MAURER VIBRATION ISOLATION
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Technical Information /l\ MAURER MAURER Vibration Isolation MAURER Vibration Isolation

MAURER Vibration IsolationVibration Isolation mx+c x + kdvnx = fex mx+c(x-xGX)+kdvn (x-x0X) = O Vibrations due to kinematic and force excitations Undesirable and inacceptable vibrations in buildings and rooms with sensitive equipment such as microscopes, lasers and other vibration sensitive devices are caused by the following two ways of excitations (Fig. 1, left): ■ Kinematic excitation: ground vibrations with displacement xex(t) due to traffic, earthquake, wind, explosions and other loadings excite the sensitive equipment. ■ Force excitation: inertial forces fex(t) of rotating machines...

MAURER Vibration Isolation MAURER Natural frequency The natural, i.e. undamped frequency in Hertz of the single degree-of-freedom oscillator is (3) Damping ratio The damping ratio C, of the oscillator is given by the viscous damper coefficient c of the oil damper c c c(27tf0) (7) where the dynamic stiffness kdyn describes the stiffness of the spring element under dynamic loading. For spiral steel springs kdyn is identical to the static stiffness k while kdyn represents a linearized value for elastomer springs. In practice kdyn is usually given in N/mm which leads to the following...

MAURER Vibration Isolation (15) Forced excitation If the single degree-of-freedom oscillator is excited by the base displacement or the machine-induced force the single degree-of-freedom system vibrates at the frequency of excitation fex. If the excitation frequency equals the natural frequency, i.e. fex = f0, resonant vibration with extremely large amplitudes occur whose magnitude depends on the damping ratio only. Amplification function The displacement amplification of a single degree-of-freedom system with force excitation is expressed by the displacement amplitude divided by the static...

MAURER Vibration Isolation MAURER Transmissibility The force transmissibility for force excitation and the displacement transmissibility for base excitation are defined by |a| in decibel (dB) Mcb =20l°gio(M) <18) Some typical values of |a| and |a|dB are given in Table 1. Table 1 - Typical values of |a| and |a|dB Trade-off behaviour of damping High values of C, reduce resonant amplitudes but lower the attenuation in the frequency range X>j2, i.e. lower a good roll-off behaviour; the opposite effect is observed for small values of t,. Thus, the optimal design of C, strongly depends on the...

MAURER Vibration Isolation Isolation efficiency The isolation efficiency i is defined in % for the region of attenuation (X > V2 ) only (Fig. 9) i [%] = (l-|ot|)-100 (21) which can be approximated for small damping (£< 5%) (22) Expression (22) can be solved for the frequency ratio X and thereby for the natural frequency f0 Putting the required isolation efficiency ireq into (23) yields the required natural frequency general formulation (21) of the isolation efficiency. Assuming £ =30%, which generates sufficient mitigation of resonant vibrations, leads to f0«fex/3.5 and ensures i>ireq...

MAURER Vibration Isolation MAURER Transfer function for flexible structures The impedance of the structure Z2 must be considered for the computation of the transfer function |a| if (Fig. 10, left): ■ the flexibility of the floor structure cannot be neglected, i.e. Z2 cannot be assumed to be infinitely high, and ■ the modal mass m2 of the floor structure is less than 10 times the mass m, of the machine. For the derivation of the transfer function |a| in its general format the model of the single degree-of-freedom system (Fig. 1, right) must be replaced by a two degree-of-freedom system...

MAURER Vibration Isolation MAURER Vibration Isolation in Seismic Zones Building vibrations due to earthquake excitation For the vibration isolation of sensitive equipment / sensitive structures in buildings that are located in seismic zones vibration isolation becomes a demanding task because of the following facts (Fig. 12): ■ Mainly horizontal vibrations: earthquakes excite buildings predominantly in horizontal direction. ■ Large horizontal displacements: compared to typical vertical vibration amplitudes of isolation systems on the order of micro-meters the relative motion in the...

MAURER Vibration IsolationDesign Considerations x2 =3xg -x3 steel spiral springs that are characterized by linear stiffness behaviour, i.e. k^n = k, very small (linear) Fundament plate An additional stiff fundament plate between machine and isolation system must be included if the steel frame of the machine is not stiff enough to ensure that all spring elements of the isolation system are working in phase. The mass of the additional fundament plate also helps to reduce the relative diplacement amplification |p| of the machine because the mass m of the single degree-of-freedom system is...