investigation of the influence of the … bandwidth on noise and vibrations of switched reluctance...

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INVESTIGATION OF THE INFLUENCE OF THE CURRENT-HYSTERESIS BANDWIDTH ON NOISE AND VIBRATIONS OF SWITCHED RELUCTANCE MACHINES

Yves Mollet and Johan Gyselinck

Université Libre de Bruxelles – ULB, Brussels School of Engineering, 1050 Brussels, Belgium

email: [email protected]

Mathieu Sarrazin and Herman Van der Auweraer

Siemens Industry Software N.V. – SISW, Digital Factory – Product Lifecycle Management – Simulation and

Test Solutions, 3001 Leuven, Belgium

The development of power converters has permitted the rise of switched reluctance machines

(SRMs), due to their simple and cheap design and of their inherent fault tolerance. However,

those machines suffer from torque ripple and noise and vibration issues, which constitute an ob-

stacle to the extension of their application domain. This paper presents the influence of the

bandwidth of a current-hysteresis controller on an 8/6 SRM in terms of noise, vibration and

harshness. Simulations in AMESim environment and measurements on a 15 kW test bench are

performed in transient state, based on continuous variation of the hysteresis bandwidth. Phase

currents, acoustic noise and radial vibrations are measured without and with load, allowing for

comparison of hysteresis-band-frequency plots. This transient state approach enables showing

the evolution of a part of the frequency components with hysteresis bandwidth and distinguish-

ing them from other components linked to speed or to structural behaviour of the motor. Results

show that the current chopping by means of a hysteresis controller generates broadband fre-

quencies in the phase currents that also appear in the vibration and sound pressure wave meas-

urements. As the bandwidth increases, switching-related components are shifted towards lower

frequencies, resulting in a higher excitation of the main resonance modes of the machine. Due to

the higher current ripple in the case of hard chopping mode, the influence of the bandwidth is in

general more important than in soft chopping mode. However, for the same bandwidth the rip-

ple occurs at much lower frequencies in the latter case and therefore more attention has to be

paid to possible interaction with the resonance frequencies.

1. Introduction

Thanks to the development of power converters switched reluctance machines (SRMs) have de-

veloped recently. Their increasing interest in state-of-the-art drive configurations make them poten-

tially good candidates for automotive [1, 2] or aerospace applications [3]. They are composed of a

salient stator with concentrated windings and of a salient soft-iron rotor (without any coil or mag-

net). Torque is produced by successively activating stator phases to attract step by step the nearest

rotor poles. Each of the phase activations is called ‘stroke’.

This configuration is cheap and robust [1, 2, 4, 5, 6, 7, 8]. It is also adapted for severe environ-

ment [6, 9, 10] and for wide speed range applications [10] and offers high compactness [5, 8].

SRMs also benefit from inherent fault tolerance thanks to the low magnetic coupling between their

phases [2, 6, 8, 10].

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International Congress on Sound and Vibration

2 ICSV23, Athens (Greece), 10-14 July 2016

However, the SRMs’ main drawbacks compared to conventional machines are torque ripple [2,

7, 11] and production of vibration and acoustic noise [1, 2, 4, 6, 7, 8, 10, 11, 12] contributing to the

excitation of natural modes of the stator [11]. Those disadvantages still remain an obstacle to a wide

development of this technology in noise-critical applications, such as electrical vehicles.

Therefore, noise, vibration and harshness (NVH) concerns are tackled in literature. An analytical

model to predict radial vibration in SRMs is developed in [4], and tuned by experimental or finite-

element (FE) modal analysis. The obtained point-wise accelerations at the stator surface are ex-

panded in [8] to the whole surface and used as boundary condition to compute the resulting acoustic

noise. The radial vibration prediction model is used in [12] to permit fast design optimization of

SRMs regarding NVH. In [9], successive AMESim software and FE are combined to successively

estimate the working point of the SRM, the internal forces and the resulting vibrations and acoustic

noise. An optimized current control technique is developed in [5] to cancel the SRM’s circumferen-

tial breathing mode. Reference [2] proposes a mapping of the resonance frequencies of an 8/6 SRM

by experimental modal analysis using mini-shakers and compares this technique with the classical

hammer-based one. Experimental tests in transient conditions are performed in [1] on a 12/8 SRM.

This technique permits exciting a wide range of frequencies and easily distinguishing speed orders

from resonance peaks, frequency components related to the switching process and background

noise. Similar tests are performed in [13] with further investigation of sound quality aspects and

propositions to limit NVH issues.

The presence of anisotropic materials and of cooling or mounting accessories makes, however,

the modelling of SRMs difficult and does not guarantee the reliability of simulation results [2]. Fur-

thermore, experimental results are expensive and therefore not common [2].

The present paper investigates the influence of the hysteresis controller bandwidth on noise and

vibrations by measuring the frequency content of phase current, radial vibration and acoustic noise

when hysteresis bandwidth ramps are applied at constant speed and load. The harshness through the

evolution of loudness and sharpness with hysteresis bandwidth is also investigated. Simulations are

performed in AMESim software for the same running conditions for comparison.

Section 2 describes the main characteristics of the investigated machine, its control structure and

the main origins of vibrations. The test bench and its measurement set-up are presented in section 3,

while results are shown and discussed in section 4.

2. Typical waveforms and NVH aspects of the investigated SRM

2.1 Main characteristics and typical waveforms

The rated and peak power, peak torque and peak current of the investigated 8/6 SRM are 15 kW,

30 kW, 200 Nm and 200 A respectively, while its maximum speed is 10 krpm.

The desired torque is produced by chopping each phase current by means of a dedicated asym-

metrical H-bridge converter. In case of hard chopping both controllable devices are synchronously

switched during the stroke, the current path being successively represented in Figure 1a and c. On

the contrary, only one switch is used in case of soft chopping, the other one remaining on until the

phase is turned off (the current path being successively represented in Figure 1a and b).

a. b. c.

Figure 1: Possible conduction modes of one phase of the SRM. Depending on the states of both power

switches T1 and T2 of the asymmetric H-bridge the applied voltage on the SRM phase winding may be +Vdc,

0 or –Vdc (cases a, b and c respectively).

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ICSV23, Athens (Greece), 10-14 July 2016 3

As the speed increases, the back-electromotive force of the SRM grows and the full DC-bus

voltage Vdc (without chopping) is finally needed to maintain the desired current. For higher speeds

only the power can be maintained and the current is then controlled (without any more chopping) by

adjusting the turn-on and turn-off angles at the beginning and at the end of each stroke.

Typical waveforms of motoring mode at low, medium and high speed are shown in Figure 2.

a. hard chopping b. soft chopping

Figure 2: Simulated flux linkage, current and torque waveforms corresponding to one phase of the investi-

gated 8/6 SRM with 10 Nm load for different rotational speeds (in hard-chopping (a.) and soft-chopping (b.)

modes). The 0° position corresponds to the aligned position.

2.2 NVH aspects

Besides their tangential components the attraction forces between stator and rotor poles also

comprise radial components. While the former ones are desired and generate torque, the latter ones

are the main cause of deformation of the stator yoke and its surrounding pieces (such as its water-

cooling jacket) and thus of the vibration of the machine [1, 4, 8, 14]. Those vibrations are essential-

ly produced during the commutations, their amplitudes increasing with the flux level (and thus with

the current) present at that time in the concerned phases [4, 8, 12]. As a result sound pressure waves

(i.e. acoustic noise) are produced in the surrounding air.

This very close relationship between currents and NVH aspects allows estimating the main vi-

bration and acoustic noise frequencies by looking at the frequency components of the phase currents

[9]. The typical waveforms in Figure 2 present two main groups of frequency components: speed

orders linked to the successive phase commutations (frequencies proportional with rotational speed)

and high-frequency components related to the chopping of the current at low speed (frequencies

depending of chopping parameters, such as bandwidth, and to a minor extent on speed).

Furthermore, these vibrations also excite the structural modes of the stator and of its accessories

[1, 4, 12, 13, 14]. Considering the stator as a cylindrical shell without constraints at both ends, dif-

ferent circumferential modes shapes with their corresponding order m and frequencies can be com-

puted [14]. However, the frequency measured in practice on the machine can differ due to the pres-

ence of the poles, end caps, windings, clamps etc [14]… According to the working principle of the

motor, the order m of the dominant circumferential mode corresponds to the ratio between stator

poles and phases [6]. In the case of the 8/6 SRM, having two opposite stator poles per phase, each

activation of a phase excites mainly the ovalization mode (m = 2).

3. Measurement set-up and simulation model

3.1 Measurement setup and AMESim model

The present paper investigates the influence of the hysteresis bandwidth of the current control on

the frequency spectra of phase currents, radial vibration and acoustic noise of the SRM. Experi-

mental tests are performed, applying hysteresis-band ramps to the controller in both load and no-

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load conditions, and in both hard- and soft-chopping conditions. Simulations are also run in the

same situations to compare current waveforms with the experimental ones.

A schematic of the electrical circuit of the test bench is presented in Figure 3a. The SRM is con-

nected to a 4-phase converter fed by a DC supply, while it is loaded using a DC machine. The cur-

rent sensors as well as the accelerometer and the microphone used for the performed experimental

tests are shown in Figure 3b.

Simulations are run in AMESim environment. Only the SRM, its converter and its control are

modelled in detail, a constant load torque playing the role of the DC machine.

a. Main electrical circuit b. Principal components of the experimental setup

Figure 3: Practical implementation of the test bench

3.2 Structure and implementation of the control

The control of the bench (comprising the DC machine) is implemented in MATLAB/Simulink

environment and uploaded on 1103 dSPACE hardware fast-prototyping hardware, running at 10

kHz. The hysteresis needs however a higher sampling frequency to avoid degraded performance

[15] and is implemented on external microcontroller cards, running at 200 kHz.

Implemented control structure of the SRM is shown in Figure 4. A single bit enables to select

hard or soft chopping. Currents are kept in a defined band around the reference by means of hyste-

resis controllers running on microcontroller cards. Practically the DC-bus voltage Vdc is applied to

the active phase till the current (measured on each phase) reaches its upper limit and again applied

as soon as the current crosses the lower limit of the band. Therefore, the switching frequency is not

fixed and depends on the current rate of change, that is, on position and torque. The switching fre-

quency is also lower with soft chopping, since it makes usage of the zero-voltage level (Figure 2b).

Figure 4: Structure and implementation of the SRM test-bench control structure. The T1 and T2 inputs of the

‘Inverter + SRM’ block represent the control inputs of the upper and lower power switches in Figure 1.

In the presently implemented average torque control (ATC) the phases are activated one by one

depending on the rotor position. The phase turn-on and turn-off angles, θon and θoff, and the current

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reference I* are computed from torque reference T* and from speed Ω by means of look-up tables.

A classical PI controller is used for speed control and generates the torque reference. The imple-

mentation on both hardware platforms is represented by the dashed rectangles in Figure 4.

In AMESim the discretization of the hysteresis controller is modelled by applying zero-order

holds on current measurements and references. The output of those blocks (and therefore the ones

of the hysteresis controller) are updated every 5 µs.

4. Experimental and simulation results

Measurements are performed at 1000 rpm with 300 V DC-bus voltage, while the hysteresis

bandwidth is increased from 0.5 to 5 A with a constant rate of 0.1 A/s. For load tests a constant

torque is imposed by the DC machine. The conditions are identical in simulation, except the rate set

to 1 A/s for simulation time and memory reasons. All results are presented as waterfall diagrams

with signal magnitudes in dB in function of frequency (horizontal axis) and bandwidth (vertical

axis) to highlight the affected frequency components (the 0 dB references being 1 A, 1 m/s2 and 1

Pa for current, vibration and sound pressure wave respectively).

The plots concerning hard chopping mode are presented in Figure 5. The no-load and load (5

Nm) cases are displayed on the left (a.) and on the right (b.) respectively. On both simulated and

measured current plots speed orders are visible as straight vertical lines at frequencies multiple of

100 Hz (i.e. six times the frequency corresponding to the rotor speed as the rotor has six poles).

These speed orders are also present (but attenuated) in the vibration and acoustic noise plots.

a. Hard chopping, no-load b. Hard chopping, 5 Nm load

Figure 5: Simulated phase-current and measured phase-current, radial-vibration and acoustic-noise frequency

contents for hysteresis-bandwidth ramp from 0.5 to 5 A at 1000 rpm with hard chopping (the 0 dB references

being 1 A, 1 m/s2 and 1 Pa respectively).

On all plots of measured values, oblique zones of higher amplitudes are observed approximately

from 1 to 4 kHz at 5 A bandwidth to 7 to 10 kHz at 2.5 A bandwidth. These zones reflect the influ-

ence of the hysteresis bandwidth on the current frequency content and indirectly on vibration and

sound pressure wave contents. Their hyperbolic shape can be explained by the fact that the switch-

ing period linearly increases with the hysteresis bandwidth, assuming a triangular waveform of the

phase current during chopping. These zones also cross resonance frequencies of the SRM, leading

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to amplified vibration amplitudes for the highest bandwidth values, especially around 1.4 (ovaliza-

tion mode [2]) and 3.2 kHz. Concerning the acoustic noise, the highest amplitudes are found around

1.4, 2.0 and 2.4 kHz, again for the highest bandwidth values. Due to the higher phase currents there

is a general increase of amplitudes with load compared to the no-load case.

Considering the no-load simulated currents, higher amplitudes are effectively found for the same

frequencies and bandwidths as for measured currents, but they are dominated by a narrow band

starting at 5 kHz at 5 A and going to 10 kHz at 1 A bandwidth. It is however attenuated in the load

case, and only some low-amplitude high-frequency content remains in the upper part of the plot.

The reason is the speed ripple resulting from the inherent torque fluctuations of the SRM. For suffi-

ciently small loads, the reaction of the speed controller makes the machine enter temporarily in gen-

erator mode, changing the activation order of the phases and adding extra current ripple. Due to the

presence of friction, this phenomenon is less important on the test bench than in simulation.

The plots concerning soft chopping mode are presented in Figure 6. Again, the no-load and load

(5 Nm) cases, displayed on the left (a.) and on the right (b.) respectively, show speed orders multi-

ple of 100 Hz. Considering the simulated currents a large oblique zone can be approximately de-

fined from 1 to 4 kHz at 5 A bandwidth to 7 to 10 kHz at 1 A bandwidth. Similarly to the hard

chopping case a supplementary hyperbolic zone of higher frequencies appears at no-load. As also

shown in [16] there is a global shift to lower frequencies compared to the hard chopping case.

a. Soft chopping, no-load b. Soft chopping, 5 Nm load

Figure 6: Simulated phase-current and measured phase-current, radial-vibration and acoustic-noise frequency

contents for hysteresis-bandwidth ramp from 0.5 to 5 A at 1000 rpm with soft chopping (the 0 dB references

being 1 m/s2, 1 A and 1Pa respectively).

However, the hyperbolic zones of higher amplitudes are much less visible in measurements, but

their presence is still suggested by the increased dB-level of low- and high-frequency vertical bands

(e.g. at 1.4 kHz and between 6 and 7 kHz) for high and low bandwidth values respectively. The

soft-chopping technique looks then less sensitive to changes in hysteresis bandwidth as it also (in

accordance with [16]) globally generates smaller vibration and acoustic noise amplitudes.

This observation is confirmed by the evolution of loudness and of sharpness in function of hyste-

resis bandwidth shown in Figure 7. Except at no load and small hysteresis bandwidth where soft

and hard chopping give similar results, a louder sound is produced in the hard-chopping case.

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a. Loudness b. Sharpness

Figure 7: Comparison of loudness and sharpness of the sound for the considered tests.

Looking at Figure 7a, similar curve shapes can also be remarked for tests performed with the

same chopping mode, the addition of the load essentially shifting the curve to higher loudness, due

to the higher flux level in the SRM. The loudness generally grows also with bandwidth, due to the

higher amplitude of the current ripple. It especially increases from 2.5 A bandwidth on in case of

hard chopping, as the reduction of switching frequency with bandwidth causes a higher excitation

of resonance. However, in soft-chopping mode, this faster growth of loudness occurs at lower hys-

teresis bandwidth due to the reduced chopping frequency and the loudness tends to stabilize at

bandwidths higher than 4 A.

By comparing Figure 7 with Figure 5 and Figure 6, the presence of a maximum of sharpness has

to be related to both an increase of amplitude and a reduction of frequency of the switching compo-

nents as the hysteresis bandwidth grows. For low bandwidths the former is dominant, leading to an

increase of sharpness. However, the latter dominates for higher values of hysteresis bandwidth as

the excitation of resonances (at relative low frequency) is more important. A maximum sharpness

can therefore be observed around 2.5 A for hard chopping. In case of soft chopping the reduced

switching frequency leads to lower sharpness, with a maximum at lower values of hysteresis band-

width.

5. Conclusions

The influence of current hysteresis bandwidth on NVH aspects of a 15 kW 8/6 SRM has been

experimentally investigated by comparing the frequency content of phase current, vibration and

acoustic noise during hysteresis bandwidth ramp tests. Results have been plotted as waterfall dia-

grams and present hyperbola-shaped curves that show interaction with the resonance frequencies of

the structure. Hard chopping leads to higher frequencies and higher amplitudes, especially when the

switching frequency components are close to the main resonances. This results in an increase of the

loudness in hard chopping compared to soft chopping, particularly at high hysteresis bandwidth,

while the sharpness (also higher for hard chopping) shows a maximum at medium bandwidth.

Simulations show similar current frequency content, except supplementary components at no-

load. Those are due to repetitive periods of generating mode resulting from the combination of

torque ripple and reduced friction compared to experiments.

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investigation of the influence of the … bandwidth on noise and vibrations of switched reluctance...

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