The purpose of vibration isolation supports is to isolate the optical table from building and surrounding environmental vibrations. True seismic mounting of an optical table requires a mounting system which addresses two issues.
Ambient building vibrations occur at low frequencies; therefore, the mounting system must have very low vertical and horizontal resonant frequencies in order to function as a seismic isolator.
The motion of the table must be damped in order to suppress the resonant response of the optical table.
6.2 Air Spring Vertical Isolation
The simplest and most successful optical table supports have internal air springs. In Fig. 23, the simple air spring is constructed by placing a rigid disk, which is constrained to only allow vertical motion, on top of a deformable air reservoir. When a heavy object is placed on top of the rigid disk, that object is isolated from floor vibrations by the expansion/contraction of the air reservoir.
Figure 23. A simple air spring
Air springs differ from a conventional mechanical spring in that they have a very small spring constant for a given range of travel. In an air spring, the relationship between restoring force and deflection varies with the shape and material of the air spring envelope. The resonant frequency of an air spring isolator is given by
Here, fn is the resonant frequency of the oscillation, r is the specific heat ratio for the gas (air) in the spring, A is the piston area, g is the acceleration due to gravity, and V is the volume of the air bag (or cylinder).
From Eq. (13), we can conclude that the stiffness of the spring (and hence the natural resonant frequency of a mass supported on the spring) is dependent on the height of the spring (volume of air) but is independent of the load. Consequently, if the load is changed but the pressure is adjusted to maintain a constant height, then the resonant frequency remains constant. This is highly desirable for optical tables; if the resonant frequency of the optical table supports increased with load rather than with spring height, then the frequency at which the optical table is effectively seismically mounted would also increase. In addition, this allows optical table supports to be design with an internal damping mechanism that is tuned to the resonance of the optical table support, regardless of the load being supported.
Since most optical tables are supported by four optical table supports, there are several vertical vibrational modes (i.e., resonant vibrations) of the table on the support system. These modes consist of various in- and out-of-phase combinations of the vertical resonance modes of the individual optical table supports; these linear combinations not only affect the vertical movement of the surface but also lead to pitch and roll of the surface. The frequencies of the optical table’s oscillation modes are near the resonant frequency for vertical vibrations in an individual leg. As a result, the modes of oscillation involving the entire optical table surface can be damped by any mechanism in the optical table support designed to damp the supports vertical vibrational resonance.
6.3 Choosing an Isolation System
Thorlabs offers three levels of optical table supports: rigid, passive, and active. All three varieties of optical table supports are available from stock in two heights: 600 mm (24") for use with a 310 mm (12.2") thick optical table and 700 mm (28") for use with a 210 mm (8.3") thick optical table. Special optical table support heights are available upon request. Typically, the vertical vibrations range in frequency from 10 to 50 Hz while horizontal vibrations range from 1 to 20 Hz.
The simple air spring design described previously is more than adequate for use in lower vibration environments or for less sensitive experiments; they also provide a vast improvement over rigid support systems such as steel legs. However, three issues are not directly addressed. (1) There is no attempt to increase the amount of damping beyond that provided by the viscoelastic damping achieved by deforming the walls of the air bag. As a result, the vibration peak at the resonant frequency can be quite large. (2) The design does not actively address the issue of horizontal isolation, and the table is able to rock on its legs. (3) The vertical resonance frequency depends on the nature and shape of the linkage between the table and the airbags but is typically in the 3 to 5 Hz range.
Ambient horizontal vibrations tend to occur at lower frequencies than vertical floor vibrations (1 to 20 Hz versus 10 to 50 Hz) and are therefore more difficult to isolate. However, unless the laboratory is located on the upper floor of a tall building, the horizontal floor motions will generally be much smaller than the vertical vibrations. The simple air spring design does not have any mechanism for self-leveling and automatic height adjustment. Therefore, if a large load is placed on the tabletop, it will be lowered slightly; in addition, if that load is not placed centrally, the tabletop will no longer be level. Therefore, before choosing an isolation system, consider the severity of the environment in which the table is located and what type of vibrations can be expected. Each subsection below details the capabilities of each type of optical table support.
Rigid optical table supports are used primarily when the environment and/or application does not require the optical table to be isolated from vibrations. Instead the optical table is being used because it provides a rigid, flat surface on which to build an application.
Excellent Horizontal and Vertical Stability
High Load Capacity
Leveling Adjustment on Each Support
Figure 24. Features of Thorlabs’ Rigid Optical Table Supports
The rigid (non-isolating) optical table supports made by Thorlabs have a 2500 kg (5500 lb) load capacity when four of the supports are used to support an evenly loaded optical table.
Passive optical table supports are primarily used when the optical table is located in an environment with minimal vibrations. The deformable air reservoir in the passive optical table support (see Fig. 25) is used to isolate the optical table from floor vibrations ranging in frequency from 10-50 Hz. The transmissibility above 10 Hz is below 0.3, which is a significant improvement over the performance of isolators using rubber or neoprene padding.
Simple, Effective Vertical Vibration Isolation
Excellent Horizontal and Vertical Stability
Easy to Pressurize (No Need for a Constant Source of Pressurized Air)
Two Load Capacity Choices
Figure 25. Features of Thorlabs’ Passive Optical Table Supports
Each isolator consists of a cylindrical reinforced rubber air reservoir mounted in the top of a cylindrical steel leg. The pressure of the isolator can be adjusted by increasing or decreasing the pressure in the air reservoir through a standard Schrader valve on the side of each isolator. The passive optical table support is designed so that the cylindrical steel leg will support the optical table when the air reservoir is underinflated. The optical table can be leveled by adjusting the pressure in each air reservoir.
Active optical table supports, which require a constant supply of pressurized gas, should be used for vibration-sensitive applications and when the optical table is located in an environment with significant vibrations. For example, if an experiment is conducted on an upper floor, the building may sway, causing both vertical and horizontal vibrations. The active optical table support damps vertical vibrations using a two air reservoir design (see Fig. 26) where the air flow between the two chambers is limited because of the size of the aperture connecting the two chambers. This design reduces the 0.3 transmissibility point to less than 2 Hz. Unlike the rigid and passive optical table support discussed above, the active optical table support includes a horizontal damping mechanism. In addition, the active optical table supports have a self-leveling feature. Thorlabs’ isolators are large-diameter free-standing supports that provide a safe and stable foundation without the need for tie bars that can introduce additional resonances into the support structure. The low vertical and horizontal transmissibility of these isolators results in the least possible relative tabletop motion.
Superior Vertical and Horizontal Vibration Isolation
Excellent Horizontal and Vertical Stability
Vertical damping is achieved by the use of a dual chamber, damped pneumatic spring. The table is supported by the air pressure in these chambers. A piston, in contact with the bottom of the optical table, is sealed to the upper pressurized chamber using a rolling rubber diaphragm that allows virtually friction-free displacement of the piston in the vertical direction while preventing horizontal displacement of the piston. Floor or tabletop motion forces air to flow from one chamber to the other through a high-resistance damper. This restriction in the airflow between the two chambers damps the oscillatory motion between the floor and table, dramatically reducing settling time. The volume ratio of the chambers has been optimized to produce a well damped optical table support with a low resonance frequency.
Figure 26. Features of Thorlabs’ Active Optical Table Supports
A simple method for mounting an optical table that allows for the damping of horizontal vibrations is to allow the optical table support to move with a pendulum-like motion. The resonant frequency of a pendulum is independent of the mass and is given by
Here, fn is the resonant frequency of the oscillation, g is the acceleration due to gravity, and l is the length of the pendulum. Thorlabs’ active isolators damp horizontal vibrations by supporting the pneumatic vertical isolator on a trifilar suspension system. This innovative pendulum design uses gravity to provide the restoring force following horizontal displacement. Horizontal oscillations at the system’s resonant frequency are damped by linking the base of the vertical isolator to the outer cylinder with an oil-free vibration-absorbing damper.
The active optical table supports are connected to a constant pressurized gas source via a three-way valve that regulates the gas pressure in the supports in order to self level the optical table. Remember, the pressure in the air chamber determines the height of the optical table when the table is at rest. Because these valves are actuated by tabletop movement, the system will return after a disturbance to within ±0.25 mm (0.01") of its original level position. The valves also compensate automatically for any changes in tabletop load distribution. Additionally, this system allows the table height to be adjusted over a range of 26 mm (1.5") and can be used to compensate for an uneven floor. If the constant source of pressurized gas is removed, the optical table will lower until it rests securely on top of the optical table supports. At this point, although the isolating properties of the supports are disabled, the optical table will still be securely and stably supported.
6.4 Instability and Oscillation
Systems with a high center of gravity (CG) can experience stability problems when supported on pneumatic isolators, particularly when the tabletop is narrow and/or thick. A high CG, combined with narrow isolator spacing, can cause static instability, and the table tends to rock slowly backwards and forwards about an axis midway between the two isolators. Furthermore, a dynamic instability can be experienced in the levelling system, causing the table to rock quickly from side to side.
6.4.1 Static Instability
Most table systems have a CG which is above the height of the diaphragms, and narrow spaced isolators at either end of the table. Any disturbance of the tabletop causes the CG to move away from the centerline between the isolators, and the weight of the table and equipment assists this sideways motion, causing the table to tilt further.
This tilting action is resisted by the stiffness of the isolators, stiffer isolators means more stability. However, we concluded previously, that it is softer isolators that are more effective in removing vibration, therefore a trade off must be made between isolation and stability.
It is generally accepted that in order to avoid instability and oscillation due to excessive rocking, the CG, including that of the table, should be within the pyramid shown in the figure below.
The base of this pyramid is defined by connecting the center point of each isolator, and the height is equal to 1/2 the shortest distance between isolators.
Static instability is not dependent on the air pressure in the system or (for active systems) the adjustment of the leveling valves. If the optical table is not stable, the only solutions are either to lower the CG by purchasing accessory shelves and moving the equipment below the table’s surface or to increase the distance between the optical table supports.
6.4.2 Dynamic Instability
In an active isolation system, the table height is controlled by leveling valves that increase or decrease the pressure of air in the optical table support reservoir. If the pressure is adjusted too rapidly, then the optical table will oscillate. This oscillation can be removed by reducing the air flow to and from the optical table supports.