When installing the equipment and machinery which create periodic loads (machines with rotating parts, crank mechanisms, etc.) on the structures, the amplitude of a certain displacement or internal force depends both on the natural frequencies of the structure ωi (i = 1, …, n), and on the frequency θ of the exciting force
P = P0 sin (θt).
Peak value P0 of the harmonic load is defined by the design assignment and depends on the design of the equipment which causes this load. If there are no accurate data, you can use the recommendations of SNiP 2.02.05-87 “Foundations of Machines with Dynamic Loads” and assume
\[ P_{\mathrm{0}} = \mu \sum\limits_{k=1}^m {Q_{k} } \quad, \]
where Qk — weight of each rotor of the machine, and the coefficient μ is determined by the Table 1:
Table 1
Type of the machine |
Coefficient μ |
|---|---|
Turbomachines |
0,20 |
Electric machines with the number of revolutions nrev per minute: more than 750 from 750 to 500 less than 500 |
0,20 0,15 0,10 |
Centrifuges with a rotor diameter d, m |
d (nrev/1000)2 |
Centrifugal pumps |
0,15 |
Smoke exhaust fans and fans |
0,8 (nrev/1000)2, but not less than 0,20 |
Due to the inaccuracy of determining the natural frequencies caused both by the approximate representation of the design model, and the rounding errors in the arithmetic calculations, as well as the possible instability of the angular frequency of excitation θ, reaching 10%, it is necessary to assess the behavior of the system when the frequency θ varies in a certain range from θ1 to θ2. It might be particularly important for the values θ, approaching one of the natural frequencies ωi (near-resonant mode), that can occur when starting or stopping the machine. The amplitude-frequency characteristic (AFC) is a relationship between the peak value of a certain component of the stress-strain state (displacement, stress, internal force) and the frequency of the excitation θ. It is determined by the calculation of the system for the harmonic action at the frequencies of the exciting force changing in the specified range. The peak value of the force P0 remains unchanged.