Optical Tables 101... What You Need to Know
VIBRAPLANE Vibration Isolation Protects the Critical Subsystems of Large Equipment
All equipment have components with natural frequencies that are critical because they exist in the generalized 8 to 200 Hz environmental spectrum.
For illustration, Figure 46.1 shows the Transmissibility and resonant responses of three components in typical equipment. The resonant responses, or Q’s of these components exceed the allowable level, which is set at Q=1.75 for this example. Figure 46.2 shows the responses of the same components above, after the introduction of isolation at 1 Hz. The roll off isolator transmissibility acts to reduce the input to each of the three critical components illustrated. Now without altering the design of each component, their respective resonant responses are all below the allowable limit, and no failure will occur.
KSI Optical Tables... Better Built Through Better Design
Understanding Optical Table Specifications
At present there is no single accepted standard practice for comparison of optical tables from different manufacturers. This accounts for much of the unnecessary complexity in technical performance specifications introduced by different makers.
At KSI, we want you to be aware of the important difference between reality and specification hype. For example – flatness, stiffness, weight, static deflection, dynamic compliance, natural frequency, and damping are real properties of any optical table, and these are directly measurable by standard instruments and techniques. However, some manufacturers use theoretical estimates of intangible performance parameters which cannot be verified. For optical table selection and comparison, real measured data and test results can never be replaced by theoretical computed estimates based on idealized assumptions and unproven hypotheses.
Consider the Basics When Selecting and Specifying Optical Tables
There is so much technical jargon and unnecessarily complicated static and dynamic deflection concepts being used to sell optical tables and vibration isolation equipment that it’s easy to become confused and distracted from what you really need to know. We would like you to review the following basics so you can feel confident when selecting an optical table or isolation system for your application.
Natural Frequency
Static Deflection
Optical tables should be stiff to minimize relative deflection, or sag, between supports due to their own weight. High stiffness in our tables and breadboards is insured by our proprietary damped rigid epoxy, and is not compromised by plastic or viscoelastic laminations. The high stiffness of our tables is confirmed by their high natural frequencies in Figure 47.1 and the corresponding very small static deflections shown in Figure 47.2. The maximum static (1g) deflection of KSI tables relative to their supports has been tested and conforms to simple beam deflection theory. It should also be noted that the tables’ static deflections are significantly less than their flatness tolerances.
Deflection Due to Equipment Load
In addition to minimizing static deflection, the high stiffness of our tables minimizes relative deflection due to weight of components and equipment installed on the table. If you assume that the installed equipment is uniformly distributed across the table, then the added table deflection due to the equipment is determined simply by multiplying the deflection from Figure 47.2 by the (equipment/table) weight ratio. If you are using heavy equipment, we recommend that you repeat this deflection computation with different table lengths and thicknesses until you obtain an acceptably low value, say 10%, of the precision required by your application.
Unit Load Deflection
Optical Table Weight
Figure 48.1 presents the approximate weights for 48" wide 5300 Series tables of various standard thicknesses. The weights of other corresponding tables of different width and skin thickness may be estimated by multiplying the values in Figure 48.1 by the ratios of (actual width/48") or (actual skin thickness/ .180") as appropriate. Our steel honeycomb optical tables are inherently structurally efficient and weigh substantially less than a solid steel or granite equivalent flat surface plate. Nevertheless, a certain amount of weight is desirable for stability and resistance to vibratory forces. Thickness and length govern the table weight. Two rules of thumb are: (1) the table should weigh between 2.5 and 5 times the mounted equipment; and (2) the minimum table thickness should be between 6% and 10% of the length. Use these rules to define the minimum weight of your table selection. For example, for precision applications the minimum recommended standard thickness of a 10' long table should be 8" or 12" thick.
Static and Dynamic Deflection and Compliance
The Unit Load Deflections in Figure 47.3 can be regarded as a graph of Static Compliance values at the centerpoints of the tables presented. In contrast, Dynamic Compliance is the deflection response due to a unit vibratory force. Hence vibration frequency, table resonance and internal damping will define maximum response deflection. The table’s dynamic response at the corner; i.e.; Corner Compliance, has become a standard measurement for specification comparisons.
Damping and Dynamic Compliance
Optical tables should possess sufficient internal structural damping (energy dissipation) to control their relative deflection resonant response to random high frequency building vibration. Internal damping also minimizes modal resonant response to transient disturbances.
The excellent damping properties in all our VIBRAPLANE Optical Tables is demonstrated by the typical Compliance Spectra included in the technical data with each of our products. The Compliance Spectra serve the same function as conventional Transmissibility Curves. These characterize the system response deflection, including resonant amplification, as a function of frequency. A low resonant response is one of the important criteria for selection of optical tables.
The resonant Q factor, or maximum transmissibility of the lowest resonance mode for KSI Optical Tables is set during production in a range as follows:
5300 Series:
Q = 2–6
The corresponding Maximum Compliance values for 5300 Series Tables are represented in Figure 48.2.
To aid you in the selection of optical tables for your application we provide you with manufacturing specifications in addition to real measured and verifiable static and dynamic table properties such as shown in Figures 47.1 to 49.2. However, for reference purposes and comparison to various manufacturers’ calculated table specifications, we want you to know that regardless of model or price category, the computed or predicted “Dynamic Deflection Coefficients” and “Maximum Relative Deflection”responses of KSI honeycomb tabletops are the lowest in the industry. These are presented in Figures 49.1 and 49.2 as discussed.
RD = (yx) = W_{ a} Q g^{ 2} / 32 (pie symbol)^{ 3} f_{ n} ^{ 3} )^{ 1/2} = 12.25 (W_{ a} Q / f_{ n} ^{ 3} )^{ 1/2} (8)
Where:
(Q / f_{ n} ^{ 3} )^{ 1/2} = (DDC) = Dynamic Deflection Coefficient of tabletop (9)
Q = Resonant transmissibility of table W_{ a} = Floor Random Vibration Spectral Density, (g^{ 2} /Hz = floor mean squared vibration acceleration per 1 Hz band) RD_{ max} = (nonisolated) maximum Relative Deflection of tabletop on rigid supports
Typical estimated random floor vibration conditions are:
Light traffic:
W_{
a}
= 10^{
10}
g^{
2}
/Hz
The Dynamic Deflection Coefficient (DDC) for 5300 Series Tables is derived from Equation (9) in conjunction with natural frequency and Q data contained in Figures 47.1 and 48.2, and plotted in Figure 49.1 for ready reference.
In vibration analysis it is reasonable to assume that an optical tabletop can be represented as a rigid massspringanddamper single degreeoffreedom system up to its first resonance. Therefore, the above single degreeoffreedom Equation (8) is only applicable to a tabletop without isolation supports.
If isolators are added, the system has additional deflection coordinates or degreesoffreedom and Equation (8) is not applicable. To resolve this in a simplified (quasitheoretical) manner, Industry has proposed two correction factors and a modified interpretation of damping parameter Q . The correction factors are:
IRD_{ max} = 12.25 (W_{ a} Q / f_{ n} ^{ 3} )^{ 1/2} x 0.02 (10)
The Maximum Relative Deflection of vibration isolated 5300 Series tabletops is derived from Equations (8) and (10) in conjunction with Figure 49.1 and is presented in Figure 49.2 for ready reference.
^{ 1} Crede, C.E. “Failure Resulting From Vibration”, Random Vibration, Volume 2, Edited by S.H. Crandall, MIT Press, 1963
