Spherical Air Bearing Research Articles

A High-Precision Random Forest-Based Maximum Lyapunov Exponent Prediction Model for Spherical Porous Gas Bearing Systems

Spherical porous air bearing (SPAB) systems have been extensively used in various mechanical engineering applications. SPABs are promising materials in high-rotational speed, high-precision, and high-stiffness instruments. In SPAB systems, a rotor is supported by gas bearings, which provides higher rotational speed and lower heat generation environment than oil bearings do. Furthermore, SPAB does not cause deformation. Although, the supporting force of gas bearings is less, their stability is better than that of oil films. However, because the pressure distribution in the gas films is nonlinear, they are prone to failure at specific critical speeds, rotor imbalances, or inappropriate operations, which results in nonperiodic or chaotic motion and causes structural fatigue to the system. To understand and control the operating conditions of the SPAB systems during the nonperiodic motion, first, the governing equations of the SPAB system were solved to obtain the dynamic behavior of the rotor center. Then, the performance of the SPAB system were examined under different operating conditions by generating the maximum Lyapunov exponents (MLEs). However, the calculation process of MLE is extremely time consuming and complex. To solve this problem efficiently, a high-precision machine learning (ML)-based MLE prediction model was proposed in this study. The results show that the training process can be finished within few minutes, and the prediction process is able to be completed within few seconds. Meanwhile, the results demonstrate the merit of using the machine learning method for solving the MLE prediction problem and shorten the calculation time significantly. The proposed prediction model achieves excellent prediction outcome and it is more efficient and precise than traditional iteration scheme for the calculation of MLE. The feasibility of the proposed model is validated and the results also are the major contribution of this study.

Simulation and Validation of Satellite Attitude Control Algorithms in a Spherical Air Bearing

This work presents the application and comparison of two satellite attitude control methods, using the satellite simulation platform developed by ITA, the MuSat, as a test bench. One of the algorithms under test applies feedback linearization, a method that was already validated using this test bed. The second control algorithm, developed during this research, applies control by state-dependent Riccati equation (SDRE) technique. A numerical simulation using a computational model of the MuSat, followed by an experiment using the physical platforms, is used to compare the control performance of both algorithms. The system in which the control is applied consists in a frictionless spherical air bearing that is able to rotate in three axes, allowing for validating attitude control algorithms in laboratory. The experimental results obtained indicate that the system had a better control performance under the SDRE algorithm than the algorithm based on feedback linearization.

A roller posture adjustment device with remote-center-of-motion for roll-to-roll printed electronics

Nonuniform web tension has a great negative effect on product quality of roll-to-roll printed electronics. In this paper, a roller posture adjustment device with remote-center-of-motion (RCM) characteristic is proposed to guarantee web tension uniformity. The device combines a high-stiffness spherical air bearing (SAB) and a multi-degree-of-freedom flexure-based mechanism. The nonuniform web tension in lateral direction can be divided into an equivalent force and two equivalent moments. The equivalent moments are caused by the nonuniformity of the web tension. By adjusting the roller angle around y and z-axes, the equivalent moments can be eliminated to guarantee the web tension uniformity. The multi-DOF flexure-based mechanism is composed of a linear mechanism, a rotary mechanism and a 3-DOF off-plane mechanism. Besides, the RCM characteristic of the proposed device is realized to eliminate extra parasitic movement when the roller posture is changed. Based on pseudo-rigid-body model (PRBM) method, the theoretical analysis is conducted to evaluate the kinematics, stiffness and dynamics of the device. Moreover, the parameter optimization is conducted to maximize the first two resonance frequencies of the system. After that, finite element analysis is conducted to validate the established models. Finally, a prototype of the proposed device is fabricated performance verification. The experimental results show that the proposed device has a workspace of 10.22 mrad and 8.16 mrad about two working axes with center shifts of the RCM point less than 0.75%, which demonstrate the superior property of the proposed device.

TEST BED FOR THE SIMULATION OF MAGNETIC FIELD MEASUREMENTS OF LOW EARTH ORBIT SATELLITES

The paper presents a test bed designed to simulate magnetic environment experienced by a spacecraft on low Earth orbit. It consists of a spherical air bearing located inside a Helmholtz cage. The spherical air bearing is used for simulating microgravity conditions of orbiting bodies while the Helmholtz cage generates a controllable magnetic field resembling the one surrounding a satellite during its motion. Dedicated computer software is used to initially calculate the magnetic field on an established orbit. The magnetic field data is then translated into current values and transmitted to programmable power supplies energizing the cage. The magnetic field within the cage is finally measured by a test article mounted on the air bearing. The paper provides a description of the test bed and the test article design. An experimental test proves the good performance of the entire system.

A parallel alignment device with dynamic force compensation for nanoimprint lithography

Nanoimprint lithography is a nano/micro patterning technology to fabricate functional devices by pressing a template with predefined structures on a substrate. Uniformity of the force distribution between the contacting surfaces should be ensured to produce features with high fidelity. In this paper, a parallel alignment device with the abilities of dynamic force distribution control is developed. By adopting a spherical air bearing held with a 5-degree-of-freedom flexure-based stage, wedge errors between the template and the substrate can be eliminated passively without friction when an imprint force is applied. Since the vertical imprint force is mainly supported by the spherical air bearing, the device is very suitable for high force applications, without causing damage to the delicate compliant stage or precision degradation. Besides, the force distribution of the imprint process is measured, based on which dynamic force compensation is performed by actuating the compliant stage actively. Five-hundred-nm-period grating structures are transferred successfully with the device and proofs effectiveness of the device.

Development of a force-decoupled parallel alignment device for nanoimprint applications

High-precision parallel alignment between the substrate and the template is of great importance for nanoimprint lithography. Recently, flexure-based mechanism is commonly employed to realize high-precision parallel alignment; however, stiffness in imprint axis is hard to guarantee. In this article, a new parallel alignment device is proposed, which enables the imprinting force bypass the delicate alignment mechanism, thus eliminating the side effects of imprint forces and ensuring parallel alignment able to be carried out properly. A spherical air bearing is adopted in the device for the above-mentioned purpose through decoupling the nonuniform imprinting forces distributing on the template, allowing only the torque to reach the delicate alignment mechanism. The structural parameters of the air bearing are optimized through modeling and analysis of the bearing performances in terms of load-carrying capacity and stiffness. For the bearing preload, a set of permanent magnets are employed. The preliminary experimental results show that high load capacity and stiffness are achieved, which are consistent with the derived model.

Characteristics of supersonic flow in new type externally pressurized spherical air bearings

In order to predict accurately the characteristics of supersonic flow in new type externally pressurized spherical air bearings under large bearing clearance and high air supply pressure, which could decrease their load carrying capacity and stability, a CFD-based analysis was introduced to solve the three-dimensional turbulent complete compressible air flow governing equations. The realizable κ−e model was used as a turbulent closure. The supersonic flow field near air inlets was analyzed. The flow structures illustrate that the interaction exists between shock waves and boundary layer, and the flow separation is formed at the lower corner and the lower wall around the point of a maximum velocity. The numerical results show that the conversion from supersonic flow to subsonic flow in spherical air bearing occurs through a shock region (pseudo-shock), and the viscous boundary layer results in the flow separation and reverse flow near the shock. The calculation results basically agree with the corresponding experimental data.

Static characteristics of new type externally pressurized spherical air bearings

In order to provide some theoretical guideline for the structure design of the new type externally pressurized spherical air bearings, the static characteristics and the factors affecting the static characteristics of the air bearings were analyzed. A finite volume method was adopted to discretize the three-dimensional steady-state compressible Navier-Stokes equations, and a modified SIMPLE algorithm for compressible fluid was applied to solve the discretized governing equations. The pressure field and velocity field of the air bearings were obtained, and the factors and rules affecting the static characteristics were analyzed. The results show that the pressure of near air intakes can reach above 80% of air supply pressure, and there is a pressure steep fall around the air intakes. When the film thickness is greater than 20 μm, the bearing capacity rapidly decreases as film thickness increases. As the air supply pressure increases from 0.2 to 0.6 MPa, the maximum static stiffness increases by more than three times. The calculation method proposed well fits the general principle, which can be extended to the characteristic analysis of other air bearings.

Research on a New Type of Center of Mass Measuring Instruments

The accurate measurement and control of center of mass (CM) in mass properties for satellite attitude control are the most important. In order to accurately measure CM, this paper describes a new type of CM measuring instruments which are particularly recommended for determining mass properties of rockets, satellite and ballistic objects. A spherical air-bearing supports a precision rotary table and acts as a frictionless pivot axis for measuring unbalance moments due to the displacement of the test part CM relative to the central axis of the bearing. This paper emphasizes the research on reasons and laws of the load table CM offset caused by the elastic deformation, and according to curve theory of thin plates derives the formulary for the element center of mass displacement of the finite element and for the platform structure center of mass elastic displacement, and calculates the CM elasticity offset and the unbalance moment caused by the deformation of loaded table. The research results provide bases for the structure design of rotary tables.

Automatic Balancing for a Three-Axis Spacecraft Simulator

A ground-based spacecraft simulator is useful for experimental validation of advanced control laws. The minimization of the offset between the center of gravity and the center of rotation of the simulator is necessary for accurate simulation of a zero-gravity space environment. This study focuses on the automatic balancing of a ground-based spacecraft simulator on which moving masses required for the balancing are installed. We propose a novel automatic balancing method based on the recursive least squares approach. The proposed method is tested on a spacecraft simulator equipped with spherical air bearing. Experimental results show that accurate offset compensation and accurate space environment simulation are achieved using the proposed method.

Construction of a simple spherical air bearing

A simple method requiring minimal tools and mechanical ability, is presented for making a spherical air bearing. The air bearings are used for an exploration of precession. Results of test measurements are presented.

Effect of Manufacturing Errors on Static Characteristics of Externally Pressurized Spherical Air Bearings

Externally pressurized spherical air bearings are the key component of the three-axis air bearing table, and the manufacturing errors of the bearing affects the performance of the air bearing table. However, the manufacturing errors are unavoidable, and the pursuit to enhance the manufacturing accuracy will increase the cost greatly. In order to provide some theoretical guideline for the tolerance choice in the design of the externally pressurized spherical air bearings with inherent compensation, the effects of several manufacturing errors on the static characteristics of the air bearing are studied. Due to the complex geometry of the computational domain, an unstructured meshing technology is used for mesh generation. A finite-volume method is adopted to discretize the three-dimensional steady-state compressible Navier-Stokes equations. A modified SIMPLE algorithm which is suitable for compressible flows is applied to solve the discretized governing equations. The effects of the dimension error and the roundness error of the ball head and the ball socket on the static characteristics are investigated. The investigation result shows that the positive dimension error and the oblate spheroid-type roundness error of the ball head as well as the negative dimension error and the prolate spheroid-type roundness error of the ball socket can improve the bearing capacity and static stiffness of the air bearings by reducing the mass flow. The calculation method proposed in this paper fits well for the general principle, which can be extended to the characteristics analysis of other air bearings.

Three-axis air-bearing based platform for small satellite attitude determination and control simulation

A frictionless environment simulation platform, utilized for accomplishing three-axis attitude control tests in small satellites, is introduced. It is employed to develop, improve, and carry out objective tests of sensors, actuators, and algorithms in the experimental framework. Different sensors (i.e. sun, earth, magnetometer, and an inertial measurement unit) are utilized to assess three-axis deviations. A set of three inertial wheels is used as primary actuators for attitude control, together with three mutually perpendicular magnetic coils intended for desaturation purposes, and as a backup control system. Accurate balancing, through the platform’s center of mass relocation into the geometrical center of the spherical air-bearing, significatively reduces gravitational torques, generating a virtually torque-free environment. A very practical balancing procedure was developed for equilibrating the table in the local horizontal plane, with a reduced final residual torque. A wireless monitoring system was developed for on-line and post-processing analysis; attitude data are displayed and stored, allowing properly evaluate the sensors, actuators, and algorithms. A specifically designed onboard computer and a set of microcontrollers are used to carry out attitude determination and control tasks in a distributed control scheme. The main components and subsystems of the simulation platform are described in detail.

A liquid-filled projectile simulator

The similarity between the oscillatory motions of a top and a projectile is used in the design of a laboratory-based liquid-filled projectile simulator. The simulator uses a free floating rotor which is supported on a spherical air bearing. Its position is monitored by using novel noncontact transducer systems. It is shown that the behaviour when empty can be matched by theory and some of the results from tests with the cavity filled with liquid are presented.

Theory, Simulation, and Practical Tests of a Counterspun Nutation Damper for Prolate Spinners

A nutation damper described in some previous papers is considered. It consists of a flywheel attached by a dissipative tilting mounting on the axle of a motor parallel to the spacecraft spin axis, but spinning in the opposite direction to the spacecraft. It is treated first by theory using differential equations applied to a quasisteady-state showing that it stabilizes oblate and prolate spinners and that it fits into a comparatively unexplored corner of the field that is generally understood. As a result of the theory, some optimization is done and design goals suggested. The equations are simulated on an analog computer and some examination made of performance on spacecraft that are inertially more difficult to treat by theoretical means. Stabilization is demonstrated on triaxial prolate spacecraft and spherical spacecraft are made to spin about a preferred axis. A little success has been achieved with spacecraft spinning about an intermediate inertia axis. A rudimentary damper has been made and fitted to a prolate body with an inertia ratio of 0.6, mounted on a spherical air bearing. Stabilization is demonstrated and it is shown how the results relate to theory. There is some discussion of the shortcomings of the damper tested and probable methods of engineering for space.

INFLUENCE OF CANTILEVER VIBRATION ON THE READING OF A TWO-AXIS GYROCOMPASS

A GEOGRAPHICAL coordinate 0£ijf is used to derive the equations of motion of a two-axis gyrocompass with spherical air bearings (Fig. 1). Let the £ axis be directed along the meridional line in the north, the f axis vertically to the zenith, and the 77 axis such that we obtain a right-handed coordinate system. For simplicity in further investigations, let us assume that the axis of precession, that is, the axis passing through the centers of the spherical air bearings, is placed vertically, and that the center of gravity of the sensitive element coincides with the point of support. Let us connect the Oxyz coordinate system with the sensitive element and direct the y axis along the axis which passes through the centers of the ball journals (let us call it the axis of rotation of the sensitive element). We shall direct the z axis along the vector of the kinetic moment, assuming that it is perpendicular to the y axis. The position of the sensitive element relative to the 0£?jf coordinate system is determined by angles a, ft, and.7, and its motion is determined by the angular velocities a, ft, and 7 (Fig. 2). The cosines of the small angles between the axes of the 0£r?f and Ox'y'z coordinate systems are shown in Table 1. The projections of the angular velocities on the x', y', and z axes, respectively, will be the following: p'