Showing papers on "Deflection (engineering) published in 1995"

Calculation of thermal noise in atomic force microscopy

Abstract: Thermal fluctuations of the cantilever are a fundamental source of noise in atomic force microscopy. We calculated thermal noise using the equipartition theorem and considering all possible vibration modes of the cantilever. The measurable amplitude of thermal noise depends on the temperature, the spring constant K of the cantilever and on the method by which the cantilever deflection is detected. If the deflection is measured directly, e.g. with an interferometer or a scanning tunneling microscope, the thermal noise of a cantilever with a free end can be calculated from square root kT/K. If the end of the cantilever is supported by a hard surface no thermal fluctuations of the deflection are possible. If the optical lever technique is applied to measure the deflection, the thermal noise of a cantilever with a free end is square root 4kT/3K. When the cantilever is supported thermal noise decreases to square root kT/3K, but it does not vanish.

Parametric Deflection Approximations for End-Loaded, Large-Deflection Beams in Compliant Mechanisms

Abstract: Geometric nonlinearities often complicate the analysis of systems containing largedeflection members. The time and resources required to develop closed-form or numerical solutions have inspired the development of a simple method of approximating the deflection path of end-loaded, large-deflection cantilever beams. The path coordinates are parameterized in a single parameter called the pseudo-rigid-body angle. The approximations are accurate to within 0.5 percent of the closedform elliptic integral solutions. A physical model is associated with the method, and may be used to simplify complex problems. The method proves to be particularly useful in the analysis and design of compliant mechanisms

Electrostatic curved electrode actuators

Abstract: This paper presents the design and performance of an electrostatic actuator consisting of a laterally compliant cantilever beam and a fixed curved electrode, both suspended above a ground plane. A theoretical description of the static behavior of the cantilever as it is pulled into contact with the rigid fixed-electrode structure is given. Two models are presented: a simplified semi-analytical model based on energy methods, and fully three-dimensional (3-D) coupled electromechanical numerical simulations using CoSolve-EM. The two models are in qualitative agreement with each other, and predict stable actuator behavior when the beam deflection becomes constrained by the curved electrode geometry before electrostatic pull-in can occur. The pull-in behavior depends on the shape of the curved electrode. Test devices have been fabricated by polysilicon surface micromachining techniques. Experimental results confirm the basic theoretical results. Stable behavior with relatively large displacements and forces can be generated by these curved electrode actuators. Depending on the design, or as a result of geometrical imperfections, regions of unstable (pull-in) deflection behavior are also observed.

A new analytical solution for the load-deflection of square membranes

Abstract: Accurate models are essential for the determination of the elastic properties of thin films from load-deflection experiments. Although finite element method (FEM) models have the potential to be very accurate, analytical models are desirable because of their simplicity. In this paper we present a new analytical solution for the load-deflection of membranes. Our solution yields the same relationship between the load and the deflection as the known analytical solution. However, the values of two constants are up to 35% higher and correspond well with the results from FEM analysis. In addition, the new solution yields analytical forms of the bending lines, which agree well with experimental measurements carried out with silicon nitride membranes.

Modeling and avoidance of static form errors in peripheral milling of plates

Abstract: Peripheral milling of very flexible, cantilevered plates with slender end mills is modeled. The plate has varying structural properties in the axial and feed directions due to metal removal. The cutter is modeled as a cantilevered continuous elastic beam with flexible clamping in the collet. The plate structural properties are updated using the finite element technique as the cutter and plate interact at changing contact zones along the feed direction. The analytical cutting force and surface generation model considers partial separation of tool and plate structures due to static displacements. The experimentally verified model predicts the cutting forces and dimensional surface error on the plate. The model identifies the required feed variation along the plate in order to keep the static form errors within the specified tolerance of the part. The model is developed to improve dimensional accuracy in peripheral milling of very flexible aerospace components.

X-ray source with shaped radiation pattern

Abstract: This invention is directed to an x-ray source comprising a housing (12), a power supply (12A), an elongated tubular probe (14), a target assembly (26), and a beam steering assembly (29). The housing encloses an electron beam source (22), and has elements for generating an electron beam along a beam path. The power supply (12A) is programmable to control the voltage, current and timing of an electron beam. The elongated tubular probe (14) extends along a central axis from the housing (12) about the beam path. The target assembly (26) extends along the central axis and is adapted for coupling to end of the probe (14) distal from the housing (12). The target assembly (26) includes target element (26A) positioned along the beam path, wherein the target element (26A) is adapted to emit x-rays in a predetermined spectral range in response to incident electrons. The beam steering assembly (29) includes a deflection element (30), a feedback network (31) and a deflection controller (144). The deflection element (30) deflects the beam from a nominal axis to a selected surface region on the target element (26) in response to a deflection control signal. The feedback network (31) includes deflection sensing elements for sensing the deflection of the beam and elements for generating a feedback signal representative thereof.

Micro-machined accelerometer array with shield plane

Abstract: An accelerative force may be measured using a plurality of deflection elements (102), each deflection element (102) comprising an inertial mass (104), and at least one hinge (104) supporting the inertial mass (104) in a normal position. Application of a force to inertial mass (104) will result in the deflection of the inertial mass (104) in a first direction out of the normal position. The movement of the inertial mass (104) from the normal position stores energy in the hinges (108) which tends to move the inertial mass (104) in a second direction back to its normal position. Either the mass of the inertial mass (104), or the compliance of the hinges (108) is varied from one deflection element (102) in the array to another so that the force applied to the inertial masses (104) by simultaneous acceleration of the deflection elements (102) deflects some of the inertial masses (104). A detection means (112) senses if inertial masses (104) have deflected and produces an output representative of the applied force.

Analysis and comparison of hot-potato and single-buffer deflection routing in very high bit rate optical mesh networks

Abstract: The steady state behavior of regular two-connected multihop networks in uniform traffic under a hot-potato and a simple single-buffer deflection routing technique is analyzed for very high bit rate optical applications. Manhattan Street Network and ShuffleNet are compared in terms of throughput, delay, deflection probability, and hop distribution both analytically and by simulation. It is analytically verified that this single-buffer deflection routing technique recovers in both networks more than 60% of the throughput loss of hot-potato with respect to store-and-forward when packets are generated with independent destinations. This gain, however, decreases to below 40% when the average message length exceeds 20 packets. >

On deflection as a performance criterion in detection

Abstract: The performance of detection systems is usually characterized by the receiver operating characteristics (ROC) curves. Because of the complexity of the calculation of such curves simpler performance criteria are useful. Among these, the deflection criterion, or output signal-to-noise ratio, is one of the most interesting. The advantages and limitations of the deflection are first analyzed. Attention is especially paid to the relation between singular detection and infinite deflection. Maximization of the deflection in the class of linear-quadratic (L-Q) systems is also discussed and it is shown that in order to detect a deterministic signal in some kinds of non-gaussian noise a quadratic term can introduce an almost singular detection. This situation is analyzed by computer simulations and comparisons between results obtained via the deflection or the ROC curves indicate the interest of the deflection in the analysis of the performance of some nonlinear system. >

A beam steering technique using dielectric wedges

Abstract: The thesis describes a method of' beam steering aimed at producing a useful amount of deflection of an antenna beam from boresight, by a simple and Inexpensive method. For large antennas, It is difficult, as well as expensive, to steer the beam by more than a few beamwidths. The method studied was developed with particular reference to the beam steering requirements of Direct Broadcast Satellite flat plate antennas. The method involves two dielectric wedges, having circular faces, placed In front of the antenna. By adjusting the relative angular position of the wedges, the beam can be steered In any direction, up to a maximum value from the antenna boresight direction. The maximum value of the deflection is determined by the wedge angle and the dielectric constant of the wedge material. This method of beam steering Is Independent of frequency. Frequency limitations are, however, set by the need for a matching layer on the wedge faces to reduce the loss due to reflection and also due to interference of multiple reflection effects on the radiation pattern. Extensive investigations are made (both theoretical and experimental) to predict the performance of the wedges as the beam Is steered. The effect of reflection is studied and a new matching technique is devised. Other practical considerations for example, stepping the wedges for weight reduction, the effect of loss in the dielectric material and cross polar performance are also taken into account. Some effort is given to explore the possibility of using metal loaded artificial dielectrics using polyurethane as the base material. Finally, a number of charts are presented to determine the amount of beam steering for an arbitrary position of the wedges.

Crack deflection in ceramic/ceramic laminates with strong interfaces

Abstract: Crack deflection in electrophoretically deposited Al2O3/ TZ-3Y (3 mol% Y2O3-stabilized tetragonal ZrO2) lamellar composites with strong interfaces is described. The fracture behavior of, and crack paths in, these materials were evaluated using indentation and four-point bend tests. The effects of residual and induced stresses on crack deflection are considered.

The prediction of dimensional error for sculptured surface productions using the ball-end milling process. Part 1: Chip geometry analysis and cutting force prediction

Abstract: The study of machining errors caused by tool deflection in the balkend milling process involves four issues, namely the chip geometry, the cutting force, the tool deflection and the deflection sensitivity of the surface geometry. In this paper, chip geometry and cutting force are investigated. The study on chip geometry includes the undeformed radial chip thickness, the chip engagement surface and the relationship between feed boundary and feed angle. For cutting force prediction, a rigid force model and a flexible force model are developed. Instantaneous cutting forces of a machining experiment for two 2D sculptured surfaces produced by the ball-end milling process are simulated using these force models and are verified by force measurements. This information is used in Part 2 of this paper, together with a tool deflection model and the deflection sensitivity of the surface geometry, to predict the machining errors of the machined sculptured surfaces.

Equilibrium Displacement and Stress Distribution in a Two-Dimensional, Axially Moving Web Under Transverse Loading

Abstract: Von Karman nonlinear plate equations are modified to describe the motion of wide, axially moving web with small flexural stiffness under transverse loading. The model can represent a paper web or plastic sheet under some conditions. Closed-form solutions to two nonlinear, coupled equations governing the transverse displacement and stress function probably do not exist. The transverse forces arising from the bending stiffness are much smaller than those arising from the applied axial tension except near the edges of the web. This opens the possibility that boundary layer and singular perturbation theories can be used to model the bending forces near the edges of the web when determining the equilibrium solution and stress distribution. The present analysis is applied to two examples : (I) a web deflecting under its own uniformly distributed weight ; (II) a web deflecting under a transverse load whose distribution is described by the product of sine functions in the axial and width directions. Membrane theory and linear plate theory solutions are used to characterize the importance of the web deformation solutions.

Modelling of the mechanical behaviour of a differential capacitor acceleration sensor

Abstract: A mechanical model and its mathematical solution are presented, which have been developed in order to calculate the sensitivity and frequency behaviour of an acceleration sensor. The sensor is built up as an interdigitated differential capacitor and is driven in a 'high frequency' detection circuitry with an overall electromechanical closed-loop configuration. It is fabricated using surface micromachining techniques and consists of 2 μm thick polysilicon beams. Due to the processes during manufacturing technology, the material contains an inherent tensile stress, such that the mechanical behaviour is not only determined by the restoring bending moments of the suspension tethers. The calculated deflection of the sensor element amounts to only 0.6 nm g−1; its resonance frequency is about 21 kHz. The results will be discussed and compared with the results obtained by finite-element analysis.

Method and apparatus for calibrating a control apparatus for deflecting a laser beam

Abstract: In a method for calibrating the deflection control of a laser beam a light-sensitive medium (5) is exposed to a laser beam (2) at predetermined positions for generating a test pattern (20), thereafter digitized partial pictures of pattern portions (21) of the test pattern (20) are produced and the digitized partial pictures are composed to a digitized overall picture of the test pattern (20). The correction data for the control (4) for deflecting the laser beam (2) are calculated on the basis of a comparison of actual positions of the laser beam (2) on the digitized overall picture with predetermined desired coordinates.

New methods for measuring mechanical properties of thin films in micromachining: Beam pull-in voltage (VPI) method and long beam deflection (LBD) method

Abstract: New stress-measurement methods for determining both tensile and compressive stress and Young's modulus in surface micromachining are presented. The investigation is concentrated on the development of two techniques: (1) beam pull-in voltage (VPI) and (2) long beam deflection (LBD). The VPI method is based on the pulling down of the upper electrode (beam) when the voltage between two electrodes exceeds a critical level. Both tensile and compressive stress and Young's modulus of a thin film can be derived using this method. the LBD method, on the other hand, converts the axial strain in the beam into a transverse deflection w(x) after the structure is released to be free standing; this deflection is large enough to be measured easily. These techniques have been analysed and tested experimentally. A comparison with other known stress-measurement techniques shows good agreement using polysilicon films. Both techniques have been shown to be quite promising for simple and accurate on-chip thin-film stress measurements.

Micro-opto mechanical switch integrated on silicon

Abstract: A micro-opto-mechanical switch 1*2 has been achieved using a combination of two technologies, integrated optics and micromachining on silicon The commutation is obtained by means of the mechanical deflection of a cantilever beam driven by an electrostatic force The first functional results are reported

Self-compensating rolling weight deflectometer

Abstract: A rolling weight deflectometer for monitoring deflection of pavement under load The deflectometer incorporates an alignment laser beam emitter that measures vertical displacement of each of a plurality of distance sensors mounted on a horizontal sensor bearer member that bends or vibrates as it is transported over a pavement for deflection measurement The measured vertical displacements, due to member bending, allow the deflectometer to compensate for errors introduced by member bending and thereby provide a more accurate measurement of pavement deflection

The prediction of dimensional error for sculptured surface productions using the ball-end milling process. Part 2: Surface generation model and experimental verification

Abstract: This paper presents a surface generation model for sculptured surface productions using the ball-end milling process. In this model, machining errors caused by tool deflections are studied. As shown in Part 1 of this paper, instantaneous horizontal cutting forces can be evaluated from the cutting geometries using mechanistic force models. In this paper, a tool deflection model is developed to calculate the corresponding horizontal tool deflection at the surface generation points on the cutter. The sensitivity of the machining errors to tool deflections, both in magnitude and direction, has been analyzed via the deflection sensitivity of the surface geometry. Machining errors are then determined from the tool deflection and the deflection sensitivity of the designed surface. The ability of this model in predicting dimensional errors for sculptured surfaces produced by the ball-end milling process has been verified by a machining experiment. In addition to providing a means to predict dimensional accuracy prior to actual cutting, this surface generation model can also be used as a tool for quality control and machining planning.

Temperature correction of deflections and backcalculated asphalt concrete moduli

Abstract: A temperature correction procedure for deflections and backcalculated asphalt concrete (AC) moduli for flexible pavements in North Carolina is presented. The data used in developing this procedure were collected from four pavements in the Piedmont area of North Carolina with various types of layer materials and thicknesses. Four trips, one in each season, were made to each of these pavements so that deflections in the maximum range of temperatures could be obtained without significant structural deterioration of the pavements. During each trip deflection testing was conducted on an hourly basis for 1 full day per test section. Pavement surface and depth temperatures were measured at the time of deflection testing with a falling weight deflectometer. The measured deflection and temperature values were used to validate the temperature correction procedure presented in the 1993 AASHTO "Guide for Design of Pavement Structures". It was found that the AASHTO procedure produced significant errors in the corrected deflections. The main reasons for these errors were that the AASHTO mean temperature cannot account for the difference in temperature-depth gradients during heating versus cooling cycles and that the AASHTO temperature correction factors overcorrect the deflections at higher temperatures. A new temperature correction procedure for deflections and backcalculated moduli was developed on the basis of the fact that the middepth temperature of the AC layer is an effective AC layer temperature. The accuracy of this procedure was validated with deflection and surface temperature data collected from four other pavement sections in North Carolina.

Elastica of Simple Variable-Arc-Length Beam Subjected to End Moment

Abstract: This paper presents two methods to find the elastica of a bar or a beam of given span length, but unknown arc length. The beam is subjected to a moment at a hinged end that can slide freely over another support. In the first method the differential equation based on large-deflection theory is formulated and solved by using elliptic integrals. The method yields an exact closed-form solution. The critical or maximum applied moment the beam can resist is also obtained by this formulation. Further, the well-known small displacement solution can be obtained from the degeneration of the exact solution by considering small rotations. The second method is based on a variational formulation, which involves the bending strain energy and work done by the end moment. The finite-element discretization of span length instead of bar length is used to solve the problem. Numerical comparisons are given and results from the finite-element method show good agreement with the elliptic integrals solutions.