Equation 3, the basis for the Relative Motion Formula in Figure 1, enables you to calculate the worst-case relative motion between two points on a table at the natural frequency (fn). Calculated results agree closely with measured performance generated by interferometric methods. For your convenience, Newport also provides a calculated Relative Motion value for all tables and breadboards, which accurately reflects performance in a typical quiet laboratory environment.
The second term of the Relative Motion equation, (Q/fn3)1/2, is the Dynamic Deflection Coefficient, a figure of merit derived from the table top’s minimum resonant frequency and damping efficiency, which together quantify the table top’s dynamic performance. The third term, (PSD)1/2, is the contribution of the applied vibration intensity level, which can be measured directly or estimated using the table (random vibration is assumed). Isolator transmissibility, the fourth term, accounts for the attenuation of ground vibrations at the frequency range of interest through the support structure.
Note that this formula is a worst-case estimate of relative motion, and that the actual relative motion experienced in most typical installations will be less. On the other hand, if the applied vibration includes sharp peaks at certain frequencies (i.e., non-random vibration), the actual relative motion may be considerably higher.
Calculate the worst-case (or maximum) Relative Motion value (RM) between two points on a 4 ft x 8 ft x 12 in. (1200 x 2400 x 305 mm) RS 2000™ table top installed in a lab near a street. Please see Research Grade Optical Tables for the compliance curve.
First of all, find the maximum Dynamic Deflection Coefficient.
For the resonance peak at:
fn ≈ 190 Hz, Q ≈ 2.7, (Q/fn3)1/2 ≈ 0.6 x 10-3.
For the resonance peak at:
fn ≈ 270 Hz, Q ≈ 22, (Q/fn3)1/2 ≈ 1.1 x 10-3.
Assume
g = 386 in./sec2
PSD = 10-9 g2/Hz
T <0.01 at typical frequency range of interest
Then the relative motion: