Category Archives: Fundamentals

Classic Fluid Mechanics Lecture Series by Ascher Shapiro

A great set of video lectures by Ascher Shapiro of MIT on Fluid Mechanics is available on youtube.  The videos are old, but fluid mechanics hasn’t changed.   Each video is presented by a world renowned fluids expert such as Ascher Shapiro (wikipedia link) or G.I. Taylor (wikipedia link).  An accompanying set of notes is available at http://web.mit.edu/hml/notes.html.  He uses experiments to explain the topics in a way which helps develop one’s intuition for understanding and solving fluids problems.

 

Good References for Vacuum Flow Calculations

High vacuum systems are becoming more common and a number of semiconductor processes already operate in high vacuum.  The following references are ones that I have found useful in performing vacuum system calculations.

Pfeiffer Vacuum, which manufactures vacuum pumps and other components, has a nice PDF handbook which is free to download.  It covers the basics of vacuum as well as operating principles of various pumps and as well as a number of practical issues.
https://www.pfeiffer-vacuum.com/filepool/File/Vacuum-Technology-Book/Vacuum-Technology-Book-II-Part-2.pdf?referer=1456&request_locale=en_US

The Handbook of Vacuum Technology edited by Karl Jousten is a thorough reference with detailed calculations for wide variety of problems in vacuum systems.
amazon.com link

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Tuned-Mass Damper on a Cantilever Beam

In this article, we compare the performance of a tuned-mass damper mounted at the end of a cantilever beam to the Lanchester damper which was shown in the previous article.  The classic single-degree-of-freedom (SDOF) tuned-mass damper is sketched in the figure below.  The design approach is to find the equivalent SDOF system for the cantilever beam’s mode of interest and then use the design formulas for an optimal SDOF TMD to determine the stiffness and damping of the absorber.

SDOF tuned-mass damper
SDOF tuned-mass damper

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Writing Constraint Equations for Two-Point and Three-Point Mounts

We describe how to obtain the constraint equations for a two point pivot and three point pivot.  Designing a mechanism which can obtain a desired set of constraints is often an important step in kinematic or exact constraint machine design.

We begin with the simple lever mechanism shown in the figure below constraining the motion of two points A and C using the pivot at O.

two point constraint lever

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Airy Points, Bessel Points, Minimum Gravity Sag, and Vibration Nodal Points of Uniform Beams

Beams are often used in precision engineering applications.  One common question is “what are the optimal support locations for a beam?”  The answer depends on the desired objective.  Below we describe some of the most common support locations:  Airy points, Bessel points, minimum deflection, and nodal points.  It turns out that these points are relatively close to each other for the uniform beam.  The basic problem is sketched in the figure below.  A uniform beam is supported on two points and the objective is the determine the placement of the supports in the presence of gravity.

beam support locations

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Thermal Expansion: CTE Definitions and Thermal Strain

This entry discusses different definitions of CTE, their relation to thermal strain, how to convert between the different forms, and how to use them in a model. The forms discussed below include instantaneous coefficient of thermal expansion (CTE), secant coefficient of thermal expansion, and direct use of a thermal strain function.

nonlinear thermal strain
Figure 1

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Expansion and Stiffness of Thin Adhesive or Rubber Layers


Thin layers of adhesive, plastic, or rubber are often employed in precision machines for joining, shimming, and sealing. These layers are often the most compliant and most dimensionally unstable elements of an assembly, so it is important to understand their behavior.

thinlayer

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