Tag Archives: mechanics

Star sequence minimises distortion

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It is some months since I have written about engineering so this post is focussed on some mechanical engineering.  The advent of pneumatic and electric torque wrenches has made it impossible for the ordinary motorist to change a wheel because it is very difficult to loosen wheel nuts by hand when they have been tightened by a powered wrench which most of us do not have available.  This has probably made motoring safer but also means we are more likely to need assistance when we have a flat tire.  It also means that the correct tightening pattern for nuts and bolts is less widely known.  A star-shaped sequence is optimum, i.e., if you have six bolts numbered sequentially around a circle then you start with #1, move across the diameter to #4, then to #2 followed by #5 across the diameter, then to #3 and across the diameter to #6.  This sequence is optimum for flanges, bolted joints in the frames of buildings and joining machine parts as well as wheel nuts.  We have recently discovered that it works in reverse, in the sense that it is the optimum sequence for releasing parts made by additive manufacturing (AM) from the baseplate of the AM machine (see ‘If you don’t succeed try and try again’ on September 29th, 2021).  Additive manufacturing induces large residual stresses as a consequence of the cycles of heat input to the part during manufacturing and some of these stresses are released when it is removed from the baseplate of the AM machine, which causes distortion of the part.  Together with a number of collaborators, I have been researching the most effective method of building thin flat plates using additive manufacturing (see ‘On flatness and roughness’ on January 19th, 2022).  We have found that building the plate vertically layer-by-layer works well when the plate is supported by buttresses on its edges.  We have used two in-plane buttresses and four out-of-plane buttresses, as shown in the photograph, to achieve parts that have comparable flatness to those made using traditional methods.  It turns out that optimum order for the removal of the buttresses is the same star sequence used for tightening bolts and it substantially reduces distortion of the plate compared to some other sequences.  Perhaps in retrospect, we should not be surprised by this result; however, hindsight is a wonderful thing.

The current research is funded jointly by the National Science Foundation (NSF) in the USA and the Engineering and Physical Sciences Research Council (EPSRC) in the UK and the project was described in ‘Slow start to an exciting new project on thermoacoustic response of AM metals’ on September 9th 2020.

Image: Photograph of a geometrically-reinforced thin plate (230 x 130 x 1.2 mm) built vertically layer-by-layer using the laser powder bed fusion process on a baseplate (shown removed from the AM machine) with the supporting buttresses in place.

Sources:

Patterson EA, Lambros J, Magana-Carranza R, Sutcliffe CJ. Residual stress effects during additive manufacturing of reinforced thin nickel–chromium plates. IJ Advanced Manufacturing Technology;123(5):1845-57, 2022.

Khanbolouki P, Magana-Carranza R, Sutcliffe C, Patterson E, Lambros J. In situ measurements and simulation of residual stresses and deformations in additively manufactured thin plates. IJ Advanced Manufacturing Technology; 132(7):4055-68, 2024.

Corona-induced transition from molecular to particle motion in biological media

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Light signatures generated by particles in a nanoscopeIn last month’s post [see ‘Nanoparticle motion through heterogeneous hydrogels’ on November 6th, 2024], I described our recent work on tracking nanoparticles through a model of the vitreous humour and mentioned it was the first of two articles published in the Nature journal, Scientific Reports.  In the second article, we explored the use of caustics in an optical microscope [see ‘Seeing the invisible’ on October 29th, 2014] to track nanoparticles in biofluids.  Nanoparticles are below the resolution of an optical microscope because they are substantially smaller than the wavelength of visible light; hence, they are usually tracked using fluorescent markers or tags attached chemically to the nanoparticles.  These tags can influence both the motion of the particles and biological activity so caustics provide a label-free technique that allows particles to be tracked in real-time using a standard optical microscope.  In most of our previous research, we have tracked nanoparticles in transparent fluids such as water, glycerol-water mixtures, or the hydrogels described in last month’s post.  In our latest work, we have tracked small nanoparticles with diameters from 10 to 100 nm in common cell culture media with different concentrations of serum proteins.  These fluids are a ‘soup’ of complex protein molecules that interact with one another and the gold nanoparticles being tracked.  We found that the presence of proteins caused a reduction in the rate of diffusion for both positively- and negatively-charged particles and we concluded that the proteins form a corona around each nanoparticle effectively enlarging its diameter.  For larger nanoparticles, and those positively-charged, the enlargement appears to cause a transition from molecular motion, in which particle diameter is unimportant, to particle motion where larger particles diffuse more slowly.  We first explored this transition from fractional to classical Stokes-Einstein behaviour in simple fluids in 2017 [‘Slow moving nanoparticles‘ on December 13th 2017] and it seems likely to be complicated in these complex fluids.  Hence, understanding protein dynamics as well nanoparticle dynamics will be essential to the development of nanotechnologies applicable in biological environments.  So, we have lots more work to do!

Sources:

Schleyer G, Patterson EA, Curran JM. Label free tracking to quantify nanoparticle diffusion through biological media. Scientific Reports. 2024 Aug 13;14(1):18822.

Coglitore D, Edwardson SP, Macko P, Patterson EA, Whelan MP, Transition from fractional to classical Stokes-Einstein behaviour in simple fluids, Royal Society Open Science, 4:170507, 2017.

Nanoparticle motion through heterogeneous hydrogels

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Over the last couple of years, we have been transitioning a technique, which we developed for tracking the motion of nanoparticles using caustics [see ‘Slow moving nanoparticles‘ on December 13th 2017], from its initial use in exploring mechanics at the nanoscale to applications in nanobiology [See ‘Label-free real-time tracking of individual bacterium‘ on January 25th, 2023] where it has the advantages of functioning in real-time and being label-free (chemical labels can impact motion, protein interactions and cell behaviour).  In the summer, we had couple of articles published in consecutive issues of the Nature journal, Scientific Reports which describe our recent work.  In the first, we have explored the diffusion of nanoparticles through a synthetic analogue of the vitreous humour in order to support the design of novel therapeutics for retinal diseases.  Retinal diseases, such as macular degeneration and diabetic retinopathy, affects millions of people globally and treatment often involves frequent intravitreal injections of anti-vascular endothelium growth factor agents and corticoids.  Delivery of the appropriate dose to the retinal cell layer is challenging due to the complex nature of the vitreous and functionalised nanoparticles offer a potential solution.  In vivo animal testing is inappropriate because of the ethical concerns and poor representation of human eyes and ex vivo testing of cadaveric eyes is unreliable due to the instability of biomechanical and biochemical properties of the vitreous humour.  Hence, we used agar-hyaluronic acid hydrogels as an in vitro model of the vitreous and employed the caustic technique to track the motion of nanoparticles through the hydrogels.  The hydrogels had been validated as a representative model of the vitreous humour by other research groups.  Our tracking technique revealed that the electric charge on the nanoparticles did not affect their diffusion through the hydrogel; however, both the diameter of the particles and the heterogeneous nature of the gel influenced the diffusion.  Nanoparticles with diameters of 200, 100 and 50 nm moved progressively more quickly and over a larger area.  The diffusion rates in hydrogels with a high viscosity (about 450  Pa.s) were consistent throughout the gel implying that the gel was homogeneous, while gels with medium (about 40 Pa.s) to low (about 3 Pa.s) viscosity generated diffusion rates that were distributed bi-modally suggesting a heterogeneous gel with zones of low and high density in which the particles moved more or less freely.  The heterogeneity of a gel renders a global value for viscosity somewhat meaningless and makes comparisons difficult with the vitreous humour because it is also heterogeneous; however, global values of viscosity for porcine vitreous humour are typically 1 Pa.s.  We are continuing this research; however, our published work has demonstrated that the use of caustics in an optical microscope is a reproducible and inexpensive technique for exploring the design of novel nanoscale drug delivery systems for the eye.

Source: Lorenzo Lopez M, Kearns VR, Curran JM, Patterson EA. Diffusion of nanoparticles in heterogeneous hydrogels as vitreous humour in vitro substitutes. Scientific reports. 2024 Jul 29;14(1):1744.

Image: Random track of a nanoparticle superimposed on its image generated in the microscope using a pin-hole and narrowband filter.

More on fairy lights and volume decomposition (with ice cream included)

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Explanation in textLast June, I wrote about representing five-dimensional data using a three-dimensional stack of transparent cubes containing fairy lights whose brightness varied with time and also using feature vectors in which the data are compressed into a relatively short string of numbers [see ‘Fairy lights and decomposing multi-dimensional datasets’ on June 14th, 2023].  After many iterations, we have finally had an article published describing our method of orthogonally decomposing multi-dimensional data arrays using Chebyshev polynomials.  In this context, orthogonal means that components of the resultant feature vector are statistically independent of one another.  The decomposition process consists of fitting a particular form of polynomials, or equations, to the data by varying the coefficients in the polynomials.  The values of the coefficients become the components of the feature vector.  This is what we do when we fit a straight line of the form y=mx+c to set of values of x and y and the coefficients are m and c which can be used to compare data from different sources, instead of the datasets themselves.  For example, x and y might be the daily sales of ice cream and the daily average temperature with different datasets relating to different locations.  Of course, it is much harder for data that is non-linear and varying with w, x, y and z, such as the intensity of light in the stack of transparent cubes with fairy lights inside.  In our article, we did not use fairy lights or icecream sales, instead we compared the measurements and predictions in two case studies: the internal stresses in a simple composite specimen and the time-varying surface displacements of a vibrating panel.

The image shows the normalised out-of-plane displacements as the colour as a function of time in the z-direction for the surface of a panel represented by the xy-plane.

Source:

Amjad KH, Christian WJ, Dvurecenska KS, Mollenhauer D, Przybyla CP, Patterson EA. Quantitative Comparisons of Volumetric Datasets from Experiments and Computational Models. IEEE Access. 11: 123401-123417, 2023.