| On the Use of Vibration Synthesis to ease Electric Machine Powertrain Design Chauvicourt F., Ciceo S., Van der Auweraer H. Engineering Services RTD Siemens Industry Software NV Leuven, Belgium fabien.chauvicourt@siemens.com Abstract—This paper provides e-machine designers a critical study on the vibration synthesis algorithm that calculates the vibrations of an electric machine responsible for magnetic noise. It separates the computations into two distinct categories: offline and online. Comprehensive parameters are input to an offline simulation system where generic magnetic forces and vibration transfer functions are created. This generic data combined with operational loads from system-level simulations refers to the online simulation environment. The methodology is applied to an interior Permanent Magnet Synchronous Machine (PMSM), and compared to the standard procedure where run-up simulation can become time-expensive due to the extensive use of Finite Elements (FE) methods. Vibration results show discrepancies of harmonic amplitude content essentially coming from the force truncation made in the vibration synthesis, for which a selection protocol is proposed. Yet the offline simulations permit to front- load the computational efforts thus implying the use of the technique in system-simulation environments. Index Terms—vibration synthesis, electric machine, simulation, PMSM, computational effort I. INTRODUCTION With the growing expansion of electric vehicles and the need for efficient system-level designing processes, it is essential to define simulation frameworks that comply with accuracy, speed while incorporating every important physics of the system. For electric machine powertrains, not only the overall efficiency but also the Noise and Vibration (NV) charac- teristics are gradually introduced in the design optimization schemes, essentially with the emerging technologies relying less on permanent magnets [1]. The particular whining noise associated to electric machines eventually disturbs comfort and originates from a chain of multiple physical phenomena. Electromagnetic field variations generate magnetic forces in the air-gap which apply on both the stator and the rotor. In the case of outer stator topology, the forces activate the stator in the form of vibrations that latter translate to acoustic pressure fluctuations through structural surface velocity [2]. In practice, this phenomenon can be simulated fully analyt- ically. Eventually equivalent circuits of the machine permit to compute airgap forces which are input of a simple structural ring model, and where acoustic pressure is estimated from finite/infinite cylinder theory [3]. Although impressively fast, this method lacks accuracy. Finite Element (FE) models might address this issue by modelling precisely the machine geome- try and components, for all physical phases of the simulation [4]. Yet for variable-speed/torque simulation purposes and for including system level simulation, FE models or co- simulation approaches cannot be considered for computational reasons. Thus, hybrid modelling frameworks can be envisaged [5]. These methods try to establish an efficient and reduced simulation approach by smartly combining the two previous ones. An example of such application is often referred to as look-up table approach. Offline simulations - electromagnetic, structural, acoustic - are performed and generate a component behavior depending on a set of inputs. Stored in tables, they are utilized in online system-level simulations where variable operating conditions are imposed. This type of approach al- lows to isolate computationally expensive tasks, to concentrate on fast operating condition simulation. Particularly regarding vibro-acoustic behavior, another approach is referred to as vibration synthesis, where instead of building tables, the FE model is reduced using a priori known generic force shapes. The method has gained interest over the last decade thanks to the exhaustive work of Boesing et al. [6], e.g. for combined experimental and numerical predictions [7], or as a quick alternative to standard FE methods reviewed in [8]. However consistent comparisons with FE methods in terms of accuracy against computational efforts is not documented to the authors knowledge. In this paper, the efficiency of vibration synthesis methodol- ogy is evaluated. Section II lays the foundations to the multi- physical problem to solve, by introducing the standard FE technique and the vibration synthesis. Section III describes the application case which is a PMSM sized for an automotive vehicle and the offline simulation results. Finally Section IV confronts both methods in terms of accuracy of the simulated vibration and their associated computational efforts, to con- clude on the vibration synthesis advantages and drawbacks. II. THEORETICAL BACKGROUND A. Standard modelling process In a standard modelling process for vibration prediction, a magnetostatic time-stepping 2D FE analysis is performed for an operating point (torque T defined from a set of direct and quadrature currents (id,iq), speed N ) [8]. The resulted time-dependent magnetic field allows to calculate the magnetic force densities in the air-gap F T,N (t) using the Maxwell stress tensor [9]. They contain radial, tangential and axial