Centrally fed orifice based active aerostatic bearing with quasi-infinite static stiffness and high servo compliance
Graphical abstract
Introduction
Aerostatic bearings have been extensively used in precision motion systems, specifically in semi-conductor manufacturing and inspection. The absence of stick-slip in aerostatic bearings results in a precise and repeatable motion. Air pads are generally classified based on the type of inlet restrictor [1]. Centrally fed orifices-based compensation sketched in Fig. 1 are commonly employed due to their ease of manufacturing. Pressurized air is forced into the pad with a supply pressure . The orifice acts as an inlet restrictor, and the exhaust restrictor is composed by the thin gap between the guideway surface and the pad's lower surface. Loading/unloading the pad changes the pressure distribution resulting from the alteration of the gap height and the recess pressure .
One of the disadvantages of air bearings is their limited specific stiffness, consequently multiple configurations have been attempted to enhance the stiffness. Fourka et al. [2] benchmarked the impact of different types of inlet restrictors and demonstrated that pads with porous restrictor and low permeability achieved the highest static stiffness mainly due to a uniform pressure distribution.
Alternatively, static stiffness can be increased by changing the exhaust restrictor. Rowe and Kilmister [3] presented the first type of passive load compensation. A deformable membrane replaced the pad's lower surface. In this case, the response of the pad involves both rigid body motion and the deformation of the membrane. Franken and Hagen [4] added a pivoting membrane which allowed an infinite static stiffness. Enderle and Kaufmann [5] extended the range of infinite stiffness by using inner and outer gas chambers. Snoeys et al. [6] also achieved infinite stiffness with a simpler design using a single chamber, where the pressure is equal to the gap inlet pressure . Bryant et al. [7] established a design chart based on optimization methods to obtain infinite static stiffness. The main disadvantage of these passive load compensation methods is the requirement of a pressurized chambers increasing the manufacturing complexity. Additionally, the geometric inaccuracies of the guiding surfaces remain uncompensated leading to tool point errors Jaumann et al. [8]. Actively controlled air bearings offer a way to overcome these limitations and add a macro-positioning capability to compensate for the geometrical inaccuracies of the guiding surface.
Active compensation strategies can be grouped into two categories: flow restriction control and gap geometry control. Morosi et al. [9] and Pierart et al. [10] achieved upstream pressure control using a piezo actuator on a journal bearing. The piezo regulated the supply pressure resulting in a controlled radial injection of fluid into the bearing. Huang et al. [11] described alternative means of actuation based on magnetostrictive material. Similarly up stream control was implemented by Ghodsiyeh et al. [12] using a diaphragm valve to pneumatically control the feed pressure. Their results showed 40% increase is static stiffness. Further down-stream control involves regulating the recess pressure by controlling the opening of the inlet restrictor. Mizumoto et al. [13] developed an Active Inlet Resistance (AIR) for a journal and axial thrust bearing using a piezo-actuator. This allowed a change in the pressure distribution without a disturbing the film geometry. The main limitation of flow restriction control is in its limited bandwidth caused by the latency in the response [14].
Gap geometry control offers a collocated actuation. In this approach, the force is directly injected into the gap and instantly changes the pressure distribution. Ro et al. [15] described a simple method of gap actuation. The linear axes used four iron core motors with permanent magnets to actively preload a set of eight porous media air bearings. Additionally, feedforward compensation and laser interferometer measurements were implemented to reduce geometrical inaccuracies from ±1 μm to ±0.11 μm in the vertical direction. Since the motors are acting against the inherent stiffness of the pad, a low mechanical stiffness is required to ensure optimal servo compliance with acceptable force density.
Al-Bender et al. [14] developed a novel active bearing based on gap deformation control using piezo-actuators. This approach achieves a gap activation without reducing the mechanical stiffness. A high-end capacitive measurement was needed to ensure high stiffness for disturbance rejection. Van Ostayen et al. presented another design by combining the configurations as presented by Al-Bender et al. [14] and Kilmister [3]. The active pad supported in the center, consisted of a flexible plate with intermediated circumferential support, and an electromagnetic actuator mounted on the edge of the pad to deform the plate. This method increases the design complexity because it involves a plate deformation. A membrane like thin plate was required to obtain high mechanical stiffness comparable to passive load compensation levels. However, membranes like thin plates under point loading (i.e.: servo force) only lead to local deformation. Thus, the servo force will not impact the pressure and gap height across the whole pad, limiting the servo's impact on the load capacity [16].
The main disadvantage of current active methods [11,12] is the need for gap sensing. The stiffness of the active pad is generated from the controller proportional gains. This adds a high requirement on resolution and linearity of the position sensor, which needs to cope with the planar motion of the pad on a non-conducting surface of the granite. The field of positioning systems would benefit from the development of an aerostatic bearing with high passive mechanical stiffness for disturbance rejection without the requirement of gap measurement, while maintaining a high servo compliance to compensate the geometrical inaccuracies of the guideway surface.
This work presents an alternative active aerostatic bearing based on conicity actuation. The current design perfectly balances the pressure and servo induced deformation, thus any load capacity within theoretical limits is attainable with low actuator forces.
The final goal is to control the active pad in closed loop without any gap sensing measurement using either a velocity or conicity feedback. However, a characterization of the static behavior and the open loop stability is essential before the development of a control architecture.
This article presents the mechanical concept and the governing equations based on a static lumped approach. A dynamic lumped model is used to assess the stability of the pad in open loop. Later, the mechanical design is presented and a Finite Element (FE) model encapsulating the solid deformation, thin-film flow and magneto-static actuation is compared to the lumped approach. The results of the manufactured prototype are also presented and compared to simulation results. Finally, the findings reported in this article establish a novel approach to ensure quasi-infinite static stiffness and high servo compliance.
Section snippets
Mechanical concept
The schematic of the active aerostatic bearing is represented in Fig. 2(a). The compliant surface consists of a lower plate with two pivoting radii, the first near the recess region at radial distance and the second at a radial distance approximately 2/3 of the pad radius . A second plate with two pivoting radii is added at a distance from the first plate. This configuration ensures the guiding of the lower plate deformation leading to linearly varying gap height along the radial
Governing equations
The mathematical formulation of the presented concept involves four domains: thin film flow, nozzle restriction, structural deformation, and electromagnetism. Each of these are formulated in the following sections using an axisymmetric model.
Results and discussion
The following sections present the results obtained from the multi-physical lumped model presented earlier. First the static analysis is solved to reach the infinite static stiffness and servo compliance. Then based on a linearized lumped model, the stability of the active pad in open loop configuration is evaluated.
Design and finite element analysis
The following section involves the transformation of the presented concept into a mechanical design, able to exhibit the same behavior as the lumped model in terms of static stiffness and servo compliance. First the mechanical design is illustrated, then the FE and the lumped model results are compared.
Experimental measurement
A prototype based on the mechanical design was manufactured and assembled to test the performance and the functionality of the active bearing. The prototype is illustrated in Fig. 18. Since the concept involves a multi-disciplinary analysis, the validation process is performed in 3 steps. First the servo induced deformation from the FE model and the prototype are compared corroborating conicity compliance and motor constant . Then the load curve is generated to compare the static stiffness
Conclusion and outlook
This work presents an active aerostatic bearing that overcomes the dilemma between servo compliance and disturbance rejection. The active pad exhibits an infinite static stiffness over an acceptable loading range without any gap sensing measurement, while maintaining a high compliance for macro-positioning using Lorentz based actuation.
The lower bearing surface of the pad is made compliant and guided using an integrated leaf springs, ensuring a linear gap variation along the radial direction.
Acknowledgment
The author would like to thank ETEL S.A for its financial support, specifically Mr. Jean Pierre Morel for manufacturing the parts and Dr. Graf and Dr. Kobel for their instrumental inputs.
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