Analysis of NVH Behavior of Synchronous Reluctance Machine for EV Applications

: In this paper, an analysis of noise and vibration of a synchronous reluctance machine for EV applications is performed. The analyzed machine was designed for electric vehicle application. The noise and vibration of a synchronous reluctance machine were ﬁrst estimated during simulations; next, the obtained results were validated during laboratory tests. The analyzed model of the machine was simpliﬁed and included only stator core as it was assumed to be the main source of the machine vibration and generated noise. To simulate the noise and vibration of the machine, multiphysics modeling of the machine was performed. Laboratory tests proved the correctness of performed simulations. The obtained results allowed us to investigate the inﬂuence of the machine’s operating point on the generated noise and vibration. The frequency of the magnetic radial forces were proven to be the dominant factor in noise generation. The inﬂuence of the load and current angle on the machine’s noise and vibration was proven to be negligible. It was also proven that considering only the stator structure in numerical analysis of the noise and vibration of the machine leads to valuable results.


Introduction
Reluctance machines are becoming very popular nowadays due to their advantages such as low cost and a simple construction which does not require any external excitation source. Power electronics development makes it possible for the reluctance machines to be used in drive systems in many industry applications. This makes them of great interest nowadays [1]. Currently, reluctance motors can be divided into four types: those with a salient poles rotor, a rotor with circumferential segments, a rotor with magnetic barriers and magnetically anisotropy laminations-consisting rotors [2]. Each of these types has its advantages and disadvantages such as efficiency, power factor or cost. A synchronous reluctance machine (SynRM) is another type of variable reluctance machine whose stator geometry is based on a cylindrical structure. The stator of a synchronous reluctance motor is identical to that of an induction motor and only the rotor has salient poles [3]. The rotor does not require any cage or field winding, making it potentially less expensive than a permanent magnet motor or an induction motor [4]. The most common types of reluctance motors are the simple salient pole, the transversally and the axially laminated rotor [5]. Conventional SynRMs have simple rotor geometry but unfortunately this significantly lowers their performance due to a quite low ratio between the direct and quadrature inductances. The axially laminated rotors have a higher saliency ratio values and performance, but on the other hand eddy current losses are large. This is caused by the fact that the laminations are placed perpendicularly to the magnetic field lines and the magnetic field penetrates a very big surface of steel sheet. In practice, transversally The modal analysis of the stator was performed in VirtualLab ® software using a finite element method. Only the stator core was investigated, thus the influence of the winding and the housing was omitted. Modal analysis allowed us to obtain resonance frequencies and corresponding normal modes of the structure. With this information it was possible to estimate the noise and vibration of the machine operating in various states.
Several normal modes of the stator are presented in Figure 1. Each normal mode of the structure has a corresponding resonance frequency at which it occurs, and a corresponding deformation pattern [27]. Every solid body has an Each normal mode of the structure has a corresponding resonance frequency at which it occurs, and a corresponding deformation pattern [27]. Every solid body has an infinite number of normal modes and resonance frequencies, but the higher the resonance frequency the lower the impact of the normal mode since it is hard to excite the structure to vibrate at very high frequency. When the resonance frequencies and the normal modes of the stator structure were calculated, it was possible to simulate the NVH behavior of the machine in various operating states. Since the stator vibration is caused by the radial magnetic forces caused by the magnetic field in the machine, it was necessary to calculate the distribution of radial forces in the stator. Only the radial forces acting on the inner surface of the stator were considered during the simulation. The distribution of radial forces on the inner surface of the stator is presented in Figure 2 for the machine with skewed and non-skewed rotor [13].
infinite number of normal modes and resonance frequencies, but the higher the resonance frequency the lower the impact of the normal mode since it is hard to excite the structure to vibrate at very high frequency. When the resonance frequencies and the normal modes of the stator structure were calculated, it was possible to simulate the NVH behavior of the machine in various operating states. Since the stator vibration is caused by the radial magnetic forces caused by the magnetic field in the machine, it was necessary to calculate the distribution of radial forces in the stator. Only the radial forces acting on the inner surface of the stator were considered during the simulation. The distribution of radial forces on the inner surface of the stator is presented in Figure 2 for the machine with skewed and non-skewed rotor [13].
The electromagnetic forces were calculated during electromagnetic analysis using finite element method in JMAG software. The analyzed machine had a skewed rotor and thus the electromagnetic analysis was performed using a 2D model with five slices along the axial length of the machine. One can see that for the machine with skewed rotor, the distribution of the radial forces on the stator inner surface is not uniform along the axial length of the machine. The amplitude of the radial forces is different in various parts of the stator. This is shown in Figure 3. The radial forces distribution is displayed for three slices of the machine. The points in which the slices of the machine were considered are also presented.  The electromagnetic forces were calculated during electromagnetic analysis using finite element method in JMAG software.
The analyzed machine had a skewed rotor and thus the electromagnetic analysis was performed using a 2D model with five slices along the axial length of the machine. One can see that for the machine with skewed rotor, the distribution of the radial forces on the stator inner surface is not uniform along the axial length of the machine. The amplitude of the radial forces is different in various parts of the stator. This is shown in Figure 3. The radial forces distribution is displayed for three slices of the machine. The points in which the slices of the machine were considered are also presented. infinite number of normal modes and resonance frequencies, but the higher the resonance frequency the lower the impact of the normal mode since it is hard to excite the structure to vibrate at very high frequency. When the resonance frequencies and the normal modes of the stator structure were calculated, it was possible to simulate the NVH behavior of the machine in various operating states. Since the stator vibration is caused by the radial magnetic forces caused by the magnetic field in the machine, it was necessary to calculate the distribution of radial forces in the stator. Only the radial forces acting on the inner surface of the stator were considered during the simulation. The distribution of radial forces on the inner surface of the stator is presented in Figure 2 for the machine with skewed and non-skewed rotor [13]. The electromagnetic forces were calculated during electromagnetic analysis using finite element method in JMAG software. The analyzed machine had a skewed rotor and thus the electromagnetic analysis was performed using a 2D model with five slices along the axial length of the machine. One can see that for the machine with skewed rotor, the distribution of the radial forces on the stator inner surface is not uniform along the axial length of the machine. The amplitude of the radial forces is different in various parts of the stator. This is shown in Figure 3. The radial forces distribution is displayed for three slices of the machine. The points in which the slices of the machine were considered are also presented.  One can see that the amplitudes of the radial forces vary in different parts of the machine. Once the radial forces were calculated during electromagnetic simulation, they were mapped to the structural mesh of the stator structure and combined with the previously calculated normal modes, the analysis of noise and vibration of the machine could be performed.
The amplitude of the vibrations depends on the amplitudes of radial forces and on the rotational speed. The amplitudes of the radial forces change with the magnetic flux density in the machine. The higher the value of magnetic flux density in the machine the higher amplitudes of radial forces. In order to weaken the radial forces, one needs to weaken the magnetic flux in the machine. This can be achieved by changing the current angle by increasing the i q current component.
By changing the i d and i q current components one can change the magnetic flux of the machine as shown in Figure 4. One can see that the amplitudes of the radial forces vary in different parts of the machine. Once the radial forces were calculated during electromagnetic simulation, they were mapped to the structural mesh of the stator structure and combined with the previously calculated normal modes, the analysis of noise and vibration of the machine could be performed.
The amplitude of the vibrations depends on the amplitudes of radial forces and on the rotational speed. The amplitudes of the radial forces change with the magnetic flux density in the machine. The higher the value of magnetic flux density in the machine the higher amplitudes of radial forces. In order to weaken the radial forces, one needs to weaken the magnetic flux in the machine. This can be achieved by changing the current angle by increasing the iq current component.
By changing the id and iq current components one can change the magnetic flux of the machine as shown in Figure 4.  When the machine operates at current angles close to 90 electrical degrees, the magnetic flux in the machine is weakened.
During the simulations, the vibrations of the stator structure were measured at various rotational speeds and at different current angles to investigate the impact of the rotational speed and the current angle on the vibration of the structure.
The results of the simulations are presented below. Figure 5 shows the comparison of vibration measured at two rotational speeds at different current angles. In case of the machine operating at 600 rpm, the vibration looks similar for both current angles; however, at 4500 rpm the vibration amplitude is lower for the higher current angle as the radial forces are lower. Additionally, it can be noticed that the vibration amplitude is higher when the machine operates at 600 rpm. This is because, depending on the rotational speed, the frequency of the applied force is different and various normal modes of the structure respond, which causes the vibrations to increase at certain frequencies. This proves that the vibration of the machine depends not only on the amplitude of the radial forces but also on their frequency. When the machine operates at current angles close to 90 electrical degrees, the magnetic flux in the machine is weakened.
During the simulations, the vibrations of the stator structure were measured at various rotational speeds and at different current angles to investigate the impact of the rotational speed and the current angle on the vibration of the structure.
The results of the simulations are presented below. Figure 5 shows the comparison of vibration measured at two rotational speeds at different current angles. In case of the machine operating at 600 rpm, the vibration looks similar for both current angles; however, at 4500 rpm the vibration amplitude is lower for the higher current angle as the radial forces are lower. Additionally, it can be noticed that the vibration amplitude is higher when the machine operates at 600 rpm. This is because, depending on the rotational speed, the frequency of the applied force is different and various normal modes of the structure respond, which causes the vibrations to increase at certain frequencies. This proves that the vibration of the machine depends not only on the amplitude of the radial forces but also on their frequency.
Non-uniform radial force distribution on the inner surface of the stator caused by rotor skew has an impact on the vibration of the stator structure. The simulation results presented in Figure 6 show the vibration of the structure measured in three points on the stator along the axial length. One can see that in various points on the stator the vibration amplitude is different, which is caused by the non-uniform radial force distribution. Non-uniform radial force distribution on the inner surface of the stator caused b rotor skew has an impact on the vibration of the stator structure. The simulation result presented in Figure 6 show the vibration of the structure measured in three points on th stator along the axial length. One can see that in various points on the stator the vibratio amplitude is different, which is caused by the non-uniform radial force distribution.   Non-uniform radial force distribution on the inner surface of the stator caused b rotor skew has an impact on the vibration of the stator structure. The simulation result presented in Figure 6 show the vibration of the structure measured in three points on th stator along the axial length. One can see that in various points on the stator the vibratio amplitude is different, which is caused by the non-uniform radial force distribution. The vibration of the stator was investigated for four different rotational speeds. On can see that the amplitudes of the vibrations vary depending on the point on the stator i which they were measured. However, this difference between the amplitudes change The vibration of the stator was investigated for four different rotational speeds. One can see that the amplitudes of the vibrations vary depending on the point on the stator in which they were measured. However, this difference between the amplitudes changes with the rotational speed. This is because at some rotational speeds, various normal modes are excited, which leads to very high vibrations of the structure.

Laboratory Test Bench
The laboratory stand used during the measurements consists of tested SynRM and an induction machine operating as a load. Cross section of the tested machine is presented in Figure 7. Mechanical coupling of the SynRM with induction machine is presented in Figure 8. Both machines were supplied from four quadrant inverters. The switching frequency of the induction machine was 8 kHz. Before the experiment, the rotor of the examined machine was balanced.
Tests that can be carried out on the test bench: Main dimensions of the machine are contained in Table 2.   Vibration sensors' placement and water-cooling connection is shown in Figure 9. Test bench specifications are presented in Table 1.
Tests that can be carried out on the test bench: Main dimensions of the machine are contained in Table 2. Vibration sensors' placement and water-cooling connection is shown in Figure 9.  Vibration sensors' placement and water-cooling connection is shown in Figure 9. The vibration sensors were placed in x, y and z direction on machine's housing. Additionally, as shown in Figure 9, on the top of the machine three sensors were placed along machine's axial length. The system was controlled using dSPACE hardware with dedicated software. Control model of the drive was built in Matlab/Simulink. Selected parameters of the vibration sensor and the microphone are presented in Tables 3 and 4.  The vibration sensors were placed in x, y and z direction on machine's housing. Additionally, as shown in Figure 9, on the top of the machine three sensors were placed along machine's axial length. The system was controlled using dSPACE hardware with dedicated software. Control model of the drive was built in Matlab/Simulink. Selected parameters of the vibration sensor and the microphone are presented in Tables 3 and 4.  Figure 10. Non-linearity ≤1% Transverse sensitivity ≤5% Diagram of the test bench is presented in Figure 10.

Experimental Results
Laboratory tests were carried out to validate the simulation results. The goals of NVH simulations were: • Investigation of noise and vibration level; • Investigation of the influence of current angle and load on noise and vibration; • Investigation of the influence of switching frequency on noise; • Identification of normal modes and natural frequencies.
The tests were run in no-load and load conditions of the machine. The machine was supplied from an inverter and only steady-state tests were analyzed (no dynamic state tests were performed). A no-load state was used to investigate the impact of switching frequency on noise and vibration of the machine. In the load state, the impact of the current angle and load torque on noise and vibration was analyzed. The sampling frequency was 50 kHz. The measurements of noise and vibration signals were triggered using TestLAB software.
The SynRM was run from 0 to 1500 rpm to measure the machine's vibration and obtain the information about the normal mode frequencies of the structure.
In Figure 11 one can see vibration of the SynRM measured in three points along its axial length. Like in the numerical tests, the vibration varies along the machine's axial length due to non-uniform radial forces distribution caused by skewing the stator core. Moreover, in the case of laboratory tests this effect was amplified by the assembly of the

Experimental Results
Laboratory tests were carried out to validate the simulation results. The goals of NVH simulations were: • Investigation of noise and vibration level; • Investigation of the influence of current angle and load on noise and vibration; • Investigation of the influence of switching frequency on noise; • Identification of normal modes and natural frequencies.
The tests were run in no-load and load conditions of the machine. The machine was supplied from an inverter and only steady-state tests were analyzed (no dynamic state tests were performed). A no-load state was used to investigate the impact of switching frequency on noise and vibration of the machine. In the load state, the impact of the current angle and load torque on noise and vibration was analyzed. The sampling frequency was 50 kHz. The measurements of noise and vibration signals were triggered using TestLAB software.
The SynRM was run from 0 to 1500 rpm to measure the machine's vibration and obtain the information about the normal mode frequencies of the structure.
In Figure 11 one can see vibration of the SynRM measured in three points along its axial length. Like in the numerical tests, the vibration varies along the machine's axial length due to non-uniform radial forces distribution caused by skewing the stator core. Moreover, in the case of laboratory tests this effect was amplified by the assembly of the machine. The vibration signal was measured at three switching frequencies of the inverter: 8 kHz, 10 kHz, and 12 kHz.
It can be noticed that the vibration signal in the colormap has higher amplitudes at switching frequency. This is caused by the PWM, signal whose harmonics are present in the spectrum of vibration signal. For 8 kHz switching frequency, in the colormap one can observe the vibrations at 8 kHz, 16 kHz and 24 kHz ( Figure 12) since these are the first-, second-and third-order harmonics of the switching frequency. The situation is similar in case of 10 kHz and 12 kHz switching frequency. For the 10 kHz switching frequency, the vibration occurs at 10 kHz and 20 kHz ( Figure 13) and for the 12 kHz switching frequency the vibration occurs at 12 kHz and 24 kHz ( Figure 14). The switching frequency signal and its harmonics contribute to vibration and noise signal.  The vibration signal was measured at three switching frequencies of the inverter: 8 kHz, 10 kHz, and 12 kHz.
It can be noticed that the vibration signal in the colormap has higher amplitudes at switching frequency. This is caused by the PWM, signal whose harmonics are present in the spectrum of vibration signal. For 8 kHz switching frequency, in the colormap one can observe the vibrations at 8 kHz, 16 kHz and 24 kHz ( Figure 12) since these are the first-, second-and third-order harmonics of the switching frequency. The situation is similar in case of 10 kHz and 12 kHz switching frequency. For the 10 kHz switching frequency, the vibration occurs at 10 kHz and 20 kHz ( Figure 13) and for the 12 kHz switching frequency the vibration occurs at 12 kHz and 24 kHz ( Figure 14). The switching frequency signal and its harmonics contribute to vibration and noise signal. The vibration signal was measured at three switching frequencies of the inverter: 8 kHz, 10 kHz, and 12 kHz.
It can be noticed that the vibration signal in the colormap has higher amplitudes at switching frequency. This is caused by the PWM, signal whose harmonics are present in the spectrum of vibration signal. For 8 kHz switching frequency, in the colormap one can observe the vibrations at 8 kHz, 16 kHz and 24 kHz ( Figure 12) since these are the first-, second-and third-order harmonics of the switching frequency. The situation is similar in case of 10 kHz and 12 kHz switching frequency. For the 10 kHz switching frequency, the vibration occurs at 10 kHz and 20 kHz ( Figure 13) and for the 12 kHz switching frequency the vibration occurs at 12 kHz and 24 kHz ( Figure 14). The switching frequency signal and its harmonics contribute to vibration and noise signal.         Stator's natural frequencies can be found in the vibration colormap. The resonance frequencies appear on the colormap as vertical line of higher amplitude. This is presented in Figure 16. One can notice three typical modes of the stator: ovalization, triangular and square mode. These modes have their corresponding natural frequencies. Stator's natural frequencies can be found in the vibration colormap. The resonance frequencies appear on the colormap as vertical line of higher amplitude. This is presented in Figure 16. One can notice three typical modes of the stator: ovalization, triangular and square mode. These modes have their corresponding natural frequencies. One can see that the noise of the switching frequency and its harmonics are present in the acoustic signal of the machine. A comparison of acoustic noise FFTs is shown in Figure 17.
Just like in the case of the vibration signal, switching frequency harmonics are rotational-speed independent. The higher switching frequency the more noise the machine generates. Stator's natural frequencies can be found in the vibration colormap. The resonance frequencies appear on the colormap as vertical line of higher amplitude. This is presented in Figure 16. One can notice three typical modes of the stator: ovalization, triangular and square mode. These modes have their corresponding natural frequencies. One can see that the noise of the switching frequency and its harmonics are present in the acoustic signal of the machine. A comparison of acoustic noise FFTs is shown in Figure 17.
Just like in the case of the vibration signal, switching frequency harmonics are rotational-speed independent. The higher switching frequency the more noise the machine generates. One can see that the noise of the switching frequency and its harmonics are present in the acoustic signal of the machine. A comparison of acoustic noise FFTs is shown in Figure 17.
Just like in the case of the vibration signal, switching frequency harmonics are rotational-speed independent. The higher switching frequency the more noise the machine generates.
In load state the vibration of the machine was measured for various loads at different rotational speed and current angles using the accelerometers mounted on the machine, as presented in Figure 9. The operating points of the machine at different load and current angles are presented in Table 5. Red color indicates operating points which could not be measured due to technical limitations of the test bench. The examined machine was supplied from the inverter at 10 kHz PWM frequency. In load state the vibration of the machine was measured for various loads at different rotational speed and current angles using the accelerometers mounted on the machine, as presented in Figure 9. The operating points of the machine at different load and current angles are presented in Table 5. Red color indicates operating points which could not be measured due to technical limitations of the test bench. The examined machine was supplied from the inverter at 10 kHz PWM frequency.   The comparison of vibration signals from three accelerometers mounted on the machine in Y direction is shown in Figure 18. The vibration of the machine along its axial length is not uniform as it was in case of a no-load state. This is caused by the fact that the machine has a skewed rotor, which makes the radial forces distribution non-uniform along the axial length of the machine. Moreover, the mounting of the machine significantly limits the vibration level close to the mounting plate.

rpm 118 A 163 A 190 A
The comparison of vibration signals from three accelerometers mounted on the ma chine in Y direction is shown in Figure 18. The vibration of the machine along its axia length is not uniform as it was in case of a no-load state. This is caused by the fact that th machine has a skewed rotor, which makes the radial forces distribution non-uniform along the axial length of the machine. Moreover, the mounting of the machine signif cantly limits the vibration level close to the mounting plate. The rotational speed affects the vibration of the machine because at different frequen cies the normal modes of the machine are excited in different manner. Comparison of v bration for different rotational speeds is presented below. Figure 19, shows example results of vibration measurement for three different value of rotational speed and two different values of load torque. Figure 19a,b show time wave form of vibration signal for 20 Nm and 60 Nm load, respectively. It can be noticed that th higher the speed, the higher the amplitude of vibration signal. Comparison of the FFT o vibration signal as shown in Figure 19c,d gives a better image of how the speed influence the vibration of the structure. The power spectrum of the vibration signal is shown i Figure 19e,f. One can see clearly that the vibration strongly depends on the rotationa speed. The highest amplitude of both the signal's FFT and the power spectrum occurs a 20 kHz, which is double the switching frequency. The rotational speed affects the vibration of the machine because at different frequencies the normal modes of the machine are excited in different manner. Comparison of vibration for different rotational speeds is presented below. Figure 19, shows example results of vibration measurement for three different values of rotational speed and two different values of load torque. Figure 19a,b show time waveform of vibration signal for 20 Nm and 60 Nm load, respectively. It can be noticed that the higher the speed, the higher the amplitude of vibration signal. Comparison of the FFT of vibration signal as shown in Figure 19c,d gives a better image of how the speed influences the vibration of the structure. The power spectrum of the vibration signal is shown in Figure 19e,f. One can see clearly that the vibration strongly depends on the rotational speed. The highest amplitude of both the signal's FFT and the power spectrum occurs at 20 kHz, which is double the switching frequency. The load has also an impact on the vibration of the structure. One can see in F 20 that the vibration changes along with the load. Higher torque requires a higher p current, which in turn increases the magnetic field in the machine and causes the r magnetic forces to rise. The load has also an impact on the vibration of the structure. One can see in Figure 20 that the vibration changes along with the load. Higher torque requires a higher phase current, which in turn increases the magnetic field in the machine and causes the radial magnetic forces to rise.
The influence of the load on vibration, however, is not as strong as the influence of rotational speed. In Figure 20a,b one can see the time waveforms of vibration signals for different load values at 1000 rpm and 4500 rpm, respectively. As one can notice, the amplitude of vibration is affected by the load; a higher load increases the vibration amplitude. This effect is more visible at 4500 rpm rather than at 1000 rpm. The FFT of the vibration signals is shown in Figure 20c,d. One can see that the amplitudes are quite similar; at some frequencies the higher amplitudes of vibration occur for the highest load. The influence of the load on vibration, however, is not as strong as the influen rotational speed. In Figure 20a,b one can see the time waveforms of vibration signa different load values at 1000 rpm and 4500 rpm, respectively. As one can notice, the plitude of vibration is affected by the load; a higher load increases the vibration a tude. This effect is more visible at 4500 rpm rather than at 1000 rpm. The FFT of the v tion signals is shown in Figure 20c,d. One can see that the amplitudes are quite simil some frequencies the higher amplitudes of vibration occur for the highest load.
Comparison of the power spectrum shows the load's impact on the machine's v tion. One can observe that for the highest load (60 Nm) the amplitudes of power spec achieve the highest values, but at some frequencies the amplitudes of power spectrum the highest for the lowest load (20 Nm). Comparison of the power spectrum shows the load's impact on the machine's vibration. One can observe that for the highest load (60 Nm) the amplitudes of power spectrum achieve the highest values, but at some frequencies the amplitudes of power spectrum are the highest for the lowest load (20 Nm).
Although the current angle has an influence on the radial forces acting on the stator, its impact on the machine's vibration is not that clear. In Figure 21, one can see the comparison of the vibration measured at two different rotational speeds for the same load. It can be noticed that the vibration signals' amplitudes are similar for different current angles. In case of 1000 rpm rotational speed, the difference in amplitudes at different current angles is clearer than in the case of 3000 rpm. When comparing the power spectrum of the vibration signal, one can notice that for 1000 rpm at some frequencies the vibration is higher for the lowest current angle (higher radial forces) but around 10 kHz and 20 kHz, which are switching frequency and its double, the vibrations for all measured current angles are quite similar. In case of machine running at 3000 rpm, the power spectrum of vibration signal achieves the highest values for a 60 • current angle, which is quite strange since at this current angle, the flux and thus the radial forces are the lowest. This proves that the vibration of the stator is affected not only by the amplitude of the radial force but also, for the most part, by the frequency of the radial forces, since it excites the particular normal modes of the structure.
can be noticed that the vibration signals' amplitudes are similar for different curren gles. In case of 1000 rpm rotational speed, the difference in amplitudes at different cu angles is clearer than in the case of 3000 rpm. When comparing the power spectrum vibration signal, one can notice that for 1000 rpm at some frequencies the vibrat higher for the lowest current angle (higher radial forces) but around 10 kHz and 20 which are switching frequency and its double, the vibrations for all measured curren gles are quite similar. In case of machine running at 3000 rpm, the power spectru vibration signal achieves the highest values for a 60° current angle, which is quite st since at this current angle, the flux and thus the radial forces are the lowest. This p that the vibration of the stator is affected not only by the amplitude of the radial forc also, for the most part, by the frequency of the radial forces, since it excites the part normal modes of the structure. The acoustic signal was measured using two microphones: one placed next to the motor and another hung 1.5 m above the machine. Below, one can see a comparison of noise power spectrum measured in two different points at different rotational speeds.
In Figure 22 one can see the comparison of the noise power spectrum obtained from two microphones. As one could expect, the power spectrum achieves higher values for the signal measured by the microphone closer to the machine. The difference is more visible for higher rotational speeds. Figure 22a,b show the power spectrum of noise measured at 1000 rpm at 20 Nm and 60 Nm, respectively. The power spectrum of noise measured at 3000 rpm for the same load is shown in Figure 22c,d. The difference in power spectrum for two different microphones is greater for higher speeds. One can see peaks at 8 kHz and 16 kHz which are the switching frequency and its double of the supply system of the induction machine. motor and another hung 1.5 m above the machine. Below, one can see a comparis noise power spectrum measured in two different points at different rotational speed In Figure 22 one can see the comparison of the noise power spectrum obtained two microphones. As one could expect, the power spectrum achieves higher valu the signal measured by the microphone closer to the machine. The difference is mor ible for higher rotational speeds. Figure 22a,b show the power spectrum of noise ured at 1000 rpm at 20 Nm and 60 Nm, respectively. The power spectrum of noise ured at 3000 rpm for the same load is shown in Figure 22c,d. The difference in p spectrum for two different microphones is greater for higher speeds. One can see pe 8 kHz and 16 kHz which are the switching frequency and its double of the supply s of the induction machine. Comparison of the noise power spectrum measured at different rotational spe shown in Figure 23. Comparison of the noise power spectrum measured at different rotational speeds is shown in Figure 23. Noise power achieves higher values as the rotational speed increases. One that the noise has the greatest power at 4500 rpm and is the lowest at 1000 rpm. O see that the noise power spectrum achieves higher values for the noise signal me by the microphone closer to the machine. Figure 24 presents the comparison of the noise power spectrum for differe values to show the influence of the load on the noise emitted by the machine. Noise power achieves higher values as the rotational speed increases. One can see that the noise has the greatest power at 4500 rpm and is the lowest at 1000 rpm. One can see that the noise power spectrum achieves higher values for the noise signal measured by the microphone closer to the machine. Figure 24 presents the comparison of the noise power spectrum for different load values to show the influence of the load on the noise emitted by the machine.
Noise power achieves higher values as the rotational speed increases. One ca that the noise has the greatest power at 4500 rpm and is the lowest at 1000 rpm. On see that the noise power spectrum achieves higher values for the noise signal mea by the microphone closer to the machine. Figure 24 presents the comparison of the noise power spectrum for different values to show the influence of the load on the noise emitted by the machine. It can be observed that the load has also some effect on the noise generated b machine. Around the switching frequency (10 kHz) and its double, the power spec of the noise behaves as one might expect: the higher the load the higher the noise p spectrum. However, in some frequency ranges this rule is not followed. This is caus the fact that in the laboratory during the tests there were two machines, both contrib to the overall noise measured by the microphones. It can be observed that the load has also some effect on the noise generated by the machine. Around the switching frequency (10 kHz) and its double, the power spectrum of the noise behaves as one might expect: the higher the load the higher the noise power spectrum. However, in some frequency ranges this rule is not followed. This is caused by the fact that in the laboratory during the tests there were two machines, both contributing to the overall noise measured by the microphones.
At higher speed, the effect of the load on the noise is less visible. The impact of current angle on the noise is shown in Figure 25.
Energies 2022, 15, x FOR PEER REVIEW At higher speed, the effect of the load on the noise is less visible. The impact of current angle on the noise is shown in Figure 25. Similarly, to the vibration signal, the impact of the current angle on the n very clear. Although the radial forces are the weakest for the highest current does not seem to affect the noise. The rotational speed and thus the radial forces is the dominant factor in vibration and noise generation.
The machine's calculated natural frequencies and vibrational signal were with the measured ones to verify the correctness of the model.
A comparison of measured and calculated resonance frequency of the mac mal modes is presented in Table 6. Similarly, to the vibration signal, the impact of the current angle on the noise is not very clear. Although the radial forces are the weakest for the highest current angle, this does not seem to affect the noise. The rotational speed and thus the radial forces frequency is the dominant factor in vibration and noise generation. The machine's calculated natural frequencies and vibrational signal were compared with the measured ones to verify the correctness of the model.
A comparison of measured and calculated resonance frequency of the machine's normal modes is presented in Table 6. As one can see, there is a difference between the calculated and measured natural frequencies. The measured frequencies are higher than the calculated one. The difference is caused by the fact that during the simulation, only the stator core was considered. The windings, the housing and the water jacket were not modeled. The presence of the windings and housing increases the natural frequencies of the entire machine, which is shown in Table 6. Figure 26 shows a comparison of vibration signal obtained from measurements and simulation. very clear. Although the radial forces are the weakest for the highest current angl does not seem to affect the noise. The rotational speed and thus the radial forces freq is the dominant factor in vibration and noise generation.
The machine's calculated natural frequencies and vibrational signal were com with the measured ones to verify the correctness of the model.
A comparison of measured and calculated resonance frequency of the machine' mal modes is presented in Table 6. As one can see, there is a difference between the calculated and measured n frequencies. The measured frequencies are higher than the calculated one. The diffe is caused by the fact that during the simulation, only the stator core was considered windings, the housing and the water jacket were not modeled. The presence of the ings and housing increases the natural frequencies of the entire machine, which is s in Table 6. Figure 26 shows a comparison of vibration signal obtained from measurement simulation.  One can see that the vibration signal along axial length of the stator changes both in measurements and in simulation. The amplitude of the signal is greater on one end of the stator. The vibration signal waveforms are different, however. In case of simulation, the machine was supplied from sinusoidal current source, but during measurements the machine was supplied from an inverter with PWM. The amplitudes and harmonics present in the vibration signal are different in measured and simulated signals. However, it was possible to predict the behavior of the structure by running NVH simulations.

Conclusions
This paper presents the results of NVH analysis of a synchronous reluctance machine designed for EV application. Multiphysics analysis consisting of NVH, and electromagnetic analyses were performed to estimate the vibration and the noise generated by the machine. The natural frequencies of the stator core were calculated using modal analysis. The presence of the stator winding and the housing was neglected, thus the obtained natural frequencies were lower than the measured frequencies. Due to this simplification, the obtained values of resonance frequencies were lower than the actual resonance frequencies obtained from the measurement. However, the NVH behavior of the machine was properly modeled. Despite the simplified machine model used, the simulation provided valuable information about the NVH behavior of the machine. It was proven that the rotational speed of the rotor has the biggest impact on the noise and vibration of the machine. The vibration of the stator structure is caused by the variation of the radial magnetic forces. However, it was shown that the amplitude of the radial forces has a lower impact on the noise and vibration than the frequency of these forces. Additionally, the non-uniform axial distribution of radial forces on the stator inner surface caused by the rotor skew affects the vibration of the machine.