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Parallel processing application in traction motor fault diagnosis
Electric Power Systems Research 52 (1999) 241 – 249
Parallel processing application in traction motor fault diagnosis A.K. Sen a,*, A.S.R Murty b b
a Faculty Marine Engineering and Research Institute. P-19, Taratolla Road, Calcutta-700 088, India Reliability Engineering Centre, Department of Industrial Engineering and Management, Indian Institute of Technology, Kharagpur-721302, India
Received 5 August 1998; accepted 15 February 1999
Abstract Parallel processing-based system condition monitoring and fault detection are the order of the day for providing greater safety and reliability of the system. Fast and accurate fault diagnosis and detection predictor provides better system protection and maintenance planning of spare parts. In this paper, an attempt has been made to predict the temperature profile of different parts of a traction motor by using parallel processing techniques. The prediction of temperature of different parts of the motor during healthy and faulty condition have been established by developing a thermal model of the machine and transputer based concurrent process predictor has been taken up to assess the thermal behaviour of the machine The significant advantage of this predictor is its capability of providing early warning about the condition of the machine with greater confidence and built in redundancy and thereby ensured the protection of the machine. © 1999 Elsevier Science S.A. All rights reserved. Keywords: Diagnosis with greater confidence; Parallel processing; Traction motor; Thermal model; Transputer based predictor
1. Introduction: Demands for reliability and safety of technical systems and equipments necessitate the improvement of process supervision and monitoring methods as part of the overall control scheme. The early indication of failures can help to avoid major breakdowns and catastrophes that could otherwise result in substantial material damage and human injuries. Similarly, failure detection and isolation have become a critical issue in the operation of high-performance systems where safety, mission accomplishment and material value are at stake. By assisting the human operator in assessing the nature and extent of the fault, automatic diagnostic system may contribute significantly to the fast and proper reaction to failure situations, with such reactions ranging from immediate emergency actions to long term modification of the maintenance schedule [6]. An essential prerequisite for further development of automatic supervision is real time process fault detection. Real time processing and detection of faults are not only cost-effective, but it also provide high accuracy and throughput required for systems. * Corresponding author.
A method with which to deal with this sort of problem is the use of real time fault detection algorithms, which detect faults by estimating several parameters. An unexpected change in these parameters indicate the gradual build up of the fault. A major concern of such method is the number of computations that have to be performed in real time. To achieve these objectives, a fast processor is required which not only computes the performance, but also provides the quick response of the system during the development of faults. This necessities the use of parallel processing techniques and multiprocessing environment in an innovative architecture to increase the overall processing speed. The implementation of multiprocessing system is possible with the advent of transputer technology, which provides the facilities for development of highly efficient parallel systems in a simple and user friendly manner. It has gained great benefit by the direct relationship with the concurrent programming language OCCAM and its ability to link other neighbouring processors in a software transparent manner. The tremendous capability of transputer has been exploited here in the condition monitoring and fault diagnosis of a d.c traction motor which is useful in rail transportation. The machine condition has been as-
0378-7796/99/$ - see front matter © 1999 Elsevier Science S.A. All rights reserved. PII: S 0 3 7 8 - 7 7 9 6 ( 9 9 ) 0 0 0 2 6 - 7
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A.K. Sen, A.S.R. Murty / Electric Power Systems Research 52 (1999) 241–249
sessed by analysing the temperature signals of different parts of the motor through thermal modelling and transputer based real time processing.
2. Development of thermal model Temperature measurement plays a dominant role in condition monitoring and fault detection of different parts of a traction motor, because the limits of rating of
electrical machines are generally set by the maximum permissible temperature which the insulation can withstand. Excessive insulation temperature due to supply and loading faults causes the majority of failures of traction motor. To avoid excessive insulation temperature, finer degree of protection mechanism is required which will also reduce the unnecessary shutdowns and loss of production. For studying the temperature profile of different parts of traction motor, a thermal model is required
Fig. 1. Machine quarter section showing idealized geometry and thermal node division. (1) Shaft; (2) bearing; (3) end bracket; (4) ambient (5) frame; (6) stator end plate; (7) axial duct; (8) stator core; (9) stator winding; (10) rotor core; (11) rotor embeded winding; (12) rotor teeth; (13) rotor end winding; (14) rotor end; (15) air-gap air; (16) commutator; (17) brush and brush gear; (18) radial duct; (19) overhang air.
Fig. 2. D.C. traction motor thermal equivalent circuit.
A.K. Sen, A.S.R. Murty / Electric Power Systems Research 52 (1999) 241–249 Table 1 Motor data sheeta Rotating continuous at 45°C ambient Volts Amps R.P.M H. P/K. W Insulation Weight of the machine with pinion and axle Weight of armature Weight of gear case Armature dimensions Core diameter Core length Overall length of armature Distance between bearing abutment faces Wire diameter Core band turns Pinion end/commutator end winding band turns Type of wire
Commutator dimension Length of commutator working face Nominal new diameter Maximum worn diameter Mica thickness nominal Mica undercutting depth Pole dimension Main pole length Compole length Liners at back of poles
Brush gear dimension Number of brush holder Number of brushes per holder Clearance between brush holder and commutator Size of split brush Thickness over both halves Minimum length (length at which brush becomes inoperative) Resistances Resistance values at 25°C in ohm average Armature Series field Commutating field Thermal conducti6ity Thermal conductivity of copper Thermal conductivity of insulation Thermal conductivity of air
285 980 360 333/248 Class B 3340 kg 988 kg 119 kg 488.95 mm 393.70 mm 1276 mm 933.45 mm 1.6 mm 100 45 Copper wire with minimum ultimate tensile strength of 165 kg/mm2 and yield point 142 kg/mm2 187 mm 422 mm 390 mm 1.5 mm 0.75 mm to 1.25 mm 499 mm 507 mm (1) Main pole, None (2) Compole, 2.77 mm thick stainless steel 4 3 1.6–2.4 mm (a) length = 51 mm (b) width= 57.1 mm 19 mm 27.8 mm
0.0100 V 0.0052 V 0.0064 V 380 W/°Cm 0.15 W/°Cm 0.03 W/°Cm
243
which will assess the temperature rise at the expected hot spots in the machine, when the construction data such as dimensions and material properties and operating conditions such as losses and cooling arrangement data are entirely specified. Construction of thermal model is also dominated by the requirement of the process predictor. The predictor requires both accuracy and simplicity and to meet this goal the bulk conduction parameters have been considered similar in line as discussed in the models of the references [1,5,9,10,12]. The steady state heat transfer between different components of an induction machine have been discussed by a number of authors [4,5] and the transient state by the authors [1,10,12], by associating thermal capacitance with each bulk component with a good effect. In the present model, similar ideas have been undertaken and suitably modified to yield good results. The traction motor has been modelled by considering an idealized machine geometry as shown in Fig. 1, with assumed symmetry about the shaft and a radial plane through the centre of the machine. The machine has been divided into a number of lumped components given in Fig. 1, which are connected through a linear scheme of thermal resistances [9]. The value of the resistances can be calculated from the simple heat transfer formulae. In Fig. 2, the thermal circuit of the motor has been shown, in which the nodes represent the respective parts of the motor. The element which is connected between the nodes denotes the thermal resistance between the nodes. The thermal resistance depends on the nature of heat transfer between the nodes. For simplicity, radiation mode of heat transfer has been neglected. The thermal resistance has been calculated in the following manner. Thermal resistance, R=1/kA°C/watts – for conductive heat transfer
(1)
and R= 1/hA°C/watts – for convective heat transfer.
(2)
where 1 is the effective length of the conduction path required to give the correct temperature rise (m); A is the area of conductive/or convective path (m2); k is the thermal conductivity of the medium (watts/m°C) and h is the film coefficient (watts/m 2°C) In certain cases, where heat transfer between the nodes will be in both conductive and convective modes, the equivalent resistance has been considered to facilitate the calculations. They follow the same treatment as in the case of electrical resistances, and discussed in Refs [2,5,9]. Part of the nodes in the thermal equivalent circuit are heat sources where internal heat generation occurs owing to the losses such as copper losses, stray
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Table 1 (Continued)
C= 6rCp = m Cp
Thermal conducti6ity Thermal conductivity of stator iron Thermal conductivity of the frame and end-shields iron: 45
40 W/°Cm W/°Cm
Film coefficient Heat transfer coefficient between the rotor and stator through the air gap Heat transfer coefficient from the rotor surface to the inner part of the motor Heat transfer coefficient from the motor frame to the ambients Heat transfer coefficient from the shaft to the ambients
65 W/°C m2
46 W/°C m2
58 W/°C m2 20 W/°C m2
a The motor used for our experimental purposes is a 4 pole, fan cooled machine axle hung on sleeve bearings. The drive is transmitted from the motor shaft to the axle through single reduction spur gearing contained in a sheet steel gear case.
load losses and rotational losses. Losses are acting as an input to the nodes and marked with W, all the nodes have thermal capacities C given by, Table 2 The thermal resistance Rij (C/°W) between different parts of traction motor R1,2 R1,10 R1,14 R1,16 R2,4 R3,4 R3,5 R3,6 R3,19 R4,5 R5,6 R5,7 R5,8 R5,17 R6,8 R6,19 R7,8 R7,18 R8,9 R8,15 R8,18 R9,19 R10,12 R10,14 R10,15 R11,12 R11,13 R13,14 R13,16 R14,19 R16,17
0.0350 0.0280 0.0150 0.0220 0.3070 0.3850 0.0145 0.0104 0.7520 0.0852 0.0125 0.0810 0.0198 0.0200 0.0220 0.2950 0.2870 0.6070 0.1270 0.9250 0.3050 0.2150 0.0250 1.1000 0.7120 0.3610 0.4850 1.0600 0.2020 0.7920 0.0331
watt-seconds/°C
(3)
where 6 is the volume of the element (m2); r is the density of element material (kg/m2); C is the specific heat at constant pressure of the element (Kca1/Kg°C) and m is the mass of the element (Kg). The temperatures of the different circuit nodes correspond to the temperatures of different parts of the motor, approximated to the mean temperature of the different parts [5,8]. Heat transfer resistances between the different nodes have been calculated from the data sheet of the motor as recorded in Table 1. The results of calculation or the resistance values have been shown in Table 2. These resistance values are required for model equation calculation as described below, for prediction of node temperature.
3. Mathematical model After developing the thermal model, the model equations are written for each node similar to electrical network. The network shown in Fig. 2 corresponds to 19 components as shown in Fig. 1 and has 19 nodes. So, 19 heat balance equations are needed to describe the model. The temperature of the nodes have to be determined from these equations, the general form of which is Ci
du 1 = − (ui − uj )+ Wi (i, j= 1, 2, … , 19) dt Rji
(4)
where Ci is the ith node thermal capacitance; ui, uj are the ith and jth; node mean temperatures, Rji is the equivalent thermal resistance between node i and node j; Wi is the heat generation at ith node. Now, heat generation in the traction motor is due to electrical and mechanical losses occurring in the machine when it is in the running condition. The losses are either current dependent or voltage dependent depending on the position of the component in the machine. Generally, the losses in the traction motor are of three general types: (a) rotational losses; (b) copper losses and (c) stray load losses. Swaney [3] and Sen [11] have discussed in details about the above mentioned losses and from there, we can conclude that the heat generation is a function of both the terminal voltage and input current of the motor and are therefore given by the expression of the form: Wi = [A]V 2 + [B]I 2
(5)
where A and B are matrices, the elements of which are the parameters of the motor. Matrix A consists of the elements of brush friction loss, windage loss and the iron loss of the machine, which are invariant and depend on motor element dimensions. Matrix B con-
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Fig. 3. Implementation of transputer-based trouble shooting.
tains the electrical resistance elements such as field winding resistance, armature winding resistance, interpole winding resistance etc. and are temperature variant. Substituting the value of Wi in Eq. (4) we get, Ci
du 1 =− (u − uj ) + [A]V 2 +[B]I 2 dt Rji i
[u] is the column matrix of nodal temperatures,
Æ u1 Ç Ã Ã Èu 19É
(6) and [Zr ] is the square matrix of internodal impedances,
Considering, all the nodes of the thermal equivalent circuit, the general system equation can be written in the matrix form as follows: [C]
d[u] = [Zr ][u] + [A]V2 +[B]I 2 dt
(7)
where [C] is the column, matrix of thermal capacitances
Æ C1 Ç Ã Ã; ÈC 19É
Fig. 4. Motor current during the test.
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246
Fig. 5. Frame temperature.
Fig. 6. Stator core temperature.
Æ 1 1 1 1 Ã− R +R +R +R 1,2 1,10 1,14 1,16 Ã 1 Ã R 1,2 Ã Ã Ã Ã 0 È
1 R 1,2 1 1 − + R 1,2 R2,4
0
0
0
−
1 1 1 1 + + + R 19,3 R19,6 R19,9 R19,14
Ç Ã Ã Ã Ã Ã Ã Ã É
[um + 1]= [Gr][um ]+ [HV](V 2)m + [HI](I 2)m
(8)
The R terms in the [Zr ] matrix are the equivalent thermal impedances of each node of the thermal circuit and have been listed in Table 2. The subscripts in R indicate the node number. Eq. (7) can be solved by eigen vector technique and in mth time interval is of the form:
where [um + 1] is the temperature at (m+1)th interval, [um] is the temperature at the end of the mth interval, [Gr ] is the running transfer matrix, [HV] is the voltage dependent temperature rise over mth interval, [HI] is the current dependent temperature rise over mth inter-
Fig. 7. Stator winding temperature.
Fig. 8. Rotor core temperature.
A.K. Sen, A.S.R. Murty / Electric Power Systems Research 52 (1999) 241–249
Fig. 9. Rotor winding temperature.
val, (V 2)m is the square of mth voltage sample and (I 2)m is the square of mth load current sample. The current dependent temperature rise matrix [HI] changes its value due to variation of elements of matrix [B], which contains the elements of winding resistances The change in winding resistance with temperature can be taken into account by recalculating the generation factors at each time step. Then the running temperatures can be found from: [um + 1]=[Gr][um]+ (1 + [b] [um ])[HI](I 2)m +[HV](V 2)m (9) where the matrix [b] containing the elements of temperature coefficient of resistances. It describes the dependence of each heat generator on components in the model. All the above equations are referred to ambient temperature which is to be added to obtain the absolute motor temperatures.
Fig. 10. Rotor teeth temperature.
4. Transputer based predictor Temperature prediction of different parts of the traction motor and the associated faults developed in the parts due to malfunctioning of the motor have been implemented in the parallel processing machine —the transputer, for speedy trouble shooting and maintenance planning activity [7]. The block diagram of the transputer based prediction device is shown in Fig. 3. Three T-424, 32 bit transputers, with four serial links and 4K bytes of on-chip RAM have been used for developing the predictor. The predictor device assesses the temperature profile of the different parts of the motor utilizing the thermal model Eq. (9) The thermal model equation consists of two variables—the initial temperature of the nodes and the line current of the motor, assuming the supply voltage of the motor is constant. The temperature of the nodes are dependent upon the current flow through the nodes. So, any change in current flow through the nodes,
Fig. 11. End winding temperature.
Fig. 12. Commutator temperature.
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changes the temperature of the nodes, indicating a possible fault in that node, which corresponds to a particular part of the motor. As a result, monitoring both the variables at the same instant of time is essential for correct prediction of temperature of parts and its associated faults. Two transputers marked I and II have been used to collect the sampled signals of current and temperature respectively, through analog to digital converters. The sampling period of the signals is determined by the time constant of the machine and the characteristics or delay in the transducers and converters. The sampling period may also be dynamically altered by the third transputer for fault detection and verification. The values of the sampled current and temperature signals are stored in the memory of transputers I and II respectively. Transputers I and II are synchronized by the processing transputer. The interprocessor connection topologies are realized by using the Inmos C001 link adapter. The function of the processing transputer is to collect the sampled signals of current and temperature concurrently from transputers I and II, respectively, and to calculate the temperature of each node of the thermal circuit using the model equations. The normal difference between measured and predicted temperatures are stored in the memory of transputer III, when the machine is in the healthy condition. For the detection of faults, in the parts of the motor, the temperature deviation between the measured and predicted one during faulty condition is compared with the normal deviation which is stored in the memory of the processing transputer. This deviation is calculated and compared at each instant of time by transputer III. A large temperature deviation from the healthy condition is regarded as an early warning of fault development, thereby providing an indication of the beginning of motor malfunctioning. The matrices of the thermal model equations and the ambient temperature value are previously stored in the on-chip memory of the processing transputer, to facilitate the calculation of the predicted temperatures. The nature of the signatures of the temperatures of some parts of the machine during healthy and faulty conditions are shown in Figs. 4–12. In the present scheme, supply voltage signal of the motor has been assumed constant. But., it may not necessarily be so in certain cases. So, in such cases, voltage signal has to be sampled in a manner similar to the sampling of the current signal and has to be wired in with the transputer based predictor. External noise or electrical spikes can sometimes affect the signal processing environment. As a result, the measurement can be disturbed. This can be taken care by increasing the sampling rate of the signals and making signal to noise ratio high. All the data transfer and signal processing tasks performance programs have been written in OCCAM code. Temperature sensing and current sensing have been performed by using infrared camera and D.C.C.T (D.C. current transformer) respectively.
5. Parallel algorithm for the predictor The parallel processing algorithm of the above mentioned process and the different tasks to be performed by different transputers for implementing the above scheme are as follows: HOST TASK (performed in the host computer) : : Initiate transputer III : : SEQ i= 1 FOR m link 0? Received information and send it to screen and display. : : MASTER TASK (performed in the Transputer III) SEQ link 0? Receive data and load thermal equations from the host computer. Initialize sampling period. Calculate and store the results of matrix operations. PAR link 1? Receive sampling period value. link 2? Receive sampling period value. SEQ i= 1 FOR n Wait for sampling period to expire. PAR link 1! Receive sampled current signal. link 2! Receive sampled temperature signal. SEQ Calculate predicted temperature. Temperature deviation= measured−predicted. Store deviation in the memory. link 0! Send temperature information for display and record. IF Measured deviation\Stored deviation. THEN A fault has occurred. ELSE Continue. WORKER TASK 1 (performed in the transputer I) link 1? Receive sampling period value. Initiate A/D converter. SEQ i=1 FOR n Wait for the sampling period to expire. link 3? Receive sampled signal. Update next sampling time.
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WORKER TASK 2 (performed in the transputer II) link 2? Receive sampling period value. Initiate A/D converter.
fastest possible time by processing large chunk of data— a vital need for trouble shooting and maintenance planning activities of the motor.
SEQ i=1 FOR n Wait for the sampling period to expire. link 4? Receive sampled signal. Update next sampling time.
References
6. Conclusion Transputer-based condition monitoring and fault detection scheme has been successfully implemented by considering the thermal model of the traction motor. The predicted and measured temperatures during healthy and faulty conditions of the machine are in good agreement with each other. The small discrepancies in the signatures are due to low value of the branch impedances of the thermal circuit and also due to variation of heat flow coefficients. Improper adjustment of the sensing devices is another cause of variation in the result. Only a part of the transputer’s vast potential has been utilized but more monitoring or protection schemes can be wired into it which will ultimately reduce the hardware cost and space requirement problems. It will also help the maintenance engineers to maintain the system with minimum effort. The system provides a reliable and accurate response in
.
[1] A.A. Natarajan, N. Rudraiah, Transient temperature rise of squirrel cage rotors of induction machines, Proc. National Heat and Mass Transfer Conf. BHEL, Hyderabad, 1980. [2] A.J. Chapman, Heat Transfer, Macmillan, New York, 1974. [3] A.K. Sawhney, A course in Electrical Machine Design, Dhanpat Rai & Sons, Delhi, 1990. [4] C.R. Soderberg, Steady flow of heat in large turbine-generators, A.I.E.E Trans. 50 (1931) 782 – 802. [5] I.J. Perez, J.K. Kassakian, A stationary thermal model for smooth air-gap rotating electric machine, Electric Mach. Electromech. 3 (1979) 285 – 303. [6] J. Gertler, Survey of model-based failure detection and isolation in complex plants, IEEE Control System Magazine, 5(6), 3 – 11 (1992). [7] J.M. Karwatzki, Transputers in Condition Monitoring, CME, 1987, pp 41 – 43. [8] J.P. Holman, Heat Transfer, Mcgraw-Hill, New York, 1989. [9] M. Chertkov, A. Shenkman, Determination of heat state of normal load induction motors by a no-load test run, Electric Mach. Power Syst. 21 (1993) 355 – 369. [10] P.H. Mellor, D.R. Turner, Real time prediction of temperatures in an induction motors using a microprocessor, Electric Mach. Power Syst. 15 (1988) 333 – 352. [11] S.K. Sen, Rotating Electrical Machinery, Khanna, Delhi, 1976. [12] V.K. Sreenivasan, D.P. Sengupta, Prediction of the thermal behaviour of duty-cycling T.E.F.C motors’, Proc. National Heat and Mass Transfer Conf., BHEL, Hyderabad, 1980.
.
Parallel processing application in traction motor fault diagnosis A.K. Sen a,*, A.S.R Murty b b
a Faculty Marine Engineering and Research Institute. P-19, Taratolla Road, Calcutta-700 088, India Reliability Engineering Centre, Department of Industrial Engineering and Management, Indian Institute of Technology, Kharagpur-721302, India
Received 5 August 1998; accepted 15 February 1999
Abstract Parallel processing-based system condition monitoring and fault detection are the order of the day for providing greater safety and reliability of the system. Fast and accurate fault diagnosis and detection predictor provides better system protection and maintenance planning of spare parts. In this paper, an attempt has been made to predict the temperature profile of different parts of a traction motor by using parallel processing techniques. The prediction of temperature of different parts of the motor during healthy and faulty condition have been established by developing a thermal model of the machine and transputer based concurrent process predictor has been taken up to assess the thermal behaviour of the machine The significant advantage of this predictor is its capability of providing early warning about the condition of the machine with greater confidence and built in redundancy and thereby ensured the protection of the machine. © 1999 Elsevier Science S.A. All rights reserved. Keywords: Diagnosis with greater confidence; Parallel processing; Traction motor; Thermal model; Transputer based predictor
1. Introduction: Demands for reliability and safety of technical systems and equipments necessitate the improvement of process supervision and monitoring methods as part of the overall control scheme. The early indication of failures can help to avoid major breakdowns and catastrophes that could otherwise result in substantial material damage and human injuries. Similarly, failure detection and isolation have become a critical issue in the operation of high-performance systems where safety, mission accomplishment and material value are at stake. By assisting the human operator in assessing the nature and extent of the fault, automatic diagnostic system may contribute significantly to the fast and proper reaction to failure situations, with such reactions ranging from immediate emergency actions to long term modification of the maintenance schedule [6]. An essential prerequisite for further development of automatic supervision is real time process fault detection. Real time processing and detection of faults are not only cost-effective, but it also provide high accuracy and throughput required for systems. * Corresponding author.
A method with which to deal with this sort of problem is the use of real time fault detection algorithms, which detect faults by estimating several parameters. An unexpected change in these parameters indicate the gradual build up of the fault. A major concern of such method is the number of computations that have to be performed in real time. To achieve these objectives, a fast processor is required which not only computes the performance, but also provides the quick response of the system during the development of faults. This necessities the use of parallel processing techniques and multiprocessing environment in an innovative architecture to increase the overall processing speed. The implementation of multiprocessing system is possible with the advent of transputer technology, which provides the facilities for development of highly efficient parallel systems in a simple and user friendly manner. It has gained great benefit by the direct relationship with the concurrent programming language OCCAM and its ability to link other neighbouring processors in a software transparent manner. The tremendous capability of transputer has been exploited here in the condition monitoring and fault diagnosis of a d.c traction motor which is useful in rail transportation. The machine condition has been as-
0378-7796/99/$ - see front matter © 1999 Elsevier Science S.A. All rights reserved. PII: S 0 3 7 8 - 7 7 9 6 ( 9 9 ) 0 0 0 2 6 - 7
242
A.K. Sen, A.S.R. Murty / Electric Power Systems Research 52 (1999) 241–249
sessed by analysing the temperature signals of different parts of the motor through thermal modelling and transputer based real time processing.
2. Development of thermal model Temperature measurement plays a dominant role in condition monitoring and fault detection of different parts of a traction motor, because the limits of rating of
electrical machines are generally set by the maximum permissible temperature which the insulation can withstand. Excessive insulation temperature due to supply and loading faults causes the majority of failures of traction motor. To avoid excessive insulation temperature, finer degree of protection mechanism is required which will also reduce the unnecessary shutdowns and loss of production. For studying the temperature profile of different parts of traction motor, a thermal model is required
Fig. 1. Machine quarter section showing idealized geometry and thermal node division. (1) Shaft; (2) bearing; (3) end bracket; (4) ambient (5) frame; (6) stator end plate; (7) axial duct; (8) stator core; (9) stator winding; (10) rotor core; (11) rotor embeded winding; (12) rotor teeth; (13) rotor end winding; (14) rotor end; (15) air-gap air; (16) commutator; (17) brush and brush gear; (18) radial duct; (19) overhang air.
Fig. 2. D.C. traction motor thermal equivalent circuit.
A.K. Sen, A.S.R. Murty / Electric Power Systems Research 52 (1999) 241–249 Table 1 Motor data sheeta Rotating continuous at 45°C ambient Volts Amps R.P.M H. P/K. W Insulation Weight of the machine with pinion and axle Weight of armature Weight of gear case Armature dimensions Core diameter Core length Overall length of armature Distance between bearing abutment faces Wire diameter Core band turns Pinion end/commutator end winding band turns Type of wire
Commutator dimension Length of commutator working face Nominal new diameter Maximum worn diameter Mica thickness nominal Mica undercutting depth Pole dimension Main pole length Compole length Liners at back of poles
Brush gear dimension Number of brush holder Number of brushes per holder Clearance between brush holder and commutator Size of split brush Thickness over both halves Minimum length (length at which brush becomes inoperative) Resistances Resistance values at 25°C in ohm average Armature Series field Commutating field Thermal conducti6ity Thermal conductivity of copper Thermal conductivity of insulation Thermal conductivity of air
285 980 360 333/248 Class B 3340 kg 988 kg 119 kg 488.95 mm 393.70 mm 1276 mm 933.45 mm 1.6 mm 100 45 Copper wire with minimum ultimate tensile strength of 165 kg/mm2 and yield point 142 kg/mm2 187 mm 422 mm 390 mm 1.5 mm 0.75 mm to 1.25 mm 499 mm 507 mm (1) Main pole, None (2) Compole, 2.77 mm thick stainless steel 4 3 1.6–2.4 mm (a) length = 51 mm (b) width= 57.1 mm 19 mm 27.8 mm
0.0100 V 0.0052 V 0.0064 V 380 W/°Cm 0.15 W/°Cm 0.03 W/°Cm
243
which will assess the temperature rise at the expected hot spots in the machine, when the construction data such as dimensions and material properties and operating conditions such as losses and cooling arrangement data are entirely specified. Construction of thermal model is also dominated by the requirement of the process predictor. The predictor requires both accuracy and simplicity and to meet this goal the bulk conduction parameters have been considered similar in line as discussed in the models of the references [1,5,9,10,12]. The steady state heat transfer between different components of an induction machine have been discussed by a number of authors [4,5] and the transient state by the authors [1,10,12], by associating thermal capacitance with each bulk component with a good effect. In the present model, similar ideas have been undertaken and suitably modified to yield good results. The traction motor has been modelled by considering an idealized machine geometry as shown in Fig. 1, with assumed symmetry about the shaft and a radial plane through the centre of the machine. The machine has been divided into a number of lumped components given in Fig. 1, which are connected through a linear scheme of thermal resistances [9]. The value of the resistances can be calculated from the simple heat transfer formulae. In Fig. 2, the thermal circuit of the motor has been shown, in which the nodes represent the respective parts of the motor. The element which is connected between the nodes denotes the thermal resistance between the nodes. The thermal resistance depends on the nature of heat transfer between the nodes. For simplicity, radiation mode of heat transfer has been neglected. The thermal resistance has been calculated in the following manner. Thermal resistance, R=1/kA°C/watts – for conductive heat transfer
(1)
and R= 1/hA°C/watts – for convective heat transfer.
(2)
where 1 is the effective length of the conduction path required to give the correct temperature rise (m); A is the area of conductive/or convective path (m2); k is the thermal conductivity of the medium (watts/m°C) and h is the film coefficient (watts/m 2°C) In certain cases, where heat transfer between the nodes will be in both conductive and convective modes, the equivalent resistance has been considered to facilitate the calculations. They follow the same treatment as in the case of electrical resistances, and discussed in Refs [2,5,9]. Part of the nodes in the thermal equivalent circuit are heat sources where internal heat generation occurs owing to the losses such as copper losses, stray
244
A.K. Sen, A.S.R. Murty / Electric Power Systems Research 52 (1999) 241–249
Table 1 (Continued)
C= 6rCp = m Cp
Thermal conducti6ity Thermal conductivity of stator iron Thermal conductivity of the frame and end-shields iron: 45
40 W/°Cm W/°Cm
Film coefficient Heat transfer coefficient between the rotor and stator through the air gap Heat transfer coefficient from the rotor surface to the inner part of the motor Heat transfer coefficient from the motor frame to the ambients Heat transfer coefficient from the shaft to the ambients
65 W/°C m2
46 W/°C m2
58 W/°C m2 20 W/°C m2
a The motor used for our experimental purposes is a 4 pole, fan cooled machine axle hung on sleeve bearings. The drive is transmitted from the motor shaft to the axle through single reduction spur gearing contained in a sheet steel gear case.
load losses and rotational losses. Losses are acting as an input to the nodes and marked with W, all the nodes have thermal capacities C given by, Table 2 The thermal resistance Rij (C/°W) between different parts of traction motor R1,2 R1,10 R1,14 R1,16 R2,4 R3,4 R3,5 R3,6 R3,19 R4,5 R5,6 R5,7 R5,8 R5,17 R6,8 R6,19 R7,8 R7,18 R8,9 R8,15 R8,18 R9,19 R10,12 R10,14 R10,15 R11,12 R11,13 R13,14 R13,16 R14,19 R16,17
0.0350 0.0280 0.0150 0.0220 0.3070 0.3850 0.0145 0.0104 0.7520 0.0852 0.0125 0.0810 0.0198 0.0200 0.0220 0.2950 0.2870 0.6070 0.1270 0.9250 0.3050 0.2150 0.0250 1.1000 0.7120 0.3610 0.4850 1.0600 0.2020 0.7920 0.0331
watt-seconds/°C
(3)
where 6 is the volume of the element (m2); r is the density of element material (kg/m2); C is the specific heat at constant pressure of the element (Kca1/Kg°C) and m is the mass of the element (Kg). The temperatures of the different circuit nodes correspond to the temperatures of different parts of the motor, approximated to the mean temperature of the different parts [5,8]. Heat transfer resistances between the different nodes have been calculated from the data sheet of the motor as recorded in Table 1. The results of calculation or the resistance values have been shown in Table 2. These resistance values are required for model equation calculation as described below, for prediction of node temperature.
3. Mathematical model After developing the thermal model, the model equations are written for each node similar to electrical network. The network shown in Fig. 2 corresponds to 19 components as shown in Fig. 1 and has 19 nodes. So, 19 heat balance equations are needed to describe the model. The temperature of the nodes have to be determined from these equations, the general form of which is Ci
du 1 = − (ui − uj )+ Wi (i, j= 1, 2, … , 19) dt Rji
(4)
where Ci is the ith node thermal capacitance; ui, uj are the ith and jth; node mean temperatures, Rji is the equivalent thermal resistance between node i and node j; Wi is the heat generation at ith node. Now, heat generation in the traction motor is due to electrical and mechanical losses occurring in the machine when it is in the running condition. The losses are either current dependent or voltage dependent depending on the position of the component in the machine. Generally, the losses in the traction motor are of three general types: (a) rotational losses; (b) copper losses and (c) stray load losses. Swaney [3] and Sen [11] have discussed in details about the above mentioned losses and from there, we can conclude that the heat generation is a function of both the terminal voltage and input current of the motor and are therefore given by the expression of the form: Wi = [A]V 2 + [B]I 2
(5)
where A and B are matrices, the elements of which are the parameters of the motor. Matrix A consists of the elements of brush friction loss, windage loss and the iron loss of the machine, which are invariant and depend on motor element dimensions. Matrix B con-
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Fig. 3. Implementation of transputer-based trouble shooting.
tains the electrical resistance elements such as field winding resistance, armature winding resistance, interpole winding resistance etc. and are temperature variant. Substituting the value of Wi in Eq. (4) we get, Ci
du 1 =− (u − uj ) + [A]V 2 +[B]I 2 dt Rji i
[u] is the column matrix of nodal temperatures,
Æ u1 Ç Ã Ã Èu 19É
(6) and [Zr ] is the square matrix of internodal impedances,
Considering, all the nodes of the thermal equivalent circuit, the general system equation can be written in the matrix form as follows: [C]
d[u] = [Zr ][u] + [A]V2 +[B]I 2 dt
(7)
where [C] is the column, matrix of thermal capacitances
Æ C1 Ç Ã Ã; ÈC 19É
Fig. 4. Motor current during the test.
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Fig. 5. Frame temperature.
Fig. 6. Stator core temperature.
Æ 1 1 1 1 Ã− R +R +R +R 1,2 1,10 1,14 1,16 Ã 1 Ã R 1,2 Ã Ã Ã Ã 0 È
1 R 1,2 1 1 − + R 1,2 R2,4
0
0
0
−
1 1 1 1 + + + R 19,3 R19,6 R19,9 R19,14
Ç Ã Ã Ã Ã Ã Ã Ã É
[um + 1]= [Gr][um ]+ [HV](V 2)m + [HI](I 2)m
(8)
The R terms in the [Zr ] matrix are the equivalent thermal impedances of each node of the thermal circuit and have been listed in Table 2. The subscripts in R indicate the node number. Eq. (7) can be solved by eigen vector technique and in mth time interval is of the form:
where [um + 1] is the temperature at (m+1)th interval, [um] is the temperature at the end of the mth interval, [Gr ] is the running transfer matrix, [HV] is the voltage dependent temperature rise over mth interval, [HI] is the current dependent temperature rise over mth inter-
Fig. 7. Stator winding temperature.
Fig. 8. Rotor core temperature.
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Fig. 9. Rotor winding temperature.
val, (V 2)m is the square of mth voltage sample and (I 2)m is the square of mth load current sample. The current dependent temperature rise matrix [HI] changes its value due to variation of elements of matrix [B], which contains the elements of winding resistances The change in winding resistance with temperature can be taken into account by recalculating the generation factors at each time step. Then the running temperatures can be found from: [um + 1]=[Gr][um]+ (1 + [b] [um ])[HI](I 2)m +[HV](V 2)m (9) where the matrix [b] containing the elements of temperature coefficient of resistances. It describes the dependence of each heat generator on components in the model. All the above equations are referred to ambient temperature which is to be added to obtain the absolute motor temperatures.
Fig. 10. Rotor teeth temperature.
4. Transputer based predictor Temperature prediction of different parts of the traction motor and the associated faults developed in the parts due to malfunctioning of the motor have been implemented in the parallel processing machine —the transputer, for speedy trouble shooting and maintenance planning activity [7]. The block diagram of the transputer based prediction device is shown in Fig. 3. Three T-424, 32 bit transputers, with four serial links and 4K bytes of on-chip RAM have been used for developing the predictor. The predictor device assesses the temperature profile of the different parts of the motor utilizing the thermal model Eq. (9) The thermal model equation consists of two variables—the initial temperature of the nodes and the line current of the motor, assuming the supply voltage of the motor is constant. The temperature of the nodes are dependent upon the current flow through the nodes. So, any change in current flow through the nodes,
Fig. 11. End winding temperature.
Fig. 12. Commutator temperature.
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changes the temperature of the nodes, indicating a possible fault in that node, which corresponds to a particular part of the motor. As a result, monitoring both the variables at the same instant of time is essential for correct prediction of temperature of parts and its associated faults. Two transputers marked I and II have been used to collect the sampled signals of current and temperature respectively, through analog to digital converters. The sampling period of the signals is determined by the time constant of the machine and the characteristics or delay in the transducers and converters. The sampling period may also be dynamically altered by the third transputer for fault detection and verification. The values of the sampled current and temperature signals are stored in the memory of transputers I and II respectively. Transputers I and II are synchronized by the processing transputer. The interprocessor connection topologies are realized by using the Inmos C001 link adapter. The function of the processing transputer is to collect the sampled signals of current and temperature concurrently from transputers I and II, respectively, and to calculate the temperature of each node of the thermal circuit using the model equations. The normal difference between measured and predicted temperatures are stored in the memory of transputer III, when the machine is in the healthy condition. For the detection of faults, in the parts of the motor, the temperature deviation between the measured and predicted one during faulty condition is compared with the normal deviation which is stored in the memory of the processing transputer. This deviation is calculated and compared at each instant of time by transputer III. A large temperature deviation from the healthy condition is regarded as an early warning of fault development, thereby providing an indication of the beginning of motor malfunctioning. The matrices of the thermal model equations and the ambient temperature value are previously stored in the on-chip memory of the processing transputer, to facilitate the calculation of the predicted temperatures. The nature of the signatures of the temperatures of some parts of the machine during healthy and faulty conditions are shown in Figs. 4–12. In the present scheme, supply voltage signal of the motor has been assumed constant. But., it may not necessarily be so in certain cases. So, in such cases, voltage signal has to be sampled in a manner similar to the sampling of the current signal and has to be wired in with the transputer based predictor. External noise or electrical spikes can sometimes affect the signal processing environment. As a result, the measurement can be disturbed. This can be taken care by increasing the sampling rate of the signals and making signal to noise ratio high. All the data transfer and signal processing tasks performance programs have been written in OCCAM code. Temperature sensing and current sensing have been performed by using infrared camera and D.C.C.T (D.C. current transformer) respectively.
5. Parallel algorithm for the predictor The parallel processing algorithm of the above mentioned process and the different tasks to be performed by different transputers for implementing the above scheme are as follows: HOST TASK (performed in the host computer) : : Initiate transputer III : : SEQ i= 1 FOR m link 0? Received information and send it to screen and display. : : MASTER TASK (performed in the Transputer III) SEQ link 0? Receive data and load thermal equations from the host computer. Initialize sampling period. Calculate and store the results of matrix operations. PAR link 1? Receive sampling period value. link 2? Receive sampling period value. SEQ i= 1 FOR n Wait for sampling period to expire. PAR link 1! Receive sampled current signal. link 2! Receive sampled temperature signal. SEQ Calculate predicted temperature. Temperature deviation= measured−predicted. Store deviation in the memory. link 0! Send temperature information for display and record. IF Measured deviation\Stored deviation. THEN A fault has occurred. ELSE Continue. WORKER TASK 1 (performed in the transputer I) link 1? Receive sampling period value. Initiate A/D converter. SEQ i=1 FOR n Wait for the sampling period to expire. link 3? Receive sampled signal. Update next sampling time.
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WORKER TASK 2 (performed in the transputer II) link 2? Receive sampling period value. Initiate A/D converter.
fastest possible time by processing large chunk of data— a vital need for trouble shooting and maintenance planning activities of the motor.
SEQ i=1 FOR n Wait for the sampling period to expire. link 4? Receive sampled signal. Update next sampling time.
References
6. Conclusion Transputer-based condition monitoring and fault detection scheme has been successfully implemented by considering the thermal model of the traction motor. The predicted and measured temperatures during healthy and faulty conditions of the machine are in good agreement with each other. The small discrepancies in the signatures are due to low value of the branch impedances of the thermal circuit and also due to variation of heat flow coefficients. Improper adjustment of the sensing devices is another cause of variation in the result. Only a part of the transputer’s vast potential has been utilized but more monitoring or protection schemes can be wired into it which will ultimately reduce the hardware cost and space requirement problems. It will also help the maintenance engineers to maintain the system with minimum effort. The system provides a reliable and accurate response in
.
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