TMC Technical Background Page 3

TMC Technical Background

3.0 Practical Pneumatic Isolators


	Figure 6 shows a cutaway view of TMC’s Gimbal Piston™ isolator. It uses two air chambers instead of one. These are connected by a small orifice. As the piston moves up and down, air is forced to move through this orifice, producing a damping force on the payload. This type of damping is very strong for large displacements of the piston and less for small displacements. This allows for fast settling of the payload, without compromising small amplitude vibration isolation performance. Damping of this type usually produces a Q 3 for displacements on the order of a few millimeters.

	The damping provided by an orifice is limited by several factors. TMC’s MaxDamp^® isolators use a different method: multi-axis viscous fluid damping (Patent No. 5,918,862). These isolators can extend the damping to near critical levels for those applications which require it. For example, semiconductor inspection equipment often uses very fast moving stages to transport wafers. MaxDamp^® isolators allow the payload to settle very quickly after a stage motion, while still providing significant levels of vibration isolation. The isolator uses a very low outgassing, high-viscosity synthetic oil which is hermetically sealed within the isolator’s single air chamber. A special geometry ensures that the isolator damps both vertical and horizontal motions (in both X and Y directions) with equal efficiency.
	Both the Gimbal Piston™ and MaxDamp^® isolators incorporate a simple and robust pendulum isolator to provide horizontal isolation. Like air springs, pendulums also produce an ₀, which is payload-independent, and equal to /l , where l is the length of the pendulum. In the Gimbal Piston™, the pendulum is actually the piston itself: The payload is supported by a load disk, which transfers its burden to the bottom of the piston well through the load pin. The load pin contacts the bottom of the well with a pivoting thrust bearing. As the payload moves sideways, the piston well pivots like a gimbal in the plane of the diaphragm. Thus a pendulum is formed, whose length is equal to the vertical distance from the roll in the diaphragm to the bottom of the load pin.
	TMC’s CSP ^® (Compact Sub-Hertz Pendulum System) (Patent No. 5,779,010) uses a different type of pendulum concept to extend horizontal resonant frequencies as low as 0.3 Hz. This isolator uses a geometrical lever effect to “fold” a 0.3 Hz pendulum into a package less than 16 in. (400 mm) high. An equivalent simple pendulum would have to be 110 in. (almost 3 m) tall. For more information see the Pneumatic Vibration Isolators for OEM Applications page of this site.
	Horizontal damping in most isolators comes from horizontal-to-tilt coupling: As a payload moves sideways, it also exercises the isolators in the vertical direction (through tilt), thereby providing damping. Some systems, like TMC’s MaxDamp^® isolators, damp horizontal motions directly with fluidic damping.
	At small amplitudes, small amounts of friction in the rolling diaphragm and the small resistance to flow presented by the damping orifice have an impact on the isolator’s performance. For this reason it is important to use as small an excitation level as possible when measuring their transmissibility. Back to Technical Background Index
3.1 Number and Placement of Isolators
	Three or more isolators are required to support a payload, the most common number being four. Since there can only be three valves in a system (see Section 3.3), two legs in a 4-post system must be connected as a master/slave combination. Although a master/slave combination forms an effective support point, the damping it produces is much different than a single (larger) isolator at that point would provide. TMC always recommends using at least four isolators (except for “round” payloads like NMR spectrometers). Placement of these isolators under a payload has a dramatic effect on the performance of systems.
	For small rigid payloads, like the granite structures in semiconductor manufacturing equipment, it is best to place the isolators as close to the corners of the payload as possible. This dramatically improves the tilt stability of the system, reduces the motions of the payload caused by onboard disturbances, and improves both the leveling and settling times for the system. Leveling time is the time for the valving system to bring the payload to the correct height and tilt. Settling time is the time for a payload to come to rest after an impulse disturbance.
	For extended surfaces, such as large optical tables, the isolators should be placed under the surface’s nodal lines. This minimizes the influence of forces transmitted to the table through the isolators. This is discussed in Section 4.3. For either type of payload, it is always better to position the payload’s center-of-mass in the same plane as the isolator’s effective support points. This improves the stability of the system (see Section 3.4) and decouples the horizontal and tilt motions of the payload.
	Uneven floors can be accommodated in several ways. Most TMC isolators have a ±0.5 inch travel range, and this provides enough flexibility for almost all applications. Some systems also provide leveling feet. If a floor is extremely uneven, providing piers for the isolators may be required. Some free-standing isolators or other types of supports (like rigid tripods) must be grouted to the floor if the floor’s surface has a poor surface quality. Quick-setting “ready-mix” concretes or epoxies are well suited for this purpose. Back to Technical Background Index
3.2 Safety Features
	The ease with which pneumatic isolators can lift payloads weighing several thousand pounds belies the severity of their burden. By tying isolators together with “tiebars,” the risk of toppling such massive loads through accident or events like earthquakes is dramatically reduced. TMC’s tiebars are heavy-gauge, formed channels which use constrained-layer damping to prevent them from resonating. Such damping is hardly required, however, since the isolation efficiency of the isolators at those frequencies is extremely high. Systems can also be provided with earthquake restraint brackets which prevent the payload from shaking off the isolators in an extreme event.
	Of great importance to safety are the travel limits built into all TMC’s isolators. Figure 6 shows an internal “key” (yellow) which prevents the system from overextending even when pressurized to 120 psi (830 k Pa ) under “no load” conditions. Since there can be several thousand pounds of force behind the isolator’s piston, an isolator without such a travel limit can quickly become a cannon if suddenly unloaded. Protection, such as chain-linked pressure reliefs, does not provide the intrinsically high level of safety a mechanical travel limit does. Back to Technical Background Index
3.3 Leveling Valves
	All rigid payloads, even those with ten isolators, use only three height control valves. Because three points define a plane, using a greater number of valves would mechanically overconstrain the system and result in poor position stability (like a four-legged restaurant table) and a continuous consumption of air. Proper placement and plumbing of these three valves is crucial to optimizing the performance of a system.

	Figure 7a and Figure 7b show the typical plumbing for a 4-post and 6-post system. A system contains three valves, a pressure regulator/filter (optional), some quick-connect tees and an orifice “pigtail” on each isolator. The pigtail is a short section of tubing with an orifice inserted inside. This section is marked with a red ring, and has a union on one end to connect to the height control valves’ air lines. A mechanical valving system is a type of servo, and these orifices limit the “gain” of the servo to prevent oscillation. Some very high center-of-gravity systems may require smaller orifices to prevent instabilities. TMC uses fixed orifices rather than adjustable needle valves because of their long-term stability and ease of use.

	In a system with four or more isolators, two or more of those isolators need to be tied together. Usually the valve is mounted near an isolator (for convenience) and that isolator is called the “master.” The remote isolators(S) using that valve are called “slaves.” Choosing which legs are “master” and “slave” affects the stability of the system (see Section 3.4) and has a large impact on a system’s dynamic behavior. Dynamic performance is particularly important in semiconductor inspection machines which have fast moving stages. There are several “rules of thumb” which can be applied to make the correct choice. These can conflict with each other on some systems. Some experimentation may be required to determine the optimal choice.
	These rules, in approximate order of importance, are:
	1. The effective support point for a master and its slaves is at their geometric center. For a master with a single slave, this point is midway between the mounts. There are always only three “effective” support points for any system. Connecting these points forms a “load triangle.” The closer the payload’s center-of-mass (COM) is to the center of this triangle, the more stable the system will be. For example, on a 4-post system, the master/slave combination should support the lighter end of the payload.
	2. A corollary to rule #1 is that the system should be plumbed so that the pressure difference between all isolators is minimized.
	3. The gravitational tilt stability of a system is proportional to the square of the distance between the isolators. Therefore, for greatest stability, the master/slave combinations should be on the long side of a payload.
	4. The tilt axis with the highest stiffness, damping and stability is the one parallel to the line between the master and slave legs (in a 4-post system). For moving stage applications, the main stage motion should be perpendicular to the line between the master and slave leg.
	5. A moving stage can cause a cross-axis tilt because the valve for the master/slave legs is not co-located with the effective support point. For this reason, many systems should have the valve moved from the master leg to the effective support point.
	6. A control triangle is formed by the three points where the valves contact the payload. Like the load triangle, the system will have the greatest stability and best positioning accuracy if the COM is inside this triangle. The valves should be mounted and their “arms” rotated such that this triangle has the largest possible area.
	7. Sometimes following the above rules results in a system with poor height and tilt positioning accuracy. In this case, an alternate choice for the master/slave combination(s) might be required.
	In addition to valve location, there are several different types of valves which are available. TMC offers standard and precision mechanical valves. The standard valve is less expensive and has a positioning accuracy (dead band) of around 0.1 in. (2.5 mm). It has the property that the valve is tightly sealed for motions smaller than this. This makes it ideal for systems which must use pressurized gas bottles for an air supply. Precision valves offer a 0.01 in. (0.3 mm) or better positioning accuracy but leak a very small amount of air (they use all-metal valve seats internally). This makes them less suitable for gas bottle operation. Finally, TMC offers electronic valving systems such as the PEPS^® (Precision Electronic Positioning System, U.S. Patent No. 5,832,806), which has a 0.0001in. ( 2 m) position stability. For more information visit the PEPS and PEPS-VX pages.
	For cleanroom applications, TMC offers versions of the mechanical valves made from stainless steel and/or supplied with a vented exhaust line. Back to Technical Background Index
3.4 Gravitational Instability
	Like a pen balanced on its tip, payloads supported below their center of mass are inherently unstable: As the payload tilts, its center-of-mass moves horizontally in a way that wants to further increase the tilt. Fighting this is the stiffness of the pneumatic isolators, which try to restore the payload to level.

	The balance of these two forces determines whether the system is gravitationally stable or not. Figure 8 shows a payload supported by two idealized pneumatic isolators. The width between the isolators’ centers is W, the height of the payload’s COM is H above the effective support point for the isolators, and the horizontal position of the COM from the centerline between the isolators is X. It can be shown that there is a region of stability given by the condition:

	or, for X = 0,

	where n is the gas constant and is equal to 1.4.
	This relationship is shown in Figure 8 as an inverted parabola which defines the stable and unstable regions for the COM location. The second equation clearly shows that the stability improves with the square of the isolator separation. This is important as it demonstrates that it is not the aspect ratio H/W that determines the stability of a system (as some references claim) and that the stable region is not a “triangle” or “pyramid.” Unfortunately, real systems are not as simple as the one in Figure 8.
	The ratio A/V in Equations 10 and 11 represents the stiffness of the isolators (see Equation 9). In a two-chamber isolator, however, what is the proper V? Unlike the isolators in Figure 8, which have a fixed spring constant, real isolators have a spring constant which is frequency dependent. At high frequencies, the orifice between the two chambers effectively blocks air flow, and V may be considered the top air volume alone. At the system’s resonance, the “effective” air volume is somewhere between the top and total (top plus bottom) volumes. At low frequencies, the action of the height control valves gives the isolators an extremely high stiffness (corresponding to a very small V). Moreover, the action of the height control valves also tries to force the payload back towards level. These are only a few reasons why Equation 10 can’t be applied to two chamber isolators. Instead, we assign three regions: stable, unstable, and borderline, the first two being based on the “total” and “top only” air volumes, respectively. The stability region is also different for the axes parallel and perpendicular to the master/slave isolator axis.

	Figure 9 defines the two different axes for a four-leg system. The pitch axis is less stable because the master/slave legs on the left of the figure offer no resistance to pitch at low frequencies (though they do resist pitch at frequencies above 1 Hz). To compensate for this, the master/slave combination is chosen such that W_p is greater than W_r (rule 3 from Section 3.3). The region of stability is the volume defined by the inverted parabolas along the two axes.
	The condition for absolute stability is:

	and the formula for absolute instability is:

	with the volume between being “possibly” or “marginally” stable. The ratios A/V are not universal and should be confirmed for different capacities and models of isolators but are approximately 0.1 in^–1 for (A/V)_Top and 0.05 in^–1 for (A/V)_Tot . Figure 10 illustrates what the marginally stable region looks like for two chamber isolators. Unfortunately, the COM of many systems ends up in this indeterminate region. These rules do not account for the actions of the height control valves, which will always improve a system’s stability. If the payload has a mass which can shift (a liquid bath or a pendulum) these rules can also change.

	Equations 14 and 15 give “rules of thumb” for calculating the stability of a system. As with all such rules, it is only an approximation based on an “average” isolation system. It is always best to use as low a COM as possible.

	Because MaxDamp^® isolators use a single air chamber, they are more stable, and the rule becomes:

	Note that the effective support point for TMC’s Gimbal Piston™ isolators is approximately 7 in. below the top of the isolator. For lightly loaded isolators, these rules underestimate system stability. If your system violates these equations, or is borderline, the stability can be improved using counterweights, special volume isolators, different isolator valving, etc. Contact a TMC Sales Engineer for advice on the best approach. Back to Technical Background Index next page >
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