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Tutorial Selection of vibration isolators

Abstract

Controlling or isolating vibration caused by a ground motion or an acoustic noise is critically important in precise optical fabrications and measurements. There are two methods for controlling or isolating vibration, passive and active vibration isolation. The goal here is to compare passive and active vibration isolation and examine applications for both vibration isolation, such as an optical table and a stage for an optical lithography.

Introduction

For precise optical fabrications and measurements, a vibrational circumstance can be tremendously important and critical issue. Vibrational disturbances consist of periodic or nonperiodic forces and include acoustic noise. A particularly important condition occurs when the frequency of the periodic force nearly or exactly corresponds to the natural frequency fn of an equipment. In the region around fn, the transmissibility is over 1, which means the amplified vibration of a ground motion transmits to the equipment. If the transmissibility is lower than 1, the equipment is isolated from the ground motion. The natural frequency fn of the equipment is given by

By this equation, the natural frequency can be small, if one designs the equipment with very low stiffness and very heavy. But it is not a reasonable way. Instead of changing the design of the equipment, the natural frequency also can be decreased if a vibration isolation system is employed strategically to the equipment.

There are two methods for controlling or isolating vibration, passive and active vibration isolation. In the following chapters, general issues, types, and examples about these tow isolations are discussed.

Passive vibration isolation

1. General issue

The passive vibration isolation system basically consists of a mass M, a spring K and damper (dash-pot) C shown in Figure 2 [1]. In this case, one assumes that a mass M is a rigid body for simplifying the system and can be replaced by an equipment. The vibration which a unit transmits to a supporting structure or the vibration which a unit feels when it is being excited by a vibrating structure can be reduced or attenuated by this isolator.

Isolation is attained primarily by maintaining the proper relationship between the disturbing frequency and the system’s natural frequency. The damped natural frequency of the system is described by


C is a damping coefficient with a unit of [Kgsec/m]. CC is a critical damping with a unit of [Kg-sec/m]. C/CC is a damping factor with unitless.
Figure1 Schematic of a passive isolator

Figure1: Schematic of a passive isolator

In this case, the equipment on the isolator is assumed to be a rigid body. But, in the real system, the equipment should have its resonant frequency. Then, it is desirable to select the proper isolator so that its natural frequency will not coincide with any critical frequencies of the equipment.

Figure2 Transmissibility curve for an isolated system

Figure2. Transmissibility curve for an isolated system

Figure 2 shows that a typical transmissibility curve for an isolated system where fd = disturbance frequency and fn = isolation system natural frequency.

Damping is advantageous when the mounted equipment is operating at or near its natural frequency because it helps to reduce transmissibility. Increasing a damping factor C/CC reduces an isolation system natural frequency. Then a frequency ratio fd/fn increase and transmissibility decreases.

2. Selection of passive vibration isolators

First of all, a disturbing frequency fd should be defined. If there is more than one disturbing frequency, one should focus on the lowest frequency. When the lowest frequency is isolated, then all of the other higher frequencies will also be isolated. The disturbing frequency sometimes can be measured directly, but in almost cases, one should estimate the disturbing frequency from several known data or criterion. For typical military and aerospace environments, one can choose the disturbing frequency from  Table 1 indicated by Vukobratovich [2]. Also, one can define the disturbing frequency from generic vibration criterion (VC) in appendix A [3].


Next, one should determine the minimum isolator natural frequency fn defined by

Determining fn makes it possible to choose the passive vibration isolator. When the passive vibration isolator is chosen, the damping factor C/CC can be known. Thus, one can calculate transmissibility T given by

By the transmissibility, we can estimate the performance of the passive vibration isolator. Also, the selection can be narrowed down by operating temperature range, size of the isolator, the mount capacity, etc. In general, there are several types of the passive vibration isolators, such as elastomeric isolators, metal springs, Spring-Friction dampers, and spring combined by air damping etc.

3. Example of passive vibration isolator Thorlabs shows a selection matrix for optical tables and optical table supports based on the working environment and application [4] as shown as in Table 2 and 3.

Table2. A selection matrix for optical tables and optical tables supports based on the working environment and application.

Table3. A comparison table for the optical tables supports made by Thorlabs

These tables indicates that :

  • Less demanding applications do not need a vibration isolator in quiet environment.
  • The passive vibration isolator cannot be applied to noisy environment or demanding applications.
  • The active vibration isolator can be applied to every application. (If the budget is approved.)

Active vibration isolation

1. General issue and comparison with passive vibration isolator

The active vibration isolation system essentially uses a feedback or a feedforward circuit which consists of an accelerometer, a controller, and an electromagnetic transducer in addition to a mass, spring and damper. Since the passive vibration isolation system has a resonant frequency fn, it can isolate a vibration over square root of 2 times fn. On the other hand, the active vibration isolation system basically does not have a region of amplification, thus it can isolate a vibration in low frequency.

An accelerometer is attached on the table including the passive vibration isolators. The accelerometer can detect a vibration transmitted from the passive vibration isolators. For a feedback control, a controller analyses the frequency and amplitude of the vibration and outputs a feedback signals. An electromagnetic transducer receives the feedback signal and creates a force canceling the vibration. This system can be applied to 6 degree of freedom. In the case of a feedforward control, the accelerometer is located on the floor.

As mentioned above in the chapter 2-1, the passive vibration isolator has a natural frequency. Then, if a floor has a frequency equal to the natural frequency, the vibration is amplified and transmitted to the equipment. Then, the passive vibration is only available in the region over square root of 2 times fn. If one tries to reduce the natural frequency of the passive vibration isolator, it becomes compliant. This means that it takes a long time to stabilize a vibration of the equipment caused by someone’s touching to this equipment. For example, after an adjustment of the equipment or an exchange of a sample, it takes a long time so that one can use this equipment. On the other hand, there is no the region of amplification on the active vibration isolators ideally, and it can isolate a vibration from very low frequency. In addition, since the damping time is very short, the equipment can be stabilized in a short time. In a real active vibration isolator, since it also uses a passive vibration isolator and feedback or feedforward control is not perfect, there might be the region of amplification.

2. Selection of active vibration isolators

The active vibration isolators are used for isolating tremendously low frequency, like about 1 Hz or under 1 Hz, and used with the passive vibration isolators. There are two radically different approaches about the active vibration isolators, feedback and feedforward control [5]. A feedback control is used in general but a feedforward control is used in acoustic field frequently.

The principle of feedback is presented in Figure 3.

Figure 3. Principle of feedback control

The output y of the system is compared to the reference input r and the error signal, e = ry, is passed into a compensator H(s) and applied to the system G(s). The design problem consists of finding the appropriate compensator H(s) such that the closed-loop system is stable and behaves in the appropriate manner. The bandwidth ωC of the control system is limited by the accuracy of the model. There is always some destabilization of the flexible modes outside ωC.

The principle of feedforward is presented in Figure 4.

Figure 4. Principle of feedforward control

Figure 4. Principle of feedforward control

When a signal correlated to the disturbance is available, the feedforward control can be used. It was originally developed for noise control. The feedforward strongly relies on the availability of a reference signal. The reference signal is passed through an adaptive filter, the output of which is applied to the system by secondary sources. The filter coefficients are adapted in such a way that the error signal at one or several critical points is minimized. Unlike the feedback control, which can only attenuate the disturbances near the resonances, the feedforward control works for any frequency and attempts to cancel the disturbance completely by generating a secondary signal of opposite phase.

The brief summary and comparison about the feedback and feedforward control are listed in Table 4.

Table 4. Comparison of control strategies

Table 4. Comparison of control strategies

3. Example of active vibration isolator

Canon develops a lithography system with active vibration isolators as described in the following [6].

Figure 5. the mechanical structure of the active vibration isolator

Figure 5. the mechanical structure of the active vibration isolator

Figure 5 illustrates the mechanical structure of an active vibration isolator for controlling the movement and attitude of a generally triangular vibration isolation platform with six degrees of freedom. An optical barrel can be mounted on the vibration isolation platform. It is supported by active supporting legs, which can control two vertical and horizontal axes. The active supporting leg has vibration measurement sensors outputting acceleration and velocity, position measurement sensors, pressure sensors, servo valves, and air-spring actuators.

Figure 6. Block diagram of performing control

Figure 6. Block diagram of performing control

As Figure 6 shows, this system has three feedback controls for isolating vibration. The first feedback loop feeds back an output of pressure sensor, which measures a working force applied by air-spring actuators to the vibration isolation platform. The first feedback loop can control the working force applied by an air spring actuator. The second feedback loop has Proportional Plus Integral (PI) (#55 in Figure 6). It produces damping and spring effects to the vibration isolation platform. The third feedback loop feeds back an output from position measurement sensor. Then the position of the vibration isolation platform can be designated.

By this patent,

  • The combination of feedback loop makes the equipment stable from vibration.
  • The active vibration isolator is necessary for precision optical fabrication.

Conclusion

This paper provides two methods for controlling or isolating vibration, passive and active vibration isolation. For both isolation, the general issues, types, and examples are discussed. The passive vibration isolator can be selected by an environmental vibration criterion. The active vibration isolator can be selected by a requirement of low frequency isolation and types of control. Also, as example of both vibration isolation, optical tables by THROLAB and the stage for lithography by Canon is examined.

Reference

1. Barry controls, Isolator guide at http://www.barrycontrols.com/defenseandindustrial/isolatorselectionguide/iso_sel ect.pdf 

2. D. Vukobratovich, in Handbook of Optomechanical Design, CRC Press, Boca Raton, FL, 1997, p. 65, chap 2.

3. P. R. Yoder, in Opto-Mechanical Systems Design, CRC Press, Roca Raton, FL, 2006, p. 50-51

4. THORLAB, http://www.thorlabs.com/newgrouppage9.cfm?objectgroup_id=1105 

5. Micromega-dynamics, http://www.micromega-dynamics.com/vibrationstrategies.htm 

6. S. Wakui, “Active vibration isolator, exposure apparatus, exposure method and device manufacturing method”, United States Patent 6,286,644 B1 (2001)

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