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What is RotorDynamics
• Specialized branch of applied mechanics concerned with the behavior and diagnosis of rotating
structures.
• Rotordynamics is that branch of systems dynamics dealing with mechanical devices in which at least
one part, usually defined as rotor, rotates with significant angular momentum.
• The meaning of rotor dynamics is the branch of engineering that studies the lateral and torsional
vibrations of rotating shafts
• The factors affecting rotor failure are misalignment, bent shaft, looseness, bearing failures &
imbalance.
• As large forces are generated in rotating machines at varying speeds the primary failure in the
rotor is found to be imbalance.
• The main objective of rotor dynamics are estimating the rotor vibrations and containing the vibration
level under an acceptable limit.
• When a rotational speeds matches with natural frequency, the critical speed of rotating machine can
be occurred.
• First critical speed happened when the lowest speed which is natural frequency is first considered.
• However, when the speed increases, it can be an additional critical speed to the structure.
• Therefore, by using reducing rotational unbalance and the unwanted external forces plays an
important role to reduce the all the forces which can initiate resonance
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Analysis Cell
Energy flow in Rotors
• The rotational energy has a potential for
serious leaks and can easily be
transformed into other forms of energy
such as heat.
• In addition, in rotors there exist additional
sources of energy leaks, transforming the
rotor rotational energy into other forms of
mechanical energy.
Why do we need Rotational Motion in machinery
Rotational motion is employed
• to achieve translation, as from the wheel
to the axle
• to store energy, as in the ancient sling
or modern flywheels
• to transfer power from one point to
another by using belts, cogwheels, or
• gear trains
• to obtain kinetic energy from other kinds
of energy, such as thermal, chemical,
nuclear, or wind energy
The purpose of rotor dynamics as a subject is to
keep the vibrational energy as small as possible
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Analysis Cell
Modes of Vibrations during Rotation
• Due to several factors, which contribute to the energy
transfer - from rotation to other forms of motion - the
rotor rotation may be accompanied by various modes of
vibrations
1. Torsional Vibrations
2. Longitudinal Vibrations(Axial)
3. Lateral Vibration(Bending)
• Among these modes, the lateral modes of the rotor
are of the greatest concern.
• Most often, they represent the lowest modes of the
entire machine structure.
• Through the supporting bearings and through the fluid
encircling the rotor (unless the rotor operates in
vacuum), the rotor lateral vibrations are transmitted
to the non-rotating parts of the machine.
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Equation of Motion involving Rotation
• In a rotating machine, unbalance
exists if the centre of mass of the
rotor does not coincide with the
axis of rotation
• The unbalance me is measured
in terms of an equivalent point
mass m with an eccentricity e.
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The three major areas of concern are
1. Critical speeds
2. System Stability
a. Oil Whip (depends on bearing pressure & Viscousity of oil. Whip means a severe vibration of
a shaft)
b. Due to asymmetry( can be due to inertia or stiffness)
c. Material damping
The limiting speeds and resonance frequencies strongly depend on the distribution of elasticity and
mass in the machine. A stability analysis (numerical or analytical) for determining the limiting
speeds by means of stability criteria would be an important step
3. Unbalance Response
a. Exciting force is the centrifugal force
Criteria for Vibrational Behaviour of any body:
First, the (external) displacements should be as
small as possible. The tolerable values are often much smaller than 1 mm.
Secondly, despite high imbalances and an unfixed installation, the device must remain stationary
and must not make any movements when spinning.
Third, the emission of noise and vibration should be as low as possible
A combination of spring suspension, friction dampers and imbalance detection is the most
common solution to the problem
Concerns during Rotation
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Critical Speed
•Critical speeds are the undamped natural
frequencies of the rotor system where the amplitude
of vibration is maximum.
•This amplitude is commonly excited by unbalance
of the rotating structure.
•All rotating shafts, even in the absence of external
load will deflect during rotation.
•The magnitude of deflection depends upon the
following:
(a) stiffness of the shaft and its support
(b) total mass of shaft and attached parts
(c) unbalance of the mass with respect to the axis of
rotation
(d) the amount of damping in the system
Usually the critical speeds are desired to be 10%
to 20% above or below the operating speed
range.
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Analysis Cell
Stability
• However, there are many rotors that operate on
top of the second critical speed due to sufficient
bearing damping.
• Often attempts to elevate the 2nd critical speed
by increased bearing stiffness leads to serious
1st mode stability problems
• When bearing and seal damping is included, we
can compute the damped natural frequencies or
complex eigenvalues of the system.
• The real part of the complex eigenvalue
determines the modal log decrement.
• From this quantity we can evaluate the stability
margin and compute the rotor critical speed
amplification factors.
• If the log dec is positive, the system is stable for
that mode. If the log dec is > 2, then there will
be little unbalance excitation.
Self-excited vibrations in a rotating structure
cause an increase of the vibration
amplitude over time such as shown below
Such instabilities, if unchecked, can result
in equipment damage.
The most common sources of instability
are:
1. Bearing characteristics (in particular
when nonsymmetric cross-terms are
present)
2. Internal rotating damping (material
damping)
3. Contact between rotating and static
parts(shaft & the bearing)
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Unbalance
• There is a long list of factors which contribute to
the energy transfer from rotation to these ‘‘side-
effect’’ vibrations.
• The first and best known among them is rotor
unbalance.
• When the rotor mass centerline does not
coincide with its rotational axis, then mass
unbalanced inertia related rotating forces
occur.
• The rotor unbalance acts, therefore, in the
lateral vibration mode, like an external
exciting centrifugal force.
• As a result, the rotor responds with lateral
vibrations with frequency, synchronous to
rotational speed.
• Unbalance can be either by steady Forced
excitation or Self Exitation
Unbalance due to Forced Excitation:
The frequency of the rotor lateral vibrations due to unbalance will be the
same as the rotational speed.In industry,the frequency of vibrations is
usually related as ratios of the rotational speed; thus, the unbalance-
related synchronous lateral vibrations are referred to as (1X) vibrations. If
the rotor system is nonlinear, which is usually the case to a certain
degree, then, in the system, more frequency components can be
generated in response to an exciting force of a single frequency
Unbalance due to Self Excitation: They are sustained by a constant
source of energy, which may be external, or is a part of the system.
These vibrations are steady, usually with constant amplitude, phase, and
frequency.The frequency of self-excited vibrations is close to one of the
system natural frequencies
Rotating machines belong to the self excitation category
• Constant supply of energy comes from rotor rotation.
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Campbell Diagram
•In understanding the dynamic behaviour of the rotating machines, the Campbell diagram is one of the most
important tools in rotor dynamic analysis.
•It is basically consisting of a plot of the natural frequencies of the system as functions of the spin speed
•The critical speed is mainly to generate the whirl speed map. This include excitation frequency lines of
interest, and graphically note the intersections to obtain the critical speeds associated with each excitation
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• When a rotor is in a motion or movement, the rotor will eventually curve
or bend.
• It will follow in a circular or elliptical motion. This happened because a
whirling has occurred.
• There are two types of whirling which are backward whirling and
forward whirling
• A forward whirl is when the direction of the whirl undergoes the same
direction of the shaft & occur when the rotation speed is added to the
propagation speed of the travelling wave.
• Backward Whirl is the goes the opposite of the direction of the shaft
& occurs when subtracted from the propagation speed of the travelling
wave in the opposite direction.
• Therefore, the frequencies of the forward modes increase and the
frequencies of the backward modes decrease in relation to the
rotation speed
• This leads to a splitting of each mode shape into two different
frequencies
• One of the reason for backward whirl are because of directionally
dependent of the bearings .
• The natural frequency of whirling both whirling is called natural whirling
frequency.
Motion during Rotation
