physical properties of bagasse

1955
-
TWENTV-SECOND CONFERENCE
--
1 47
p
-
PHYSICAL PROPERTIES OF BAGASSE
By J. PIDDUCK
Introduction
This paper gives an account of the determination of the density of
fibre, both dry and in contact with water, and gives a relationship
between pressure and density. Young's Modulus and Poisson's Ratio are
calculated. The relationship between radial and axial pressure in bagasse
in a cylinder, under static and dynamic loading, is also discussed.
General
As part of a fundamental research into the milling process it was
necessary to determine some of the physical properties of cane, bagasse
and fibre. The density of dry fibre has been quoted as 1.20-1.40 g.
per C.C.jl], 1.33 [2], 1.35 and incompressible [33 and 1.53 [4],hence a
fresh determination, under various pressures, appeared desirable. I t was
decided to attempt the determination under both dry and wet conditions.
In order to eliminate certain errors it was necessary to measure the
radial pressure in the bagasse when compressed in a cylinder in the axial
direction. I t is felt that the tentative conclusions reached here may
have a bearing on the design of pressure feeder chutes, and on the failure
of roller flanges.
Equipment
The tests were made with the aid of the press described by Atherton
2in. diameter. Another cylinder
2in. diameter, open at each end, was used in the radial pressure measurement. This equipment is illustrated in Figs. 1 and 2.
151 using bagasse cylinders 4in. and
Dry Fibre Tests
A quantity of cane (Q.50) of fair average quality was fibrated, and
after pressure to expel most of the juice it was washed, boiled and again
washed before drylng in a Spencer oven. The fibre was re-dried in a
laboratory oven at 110' C. as required.
Suitable quantities were placed in the 4in. dia. cylinder, the load
was applied and maintained for about five minutes. The displacement
of the bagasse piston was measured by a dial gauge reading to 0.001 in.
Zero checks were made before and after loading and correction applied
for elastic deflection of the lower plate and bagasse piston. After compression, the piston was withdrawn, the sample extracted and weighed.
I t was then placed in an oven at 110' C. for 24 hours and again weighed.
Due allowance for the weight and volume of any moisture was made in
the calculation of density. Fifteen samples, thickness varyin6 from
0.12 in. to 1.5 in., were tested in this way; the maximum zero sh~ftwas
0.001 in. and this was considered negligible on samples of this thickness.
Tests at a pressure of 8,500 p.s.i. gave an average density of 1.14 g.
per c.c., and tests at 13,500 p.s.i. averaged 1.33 g. per c.c.; showing that,
at the lower pressures at least, there were very considerable voids. It
was then decided to carry out tests using the 2 in. diameter cylinder at
pressures up to 28,500 p s i . Five tests at this pressure averaged 1.38,
which was still well below the figure of 1.53 communicated by the Sugar
Research Institute.
Fig. I---General view o f press and controls.
Suspicions that there were still considerable voids, filled with air a t
an indeterminate pressure, were confirmed by carrying out two tests on
steel wool, whose fibrous nature was roughly similar to dry cane fibre.
These two tests at 28,(;00 p.s.i. gave densities only about 50 per cent.
of the accepted density of steel. Theoretical cnnsiderations led to the
conclusion that better elimination of air would be obtained with very
thin sarrples.
1955
----
TWENTY-SECOND CONFERENCE
I
_
_
-
-2-
.---_--.^_-------------_
----_
149
A dial gauge reading to 0.0001 in. was used, and the elastic dqflection correction was re-checked. Nineteen tests were made, on samples
varying in thickness from 0.012 in. to 0.086 in. Zero shifts proved
troublesome, but as these were random in nature, and of the order of
0.001 in., it was decided to calcuIate on the average zero.
A refinement of the equipment, and a much larger number of determination~,will be necessary before a figure can be stated with certainty.
The present series of tests indicates a dry fibre density of 1.55 &- 0.05 g.
per C.C. at 28,500 p.s.i.
Fig. 2 4 e n e m l view of press and Phillips strain measuring bridge.
Wet Fibre Tests
Dry fibre, prepared as before, was taken as required and soaked
in boiling water for 20 minutes to expel air. \TJhen wet, the samples
were placed in the 2 in. diameter cylinder, and load applied for approximately five minutes. Excess water was expelled over the top of the
cylinder and was dried off the top of the cylinder with blotting paper.
The displacement of the plunger, and hence sample thickness, was
measured with the 0.001 in. dial gauge. Sample thickness varied between
0.832 in. and 0.323 in. After release of pressure, the sample was removed
and immediately weighed. I t was then dried in an oven at 110" C.
for 24 hours and re-weighed. Corrections for expansion of the cylinder
under pressure, for the volume of water in the annulus between cylinder
and piston, and for compressibility of water in the sample, were made,
and the density (wt. of fibre divided by net fibre 1-01ume) was
calculated.
150
TWENTY-SECOND
1955
CONFERENCE
Seven samples were taken, and after the final weighing each sample
was placed in boiling water for 20 minutes and the procedure repeated
at a higher pressure. The four pressures selected were 3800,9500, 19000
and 28500 p.s.i. The results are shown in Table I.
TABLE l.-Fibre
Density g. per
C.C.
at pressure p.s.i.
I
1800
/
Mean
1
1.520
l
Pressure p.s.i.
9500
/F/
28500
1.529
1
1.543
1
1.561
1
These 26 results were analysed statistically, and the line of regression
was calculated. The probable error in any one mean is not more than
-& 0.010. The significance level is less than 0.1 per cent., proving that
the following equation is statistically sound:where p,
= pressure
in the axial direction.
Thus the density at atmospheric pressure is 1.51 rf 0.01 g. per C.C.or
94.5 & 0.6 lb. per cu. ft. The increase in density due to compression
is 1.05 per cent. for a pressure of 10,000 p.s.i. Calculation of bulk
density is shown in Appendix A.
Radial and Axial Pressure Relationship
The bagasse in the cylinder is subject to a known axial load, and
hence axial pressure, together with an undetermined radial pressure.
This radial pressure causes an expansion of the cylinder, thus introducing
a possible error into the density calculations, and is of interest in itself
as unidirectional pressure combined with lateral restraint occurs in
pressure feeder chutes and between mill rollers.
An open-ended cylinder which eliminates end constraint was constructed, 2 in. internal diameter and -&in. thick. The bore was carefully
finished so that the plunger was a sliding fit (radial clearance 0.001 in.),
and the ends were square with the base. Resistance strain gauges were
fixed to the outer surface circumferentially and longitudinally close to
the lower end. These gauges were connected to either the Phillips Strain
Measuring Bridge (Fig. 2) for static measurements or to the Kelvin
Hughes Dynamic Strain measuring equipment.
Tests were carried out on dry fibre and on freshly fihrated cane.
The cylinder was tightly packed with the material, and the depth checked
to ensure that the material was well above the gauges. In the static
measurements loads were applied at intervals of one minute, and the
1955
TWENTY-SECOND CONFERENCE
0
l500
3000
Fig. 3-Relationship
0
(1004
Fig. 4--Relationship
S500
600a
7500
151
9000
/0500
A x ~ a lPressure Ib/mz
between radial and axial pressure for wet fibre.
8000
IZOW
16000
20000
2,9000
28WO
Axrol Pressure Ib/m5
between radial and axial pressure for dry fibre.
i52
TWENTY-SECOND
CONFERENCE
1955
values of the axial and radial pressure calculated from the oil pressure
and bridge measurements. Dynamic measurements were made as
follows :The relief valve was preset to the desired pressure, with the throttle
valve closed and three way cock open to bypass. The throttle valve
was then fully opened, and the three-way cock turned to pressure. The
Fig. 5-Typical
.
trace from Kelvin Hughes Pen Recorder.
maximum oil pressure was read from the pressure gauge, and was reached
in about two seconds. The radial pressure was calculated from the trace
obtained on the Kelvin Hughes pen recorder. I n some cases, the oil
pressure was also measured on the pen recorder. A typical trace is
shown in Fig. 5.
The theory and calculations are outlined in Appendix B.
The resylts are illustrated in the Figs. 3 and 4. These indicate
that for the rates of pressure application used, there is no variation in
the ratio of radial/axial pressure in the case of dry fibre, the ratio being
0.365. In the case of wet fibre, the ratio is increased from 0.60 to 0.76
by the increased rate of loading. Comparison of the rate of increase of
radial pressure and the rate of increase of axial pressure gave, in one
case, a ratio of 0.80.
Theory and calculation, outlined in Appendix C, give the following
elastic constants for dry fibre:Young's Modulus (E)
Bulk Modulus (K)
1
Poisson's Ratio m
=
1.2 X 106 p s i .
9.7 X 105 p.s.i.
=
0.3
=
These figures will only apply to the material in bulk, not necessarily to
single fibres.
Conclusions
l. The density of fibre in contact with water has been determined
as 1.512 g. per C.C.= 94.5 lb. per cu. ft. at atmospheric pressure. At a
pressure of 12,000 p.s.i. the density is 1.531 g. per c.c. = 95.7 lb. per
1955
i 53
TWENTY-SECOND CONFERENCE
--
cu. ft., showing that fibre is slightly compressible. The probable error
in these densities is -I: 0.01 g. per C.C. & 0.6 lb. per cu. ft.
2. The determination under dry conditions gave a figure of 1.65
-J= 0.05 g. per C.C.= 97 -$r 3 lb. per cu. ft.
3. When wet fibre is compressed in a cyhder, the radial pressure
is considerably less than the axial, under the conditions of the experiments. When the axial pressure rises to its maximum in two seconds
the radial pressure is 0.76 of the axial. The radial pressure on dry fibre,
under the same conditions, is 0.365 of the axial. Further investigation
under more rapid loading appears justified.
4. Calculation of the elastic constants of a well consolidated mass
of fibre, assuming this to approximate to an isotropic material, gave the
following values as a first approximation:-
Young's Modulus -= 1.2 X lOs p s i .
Poisson's Ratio
0.3
Bulk Modulus
= 9.7 X 105 p.s.i.
This last figure is derived from the preceding values.
;
:
*
Acknowledgments
The author wishes to thank Professor M. Shaw, Dean of the Faculty
of Engineering, Mr. G. H. Jenkins, Senior Lecturer in Sugar Technology,
and Mr. K. J. Bullock, Sugar Research Institute Fellow, for advice and
assistance given in this work. Professor T. G. H. Jones and Professor
E. S. Edmiston made much needed and appreciated laboratory space
available. Mr. I. R. Way and Mr. R. Andrew gave valuable assistance
with the calculations and diagrams. The staff of the Mechanical
Engineering Workshop manufactured most of the equipment.
REFERENCES.
[l] Hugot, E.: 1950. "La Sucrerie de Cannes," p. 157.
E23 Crawford, W. R.: 1954. " Pressure Feeder Behaviuur." Proceedings
Q.S.S.C.T. Twenty-first Conference, p. 132.
[3] Kerr, H. W.: 1954. "The Milling of Cane." Proceedings Q.S.S.C.T. Twentyfirst Annual Conference, p. 231.
[4] Sugar Research Institute: 1955. Private communication.
[5] Atherton, P. G.: 1984. "Bagasse Compression Tests." Proceedings Q.S.S.C.T.
Twenty-first Annual Conference, p. 235 et seq.
Department of 1l;iecha.~2icaZEngineering,
University of Queenstand.
APPENDIX A.
Calculation of Bulk Density of cane.
Let p~ = density of dry fibre.
p j = density of juice of known brix.
F = fibre content, as a fraction.
P E = bulk density.
Then p s = F p p
(I -F)pj.
+
1 54
1955
TWENTY-SECOND CONFERENCE
In the mill experiments described by K. J. Bullock in his paper to be presented
a t the Twenty-second Annual Conference of the Queensland Society of Sugar Cane
Technologists, the following limits were recorded:Fibre 10-14 per cent.
Brix 18-22 per cent.
and P F is taken as 1.51 f 0.02 g. per C.C.
From tables*: Brix
Density g. per C.C.
18
1.072
20
1.0809
22
1.0899
Hence lowest density
= (0.10 X 1.49 $ 0.90 X 1.072) = 1.1138
and similarly average density = 1.1324
highest density = 1.1515
Converting to lb. per cu. ft., the density is $0.8 lb. per cu. ft., with a range of
& 1.2 lb. per cu. ft.
* Laboratory Manual for Queensland Sugar Mills, 1939, p. 171.
APPENDIX B.
Calculation of Radial Preasure.
Let p = radial internal pressure, p.s.i.
v, == internal radius = 1.002 in.
r, = external radius = 1.321 in.
So = circumferential stress a t outer surface
ell = circumferential strain ,,
,,
,,
er = longitudinal strain
,, ,,
,,
Assume E = 30 X 106 p.s.i. and m = 4 for steel.
Text books on Strength of Materials give
-
S
e=
2vlaP
p
P
whence e
rL2-vll
272
and ep
1
=.
- -e e
m
Since the gauges are in opposite arms, the net strain = eg-ez
= (1
+ m-)1 '8'
The makers gauge factor is F (= 2.07) and the Phillips instrument is set to a gauge
factor of 2.
When the strain as read is X ,
Whence
p
Em
-
rza-v%*
X = 8.55 X 106 X
(m
1)F
rI2
When using the Kelvin Hughes dynamic strain recorder, a built in calibration
is used. This calibration corresponds to a given percentage change of resistance a t
the gauge.
Let y = pen deflection, mm, on test
a = pen deflection, mm, on calibration
c = calibration standard, per cent.
Em
r
y.c
Then p = ------- (m
+ ) F 2vl2
a.100
=
+
+
1955
TWENTY-SECOND CONFERENCE
1 55
APPENDIX C.
Calculation of Elastic Constants.
In the wet density tests, the'fibre is subject to an axial stress = S, and radial
stresses = 0.6 S (0.6 is taken from the graph p/+a, Fig. 3).
If x denotes the axial direction, y and z mutually perpendicular transverse
directions, and if strain be denoted by e
Eer = S x
- S y -i- Sr
.--------
=S---S
m
9n
Eey = Eee
=
Volumetric strain = e x $ e y
Sy
-
1.3
Sz
+ Sr - 0.6 S -
I
-
1.6
----S
m
m
+ ex =
= fractional increase in density
When S = 10,000 p.s.i., fractional increase in density = 0.0106
... T ( 2 . 2 - g )
= 0.0105
....................
(1)
I n the tests on dry fibre, p/p, = 0.365 (Fig. 4)
- 0.365
---S - S-
and Eey = EEZ= 0.365 S
m
m
From the cylinder dimensions e y can be calculated, and is readily shown to be
-30
-S for this particular
X 108
cylinder. (The
- sign indicates tensile strain).
Equating,
Solving these equations, m = 3.4, E = 1.2 X 106 p.s.i.
Em
Bulk I~IodulusK = 13= 9.7 X 105 p.s.i.