Figure 52 shows that the shaft centers itself at high rotating speeds The disk

Figure 52 shows that the shaft centers itself at high

This preview shows page 325 - 327 out of 553 pages.

Figure 5.2 shows that the shaft centers itself at high rotating speeds. The disk rotates about its axis through the center of gravity at speeds above the critical ( Ω ω 1 ) . This fact is utilized in centrifuges and other machines in which bal- ancing is not an option due to the eccentric stock (Fig. 5.9). The system is tuned to run above the critical speed using soft springs in neck bearings. The disk rotates about its axis through the center of gravity, i. e. the springs in the neck bearings are deflected at the rotational frequency by the magnitude of eccentricity and apply a corresponding force to the frame. It is considerably smaller for a soft neck bearing than the respective unbalancing force that would occur with a rigid bearing. 5.2.2 Passing through the Resonance Point Many drives are operated at speeds above the critical, i.e. the rotors have to pass through one or several resonance points during start-up until they reach their oper- ating speed, and the same is true for coasting down and braking. This applies to the bending vibrations of rotors (such as turbomachines, textile mandrils, spin-driers, centrifuges), but also to machine foundations (see, for example, Fig. 3.14), torsional oscillators (such as vehicle drive trains, fans), and coupled-mass oscillators (such as screens, belt drives). Extreme loads are reached during this passing through res- onance. Of primary interest is the behavior of the rotor near resonance since the largest dynamic deflections occur there. If one can assume that the rotor starts with a constant angular acceleration α , the resulting amplitudes are as shown in Fig. 5.3. Fig. 5.3 Amplitude when passing through resonance as a function of acceleration
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316 5 Bending Oscillators This is to show the result of the calculation only, see Fig. 5.3. The maximum am- plitude is not reached when excitation frequency and natural frequency coincide, but slightly later. The maxima shift towards higher speeds during acceleration and towards lower speeds during deceleration processes. The faster the passing through resonance the smaller are the amplitudes. The dimensionless characteristic param- eter α/ω 2 1 serves as a measure. If one simulates the start-up process considering the motor characteristic, it turns out that the speed increases at a slower rate near resonance because the drive has to generate energy for moving the resonating foun- dation. The rotor puts up a larger resistance than the one that would match its own rotational inertia when passing through the resonance point. The reverse effect occurs when decelerating, i. e. at declining speed: a moment is exerted by the foundation onto the rotor so that the latter accelerates in excess of what the input torque would cause. The excess energy of the vibrating foundation is then transferred onto the rotor. The effect that the foundation acts as an additional drive can be utilized for the efficient operation of vibrating machines as oscillators, e. g. in a vibrating compactor, see Sect. 5.4.5 “Passing through resonance” in [4].
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