Architectural Environmental and Engineering
VIBRATION ISOLATION Lecture objectives By the end of this lecture you should be able to
• explain why vibration is a potential problem in buildings and why it is best to isolate machinery and reduce the problem at source • calculate the operating frequency of a machine, given its RPM
• calculate the resonant frequency of a mass-spring system
• describe what transmissibility is
• sketch a graph showing the transmissibility of a mass-spring system at different frequencies and describe how the isolation varies
• calculate transmissibility, given the operating frequency and mass of a machine and the stiffness of the spring that supports it
• calculate the stiffness of a set of springs that will provide a specified transmissibility for a machine of known mass and operating frequency
• calculate the stiffness of a set of springs that will provide a specified transmissibility for a building/room of known mass supported on a site with high levels of vibration
• understand how the practicalities of operating rotating machinery impact upon vibration isolation and what measures may be implemented to reduce the risk of complaints
• describe other examples of isolation in buildings
The structure of a building provides a convenient transmission path for sound. Once sound has entered the structure, it is able to propagate relatively freely in the form of vibrations and can give rise to serious noise problems. Figure 6.1: Airborne and structureborne excitation in a building Sound can enter the structure of a building in two ways, either by sound waves causing the structure to vibrate, or by a fluctuating force acting directly on the structure (for example from a machine, a footstep or a slamming door). Of these two forms of excitation, the second is potentially the most serious as it is capable of injecting considerable amounts of energy into the building and cause severe noise problems, often some considerable distance from the source. Noise problems generally have three components, a source (in the case above, a machine), a transmission path (the building) and a receiver (the occupant).
The preferred method of dealing with a noise problem is to tackle it at source, which in this case means trying to prevent, or at least reduce, the amount of sound entering the structure. This lecture looks at techniques that may be used to achieve this. These use springs or resilient materials to isolate the source of vibration from the structure, allowing it to vibrate but reducing the amount of vibration energy that is Airborne excitation of the structure only injects small amounts of power that are less likely to cause noise problems in distant rooms. Direct excitation of the structure injects significant amounts of power that can travel large distances through the building and cause noise problems in distant rooms. Vibration can travel relatively freely through the building structure Vibration excites sound waves in rooms distant from the source and can result in noise problems Lecture 6a Vibration Isolation 2 transmitted. We begin by looking at a special class of vibration problem commonly encountered in building design – that of the machines we use to move air, water and other things around buildings. The general behaviour of fans pumps and other motor driven devices will help us develop a general understanding of the concepts of vibration and what may be done to minimise problems. We then move on to more general examples of vibration generation and its isolation encountered in buildings.
1 Isolation of rotating machinery If you wish to solve a vibration problem, it is necessary to have some understanding about how isolators work. When selecting an isolator, great care has to be exercised to ensure that it is properly matched to the source of vibration. An unsuitable design can have a detrimental effect, resulting in the amplification rather than the isolation of vibration. The behaviour and isolation of rotating machinery (pumps, fans, electric motors, etc.) is a convenient example for illustrating how vibration problems arise, the techniques for reducing vibration, and how the potential pitfalls associated with isolators may be avoided. 1.1 How does rotating machinery cause vibration?
Machinery that makes use of rotating components always represents a potential source of vibration. Great care is usually taken during manufacture to ensure that there is an even distribution of material about the axle in order to guarantee smooth running. However, it is not possible to perfectly balance components with the consequence that when the machine is switched on, even a slight imbalance will cause the whole machine to bounce up and down, once each time the machine rotates. This transmits a force into the building structure causing it to vibrate. Figure 6.2: Out of balance force and its impact on vibration The frequency of this excitation is related to the speed at which the machine rotates. The speed of a machine is often described by its RPM – revolutions per minute. As frequency is defined as the number of oscillations per second, the operating frequency of the machine, fo (the frequency of the exciting force), is given by: �! = “#$ %& (Eqn. 1)
The faster a machine operates, the higher the frequency of the exciting force. Floor When the mass is distributed evenly about an axle, there is no vibration An imbalance causes the machine to bounce up and down once during each and every revolution. Out of balance mass Machine This motion is transmitted through the case of the machine causing the out of balance force to act on the building, resulting in vibration of the building’s structure Example 1 Find the operating frequency, fo of a machine that rotates at 4000 RPM. �! = “#$ %& = ‘&&& %& = 66.7 �� Lecture 6a Vibration Isolation 3 1.2 Simple model of a machine supported on an isolator Supporting the machine on springs is one potential way of reducing the force transmitted to the building. To understand how isolators work it is convenient to simplify the physical system shown on the left and represent it with the model on the right of figure 6.3. Figure 6.3: Machine isolation as a mass-spring system The machine is represented by a mass, m, on which the out of balance force, Fi, acts. The individual springs that support the machine can be grouped to form one big spring of stiffness, k, on which the mass is supported. This single spring transmits a force, Ft, to the building, represented by the rigid foundation. �()*+,- = Σ�)*.)/).01, (�/�) Every mass-spring system has a particular frequency at which it will vibrate freely. If you were to press down on the mass in figure 6.3 and then release it, it would spring back up and then continue to oscillate at its resonant frequency, fn, given by: �* = 2 34 05 6 �� (Eqn. 2) where m is the mass of the vibrating object (in kg) and k is the stiffness of the isolator (in N/m) on which it is supported. + = The physical system of a machine isolated from a building using springs is represented by a mass, M, on a spring of stiffness, k, supported on a rigid foundation Fi Ft M k Example 2 A machine is supported on four springs each of stiffness 3000N/m. If you wish to represent these as a single spring, how stiff would it be? �!”#$%& = Σ�”#'”(“‘)*% (�/�) = 3000 × 4 = 12000 �/� Example 3 Find fn for a machine of mass 100kg supported on four springs each of stiffness 1000N/m. �# = 1 2� 2� � �� = 1 2� 2(4 × 1000) 100 = 1.01 �� Lecture 6a Vibration Isolation 4 1.3 Transmissibility, �
It is desirable to have some means of assessing how efficient a spring is at reducing vibration in order to compare different isolators and select those that are most suitable. The quantity that describes how efficient the spring is at isolating the building from an applied force is called transmissibility, �. This is defined as the ratio of the transmitted force to the incident force. � = 7+ 7, = 1+ 1, = /+ /, = 8+ 8, (Eqn. 3) Similar definitions of � can be written in terms of the acceleration, a, velocity, v, or displacement, x, occurring at either end of the spring as indicated above.
The transmissibility is related to the ratio of the forcing (or operating) frequency, fo, to the resonant frequency of the mass-spring system, fn, and may be calculated using: � = 2 2 29: -. -/ ; 02 this can be rearranged to give 3 <. fn x √2 it becomes less than 1. The transmitted force is less than the incident force and the spring provides isolation. Well-designed isolators operate in this region. fn fn x √2 Frequency (Hz) Transmissibility � 1 � =1 no isolation � >1 amplification � <1 isolatio Lecture 6a Vibration Isolation 5 1.3.2 Selecting an isolator The transmissibility curve tells us that to select a suitable isolator for a piece of machinery it is important that the operating frequency, fo, is at least equal to fn x √2 for the mass-spring system and should ideally be much higher than this. Figure 6.4: Isolation regions Often the mass of the machine and its operating frequency will be known and the stiffness of the isolator will need to be calculated based on the degree of isolation required.
The example below illustrates the procedure. fn fn x √2 Frequency (Hz) Transmissibility 1 Avoid!!! Design isolators to operate in this region, ie ensure fo>>√2fn Fi Ft Fi Ft Ft Fi Example 4 A machine of mass 100kg has an operating frequency of 83.3Hz and an out of balance force of 10N. It is supported on four springs with a total stiffness of 7.96×105 N/m. Determine: 1. The resonant frequency of the system 2. The transmissibility of the system at the operating frequency 3. The force transmitted to the building 1. To determine the resonant frequency of the system, fn �# = 1 23 84 5 �� = 1 23 86.89×1;! 1;; = 14.2 �� 2. Transmissibility of the system � = 9 1 1<= “# “$ > %9 = : 1 1<= &’.’ )*.%> %: = 0.03 3. Force transmitted � = ?+ ?, �ℎ������� �@ = � × �” = 0.03 × 10 = 0.3 Lecture 6a Vibration Isolation 6 The second commonly encountered problem is that of designing an isolator when you have been given the required transmissibility. The design procedure in this case is a little different. 2 Design practicalities It is common for machinery in buildings to operate intermittently, i.e. there will be periods of inactivity when they are not switched on. These are interspersed with periods of activity when they have to be run up to their operating speed and then, when they are no longer required, back to stationary. This has implications on isolator design as it means that the operating speed will increase from zero up to the rated speed and then back to zero again. Figure 6.5: Passing through the resonant frequency of a system Example 5 A machine of mass 135kg has an operating frequency of 40Hz and an out of balance force of 0.8N. You have been asked to design an isolator that will ensure the transmitted force is no greater than 0.08N.
Determine: 1 The transmissibility 2 The resonant frequency of the mass-spring system 3 The total stiffness of the isolators 1 Determine the transmissibility of the system, � � = ?+ ?, = ;.;A ;.A = 0.1 2 Determine the resonant frequency of the mass-spring system, fn A B# B$ B 2 = 1 + 1 C �� �� ���� �� ��������� ��� �# �# = B# D1E) – = F; D1E ) ..) = 12.06 �� 3 Determine total stiffness of the isolators, k �# = 1 23 84 5 �� �� �� ���� �� ��������� ��� � � = �(�# × 2�)2 = 135 × (12.06 × 2�)2 = 7.75 × 10G �/� fn fn x √2 Frequency (Hz) Transmissibility e 1 Avoid!!! Operating frequency fn fn x √2 Frequency (Hz) Transmissibility e Avoid!!! Standby frequency 1 Lecture 6a Vibration Isolation 7 During start up, the operating frequency increase from 0Hz to fo and has to pass from the low frequency region where no isolation is offered and through the resonant, amplification region, fn before the isolator system starts to do its job. When the machine shuts down and the operating frequency drops from fo back to 0Hz, the system again passes through the amplification region, fn. In both cases, the effect of the machine on the building is amplified and if care is not taken, serious noise problems can be observed. To minimise the likelihood of complaint, isolators usually include a damper that works in parallel with the spring.
This significantly reduces the amplification around the resonant frequency. Displacement limiters can also be used to limit the vibration of the machine as it passes through the peak resonant region. The effects can be reduced further by designing the machine to speed up and slow down quickly so as little time as possible is spent in the region of no isolation. Figure 6.6: Using additional damping to minimise effects of resonant frequency 3 Design shortcuts 3.1 Estimating resonant frequency A simple method for determining the resonant frequency, fn, of a mass-spring system is to measure the static deflection, �, of the isolator caused by the weight of the machine. This can be measured with a ruler by jacking the machine up until the isolator reaches its uncompressed position. If the manufacturer’s data for the isolator is available, this will usually give the uncompressed length of the isolator, from which the displacement may be found by subtracting the length of the compressed isolator beneath the machine. The resonant frequency may then be found from: �* = 2 34 0+ > (Eqn. 5) where g is the acceleration due to gravity. 3.2 Selecting isolators to solve noise problems Occasionally isolators are inadvertently omitted from machinery. Under such circumstances the transmissibility, �, is equal to 1 and problems are likely to result from the vibration entering the building structure and radiating into nearby rooms. In any affected room, it may be desirable to reduce the resulting noise level by an amount Δ�H in order to alleviate the problem. It is possible to use this as the basis on which to design the isolator, the transmissibility of which may be found from: Δ�# = 10��� 2 = (Eqn. 6) If there is an isolator present and its transmissibility, �1, is known but is found to be providing inadequate noise protection, the transmissibility of a new isolator, �2, required to reduce the noise by Δ�H can be estimated using: Δ�# = 10��� =I =0 (Eqn. 7) fn fn x √2 Frequency (Hz) Transmissibility e 1 Un-damped isolator Damped isolator M k R Lecture 6a Vibration Isolation 8 4 Other examples of isolation in buildings There are numerous examples of vibration isolation in buildings. These do not always make use of springs, often using resilient or flexible materials instead. Although these do not look like springs, they behave in an almost identical manner. 4.1 Floors for noise sensitive areas One of the most common examples of an isolator in a domestic building is a floating floor. This is often used to isolate dwellings (e.g. flats). Footsteps and any other form of impact, if they are allowed to take place directly on the structural part of the floor, can result in unacceptably high levels of sound being transmitted to rooms below.
To reduce transmission a floating floor is used. This consists of a timber top surface (boards, ply or chipboard) supported on a layer of very soft material – open cell plastic foam or mineral wool quilt. Figure 6.7: Impact noise through floors These materials behave like many little springs acting in parallel and isolate the walking surface from the structural part of the floor. Care must be taken to ensure that you do not unintentionally provide a transmission path for the vibration to enter the structure of the building. It is important to ensure that the walking surface does not touch the wall or the skirting board i.e. Figure 6.8: Short circuiting an isolator Another potential problem is associated with sound bridges created by driving nails through the resilient layer (in timber floors) or by incomplete coverage by the resilient layer when a concrete walking surface is used i.e. Impacts made directly onto a solid floor can transmit a great deal of sound to the room below and through the supporting structure to distant parts of the building. Providing a resilient layer isolates the walking surface from the building and minimises vibration transmitted to the floor and its supporting structure. LOUD QUIET Walking surface Isolation BAD Vibration is transmitted in this region GOOD Neoprene to isolate perimeter of walking surface from structure Lecture 6a Vibration Isolation 9 Figure 6.9: More isolator short circuits 4.2 Doors Slamming doors can lead to noise problems in buildings. This may be alleviated by providing door closers (designed to arrest the door and close it gently) or by providing foam inserts in the doorframe to reduce the impact and hence the vibration. Figure 6.10: Isolating for impact noise 4.3 Fans Fans have rotating components and therefore represent a potential source of vibration.
They are usually supported on springs to isolate them from the building, however, it is also important that they are also isolated from the ductwork using a bellows isolator. Figure 6.11: Isolating fans / machinery Driving nails through the resilient layer provides vibration transmission bridges through to the structural floor. Thin area in quilt allows bridging of the resilient layer Cement screed Door Wall Slamming doors can generate high levels of vibration Flexible inserts in the frame can reduce vibration levels Much less noise is radiated into duct Much less noise is radiated into room Much less vibration is transmitted along duct Fan isolated from building but not duct Noise is radiated into duct Noise radiated into room Vibration is transmitted along duct Fan isolated from building but not duct Bellows isolator Lecture 6a Vibration Isolation 10 If high levels of vibration are present in duct walls sound will be radiated into surrounding rooms, and into the duct itself often causing noise problems at the outlet. Further precautions may be taken to reduce the likelihood of any vibration in the duct walls from causing problems. Examples include suspending ductwork from resilient hangers and isolating the ductwork from any walls it might pass through. Figure 6.12: Isolating services in buildings 4.4 Isolating building elements
There are often occasions when it is necessary to isolate a whole building from its surroundings in order to reduce noise problems. An entire building may be supported on large rubber blocks to prevent ground borne vibration from entering the structure. In extreme cases the vibrations may be caused by earthquakes, in which case the isolation is provided to prevent collapse. In some specialist buildings (e.g. auditoria) very low background noise levels are required and the whole building may be isolated to prevent ground borne vibration, from nearby railway lines or roads for example, being transmitted to the structure. Figure 6.13: Isolating buildings / rooms within buildings When this proves too expensive, or if only parts of the building contain noise sensitive areas, it is possible to isolate rooms from the rest of the structure. Examples where this strategy is adopted include recording studios and radio studios. 5 Summary It is important to remember that isolating a piece of machinery is not just a case of “sticking a spring underneath it”.
Isolators can make vibration problems much worse unless care is taken over their selection. The greatest danger arises when someone who does not have a clear understanding about how isolators operate proposes their use as an ad-hoc solution to an unforeseen problem. It is therefore important to ensure that someone in the design team goes through the proper design procedure to select a suitable isolator for each potential source of vibration. Many vibration problems Suspend ductwork from resilient hangers in noise sensitive areas Isolate ducts where they pass through structural elements Building is isolated from foundation ring beam using rubber pads to protect it from ground borne vibration, e.g. earthquakes or vibration from trains and road vehicles, industrial processes, etc. Box in a box vibration strategy to protect sensitive areas from vibration within a building.
Structure of noise sensitive room Ring beam to support room and transfer load to isolators Vibration in primary structure Ground borne vibration Lecture 6a Vibration Isolation 11 can be alleviated at the design stage through the selection of quiet, smooth running machinery and then maintaining it correctly during its lifetime to ensure that it continues to run smoothly. Although the initial cost of quieter machinery can be quite high, this will often be offset by the reduced noise control costs. Finally, when dealing with potential vibration problems, ensure that all the possible transmission paths are dealt with. Failure to do so will short circuit and undo the benefit provided by any isolators you may have included in your design.