AN INVESTIGATION INTO THE THERMAL MODELLING OF INDUCTION MOTORS BY Amar ...

219 Pages·2008·17.45 MB·English

4.6.1 Convective heat transfer model between frame and ambient. . 61
4.6.2 Convective heat transfer model for the air gap 63
4.6.3 Heat transfer model between end windings and endcap air . . 65
4.6.4 Heat transfer model for the end shield 66
4.7 Thermal contact resistances 67
4.8 Radiation mode of heat transfer 68
4.9 Conclusion 70
5 Development and evaluation of thermal model theoretical and ex-
perimental results 71
5.1 Introduction 71
5.2 Allocation of motor losses in the thermal model 72
5.2.1 Distribution of the motor losses 73
5.3 Evaluation of the thermal model parameters 75
5.3.1 Evaluation of materials thermal conductivity 75
5.3.2 Evaluation of film coefficients 76
5.4 Setting up and solving the network equations 78
5.5 Temperature measurements 80
5.5.1 Selection of measurement points 80
5.5.1.1 Mean temperature position in case of axial heat flow 80
5.5.1.2 The position of the mean temperature in case of ra-
dial heat flow 80
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5.6 Location of thermocouples 82
5.7 Results and discussions 83
5.7.1 Effect of stray load losses on the machine heating 84
5.8 Sensitivity analysis 85
5.8.1 Sensitivity to loss distribution 85
5.8.2 Sensitivity to the heat transfer coefficients 86
5.9 Conclusion 87
6 In-situ determination of thermal coefficients 88
6.1 Introduction 88
6.2 Derivation of the modified thermal network equations 89
6.2.1 Model of the thermal circuit conductances 92
6.3 Implementation of the method 94
6.3.1 General consideration in the measurement of thermal conduc-
tivity 94
6.3.2 Formulation of equations 97
6.4 Results 99
6.5 Conclusion 100
7 Finite element analysis of temperature distribution 103
7.1 Introduction 103
7.2 Formulation of the problem 105
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7.3 Results and discussion 110
7.4 Conclusion 112
8 Conclusions 113
8.1 Further work 117
A Performance calculations 119
A.1 Determination of the circuit parameters 120
A.1.1 Measurement technique 120
A.1.2 D.C. test for stator resistance 121
A.1.3 No load test 121
A.1.4 Locked rotor test 122
B Development of the equivalent thermal circuit 128
B.1 Introduction 128
B.1.1 Unidirectional beat flow with only external heat input 130
B.1.2 Unidirectional heat flow with only internal heat generation . 131
B.1.3 Unidirectional heat flow with external heat input and internal
heat generation 132
B.2 Case of cylinder 135
B.2.1 Radial heat flow in a hollow cylinder 135
B.2.1.1 No internal heat generation 136
B.2.1.2 With internal beat generation 138
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B.2.2 Axial beat flow in hollow cylinder 140
C Steady state theory of the equivalent circuit 142
D Thermal constants and motor dimensions 145
E Derivation of finite element equations 149
E.1 Derivation of the interpolation function 149
E.2 Derivation of element matrices 151
List of symbols
A Surface (m2)
A Cross sectional area of fin (m2)
A1 Internal surface of a cylinder (m2)
A1 Surface of the frame casing which is in contact with the cooling air (m2)
AFin Surface of the fins (m2)
Af Effective area of the frame casing (m2)
Thermal capacitance (W x sl°C)
Cp Specific heat capacity at constant pressure (JIK11°C)
Overall diameter (m)
scalar factor
Thermal admittance (WI°C)
[G] Admittance matrix
Convective heat transfer coefficient (w/ocm2)
hf Film coefficient of the frame (WI°Cm2)
Length (in)
hFi„ Film coefficient of the fin (W/°Cm2)
H Fi„ Axial length of cooling fins (m)
Current (A)
ka Lamination axial thermal conductivity (WI°Cm)
kr Lamination radial thermal conductivity (WI°Cm)
ke Apparent thermal conductivity (WI°Cm)
ki Thermal conductivity of the slot insulation (WI°Cm)
kFin Thermal conductivity of the fin (WI°Cm)
kair Thermal conductivity of air (WI°Cm)
lg Airgap length (m)
Npr Prandlt number
Aru Nusselt number
Q1 Rotor copper losses (W)
Qin Power input to the motor (W)
Stray load losses (W)
Q stray
QI Iron losses (W)
Qt Total losses (W)
Qfc Friction losses (W)
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Qs, Stator copper losses (W)
Q„ Rotor copper losses (W)
Qb1 Proportion of iron losses allocated to back iron (W)
Qtr Proportion of iron losses allocated to teeth (W)
Q Heat generated (W)
Qi External heat input (W)
[Q] Loss vector
q Heat generated per unit volume (W/m3)
R Resistance (Q)
Ro Thermal resistance (°C/W)
r Radius (7n)
r1 Internal radius of a cylinder (m)
r2 external radius of a cylinder (m)
R1 Thermal resistance (°C/W)
R2 Thermal resistance (°C/W)
/in, Thermal resistance (°C/W)
Ra Axial thermal resistance of a rode (°C/W)
R, radial thermal resistance of a rode (°C/W)
r Rotor radius (m)
rsh Radius of the shaft (m)
Rx Thermal resistance (°C/W)
Ry Thermal resistance (°C/W)
Rx, Slot copper thermal resistance in the x direction (°C/W)
Rzi Slot liner thermal resistance in the x direction (°C/W)
R Slot copper thermal resistance in the y direction (°C/W)
yc
Ryi Slot liner thermal resistance in the y direction (°C/W)
Rz Resultant thermal resistance of the slot in the x direction (°C /W)
Resultant thermal resistance of the slot in the y direction (°C/W)
HY
Rex, End winding thermal resistance in the x direction (°C/W)
Rey, End winding thermal resistance in the y direction (°C/W)
Rex Resultant thermal resistance of the end winding in the x direction (°C/W)
Rey Resultant thermal resistance of the end winding in the y direction (°C/W)
Ra, Axial copper thermal resistance (°C/W)
R,,, Convective thermal resistance (°C/W)
Re Reynolds number
t Slot liner thickness (7n)
8 Equivalent width of the slot liner plus insulation between wires (772)
S Slip
V Speed (m/s)
Ta Taylor number
Vbi Volume of back iron (m3)
Volume of teeth (m3)
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W Equivalent width of a copper wire (m)
[0] Temperature vector
[0] Temperature matrix
x
a Resistance temperature coefficient (1/°C)
a Coefficient
II Viscosity (Pa x s)
w Angular rotor velocity (rads I s)
p Density of air (Kg/m3)
Oa, Average temperature (°C)
0 Temperature (°C)
Ambient temperature (°C)
O.
Of Temperature of the frame (°C)
Efficiency of fins
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Pc The contact pressure (N/m2)
a Half the stator bore (in)
b The radius of the core frame interface (m)
c The frame barrel diameter (in)
Poisson ratio for the frame material
[if
Poisson ratio for the core material
P.
The elastic modulus of the frame (N/m2)
Ef
E, The elastic modulus of the core (N/m2)
S The outer core radius - inner frame radius (m)
Chapter 1
General introduction
Electric motors and drive systems account for 64% of industrial electricity consump-
tion [1]. With the rise in energy costs it has become increasingly desirable to save
electrical energy whenever possible. Energy which is not converted into useful work
results in heating of the various motor components, and accounts for the motor
losses. Obviously, the quantity of heat generated must be effectively removed to
prevent damage to the machine. Although the losses are lower in smaller motors,
they are no less susceptible to thermal problems. In absolute quantity, the losses in
small machines are generally higher, per unit output, than for large machines [2].
Today the importance of energy conservation is widely recognised, and has given
rise to many publications aimed at reducing energy consumption in industry. It is
estimated that about 50% of electricity supplied to industry in the UK, in 1976,
was consumed by electric motor drives [3]. A corresponding study in the USA
revealed that 64% of the energy generated was consumed by electric motors [4].
These indicate the global importance and wide spread application of electric motor
drives in industry.
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With the implementation of more advanced cooling systems and the development of
efficient integrated combinations of machine and power electronic circuits the use of
the AC machine is now more widespread and a recent survey [3] in America found
that about 53% of the total industrial electricity consumption was by AC motors. A
similar survey [5] in Japan suggested that AC motors account for 85% of the market.
It has been predicted that for the period 90-95, European sales for DC drives will
increase by 20% whilst AC drives will leap by a massive 83%.
Of the various types of AC motors, the induction type is by far the most popular and
most widely used. Their major advantages are low cost per kW output, simplicity,
robustness, and high reliability. They operate for considerable periods in harsh
environments with minimum maintenance, and have consequently become the work
horse of modern industry. With the continued development of new methods of
increasing efficiency, the induction motors will continue to dominate industry [6,7].
For years, industry accepted low load efficiency as a compromise for the many ad-
vantages of induction motors. However, the losses which were tolerable are now
no longer acceptable as the trend is towards increasing rating for each frame size.
Modern AC electric motors are now being operated much nearer to their point of
overload than a few years ago. The traditional large motors, well endowed with ther-
mal capacity and tolerance to over load, have given way to more efficient compact
types which are designed to exact ratings using high quality materials, improved
manufacturing techniques, and computer derived optimum designs.
Thermal modelling and efficiency are very relevant topics in the designs of today's
engineers. Moreover, the trend towards the design of high power to weight ratio
induction motors has stimulated renewed interest in the measurement and prediction
of losses. The calculation of losses in induction motors is particularly important, as it
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directly influences the temperature distribution, and also the overall motor efficiency.
Predicting the temperature distribution is made difficult because of the uncertainties
associated with assigning losses and thermal coefficients. With advanced analytical
techniques, copper losses, can be predicted to a reasonable degree of accuracy. In
contrast determination of iron losses results in different values depending on the
method in use. The discrepancy between the calculated iron loss value and the
experimentally determined value may be of the order of 20% [8].
These losses play an important role in determining the efficiency and temperature
rise [9], and hence, the rating of a machine. The importance of stray load losses in
induction machines was illustrated by Odok [10], who indicated that an improvement
of 5% on the efficiency would mean a reduction in the losses of about 10%45% of
the input power. For the same temperature rise, the power output of the motor
can then be raised by about 15%-20%. Hence, a small improvement of the average
effective efficiency of the industrial motor would save energy. An improvement of
5% would amount to about a 2.5% saving of the total industrial electrical energy bill
of 1977 in this country [3]. Theoretical and experimental work on stray load losses
in induction motors have been carried out previously, but yet the present knowledge
of the phenomena is by no means adequate for design purposes. The works of
Murkherji [11], Schwarz [12], and Jimoh et al [13] provides a comprehensive list of
references to published works on measurement of these losses, and discusses their
origins.
The discrepancy between the practical and analytical results, on iron losses in general
and stray load losses in particular, calls for the consideration of different approaches
to the study of this topic [13]. The designer is in need of an easy and accurate method
of measurement that would permit these losses to be studied more intensively, and
in all probability to be ultimately reduced.
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