Final_Report

August 2015, Dresden
Institute of Electrical Power Engineering, Department of Electrical Machines and Drives
Dresden University of Technology
Dresden, Germany
Trainees report:
FRICTION LOSSES, HEAT TRANSFES AND VIBRATION IN
AN INDUCTION MOTOR
univ. bacc. ing. mech. Barbara Posavac
Supervisor: Dipl. Ing. Gunar Steinborn - Research Associate

Table of contents:
1 INTRODUCTION...............................................................................................................1
2 POWER LOSSES IN ELECTRICAL MACHINES .............................................................1
2.1 Resistive losses in stator and rotor conductors...............................................................1
2.2 Iron losses.....................................................................................................................2
2.3 Additional losses...........................................................................................................2
2.4 Mechanical losses .........................................................................................................2
3 HEAT TRANSFER IN ELECTRICAL MACHINES...........................................................5
4 VIBRATION EFFECTS OF STATOR IN THE ELECTRICAL MACHINES .....................8
5 CONCLUSION .................................................................................................................10
6 REFERENCES..................................................................................................................10

1 | b a r b a r a . p o s a v a c @ g m a i l . c o m
Abstract – This paper reviews the basic
calculation of the mechanical losses, heat
transfer and vibration in an induction
motor. Losses in electrical machines
coordinate the product life and they are
crucial in efficiency of the electrical motor.
This topic considers only mechanical
losses. Heat is transferred by convection
between a region of higher temperature
(solid surface) and a region of a cooler
temperature (coolant) which will be
explained later. That takes place as a
consequence of motion of the cooling fluid
relative to the solid surface although heat
can be transferred by conduction and
radiation as well. Vibrations during the
machine work are important for stability
and safety of electrical motor. Influence of
vibration has to be as low as possible to
prevent the damage in electrical motor and
environment where is motor implemented.
Key words – Electrical motor, mechanical
losses, heat transfer, vibration system in
electrical machines.
1 INTRODUCTION
lectrical motor is a device which
converts electrical energy to
mechanical energy. An induction motor
known as asynchronous motor is an AC
electric motor in which the electrical
current in the rotor needed to produce
torque, is obtained by the electromagnetic
induction from the magnetic field of the
stator winding. Types of induction motor
are single phase induction motor (split
phase induction motor, capacitor start
induction motor, capacitor start capacitor
run induction motor, shaded pole induction
motor) and three phase induction motor
(squirrel cage induction motor, split ring
induction motor). Single phase induction
motor is not a self-starting while three
phase motor is self-starting, which means
that the machine starts running
automatically when it is turned on without
any external force to the machine. In the
three phase system are three single phase
line with 120° phase difference and the
rotating magnetic-filed is having the same
phase difference which will make the rotor
to move. This paper seeks to give an
overview of the squirrel cage induction
motor (cylindrical motor) with a
calculation of mechanical losses, heat
transfer and influence of vibration in work
state.
2 POWER LOSSES IN ELECTRICAL
MACHINES
ower losses in electric machines are an
important issue because these losses
determine the efficiency of the motor and
its heating. Power losses in electrical
machines are composed from:
1. Resistive losses in stator and rotors
conductors
2. Iron losses in the magnetic circuit
3. Additional losses
4. Mechanical losses
2.1 Resistive losses in stator and rotor
conductors
Resistive losses in conductors are
sometimes called Joule losses or copper
losses. Resistive losses in a winding with
m phases and current I [1]:
𝑃𝐶𝑢 = 𝑚𝐼2
𝑅 𝐴𝐶 =
𝑘 𝑅
𝜌𝜎
𝐽2
𝑚 𝐶𝑢 (1)
Where is:
𝑅 𝐴𝐶- AC resistance of the phase winding,
Ω
𝑚-phase
𝐼-current, A
𝑘 𝑅-skin effect factor
E
P

𝜎-the specific conductivity of conductor,
1/Ωm
𝜌-density of the conductors, kg/m3
𝑚 𝐶𝑢-mass of the conductors, m
𝐽-current density in the conductors
In commutator and slip-ring machines are
losses in brushes but there are very small
because the current density in brushes is
low although the contact voltage between
brushes and commutator may produce
significant losses.
2.2 Iron losses
Iron losses are also known as Core losses.
Those losses consist of Hysteresis loss and
Eddy current losses. Hysteresis losses
appear because of reserve of magnetization
of the armature core. When the core passes
under one pair of poles it undergoes one
complete cycle of magnetic reversal.
Hysteresis loss is given by Steinmetz
formula [4]:
𝑊ℎ = 𝜂𝐵 𝑚𝑎𝑥
1,6
𝑓𝑉 (2)
Where the frequency of magnetic reversal
is equal to:
𝑓 = 𝑝
𝑛
120
(3)
Where is:
𝑉-volume of the core, 𝑚3
𝜂- Steinmetz hysteresis constant
𝐵-teeth flux density, T
𝑝-number of poles
𝑛-speed, r/min
Eddy current losses are caused when the
armature core rotates in the magnetic-field
and electro motive force is also induced in
the core according to the Faraday's law of
electromagnetic induction. Though this
induced EMF is small it causes a large
current of flow in the body due to low
resistance of the core and then appear
losses like this.
2.3 Additional losses
They are lumped together by all the
electromagnetic losses which are not
included in the resistive losses and iron
losses. Additional losses are very difficult
to calculate and measure. Additional losses
are present in the equation [1]:
𝑃𝑎𝑑~𝐼2 𝑓 1.5
(4)
Where is:
𝑃𝑎𝑑-additional losses
𝐼-current, A
𝑓-frequency, Hz
2.4 Mechanical losses
Mechanical losses are a consequence of
bearing friction and windage. While
friction losses depend on the bearing type,
shaft speed, load on a bearing and
properties of the lubricant, windage losses
are significant with increasing machine
speed. Friction and windage losses are
caused by the friction in the bearings of the
motor and aerodynamic losses associated
with the ventilation fan and other rotating
parts. Ventilator losses are also part of
mechanical losses but they are negligible
and they present the small part in losses,
although their influence can be quite large
for some other cases, that’s why they will
not be considered in this report.
Bearing manufactures give guide
lines for calculating bearing losses. In this
case, according to SKF (1994) bearing
friction losses are [1]:
𝑃𝜌,𝑏𝑒𝑎𝑟𝑖𝑛𝑔 = 0.5Ω𝜇𝐹𝐷 𝑏𝑒𝑎𝑟𝑖𝑛𝑔 (5)
Where is:
Ω-angular frequency of the shaft supportet
by a bearing, rad/sec
𝜇-friction coefficient (0.001÷0.005)

𝐹-bearing load, N
𝐷 𝑏𝑒𝑎𝑟𝑖𝑛𝑔-inner diameter of the bearing, m
For calculating the bearing friction losses
first there have to be picked the type of
motor which will be considered under
several conditions. The type of motor is
DSM1 33 2xx1 by Wittur electric Drives.
The type of bearings are ball bearings
6208-2Z-C3 and 6308-2Z-C3 with
different radial and axial forces on them
given by the type of motor. Those radial
and axial forces depend on shaft speed. For
this case radial and axial force for both
type of ball bearings are the same. This
type of deep grove ball bearings are mostly
used in the industry, they have less friction
and high speed as well. The only different
between these two ball bearings are in
construction dimension, dynamic and static
load rating, reference and limited speed of
rotation which is given by manufactures.
The limited speed of bearings must be
observed even under the most favorable
friction and cooling conditions. The
friction of ball bearings is reduced using
the lubricant grease.
Using axial and radial forces, the real force
can be easily calculated on ball bearing,
not just knowing their components.
According to this statement there is
formula for dynamic equivalent load [3]:
𝐹 = 𝑋𝐹𝑟 + 𝑌𝐹𝑎 , (6)
Where is:
𝑋-radial load factor given by manufacture
(2.04 )
𝐹𝑟-radial load, N
𝑌-axial load factor given by manufacture
(0.54)
𝐹𝑎-axial load, N
After the calculated loads on a ball
bearings the friction losses can be
calculated by the equation number (5).
While the shaft speed is increasing,
windage losses are becoming more
significant. They are consequence of
friction between the rotating surface and
the surrounding gas (usually the air).
Windage losses are independent of the
load. The windage losses are reduced with
the diameter of fan leading to reduction in
windage losses. Windage losses contains
two parts of losses. The first one is given
by Saari equation which represents the
power associates with the resisting drag
torque of the rotating cylinder [1]:
𝑃𝜌 𝑤1 =
1
32
𝑘𝐶 𝑀1 𝜋𝜌Ω3
𝐷𝑟
4
𝑙 𝑟 (7)
Where is:
𝑘-roughness coefficient (smooth surface,
𝑘 = 1; usually 𝑘 = 1 ÷ 1.4)
𝐶 𝑀1-torque coefficient (determinate by
measurements)
𝜌-density of the coolant (air), kg/m3
Ω-angular velocity, m/s
𝐷𝑟-outer diameter of the rotor, m
𝑙 𝑟-rotor length, m
Torque coefficient is depend on a
Reynolds number [1]:
𝑅 𝑒𝛿 =
𝜌Ω𝛿𝐷 𝑟
2𝜇
(8)
Where is:
𝛿-air gap length, m
𝜇-dynamic viscosity of the coolant, m2
/s

Relations between torque coefficient and
Reynolds number are shown in following
equations [1]:
𝐶 𝑀1 = 10
(
2𝛿
𝐷 𝑟
)
0.3
𝑅 𝑒𝛿
, 𝑅 𝑒𝛿 < 64 (9)
𝐶 𝑀1 = 2
(
2𝛿
𝐷 𝑟
)
0.3
𝑅 𝑒𝛿
0.6 , 64 < 𝑅 𝑒𝛿 < 500 (10)
𝐶 𝑀1 = 1.03
(
2𝛿
𝐷 𝑟
)
0.3
𝑅 𝑒𝛿
0.5 , 500 < 𝑅 𝑒𝛿 < 104
(11)
𝐶 𝑀1 = 0.065
(
2𝛿
𝐷 𝑟
)
0.3
𝑅 𝑒𝛿
0.2 , 104
< 𝑅 𝑒𝛿 (12)
Reynolds number is non-dimensional
number and it encapsulates the rotor speed
and machine size. If Reynolds number is
less than 64 the flow is laminar, and if
Reynolds number is higher than 104
than
the flow is turbulent.
The second part of windage losses are on
the end of surfaces of rotor and it can
create friction losses. The power loss is
also given by Saari [1]:
𝑃𝜌 𝑤2 =
1
64
𝐶 𝑀2 𝜌Ω3(𝐷𝑟
5
− 𝐷𝑟𝑖
5
) (13)
Where is:
𝐶 𝑀2-torque coefficient (determinate by
measurements)
𝐷𝑟𝑖-shaft diameter, m
Also in this case the torque coefficient is
depending on a Reynolds number [1]:
𝑅 𝑒𝑟 =
𝜌Ω𝐷 𝑟
2
4𝜇
(14)
Where is:
𝜇-dynamic viscosity of the coolant, m2
/s
The torque coefficient is given by
following term [1]:
𝐶 𝑀2 =
3.87
𝑅 𝑒𝛿
0.5 , 𝑅 𝑒𝛿 < 3 × 105
(15)
Figure 1 Mechanical losses

𝐶 𝑀2 =
0.146
𝑅 𝑒𝛿
0.2 , 𝑅 𝑒𝛿 > 3 × 105
(16)
The windage losses caused by the rotating
parts of the machine are given by the
equation [1]:
𝑃𝜌 𝑤 = 𝑃𝜌 𝑤1 + 𝑃𝜌 𝑤2 (17)
As it is mentioned earlier the
ventilator losses are also part of the
mechanical losses. The influence of this
kind of losses, are insignificant and
therefore won’t be considered in this
report. Schuisky gives an experimental
equation for the sum of windage and
ventilator losses [1]:
𝑃𝜌 = 𝑘 𝜌 𝐷𝑟(𝑙 𝑟 + 0.6𝜏 𝑝)𝑣𝑟
2
(18)
Where is:
𝑘 𝜌-experimental factor
𝐷𝑟-rotor diameter, m
𝑙 𝑟-rotor length, m
𝜏 𝑝-pole pitch
𝑣𝑟-surface speed of the rotor, m/s
Mechanical losses, which contains
the bearing friction and windage losses are
compared in a diagram on figure 1. The
points on the diagrams represent exact
value of losses on different speeds rotation
and the growth of curves which depends on
the speed of rotation and losses such as
bearing friction and windage.
3 HEAT TRANSFER IN ELECTRICAL
MACHINES
f there is difference in temperature in
systems there will be always heat
transfer. According to the second law of
thermodynamics the heat will always
transfers from higher temperature to lower
temperature.
The design of heat transfer is
important in electrical machines. The
temperature rise of the machine eventually
determines the maximum output power
with which the machine is allowed to be
constantly loaded [1]. Heat and fluid
transfer is more complicated and difficult
issue than the conventional
electromagnetic design of an electrical
machine. Problems related to the heat
transfer can to some degree be avoided by
utilizing empirical knowledge of the
machine constants available, but that
empirical knowledge is not enough in
creating completely new constructions.
The heat is removed by convection,
conduction and radiation. Usually the
convection through air, liquid or steam is
the most significant method of heat
transfer. Convection is the most efficient
cooling method if there is not taken direct
water cooling into account. Convection
heat transfer will be considered here. There
are three important boundary layer
theorems in convection:
1. Surface friction
2. Convection transfer
3. Convection mass transfer.
Figure 2 Development of velocity and
boundary layers
The steam of air meets a plane, the velocity
of the steam is zero on the surface of the
plane. And inside the boundary layer the
speed increases to the speed on free space.
δ 𝑣 is the thickness of the velocity boundary
I

layer and it is defined as the height from
the surface where the speed of steam is
0.99 times the speed in free space. The
temperature T𝑠is assumed to be higher than
the temperature of the steam of air. The
thermal boundary layer δ 𝑇 is defined as the
height from the surface where the ratio of
the difference of the surface and boundary
layer temperatures T𝑠 and T, to the
difference between the surface and the
ambient temperature. The temperature
profile is similar to the velocity profile
what is represented on the figure 2.
For the radial flux electrical machine there
are three significant convection
coefficients relates to the frame, air gap
and coil ends. The frame can be
approximated by the Miller’s equations,
but the other two are more complex case.
The coefficient for an annulus depends on
the air gap length, rotation speed of the
rotor, the length of the rotor and the
kinematic viscosity of the streaming fluid.
Therefore Taylors number can be used to
determine the flow type and the convection
heat transfer coefficient in the annulus. The
annular flow in the tangential direction is
usually referred to Taylor-Couette flow of
Taylor vortex flow. It differs from the flow
between two parallel plates by the toroidal
vortices that appear as a result of tangential
forces [1]. These eddies influence the heat
transfer characteristic of the air gap. Taylor
vortices are described by the Taylor
number:
𝑇𝑎 =
𝜌2Ω2 𝑟 𝑚 𝛿3
𝜇2 (19)
Where is:
𝜌- mass density of the fluid, kg/m3
Ω- angular velocity of the rotor, m/s
𝑟 𝑚- average of the rotor and stator radii, m
𝛿- radial air gap length, m
𝜇- dynamic viscosity of the fluid, kg/s
On the figure 3 there is present value of the
Taylor number and vortices on the
diagram. With increasing of the speed of
rotation there is also increasing the Taylors
number. The dots on the diagram represent
the exact values depending on the speed of
rotation given by the motor characteristic.
Figure 3 Value of Taylors number

According to Becker and Kaye, Nusselt
number is:
𝑁𝑢 = 2 𝑇𝑎 𝑚 < 1700 (20)
𝑁𝑢 = 0.128𝑇𝑎 𝑚
0.367
1700 < 𝑇𝑎 𝑚 < 104
(21)
𝑁𝑢 = 0.409𝑇𝑎 𝑚
0.241
104
< 𝑇𝑎 𝑚 < 107
(22)
The Nusselt number and thermal
resistance are present on the figure 4.
Curves are increasing and they depend of
speed of rotation of the shaft. Dots on the
curves represent the exact values used in
calculating according to motor
characteristics.
Figure 4 Nuselt number and thermal
resistance
According to this statement, there is
formula for calculating the thermal
resistance of convection:
𝑅𝑡ℎ =
1
𝛼 𝑡ℎ 𝑆
(23)
Where is:
𝛼 𝑡ℎ-heat transfer coefficient, W/(m2
K)
𝑆-area of the tube, m
Figure 5 Heat trasfere coefficient and
density of the flow
With increasing the speed of rotation there
is also increasing the heat transfer
coefficient which is given by next
statement:
𝛼 𝑡ℎ =
𝑁 𝑢 𝜆
𝛿
(24)
Where is:
𝑁 𝑢-Nusselt number
𝜆-thermal conductivity of air, kW/(mK)
𝛿-radial air gap length, m
The convection heat transfer coefficient in
the coil ends is the most difficult to
approximate because the flow field is too
complex to model. The cooling method of
the electrical machine also affects the
convection heat transfer coefficient of the
coil ends.
Following this case, there is also increasing
of the heat flow density created by
convection:
𝑞𝑡ℎ = 𝛼 𝑡ℎ 𝜃 (25)
Where is:
𝜃-temperature difference between the
cylinder and the surroundings, K, °C
𝛼 𝑡ℎ- heat transfer coefficient, W/(m2
K)

On the figure 5 are represent the increasing
the curves and there depended of the speed
of the shaft. The dots are represent the
exact values given by motor
characteristics.
In this chapter there is only
consider the convection heat transfer
because it is most spread in electrical
machines. Although the radiation and
conduction can have the big influence in
the heat transfer, but for this type of motor
there are not considered. There are
represent several diagrams who describe
the increasing curves depending of
developing the shaft speed.
4 VIBRATION EFFECTS OF STATOR
IN THE ELECTRICAL MACHINES
lectromagnetic forces are the most
important source of the vibration in
electrical machines. The electromagnetic
force is excitation load which is a
sinusoidal - varying excitation across a
range of the frequencies and the out
parameter is deflection of the structure that
is sinusoidal – varying response at each
corresponding natural frequency.
Harmonic response analysis is used to
simulate the vibration response of the
electric machine.
The vibration forces can be divided into
three groups:
1. Electromagnetic force
2. Mechanical force
3. Air friction force [7].
The electromagnetic force and rotating
torque which will provide the power to
drive the electric machine is produced in
the magnetic field in the air gap. Magnetic
force producing vibrations of the motor is
due to the flux in the air gap. Maxwell’s
stress can be used to compute the total
force and torque acting between the stator
and rotor.
The most important vibration excitations is
the reluctance force produced in the air gap
between the stator and rotor because of the
larger magnitude and the less complexity
compared with the other forces. Forces
associated with the magnetic field are one
of the most important sources of structural
vibrations in electrical machines. The other
sources of vibration and noise are related
to rotordynamics and air flow [6].
This paper won’t contain the vibrations
caused by electromagnetic force, only the
mechanical force in the simple stator 3D
model. Then all calculation are simplified.
Figure 6 3D model of the stator
Stator structure is supported by end shields
which are stiff enough to maintain a
circular shape at the ends of the stator
frame. This increases the natural
frequencies and makes the vibration modes
three dimensional. For analysis the all
model is considered of the one part and the
properties of material that is used for
calculating are from copper.
Method which is used for calculating the
vibrations is Rayleigh-Ritz method. 3D
model of the stator is analysis with
E

tetraeder method. This method will not
give exact results, but it will give
approximately results.
The vibration is changing dependent on the
speed of rotation, and modes are just taken
from one radial axis (in this paper for this
example it is x-axis).
The vibration of the stator is governed by
[5]:
𝑀 𝑚 𝑢̈ + 𝐶 𝑚 𝑢̇ + 𝐾𝑢 = 𝑓(𝑡) (26)
Where is:
𝑢(𝑡)-nodal displacement, m
𝑓(𝑡)- distribution acting on the stator, N
𝑀 𝑚-mechanical mass matrices
𝐶 𝑚-damping matrices
𝐾-stiffness matrices
Using the 3D program for analysis the
behavior of the stator under several
conditions, there is shown the difference
between speed of rotation and frequency as
well. On following pictures there is present
the all spectrum of values in different
frequency, for this case just for frequency
of 25 Hz (1500 r/min) and 100 Hz (6000
r/min). The amplitude is falling down from
maximum to minimum values of
frequencies. That is well known as
frequency response. The phase angle is a
measure of the time by which the load lags
(or leads) a frame of reference. If the phase
angel is 0° or 180° those are usually radial
vibrations in dynamic nonbalance systems.
The system is trying to avoid the resonance
part. If the part of machine seems to be one
period of time in resonance part, it can
damage the part of machine or broke him
which can have bad consequences for
machine or environment. In this example
there is shown that all frequencies caused
by mechanical forces are well appropriate
for this type of machine.
The more correct results will be
detected if there was considered all types
Figure 7 Frequency response 25Hz - 1500 r/min
Figure 8 Frequency response 100Hz - 6000 r/min

of vibrations such as electromagnetic, air
friction and mechanical forces. Figure 9 is
representing the elastic effective strain for
the 25 Hz and 1500 r/min. On the picture
there is present that inner diameter of the
stator have the maximum value of the
elastic effective strain, and the minimum
value is on the outer diameter which
represent the good stability of the motor.
5 CONCLUSION
osses are important in electrical
machines. In the mechanical losses
there is present bearing friction losses and
windage losses. Those kind of losses are
important to calculate before making the
real model of machine. Losses like that can
be avoided using correct type of bearings
and good cooling system. Heat is
transferred by convection between a region
of higher temperature and a region of a
cooler temperature. For calculating the
thermal resistance, density of the coolant,
Nusselt number and the heat transfer
coefficient there was used several
equations to analysis behavior of the
machine in different speed of rotations.
One of the most important issue in this part
are the vortices given by the Taylors
number who can be laminar and turbulent.
Vibrations during the machine work are
important for safety of electrical motor.
Influence of vibration have to be as low to
prevent the damage in electrical motor.
There was analysis of the stator in simple
3D model and his amplitude of vibrations.
In this part there was only consider the
mechanical frequencies and theirs basic
influence on the electrical motor.
6 REFERENCES
[1] T. J. V. H. J. Pyrhonen, Design of rotating
electrical machines, Wiley, 2014.
[2] P. R. N. C. A. S. H. D. A. Howey, Air-gap
Convection in Rotating Electrical Machines,
2012.
[3] K. H. Decke, Elementi strojeva, Tehnicka knjiga
Zagreb, 1975.
[4] http://www.electricaleasy.com/2014/01/losses-in-
dc-machine.html.
[5] S.P.Verma, „Noise and vibrations of electrical
machine and drives, their production and means
of reduction,“ New Delhi, 1996.
[6] J. Roivainen, „Unit wawe response based
modeling,“ Picaset Oy, Helsinki , 2009.
[7] https://noppa.aalto.fi/noppa/kurssi/s-
17.3030/luennot/S-17_3030_lecture_11.pdf.
L
Figure 9 Elastic effective strain

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