High frequency modelling of electric motor vibration in the presence of adhesive bonded components

Gao, B. 1

Department of Aeronautical and Automotive Engineering Loughborough University, Loughborough, LE11 3TU, UK

O’Boy, D. J. 2

Department of Aeronautical and Automotive Engineering Loughborough University, Loughborough, LE11 3TU, UK

Mavros, Georgios 3

Department of Aeronautical and Automotive Engineering Loughborough University, Loughborough, LE11 3TU, UK

ABSTRACT Electric motors often include adhesive joints to bond magnets to shells. In this paper, the variability of the frequency response function is assessed with regards to high frequency, finite element modelling and validation. The adhesive bond is used to fix the permanent magnets to the motor shell for the typical PMDC motor as it provides a smoother, more continuous surface than fixings without discontinuity of the magnetic field. To obtain the dynamic response of the motor housing at specified settings of the adhesive layer, which include variations in thickness and sti ff ness, a finite element model is established in ABAQUS. Given the relative sti ff ness of the adhesive is lower, this has a significant e ff ect on the overall sti ff ness of the casing, for a fixed mass and thus the response frequencies and loss factor. When using frequency response functions to couple motors to components, this variability can be significant and thus this work is useful for the e-motor noise optimization at its design stage.

1. INTRODUCTION

Automotive vehicle powertrains were typically analysed for Noise, Vibration and Harshness (NVH) through benchmark measurements at the driver’s ear and seat positions, for driving inputs from an internal combustion engine motor. These benchmarks were internally set with reference to previous vehicles or competitors platforms. The noise and vibration is often seen as a negative trait but does provide significant feedback to the driver on vehicle speed, engine load and road surface condition.

1 b.gao2@lboro.ac.uk

2 d.j.oboy@lboro.ac.uk

3 g.mavros@lboro.ac.uk

a slaty. inter.noise 21-24 AUGUST SCOTTISH EVENT CAMPUS O ¥, ? GLASGOW

With the move to electric motors in the powertrain, either as direct drive or generators, the frequencies and physical mechanisms behind these sounds are di ff erent, leading to an advantage for the designer in terms of luxury and comfort, but also an opportunity to develop transmission paths which augment desirable characteristics. In this paper, the methodology for simulating an electric motor in real time, for a driver in the loop test is provided, with an emphasis on the real physical sound sources linked closely to the actual vehicle design specification. A short background is provided, with experimental and numerical details of a Simulink model shown. As the frequencies are di ff erent to those found in the IC engine, one significant source of variability in deterministic modelling is described, where adhesive is used to join two sti ff components. The paper provides illustrative results of finite element modelling on the frequency response functions between the electromagnetic forcing locations and the shell of the electric motor, with conclusions.

2. BACKGROUND

Generating a predictive noise and vibration model of an electric motor requires knowledge of the physical mechanisms which lead to unsteady forces on the motor shell. Once these unsteady forces are known as a function of frequency, to obtain the sound and vibration at the driver’s seat and ear uses the same procedure as with the IC engine. A frequency response function (FRF) is usually obtained to link the force applied at the motor mount position to the seat rail and steering wheel, all as a function of frequency. The acoustic response is measured via microphones at the driver’s ear position, although it is also possible to use reciprocal measurements, where the force is applied in the cabin and the sound measured at the motor mount. Reductions (or enhancements) of the frequencies can be carried out through alterations either to the source of unsteady force or via the transmission path. Previous requirements for low noise and vibration, directly linked to a luxurious environment has led to significant amounts of damping material being included in the cabin, requiring manufacture, installation and space. The perception of interior noise derives from acoustic frequencies lower than 550 Hz, whilst exterior noise is typically important for frequencies greater than 550 Hz, although there is some overlap depending on transmission path and window sealing. Whilst the overall amplitude of the noise generated by an electric motor e.g. permanent magnet synchronous motor (PMSM) is far lower than an IC engine equivalent, there are important di ff erences which need to be taken into account at the design and specification stage. IC engines are characterised by narrow band fundamental and harmonic frequencies which change with both demanded loading and rotational speed, with frequencies typically in the order of the interior noise range, whereas the sources in the electric motor include frequencies up to 10 kHz, of importance to airborne transmission and those which don’t change with vehicle speed. This introduces narrow band and highly annoying fixed tones. In this paper, rather than simulate and validate a permanent magnet synchronous motor from an automotive vehicle, the basis is tested on a brushed DC permanent magnet motor, for scale experiments. The sources of noise in an electric motor include:

– Radial unsteady forces caused by the rotation of windings in the presence of a magnetic field. As the rotor turns, the windings pass the fixed permanent magnets and the flux density changes. This source of noise changes with rotation speed of the rotor and thus can be useful for a driver in terms of feedback [1,2]. – Radial and tangential unsteady forces caused by the current flowing in the windings, causing an armature reaction with the magnetic field. This is also dependent on the rotational speed of the motor. This is dependent on a number of factors, including the air gap between coils and magnets [1,3,4].

– Bearing orders and friction sources; These are well understood and present in IC engines. For brushed motors, the friction force generates an equivalent of a white noise signal on the casing, causing excitations which amplify structural resonances. For vehicle motors, no brushes are included. – The most e ffi cient method of applying variable voltage, whether three phase AC or direct DC is through a pulse width modulated signal (PWM) where the duty cycle varies from 0% to 100%. This is highly narrow band and of a fixed frequency, set by the inverter electronics. Thus it is highly noticable, high frequency and relatively annoying as it doesn’t vary with vehicle speed. Damping can attenuate the structure borne transmission path but the airborne path is more di ffi cult. These PWM signals are propagated through the armature reaction forces. – The radial and tangential forces act on the motor casing, causing surface accelerations. There are a set of viscoelastic motor mounts that aim to minimise transmitted vibration but cannot be too soft as the motor will move in the powertrain. Airborne propagation derives from this surface acceleration.

The vehicle designers need tools in order to facilitate good decision making at the right time, hence these tools need to be at the right fidelity. Many examples of simulation tools in the literature are based upon finite elements. These are complex and need significant design information usually not available at the early design stage, such as coil winding shapes, damping between coil and armature, specific material properties and detailed cooling paths. Alterations to the design are not easy, nor is validation for each design. Real time methods are usually based on emulated sounds not directly linked to the design specification. In this paper, the Simulink model has electromagnetic equations which are analytical but based on real physical generation mechanisms, with an avoidance on empirical modelling. The structural behaviour of the motor is characterised by a modal superposition method [5, 6], using a limited number of natural frequencies and mode shapes. Each of these stages is linked as reductions in shell thickness of the motor (weight saving and manufacture choices) can amplify the sound heard by the driver.

3. EXPERIMENTAL AND NUMERICAL IMPLEMENTATION

In this paper, the methodology and flow for the prediction of real time noise and vibration on an electric motor is shown through a permanent magnet brushed DC motor (PMDC), with an experimental rig shown in Figure 1 with the DC motor on top, connected to a frame and shaft. The shaft joins to a smaller DC motor used as a resistance load for the experiment, so that the armature reaction forces are properly excited. Accelerometers are used to obtain the surface acceleration of the motor shell while the custom electronics allows the motor to be excited at a range of duty cycles and frequencies (allowing the decoupling of the PWM excitation from the structural response). The real time implementation of the electromagnetic equations with a modal superposition structural model is shown in Figure 2 where Simulink (running faster than real time) is connected via a LabView network interface to a throttle pedal input, providing a proportional 0-5V analogue voltage input. The time series acceleration is integrated over the motor surface and output through a power amplifier to a speaker. This rig can then be implemented in a driver in the loop simulator with real physical motor responses. The modal superposition requires a set of natural frequencies for the motor and associated mass normalised mode shapes. These are obtained through finite element prediction, where any excitation

Figure 1: Experimental rig for obtaining electric motor accelerations

Physical motor + Accelerometer / microphone: + Electrical loading through smaller resistance motor ‘+ Custom PWM circuit and driver PWM duty cycle Resistance [variable loading? Frequency [varying away from resonances]

Figure 2: Simulink implementation of electromagnetic equations and modal superposition method

EMotor + Labview interface to electrical potentiometerinput Network interfaceto amplifier speaker Current and inertia modelled Electromagnetic flux equationslink to radialand tangential forcing Structural modal superposition Simulink model single precision, signif. optimisation

frequencies that coincide with the structural natural frequency would cause an amplification of physical response. Therefore, the accurate prediction of these mode shapes and frequencies is important at ranges where modal overlap is important, and where methods such as statistical energy analysis and band averaging are typically used.

4. STRUCTURAL MOTOR RESPONSE

The outer shell of the motor is a rolled steel material, and the magnets themselves are ferrite bonded, with a similar Young’s modulus. For a PMDC motor, the permanent magnets are usually bonded onto the inner surface of the motor shell with a adhesive layer. The e ff ect of how the adhesive layer influence the dynamic behaviour of the motor shell is not clear. Hence, in this paper a research focused on the impact of the glue layer to the dynamic behaviour of a PMDC motor is presented. The modelling analysis is performed on a Parvalux M63QN-0011 (Figure 3a), with a regulated 12V supply voltage and 250W power rating, the no-load output speed is 3000 RPM with a maximum torque of 0.8 Nm. Two ferrite magnets are adhesively bonded to the rolled steel casing, as Figure 3b shows. The rotor has 16 slots with 93 mm e ff ective length (Figure 3c). In order to simplify the calculation of the sound pressures of the motor, the accelerations of the outer surface of the motor are solely applied to the FRF point mobility generated by the FE simulation in ABAQUS, because the noise is mainly generated by the vibration of the outer surface of the motor. Thus a force of 1N is applied to the inner surface and a linear acceleration response is obtained on the outer surface, both being normal to the surface (all tangential displacements through Poisson’s ratio are neglected). The impact of the displacement on the electromagnetic equations is also neglected as small in comparison to the main unsteady forces.

4.1. Motor structural components The geometry of the PMDC motor housing, includes the motor shell, magnets and the glue are shown in Figure 4. The motor shell is made of steel, with some assembling holes to fix the other components. The magnets are made of ferrite magnet, and fixed firmly on the shell by a adhesive layer. This is one of the critical findings from this research, that the variability of these adhesive joins can be significant. In order to model this setup in finite elements at frequencies of importance for PWM excitation, the user requires either the Young’s modulus of the adhesive layer, and / or the thickness of the adhesive, assuming that it is one uniform layer with uniform properties at the edges of the magnets. As the adhesive has a lower e ff ective sti ff ness, and thus is an equivalent spring between two sti ff materials, the composite response is governed by the spring sti ff ness.

4.2. Experiment of FRF response function Experimental measurements of the shell response were taken using both a shaker and impact hammer, with the main motor rotor removed, see Figure 5. The motor was suspended by fishing line to avoid contamination and attempt to emulate free-free boundaries. These results were used as guides and partial validation for the settings of the adhesive layer in finite elements.

5. FINITE ELEMENT PREDICTIONS

The finite element method can be used to generate natural frequencies and mode shapes, however, this is computationally expensive and does not meet the requirement for real-time simulation. It does allow the generation of frequency response functions (structural radial surface acceleration for an impulse input). A faster method to get this FRF is though the modal superposition method. The outer shell of the DC motor comprising the magnets and holes for the brushes is generated in the finite element program in ABAQUS. As shown in 6 , the steel shell comprises 11220 of hexahedral

(a)

(b)

(c)

Figure 3: The exterior and interior of the DC motor for measurement: (a) motor shell and shaft; (b) motor magnet, brushes and commutator; (c) rotor and caps.

Figure 4: Schematic diagram of a PMDC motor.

Permanent Magnetics Rotor with winding Adhesive layer _/ Motor shell Shaft Rm Rs

elements (type C3D8R), the magnets are formed of 6720 of elements while the glue interface is represented as a tie constraint. A virtual hammer test is conducted to provide the accelerance of the surface against frequency. The ABAQUS model utilizes structural damping, set at a constant for all frequencies as an initial guess.

5.1. Frequency response functions for the electric motor shell Two point mobility predictions are shown for the relatively simple geometry in Figure 6, one where the glue bonding is 0.5 mm thick and one where it is 0.8 mm thick. As can be seen in Figure 7, the first mode shape is located at the right frequency but between 5-6 kHz, the impact of a small change in this thickness is apparent. The experimental results for the adhesive layer for these high frequencies with small wavelength show that both the locations of natural frequencies in this range, plus their amplitude are very sensitive to small changes in the glue properties. Future work involves using the experimental point mobility results to inform an optimisation approach to finding the best thickness of glue and / or how far it reaches across the magnets.

6. CONCLUSIONS

A modal superposition method is integrated into a real time simulation of electric motor noise and vibration. In order to obtain the natural frequencies and mode shapes of the motor structure, a finite element representation of the magnets and shell are created. The shell and magnets are broadly the same Young’s modulus, however the sti ff ness of the adhesive layer is far less. Results are shown for di ff erent thickness of the adhesive layer, for frequencies of interest to noise and vibration engineers where PWM excitation is likely to occur. For a DC brushed motor, these results have demonstrated that the whole structural response is very sensitive to small changes in this adhesive layer. Future work will include an optimisation strategy to best fit numerical models to these experimental results.

ACKNOWLEDGEMENTS

The authors would like to acknowledge the funding support from Innovate UK and the Advanced Propulsion Centre (APC) for carrying out this work.

REFERENCES

[1] ZQ Zhu, David Howe, Ekkehard Bolte, and Bernd Ackermann. Instantaneous magnetic field distribution in brushless permanent magnet dc motors. i. open-circuit field. IEEE transactions on magnetics , 29(1):124–135, 1993. [2] Guhuan He, Zhenyu Huang, and Dayue Chen. Two-dimensional field analysis on electromagnetic vibration-and-noise sources in permanent-magnet direct current commutator motors. IEEE Transactions on Magnetics , 47(4):787–794, 2011. [3] Bernard Hague. The Principles of Electromagnetism Applied to Electrical Machines:(formerly Titled: Electromagnetic Problems in Electrical Engineering). , volume 246. Dover Publications, 1962. [4] Damir Zarko, Drago Ban, and Thomas A Lipo. Analytical calculation of magnetic field distribution in the slotted air gap of a surface permanent-magnet motor using complex relative air-gap permeance. IEEE Transactions on Magnetics , 42(7):1828–1837, 2006.

Figure 5: Experimental measurements of the frequency response function for the motor shell.

Pies FRFs with adhesive thickness

Figure 6: ABAQUS model showing shell and magnets

Figure 7: ABAQUS predictions of the frequency response function with two thickness adhesive layers, one of 0.5 mm and one of 0.8 mm.

[5] Zhimin Wan, Shande Li, Qibai Huang, and Ting Wang. Structural response reconstruction based on the modal superposition method in the presence of closely spaced modes. Mechanical Systems and Signal Processing , 42(1-2):14–30, 2014. [6] Hsiang-Chuan Tsai. Modal superposition method for dynamic analysis of structures excited by prescribed support displacements. Computers & structures , 66(5):675–683, 1998.

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