Contents lists available at ScienceDirect Tribology International journal homepage: www.elsevier.com/locate/triboint Centrally fed orifice based active aerostatic bearing with quasi-infinite static stiffness and high servo compliance N. Maamari a,* , A. Krebs a , S. Weikert b , K. Wegener b a ETEL S.A, Môtiers, Switzerland b ETH Zurich, Institute of Machine Tools and Manufacturing (IWF), Zurich, Switzerland ARTICLE INFO Keywords: Aerostatic bearing Active bearing Load compensation Servo compliance Infinite stiffness Positioning system Macro-positioning ABSTRACT Active compensation of aerostatic bearing enhances their inherent limited stiffness and adds macro positioning capabilities. Current active solution relies on a position feedback to reach high stiffness. In this study, a novel concept that replaces costly position feedback by a self-regulating stiffening mechanism is investigated. This concept features a guided conical deformation based on integrated leaf springs. This balances the pressure and servo induced deformation, leading to quasi-infinite stiffness and high servo compliance. A lumped and a finite element models governing the static behavior are presented and benchmarked. Open loop stability is assessed using a linearized lumped dynamic analysis, and solutions based on a mechanical and a mechatronic approach are proposed. Finally, the prototype is tested in open loop, proving a quasi-infinite stiffness and a servo com- pliance of μm A 3.4 / . 1. 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 p s . 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 p r () resulting from the alteration of the gap height h and the recess pressure p rec . 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 ex- haust 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 stiff- ness. 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 p rec . 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 p s 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 im- plemented by Ghodsiyeh et al. [12] using a diaphragm valve to pneu- matically control the feed pressure. Their results showed 40% increase https://doi.org/10.1016/j.triboint.2018.08.024 Received 4 May 2018; Received in revised form 20 August 2018; Accepted 21 August 2018 * Corresponding author. Rue de cote 17, 2013, Colombier, Neuchâtel, Switzerland. E-mail address: nmaamari@ethz.ch (N. Maamari). Tribology International 129 (2019) 297–313 Available online 23 August 2018 0301-679X/ © 2018 Elsevier Ltd. All rights reserved. T