An Engineer's Perspective on Mathematics
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The Engineering Sciences Center at Sandia National Laboratories provided an independent peer review of the structural analysis supporting the National Transportation Safety Board investigation of the August 1, 2007 collapse of the I-35W Bridge in Minneapolis. The purpose of the review was to provide an impartial critique of the analysis approach, assumptions, solution techniques, and conclusions. Subsequent to reviewing numerous supporting documents, a SNL team of staff and management visited NTSB to participate in analysis briefings, discussions with investigators, and examination of critical elements of the bridge wreckage. This report summarizes the opinion of the review team that the NTSB analysis effort was appropriate and provides compelling supporting evidence for the NTSB probable cause conclusion.
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Proposed for publication in Highlights- a Quarterly Update- Weapons Systems Engineering Assessment Technology Campaign (C6).
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Proposed for publication in Tribology Letters.
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The primary goals of the present study are to: (1) determine how and why MEMS-scale friction differs from friction on the macro-scale, and (2) to begin to develop a capability to perform finite element simulations of MEMS materials and components that accurately predicts response in the presence of adhesion and friction. Regarding the first goal, a newly developed nanotractor actuator was used to measure friction between molecular monolayer-coated, polysilicon surfaces. Amontons law does indeed apply over a wide range of forces. However, at low loads, which are of relevance to MEMS, there is an important adhesive contribution to the normal load that cannot be neglected. More importantly, we found that at short sliding distances, the concept of a coefficient of friction is not relevant; rather, one must invoke the notion of 'pre-sliding tangential deflections' (PSTD). Results of a simple 2-D model suggests that PSTD is a cascade of small-scale slips with a roughly constant number of contacts equilibrating the applied normal load. Regarding the second goal, an Adhesion Model and a Junction Model have been implemented in PRESTO, Sandia's transient dynamics, finite element code to enable asperity-level simulations. The Junction Model includes a tangential shear traction that opposes the relative tangential motion of contacting surfaces. An atomic force microscope (AFM)-based method was used to measure nano-scale, single asperity friction forces as a function of normal force. This data is used to determine Junction Model parameters. An illustrative simulation demonstrates the use of the Junction Model in conjunction with a mesh generated directly from an atomic force microscope (AFM) image to directly predict frictional response of a sliding asperity. Also with regards to the second goal, grid-level, homogenized models were studied. One would like to perform a finite element analysis of a MEMS component assuming nominally flat surfaces and to include the effect of roughness in such an analysis by using a homogenized contact and friction models. AFM measurements were made to determine statistical information on polysilicon surfaces with different roughnesses, and this data was used as input to a homogenized, multi-asperity contact model (the classical Greenwood and Williamson model). Extensions of the Greenwood and Williamson model are also discussed: one incorporates the effect of adhesion while the other modifies the theory so that it applies to the case of relatively few contacting asperities.
Journal of Microelectromechanical Systems
This work demonstrates a polycrystalline silicon surface-micromachined inchworm actuator that exhibits high-performance characteristics such as large force (±0.5 millinewtons), large velocity range (0 to ±4.4 mm/sec), large displacement range (±100 microns), small step size (±10, ±40 or ±100 nanometers), low power consumption (nanojoules per cycle), continuous bidirectional operation and relatively small area (600 × 200μm2). An in situ load spring calibrated on a logarithmic scale from micronewtons to millinewtons, optical microscopy and Michelson interferometry are used to characterize its performance. The actuator consists of a force-amplifying plate that spans two voltage-controlled clamps, and walking is achieved by appropriately sequencing signals to these three components. In the clamps, normal force is borne by equipotential rubbing counterfaces, enabling friction to be measured against load. Using different monolayer coatings, we show that the static coefficient of friction can be changed from 0.14 to 1.04, and that it is load-independent over a broad range. We further find that the static coefficient of friction does not accurately predict the force generated by the actuator and attribute this to nanometer-scale presliding tangential deflections.