Selection of Coil Spring for Vibratory Screen

7/17/2019 Selection of Coil Spring for Vibratory Screen

1/13

I am evaluating a old set of drawings for a vibratory screen with the following

specifications:

Vibrating Frame Weight (LF): 2265 pounds

Inclined 2 bearing "unbalanced" style

Counterweight (CW): 85 pounds total

Eccentricity of Counterweight from Shaft (R): 2.5"

Shaft Speed: 900rpm

Using the VSMA and general engineering formulas I calculated:

Static Moment = 212.5 inch-poundsDynamic Moment = 425 inch-pounds

Stroke = 0.188 inches

gFactor = 2.2g

The drawing indicates using coil springs with the following specs:

Wire Diameter: 0.5 inch Oil-Tempered Steel Wire ASTM A 229 MB Grade

Coil Mean Diameter: 3.415 inches

Coil OD: 3.915 inches

Free Length: 12 inches

Spring Rate: 195 pounds per inch

Total Coils: 13.5
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2/13

Active Coils: 11.5

There are 8 springs used, 2 in each "corner". From this I calculated the static deflection

to be about 1.45 inches. Typically it seems like springs are chosen that deflect about

30% of their maximum to handle the static load but that leaves unanswered how to

properly size the spring to handle the oscillating load.

I thought about using the 0.188 stroke but during start/stop the screens of this type

exhibit MUCH more travel than the operating stroke at full speed. I also thought about

using the 2.2g acceleration and ensuring the spring could deflect enough to handle the622 pound transient force that such an acceleration produces on this much mass per

the (Force = mass * acceleration) formula but the acceleration is for such a short

amount of time the spring doesn't "seem" to have enough time to "react" and deflect

the 2.9 inches the spring rate would calculate for the resultant force. Likely because

the spring rate formula assumes it is a "static" load for ease of calculation.

What is the rule of thumb or procedure to choose the proper spring to handle the

dynamic loading in this situation or with vibratory screens in general? Spring

manufacturers ask what the L1 and L2 loads are but I hesitate to give them an L2 load

by using F=ma or just giving them the deflection @ L2 from the estimated stroke.

Thanks for wading through all this explanation.

thanks for the techical question. Many of our p eng type contributors can give you a

more mathematical technical answer but, generally.

Most screeners use vertical coil springs which will elimate plus minus 90% of the

inertia or motion of the moving body down thru the vertical line of the coil spring into

the structure.

When the screen is operating that is one thing, but when it shuts down it must handlethe ERRATIC FORCES of the 2 bearing heavy flywheel wgts which are trying in the last

30 seconds of ramp down on shutdown to HOP JUMP AND SOMEHOW come to a stop

eventually. This is the nature of the beast on a 2 brg circle throw design unit. So the

COIL SPRINGS must be able to handle that shutdown dynamic without breaking and we

typically would have a 4" keeper cone on the spring TOP MOUNTING PLATE to help

keep the springs with the machine vs having the screen box jump off the COIL

SPRINGS.

Do not be afraid to consider the use of FIRESTONE MOUNTS, vertical rubber mounts

which work very nicely and much quieter.
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3/13

Also, plan C .......consider ROSTA TYPE SCISSOR MOUNTS.....EXCELLENT....which

dissipate the vibration on shutdown in a horizontal plane vs down thru the structure

and is superb if you are worried about structural vibration.

Best Regards,

George Baker

Regional Sales Mgr - Canada

TELSMITH Inc

Mequon, Wisconsin

1-519-242-6664 Cell

E: (work) [email protected]

E: (home) [email protected]

website: www.telsmith.com

Manufacturer of portable, modular and stationary mineral processing equipment for the

aggregate and mining industries.

Dear Chrome,

Firstly let me comment that the 0.188 inch screen stroke at 900 rpm (giving 2.2 g

acceleration) seems very low, and would not in normal applications provide efficient

screening. Refer VSMA for suggested stroke v speed combinations.

However ignoring this for the moment:

As guru George points out, when selecting support springs for vibrating equipment a

primary objective is to achieve good isolation efficiency i.e.: => 90%, and preferably

=> 95%, with about 98% considered commercially perfect.

In simple terms the greater the spring compression under load (the softer the spring),the more efficient will be its isolation efficiency, and the lower the operating frequency

of the screen, the greater will be the compression required to achieve a nominated

efficiency.

In your case a frequency of 900 rpm would require a spring compression under load of

0.49 inches to give a 90% isolation efficiency, 0.93 inches to give 95%, and 2.26

inches would give 98%. The spring dimensions you describe (with 1.47 inches static

deflection) would achieve 97% isolation, which would be satisfactory.

Furthermore as you point out we must ensure that the spring will not bottom out during

operation, and particularly during the increased motion at shut down as the screen
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4/13

coasts through the natural frequency of the spring. Normally a minimum allowance of

1.25 to 1.5 inches from the solid (fully compressed) spring height to the compressed

height under load will adequately cater for this. Once again the spring dimensions you

nominate seem satisfactory with approx 3.8 inches from solid to compressed height.

It also should be noted the higher the isolation efficiency of the spring the lower will

be its natural frequency and the less will be the bounce at rundown.

John McKenzie

Thanks for looking at the situation guys.

John, I am curious as to what method you are using to specify the deflection-

dampening relationship. I have found several formulas that relate to transmissibility

but not to an actual deflection of a spring system.

I looked into some vibration control catalogs and used the formulas presented to arrive

at the following:

The spring alone has a natural freq of around 52Hz. For the spring-mass system I used

the formula for natural frequency of 3.13*[(K/W)^.5] where K is the spring-rate and W

is the system weight.

So Fn = 3.13*(195/(2265/8)^.5 = 2.59Hz for a natural frequency of the system.

I used the equation for Transmissibility of 1/[((Fd/Fn)^2)-1] where Fd is the disturbing

frequency of 900rpm ~ 15Hz and Fn is the the 2.59Hz solved for above. The

Transmissibility I got was around 0.03 which is far into the region of isolation.

According to the commentary in the catalogs when the Fd/Fn ratio is around 1 is when

you get the amplification of output to input we see in springs where the screens bounce

4-5 times what they do normally as they pass through the natural frequency of the

system.

Could you provide a bit of explanation of how you arrive at the figures you quote? I

found one of your earlier posts where you list rpms from 750 to 1800 and give adeflection in mm required to achieve 95% isolation but there was no method shown.

Last edited by Chrome 27th April 2009 at 16:01.
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5/13

Gday Chrome

My rough workings follow

THE NATURAL FREQUENCY OF A SPRING

The natural frequency of a spring (fn) determines its efficiency as an isolator.

Effective isolators have a low natural frequency.

Natural Frequency (fn) = 188 / SQRT effective deflection (ins)

or on our case

= 188 / SQRT(1.45) = 156.13 rpm

INSULATION RATIO

The insulation ratio (z) is the ratio of the imposed frequency (fd) to natural frequency

(fn)

Insulation Ratio (z) = fd / fn

or in our case

= 900 / 156.13 = 5.76

TRANSMISSIBILITY

Transmissibility (T) is the amount of vibration energy that is transmitted to the support

structure.

Transmission (T) = 1 / (z^2 - 1)

or in our case

= 1 / (5.76 ^2 1) = 0.03

ISOLATION EFFICIENCY

Isolation efficiency is the amount of vibration energy prevented from being transmitted

through the spring.

Isolation Efficiency = 100 (T x 100)

or in our case

= 100 (0.03 x 100) = 97% isolation efficiency

------------------------------------------------------

p.s. to determine the required loaded spring deflection to achieve a nominated
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6/13

efficiency, simply transpose the formula:

for example, what loaded spring deflection is required to achieve 97% isolation

efficiency at a 900 rpm imposed frequency

Required transmission (T) = (100 isolation %) / 100 = (100 97) / 100 = 0.03

Required Natural Frequency of Spring (fn) = Fd / SQRT((1 / T) + 1)

= 900 / SQRT((1 / 0.03) + 1) 156 rpm

Required Spring Deflection = (188 / fn)^2 = (188 / 156)^2 = 1.45

John McKenzie

Ok, I see it now. I didn't realize the 0.03 I got for a value of Transmissibility was

where the 97% Isolation came from, duh

We were using the same formulas just slightly rearranged since you left frequency in

terms of RPM while I was using Hz and you had the SQRT of static deflection in the

denominator while I has its reciprocal components in the numerator of the Fn formula.

For anyone else following along in this thread in my formula:

3.13*[(K/W)^.5]

notice how I had to get the term "W" by dividing the total sprung mass by the number

of springs supporting (i.e. 2265/8). The inverse of the K/W term is by definition the

static deflection.
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7/13

Dear Mr. John

First I must thank you for a very informative post.

Please be kind enough to clarify the following:-

a. I would like to know how you arrived at 2.2 g acceleration from RPM and Stroke.

b. How can the Vibration Acceleration data be used to determine Stroke-Speed

Combinations

c. How does the size and nature of the material to be screened affect the design

requirement of Vibration acceleration

Thanks a Lot,

Regards,

Keshav
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8/13

Hi Keshav,

To try and answer your questions:

(Qa). I would like to know how you arrived at 2.2 g acceleration from RPM and Stroke.

(A).

g = (stroke (mm) x rpm^2) / 1,800,000

(this formula has been simplified and is not exact - but is close enough for all practical

purposes here)

Therefore in our example of 0.188 inch (4.8mm) screen stroke at 900 rpm

g = (4.8 x 900^2) / 1,800,000 = 2.2

(Qb). How can the Vibration Acceleration data be used to determine Stroke-Speed

Combinations

&

(Qc). How does the size and nature of the material to be screened affect the design

requirement of Vibration acceleration

(A) These two questions are best answered together.

As a starting point:

The combined effect of correct stroke and screening frequency are

amoungst the most important considerations in achieving good screening

efficiency

It is these two factors (stroke and frequency) that determine screen

acceleration ('g' factor), and this factor should be held within certain limits.

However it is quite possible to also achieve the same 'g' factor with poor

stroke and/or frequency selections, and thus have inefficient screening.

In other words the 'g' factor needs to be within certain limits - but being within those

limits does not in itself imply good screening conditions. It is the the actual stroke and

frequency selection that is important.

Stroke

If the screen stroke is too small capacity will be reduced and material may clog or

wedge in the openings. The stroke however should not be so great that it will interfere

with stratification and tend to throw near size particles out of the apertures before they

have had a chance to adjust themselves and pass through. Too much stroke will also

decrease the life of the screening medium, bearings, and screen frame components.

A practical rule of thumb is that if material is jumping violently instead of flowing,

chances are the stroke is too great.
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9/13

The magnitude of stroke is usually selected in relation to the largest split size required.

i.e.: the top deck aperture size. The thinking here is that the top deck with the largest

particles and aperture sizes will require a greater stroke than the lower decks - and if

the top deck does not screen efficiently - then the lower decks will not have the

opertunity to do so.

Frequency

The frequency of vibration will effect screening by increasing or decreasing the number

of impacts between the screening medium and the material. The speed selected mustbe fast enough to maintain the necessary travel rate and liveliness in the oversize bed.

The selected speed however is not always correct for maximum capacity or highest

efficiency, but is directly related to the required stroke. This is done to obtain

acceptable bearing life, and to keep stresses in such components as deck frames and

side plates etc. to within established limits for good life.

The sensitivity of bearing life expectancy to speed cannot be over emphasised. This

effect can be appreciated by considering that for a given stroke, a 10% increase in

speed will shorten bearing life expectancy by 50%, and an increase of 20% will reduce

life expectancy to 25% of the initial value.

In brief the stroke and frequency of vibration are closely related, and for every size

and kind of material there will be an ideal combination. If decreased stroke is selected

the frequency should be increased, and where increased stroke is used the frequency

must be reduced for the reasons outlined above.

Every manufacturer will have his own thoughts and standards for stroke and speed

combinations, but a good starting point is the table listing in the VSMA manual which

will prove satisfactory for most applications. However these may sometimes need to

be modified since the products handled differ physically with regard to shape,

irregularity of surface, moisture content, and the percentage of clays and micron size

fines present.

The g factor

A limit must be placed on the g factor due to mechanical design of the screen but

circular motion screens generally run at around 3.5 4.0g while linear motion screens

from say 4.5 to around 5.5g. The ideal is to aim for the lowest 'g' that will

satisfactorily do the required job.

In summary the steps I would use to determine stroke speed combinations are:

1. Select the screen stroke in relation to top deck aperture sizi (refer VSMA

manual)

2. Select the accompanying screen frequency (rpm). This can be done from

the VSMA table, but if differing check that it does not exceed allowable 'g'factor

Hope this answers some of your questions, but always happy to discuss further if

required

Kind Regards


10/13

John McKenzie
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11/13


12/13

Thank You for devoting your time and effort for that post John. I think I am getting ahang of 'g' now. Thanks a lot

Keshav
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Selection of Coil Spring for Vibratory Screen