Experimental Investigation of the Vibration-isolation

Characteristic of Sawdust

Principal objective of investigation was to determine the suitability of ordinary, dry sawdust as a medium for isolating vibrations resulting from movement of machine parts and engine elements

by Ahmed Ezzat

General Objective of Work Vibrations resulting from movement of machine parts and engine elements have proved to be a nuisance, particularly when such vibrations are transmitted through the frame of a machine or engine to the foundation and, consequently, to the surrounding structures. In addition to the noise and discomfort sustained by those subjected to that environment, the vibrations developed by stationary machinery may cause damage to adjacent machines and to buildings. Felt, sand, rubber, steel springs and air have been used as isolating media. The main objective of this research was to make an experimental study of the vibration-isolation charac- teristics of ordinary, dry sawdust.

Experimental Equipment The principal experimental equipment consisted

of a 5-1b Calidyne shaker and power supply, a variable oscillator, a Glennite accelerometer and an MB velocity meter. An aluminum cylindrical cup, 2~9/32 in. in diameter, 4 in. high and weighing about 0.315 lb, was fixed to the shaker plate to accommodate the sawdust. An aluminum disk, 23/4 in. in diameter and 1/~ in. thick, was supported by the sawdust and was designed so that a vibration pickup could be attached to it. Four aluminum disks, 1/4 in. thick by 21/4 in. in diameter and each having a weight of approximately 0.169 lb, were machined so that they could be fixed to the 1/2-in. thick aluminum disk to increase its mass.

The velocity of the armature of the shaker was established by measuring the voltage generated by a special coil that moved in the magnetic field of the shaker. A sensitive millivoltmeter was used to register both the voltage output of the above coil and the voltage output of the vibration pickup.

Ahmed Ezzat is Associate Professor, Faculty of Engineering, Cairo Uni- versity, Cairo, Egypt. Original manuscript o[ this paper was submitted to S E S A for publication in September 1957.

The Experimental Procedure The accelerometer was fixed to the sawdust-

supported aluminum disk and the shaker was ad- justed to its opt imum condition of operation. The frequency was held constant while accelerations were measured and recorded for several levels of amplitude. The same procedure was repeated for several frequencies that ranged from 20 to 100 cps.

The cup was fixed to the shaker table and filled with dry sawdust (see specifications in Table 1) to this required height. The aluminum disk was placed on top of the sawdust and the accelerometer was fixed to it. The tests were designed to deter- mine the behavior of the sawdust as a vibration isolator under different conditions of column height and of unit pressure developed by the supported weight. Four runs were carried out using four

We~ht ~ ro Miltivoltmeter

,Accele r ometer

Saw Dust_ ~- Cup_

/

[ ' r o m OsciUato r

!

S h a k e r

Fig. 1--Diagrammatic sketch of experimental arrangement

274 I September1962

3

,,o0

CASE 3 20 ? 0 140 v-- 21.2 INgLe / 1/

( a )

/

65 '? / ' /

(b)

I j

/ 0'

0 0.1 0.2

====. ======~

7O /

03 0.4 O.S 0,6 0.7 0.8 0,9 1D 1.1 1.2 1.3 1.4

V s SHAKER VOLTAGE VOLTS (MAXIMUM SHAKER VELOCITY)

(c)

80 // 90

/ 1oo ! i /

1.5 1.6

Fig. 2--Dam ped-accelerometer output vs max imum shaker velocity

(a) Frequency range from 20 to 40 cps

(b) Frequency range from 50 to 70 cps

(c) Frequency range from 80 to 100 cps

values of un i t pressure as developed by disk weights of 0.582, 0.760, 0.936 and 1.116 lb and a sawdust co lumn approximate ly 3 in. high. One add i t iona l r un was carried out us ing a weight of 1.116 lb a nd a co lumn of sawdust approximate ly 2 in. high. T h a t var ia t ion in dead weight and co lumn height resul ted in a pract ical range of values of vo lume of sawdust used per un i t dead weight isolated from v ibra t ion , t h a t rat io to be referred to as v. Those values of v were 11.9, 17.9, 21.2, 26.15, and 31.1 in .Ulb .

Exper imen ta l da ta ob ta ined using a 3 in. co lumn of sawdust and a suppor ted weight of 0.936 lb, corresponding to a va lue of v = 21.2 i n .U lb were chosen to represent the general behavior and are represented in Figs. 2, 3 and 4.

Results and Discussion

A general feature of the curves, shown in Fig. 2 (a, b and c) is tha t the voltage output of the damped accelerometer (VAd) increased rapidly for small values of table velocity (Vs), but the acceleration remains approximately constant for the intermediate and the highest values of shaker velocity. From a s tudy of Fig. 2, it is interesting to notice tha t the value of the accelerometer output, Va~, decreased with increased excitation frequency. I t should be noted tha t the max imum accelerometer output occurred a t 30 cps and tha t its output decreased with increasing frequency. To clarify tha t be- havior, an analysis of an idealized linear system (having a spring constant, damping factor and mass representation of the experimental system) was undertaken.

I t is known tha t the force t ransmit ted to the foundation through a spring and dashpot in which

viscous damping is developed is given by the follow- ing equation:

where:

_K~ = the equivalent spring constant F~ = the equivalent damping factor X = the amplitude w,, = the natural frequency of undamped vibration,

rad/sec = the frequency of the disturbing force, rad "sec

I t can be seen t ha t this t r a n s m i t t e d force depends upon Ke, ~e, X, and the rat io ~/o~,~; and t h a t its final va lue will be affected by the s imul taneous changes in those factors.

For an idealized l inear system, Ke a nd ~e r ema in cons tan t and i nde pe nde n t of ~ a nd X : hence, for the same shaker veloci ty (~X), the t r a n s m i t t e d force increases as the exci ta t ion f requency increases from zero to the u n d a m p e d n a t u r a l f requency

TABLE 1--SAWDUST SPECIFICATIONS

Sieve No. Sieve open ing, in. Retained in

sieve, %

4 0.185 0.2 9 0.078 1.0

40 0.0165 67.2 60 0.0097 13.5

100 0.0092 17.2 Passed through sieve 0.9

number 100 Total 100.0%

The sawdust used in th is invest igat ion was dry Oregon Pine saw- dust. The grad ing of the sawdust grain size was done by s tandard sieves moun ted on Cenco-Meinzer sieve shaker and the s ieves were shaken fo r one-hal f hour at a cons tant speed.

Experimental Mechanics [ 275

Fig. 3--Change in trans- missibility vs. change in maximum shaker vel- ocity

240

200

160 o o

0r f = 20 CPS

r CASE 3 V-" 21 2 IN3/LB

120 ~.

~ 80

4 0 -

0 O 2 4 6 8 10 12 14

A AMPLITUDE INCH x 10 -2 (MAXIMUM SHAKER AMPLITUDE) 16

Fig. 4--Change in trans. missibility vs. change in maximum amplitude of shaker

240

200

'~~ 0 ,e,,,,

I,-

. J

m 120 u~

h- 80

4 0

0 0

\vF ]

CASE 3 v=21.2 IN3/LB

, , ~ 2 0 CPS

. . . . I ~oo7" ~ , ~ - -

I 0 .2 0.4 0.6 0.8 1.0 1.2. 1.4

V s SHAKER VOLTAGf VOLTS (MAXIMUM SHAKER VELOCITY)

1.6

(as w/w,~ -~ 1). When the excitation frequency exceeds the undamped natural frequency, the trans- mitted force will decrease if the damping constant is small, but will continue to rise if the damping con- stant exceeds about 0.4 times critical damping.

The dynamic tests carried out on sawdust show that the resonant frequency of the system is approxi- mately 30 to 40 cps,

The term transmissibility (R) is now defined as quotient obtained by dividing the voltage output of the damped accelerometer by the voltage gener-

ated in the coil used to measure the armature or table velocity multiplied by 100: (VA~/VA • 100). Separate curves of transmissibility were plotted as a function of shaker velocity for each frequency of excitation (see Fig, 3). A similar set of curves in which transmissibility was plotted vs. shaker ampli- tude for each frequency of excitation is shown in Fig. 4.

I t may be observed, from those curves, that the transmissibility decreases with increased velocity or amplitude of the shaker table. I t also may be ob-

276 ] September 1962

160

120

>- b..

,.J

m 80

z

Z

r ~ 4 0

/ 'v'=17.90 IN.3/LB. ~ e = 0.322.

/ / / / / / - ~-34.1o t..~/LB ~;o- 0.4=7_

05 1.0 1.5 2.0 2.5

~N

3.0

Fig. 5--Change in transmis- sibil i ty vs.%/~.~ for a con- stant value of max imum disturbing velocity (Vs = 1.0 volt)

served that , a t the larger ampli tudes and velocities, 1.z the transmissibi l i ty decreases significantly. How- ever, the force t ransmi t ted may or may not decrease with increased velocity or ampli tude. 1.0

In order to demonstra te the effect of the factor v (the volume of sawdust used in in. 3 per pound of dead weight) on the transmissibil i ty, the curves in 0s Fig. 5 were drawn. In tha t figure, curves of t rans- missibil i ty were plot ted vs. the frequency ratio o~/~ for values of v ranging from 17.90 to 34.10 in.3/lb.

0 6 Each of the curves show a decrease in the t rans- missibil i ty for increasing values of o~/r I t may be observed that , for the same value of r the largest t ransmissibi l i ty was obtained for v = 17.90 0.4

inA/ lb while the lowest value corresponded to v = 34.10 in.d/lb.

To explain the influence of v on transmissibi l i ty, 0.2

the equivalent damping coefficient C~, the equivalent crit ical damping coefficient Cce, the equivalent damp- ing factor ,~ and the equivalent spring constant K~ 0 were all computed from the dynamic tests carried 10

out for four values of v and are shown in Table 2. I t is clear t ha t al though both C~ and Cc~ decrease with an increase in v, yet their quot ient ~ increases as v increases.

I t may be noted (see Fig. 5) t ha t the transmissi- bi l i ty decreased for decreasing values of v and ~. This fact is in general agreement with the idealized linear system where if ~/r162 > 1, the t ransmissibi l i ty decreases with decreases in the damping factor.

I t is obvious t ha t sawdust is unsui table for low- frequency, low-ampli tude vibrations.

TABLE 2--EQUIVALENT COEFFICIENTS

Dead weight ,

W v, Ke, Ib m~/Ib fn, cps Ib/ in ~;e

Ce, Cce, L b / i n . / s e c . I b / i n / s e c .

0.582 34.10 32.5 64.0 0.427 0.262 0.615 0.760 26.15 35.0 96.5 0.329 0.286 0.870 0.936 21.20 33.0 105.5 0.356 0.356 1.00 1.116 17.90 30.5 111.0 0.322 0.370 1.150

o

f

15 20 25 30 35 40

V rN.3/L B.

Fig. 6--Change in volume of sawdust per unit of weight sup- ported (v) vs. damping coefficient Ce, damping factor ~'e and coefficient of critical damping Cce.

Conclusions 1. The transmissibi l i ty of the sawdust decreased

with increases in frequency above 30 cps for any given ampl i tude of excitation.

2. The t ransmissibi l i ty of the sawdust decreased with increases of ampl i tude a t constant frequency of vibrat ion.

3. The t ransmissibi l i ty of sawdust depends mainly upon the equivalent damping factor of the system. Bet te r isolation is obta ined by choosing a value of sawdust volume per uni t weight isolated which would secure a low equivalent damping factor.

4. The damping factor ~-~ of sawdust increases with an increase in the volume of sawdust used per uni t dead weight isolated from vibrat ion.

Experimental Mechanics I 277