Design Considerations

The rubber mountings are used to support machines isolating the vibration generated or to prevent precision equipment from external vibration.

Suppose the force transferred to the foundation with the rubber mountings used to support the machine is F and the force without using the rubber mountings is Fo, then the vibration transmissibility TR can be represented as follows.

Fo . vibration generated by machine

F : vibration transferred to the foundation.

u : vibration frequency ratio = f / fN --------------------------- (2)

f : vibration frequency of machine

fN : natural frequency with machine supported by rubber mountings

Formula (l) is illustrated in TR-u chart.

As is evident in the chart, when TR=1(100%)vibration isolating effect is 0% and vibration frequency ratio u is   1.414

Sufficient effect can be obtained when TR<1; therefore u > 1.   Generally, the purpose can be achieved when u = 2~3

Relationship between vibration frequency ratio and vibration isolating effect.

vibration frequency ratio

vibration transmissibility

state of vibration

vibration isolating effects

u=0

TR=1

Fo=F

No effect

u=1

TR

Fo<F

Resonance

u=

TR=1

Fo=F

No effect

u>

TR<1

Fo>F

Sufficient  effect

The vibration transmissibility is decided by the vibration frequency ratio u given by (2)

Machine vibration is generated during operation and the vibration frequency can be given for example as follows:

Type of machine

Vibration frequency

Blowers

Shaft rotating speed, shaft rotating

Speed x number of blades

Motors

Shaft rotating speed，shaft rotating

Speed x number of poles

Gears

Shaft Rotating Speed x Number of gears f

gears elastic vibration of gears (very high

frequency)

Ball bearings

Shaft rotating speed x number of balls x 2

AC machines

(transformers)

Ac machines ac frequency x 2

Compressors

Internal Combustion Engines

Shaft rotating speed

Vibration frequency of secondary or over

The natural frequency is decided by the weight of machine and spring rate of rubber mounting.

fN : natural frequency (Hz)

K: spring rate (lb/in or kg/cm)

W : machine weight (lb or kg)

g : acceleration of gravity (386.4 in/sec2 or 980cm/sec2 )

Vibration transmissibility

The natural frequency in vertical direction is related with the deflection of rubber mounting due to the machine weight, and can be represented as follows:

where  = deflection of rubber mounting (cm).

The standard vibration transmissibility according to the size of machine, installation place type of equipment and purpose of building are shown in the following.

1.Classified by output of machine

Power

Vibration transmissibility  (%)

Basement and 1st floor

Higher floors heavy structure

Higher floors light structure

~5

Noise control

50

10

7.5~15

50

25

7

20~40

20

10

5

50~100

10

5

2.5

100~300

5

3

1.5

2.Classified by type of machine

Type

Vibration transmissibility  (%)

Basement 1st floor

Higher floors heavy structure

Package type coolers

30

10

Air conditioners

30

20

Centrifugal refrigerators

20

10

Reciprocating          ~10 hp

 Refrigerators       15 hp~50 hp

                                                                                                                                                                60 HP~150 HP

30

15

25

10

20

5

Cooling towers

30

15~20

Condensers

30

20

Ventilation units

30

20

Piping

30

5~10

Pumps                   ~3 hp

                            5~ HP

30

20

20

5

3.Classified by purpose of building

Location

Buildings

Vibration transmissibility  (%)

Only noise control

Factories, Basements,

Warehouses, Garages

80~150

General purpose

Offices, Shops, Restaurants

20~80 (approx.30)

Places requiring caution

Hotels, Hospitals, Schools,

Churches, Conference Rooms

5~20 (approx.30)

Places requiring special caution

Studios, Concert Halls

High Rise Buildings

1~5

Practical design guide line

l. Determination of positions

The support positions must be decided so that the static loads at the support points are nearly equal. In the case of general industrial machines, the anchor bolt positions are used as the support points but it is necessary to re-check the positions when the load is unevenly distributed.

2. Determination of natural vibration frequency and spring rate

Calculate the natural frequency and spring rate according to the aforementioned ''Vibration isolating principles''.

3. Selection of rubber mountings

Select appropriate rubber mountings taking into account the spring rate, allowable load, allowable deflection and forcible power direction.

If vibration transmissibility TR=25%or less is intended, then the frequency ratio u=f/fn=2.24 from formula (1), and the natural frequency f N =f/u = l,170/2.24 = 523 cpm.

2-3 Calculation of spring rate

Since the static load per point is 617 lb,the required spring rate is as follows from formula (3).

Determination of spring mount isolators

3-1 Selection of mountings：Select the mountings which satisfy the following conditions.

(1) Spring rate K= 4820 lb/in or less

(2) Load W = 617 lb

(3) Deflection  = 617/4820 = 0.13 in

QDI spring mounts SMA-1-8 can satisfy these conditions.

3-2 Check of vibration transmissibility

JA-1-400 Spring rate K= 789 lb/in.     Allowable load W=800 lb max.

Natural frequency fx=212 cpm from formula (3).Vibration frequency ratio from formula (2).

u1 = l,170/212 = 5.52 against compressor rotating speed;

u2 = 1,750/212=8.25 against motor rotating speed. Vibration transmissibility from formula (1):

TR1 = 3.37% against compressor rotating speed,

TR2=1.48% against motor rotating speed. The vibration transmissibility as a whole is 8.29% or less.

3-3 Determination of rubber mountings

Type . QDI Spring Mounts

Product No. : SMA-1-8

Quantity . 6 pcs