450rpm. (NOTE : Had there been equipment with differing running speeds then the lower running speed would be used in the calculations.)

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With reference to the graphical illustration of the relationship between vibration transmission, disturbing frequency and deflection (figure 1.11), a static deflection of approximately 1.8mm is required to give 70% isolation at a running speed of 1450 rpm. A suitable mounting to obtain this desired deflection for the calculated load is a GMT Machine Foot Part No.M/C-MF1890 in 50° Shore A rubber hardness. (An alternative to this part is a GMT Buffer Type A 50/30 in 57° Shore A rubber hardness which gives a deflection of approximately 2.2mm under a load of 90kg which will increase the isolation to 76%.)


Example 2 — Shock Protection, e.g.: A Mass Driven Down By A Force, Striking A Rubber Buffer

It is often necessary to reduce the shock/impact of objects coming to rest and in such applications a rubber element is used as a spring to absorb the energy of the moving object. A typical example is illustrated as follows: A mass of 200kg, initially at rest in position 1 (refer to figure 1.15), is driven down by a force of 0.25kN and by the force of gravity through a distance of 0.22 metres. By the conservation of energy principle:

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Figure 1.15

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The acceleration of the mass due to the 0.25kN force is calculated from:

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The acceleration of the mass due to the gravitational force is:

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Substituting in equation 1(d):

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The formula for calculating the required energy absorption is:

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A GMT Stop Buffer would provide suitable impact protection due to its ability to absorb high shock loads. By a series of linear approximations to the curve at intervals of dx metres deflection, the total area under the graph can be obtained and hence the maximum permissible energy by the buffer can be evaluated (Refer to figure 1.16)

Figure 1.16

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We find that, applying equation1(e) to a GMT Stop Buffer Type RB1073 in 71° Shore A rubber hardness with a value for Xmax taken to be 0.04m (i.e. 50% compression strain - this percentage being dependant upon how frequently the mounting is subjected to the shock loading):

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And applying equation 1(f):

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Therefore, the selected GMT Stop Buffer Type RB1073 in 71° Shore A can absorb the 494J of energy, as it has the capacity to absorb 880J at 50% strain. Alternatively if space is a problem, parts of smaller size and capacity can be selected and mounted in sets of 2, 3, 4 etc.


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