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Traditional AC/AC Converters
Published in Fang Lin Luo, Hong Ye, Power Electronics, 2018
where k is any integer from unity to infinity, and n is any integer from zero to infinity. It may be observed that for certain ratios of fO/fi, the order of harmonics may be less than or equal to the desired output frequency. All such harmonics are known as subharmonics as they are not higher multiples of the input frequency. These subharmonics may have considerable amplitudes (e.g., with a 50-Hz input frequency and a 35-Hz output frequency, a subharmonic of frequency 3 × 50 to 4 × 35 = 10 Hz is produced, the magnitude of which is 12.5% of that of the 35-Hz component) and are difficult to filter and thus are objectionable. Their spectrum increases with an increase of the ratio fO/fi and thus limits its value at which a tolerable waveform can be generated.
Effects of Harmonics
Published in J.C. Das, Harmonic Generation Effects Propagation and Control, 2018
We discussed subharmonic frequencies in Chapter 2 in conjunction with a series compensation of transmission lines. Generally, the transient currents excited by subharmonic resonant frequencies damp out quickly due to positive damping. This is a stable subharmonic mode. Under certain conditions, this can become unstable. We know that in a synchronous machine, the positive sequence subharmonic frequencies will set up a flux that rotate in the same direction as the rotor, and its slip frequency = fe − f, where fe is the frequency of the subharmonic. As fe is <f, it is a negative slip and contributes to the negative damping. The synchronous machine can convert mechanical energy into electrical energy associated with subharmonic mode. If the negative damping is large, it can swap the positive resistance damping in the system and a small disturbance can result in large levels of currents and voltages. The subharmonic torque brought about by the difference frequency fe − f rotates in a backward direction with respect to the main field and if this frequency coincides with one of natural torsional frequencies of the machine rotating system, damaging torsional oscillations can be excited. This phenomenon is called subsynchronous resonance.
Vibration-Based Condition Monitoring in Rotating Machinery
Published in Rajiv Tiwari, Rotor Systems: Analysis and Identification, 2017
The complicated nonlinear phenomena of rotor system with pedestal looseness were analyzed by applying rotor dynamics and nonlinear dynamics theory by Li et al. (2005). Through the bifurcation diagrams of the change of rotating speed, it was discovered that the vibration of rotor system with pedestal looseness was violent in the subcritical whirling speed. On the contrary, in the supercritical whirling speed, vibration of the rotor was weak. But, under certain conditions, subharmonic resonance could occur and induce violent vibration. In addition, characteristics of vibration of the rotor with pedestal slackness were studied by frequency spectrums. The result of the analysis provided a theoretical reference for the rotor fault diagnosis of the rotating machinery.
Impact of Whirl and Axial Motion on Ball Bearing Turbocharger Dynamics
Published in Tribology Transactions, 2023
Benjamin Conley, Farshid Sadeghi
Overall, the frequency spectrum of the whirl measured from the test rig is similar to that produced by the turbocharger model. Figures 6a and 6b portray the frequency spectrum of the experimental whirl and simulated whirl, respectively. The experimental spectrum shows a significant half-speed subharmonic that occurs up to 30 krpm, with less significant third- and quarter-speed subharmonics. The simulated subharmonics start and extend higher into the speed range. However, by 50 krpm both results are synchronous.
Primary and secondary resonance analysis of FG/lipid nanoplate with considering porosity distribution based on a nonlinear elastic medium
Published in Mechanics of Advanced Materials and Structures, 2020
Moslem Mohammadi, Abbas Rastgoo
The subharmonic resonance case is studied in this section. The subharmonic resonance case happens when the excitation frequency is larger than the natural frequency. The subharmonic resonance happens in the triple of the linear natural frequency. In this section, some of the interesting results of the subharmonic resonance case are presented.