Topologically optimized forged glass | glassonweb.com

 

Authors: Wilfried Damen, Faidra Oikonomopoulou, Telesilla Bristogianni & Michela Turrin

Supply: Glass Buildings & Engineering quantity 7, (2022) – https://doi.org/10.1007/s40940-022-00181-1

 

Summary

Thus far, fabricating forged glass elements of considerable mass and/or thickness includes a prolonged and perplex annealing course of. This has restricted using this glass manufacturing technique within the constructed atmosphere to easy objects as much as the dimensions of normal constructing bricks, which may be annealed inside a couple of hours. For the primary time, structural topological optimization (TO) is investigated as an strategy to design monolithic loadbearing cast-glass components of considerable mass and dimensions, with considerably decreased annealing occasions. The analysis is two-fold. First, a numerical exploration is carried out. The potential of lowering mass whereas sustaining passable stiffness of a structural element is finished via a case-study, through which a cast-glass grid shell node is designed and optimised.

To realize this, a number of design standards in respect to glass as a fabric, casting because the manufacturing course of and TO as a design technique, are formulated and utilized within the optimisation. It’s concluded {that a} TO strategy absolutely fitted to three-dimensional glass design is as of but not obtainable. For this analysis, strain- or compliance primarily based TO is chosen for the optimization of the three-dimensional, forged glass grid shell node; in our case, we take into account {that a} pressure primarily based TO permits for a greater exploration of the thickness discount, which, in flip, has a significant affect on the annealing time of forged glass. Compared, in a stress-based optimization, the significantly decrease tensile energy of glass would develop into the principle restrain, leaving underutilized the upper compressive energy. Moreover, it’s decided {that a} single, unchanging and dominant load-case is most fitted to TO optimisation.

Utilizing ANSYS Workbench, mass reductions of as much as 69% in comparison with an preliminary, unoptimized geometry are achieved, lowering annealing occasions by an estimated 90%. Following this, the feasibility of producing the ensuing complex-shaped glass elements is investigated although bodily prototypes. Two manufacturing methods are explored: lost-wax casting utilizing 3D-printed wax geometries, and kiln-casting utilizing 3D-printed disposable sand moulds. A number of glass prototypes had been efficiently forged and annealed. From this, a number of conclusions are drawn relating to the applicability and limitations of TO for forged glass elements and the potential of different manufacturing strategies for making such complex-shaped glass elements.

Introduction

The shaping of forged glass: prospects and limitations

Over the past a long time, glass’s notion within the engineering group has developed from that of a brittle, fragile materials used just for infill components, to a clear load-bearing materials of a excessive compressive energy—acknowledged as much as 1000 MPa for float soda-lime glass by (Saint Gobain 2016; Weller et al. 2008; Ashby and Jones 2006), larger than that of even structural metal. Certainly, the structural purposes of glass within the constructed atmosphere are constantly rising, but with a substantial geometrical limitation: because of the prevalence of the float glass business, structural glass is mostly restricted to the shapes and types that may be generated by the nearly planar, two-dimensional, float panels. Solid glass can escape the design limitations imposed by the, basically, two-dimensionality of float glass.

By pouring molten glass into moulds, this different manufacturing technique permits for the creation of strong three-dimensional glass components of nearly any form and cross-section (Oikonomopoulou et al. 2018a). Load-bearing forged glass components have as of but seen little utility in realized buildings. Some notable examples embody the Atocha Memorial (Paech and Göppert 2008), the Crown Fountain (Hannah 2009), the Optical Home (Hiroshi 2013), the Crystal Homes (Oikonomopoulou et al. 2015, 2018b) (Fig. 1), the Qwalala Sculpture (Paech and Göppert 2018), the LightVault (Parascho et al. 2020) and the Qaammat Pavilion (Oikonomopoulou et al. 2022).

What’s widespread throughout all aforementioned initiatives is that the forged glass components observe the form of standardized bricks, mimicking the performance, form and measurement of ceramic masonry; a glass quantity which may be annealed inside an affordable time size (Fig. 2). Regardless of its potential for fabrication of free-form components, little exploration has been made thus far on the shapes that may be achieved in forged glass (Oikonomopoulou et al. 2018a).

A serious impediment for the manufacturing of forged glass components of considerable mass and dimensions is the meticulous and time-consuming annealing course of concerned, which considerations the sluggish and managed cooling of the molten glass under its softening level,1,2 (Oikonomopoulou et al. 2018a). The annealing stage is crucial as a way to eradicate any doable differential pressure and stop the technology of inside residual stresses throughout additional cooling as a consequence of uneven shrinkage (Shand and Armistead 1958), which in flip, can negatively affect the structural efficiency and failure mode of the ensuing glass element. Through the annealing stage, the magnitude of the ensuing inside stresses is decided by the temperature differential between the warmest and coolest elements of the forged object.

That is instantly linked to the quantity of surfaces uncovered to cooling, the kind of glass, the quantity of residual stress required and the thickness, measurement and mass distribution of the thing concerned (Shand and Armistead 1958). Accordingly, by way of geometry, the dimensions, mass distribution and most thickness of the thing being forged can largely affect the required cooling occasions (Oikonomopoulou et al. 2018a); really any enhance within the cross-section of the thing exponentially will increase the required cooling time. A sensible instance of this may be proven by evaluating two variations of soda-lime glass bricks fabricated for the Crystal Homes challenge (Figs. 1, 2). On this challenge, the smaller glass brick of fifty × 105 × 210 mm required 8 h of annealing; whereas a brick of double this width (50 × 210 × 210 mm) was discovered to require 36–38 h of annealing (Oikonomopoulou et al. 2015). Subsequently, within the constructed atmosphere, the prolonged annealing occasions of forged glass manufacturing and the interconnected manufacturing prices have hampered the fabrication of forged glass components past the dimensions of normal constructing bricks.

Giant-scale strong forged glass components have been however realized in non-architectural purposes. Essentially the most notable ones are the monolithically forged mirror blanks of ground-based big telescopes, which span a number of meters in diameter. Because of their giant dimensions, annealing occasions are important. For instance, 12 months of annealing had been required for the strong glass mirror of the Hooker Telescope, 2.50 m in diameter and 0.32 m thick, weighing 4 tons, forged from soda-lime wine-bottle glass (Zirker 2005). To shorten annealing occasions, in subsequent designs, apart from choosing a glass composition with a decrease thermal enlargement coefficient, 3 a hole honeycomb substructure was launched, which decreased the part thickness and mass whereas nonetheless making certain a glass disk of excessive stiffness. Because of these modifications, the more moderen blanks of the Big Magellan Telescope, regardless of measuring 8.4 m in diameter and weighing 16 tons every, have required an annealing time of solely three months (Oikonomopoulou et al. 2018a), as proven in Fig. 3.

 

Topology optimization: designing structural components of decreased mass

In direction of this path, this paper explores a novel structural design strategy for designing free-form forged glass components with decreased annealing occasions, via the appliance of structural topology optimisation.

Topological Optimization (TO) is a structural design strategy which permits for the optimisation—and thus discount—of mass in connection to structural efficiency. It capabilities by approaching probably the most optimum materials distribution inside a given design area, making an allowance for specified hundreds, helps and constraints (Bendsøe and Sigmund 2003). The discount of mass, whereas sustaining excessive stiffness, makes it probably promising for structural forged glass components; via TO we are able to design monolithic, structural glass elements of decreased thickness and quantity, and thus of a decreased annealing time.

TO usually ends in highly-customized shapes which are advanced and never at all times intuitive. These shapes are typically tough and costly to supply with conventional manufacturing methods, equivalent to injection moulding, milling and forming used for mass manufacturing. The usage of computer-controlled additive and subtractive strategies makes it doable to automate the manufacturing of such elements –instantly of the elements or of the respective moulds– underneath a excessive stage of precision and inside a decreased lead manufacturing time.4 As every ingredient is produced individually, a excessive stage of customisation is feasible, stopping the overhead prices of tooling, but additionally the creation of waste as a consequence of e.g. scraps, linked to the advanced shapes. By using additive manufacturing (AM) the complete element may be made in a single course of (topic to the overall dimensions of the printer), thus the prices associated to the meeting of advanced elements may also be nullified. All of the above render additive manufacturing notably enticing for restricted batch productions.

On the draw back, AM yields a compromised floor ending high quality that requires post-processing and nonetheless presents some limitations on the utmost product measurement that may be produced (topic to the dimensions limitations of the printing mattress), in addition to on the supplies that may be (instantly) utilized; whereas, the layer by layer manufacturing continues to be topic to standardization, which may render using AM difficult in purposes the place certification is important (Kawalkar et al. 2021). Regardless, AM stays probably the most appropriate manufacturing course of for realizing TO buildings, through which every ingredient is optimised in line with the particular hundreds it has to face up to, at little further manufacturing value.

To date, sensible utility of TO, has remained largely restricted to excessive efficiency purposes, equivalent to aerospace design (Rozvany 2009). Numerous purposes of TO within the constructed atmosphere, realized with assistance from AM, have been investigated (Jipa et al. 2016; Prayudhi 2016; Galjaard et al. 2015; Naboni and Kunic 2019) (see Fig. 4); nonetheless, as a design instrument for structural glass elements it has remained relatively unexplored.

Grid shells are a category of buildings that present the environment friendly loadbearing properties of shell buildings, whereas consisting largely of one-dimensional beam components, permitting for light-weight and economical buildings. The complexity of the construction is concentrated within the nodes through which the beams are linked. Complicated grid shell nodes designed utilizing TO have been beforehand explored in metal buildings (van der Linden 2015; Prayudhi 2016; Seifi et al. 2018) discovering that important weight financial savings may be achieved whereas retaining structural integrity. To the data of the authors, structural grid shell nodes fabricated from glass are a novelty.

Methodology

To research the potential of TO for structural forged glass purposes, a glass grid shell construction has been designed, utilizing topologically optimised forged glass for the connecting nodes.

The analysis course of is twofold, consisting of numerical design adopted by bodily prototyping. For the needs of this analysis, a case-study construction has been used, which is predicated on a pavilion constructed on the Singapore College of Expertise and Design (Sevtsuk and Kalvo 2014). The construction has first been redesigned with loadbearing tubular glass components in Rhinoceros 6 and parametrised utilizing Grasshopper and the structural FEA plug-in Karamba3D. The purpose is to research using TO for the design of structural forged glass grid-shell nodes that join the tubular glass components. The dimensioning of the glass shell construction is used to find out the scale and form of the glass nodes which are to be optimised, whereas the FEA mannequin supplies the forces on the node, used for optimisation and structural validation.

For the optimisation, a number of design standards in respect to the casting and annealing technique of glass are established, derived from observations constructed from present glass castings, along with practical standards primarily based on meeting and set up of the construction. These are then utilized within the optimisation of the chosen nodes, utilizing strain-based optimisation in ANSYS workbench. In addition to being accessible via and educational licence, this program was chosen as a consequence of its in depth TO toolset, in addition to its built-in modelling and FEA instruments. A design loop is used, through which a base geometry is generated in Grasshopper, adopted by optimisation, post-processing and FEA inside ANSYS. Primarily based on these outcomes, the preliminary geometry and optimisation parameters may be tweaked as wanted.

Primarily based on the ultimate node design, two distinct mould methods for manufacturing such complex-shaped, personalized glass components with assistance from additive manufacturing are explored via the kiln-casting of small-scale prototypes within the Glass Lab: (i) a disposable silica-plaster mould utilizing funding casting and a 3D-printed wax ingredient, and (ii) a 3D-printed sand mould produced by ExOne.

Node setup and optimization objectives

Case research design

Intensive documentation of the SUTD grid shell challenge was offered via the SUTD (Fig. 5). This challenge was chosen as a consequence of its freeform form. As every of its nodes will probably be uniquely optimised with out uniform, repeating components, it turns into doable to grasp a complex-shaped construction with out nice further investments. Moreover, the shell is designed as a compression-based construction, lowering the danger of the glass components being subjected to important tensile stresses—the place glass presents a significantly weaker efficiency.

The construction of the shell has been re-designed as a hybrid steel-glass meeting. The beams of the grid include extruded glass tube profiles clamped between two POM plastic caps. These are held in place by a central metal rod working via the glass profile (Fig. 6). For the meeting of the construction the next precept is employed (Fig. 7): a skinny metal ring is inserted right into a cylindrical void on the centre of every node. By means of this ring, bolts may be inserted that connect with the metal rods of the encircling beams via a coupling nut. On this manner, the glass supplies stiffness to the construction and carries the compressive hundreds, whereas direct tensile hundreds are transferred by the metal substructure, making environment friendly use of the inherent properties of each supplies.

 

TO as a instrument for structural glass—stress vs. pressure primarily based optimisation

When utilizing topology optimisation (TO) instruments for glass, sure problems come up, as most obtainable TO instruments are designed to be used in ductile supplies with comparable tensile and compressive energy. Glass, nonetheless, is a brittle materials, with an assumed tensile energy that’s at the least an order of magnitude decrease than its acknowledged compressive energy.

Two completely different approaches to TO instruments may be distinguished: stress-based and pressure primarily based optimisation. Stress-based TO goals to minimise stress in an object for a given set of boundary circumstances. Most stress-based strategies simplify this calculation by utilizing a Mises stress standards, which is an abstraction that doesn’t distinguish between stress and compression. This permits for a simplified and sooner optimisation progress, however limits its applicability for brittle glass, the place principal stresses are the reason for failure. In essence, the Von Mises criterion affords an equal tensile stress that’s used to foretell the yielding of (ductile) supplies underneath multiaxial loading circumstances.5 

Compared, principal stresses, relevant for glass design, are strongly depending on the reference aircraft, which modifications every time the geometry modifications; making their implementation inside a TO atmosphere notably difficult. Furthermore, if utilized to glass, the Mises stress standards, ends in the significantly decrease tensile energy to develop into the limiting issue (sometimes thought of between 30–45 MPa for annealed soda-lime glass6 and 22–32 MPa for borosilicate glass (O’ Regan 2014; Granta Design Restricted 2015)), leaving underutilized the significantly larger compressive energy of the fabric (recorded as excessive as 1000 MPa by (Ashby and Jones 2006), whereas (Oikonomopoulou et al. 2017) has performed experiments with borosilicate glass that indicated a nominal compressive failure stress > 500 MPa).

Moreover, stress-based TO has a robust mesh dependency, with completely different mesh layouts and sizes leading to completely different optimised geometries (Bendsøe and Sigmund 2003). At the moment, TO instruments appropriate for brittle supplies are being researched, typically focussing on concrete design, utilizing precept stress based-optimisation (Jewett and Carstensen 2019; Chen et al. 2021) or twin materials optimisation (Gaynor et al. 2013). Not like the Von Mises-based optimisation, these strategies can differentiate between the allowable values for tensile and compressive stress within the components. Nevertheless, these strategies are nonetheless at an early stage of growth, and as a consequence of their complexity have been restricted to two-dimensional case research.

Pressure- or compliance primarily based TO is a distinct strategy which goals to maximise stiffness of an object. In comparison with stress-based optimisation, it supplies larger stiffness, whereas additionally being much less depending on the meshing. Though this strategy ought to yield extra dependable geometries, like stress-based optimization it doesn’t provide a distinction between the allowable tensile- and compressive stress values. As well as, as stress is just not instantly taken under consideration, native peak stresses could happen. Since glass is unable to deform plastically to redistribute these native peaks, a post-analysis is important additionally on this case as a way to examine that the ensuing stresses fall inside the acceptable limits.

It’s concluded that each of the introduced optimisation approaches have shortcomings when utilized to brittle supplies with a major variation between their tensile and compressive energy values, equivalent to glass. For the purpose of this analysis, the TO evaluation of a three-dimensional ingredient is most well-liked, as this permits for a greater exploration of the thickness discount, which, in flip, has a significant affect on the annealing behaviour of forged glass. Compliance-based TO evaluation was chosen, as we take into account it to permit for a greater exploration of the thickness discount of the brittle, forged glass element. Equally to a stress-based optimization, strain-based optimization does additionally not distinguish between stress and compression, and extra evaluation is required after optimisation to examine for potential native peak stresses. Nonetheless, we discover that as compared, in a stress-based optimization, the significantly decrease tensile energy of glass would govern as the principle restraint, leaving much more underutilized the considerably larger compressive energy of the fabric.

Design objectives for lowering annealing occasions

4 geometric properties have been formulated which are anticipated to cut back the annealing time of a strong glass object (Desk 1).

Desk 1 Geometric properties and topology optimization objectives for accelerated annealing – Full measurement desk

Limiting the mass reduces the general time wanted to anneal the ingredient, by reducing the quantity of heated materials that must be cooled. Utilizing TO, reductions in quantity between 60 and 80% in comparison with un-optimised geometries have been present in observe (Galjaard et al. 2015; Jipa et al. 2016).

The absence of sharp edges, and a good and skinny part thickness all through the thing are important for attaining a homogeneous cooling charge all through the forged ingredient (Oikonomopoulou et al. 2018a). Each sharp corners and skinny sections will cool sooner than the rest of the thing leading to uneven shrinkage, thus inflicting undesired ranges of inside stresses. Primarily based on the recommended fillet employed on the glass blocks of the Crystal Homes challenge (Oikonomopoulou et al. 2018b), a minimal fillet of three mm radius for sharp corners is assumed. It ought to be famous that inside TO generated geometries, sharp angles are typically not discovered. The optimisation course of applies materials in a manner that minimises stress and pressure, whereas sharply angled components both lead to stress concentrations, or contribute little to the stiffness of the thing.

To create skinny and homogeneous sections, a set of producing thickness constraints was set in ANSYS for the optimisation course of. A minimal part thickness of 15 mm has been chosen from empirical casting expertise, as thinner sections might be difficult to be efficiently forged, whereas a number of most thicknesses, between 30 and 50 mm had been used. This prevents the lengthy cooling occasions linked with thick sections, whereas additionally making certain that part thicknesses stay comparatively homogeneous.

Optimisation

Non-optimized element: Imposed hundreds and dimensions

A parametric setup was made that mechanically generates an un-optimised base geometry for every node, and lists the masses utilized on the node. A node with a diameter of 240 mm and a thickness as much as 95 mm was chosen; a central void of 100 mm diameter was discovered to be most fitted primarily based on meeting calls for, as that is deemed the minimal measurement wanted to insert and fasten a bolt within the central ring. Primarily based on structural evaluation in Karamba3D utilizing the everlasting load of the shell, a 0.5 kN/m2 cladding and a wind load of 0.6 kN/m2 (consultant for buildings underneath 4 m in top in a coastal Dutch scenario), the glass beams of the shell had been dimensioned as glass tubes with a 50 mm outer diameter and a 9 mm wall thickness. The ensuing non-optimised ingredient is proven in Fig. 8. The bending moments, shear forces and compressive regular power have been utilized at outer connections the place the glass beams connect with the node (pink), whereas any tensile regular forces are utilized on the central metal ring (blue), as these hundreds wouldn’t carried by the glass.

The coarse geometries after optimisation have been post-processed with Spaceclaim, the modelling software program included in ANSYS. The shrink-wrap and smoothing instruments had been manually utilized to re-mesh the discovered components, which removes invalid mesh components whereas making certain a easy floor. As well as, a number of components have been re-inserted on the beam connections and central ring to make sure the node may be correctly linked to the remaining construction (Fig. 9).

Three iterations of optimisations have been carried out (Desk 2), these are additional elaborated on within the following chapters. Two nodes had been chosen for optimisation (Fig. 10), characterised by a mix of each excessive compressive shell forces and tensile hoop forces within the adjoining beams.

Desk 2 Overview of optimization iterations for the glass node design – Full measurement desk

Desk 3 accommodates the properties of the glass used for the optimisation and subsequent FEA. Borosilicate glass was chosen, as a consequence of its beneficial annealing behaviour, in comparison with common soda-lime glass. The energy values of glass can fluctuate tremendously, relying on the literature supply used. For this analysis, conservative values had been chosen.

Desk 3 Materials properties of glass used throughout TO and FEA – Full measurement desk

All through the method, the optimisation purpose set was to minimise compliance, and a uniform 8 mm mesh measurement was used. The proportion of fabric retained after optimisation, and the part thickness allowed had been diversified in every iteration to look at their affect on the ensuing geometry.

Optimization TO1, minimal stiffness via a distributed load.

The primary optimisation was carried out utilizing two load circumstances. The fist load case utilized is the everlasting load of the shell construction, as this constitutes the first useless load that the node is anticipated to hold. Optimising for this load alone bears the danger of leading to a node design of inadequate stiffness as a consequence of over-optimisation, because the optimisation doesn’t take any exterior hundreds under consideration. In (van der Linden 2015), a minimal stiffness is created by making use of a further bending second to every beam of the node, anticipating exterior forces which are unaccounted for when optimising just for the useless load of the construction.

An try to recreate this impact was made by including a 0.5 kN/m2 distributed out-of-plane mesh load alongside the complete shell, offering a assured minimal load on every node. An summary of all hundreds may be present in Tables 9 And 10 within the appendix.

As proven in Desk 4, 70% and 80% materials elimination have been examined. Each ensuing geometries had been able to carrying the everlasting load of the shell with out exceeding the tensile capability of the glass (Figs. 11, 12).

Desk 4 Overview of optimisation TO1 – Full measurement desk

Additional FEA was carried out with an added 0.6 kN/m2 wind load, perpendicular to the node, with the exact forces derived from the Karamba3D mannequin. Beneath this load, the tensile stresses exceed the allowable worth for glass at a number of factors (Fig. 13). This demonstrates how TO can generate weight-efficient geometries for a single, prevailing load case, however that these outcomes develop into unreliable because the occurring hundreds begin diverging from this. The pavilion chosen as a case-study is a small, comparatively light-weight construction. Because of this, the stresses within the construction are tremendously influenced by wind loading, making it tough to find out a (prevailing) single load-case for the optimisation of the nodes. The try to realize a minimal stiffness via a distributed mesh load proved inadequate to face up to an exterior load. Accordingly, optimisation TO1 was discarded, and two variations had been made to research how these altering hundreds may be accounted for within the optimisation course of.

 

Optimization TO2, two loadcases

On this iteration, a technique to optimise a node for a number of load-cases was explored. On this case, two separate optimisations had been carried out, utilizing two distinct load-cases: the own-weight (everlasting load)of the construction, and the forces on the node ensuing from a 0.6 kN/m2 wind load perpendicular to the node. The setting used for each optimisations are proven in Desk 5; the masses may be discovered within the appendix, Tables 11 And 12. The 2 separate optimised geometries had been lastly merged collectively to create a single geometry (Fig. 14).

Desk 5 Overview of optimisation TO2 – Full measurement desk

Structural evaluation exhibits that the ensuing ingredient is able to carrying each the dead-load and the wind load used for the 2 optimisations (Fig. 15). Nevertheless, additional evaluation utilizing a wind load in the wrong way because the optimisation load, does trigger failure at a number of factors as a consequence of extreme tensile stresses (Fig. 16). This additional demonstrates that the TO course of is succesful to optimise for a number of predetermined load circumstances, however the ensuing geometries can not successfully carry hundreds that diverge from the predetermined design hundreds. Such an strategy is especially vital for a light-weight construction equivalent to this, the place wind hundreds trigger giant shifts in forces; in comparison with a heavier construction the place the everlasting load stays the prevailing load case.

 

Optimization TO3, elevated useless load

Following the findings of the earlier optimizations, and as a way to make sure that the everlasting load of the shell stays the prevailing load case underneath all circumstances, the shell construction itself is modified to decrease the relative affect of fluctuating wind hundreds on the construction. The dimensions of the pavilion has been elevated by 50% in all dimensions, whereas the beams had been elevated from a 50 mm to an 80 mm diameter, and from a 9 mm to a 12 mm wall thickness.

As well as, the mass of the façade cladding has been elevated from 0.5 kN/m2 to 1.2 kN/m2, representing a change from a light-weight glass protecting to a double-glazed meeting. The size of the node have been saved the identical. The useless load of the construction was used as the one optimisation load. On the two beams the place the node is subjected to stress, 3.0 kN compressive forces had been utilized to the glass to make sure a minimal stiffness of the node. An summary of the masses in included in Tables 13 and 14 within the Appendix, the opposite settings may be present in Desk 6.

Desk 6 Overview of optimisation TO3 – Full measurement desk

The finalised node design is proven in Fig. 17. A linear structural evaluation was carried out to check the behaviour of the node underneath each dead-load and wind. A decreased wind load of 0.49 kN/m2 has been used, similar to a Dutch inland location at low heights as dictated by the Eurocode. Beneath varied wind hundreds, the tensile stresses had been discovered to not exceed the allowable worth (Fig. 18).

Annealing time estimations

Figuring out the required annealing time for a glass object is sophisticated, as it’s decided by a large number of things (Oikonomopoulou et al. 2018a). Not solely the mannequin’s form and mass distribution, but additionally the quantity of floor uncovered to cooling, different thermal plenty current within the oven, and the properties of the oven itself, all affect the annealing cycle. Although literature exists that makes an attempt to exactly information the annealing course of, it usually depends on unspoken assumptions and particular circumstances that can not be broadly utilized (Watson 1999).

An empirical estimation of the anticipated annealing occasions is due to this fact made via comparability to present outcomes. Three soda-lime glass brick components from the Crystal Homes façade challenge have been chosen for a quantitative comparability, utilizing the recorded cooling occasions indicated in (Oikonomopoulou et al. 2018b). The principle facets that decide annealing occasions are the glass kind, mass and thickness of every ingredient. Primarily based on the belief that the identical soda-lime glass is used for all these components, the next estimation may be made by evaluating mass and part thickness (Desk 7). Optimisation TO1 was excluded, as its geometry proved inefficient to face up to an exterior load.

Desk 7 Annealing time estimations of the forged glass optimized node primarily based on the annealing occasions prodived for the forged glass brick models of the Crystal Homes facade – Full measurement desk

Outcomes of numerical design

An summary of the optimization outcomes may be present in Desk 8. Utilizing topological optimization (TO) for the design of a node that it’s able to carrying each the load/everlasting load of the shell and a variable wind load proves difficult, as a element optimised to hold the useless load of the construction turns into susceptible for any distinguished hundreds that diverge from it. It’s doable to extend the resilience of the construction by optimising its mass distribution for a mix of distinguished load circumstances, or by making certain that the optimisation load case stays the dictating one underneath all circumstances.

Desk 8 Overview of optimisation outcomes – Full measurement desk

Though any direct tensile hundreds are carried by the steel substructure, bending moments occurring as a consequence of eccentric wind-loading of the shell nonetheless lead to tensile stresses. Because the compliance-based TO utilized on this analysis doesn’t distinguish between stress and compression inside the materials, it may be deducted that the decrease tensile energy of the glass stays normative, whereas its excessive compressive capability stays underused.

Important weight financial savings had been achieved regardless of this, discovering 69% and 53% discount for TO2 and TO3 respectively. As well as, the utmost part thickness of every element was decreased to eight–30 mm and 20–40 mm respectively from an un-optimised thickness of 95 mm. Empirical annealing occasions derived from comparability to the Crystal Homes challenge present reductions of 90% and 66%, compared to the corresponding un-optimised geometries.

It ought to be famous that the preliminary geometries had been primarily based on an estimation of the required quantity, and may due to this fact be thought of over-dimensioned. Certainly, in compliance TO approaches, the optimum materials distribution is likely one of the foremost enter variables, outlined and extremely dependent by the data of the tip consumer (Gebremedhen et al. 2017). The indicated mass and annealing time reductions can due to this fact be thought of as optimistic estimates. Regardless of this, the outcomes point out that that the mass discount achieved via TO can contribute in considerably shortening the annealing course of for structural forged glass elements.

Prototype manufacturing

On this analysis, two approaches of pc aided manufacturing are employed to manufacture with ample precision the advanced and customised optimised glass geometries. The 3D-printing of the mould was most well-liked over the direct 3D-printing of the glass node because the latter nonetheless faces a number of essential drawbacks: Though direct additive manufacturing of glass has seen some developments (Klein 2015), it nonetheless has extreme limitations within the measurement and shapes that may be achieved, whereas layering of the fabric and certification stay legitimate considerations for creating structural glass elements.7 Furthermore, the shortcoming to print overhangs limits the geometries that may be produced, or requires the introduction of help materials. Due to these concerns, this analysis focuses as a substitute solely on using digital manufacturing for creating glass casting moulds.

Generally, for glass castings, both high-precision CNC-milled steel moulds or disposable, low-cost moulds are used (Fig. 19). Excessive-precision CNC-milled moulds consisting of both metal or graphite are generally employed within the mass fabrication of forged glass components, as these may be reused for high-volume manufacturing (Oikonomopoulou et al. 2018a). These re-usable moulds can yield a excessive stage of floor detailing and excessive dimensional accuracy; nonetheless, they typically contain excessive manufacturing prices, making them uneconomical for small batch productions or for single, customised elements. As well as, such moulds for the casting of optimised components of advanced form, must be extremely intricate, consisting of a number of demountable components to permit for demoulding; including to each fabrication time and price. For personalized elements, normally low-cost, disposable moulds are most well-liked. Nonetheless, these are labour-intensive and yield elements of compromised accuracy and in want of post-processing (Oikonomopoulou et al.2020).

Due to these concerns, 3D-printed disposable moulds of excessive accuracy, are proposed right here as an economical resolution for the casting of personalized strong glass elements of advanced geometry. In comparison with the laborious and time-consuming course of of ordinary funding forged moulds and the high-fabrication prices of high-precision steel moulds, 3D-printed moulds are fast, simple and cost-effective to make and permit for excellent complexity in shapes, together with undercuts and voids. On this analysis, two methods of fabricating such moulds utilizing additive manufacturing have been investigated: lost-wax funding casting utilizing additively-manufactured wax components, and 3d-printed sand moulds.

Misplaced-wax funding casting

Funding casting includes the copy of the specified geometry in a sacrificial materials; generally wax. The manufacturing consists of a number of steps, illustrated in Fig. 20. A heat-resistant mould is shaped across the disposable (wax) element. The sacrificial ingredient is eliminated via heating in a course of known as burn-out, or steaming, leaving a hole mould appropriate for casting.

Additive manufacturing via Fused Deposition Modelling (FDM) may be employed to manufacture the sacrificial components. Specialised filaments have been developed for this, which burn-out at decrease temperatures and go away much less residue within the mould, in comparison with common plastics equivalent to PLA. For this analysis, P2C-175 filament was used. It is a wax-based filament developed for funding casting, obtainable from Machineablewax.com. Utilizing a standard FDM printer, two optimised nodes had been printed at a 1:2 scale.

A number of momentary components had been added to the wax mannequin to enhance the casting high quality. These embody a bigger central channel for the pouring of the glass, six vertical channels to stop air bubbles being trapped within the mould, and a few further channels to make sure a correct circulation of glass all through the mould (Fig. 21). Across the printed wax ingredient (Fig. 22), a silica-plaster mould was forged (Fig. 23). After solidifying, the mould has been positioned in a furnace for six h at 515 °C to burn out the wax mannequin.8 The ultimate forged glass prototype may be seen in Fig. 24.

The glass has been forged utilizing kiln-casting, because the plaster mould is unable to maintain the upper temperatures of hot-pouring. Kiln-casting is carried out by putting items of glass in a heat-resilient reservoir (e.g. a ceramic flower pot) above the mould. Upon heating, the glass melts and flows into the mould, the place it’s left to anneal by controllably reducing the temperature of the kiln. This makes it doable for the thing to be forged and annealed in a single furnace. Nevertheless, compared to different glass casting strategies equivalent to hot-pouring, an extended firing schedule is important to make sure the glass has ample time to totally soften (Fig. 25). This casting was carried out utilizing recycled Schott B270 modified soda-lime glass. This glass may be forged at a decrease temperature as compared with common soda-lime glass, with a melting temperature of 827 °C and an annealing temperature of 482 °C.

After cooling, the silica-plaster mould was softened by being positioned into water, which made it simpler to interrupt and take away the mould with out risking to break the glass components inside. In post-processing, the added air and circulation channels, and any remaining sharp edges had been eliminated with assistance from a small handheld grinder.

Additively manufactured sand moulds

It’s doable to instantly manufacture moulds via 3D-printed sand, a manufacturing approach used within the steel casting business. These moulds current a excessive warmth resistance, and permit for extremely advanced shapes to be printed with out further helps. Additional benefits of printed sand moulds embody their quick manufacturing (usually restricted to some days), low value, and accuracy as much as 0.1 mm (primarily based on the sand used).9 

The most important ingredient that may presently be printed utilizing this method is 4 m x 2 m x 1 m, utilizing the Voxeljet printer VX4000. (Galjaard et al. 2015; Meibodi et al. 2019; Jipa et al. 2016) have utilized this technique for the casting of advanced topologically optimised components in metal, aluminium and concrete respectively (Fig. 26), whereas latest analysis on utilizing these moulds for glass casting by (Flygt 2018; Oikonomopoulou et al. 2020) counsel that it may be used as an economical, high-accuracy resolution for personalized forged glass objects.

Totally different binders can be found for sand-printing. Earlier experimental work by (Bhatia 2019; Oikonomopoulou et al. 2020) has indicated that inorganic binders, such because the CHP binder by ExOne, are probably the most appropriate for the extended heating of the mould within the required temperatures. In addition they highlighted the necessity for the appliance of a coating to realize a very good ending floor outcome for kiln-cast elements; because the glass floor ensuing from the contact with the mould is in precept, tough and translucent. Preliminary assessments by (Bhatia 2019) pointed in direction of the appliance through a paintbrush of Crystal Solid (silica-plaster) for coating of the moulds—this resulted right into a clear floor, but nonetheless tough in texture. Thus, additional analysis find a coating that may yield a very easy texture and clear end floor is important.

Accordingly, a 3D-printed sand mould utilizing CHP binder has been produced for the node designed in iteration TO2. The mould, printed on a 1:1 scale by ExOne, consists of 4 horizontal layers (Fig. 27), with interlocking components to make sure that the layers stay aligned. The layered design was chosen because it simplifies the elimination of left-over sand after printing, and makes the geometry extra accessible for pre-processing, equivalent to for the appliance of coatings. A skinny layer of silica-plaster (Crystal-Solid) coating,10 was utilized to stop the fusing of the sand of the mould to the molten glass, and to make sure a easy glass floor, lowering the post-processing wanted (Bhatia 2019). This coating was chosen for being simply obtainable and inexpensive. A brush was used to manually apply the liquid plaster in a skinny layer that doesn’t deteriorate the printed -water soluble- sand mould.

A kiln-casting setup was used to forged the glass. Primarily based on preliminary outcomes of (Bhatia 2019), it was decided that for the chosen binder materials, glass with a decrease melting temperature is preferable. Due to this, (recycled) lead glass was chosen. An identical firing schedule as earlier than was used, with a decrease melting temperature of 810 °C, and an annealing temperature of 430 °C.

The printed sand mould failed to supply a usable geometry, as upon opening the cooled furnace, it was discovered that the sand mould had collapsed on itself (Fig. 28). Because the binder used to print the sand was much less heat-resilient than assumed, it had evaporated, leaving the sand extremely fragile, falling aside underneath the load of the flowerpot. This seems to have occurred comparatively quickly within the firing schedule, as little glass was discovered contained in the mould, indicating that the mould collapsed earlier than the glass had time to totally liquefy. The distinction in behaviour compared to earlier assessments carried out by (Bhatia 2019) may be defined by the truth that the binder was uncovered to excessive temperatures for a significantly longer interval as a consequence of utilizing a full kiln-casting course of.

Because of time limitations, no additional experiments might be carried out on utilizing sand printed moulds for glass casting. In additional analysis by (Bhatia 2019), a glass ingredient was efficiently forged utilizing the same setup (Fig. 29). On this experiment, the ceramic container (flowerpot) containing the glass for the casting was not positioned instantly on prime of the mould, however supported individually, stopping it from pushing down and including further weight on the mould. This allowed the mould to stay intact sufficiently lengthy for glass to move in and solidify.

 

Casting outcomes

The glass components manufactured via funding casting are discovered to have a tough, layered texture; an imprint of the feel generated by the FDM course of used to print the sacrificial wax ingredient (Fig. 30). A smoother ingredient might be achieved by utilizing a printer with the next decision, or publish processing the ingredient after printing to take away seen layering; although the latter might lead to a lack of accuracy.

Nevertheless, the ensuing element additionally demonstrates the excessive stage of element that may be achieved utilizing kiln casting. Because the glass is saved above its softening level for an prolonged period of time to make sure it absolutely liquefies, it has ample time to settle within the mould and switch even the best particulars of the mould texture to the glass. Through the design section, it was estimated {that a} 15 mm part thickness can be the smallest part that might be forged reliably. The extent of element within the 1:2 funding forged demonstrates that by utilizing kiln casting thinner sections may be achieved, probably additional reducing the annealing time of the ensuing components.

Although the sand mould casting didn’t produce a sound ingredient as a consequence of collapse of the mould, different analysis has yielded promising outcomes. Additional analysis and validation is required to discover the potential of this technique.

Evaluating the 2 fabrication strategies, funding casting utilizing a wax mannequin proved to be considerably extra labour-intensive because of the a number of manufacturing steps and the extra post-processing because of the layered floor end and helps as a part of FDM printing. Though, the instruments and supplies required for this technique are generally obtainable, FDM-printing at a ample stage of precision is a sluggish course of.

The 3D-printing of sand moulds requires extra specialised instruments, however permits for the direct printing of moulds of excessive precision. Furthermore, the dimensions of the obtainable printers (as much as 4 m x 2 m x 1 m by Voxeljet printer VX4000), makes it doable to print a number of components without delay, permitting for bigger batch sizes and a decreased printing time per ingredient. Labour depth is decreased because the mould is printed instantly; furthermore, the printing technique permits for advanced shapes to be printed with out helps, lowering the quantity of post-processing wanted. Nevertheless, an quantity of labour is concerned in cleansing out the unfastened sand and making use of coatings earlier than casting as a way to enhance the floor high quality.

Conclusions and dialogue

Topology optimisation (TO) is a strong design methodology for personalized forged glass structural components. In addition to a major discount in materials use that permits for comparatively light-weight buildings, within the case of structural forged glass, TO can considerably cut back the manufacturing occasions and the intertwined vitality consumption by tremendously lowering the annealing occasions concerned. Within the introduced case research, estimated annealing occasions had been decreased by between 67 and 90%, compared to strong, un-optimised nodes. In observe, such a design strategy, which basically matches the glass mass distribution with the anticipated design hundreds, might assist overcome one of many main challenges of producing forged glass components, paving the best way for a a lot wider use of forged glass as a loadbearing materials for monolithic elements of considerable dimensions and intriguing design, equivalent to clear flooring slabs, bridges or trusses.

Mass reductions of between 53 and 69% had been reached, whereas reductions of as much as 85% had been initially predicted. Some causes for the upper than anticipated last weight embody the necessity to optimise for each the everlasting load because of the own-weight of the construction and wind hundreds, leading to further materials added in TO2 (basically consisting of two optimised components in a single) and TO3 (the quantity of eliminated materials was lowered to extend flexibility). As well as, materials was re-introduced to make sure a full connection to the connecting structural components, additional rising weight.

The outcomes of the casting of a scale mannequin have confirmed that components thinner than the estimated minimal thickness of 15 mm may be forged, which can be utilized to additional cut back annealing occasions. Nevertheless, the moulds wanted for such detailed components may develop into a limiting issue, contemplating for instance the unfastened leftover sand that must be faraway from the sand-printed mould.

One of many challenges encountered throughout using TO was accounting for variable (e.g. wind) hundreds within the design. It was demonstrated that TO is able to designing extremely optimised buildings, carrying hundreds with solely a fraction of the unique materials. The draw back of this optimisation is a discount in flexibility and skill of the construction to carry out properly underneath variable hundreds. As over-dimensioning is decreased to a minimal, buildings develop into much less capable of face up to hundreds which are variable or are unaccounted for throughout design. Buildings within the constructed atmosphere are subjected to a variety of hundreds, requiring a certain quantity of rigidity and over-dimensioning to carry out passable underneath all load-cases. Thus, it ought to be famous that TO is just not an all-encompassing structural resolution. Is it wise to make use of this design strategy in circumstances the place one or a number of dominant load-cases are current (for instance when the dead-load is dominant).

Creating moulds for the casting of those advanced, organically formed and uniquely personalized geometries stays difficult, counting on disposable moulds fabricated via CAM methods equivalent to additive manufacturing. Funding casting utilizing an additively manufactured sacrificial prototype has demonstrated that extremely intricate glass components may be realised, although the present multi-step course of is time-consuming and labour-intensive. Regardless of requiring additional validation, 3D-printed sand moulds are believed by the authors to have the potential to tremendously enhance the manufacturing technique of personalized and perplex forged glass components, as a consequence of their excessive accuracy and improved printing pace compared to typical additive manufacturing strategies. It ought to be famous right here that for any challenge utilizing forged glass, it is crucial that the manufacturing strategy of the moulds is taken into account early within the course of, as it might probably have important affect on the design choices.

Limitations of this analysis and additional analysis

As no historically designed structural glass grid shell nodes exist, the optimised designs had been in contrast with roughly chosen, un-optimised geometries. These preliminary designs may be thought of over dimensioned, which implies that the discovered complete reductions in weight/mass and annealing occasions may be thought of comparatively optimistic.

The compliance-based TO course of used on this analysis doesn’t distinguish between tensile and compressive stresses, leading to components through which each are equally current. As glass is at the least an order of magnitude stronger in compression than in stress, this strategy doesn’t align with the structural properties of the fabric. This behaviour might be improved on via the event of a TO strategy for forged glass that makes use of principle-stress primarily based optimisation, or twin materials optimisation.

Within the present methodology, the post-processing of the optimised geometry consists of a repetitive and time-consuming, guide course of. If a full glass construction equivalent to proposed within the case-study is to be realised, consisting of many forged components, a stage in automation is required to enhance its feasibility. The necessities of the weather from each a structural and fabrication viewpoint can clearly be outlined, whereas obtainable post-processing instruments, equivalent to those in Spaceclaim used on this analysis, already function with restricted enter from the consumer. Due to this, the authors imagine an automatic, parametric optimisation course of is possible.

Additional testing is important for exploring and validating the potential of 3D-printed sand moulds. The sand moulds used for this analysis failed throughout kiln casting as the chosen binder was weakened by the warmth of the kiln, leading to collapse underneath the load of the molten glass. Preliminary outcomes by (Bhatia 2019) seem to point {that a} completely different binder, ExOne Anorganic, shows higher resistance to excessive temperatures than the binder used on this analysis.

Moreover, using hot-pouring (main) casting as a substitute of kiln-casting ought to be investigated. Though at hot-pouring the glass is initially poured at a considerably larger temperature than the utmost temperature achieved throughout kiln-casting, as a consequence of the truth that the glass is molten in a separate furnace, the sand mould is subjected to excessive temperatures for a significantly shorter time frame, probably stopping evaporation of the binder.

In addition to the composition of the mould, a number of different parameters must be explored additional to make sure the sand moulds can be utilized successfully and with minimal post-processing. These embody the selection of coating, and the putting and measurement of the inlet and circulation channels wanted throughout the casting.

Notes

1. Under its softening level the viscosity of glass is ample for it to retain its form and never deform underneath its personal weight (Shelby 2005).
2. A complete description of the annealing technique of forged glass objects may be discovered at (Oikonomopoulou 2019).
3. The thermal enlargement coefficient of the employed glass, contributed additional in lowering the annealing time. For the clean of the Hooker Telescope wine bottle glass was used (α = 9 * 10–6 1/C), whereas for the clean of the Big Magellan Telescope, E6 Borosilicate Glass was employed (α = 2.8 * 10–6 1/C).
4. the interwoven logistics with the standard manufacturing of moulds, in addition to vital changes within the manufacturing facility manufacturing course of for the manufacturing of personalized and/or advanced shapes may be evaded through using AM. On this path, AM may also provide a extra environment friendly prototyping course of.
5. The Von Mises criterion is used to mix multiaxial stress states right into a uniaxial stress that may then be in contrast towards experimental outcomes and uniaxial strengths, stopping the simple incidence of matrix singularities.
6. The values relating to the attribute energy of glass can tremendously fluctuate in line with the literature supply used; sometimes a attribute tensile energy between 30–45 MPa is talked about for soda-lime glass.
7. Primarily based on private correspondence with S. Galjaard, see additionally (Galjaard et al. 2015).
8. A protracted burning time was chosen to make sure a full evaporation of the infill, although it’s suspected by the authors {that a} shorter burnout time would have been ample.
9. Primarily based on private communication with 3Dealize.
10. Primarily, this is similar materials because the mould used for the lost-wax funding casting.

References