Feb 19, 2004 - Abstract: The numerical simulations for predicting the sound power of electromagnetic origin from an inverter driven induction motor are ...
Sound power radiated from an inverter driven induction motor II: numerical analysis C. Wang, J.C.S. Lai and A. Astfalck Abstract: The numerical simulations for predicting the sound power of electromagnetic origin from an inverter driven induction motor are described. Three numerical models are developed: a 2D electromagnetic force model using the finite-element method (FEM), a 3D FEM structural model, and a 3D acoustic model based on the boundary-element method (BEM). The validation of the FEM structural model and the BEM acoustic model is discussed. The sound power as well as the sound pressure field produced by the motor driven under various conditions is analysed. Results show that FEM and BEM can be effectively employed to analyse the vibro-acoustic behaviour of an inverter-driven induction motor.
1
Introduction
Recently, with the rapid increase in the deployment of variable speed induction drives in various industrial applications, the vibro-acoustic behaviour of inverter-driven induction motors has received more and more attention. This is because inverters generally introduce numerous harmonics in the electromagnetic force waves, which may cause a significant increase in the vibration and acoustic noise of the motor. For many years, much experimental work was carried out and some valuable conclusions were obtained [1, 2]. No doubt, these results are helpful for understanding the noise generation mechanism of inverterdriven induction motors, and for developing efficient strategies to reduce the noise radiated from the motor structure. However, for the purpose of considering vibroacoustic issues at the design stage, the influence of each structural parameter or component on the noise radiation has to be fully understood. The development of mathematical models for predicting noise generation is, therefore, warranted. Modelling noise generation from the motor due to the electromagnetic forces involves the development of three models: modelling the electromagnetic force in the motor, modelling the structural vibration behaviour and modelling the resulting acoustic response of the motor structure, as shown in Fig. 1. The electromagnetic force in the motor is fundamental to the vibration and noise of the motor. For a long time, studies regarding the electromagnetic force modelling and the vibro-acoustic responses of motor structures have been carried out independently. The classical magnetomotive force and permeance wave theory has been employed to investigate the generation mechanism of the electromagnetic force in induction motors, and to analyse the effects of current harmonics [2], magnetic saturation [3], rotor eccentricity [4] etc. on the electromagnetic force wave. r IEE, 2004 IEE Proceedings online no. 20040120 doi:10.1049/ip-epa:20040120 Paper first received 5th June 2003 and in revised form 9th December 2003. Originally published online: 19th February 2004 The authors are with the Acoustics and Vibration Unit, University College, The University of New South Wales, Australian Defence Force Academy, Canberra ACT2600, Australia IEE Proc.-Electr. Power Appl., Vol. 151, No. 3, May 2004
Although the frequencies of harmonics caused by various sources in the force spectrum could be identified by this approach, it was found to be fairly difficult to predict the magnitudes of these harmonics, which are crucial to the estimation of the vibro-acoustic response of the motor structure. Hence, the finite-element method (FEM) [5, 6] has gained popularity recently because detailed distribution of the electromagnetic force in the air gap can be obtained and the effects of structural details such as the tooth shape and slot depth on the electromagnetic force can be assessed. The early vibro-acoustic studies of a motor structure were mostly concentrated on the stator core of the motor. Various analytical methods based on the vibration theory of shells were applied to calculate the natural frequencies and modal sound radiation efficiencies of simplified single stator models [7–10]. Although the vibration analysis was then extended to a stator structure consisting of a thin frame and a thick laminated core [9, 11], these models were still far simpler than the practical motor structure for which analytical methods are difficult, if not impossible, to apply [12]. Since 1970s, the finite-element method has been introduced to investigate the motor structural details and voltage, current
electromagnetic model (FEM)
electromagnetic force
structural model (FEM)
verify
modal testing
verify
sound radiation efficiency measurements
vibration velocity acoustic field or acoustic power measurements
acoustic model (BEM)
acoustic field and acoustic power
Fig. 1
Numerical simulation process 341
effects of different parts of the motor structure in the modal analysis [13–16]. The acoustic power radiated from an axisymmetric motor model including the endshields was calculated using FEM [17]. For acoustic radiation studies, however, since the far-field boundary was difficult to be treated by FEM (perhaps with the exception of the use of infinite elements), which requires prohibitively large number of elements for calculating the radiation into a space, the boundary-element method (BEM) is more suitable. Nevertheless, the calculation of the noise radiation from a motor by BEM has yet to be reported. Despite various studies on the development of the electromagnetic model, the structural model and the acoustic model for the prediction of acoustic noise from an electric motor, discussions about modelling the whole process of the noise generation by combining the three different modelling techniques are still scarce. Recently, the vibration response due to electromagnetic forces was determined only from a 2D electromagnetic force model and a 2D structural model using the finite-element method [18, 19], and the acoustic radiation from the motor was not studied. As a 2D structural model cannot capture the vibration modes in the stator’s axial direction and the effects due to the endshields, it would not be appropriate to validate simulation results using actual measurement data. For acoustic radiation studies, a 3D model would generally be required to represent correctly the interaction between the motor structure and the ambient medium and it would be imperative to use a 3D structural model to determine the vibration over the whole motor structure surface. In a recent study [1], the acoustic power radiated from a 2.2 kW motor driven by an almost sinusoidal controller and two different commercially available inverters under various operating conditions was measured. The test motor was a Brook Crompton Betts three-phase, four-pole, 415 V, 50 Hz, 2.2 kW induction motor with 44 rotor slots and 36 stator slots. In this paper, therefore, a comprehensive numerical analysis of the same induction motor driven by the same controllers is described. The formulation and development of a 2D FEM electromagnetic force model, a 3D FEM structural model and a 3D BEM acoustic model is discussed with appropriate validation. The predicted acoustic power is compared with that measured previously [1]. In addition, the acoustic field generated from the motor for various operating conditions can be easily obtained by the model, thus providing an avenue for developing noise control measures at the design stage. Two configurations for the speed controllers were considered here: benchmark and PWM inverter. The benchmark drive, consisting of a motor–generator set as described in [1], was used to replicate an almost sinusoid drive to provide an ideal state for which the effects of the harmonics can be neglected. The sinusoidal PWM inverter was type MSC2000 manufactured by Zener Electric with the switching frequency being proportional to the test speed of the motor at a rate of 21 Hz/Hz. At the rated speed of 1500 rev/min for the motor, the switching frequency was 1050 Hz [1]. The objective of this paper therefore, is to discuss the process of predicting the sound power radiated from an inverter driven induction motor using FEM/BEM based models. Validation of the numerical results using experimental measurements obtained in [1] will be made wherever appropriate. 2
Electromagnetic force calculations
The FEM model for the electromagnetic force calculation was implemented using a commercial finite-element code 342
ANSYS [20] developed by SASI. By assuming that the force in the air gap does not vary very much along the axial direction, a 2D model was developed. Because of symmetry, only one-quarter section of the four-pole stator and rotor was modelled, as shown in Fig. 2. At the boundaries of the section, the odd periodicity conditions were applied. The number of the nodes was 8432 for the rotor and 12 661 for the stator. The nonlinear properties of the magnetic material were included in the model. Note that, for modelling an inverter-driven induction motor, the dependence of the force distribution on the operating speed has to be taken into account. Quasi-static analysis in the time domain was then used so that not only the rotation of the rotor was allowed in the analysis, but also the interaction between the force harmonics due to the saturation could be analysed. However, this method requires the rotor current to be externally calculated and imposed on the rotor separately by specifying the stator current. For this purpose, in the analysis, the stator current was obtained by measurements. The stator referred rotor current was calculated by using a four-parameter statespace model, for which the parameters were also determined experimentally. The effective rotor-to-stator turns ratio was found by adjusting it so that the FEM calculated torque– speed curve correlated with that obtained by the state-space model for a given operating condition. Since the rotor referred stator current was not considered in this model, the stator slot harmonics induced in the rotor slots could not be calculated [6].
Fig. 2
FEM electromagnetic force model
In the calculations, the time period analysed was chosen as one-quarter of one rotor cycle, and divided into 198 time steps. As a result, for 450 rev/min, the force spectrum data would have a constant bandwidth of about 30 Hz, and for 1500 rev/min about 100 Hz. The upper frequency limits for the two speeds are about 3 kHz and 9.9 kHz, respectively. The stator current was measured when the motor was driven by a sinusoidal pulse-width modulation (PWM) inverter for various running conditions. In simulating the electromagnetic forces associated with the PWM inverter, these measured current data were used in the fourparameter state-space model directly to obtain the necessary inputs for the FEM model. For an ‘ideal’ sinusoidal inverter, the measured stator current data for the PWM inverter were low-pass filtered so that only the fundamental component was input to the four-parameter state-space model. Figures 3a and 3b show the calculated radial force distributions for an ‘ideal’ sinusoidal and a PWM inverter IEE Proc.-Electr. Power Appl., Vol. 151, No. 3, May 2004
drive and the PWM inverter at 1500 rev/min is plotted in P Fig. 3c. The total force F here is defined as j F j2 ¼ jfn j2 , n
where fn is the radial force component at each node along the circumferential direction. It can be seen that, for the PWM inverter with plenty of harmonics in the supply, the total force is an order of magnitude greater than that for the benchmark drive. Also when the motor is loaded, the electromagnetic force is not affected very much at high frequencies. A more detailed analysis of the force results can be found in [6]. Currently there is no direct way to validate the calculated electromagnetic force in the motor.
102
Force, N
101 100 10−1 10−2 10−3 0
3
80 1000
60
frequency, Hz
When the electromagnetic force is generated in the gap between the rotor and the stator, the force would act on the rotor and the stator, thus causing the vibration of the motor structure. Unlike the FEM electromagnetic model, the FEM structural model has to be three-dimensional. Also, the casing, endshields, support and other structural details such as the slots in the casing, which may affect the vibration behaviour of the motor structure significantly, should be included in the model. In this study, the FEM structural modelling was also made using ANSYS on a SUN SPARC20 workstation. Figure 4 shows the full model of the motor structure, consisting of two concentric cylindrical shells, one for the casing and the other for the stator. The motor casing was modelled using 1128 quadrilateral shell elements and the stator was modelled using 720 solid elements. The full model has a total number of 4480 nodes and 3423 elements.
40
2000 3000
20 0
angle,deg
a
102 101
Force, N
FEM structural model
100 10−1 10−2 0
80 1000
60 40
2000 frequency, Hz
3000
20
angle,deg
0 b
1000 'ideal' sinusoid, no load PWM inverter, no load
total force, N
100
Fig. 4
10
1
0.1
0.01 0
2000
4000
6000
8000
10000
frequency, Hz c
Fig. 3 Radial electromagnetic force acting on the stator calculated by FEM for 1500 rev/min a 3D distribution for an ‘ideal’ sinusoidal inverter b 3D distribution for a PWM inverter c Total force
in the frequency domain. In order to highlight the difference in the force magnitude, the total radial electromagnetic force acting on the stator under no load for the benchmark IEE Proc.-Electr. Power Appl., Vol. 151, No. 3, May 2004
The FEM structural model of a 2.2 kW induction motor
In developing the FEM structural model, the validation of the model is very important because the structural dynamic behaviour depends not only on the geometry, but also on the material properties and the coupling conditions at the boundary. In this study, experimental modal testing and FEM modal analysis were conducted because the natural frequencies, the mode shapes and damping of a structure are the inherent structural behaviour, irrespective of the external excitation. As the motor structure is constructed by assembling the stator, rotor, casing, endshields and the support, five different experimental conditions were designed to assess the influence of these structural parts on the vibration behaviour of the motor structure, as described by Wang and Lai [16]. Correspondingly, FEM calculations were carried out to ensure that the model is able to predict the effects reasonably well. It was found that the rotor and isolators are only important for low-frequency response and the stator should be modelled as an orthotropic structure. Although it was claimed by 343
some researchers that it is necessary to model the teeth and windings for better accuracy, for this particular motor, the teeth and winding on the stator can be treated as extra mass distributed throughout the stator in the model [16]. With the model shown in Fig. 4, it was found that, for the first 20 modes of the motor structure as listed in Table 1, not only the natural frequencies but also the mode shapes can be predicted reasonably well. Except for the modes that were not captured, the average relative error in natural frequencies was 7.5%, better than that reported in [19].
Table 1: Comparisons of natural frequencies between measurements and FEM Mode
Measurement
Damping (%)
FEM
1
404.28
3.1
375.1
2
584.40
1.2
F
3
668.39
0.9
485.8
4
736.68
0.5
695.6
5
833.75
1.4
F
6
966.83
1.4
F
7
1043.97
0.9
1121.6
8
1097.55
0.7
1123.8
9
1179.73
0.7
1097.5
10
1279.94
0.9
F
11
1418.64
0.6
1353.1
12
1551.53
0.8
1559.6
13
1636.95
0.8
F
14
1742.19
0.8
1682.1
15
1723.14
0.5
1932.6
16
1870.07
0.6
1897.0
17
1924.96
0.6
F
18
2041.52
0.7
2167.0
19
2167.28
1.0
2320.4
20
2239.56
0.9
2476.2
The analysis option used in SYSNOISE was BEM indirect coupled analysis [22]. All the calculations were made on a SUN SPARC20 workstation. To validate this acoustic model, the sound radiation efficiency of the motor structure subject to a point force excitation was calculated and compared to the experimental data [23]. The sound radiation efficiency describes the capability of a structure in energy transformation from vibration to noise, and is dependent on the material properties, geometry and the boundary conditions of the structure, and the properties of the ambient medium. Generally, it can be regarded as one of the inherent properties of a structure, although it might be affected by the distribution and the type of the excitation forces. The motor was excited using an electromagnetic shaker [23]. The averaged vibration level over the structure surface as well as the sound power radiated from the motor structure was measured in an anechoic chamber, as shown in Fig. 5. The sound radiation efficiency srad of the motor structure was calculated from srad ¼ Wa =ro co Shv2 i, where Wa is the radiated acoustic power determined by the two-microphone sound intensity technique, hv2 i is the spatial averaged mean square velocity over the radiating surface, S is the radiating surface area of the motor structure, and roco is the characteristic impedance of the medium (in this case, air). As shown in Fig. 6, the sound radiation efficiency calculated by SYSNOISE [22] overall agrees reasonably well with the measurements. At low frequencies, there are some discrepancies, which are due mainly to the error in estimating the vibration response by the FEM structural model in which vibration isolators and the rotor are neglected.
accelerometer
Unlike an FEM model, which requires the whole solution domain to be discretised, only the boundary interface of the solution domain for a BEM model needs to be discretised [21]. For acoustic analysis, BEM is more suitable for exterior sound radiation problems because the radiation condition at infinity can be easily satisfied. In this study, the acoustic radiation from the motor was modelled using a commercial BEM code, SYSNOISE (Version 5.3A), developed especially for vibro-acoustic analysis [22]. The procedure for a typical SYSNOISE analysis involves creating the boundary-element mesh of the structure, applying the loads and necessary acoustic boundary conditions, solving the problems and analysing the results. In this study, the boundary-element mesh of the motor structure was produced by skinning the FEM structural model in SYSNOISE [22]. As a result, the BEM model of the motor structure has 4056 nodes and 3711 elements. Based on six elements per acoustic wavelength, the upper frequency limit for this mesh is 2.8 kHz. Since, in the analysis, the vibration distributions over the structure due to an external excitation are the acoustic boundary conditions, the modal base of the motor structure obtained by ANSYS was used to evaluate the corresponding vibration response. 344
motor HP3569A analyser
anechoic room
Fig. 5 Schematic diagram of the experimental set-up for measuring the sound radiation efficiency Charge amplifier, B&K2635 Power amplifier, B&K2706 Shaker, B&K4810 Accelerometer, B&K4383
10
sound radiation efficiency
BEM acoustic model
charge amplifier
shaker
HP-300 computer
4
SI probe
power amplifier
B&K2032 analyser
1
0.1
0.01 experiment- horizontal excitation 0.001
BEM- horizontal excitation
0.0001 0
500
1000 1500 2000 frequency, Hz
2500
3000
Fig. 6 Comparison of the sound radiation efficiency of the motor structure calculated by BEM and experiment IEE Proc.-Electr. Power Appl., Vol. 151, No. 3, May 2004
Vibro-acoustic simulations
With the vibro-acoustic models (FEM and BEM models) developed above, and the FEM model for the electromagnetic force described in Section 2, the vibro-acoustic response of the motor under various operating conditions can be predicted. In particular, the acoustic power and the corresponding sound field produced by the motor under the excitation of the electromagnetic forces were analysed. The calculations were carried out using SYSNOISE. Since the BEM mesh of the motor was different from the FEM mesh for the force calculation, the force data given at 198 angular positions within one-quarter of the stator had to be processed to fit the BEM model in which the inner side of the stator had only 72 nodes on each circumference. For this purpose, the force required for the BEM model was obtained by synthesising every 11 raw data, and applied onto a full circumference by invoking symmetry. It needs to be emphasised, that although the structural model does not have teeth, the electromagnetic model (Fig. 2) does. The synthesised force was directly applied to each node, on the inner side of the stator mesh of the structural model, which has the same angular position as the centre point of the corresponding 11 force data points. Since the FEM force model was two-dimensional, but the BEM model was threedimensional, the electromagnetic force was applied uniformly along the axial direction of the stator. Obviously this might cause some error in the final results. The analysis option used in SYSNOISE was BEM indirect coupled analysis with the modal base calculated by the FEM structural model and the damping values extracted from the modal testing as given in Table 1. The acoustic power radiated from the motor due to electromagnetic forces for different operating conditions was calculated. The results for the motor driven by the PWM inverter [1] at 450 rev/min with no load and by the benchmark inverter [1] at 450 and 1500 rev/min with no load, together with the corresponding experimental results, are compared in Figs. 7 and 8 respectively. In order to facilitate the comparison, the measurement data are synthesised into the same bandwidth with that of the force data. Note that the experimental results include the electromagnetic noise and the aerodynamic and mechanical noise. In these Figures, the BEM results plus the measured aerodynamic and mechanical noise are also included for comparison with the experimental results. It can be seen that the agreement is generally reasonable. For reference, the measured sound power spectra due to aerodynamic and mechanical origin at 450 and 1500 rev/min are given in Fig. 9. By comparing Fig. 7 with Fig. 9, it is quite clear that, IEE Proc.-Electr. Power Appl., Vol. 151, No. 3, May 2004
measured
80
BEM
sound power level, dB
70 60 50 40 30 20 10 0 0
500
1000
1500 2000 frequency, Hz
2500
3000
Fig. 7 Comparison of the acoustic power calculated by BEM with experimental results PWM inverter, no load, 450 rev/min
70 450 rev/min 1500 rev/min measured predicted
60 sound power level, dB
5
90
50 40 30 20 10 0 0
500
1000
1500 2000 frequency, Hz
2500
3000
Fig. 8 Comparison of the acoustic power of the motor driven by the benchmark controller at no load for two operating speeds
70 450 rev/min
60
1500 rev/min sound power level, dB
It should be pointed out that the accuracy of the BEM model very much depends on that of the FEM structural model. According to Wang and Lai [16], the FEM model may be improved by taking the isolators and the rotor into account and by using a finer FEM mesh. However, for FEM analysis, there would always be a compromise between the extent of the details which the solutions are expected to reflect and the capability of the facilities used. Normally, the more accurate the solution is expected to be, the more elements the model needs, and thus the more computer space and the running time it would take. For the model developed here, about 64 and 150 Mbytes RAM for ANSYS and SYSNOISE were required to run in-core, respectively. It took about four CPU hours to obtain the modal base from ANSYS and two CPU hours to calculate the sound pressure field for one frequency step using SYSNOISE on a SUN SPARC 20 workstation.
50 40 30 20 10 0 0
500
1000 1500 2000 frequency, Hz
2500
3000
Fig. 9 Measured sound power spectra due to aerodynamic and mechanical origin
for the motor driven by the PWM inverter with no load at 450 rev/min, due to the presence of harmonics in the supply, the estimated electromagnetic noise dominates the total acoustic power and the effect of the aerodynamic and mechanical noise is negligible. By comparing Fig. 8 with Fig. 9, it can be seen that, when the motor is driven by the benchmark controller at 1500 rev/min, the total acoustic power is dominated by the aerodynamic and mechanical noise whereas the electromagnetic noise is important for 345
frequencies around 1000 Hz. All these results are consistent with those of the experimental study [1]. It should be mentioned that, in the calculations, the total electromagnetic force in a frequency bandwidth (30 Hz for 450 rev/min, and 100 Hz for 1500 rev/min) was assigned to the centre frequency. This means that the estimated acoustic response at this frequency may be artificially amplified because of the concentration of all the electromagnetic force into this frequency. Therefore, for the results shown in Figs. 7 and 8, it may not be appropriate to concentrate on the details relating to each peak. However, with the model developed, the effects of speeds, different inverters and loads on the acoustic power of the motor can be studied reasonably well. The effect on the radiated noise of changing inverter strategies can be assessed by the relative change in the total sound power level from the induction motor being driven by the benchmark controller to that being driven by the PWM inverter for no load at 450 rev/ min, as shown in Fig. 10. Both the measurements and predictions indicate a large increase in the radiated sound power level by changing from the benchmark controller to the PWM inverter. The effect of load on the radiated sound power level can be examined by the relative change in the sound power level from no load to full load for the benchmark controller at 450 rev/min (Fig. 11). The agree-
increment of sound power level, dB
50 40 30 20 10 0 −10
measured
−20
BEM
−30 0
500
1000
1500 2000 frequency, Hz
2500
3000
Fig. 10 Increment of sound power level of motor driven by PWM inverter compared to that driven by benchmark controller No load, 450 rev/min
increment of sound power level, dB
50 measured
40
BEM
30 20 10 0 −10 −20 −30 0
500
1000
1500 2000 frequency, Hz
2500
3000
Fig. 11 Increment of sound power level of motor driven by benchmark controller with full load compared to that with no load 450 rev/min 346
ment between the experiment and the prediction is generally good. In addition to the total acoustic power radiated from the motor, the sound pressure field produced by a motor is also of practical interest. In SYSNOISE, the sound field at a particular frequency can be analysed and visualised. For convenience, three image planes around the motor structure have been created. Each plane, for which the dimensions are 0.3 0.4 m, is located 0.15 m away from the axis of the stator core, as shown in Fig. 12. The contour maps of the distribution of the sound pressure levels on the image planes and the vibration levels (of the y component) on the motor driven by the benchmark inverter at two different frequencies can thus be displayed. It can be clearly seen from Fig. 12 that the major contributors to the total acoustic noise at low frequencies are the base plate and the stator. It can be expected, therefore, that the lowfrequency noise of such a motor can be efficiently controlled by reducing the vibration levels of the base plate and the stator. 6
Discussions and conclusions
In this paper, the numerical modelling of the electromagnetic noise of an inverter driven induction motor has been discussed. FEM and BEM have been effectively employed to analyse the vibro-acoustic behaviour of an induction motor driven by inverters. The advantage of this approach is, that, in addition to the total acoustic power, the local details of the vibration level over the motor structure and the corresponding sound pressure field can be estimated and studied. Although the FEM/BEM numerical approach seems to work well, there are still a number of issues that need to be considered in future exercises. As we know, the vibroacoustic response of a structure very much depends on the distribution of the excitation force. Although the magnitude of the electromagnetic force might not vary much along the axial direction of the stator and the rotor, the phase shift in the force along the axis due to the slot skew angle may affect the mechanical power input to the structure. Hence, the electromagnetic force should be modelled three-dimensionally. Also, to be able to study the interaction between the current harmonics and the structural resonance in detail, the resolution of the force calculation in the frequency domain needs to be refined. This may require developing a reasonably quick algorithm for calculating the electromagnetic forces with narrow frequency bandwidth, because the FEM electromagnetic force model used here is very time-consuming (of the order of 100 CPU hours for each run with 30 Hz bandwidth for 450 rev/min and 100 Hz bandwidth for 1500 rev/min). In this study, the FEM electromagnetic force model was verified indirectly by comparing the estimated and the measured acoustic power radiated from the motor structure. Such comparison, however, is not sufficient for the force model because the discrepancies in the final results are the accumulation of the effects from three models rather than the force model itself. Therefore, it would be helpful to have an independent approach to verify the correctness and the accuracy of the FEM electromagnetic force model. As the mechanical damping of the motor structure plays an important role in the vibration response, and thus the acoustic response, it would be necessary, in addition to the modal testing, to examine the vibration response of the FEM structural model due to a point force excitation, so that the modal damping of the structure could be IEE Proc.-Electr. Power Appl., Vol. 151, No. 3, May 2004
SYSNOISE - COMPUTATIONAL VIBRO-ACOUSTICS model mesh [1] [C]: displacement at 507.440 Hz (dB/v compoent) field point mesh [2] [C]: pressure at 507.440 Hz(dB)
MIDEL2 displacement
y
pressure
−7.000E+01
4.000E+01
−8.000E+01
3.312E+01
−9.000E+01
2.625E+01
−1.000E+02
1.938E+01
−1.100E+02
1.250E+01
−1.200E+02
5.625E+00
−1.300E+02
−1.250E+00
−1.400E+02
−8.125E+00
−1.500E+02
−1.500E+01
x
z
a
MODEL2
SYSNOISE - COMPUTATIONAL VIBRO-ACOUSTICS model mesh [1] [C]: displacement at 1134.300 Hz (dB /v component) field point mesh [2] [C]: pressure at 1134.300 Hz (dB)
displacement
y z
pressure
−7.000E+01
4.000E+01
−8.000E+01
3.312E+01
−9.000E+01
2.625E+01
−1.000E+02
1.938E+01
−1.100E+02
1.250E+01
−1.200E+02
5.625E+01
−1.300E+02
−1.250E+00
−1.400E+02
−8.125E+00
−1.500E+02
−1.500E+01
x b
Fig. 12
Sound pressure field produced by the motor calculated by BEM
Benchmark controller, no load, 450 rev/min a f ¼ 507.4 Hz b f ¼ 1134.3 Hz
determined reasonably well. In this study, the modal damping was assigned in the calculation based on the modal testing results [16]. The low-frequency vibro-acoustic response of the motor structure is very much affected by the vibration isolators and the rotor. The low-frequency results could be improved by including these components in the FEM structural model. Alternatively, these effects might be included by applying appropriate structural damping to the FEM structural model. 7
Acknowledgments
The work presented was conducted at the Australian Defence Force Academy, Australia. The project was supported by the Australian Research Council under the large grant scheme. The motor and the inverter were provided by Fasco, Australia, and Zener Electric, Australia respectively. C.Wang acknowledges receipt of an Overseas Postgraduate Research Scholarship for the pursuit of this IEE Proc.-Electr. Power Appl., Vol. 151, No. 3, May 2004
study; he is now with General Motors Corp., at Proving Ground, Milford, MI 48380, USA. A Askfalck is now with FASCO, Australia. 8
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