ELECTRIC MOTOR NOISE CONTROL FROM PRELIMINARY DESIGNTO INTEGRATION IN THE FINAL SYSTEM
VibraTec has been working on vehicle electrification and the optimization of electric motor designsince 2010. The AVELEC and MABCA research and development projects created tools and methods (VibraGear & VibraVolt) to calculate the noise and vibrations produced by electric motors and their gear transmissions.
Based on this knowhow, we have developed advanced methods to improve the acoustic performance of these electrified drivetrains. The methods use multiphysics algorithms that optimize the shapes of the active motorparts (rotor and stator) and also the active gear parts (teeth) to limit noise and vibrations (especially whining noise) without impacting the other performances. These algorithms also integrate manufacturing and assembly constraints to obtain robust designs that are essential for the automotive and aeronautic industries.
Finally, by combining our historical knowledge of the NVH business with our electrified powertrain skills, VibraTec proposes methods and tools to successfully integrate electrified powertrains into the final applications: cars, busses, trucks, trains, airplanes and bicycles.
VibraTec offers clients a complete expertise in the field of electrified powertrain acoustics, including 3 training courses covering these topics: Electric Motor Acoustics, Gear Dynamics and Vehicle Epowertrain Integration.
GEAR NOISE CONTROL
It is commonly assumed that Static Transmission Error (STE) and gear mesh stiffness fluctuations are responsible for gearbox whiningnoise, which is itself one of the main sources of noise and vibration in several industries.
The Static Transmission Error (STE) and mesh fluctuations generate dynamic mesh forces which are transmitted to the housing through wheel bodies, shafts and bearings. The gearbox housing then transmits the vibration and noise: directly, via noise transparency of surrounding panels, and indirectly via structureborne vibration propagation.Noise radiated from the gearbox (whining noise)is directly related to the housing’s vibratory state.
Optimizing tooth corrections in order to minimize meshing process excitation brings confirmed acoustic gain, reducing gear whining noise.
Generation and transmission of gearbox whining noise 1: parametric excitation between teeth, 2: propagation in the gearbox, 3: vibration of housing
The meshing processgenerates excitation that is divided in two phenomena: transmission error and mesh stiffness fluctuations. The transmission error is mainly due to voluntary (tooth modifications) and involuntary (manufacturing errors) geometric deviations of the teeth on a micrometric scale. The flexibility of the teeth, the pinion and the shafts results in additional transmission error fluctuations.
Static Transmission Error Computation
For geared systems, the Static Transmission Error (STE) under load is one of the main whining noise sources. It corresponds to the difference between the actual position of the driven gear and its theoretical position for a very slow rotation velocity and for a given applied torque. Its characteristics depend on the instantaneous meshing tooth pair locations.
Static Transmission Error (STE) results from tooth deflections, tooth surface modifications and manufacturing errors. STE calculation is relatively classical. For each position on the driving gear, a kinematical analysis of the mesh determines the theoretical contact line on the mating gear tooth surfaces within the plane of action.
When computing Static Transmission Error (STE), it is very important to take into account the actual tooth microgeometry such as tip relief, root relief, crowning or end relief (see ISO standard 11221). For an accurate evaluation of the excitation, a metrology of these parameters is required.
One important remark on the Static Transmission Error (STE) computation concerns the global system in which the gears are inserted. Indeed, when the gears are wide, the torque transmitted high, the bearing soft and the gears not centered on their shaft; the global static deflection can become a firstorder parameter.
Static deflection and its potential impact on Static Transmission Error
Dynamic Response Calculation Scheme
This computation scheme requires a finite element model of the complete gearbox in order to obtain its modal basis. At this point, it is important to identify the modes that could amplify the excitation: gearbox casing deflections and also driveline bending and torsion modes. It is possible to determine the most critical modes by considering their energy contribution to the different meshing stiffnesses.
Driveline modal deflection shape
The contact between the gears is modeled with a stiffness matrix linking the degrees of freedom of each pair of meshing gears. The scheme then uses a powerful resolution algorithm in the frequency domain to solve the dynamic equations with an iterative procedure (ISIS).
The final outputis thus the dynamic transmission error (DTE), the teeth dynamic loads and the housing vibration as a function of the frequency. The operating speeds corresponding to resonance peaks and the amplitude of the housing vibration characterize the whining noise’s severity. The process can be repeated for several applied torques.
VibraTec’s dynamic response calculation method
VibraTec’s computation scheme has been validated step by step, by comparisons with extensive and complex measurements on different products, such as automotive gearboxes. Several quantities were measured and compared to the simulation: the static transmission error fluctuation, the dynamic transmission error, housing vibration and whining noise.
Test vs. Measurements: Static Transmission Error and housing vibrations
Planetary Gears
Planetary gear sets provide high gear ratios in a compact package. They are widely used in hybrid vehicle automatic gearbox transmissions and in Eaxles. Compared to cylindrical gears with fixed and parallel axes, predicting and controlling the whining noise emitted from a planetary gear set remains a difficult problem because of the coupling between the multiple gear meshes and the mobility of the planet axes.
In the case of planetary gears, contact equations are solved taking account of all the meshing simultaneously. In a first step, one planet gear is taken as a reference and the contact points for the other gears are deduced for each successive angular position of the reference gear. Knowingthe contact line locations between sun and planets, geometric constructionmakes it possible to deduce where the contacts between ring and planets occur.
Numerical planetary gear model
The computation scheme for planetary gears also requires a finite element model of the complete system in order to obtain its modal basis. Planetary gears are complex systems, so in order to optimize computation time, smart assumptions regarding the geometry of the system are essential. These assumptions can concern the use of lumped parameters for certain components like the planet gears. Defining each component’s degrees of freedom in all directions is also important. The bearing stiffness has to be accurately defined, as well as the ring stiffness. In fact, the ring bending effect can dominate the tooth bending effect.
Typical planetary gear modes are the rotational, translational and planet modes.
Typical translation mode (dashed lines represent the initial position)
Comparing numerical simulations and measurements show the ability of the proposed numerical model to compute the overall Static Transmission Error (STE) and to accurately predictthe housing’s vibratory state, which is responsible for the whining noise.
Simulation vs. test – planetary gear
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GEAR NOISE CONTROL
ELECTRIC POWERTRAIN OPTIMIZATION
Mechanical, thermal and energy performances are usually evaluated and optimized during electric machine design. However, the machine’s acoustic behavior is rarely considered, even though the noise radiated by electric motorscreates highfrequency pure tones that can be very annoying.
In all industrial sectors, electric machines emit this electromagnetic noise:
 In the railway sector, traction motors are the source of exterior and interior noise.
 In the automotive sector, if the traction motors reduce external noise, this is not the case for the internal noise where these sounds become annoying. In a context of increasing power density, this problem will become more acute in the years to come.
VibraTec has developed a new method to optimize the electromagnetic design of electric motors in order to fulfil NVH specifications. This method is equally applicable to BEV, HEV or PHEV traction motors, as well as any other motor type.
Electric motor optimization method
The method relies on anNVH performance calculation process for electric motors submitted to electromagnetic excitation. The process is integrated into an optimization loop minimizing noise and vibration levels by reducing electromagnetic excitations. Moreover, criteria such as the mechanical power delivered by the electric engine, torque ripple, efficiency or temperature are controlled by the optimization algorithm so that a multiconstraintoptimization can be performed.
Indeed, electrical and NVH engineers work to optimize the same raw quantity,namely the flux density in the air gap, to comply with their respective specifications. The innovative approach is to treat both topics at the same time in the project and with the same tools to achieve the best compromise.
Electric enginescan be inherently quiet as long as the origin of their dynamic excitation is known and integrated in the design process without compromises against global performance. Once the NVH constraints are integrated at the same level as the other constraints, the design process becomes safer and more efficient.
A major interest of the optimization method presented is that it can be directly applied during the epowertrain design process.
Basic principle of the optimization objectives from a common electromagnetic simulation
Optimizing electric machines in order to minimize their noise or vibration levels, without deteriorating the aforementioned electromechanical performance criteria, requires the modelling of the related physical phenomena. Estimating the dynamic and acoustic behavior of electric motors requires the determination of the flux density time evolution for different rotor positions, just like estimating common electromechanical performance criteria such as torque or efficiency.
In order to determine the Maxwell pressures which apply to the stator and represent the main phenomenon responsible for noise and vibrations, the radial and tangential flux densities are calculated along the air gap, using electromagnetic 2D finite element calculations.
The calculation of the instantaneous torque is straightforward after the electromagnetic finite element computation. It can be done by integrating Maxwell tangential pressures around the surface of the air gap. Instantaneous torque can also be defined directly from the electromagnetic results using the virtual works method.
A loss model can also be implemented in order to include motor efficiency in the optimization objectives or constraints. Thermal criteria can be included by using a further thermal model. The losses can be divided into copper losses due to the current flow in the windings, and iron losses, composed of hysteretic losses and eddy current losses.
The iron losses can be computed from the electromagnetic simulation results using a loss model like the Bertotti model.
Electric motor design optimization currently aims at minimizing a cost function corresponding to the electric machine’s acoustic power level, while respecting constraint functions defined using the previously mentioned criteria, so as not to deteriorate the electric motor’s overall performance.
Minimizing the acoustic power level is done by reducing the Maxwell pressure’s harmonic contributions, which are responsible for high vibration and noise levels. These contributions’ amplitudes are very sensitive to electromagnetic design parameters, such as the shape of the rotor poles or stator teeth. Consequently, a great advantage of this optimization technique is that the geometrical changes applied to the design are small from a mechanical point of view, and they do not involve any increase of the electric motor’s mass or any significant additional cost.
Moreover, although the current use of the optimization method aims to decrease noise without deteriorating the overall performance (efficiency, torque, thermal, etc), it can also be used to maximize the overall performance without increasing the noise levels, or even to find a tradeoff that both improves overall performance and decreases noise levels.
Electric Motor Optimization –Case Study
The motor to be optimized was a 10pole interior permanent magnet synchronous motor (IPMSM) dedicated to automotive traction. The optimization targeted a minimization of the electric motor’s acoustic power level without decreasing its mean torque and without increasing its torque ripple.
Geometry of the initial IPMSM
Before performing the optimization, the motor’s dynamic behavior was evaluated using a previously validated workflowbased on electromagnetic and structural finite element models.
This diagnosis identified the optimization as a noise level reduction at 4700 rpm (the speed where the noise and vibrations prevailed). To do so, the cost function was defined as the acoustic power level when the electric engine speed was 4700 rpm.
Some inequality constraints were also defined, so that the mean torque produced by the motor and the torque ripple remained stable comparedto the initial design.
The optimizationresults showed a very significant 14dB Sound Power Leveldecrease. This reduction was achieved by small changes in therotor poles’ shape. The changes did not affect the price or the motor’sweight.
Comparison of the SWL of the initial and optimized IPMSM designs
Gear Optimization
The first part of the computation scheme, Standard Transmission Error (STE) computation, can be used to optimize the tooth geometry in order to minimize the excitation. An optimization problem requires a correctly defined fitness function and an appropriate algorithm to be solved.
The criterion retained to estimate one Standard Transmission Error (STE) fluctuation is the peaktopeak amplitude (STEpp). Considering that the modifications made have to reduce the STEpp for a given torque range, the fitness function is defined as the integral of STEpp over this torque range.
The algorithm retained is based on a Particle Swarm Optimization (PSO), which is based on the stigmergic behavior of a population in constant communication and exchanging information about their location in a given space to determine the best location according to what is being searched for. In this case, some informant particles were considered, located in an initial and random position in a hyperspace built according to the different optimization parameters. The best location is thus the combination of parameters which ensures the minimum value of the fitness function defined above.
Let’s say that a solution S0 is determined by the PSO. The robustness study is done using a MonteCarlo simulation, i.e. 10000 other solutions are computed, chosen randomly in a hyperspace centered on the optimized solution parameters values, limited by the tolerances interval of each parameter and considering possible lead and involute alignment deviations. These 10000 results establish the density probability function of each selected optimized solution. They also make it possible to compute statistical variables such as mean value and standard deviation.
Optimization results and robustness study
VibraTec has developed and validated these tools to design and optimize parallel axis helical gears, parallel axis spur gears, plastic gears and also planetary gears.
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 Watch our free Epowertrain design manufacturing webinar,
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ELECTRIC POWERTRAIN OPTIMIZATION
ELECTRIC POWERTRAIN INTEGRATION
The sound power level perceived by the user is the result of airborne and structureborne contributions:
 Structure borne noise is the product of the forces (Fi) generated by the source (EPowertrain) and the vibroacoustic transfer.
 Airborne noise is the product of the acoustic volume flow rates (Qi) generated by the surface of the source and the acoustic transfer.
Both the vibroacoustic transfer and the acoustic transfer characterize the transfer of energy between the source and the receiver, which depends on the amplifications and attenuations of the elements that constitute the transfer path (carbody beams or panels, acoustic material, air cavity, etc).
Interior noise decomposition
Thus, controlling the interior noise means:
 Mastering the excitations generated by the EPowertrain.
 Mastering the transfer paths of the structure (filtration, dampening vibrations and sound absorption).
Transfer paths
One of the main changes in the integration of Epowertrains compared to the one of Internal Combustion Engine (ICE) is the structure borne contribution. Indeed, in electric vehicles, the structurestructureborne noise is dominant up to 1.5 kHz, compared to roughly 800 Hz for ICE.
The conclusion given above has a direct consequence on the countermeasure that should be used to filter the excitation coming from the epowertrain: the use of soft filtering elements as a suspension system. The standard technical solution for the automotive industry is to use rubber mounts. It is known that rubber cannot be considered as “pure spring” for several reasons:
 Rubber is an organic material having a rheological behaviour (sensitivity to temperature/frequency, nonlinear behaviour with preload/amplitude, etc),
 The rubber mount itself has natural frequenciesthat can be excited (internal resonances).
In reality, the filtering of an engine mount have an even more chaotic behaviour. The figure below shows a measured insitu transmissibility T curve of an actual engine mount. It shows a lot of variations. Once installed in the car, the local modes of the brackets, supports, arms, connecting rodsetc may disturb the filtration. In the example given, amplifications can be observed at some frequencies, typically in the frequency range of whining noise.
Transmissibility curve of a rubber mount up to 2000 Hz
Thus, the characterization (or modelling) of the rubber mount stiffness becomes crucial for the design of a suspension system for electric powertrain. VibraTec has developed a dedicated test bench in order to test engine mounts up to the medium frequency range capable of measuring mount stiffness applying a static preload in any direction. The test rig and a typical measurement results are given in the figures below.
This result depicts the main characteristics of a rubber mount:
 The dynamic stiffness is not a constant; there is a general increase with frequency in the first part of the curve,then a decrease due to the increasing mode number,
 Peaks due to internal resonant modes are observable in the whole frequency range: loss of stiffness at resonance, increase of stiffness at antiresonance,
 Strong variations due to modes,
 Slight sensitivity to the excitation amplitude,
 High sensitivity to preload.
VibraTec’s test rig to measure the dynamic stiffness of rubber mounts in the midfrequency range
Typical dynamic stiffness of a rubber mount (influence of excitation amplitude)
Characterization of EPowertrains as an acoustic source
The essential information that characterizes EPowertrains is their acoustic power. This data can be measured or calculated.
Regarding the calculation, the workflow is presented here. Once the vibration levels on the surface of the component are calculated, the acoustic power can be obtained in 2 different ways:
 Quick and rough: in this case, the efficiency of the conversion of the vibrations into noise is considered as maximum, whatever the frequency and the deflection shape. In other words, the radiating factor is equal to 1, whatever the frequency and the deflection shape.This method is sufficient for medium or largesized motors. It is not adapted to small electric actuators. Finally, this calculation is very fast and is already available in some mechanical solvers like NASTRAN: Equivalent Radiated Power (ERP).
 Rigorous and accurate: acoustic solvers are used to calculate the acoustic power and the propagation of the sound waves around the EPowertrain. This kind of simulation is more accurate than the previous one, but it requires a more complex data entry and more computing time.
Electric motor noise source location: simulation (left) – measurements (right)
On the experimental side, there are threedifferent ways to measurean Epowertrain’sacoustic power:
 Based on acoustic pressure measurements, using ISO standard 3744, 3745 or 3746, depending on the test bench environment. This method only requires microphones.
 Usingsound intensity as per ISO standard 9614. This method is less sensible to the environment than the previous one,but it requires specific equipment: sound intensity probes. In case of measurements at a discrete point, it makes it possible to locate the main noise sources.
Using a microphone array. Certainly the most interesting method, because it not only provides the sound power level as a function of the frequency, but also as a function of the space (location). Indeed, the combination of the measurements and the 3D Epowertrain model makes it possible to obtain an accurate acoustic map of the powertrain that can be used for diagnosis or to evaluate noise reduction solutions.
Evaluation of acoustic solutions using microphone arrays
Characterization of Epowertrains as a force generator
The most common choice to characterize the structureborne contribution of components and accessories is to use blocked force measurements, which are intrinsic values for vibrating sources. When known, these values can be used at the design stage to evaluate the contribution of a vibration source on the noise and to specify targets for suppliers.
If the concept of blocked forces is recognized as a robust methodology, the way of obtaining them experimentally can be tricky, especially due to the necessary test bench. In theory, the test bench should be infinitely rigid to ensure no displacement at the interface between the source and the force sensor. In the real world, this assumption is hard to reach for several reasons. The main one is that it is difficult to design a test bench that is sufficiently rigid, especially for sources with highfrequency content; the presence of vibration modes can quickly limit the validity of the bench. The second reason is that existingsupplier test benches were often designed to measure more than only NVH values and are not rigid enough to fulfil this assumption.
Another way of proceeding is to measure the forces “without force sensors” through an inverse method. This method is based on the assumption that a source can be characterized by its effect on target sensors (the induced vibration), knowing the transfer functions between these target sensors and a known forceapplied to the structure.The principle and test setup are simple, but application can be cumbersome.
Blocked force measurements – Direct method (left) using force sensors indirect method (right) Electrical water pump
Blocked forces measured at the source fixation points
Torque ripple
Torque ripple in electric motors can be generated by:
 Current harmonics,
 Control strategy,
 Design of the active parts (rotor and stator).
Torque ripple is transmitted to the receiving structure through the fixation points (torque reaction) and thus can be characterized with the methodology presented in the previous paragraph.Torque ripple is also transmitted to the driveline through the rotor axle. Measuring this data makes it possible to:
 Study the influence of the abovelisted parameters on the torque.
 Use it as input data to simulate the dynamic behavior of the transmission (gear noise, transmission shaft torsion analysis, etc).
 Correlate measured and calculated torque ripple values, and adjust FE model parameters (if necessary).
Torque ripple can be measured with:
 A torquemeter: a fully integrated system for measuring dynamic torque. Most of the time, it measures the deformation of a calibrated cylinder. This technology is generally used in test rigs.
 Strain gage and telemetry: the shaft is instrumented with strain gages to measure its deformation, which is proportional to the torque. The gage’s signal is transmitted via telemetry. This is an alternative solution to the torquemeter for “insitu” measurements, and requires calibration.
Rotational vibration measurements are an alternative to torque ripple measurements. The torsional vibration of the shaft can be measured with optical (rotational laser) or magnetic sensors.
Torsional vibration and Torque ripple measurements Strain gage and telemetry (left) – Torquemeter (center) – Rotational laser (right)
Torsional vibration at the input of a gearbox of an EPowertrain Comparison of two different couplings
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 Watch our free Epowertrain design manufacturing webinar,
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ELECTRIC POWERTRAIN INTEGRATION
ADVANCED ELECTRIC POWERTRAIN MEASUREMENTS
In most projects, the NVH performance of Epowertrains is assessed according to two indicators: vibration levels and sound power level (or sound pressure level). Sometimes, the measurement of the dynamic forces transmitted the receiving structure (blocked forces) can be added to the required data in order to fully manage the integration of the EPowertrain in its application.
Furthermore, some advanced measurements are sometimes necessary to:
 Confirm or improve the accuracy of FEM. It’s the case in the simulation of gear systems noise where the knowledge of the Static Transmission Error is critical.
 Diagnose NVH issues like rotor eccentricities whose consequences are often responsible for noncompliance with the NVH specifications.
The two topics mentioned above are presented more in detail below.
GearBox – Transmission Error
The Static Transmission Error (STE) is the key data when talking about gear system noise and vibration. This data can be calculated, but it can also be measured.
The Static Transmission Error (STE) corresponds to the difference between the actual position of the driven gear and its theoretical position for a very slow rotation velocity and for a given applied torque. Thus, to experimentally define the STE, it is necessary to measure the position of the driving gear and the position of the driven gear. These positions are measured with specific sensors called encoders.
Encoder for Static Transmission Error measurements
The key points tocorrectlymeasuring Static Transmission Error are:

 The choice of encoders. The resolution has to be carefully chosen according to the number of gear teeth.
 The installation of the encoders on the gear system.
 Raw signal postprocessing: the encoder measures a lot of information andit is necessary to postprocess the signal to extract the STE.
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Static Transmission Error measurements – Test vs. Simulation
Electric motor – rotor displacement
Rotor assembly and manufacturing operations are always realized to target nominal dimensions. Since it is not possible to reach the exact dimensions, a tolerance range is defined,resulting in rotor eccentricities. A rotor eccentricity can significantly change the Maxwell Pressure’s harmonic content and thus the electric motor’s noise and vibration. The rotor’s displacement can also have an impact on the structural reliability of the machine, notably for long rotors or for axial flux machines.
The eccentricity data can be used to:


 Understand the rotor’s dynamic behavior,
 Compare the actual eccentricity to the specified or simulated one,
 Identify a rotor resonance due to a bending mode,
 Quantify rotor displacement in operating conditions.

Rotor eccentricity measurements are based on orbit plots. Two probes are mounted 90° apart and measure the distance between the rotor and the stator or between the shaft and the bearing housing. The orbit is generated by pairing the two probe signals so the time element is removed, leaving the X probe amplitude versus the Y probe amplitude, plotted in what is commonly known as the Cartesian coordinate system.
The following sensors can be used:


 Fiber optic sensors: these sensors are recommended to measure the displacement between the rotor and the stator, inside the electric machine.Firstly, the diameter of the probe’s active part is small and can be almost freely formed to access small areas. Secondly, the glass fiber’s flexibility reinforces the probe’s insertion capability. Finally, the optical fiber is not sensible to magnetic environments and its electric insulation ability is useful when working close to supplied windings.
 Magnetic sensors: most of these probes are based on magnetic, inductive or eddy current technologies whose main drawbacks are a big size and a high sensitivity to the materials in their close environment. This technology is recommended for measuring displacements between the rotor shaft and the bearing housing, outside the electric motor.

Displacement sensors for rotor eccentricity measurement Optical sensors (left) – Magnetic sensors (right)
Orbit plot – comparison with simulation
ADVANCED POWERTRAIN MEASUREMENTS