Control Techniques

In the control of noise we basically considered three areas: the source, the path, and the receiver. Vibration control may involve one or a combination of the following techniques.

(a) Source alteration

In the control of vibration it is important to first check and see if the noise or vibration level can be reduced by altering the source. This may be accomplished by making the source more rigid from a structural standpoint, changing certain parts, balancing, or improving dimensional tolerances. The system mass and stiffness may be adjusted in such a way so that resonant frequencies of the system do not coincide with the forcing frequency. This process is called detuning. Sometimes it is also possible to reduce the number of coupled resonators that exist between the vibration source and the receiver of interest. This technique is called decoupling. Although these techniques can be applied during design or construction, they are perhaps more often used as a correction scheme. However, it is also important to ensure that the application of these schemes does not produce other problems elsewhere.

(b) Isolation

In general, vibration isolators can be broken down into three categories: (i) metal springs, (ii) elastomeric mounts, and (iii) resilient pads. Before examining each of these areas, a few general comments can be made which are pertinent to all categories. We must always remember that we are assuming a single-degree-of-freedom system, and therefore our analysis will not be exact in every case. However, practical systems are normally reduced to this model because it is the only one that we understand thoroughly.

When building or correcting a design, always ensure that the machine under investigation and the element that drives it both rest on a common base. Always design the isolators to protect against the lowest frequency that can be generated by the machine. Design the system so that its natural frequency will be less than one-third of the lowest forcing frequency present. The isolation device should also reduce the transmissibility at every frequency contained in the Fourier spectrum of the forcing function.

 

(i) Metal springs

Metal springs are widely used in industry for vibration isolation. Their use spans the spectrum from light, delicate instruments to very heavy industrial machinery. The advantages of metal springs are: (a) they are resistant to environmental factors such as temperature, corrosion, solvents, and the like; (b) they do not drift or creep; (c) they permit maximum deflection; and (d) they are good for low-frequency isolation. The disadvantages of springs are (a) they possess almost no damping and hence the transmissibility at resonance can be very high; (b) springs act like a short circuit for high-frequency vibration; and (c) care must be taken to ensure that a rocking motion doe not exist.

Careful engineering design will minimize the effect of some of these disadvantages. For example, the damping lacked by springs can be obtained by placing dampers in parallel with the springs. Rocking motions can be minimized by selecting springs in such a way that each spring used will deflect the same amount. In addition, the use of an inertia block that weighs from one to two times the amount of the supported machinery minimizes rocking lowers the center of gravity of the system, and helps to uniformly distribute the load. High-frequency transmission through springs caused by the low damping ratio can be blocked by using rubber pads in series with the springs. A typical damping ratio for steel springs is 0.005.

The design procedure for selecting springs for vibration isolation is outlined below:

EXAMPLE 2

A machine set operating at 2400 rpm is mounted on an inertia block. The total system weighs 907 N. The weight is essentially evenly distributed. We want to select four steel springs upon which to mount the machine. The isolation required is 90%.

 

(ii) Elastomeric mounts

Elastomeric mounts consist primarily of natural rubber and synthetic rubber materials such as neoprene. In general, elastomeric mounts are used to isolate small electrical and mechanical devices from relatively high forcing frequencies. They are also useful in the protection of delicate electronic equipment. In a controlled environment, natural rubber is perhaps the best and most economical isolator. Natural rubber contains inherent damping, which is very useful if the machine operates near resonance or passes through resonance during "startup" or "shutdown." Synthetic rubber is more desirable when the environment is somewhat hazardous.

Rubber can be used in either tension, compression or shear; however, it is normally used in compression or shear and rarely used in tension. In compression it possesses the capacity for high-energy storage; however, its useful life is longer when used in shear. Rubber is classified by a durometer number. Rubber employed in isolation mounts normally ranges from 30-durometer rubber, which is soft, to 80-durometer rubber, which is hard. The typical damping ratio for natural rubber and neoprene is z = 0.05.

One word of caution when dealing with rubber: it possesses different characteristics depending upon whether the material is used in strips or bulk, and whether it is used under static or dynamic conditions. The steps for selecting an elastomeric mount are essentially those enumerated in the previous section on metal springs. The following examples will illustrate the procedure.

 

EXAMPLE 3

A drum weighing 120 N and operating at 3600 rpm induces vibration in adjacent equipment. Four vertical mounting points support the drum. Choose one of the isolators shown in Figure 6 so as to achieve 90°/ vibration isolation.

Figure 6 Typical Load vs. Deflection Curve for an Elastomeric Mount

(iii) Isolation pads

The materials in this particular classification include such things as cork, felt, and fiberglass. In general, these items are easy to use and install. They are purchased in sheets and cut to fit the particular application, and can be stacked to produce varying degrees of isolation. Cork, for example, can be obtained in squares (like floor tile) 1 to 2.5 cm in thickness or in slabs up to 15 cm thick for large deflection applications. Cork is very resistive to corrosion and solvents and is relatively insensitive to a wide range of temperatures. Some of the felt pads are constructed of organic material and hence should not be employed in an industrial environment where solvents are used. Fiberglass pads, on the other hand, are very resistant to industrial solvents. A typical damping ratio for felt and cork is z = 0.05 to 0.06.

 

EXAMPLE 4

A large machine is mounted on a concrete slab. The lowest expected forcing frequency is 60 Hz. If the isolator will be loaded at 7 N/cm2, choose the proper fiberglass isolator from the manufacturer's data shown in Figure 7 to produce 80% isolation. Assume that the damping ratio of the material is z = 0.05.

 

Figure 7 Typical Natural Frequency vs. Static Load Curves

for Fiberglass

 

(iv) Inertia blocks

Isolated concrete inertia blocks play an important part in the control of vibration transmission. Large-inertia forces at low frequencies caused by equipment such as reciprocating compressors may cause motion that is unacceptable for proper machine operation and transmit large forces to the supporting structure. One method of limiting motion is to mount the equipment on an inertia base. This heavy concrete or steel mass limits motion by overcoming the inertia forces generated by the mounted equipment.

Low natural frequency isolation requires a large deflection isolator such as a soft spring. However, the use of soft springs to control vibration can lead to rocking motions which are unacceptable. Hence, an inertia block mounted on the proper isolators can be effectively used to limit the motion and provide the needed isolation.

Inertia blocks are also useful in applications where a system composed of a number of pieces of equipment must be continuously supported. An example of such equipment is a system employing calibrated optics.

Thus, inertia blocks are important because they lower the center of gravity and thus offer an added degree of stability; they increase the mass and thus decrease vibration amplitudes and minimize rocking; they minimize alignment errors because of the inherent stiffness of the base; and they act as a noise barrier between the floor on which they are mounted and the equipment that is mounted on them. One must always keep in mind, however, that to be effective, inertia blocks must be mounted on isolators

Consider the system shown in Figure 8. The equations of motion that describe the systems are :

(9)

 

Figure 8 Model for the Analysis of Vibration Absorber

 

The magnitude of the frequency response is obtained from the following equations :

(10)

Now note what happen to the equations above if the forcing frequency w is equal to the natural frequency of the vibration absorber (i.e. ). Under this condition :

 

(11)

 

Therefore, the motion of the main mass is ideally zero and the spring force of the absorber is at all times equal and opposite to the applied force, . Hence no force is transmitted to the supporting structure.