Showing papers by "Chia-Hsiang Menq published in 2009"

Forced Response Prediction of Constrained and Unconstrained Structures Coupled Through Frictional Contacts

Abstract: In this paper, a forced response prediction method for the analysis of constrained and unconstrained structures coupled through frictional contacts is presented. This type of frictional contact problem arises in vibration damping of turbine blades, in which dampers and blades constitute the unconstrained and constrained structures, respectively. The model of the unconstrained/free structure includes six rigid body modes and several elastic modes, the number of which depends on the excitation frequency. In other words, the motion of the free structure is not artificially constrained. When modeling the contact surfaces between the constrained and free structure, discrete contact points along with contact stiffnesses are distributed on the friction interfaces. At each contact point, contact stiffness is determined and employed in order to take into account the effects of higher frequency modes that are omitted in the dynamic analysis. Depending on the normal force acting on the contact interfaces, quasistatic contact analysis is initially employed to determine the contact area as well as the initial preload or gap at each contact point due to the normal load. A friction model is employed to determine the three-dimensional nonlinear contact forces, and the relationship between the contact forces and the relative motion is utilized by the harmonic balance method. As the relative motion is expressed as a modal superposition, the unknown variables, and thus the resulting nonlinear algebraic equations in the harmonic balance method, are in proportion to the number of modes employed. Therefore the number of contact points used is irrelevant. The developed method is applied to a bladed-disk system with wedge dampers where the dampers constitute the unconstrained structure, and the effects of normal load on the rigid body motion of the damper are investigated. It is shown that the effect of rotational motion is significant, particularly for the in-phase vibration modes. Moreover, the effect of partial slip in the forced response analysis and the effect of the number of harmonics employed by the harmonic balance method are examined. Finally, the prediction for a test case is compared with the test data to verify the developed method. DOI: 10.1115/1.2940356

Minimum-variance Brownian motion control of an optically trapped probe

Abstract: This paper presents a theoretical and experimental investigation of the Brownian motion control of an optically trapped probe. The Langevin equation is employed to describe the motion of the probe experiencing random thermal force and optical trapping force. Since active feedback control is applied to suppress the probe's Brownian motion, actuator dynamics and measurement delay are included in the equation. The equation of motion is simplified to a first-order linear differential equation and transformed to a discrete model for the purpose of controller design and data analysis. The derived model is experimentally verified by comparing the model prediction to the measured response of a 1.87 microm trapped probe subject to proportional control. It is then employed to design the optimal controller that minimizes the variance of the probe's Brownian motion. Theoretical analysis is derived to evaluate the control performance of a specific optical trap. Both experiment and simulation are used to validate the design as well as theoretical analysis, and to illustrate the performance envelope of the active control. Moreover, adaptive minimum variance control is implemented to maintain the optimal performance in the case in which the system is time varying when operating the actively controlled optical trap in a complex environment.

Three-axis rapid steering of optically propelled micro/nanoparticles.

Abstract: This paper presents the design and implementation of a three-axis steering system, wherein a micro/nanoparticle is optically trapped and propelled to serve as a measurement probe The actuators in the system consist of a deformable mirror enabling axial steering and a two-axis acousto-optic deflector for lateral steering The actuation range is designed and calibrated to be over 20 μm along the two lateral axes and over 10 μm along the axial direction The actuation bandwidth of the two lateral axes is over 50 kHz and the associated resolution is 0016 nm (1σ) The axial resolution is 016 nm, while the bandwidth is enhanced to over 3 kHz by model cancellation method The performance of the three-axis steering system is illustrated by three sets of experiments First, active Brownian motion control of the trapped probe is utilized to enhance trapping stability Second, a large range three-dimensional (3D) steering of a 187 μm probe, contouring a complex 3D trajectory in a 6×6×4 μm3 volume, is demonstrate

Best linear unbiased axial localization in three-dimensional fluorescent bead tracking with subnanometer resolution using off-focus images.

Abstract: A three-dimensional particle tracking technique, based on microscope off-focus images, was introduced in Z. Zhang and C.-H. Menq, Appl. Opt.47, 2361 (2008) and applied to bright-field imaging. This paper presents two major improvements to the axial localization algorithm of the 3D particle tracking technique. First, it extends the algorithm to measure fluorescent particles in the presence of photobleaching and excitation variation. Second, it enhances the measurement resolution by achieving the best linear unbiased estimation of the particle's axial position. Similarly to the original algorithm, a radius vector is first converted from the off-focus 2D image of the particle, and the axial position is estimated by comparing the radius vector with an object-specific model, calibrated automatically prior to each experiment. Although it was an intensity-based method, by normalizing the radius vectors the improved algorithm becomes a shape-based method, thus invariant to image intensity change and robust to photobleaching. Moreover, when considering the noise variance of each point in the radius vector and their correlations, the best linear unbiased estimation based on a linearized model is achieved. It is shown that variance equalization and correlation-weighted optimization greatly reduce the estimation variance and lead to near-uniform localization resolution over the entire measurement range. Estimation resolution is theoretically analyzed and validated by experiments. Theoretical analysis enables the prediction of measurement resolution based on calibration data. Finally, experimental results are presented to illustrate the performance of the measurement method in terms of measurement precision and range, as well as its robustness to intensity variation.

Real-time in situ calibration of an optically trapped probing system.

Abstract: We present real-time in situ calibration of an optically trapped probing system. In the probing system, a micro/nanobead is stably trapped around the minimum of the field potential to serve as the measurement probe, whereas the random thermal force tends to destabilize it and causes Brownian motion around the equilibrium. The weighted recursive least-squares algorithm is applied to recursively update the system's parameters, such as the state transition coefficient, and to estimate specific system response and the unknown variance of the Gaussian white noise in real time according to the probe's motion. The real-time recursive algorithm was first applied to real-time calibration of measurement sensitivity and trapping stiffness for the case that the local temperature and the damping coefficient of the probe are known. It was then applied to estimate the probe's local temperature in real time. Two experiments were designed to illustrate the applicability of the real-time calibration method. The experimental results show that the recursive algorithm is able to real-time calibrate the trapping stiffness of the probing system and the measurement sensitivity of the back-focal-plane interferometry employed for position measurement. The experimental results also show that the method can estimate the probe's local temperature in real time.

Visual Servo Control Achieving Nanometer Resolution in $X$ – $Y$ – $Z$

Abstract: This paper presents a three-axis vision motion sensor and its applications to visual servo control. The vision sensor is integrated with a three-axis piezo stage to form a visual servo control system that achieves nanometer resolution in all three x- y-z motion axes. Motion measurement is achieved using a single interferometer-equipped optical microscope. A real-time image-processing algorithm that processes interference fringe patterns and that achieves nanometer out-of-plane resolution is presented. Furthermore, a feedback-control scheme is introduced to control the sensor plane using an Objective-Z-Positioner to enable automatic tracking of moving objects. It expands the out-of-plane measurement range of the vision sensor beyond its inherent depth of field of several micrometers to 100 mum and beyond. An integrated visual servo system is implemented and experimental results are shown.