AN ANALYSIS OF HEATING TESTS ON ELECTRICAL MACHINES .sx BY EDWARD HUGHES , Ph .sx D. , B.Sc. , Member .sx ( Paper first received 20th August , and in final form 27th November , 1929 .sx ) SUMMARY .sx The factors governing the temperature-rise of electrical machines are so interwoven that the only satisfactory method of separating them is to test actual machines with different distributions of losses , different speeds , etc. ; conclusions derived from tests on models must be accepted with caution .sx In this paper are given the results obtained on two electrical machines , one with a rotating armature and the other with a rotating field , which were tested with different load and field currents , different speeds , etc. The machines were also tested when totally , enclosed and when cooled by an induced draught .sx Temperature-rises were measured by thermometer , by thermo-junction and by the increase of resistance .sx In the case of the machine with the rotating armature it was found possible to follow the temperature variation of the latter by placing a thermo-junction a short distance away from the armature , and it is suggested that this method might be used for shortening the duration of heat-runs .sx INTRODUCTION .sx An enormous amount of work has been done on various aspects of the rise and distribution of temperature in electrical machines .sx Many investigators notably G. E. Luke in the United States have endeavoured to analyse the various factors governing the temperature-rise of a machine by studying each factor separately on suitable models .sx This method simplifies the procedure and often results in important discoveries being made ; but it must be borne in mind that the effect of two factors in combination may be different from their effects when acting .sx separately .sx For instance , Luke t found that the heat dissipation from a rotor was increased ( a ) by increasing the peripheral speed with no forced axial ventilation , and ( b ) by increasing the forced axial ventilation when the rotor was stationary ; but with a combination of peripheral speed and forced axial ventilation he found that , under certain conditions , less heat was dissipated with the rotor revolving than when it was stationary for the same rise of temperature and the same quantity of air through the air-gap per minute .sx Hence , if we are to separate the factors that determine the temperature-rise of various parts of an electrical machine and to find their interaction upon one another , the first step is to carry out an exhaustive series of tests on one machine , the losses in which have been measured accurately for the different test conditions .sx It is , of course , realized that the conclusions deduced from such an analysis cannot be applied indiscriminately to all types of dynamos and motors , but they do assist in elucidating the problem of heat dissipation .sx In this paper the test-results on two machines have been investigated .sx Machine A was a standard d.c , machine except that the commutator was replaced by 3 slip-rings and , for this reason , was chosen for these tests .sx Its rated 3-phase output was 3.5 kVA , at 50 periods per sec .sx and 1 500 r.p.m. Machine B was also a 3-phase alternator with a revolving field and a stator winding of the concentric 2-plane type .sx Its rated output was 5 kVA at 60 periods per sec .sx and 1 200 r.p.m. .sx Test Procedure .sx The machines were tested at different load currents , different exciting currents and different frequencies , each test being continued until the temperature became practically steady .sx Many of the tests were carried out with the field and output currents maintained constant throughout any one test .sx Other tests were performed by overloading either the field or the armature or both for the first half-hour or so , the currents being then adjusted to the correct values .sx The latter method is referred to in greater detail on page 922 .sx The temperature-rise of the field winding was deter-mined by a bridge arrangement described in a previous paper , whilst those of the armature and stator windings of machines A and B respectively were measured by noting the p.d. required for a known direct current , the machine being stopped occasionally for the few seconds required to take readings .sx In the case of machine A , the p.d. was determined by auxiliary copper-gauze brushes bearing on two of the rings .sx Other temperature-rises were also measured ; thus , on machine A , a copper-constantan thermo-junction was fixed midway between the uppermost pole-tips at a radial distance of 2.5 mm from the armature core .sx The object of this arrangement was to see whether it was possible to obtain externally an indication of the core temperature without having to stop the machine , and thus enable the heating test to be shortened , as discussed on page 921 .sx Also , the temperature of the armature core was determined by thermometer at the completion of each test .sx With machine B , one thermo-junction was placed under the head of a screw inserted radially into the stator core on the external surface and midway along one batch of laminations .sx Another thermojunction was rigidly fixed in the middle of the centre vent-duct at a point half-way between the internal and external surfaces of the stator core .sx The object of this junction was to investigate the temperature of the cooling air passing through the duct .sx The iron losses corresponding to the various loads , speeds and excitations were determined by measuring .sx the input power to the d.c. motor that was directly coupled to the alternator , and also the output power of the latter .sx Allowance was made for the copper loss in the armature winding , the contact-resistance loss at the slip-rings and the small increase of copper loss in the motor armature .sx ( 1 ) TESTS ON MACHINE WITH REVOLVING ARMATURE .sx Temperature-Rise of the Field Winding .sx Figs .sx 1 and 2 show the variation of the temperature-rise per watt with the total armature loss for different exciting currents and different peripheral speeds .sx It will be seen that the temperature-rise per watt is a linear function of the armature loss , but that the effect is greatly influenced by the temperature-rise of the field relatively to that of the armature .sx In a previous paper the author suggested that the temperature-rise per watt for the field could be represented in the form .sx where Wa is the armature loss , v the peripheral speed , and k , m and n are constants for a given machine .sx The data then available were not sufficient to check the general applicability of this expression .sx From Figs .sx 1 and 2 , however , it is evident that the coefficient m namely the slope of the lines , varies with ever variation of the exciting current and of the speed , and that no general expression for the temperature-rise o the field is complete if it does not take into account the speed and either the loss in , or the temperature-rise of , the armature .sx By producing the graphs of Figs .sx 1 and 2 back to the vertical axis , the temperature-rise per watt for zero armature loss can be determined for the various speeds and excitations .sx Graphs obtained by plotting the field temperature-rise per watt against the armature temperature-rise ( by resistance ) were of almost identically the same character as those of Figs .sx 1 and 2 , and the values of for no temperature-rise of the armature winding agreed very closely with the corresponding values for no armature loss .sx The mean values of for no armature loss and for no armature temperature-rise , derived from these two sets of graphs , have been plotted in Fig. 3 .sx If the curve through the mean of these points be represented by A(1 + Bvx ) , the value of x is found to decrease from 0.93 for a range of 0 to 5 metres per sec .sx down to 0.52 for a range of 11 to 16 metres per sec .sx These figures indicate that after the influence of armature heating has been eliminated , the effect of the speed upon the field is very similar to that found by Luke for a cylinder rotating in air .sx From an analysis of Luke's curve the author finds that , up .sx to a peripheral speed of 20 metres per sec .sx , the watt dissipated per degree rise of temperature is represented by A1 + B1v0 .sx 93 whilst for peripheral speeds of 25 to .sx 60 metres per sec .sx it becomes A1 + B2v0 .sx 6. It will be noticed that the variation of x is surprisingly similar to that found for the field coils above , and appears to be .sx due to the air at the dissipating surface not being removed in proportion to the velocity .sx A simple mathematical expression giving a fair approximation to the graph of Fig. 3 is .sx .sx .. ( 1)A more cumbersome expression , but one which is in closer agreement with this graph , is .sx .sx .. ( 2 ) .sx Table 1 shows how the values calculated from expressions ( 1 ) and ( 2 ) compare with those obtained experimentally .sx It will be evident from Table 1 that expression ( 1 ) underestimates the temperature-rise at low speeds .sx Effect of Armature Heating upon Field Temperature .sx In any electrical machine working under normal conditions there is a rise of temperature of the armature even on no load .sx It is therefore desirable to determine whether the effect of speed upon the field temperature is the same when the armature is hot as when it is at the room temperature , and , if possible , to derive an expression taking the temperature-rise of the armature into account .sx In Fig. 4 the temperature-rise per watt of the field winding has been plotted against the difference between the temperature-rises of the field and armature windings(both measured by resistance ) for different currents and different speeds .sx From these graphs it will be obvious that is almost independent of the field excitation and of the actual temperatures of the field and armature windings as apart from the difference between their temperatures .sx The values of for the different speeds and for equal temperature-rises by resistance of the field and armature windings have been derived from these graphs and are indicated by crosses in Fig. 5 .sx For purposes of comparison , curve A , showing the values of for no temperature-rise of the armature , has been included in this figure .sx Since the more common practice is to measure the temperature-rise by thermometer , it is of interest to ascertain whether a similar result can be derived from such temperatures .sx Unfortunately , only a few thermometer readings had been taken for the field winding .sx From these readings , however , it was found that the temperature-rise by resistance was about 1.4 times that by thermometer , and the author had previously found that this ratio was practically independent of speed and of excitation .sx By the aid of this ratio , the difference between the temperature-rises by thermometer of the field winding and armature core was estimated , and the results have been plotted against in Fig. 6 .sx These curves again demonstrate that the effect of the armature heating upon the temperature-rise of the field is de-pendent upon the difference of temperature and is practically independent of the excitation .sx The values of for equal temperatures by thermometer are indicated by circles in Fig. 5 and are in close agreement with those derived from resistance measurements .sx The average of these two sets of points is represented very closely by .sx .sx .. ( 3 ) .sx A comparison of expressions ( 1 ) and ( 3 ) shows that the speed is relatively much more important when the armature is hot than when it is cold ; also , that the relationship between and speed , derived for no armature losses , does not apply when armature losses are present .sx That the relationship derived from the no-load tests , without any allowance for armature heating , is even more inaccurate as far as speed is concerned is evident from an inspection of curve B in .sx Fig. 5 , this curve being the mean for the three exciting currents with the armature on open circuit .sx From Figs .sx 4 and 6 it will be obvious that the coefficient 2.7 in formula ( 3 ) requires to be modified whenever there is a difference of temperature between the field and the armature .sx Thus , in Fig. 4 , a change from - 5 to + 5 deg .sx C. in the relative temperatures at a peripheral speed of 16 metres per sec .sx reduces from 0.1955 to 0.1745 , a reduction of 10.7 per cent ; whilst a change from - 10 to + 10 deg .sx C. results in a decrease of 20.3 per cent .sx