210 H. Amlinger et al. The acoustic generated noise from traction motors at PWM operation depends on various electromagnetic, mechanical, acoustic, and control parameters, e.g. pole number, stator slot number, rotor slot number, motor operating frequency, PWM switching frequency, and mechanical natural frequencies and vibration modes of the system. That is, many different aspects and properties are involved in the noise generation. Electromagnetic noise from induction motors has been subject to research for a very long time, starting with the characterization of acoustic noise generated by Maxwell forces [1]. Also the influence of PWM supply has been addressed extensively [2–4], and the interaction between PWM harmonics and the mechanical structure (slotting) has been studied [5, 6]. Later, this work has continued, considering different force lines at PWM operation and modeling, simulations, and experimental validation of the same [7–10]. In this paper the operational deflection shapes of a three-phase asynchronous motor at PWM operation are investigated. The results of experimental tests are presented, discussed and compared to what is expected based on literature research. In an accompanying paper [11] a reduced order modal model of the same motor, based on experimental modal analysis, is presented and evaluated. 20.2 Magnetic Noise Characterization at PWM Operation The electromagnetically generated acoustic spectrum can be determined from the radial component of the air-gap Maxwell forces. The electromagnetic force spectrum results from the interaction between two flux density waves, i.e. a combination of two permeance harmonics and two magnetomotive (mmf) harmonics. These harmonics can be expressed using Fourier series. The vibration forces for a motor at PWM operation can be divided into three main types: slotting vibrations, PWM vibrations and slotting PWM vibrations [5, 7]. The number of force harmonics is infinite, but the amplitude of the corresponding harmonics in the vibration response is inversely proportional to m4 where mis the spatial order. Therefore, only the lowest spatial order forces result in vibration levels (and thereby noise) of significance. For traction motors, the spatial orders of interest are those of order zero to four [9]. Resonances with large vibration levels occur when there is a match in both frequency, between exciting force and structural mode natural frequency, as well as spatial order, between exciting force and structural mode shape. The propagation direction of the vibration waves can be indicated with positive/negative frequencies, or positive/negative spatial orders. The latter is used in this paper. 20.2.1 Slotting Vibrations The interaction between some slotting permeance harmonics and the fundamental stator mmf causes so called slotting vibrations. Slotting vibrations are independent of the type of supply, which means they are equally strong for both sinusoidal and PWM supplies. Therefore, a motor that is noisy at sinusoidal supply will remain noisy also at PWM operation. The main slotting forces can be divided into three groups, characterized by frequency and spatial order, see Table 20.1. Variables kr and ks are positive integers from the Fourier series of the permeance distribution, Zr and Zs are the number of rotor and stator slots respectively, s is the slip, and p the number of pole pairs. The higher kr and ks are, the lower are the permeance harmonics, and the lower is the corresponding force harmonic. Therefore, the force harmonics with highest magnitude are given by kr Dks D1[8]. Table 20.1 Frequency and spatial order of the main slotting vibrations Name Frequency f Spatial order m F slot fs.krZr.1 s/=p 2/ krZr ksZs 2p F0 slot fs.krZr.1 s/=p/ krZr ksZs FCslot fs.krZr.1 s/=pC2/ krZr ksZs C2p
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