Electromagnetic
forces arising from the operation of electric machines as a result,
for example, due to the asymmetry of the rotor windings, the
presence of short-circuited turns, etc.reasons.
The
magnitude of vibration (for example, its amplitude AB) depends not
only on the magnitude of the excitation force Fт acting on the
mechanism with the circular frequency ω, but also on the
stiffness k of the structure of the mechanism, its mass m , and
damping coefficient C.
Various
types of sensors can be used to measure vibration and balance
mechanisms, including:
-
absolute vibration sensors designed to measure vibration acceleration
(accelerometers) and vibration velocity sensors;
-
relative vibration sensors eddy-current or capacitive, designed to
measure vibration.
In
some cases (when the structure of the mechanism allows it) sensors of
force can also be used to examine its vibration load.
Particularly,
they are widely used to measure the vibration load of the supports of
pre-resonance balancing machines.
Therefore
vibration is the reaction of the mechanism to the influence of
external forces. The amount of vibration depends not only on the
magnitude of the force acting on the mechanism, but also on the
rigidity of the mechanism. Two forces with the same magnitude can
lead to different vibrations. In mechanisms with a rigid support
structure, even with the small vibration, the bearing units can be
significantly influenced by dynamic loads. Therefore, when balancing
mechanisms with stiff legs apply the force sensors, and vibration
(vibroaccelerometers). Vibration sensors are only used on mechanisms
with relatively pliable supports, right when the action of unbalanced
centrifugal forces leads to a noticeable deformation of the supports
and vibration. Force sensors are used in rigid supports even when
significant forces arising from imbalance do not lead to significant
vibration.
The
resonance of the structure.
We
have previously mentioned that rotors are divided into rigid and
flexible. The rigidity or flexibility of the rotor should not be
confused with the stiffness or mobility of the supports (foundation)
on which the rotor is located. The rotor is considered rigid when its
deformation (bending) under the action of centrifugal forces can be
neglected. The deformation of the flexible rotor is relatively large:
it cannot be neglected.
In
this article we only study the balancing of rigid rotors. The rigid
(non-deformable) rotor in its turn can be located on rigid or movable
(malleable) supports. It is clear that this stiffness/mobility of the
supports is relative depending on the speed of rotation of the rotor
and the magnitude of the resulting centrifugal forces. The
conventional border is the frequency of free oscillations of the
rotor supports/foundation. For mechanical systems, the shape and
frequency of the free oscillations are determined by the mass and
elasticity of the elements of the mechanical system. That is, the
frequency of natural oscillations is an internal characteristic of
the mechanical system and does not depend on external forces. Being
deflected from the equilibrium state, supports tend to return to its
equilibrium position due to the elasticity. But due to the inertia of
the massive rotor, this process is in the nature of damped
oscillations. These oscillations are their own oscillations of the
rotor-support system. Their frequency depends on the ratio of the
rotor mass and the elasticity of the supports.
When
the rotor begins to rotate and the frequency of its rotation
approaches the frequency of its own oscillations, the vibration
amplitude increases sharply, which can even lead to the destruction
of the structure.
There
is a phenomenon of mechanical resonance. In the resonance region, a
change in the speed of rotation by 100 rpm can lead to an increase in
a vibration tenfold. In this case (in the resonance region) the
vibration phase changes by 180°.
If
the design of the mechanism is calculated unsuccessfully, and the
operating speed of the rotor is close to the natural frequency of
oscillations, the operation of the mechanism becomes impossible due
to unacceptably high vibration. Usual balancing way is also
impossible, as parameters change dramatically even with a slight
change in the speed of vibration. Special methods in the field of
resonance balancing are used but they are not well-described in this
article. You can determine the frequency of natural oscillations of
the mechanism on the run-out (when the rotor is turned off) or by
impact with subsequent spectral analysis of the system response to
the shock. The device "Balanset-1A" provides the ability to
determine the natural frequencies of mechanical structures by these
methods.
For
mechanisms whose operating speed is higher than the resonance
frequency, that is, operating in the resonant mode, supports are
considered as mobile ones and vibration sensors are used to measure,
mainly vibration accelerometers that measure the acceleration of
structural elements. For mechanisms operating in pre-resonance mode,
supports are considered as rigid. In this case, force sensors are
used.
Linear
and nonlinear models of the mechanical system.
Mathematical
models (linear) are used for calculations when balancing rigid
rotors. The linearity of the model means that one model is directly
proportionally (linearly) dependent on the other. For example, if the
uncompensated mass on the rotor is doubled, then the vibration value
will be doubled correspondingly. For rigid rotors you can use a
linear model because such rotors are not deformed. It is no longer
possible to use a linear model for flexible rotors. For a flexible
rotor, with an increase of the mass of a heavy point during rotation,
an additional deformation will occur, and in addition to the mass,
the radius of the heavy point will also increase. Therefore, for a
flexible rotor, the vibration will more than double, and the usual
calculation methods will not work. Also, a violation of the linearity
of the model can lead to a change in the elasticity of the supports
at their large deformations, for example, when small deformations of
the supports work some structural elements, and when large in the
work include other structural elements. Therefore it is impossible to
balance the mechanisms that are not fixed at the base, and, for
example, are simply established on a floor. With significant
vibrations, the unbalance force can detach the mechanism from the
floor, thereby significantly changing the stiffness characteristics
of the system. The engine legs must be securely fastened, bolted
fasteners tightened, the thickness of the washers must provide
sufficient rigidity, etc. With broken bearings, a significant
displacement of the shaft and its impacts is possible, which will
also lead to a violation of linearity and the impossibility of
carrying out high-quality balancing.
Methods
and devices for balancing
As
mentioned above, balancing is the process of combining the main
Central axis of inertia with the axis of rotation of the rotor.
The
specified process can be executed in two ways.
The
first method involves the processing of the rotor axles, which is
performed in such a way that the axis passing through the centers of
the section of the axles with the main Central axis of inertia of the
rotor. This technique is rarely used in practice and will not be
discussed in detail in this article.
The
second (most common) method involves moving, installing or removing
corrective masses on the rotor, which are placed in such a way that
the axis of inertia of the rotor is as close as possible to the axis
of its rotation.
Moving,
adding or removing corrective masses during balancing can be done
using a variety of technological operations, including: drilling,
milling, surfacing, welding, screwing or unscrewing screws, burning
with a laser beam or electron beam, electrolysis, electromagnetic
welding, etc.
The
balancing process can be performed in two ways:
-
balanced rotors Assembly (in its own bearings);
-
balancing of rotors on balancing machines.
To
balance the rotors in their own bearings we usually use specialized
balancing devices (kits), which allows us to measure the vibration of
the balanced rotor at the speed of its rotation in a vector form,
i.e. to measure both the amplitude and phase of vibration.
Currently,
these devices are manufactured on the basis of microprocessor
technology and (in addition to the measurement and analysis of
vibration) provide automated calculation of the parameters of
corrective weghts that must be installed on the rotor to compensate
its imbalance.
These
devices include:
-
measuring and computing unit, made on the basis of a computer or
industrial controller;
-
two (or more) vibration sensors;
-
phase angle sensor;
-
equipment for installation of sensors at the facility;
-
specialized software designed to perform a full cycle of measurement
of rotor unbalance parameters in one, two or more planes of
correction.
For
balancing rotors on balancing machines in addition to a specialized
balancing device (measuring system of the machine) it is required to
have an "unwinding mechanism" designed to install the rotor
on the supports and ensure its rotation at a fixed speed.
Currently,
the most common balancing machines exist in two types:
-
over-resonant (with supple supports);
-
pre-resonant (with stiff supports).
Over-resonant
machines have a relatively pliable supports, made, for example, on
the basis of the flat springs.
The
natural oscillation frequency of these supports is usually 2-3 times
lower than the speed of the balanced rotor, which is mounted on them.
Vibration
sensors (accelerometers, vibration velocity sensors, etc.) are
usually used to measure the vibration of the supports of a resonant
machine.
In
the pre-resonant balancing machines are used relatively-rigid
supports, natural oscillation frequencies of which should be 2-3
times higher than the speed of the balanced rotor.
Force
sensors are usually used to measure the vibration load on the
supports of the machine.
The
advantage of the pre-resonant balancing machines is that they can be
balanced at relatively low rotor speeds (up to 400-500 rpm), which
greatly simplifies the design of the machine and its foundation, as
well as increases the productivity and safety of balancing.
Balancing technique
Balancing
eliminates only the vibration which is caused by the asymmetry of the
rotor mass distribution relative to its axis of rotation. Other types
of the vibration cannot be eliminated with the help of the balancing!
Balancing
is the subject to technically serviceable mechanisms, the design of
which ensures the absence of resonances at the operating speed,
securely fixed on the foundation, installed in serviceable bearings.
The
faulty mechanism is the subject to a repair, and only then - to a
balancing. Otherwise, qualitative balancing impossible.
Balancing
cannot be a substitute for repair!
The
main task of balancing is to find the mass and the place (angle) of
installation of compensating weghts, which are balanced by centrifugal
forces.
As
mentioned above, for rigid rotors it is generally necessary and
sufficient to install two compensating weghts. This will eliminate
both the static and dynamic rotor imbalance. A general scheme of the
vibration measurement during balancing looks like the following:
fig.5 Dynamic balancing - corection planes
and measure points
Vibration
sensors are installed on the bearing supports at points 1 and 2. The
speed mark is fixed right on the rotor, a reflective tape is glued
usually. The speed mark is used by the laser tachometer to determine
the speed of the rotor and the phase of the vibration signal.
fig.
6. Installation of sensors during balancing in two planes
1.2-vibration sensors, 3-phase, 4-measuring unit, 5-laptop
In
most cases, dynamic balancing is carried out by the method of three
starts. This method is based on the fact that test weghts of an
already-known mass are installed on the rotor in series in 1 and 2
planes; so the masses and the place of installation of balancing
weghts are calculated based on the results of changing the vibration
parameters.
The
place of installation of the load is called the correction plane.
Usually, the correction planes are selected in the area of the
bearing supports on which the rotor is mounted.
The
initial vibration is measured at the first start. Then, a test weight
of a known mass is installed on the rotor closer to one of the
supports. Then the second start is performed, and we measure the
vibration parameters, that should change because of the installation
of the test load. Then the test load in the first plane is removed
and installed in the second plane. The third start-up is performed
and the vibration parameters are measured. When the test load is
removed, the program automatically calculates the mass and the place
(angles) of the installation of balancing weghts.
The
point in setting up test weghts is to determine how the system
responds to the imbalance change. When we know the masses and the
location of the sample weghts, the program can calculate the so-called
influence factors, showing how the introduction of a known imbalance
affects the vibration parameters. The coefficients of influence are
the characteristics of the mechanical system itself and depend on the
stiffness of the supports and the mass (inertia) of the rotor-support
system.
For
the same type of mechanisms of the same design, the coefficients of
influence will be similar. You can save them in your computer memory
and use them afterwards for balancing the same type of mechanisms
without carrying out test runs, which greatly improves the
performance of the balancing. We should also note that the mass of
test weghts should be chosen as such so that the vibration parameters
vary markedly when installing test weghts. Otherwise, the error in
calculating the coefficients of the affect increases and the quality
of balancing deteriorates.
1111
A
guide to the device Balanset-1A provides a formula by which you can
approximately determine the mass of the test load, depending on the
mass and the speed of the rotation of the balanced rotor. As you can
understand from Fig. 1 the centrifugal force acts in the radial
direction, i.e. perpendicular to the rotor axis. Therefore, vibration
sensors should be installed so that their sensitivity axis is also
directed in the radial direction. Usually the rigidity of the
foundation in the horizontal direction is less, so the vibration in
the horizontal direction is higher. Therefore, to increase the
sensitivity of the sensors should be installed so that their axis of
sensitivity could also be directed horizontally. Although there is no
fundamental difference. In addition to the vibration in the radial
direction, it is necessary to control the vibration in the axial
direction, along the axis of rotation of the rotor. This vibration is
usually caused not by imbalance, but by other reasons, mainly due to
misalignments and misalignments of shafts connected through the
coupling. This vibration is not eliminated by balancing, in this case
alignment is required. In practice, usually in such mechanisms there
is an imbalance of the rotor and misalignment of the shafts, which
greatly complicates the task of eliminating the vibration. In such
cases, you must first align and then balance the mechanism. (Although
with a strong torque imbalance, vibration also occurs in the axial
direction due to the" twisting " of the foundation
structure).
Requirements for the balancing quality of rigid rotors.
Quality
of rotor (mechanisms) balancing can be estimated in two ways. The
first method involves comparing the value of the residual imbalance
determined during the balancing with the tolerance for the residual
imbalance. The specified tolerances for various classes of rotors
installed in the standard
ISO 1940-1-2007. «Vibration.
Requirements for the balancing quality of rigid rotors. Part 1.
Determination of permissible imbalance".
However, the
implementation of these tolerances can not fully guarantee the
operational reliability of the mechanism associated with the
achievement of a minimum level of vibration. This is due to the fact
that the vibration of the mechanism is determined not only by the
amount of force associated with the residual imbalance of its rotor,
but also depends on a number of other parameters, including: the
rigidity K of the structural elements of the mechanism, its mass M,
damping coefficient, and the speed. Therefore, to assess the dynamic
qualities of the mechanism (including the quality of its balance) in
some cases, it is recommended to assess the level of residual
vibration of the mechanism, which is regulated by a number of
standards.
The most common standard regulating permissible vibration
levels of mechanisms is
ISO 10816-3:2009 Preview
Mechanical vibration -- Evaluation of machine vibration by measurements on non-rotating parts --
Part 3: Industrial machines with nominal power above 15 kW and nominal speeds between 120 r/min and 15 000 r/min
when measured in situ.»
With its help, you can set the tolerance on all types of machines, taking into
account the power of their electric drive.
In addition to this
universal standard, there are a number of specialized standards
developed for specific types of mechanisms. For example,
ISO 14694:2003 "Industrial fans - Specifications for balance quality and vibration levels",
ISO 7919-1-2002 "Vibration of machines without reciprocating motion. Measurements on
rotating shafts and evaluation criteria. General guidance.»
