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TMC Technical Background
April 23, 2014
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4.0 High-Performance Table Tops 
Table tops are the platform for conducting many types of measurements and processes. They can serve as a mechanical reference between different components (such as lasers, lenses, film plates, etc.) as well as simply providing a quiet work surface. Tops typically use one of three constructions: a composite laminate, a solid material (granite) or a lightweight honeycomb. The choice of construction depends on the type and size of the application.
Figure 11 shows a typical laminated construction. These are usually 2 to 4 in. thick and consist of layers of steel and/or composite materials epoxy-bonded together into a seamless stainless steel pan with rounded edges and corners. A visco-elastic adhesive can be used between the plates to enhance the damping provided by the composite layers. All bonding materials are chosen to prevent delamination of the assembly due to heat, humidity, or aging. The ferromagnetic stainless steel pan provides a corrosion-resistant, durable surface which works well with magnetic fixtures. “Standard” sizes for these tops range from 24 in. square to 6 x 12 ft, and can weigh anywhere from 100 - 5,000 lbs. This type of construction is not well suited to applications which require large numbers of mounting holes (tapped or otherwise). The ratio of steel to lightweight damping composite in the core depends primarily on the desired mass for the top.
There are many applications in which a heavy top is of benefit. It can lower the center-of-gravity for systems in which gravitational stability is an issue. If the payload is dynamically “active” (like a microscope with a moving stage), then the increased mass will reduce the reaction motions of the top. Lastly, steel is very strong, and very high mass payloads may require this strength.

Granite and solid-composite tops offer a relatively high mass and stiffness, provide moderate levels of damping, and are cost effective in smaller sizes. Their non-magnetic properties are desirable in many applications, and they can be lapped to a precise surface. Mounting to granite surfaces is difficult, however, and granite is more expensive and less well damped than laminate tops in larger sizes. The highest performing work surfaces are honeycomb core tables.

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4.1 Honeycomb Optical Tables
Honeycomb core table tops are very lightweight for their rigidity and are preferred for applications requiring bolt-down mounting or larger working surfaces. They can be made in any size from 1 ft on a side and a few in. thick, to 5 x 16 ft and over 2 ft thick. Larger tops can also be “joined” to make a surface which is almost unlimited in size or shape. The smaller surfaces are often called “breadboards,” and the larger sizes “optical tops” or “optical tables.”
Honeycomb core tables were originally developed for high-precision optical experiments like holography. They evolved due to the limitations of granite surfaces, which were extremely heavy and expensive in larger sizes and were difficult to securely mount objects to. The goal was to develop a work surface with the stability of granite without these drawbacks.

Honeycomb core tables are rigid for the same reasons as a structural “I-beam.” An I-beam has a vertical “web” which supports a top and bottom flange. As weight is applied to the beam, the top flange is put in compression and the bottom in tension, because the web holds their separation constant. The primary stiffness of the beam comes from this compression and extension of the flanges. The web also contributes to the stiffness by resisting shear in its plane.

The same thing happens in an optical table (see Figure 12). The skins of the table have a very high resistance to being stretched or compressed (like the flanges of the I-beam). The honeycomb core is extremely resistant to compression along its cells (serving the same role as the I-beam’s web). As the core density increases (cell size decreases), the compressional stiffness of the core and its shear modulus increase, and the mechanical coupling to the skins improves – improving the performance of the table.

Optical tables are also much better than granite surfaces in terms of their thermal properties. Because of their metal construction and very low heat capacity (due to their relatively light mass), honeycomb core tables come to thermal equilibrium with their environment much faster than their granite counterparts. The result is a reduction in thermally induced distortions of the working surface .
figure 12

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4.2 Optical Table Construction
There are many other benefits to using a honeycomb core. The open centers of the cells allow an array of mounting holes to be placed on the table’s surface. These holes may be capped to prevent liquid contaminants from entering the core and “registered” with the core’s cells. During the construction of TMC optical tops, the top skin is placed face down against a reference surface (a lapped granite block), and the epoxy, core, sidewalls, bottom skin, and damping system built up on top of it. The whole assembly is clamped together using up to 30 tons of force. This forces the top skin to take the same shape (flatness) of the precision granite block. Once the epoxy is cured, the table’s top skin keeps this precise flatness (typically ±0.005 in.) over its entire surface.
TMC’s patented CleanTop® II design allows the core to be directly bonded to the top and bottom skins of the table. This improves the compressional stiffness of the core and reduces the thermal relaxation time for the table. The epoxy used in bonding the table is extremely rigid without being brittle yet allows for thermal expansion and contraction of the table without compromising the bond between the core and the skins.

Honeycomb core tables can also be made out of a variety of materials, including nonmagnetic stainless steel, aluminum for magnetically sensitive applications, and super invar for applications demanding the highest grade of thermal stability. Lastly, the individual cups sealing the holes in the top skin (unique to TMC’s patented CleanTop® II design) are made of stainless steel or nylon to resist a wide range of corrosive solvents.

The sidewalls of the optical table can be made out of many materials as well. Some of TMC’s competitors’ tops use a common “chipboard” sidewall which, though well damped, is not very strong and can be easily damaged in handling or by moisture. TMC tables use an all-steel sidewall construction with constrained-layer damping to provide equally high levels of damping with much greater mechanical strength.

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4.3 Honeycomb Optical Table Performance
The performance of an optical table is characterized by its static and dynamic rigidity. Both describe how the table flexes when subjected to an applied force. The first is its response to a static load, while the second describes the “free oscillations” of the table.
Figure 13 shows how the static rigidity of a table is measured. The table is placed on a set of line contact supports. A force is applied to the center of the table, and the table’s deflection (figure) measured. This gives the static rigidity in terms of figurein/lbf (or figurem/N) This rigidity is a function of the table’s dimensions and the physical properties of the top and bottom skins, sidewalls, core, and how they are assembled.
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4.3.1 The Corner Compliance Curve
Dynamic rigidity is a measure of the peak-to-peak motion of a table’s oscillations when it is excited by an applied impulse force. When hit with a hammer, several normal modes of oscillation of the table are excited, and each “rings” with its own frequency. Figure 14 shows the four lowest frequency modes of a table. Dynamic compliance is measured by striking the corner of a table with an impact testing hammer (which measures the level of the impact’s force near the corner of the table). The table’s response is measured with an accelerometer fastened to the top as close to the location of the impact as possible. The signals are fed to a spectrum analyzer which produces a corner compliance curve. This measures the deflection of the table in figurein/lbf (or mm/N) for frequencies between 10 and 1,000 Hz.
Each normal mode resonance of the top appears as a peak in this curve at its resonant frequency. The standard way to quote the dynamic compliance of a top is to state the peak amplitude and frequency of the lowest frequency peak (which normally dominates the response). Figure 15 shows the compliance curve for a table with low levels of damping (to emphasize the resonant peaks). The peaks correspond to the modes shown in Figure 14. The curve with a slope of 1/f 2is sometimes referred to (erroneously) as the “mass line,” and it represents the rigid-body motion of the table. “Mass line” is misleading because the rigid-body response of the top involves rotational as well as translational degrees of freedom, and, therefore, also involves the two moments of inertia of the table in addition to its mass. For this reason, this line may be 10 times or more above the line one would calculate using the table’s mass alone.
Figure 15: f0-f3 show the four lowest resonances of the table.   

The compliance curve is primarily used to show how well a table is damped. The higher the level of damping, the lower the peak in the compliance test, and the quicker the table will ring down after an impact disturbance. There are two ways to damp the modes of a table: narrow-band and broadband damping. The first uses tuned mechanical oscillators matched to the frequencies of the normal mode oscillations to be damped. Each matched oscillator can remove energy at a single frequency. TMC uses broadband damping, where the mode is damped by coupling the table to a second mass by a lossy compound. This damps all modes and all frequencies.

Tuned damping has several problems. If the frequency of the table changes (from placing some mass on it), then the damper can lose some of its effectiveness. Also, several dampers must be used, one for each mode (frequency) of concern. This compounds the matching problem. Each of these dampers are mounted in different corners of the table. This results in different compliance measurements for each corner of a table. Consequently, the quoted compliance curve may only apply for one of the four corners of a top. In addition, tuned dampers are strongly limited in how far they can reduce the Q. It is difficult, for example, to get within a factor of 10 of critical damping using reasonably sized dampers.

In broadband damping, the secondary masses are distributed uniformly through the table, producing a compliance curve which is corner-independent. It is also insensitive to changes in table resonant frequencies and will damp all modes – not just those which have matched dampers. In fact, TMC’s highest grade tables can have near critical damping of the lowest modes (depending on aspect ratios, thicknesses, etc.).

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4.3.2 Compliance Curves as a Standard
Although used as a standard for measuring table performance, the corner compliance curve is far from a uniform and unambiguous figure of merit. The problem is not only with tables using tuned damping. All measurements are extremely sensitive to the exact location of the test impact and the monitoring sensor. TMC measures compliance curves by placing the sensor in a corner 6 in. from the sides of the table and impacting the table on the inboard side of the sensor. Since the core of the table is recessed from the edge of the table by 1-2 in., impacting the table closer to the corner produces “edge effects.” The result is a test which is inconsistent from corner to corner or even impact to impact. On the other hand, measuring further from the corner can bring the sensor and the impact point dangerously close to a nodal line for the first few modes of the table (Figure 14). This is so sensitive that a few inches can have a dramatic effect on the measured compliance for a top

It is also important to properly support the table being tested. TMC supports tables at four points, along the two nodal lines 22% from the ends of the table. Either pneumatic isolators or more rigid rubber mounts can be used for this test (though rubber mounts may change the damping of higher-order modes). Though this is fairly standard with manufacturers, the customer must be aware that the compliance test will only represent their setup if they support their top in this way.

Nodal shapes present a major problem in the uniformity of the corner compliance curve as a standard figure of merit, since there is no industry or government standard for testing (like TMC’s 6 in. standard for sensor locations). Part of the problem is the measurement point – near nodal line(s) for the modes – is a position where the resonance amplitude varies the most: from zero at the node to a maximum at the table’s edge. The ideal place to make a compliance measurement would be where the mode shape is “flat.” For example, this would be the center of the table for the first mode in Figure 14. Here, the measurement is almost independent of the sensor or impact locations for the first mode only. For many higher modes, however, this is dead center on nodal line(s), producing essentially meaningless results. Rather than bombard customers with a separate test for each mode shape, for better or worse, the corner compliance test has become the standard.
In recent years, some attempts have been made to produce other figures of merit. TMC does not use these because they compound the uncertainty of the compliance test with several other assumptions. So-called “Dynamic Deflection Coefficients” and “Maximum Relative Motion” * take information from the compliance curve and combine it with an assumed input force spectrum. Unfortunately, the “real” relative motion you observe will also depend on the way your table is supported. If, for example, your top is properly supported by the isolators at the nodal lines of the lowest mode (0.53 L apart), then there is no excitation of the lowest mode from the isolators (on which these figures of merit are based). Likewise, if you support a top improperly, the mode can be driven to large amplitudes. Moreover, the “assumed” input depends on two very poorly defined factors: floor noise and isolator efficiency. Even if these are well defined, it is much more likely that acoustic sources of noise will dominate at these frequencies (typically 100-1,000 Hz). For all these reasons, we consider these alternate figures of merit essentially meaningless and do not use them.

* These particular figures of merit were developed by Newport Corporation of Irvine, CA.

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