The shell is one of the basic components of a typical rotary drum. The shell is
a thin-walled steel pipe, and the shell (plate) of the shell is exposed to elastic
strain generated independently of the plastic strain. The elastic strain can have
the following forms:
- bends of the drum (pipe) axis,
- torsional deflection of the shell (pipe),
- radial deformation of individual sections of the shell (pipe).
The last form of deformation is particularly dangerous, because it has a clearly
cyclical nature and the cycle period corresponds to the duration of single rotation
of the facility. This cyclic character is detrimental from the point of view of
both fatigue durability of the shell material (steel) and the durability of the
drum's inside lining (refractory, concrete), and the problems with lining are found
mostly in the rotary kiln type facilities.
Radial deformation of cross-section most frequently occurs in the support areas
of the shell. As a result of the deadweight of the shell plate and external loads
(for example weight of the lining inside the kiln), elastic strain develops on the
cross-section of the drum which is trying to adapt shell shape to the stiffening
ring which is installed on the shell with some clearance
This means that during the rotation of the facility, a point related to the shell
surface does not travel along a perfect circle, but along a deformed outline with
a different radius of curvature for each circumferential position of this point.
Relative changes of the radius can be illustrated as the function of the facility
. The fact that the radius is changing means that the shell plate
undergoes cyclical bending, and the risk of fatigue cracks of the steel drum shell
is rising as the amplitude of the changes increases.
Cyclical changes of the shell plate radius also influence the life on internal lining
in the facility. Such influence is best illustrated on the example of wedgeshaped
brick. When the drum surface becomes deformed, the lining is subjected to alternating
tensioning and compression forces
Such alternating forces can lead to the brick falling out or chipping out. Typical
mechanisms of lining degradation are shown in fig.
represents a perfect situation, that is when the shell is
not deformed and bricks correctly adjoin each other. The distribution of forces
in the contact areas between the bricks is then correct. Figure
shows a situation when the radius of curvature increases excessively,
the load on the surface of the bricks decreases, and even the gaps between them
become wider. When the shell radius becomes large enough, the bricks may move /3c/
or even fall out totally. When a brick falls out, the adjacent bricks become loose,
so in consequence it might lead to an extensive reduction of the lining, thus exposing
the steel drum shell to high temperatures. If a loosened brick does not fall out
but stays in place
, when the circumferential position of the facility changes then
as a result of the reducing radius of curvature it will undergo compression. Such
a situation might cause the braking of the moved brick in the cross-section compressed
by the edges of adjacent bricks and the chipping out of a large portion of this
one. The remaining part will resume its original position, but the lining in this
area is already significantly thinner
. In case of smaller radius changes or better fit of the bricks
(smaller initial play at installation), the movement of the bricks is limited, but
chipping can also be observed. In this latter case, the chipping is caused by micro-losses
in the areas of local accumulation of loads - on the edges
To summarize, the phenomenon of cyclic change of the radius of curvature in the shell
cross-section has a detrimental impact on both, the life of internal drum lining
and on the life of the shell plate. The said strain is unfortunately inevitable,
especially because of the frequent and necessary from the design point of view loose
fit between the outside shell diameter and the internal support ring diameter.
A periodical monitoring and keeping the strain as small as possible is consequently
the only method to extend the life of trouble-free drum operation in this area.
The most popular estimator used to evaluate the elastic strain of the shell cross-section
is the parameter called the elastic shell ovality ratio ω0
It has been discovered that a deformed cross-section of the shell can be sufficiently
approximated by a ellipse, i.e. a particular case of an oval. Then the degree of
flattening (ovality) of an ellipse can be described by the following formula:
- length of ellipse major semi-axis;
- length of ellipse minor semi-axis;
- average ellipse radius
In practice, in the formula above, a and b are respectively the largest and the
smallest radius of curvature in a given cross-section, that is rmax
. Then the above formula assumes the following form:
- nominal shell diameter in the analysed cross-section.
The sought value is then the maximum difference of the radiuses, i.e. the maximum
range of the shell radius variation.
Apparently, when the facility is rotating, it is much easier to determine the relative
variation of the radiuses than their absolute values. It can be done indirectly
by measuring the difference of distance between the cross section outline and the
chord of constant length L
- which connects two selected points A and B located
on the surface of the examined cross section
Then, in a typical ellipse the minimum and maximum values of the measured distance
are for the vertical and horizontal position of the chord, respectively. The scheme
of this measurement method is shown in figure
For this measurement method, the elastic shell ovality ratio is calculated according
to the following simplified formula:
This formula is an approximated identity in relation to the previous formula based
on the maximum and minimum radius.
SHELLTESTER, principle of operation
The embodiment of the described method is the instrument called the Shelltester.
It consists of a one-metre long beam with magnetic feet on its ends to install the
beam on the drum shell, and an electronic sensor located in the middle of beam length
which measures the relative change of the shell curvature during the rotation of
This instrument, designed, manufactured and implemented by the ZMP engineers, allows
automated data collection and storage in the instrument's memory with simultaneous
wireless transmission of results to the computer, where further analysis is processing
ROUTINE TESTS SCOPE
The routine tests scope includes the measurements on all drum stages - in each case
on two cross-sections of the shell, the inlet and outlet, just before and just behind
the ring. In each cross-section, the data is obtained from three places on the circumference
(A, B and C) - equally spaced every 120o
This standard test scope may vary, depending on the limitations of the instrument
installation in a given area of the shell and/or conscious decisions of the service
recipient - consulted with the engineer who performs the measurements.
As a standard, the following parameters are also determined:
- shell and ring temperature,
- circumferential migration of the ring relative to the stage section of the shell,
- under-ring clearance.
This data is always strongly correlated with the shell elastic ovality and is a
necessary supplement of the analysis of the drum shell deformation.
The basic parameter obtained during the measurements with the Shelltester is the
elastic shell ovality ratio. Comparing the measured value with the allowable limits
and comparing the results from individual stages of the rotary drum gives a basic
insight in the hazard of occurrence of drum shell fatigue cracks and/or forecast
life of the internal lining (if any).
Determining the allowable limits is not easy however, particularly in the context
of the fatigue durability of the shell steel plate. Without detailed strength calculations,
it is difficult to determine to what extent the stress in the shell is generated
by bending of the geometrical axis of the shell (tube bending) and to what extent
by torsional deflection. Consequently, it is difficult to determine which level
of additional residual stresses can be allowed due to the deformation of the very
cross section profile - the ovality. Nonetheless, by making some assumptions, one
can attempt to formulate general standards which enable estimating of such allowable
If for simplicity we assume that the allowable cyclically changing stresses (alternate
pulsating) for typical steel grades is 40MPa, and that 50% of this total stress
is from the pipe axis bending and 50% from the deformation of the shell cross section,
and the torsional stresses and negligibly low, that we can infer that the elastic
ovality should not exceed the values for which the corresponding stresses reach
For this limit, a range of allowable ovality values can be determined as a function
of the internal shell diameter
, but please note that the upper limit for such range of allowable
values corresponds to the minimum typical thicknesses of the stage sections of the
shell, and the lower - to the maximum ones. The typical shell thicknesses for individual
diameters are given in brackets
shows that for example for the diameter 5000mm, the ovality should
not exceed 0.35% - for the shell thickness 80mm and 0.80% - for the shell thickness
In relation to the internal shell lining, the allowable deformation limits shall
be specified by the lining manufacturer and/or supplier. Very roughly, it can be
assumed that the ovality (expressed in percent) shall not exceed one tenth of the
shell diameter part (expressed in metres). For example, for the 3600mm diameter,
the approximate allowable elastic shell ovality ratio can be 0.36% (the result of
the calculation: 0.1 x 3.6m).
ANALYSIS OF THE DIAGRAMS
Additional useful information can be obtained from the analysis of the shape of
curves in the diagrams which illustrate the changes of the cross section radius
of curvature as a function of the angle of drum rotation. The diagrams provide insight
about possible causes of increased ovality.
In case of routine tests scope, the measurements on a single stage are performed
in 6 locations of the Shelltester (2 sections x 3 positions A, B and C). Each of
such six measurements yields a separate curve. Each curve individually and their
comparison are a very valuable source of additional diagnostic information.
If there was not any shell deformation, the curve (in the Cartesian system of coordinates)
will be a straight line (meaning absence of indications from the sensor).
Such a situation however never happens, because the deformation is always there
and even if the shell is tightly fitted in the ring, the equipment recreates the
deformation corresponding to the change of its radius. These are of course very
small, but in the majority of rotary drums clearly visible and representing the
characteristic points on the circumference of the facility. Such points, which correspond
to the extremes of the shell radius of curvature (also of the ring in this case)
are shown in figure
The curve shown this figure clearly indicates that the shell (ring) is straightening
(the radius of curvature is increasing) in the location of contact with the rollers
and in the zenith position.
Let us assume that the shell behaviour according to figure
is correct. However, this curve is not always perfect. The
classic deviations from the standard are presented in the figures /10b/
. The figures represent the changes of the curve shape depending on
the type of defect present in the facility - stage.
These are for example:
- excessive load of the ring and/or under-dimensioning of the ring
- excessive under-ring clearance
- insufficient load of the ring and/or over-dimensioning of the ring
- crank of the shell geometrical axis
- misalignment of the support system axis - in the horizontal plate
- shell crack
- incorrect inclination of the rollers (and the ring) relative to the local inclination
of the rotation axis
Of course, in actual conditions such defects are present in a larger or smaller
amount and extent, and the resulting curves do not always have such unambiguous
Despite possible difficulties, the curves however provide an additional opportunity
for a general evaluation of the technical condition of a rotary drum, and in case
the analysis includes the strength calculations, the detected defects can be even
evaluated in quantitative terms.
- rotational speed of the facility: 0.5 - 3.5 rpm
(recommended 2.5 rpm),
- maximum shell temperature: < 350oC,
- ambient temperature: 0 - 40oC,
- safe access to the measured cross sections
(it may require temporary object's stopppaging),
- only for ferromagnetic shell's material.