Firestone EMDG198 manual Dynamic Spring Rate Formula, Natural Frequency Formula

AIRMOUNT® VIBRATION ISOLATION

b)What exact isolation will be attained? Use the formula:

% Transmission =		100
	(fffn )2 – 1

Where: ff = Forced Frequency

fn = Natural Frequency

The forced frequency is 850 cpm Read the natural frequency from the line at the load and pressure closest to the actual situ- ation, or 106 CPM (@ 80 psig and 4,280 Ibs.):

% Transmission =		100
	(850106)2 – 1

%Transmission = 1.6%

%Isolation = 100 – % Transmission

%Isolation = 100 – 1.6

%Isolation = 98.4%

Notice that the natural frequency of an Airmount changes only slightly with variations in pressure and load. Therefore, when working at pressures other than 40, 60, 80, or 100 psig, % iso- lation can be calculated quite accurately using the “closest” natural frequency and the formula above.

DYNAMIC SPRING RATE FORMULA

Consider the same #22 example: What is the vertical spring rate with a load of 4,100 pounds at a design height of 9.5 inches? Refer to the static data chart on page 61. Again, our “closest" pressure is 80 psig, so we'll need to read the appropriate data from the 80 psig curve.

The 80 psig information at 1/2 inch above design height would fall at the 10.0 inch height line, and 1/2 inch below design height would fall at the 9.0 inch height line. (In this example, we can read loads from the force table). The information at design height is located in the “Dynamic Characteristics Block.” So,

K= Unknown

Pg = 76.6 psig (see page 13)

Ac = 58.4 in2 (4,670 lbs). 80 lbs/in2

Ae= 47.6 in2 (3,810 lbs). 80 lbs/in2

V1 = 782 in3

Vc = 752 in3

Ve = 809 in3

K=[Pg +14.7] [Ac(VV1c)1.38–Ae(VV1e)1.38]–14.7(Ac–Ae)

Spring rate is a different matter. Unlike most conventional springs, the rate of an Airmount is not constant. It is a function of the change in effective area, volume, and pressure from design height. To determine the rate of an Airmount, use the following formula:

[ (782)1.38 (782)1.38]

K=[76.6+14.7] 58.4 –47.6–14.7

752809 (58.4–47.6)

K = 1,324 lbs/inch

K=[Pg +14.7] [Ac(VV1c)1.38–Ae(VV1e)1.38]–14.7(Ac–Ae)

WHERE:

K = Vertical Spring Rate in Ibs./inch

Pg = Gauge Pressure at design height (lbs)

in2

Ac = Effective Area at 1/2 inch below design height (in2) Ae = Effective Area at 1/2 inch above design height (in2) V1 = Internal Volume at design height (in3)

Vc = Internal Volume at 1/2 inch below design height (in3) Ve = Internal Volume at 1/2 inch above design height (in3)

NATURAL FREQUENCY FORMULA

Once the spring rate is determined, calculate the Airmount natural frequency (for an undamped system) as follows:

fn= 188√K L

Where:

fn = Natural Frequency in cycles per minute (cpm)

K= Rate (Ibs/inch)

L= Load (pounds)

in our example:

√1,324 fn= 188 4,100

fn = 106.8 cpm

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