ADDITIVELY MANUFACTURED GAS TURBINE ENGINE AND VENTILATOR

Abstract

A gas turbine engine with a rotor comprising a turbine and compressor, mounted in a housing surrounding the rotor. The rotor rotates on one or more hydro bearings, the profiles of the outer surface of the rotor and the inner surface of the housing generating the hydro bearing(s). A combustion chamber is formed within the housing, and the combustion products of the fuel/air mixture are directed from the combustion chamber to the turbine. The housing and rotor are formed by an additive manufacturing process in a single procedure, with the rotor enclosed within the housing, and unsupported by any mechanical connections. A gas turbine respiratory ventilator system is described using a compressed oxygen flow to power the turbine which rotates the centrifugal blower for generating the air flow for respiration of the patient. The oxygen exhausted from the turbine can then be used to supplement the air flow.

Claims

1. A gas turbine engine comprising: a rotor comprising a turbine and compressor; a housing that surrounds the rotor, the rotor being configured to rotate within the housing on at least one hydro bearing, the profiles of an outer surface of the rotor and the facing inner surface of the housing generating the surfaces of the at least one hydro bearing; a combustion chamber adapted for the combustion of a fuel/air mixture; and at least one channel adapted to direct combustion products from the combustion chamber to the turbine, wherein the housing and rotor are formed simultaneously and in a single procedure, with the rotor enclosed within the housing.

2. A gas turbine engine according to claim 1, wherein the single procedure is an additive manufacturing procedure.

3. A gas turbine engine according to claim 1, wherein the formation of the housing with the rotor enclosed therein is indicative of the gas turbine engine having been produced in an assembled form by an additive manufacturing procedure.

4. A gas turbine engine according to either of claim 2 or 3, wherein the additive manufacturing procedure comprises the deposition of a sequence of printed layers, and the angle which any part of the inner surface of the housing or the outer surface of the rotor makes with the plane of the printed layers, is limited such that each layer is supported only by the previously printed layer.

5. A gas turbine engine according to any of the previous claims, wherein the rotor is enclosed within the housing without internal supports between them.

6. A gas turbine engine according to any of the previous claims, wherein the at least one hydro bearing is any of a hydrostatic bearing, a hydrodynamic bearing, or a hybrid hydro bearing.

7. A gas turbine engine according to any of the previous claims, wherein the hydro bearing is driven by a gas or a liquid.

8. A gas turbine engine according to any of the previous claims, wherein the combustion chamber comprises a porous structure.

9. A gas turbine engine according to any of the previous claims, wherein the housing comprises at least one channel adapted to direct the fuel, prior to its entry into the combustion chamber, so as to provide the support medium for the at least one hydro bearing.

10. A gas turbine engine according to claim 9, wherein the flow of the fuel through the at least one hydro bearing is adapted to provide cooling to the rotor.

11. A gas turbine engine according to either of claim 9 or 10, wherein the flow of the fuel through the at least one hydro bearing is adapted to increase the temperature of the fuel prior to its passage to the combustion chamber.

12. A gas turbine engine according to any of claims 8 to 10, wherein the flow of the combustible fuel through the at least one bearing is adapted to atomize the fuel prior to combustion.

13. A gas turbine engine according to claim 1, wherein the combustion chamber is formed within the housing.

14. A gas turbine engine according to claim 1, wherein the combustion chamber is disposed external to the housing.

15. A gas turbine engine according to any of the previous claims, wherein at least the turbine region of the rotor is formed of a material capable of withstanding higher temperatures than the material of which the housing is formed.

16. A method of forming a gas turbine engine, comprising: using an additive manufacturing process to form a rotor comprising a turbine and a compressor, and a single piece housing, the rotor being formed inside the single piece housing, and the rotor being configured to rotate within the housing on at least one hydro bearing whose surfaces are generated between an outer surface of the rotor and a facing inner surface of the housing, and providing a combustion chamber for the combustion of a fuel/air mixture; and at least one channel to direct combustion products from the combustion chamber to the turbine.

17. A method according to claim 16, wherein the combustion chamber is formed within the housing as part of the additive manufacturing process

18. A method according to claim 16 wherein the rotor and the housing have a common planar end surface perpendicular to the rotor axis of rotation, that surface being in contact with a printing base plate during the additive printing process.

19. A method according to any of claims 16 to 18, wherein the rotor and the housing are printed in layers from the common printing base plate.

20. A method according to any of claims 16 to 19, wherein the angle between the outer surface profile of any part of the rotor or the inner surface profile of any part of the housing and a plane parallel to the printing base plane is sufficiently large that every layer formed by the additive printing process is supported by the previously formed layer.

21. A method according to claim 20, wherein the angle is such that any overhang of a formed layer over the preceding formed layer has sufficient strength to be self-supporting.

22. A ventilator blower assembly, comprising: a rotor comprising a turbine and a compressor, such that the rotation of the turbine generates rotation of the compressor; a housing surrounding the rotor; at least one bearing configured to enable the rotor to rotate within the housing; an inlet channel adapted to direct a pressurized stream of oxygen from an external source, over the blades of the turbine; air inlet and outlet passages positioned such that the compressor, when rotating, is adapted to force air ingested through the inlet passage through the outlet passage; and at least one additional passage adapted for adding the oxygen exhausted from the turbine to the flow of air ingested through the inlet passage.

23. A ventilator blower assembly according to claim 22, further comprising an inlet port adapted for the direct addition of oxygen from the supply of compressed oxygen to the flow of air ingested by the blower.

24. A ventilator blower assembly according to either of claims 22 and 23, wherein the at least one bearing is a hydro bearing.

25. A ventilator blower assembly according to claim 24, further comprising internal channels in the housing which direct a gas flow into the at least one hydro bearing, to support the rotor when rotating.

26. A ventilator blower assembly according to claim 25, wherein the internal channels for the hydro bearing are configured to be connected to the source of the pressurized stream of oxygen.

27. A ventilator blower assembly according to any of claims 24 to 26, wherein the flow of oxygen for the hydro bearing is adapted to cool the rotating rotor.

28. A ventilator blower assembly according to any of claims 22 to 27, wherein the rotor and housing are produced in an assembled form by an additive printing method.

29. A ventilator blower assembly according to claim 28, wherein the rotor and housing have a common planar end surface perpendicular to the rotor axis of rotation, that surface being adapted to be in contact with the printing table during the additive printing process.

30. A ventilator blower assembly according to any of claims 22 to 29, wherein the rotor is powered only by the pressurized oxygen supply.

31. A ventilator blower assembly according to claim 22, wherein the at least one additional passage adapted for adding the oxygen exhausted from the turbine to the flow of air ingested through the inlet passage is either part of the housing, or is a separate conduit.

32. A method of providing respiratory ventilation to a subject, comprising: inputting a supply of compressed oxygen to a turbine of a gas turbine engine, the turbine being part of a rotor on which are connected to the blades of a blower, such that the rotating turbine rotates the blower blades, the blower being adapted to ingest air for delivery to the subject; and mixing the oxygen after ejection from the turbine, with a flow of air ingested by the blower, such that oxygen supplemented air is supplied to the subject.

33. The method of claim 32, further comprising the step of supplying compressed oxygen to at least one hydro bearing for enabling rotation of the rotor within a housing of the gas turbine engine, such that the compressed oxygen also serves as the support medium of the at least one hydro bearing.

34. The method of either of claims 32 and 33, further comprising the direct addition of oxygen from the supply of compressed oxygen to the flow of air ingested by the blower.

35. The method of any of claims 32 to 34, further comprising the step of regulating the ventilation timing to the subject by use of a set of controlled valves.

Description

BRIEF DESCRIPTION OF THE DRAWINGS

[0039] The presently claimed invention will be understood and appreciated more fully from the following detailed description, taken in conjunction with the drawings in which:

[0040] FIG. 1A shows a schematic representation of an exemplary oxygen powered ventilator system for providing a suitable air-oxygen mix to a patient being ventilated, while FIGS. 1B and 1C show graphs of the inspiration and expiration cycles of the system;

[0041] FIG. 2 shows a cross-sectional view of the complete blower assembly mechanism in an exemplary use for ventilation of a patient;

[0042] FIG. 3 shows the air and oxygen flow paths used to power the blower, with the air intake and outlets of the blower assembly having an attached air manifold;

[0043] FIGS. 4A and 4B show isometric views of an exemplary assembled ventilator blower assembly, as viewed from the turbine end (FIG. 4A) and from the blower end (FIG. 4B);

[0044] FIGS. 5A and 5B respectively show cross-sectional and side views of an exemplary ventilator blower unit, without an end-cap attached, while FIGS. 5C and 5D respectively show cross-sectional and isometric views of the exemplary ventilator blower unit of FIGS. 5A and 5B, with an end-cap attached;

[0045] FIG. 6 is a schematic cross sectional drawing of a gas turbine engine of the present disclosure, in which the gaseous fuel used to power the engine also supplies the gas of an hydro bearing assembly;

[0046] FIG. 7 is a cut-away isometric drawing of the engine of FIG. 6; and

[0047] FIGS. 8A and 8B show schematically how the support-less additive printing of one part totally enclosed within the other can be performed.

DETAILED DESCRIPTION

[0048] Reference is now made to FIGS. 1A to 1C, which illustrate in FIG. 1A, a schematic representation of an exemplary mechanical ventilator system for providing a suitable air-oxygen mixture to the patient being ventilated, according to one exemplary implementation in the present disclosure, and in FIGS. 1B and 1C, the cycle of mechanical ventilation provided by the system. The disclosed mechanical ventilator differs primarily from previously available ventilators in that the blower is powered by the compressed oxygen which is also used to provide oxygen to the patient being ventilated. In the example system shown in FIG. 1A, the oxygen supplied from a compressed oxygen tank 101 is used for up to three separate functions:

(i) A first function, shown by branch A, is to supply supplemental oxygen for mixing with the air supplied to the patient 111 being mechanically ventilated, as is usual in conventional ventilator systems.
(ii) The primary function, through branch B, is to power a turbine 102 used to rotate the compressor or blower unit 103 of the ventilator.
(iii) A third, and optional function is to provide, through branch C, the hydrodynamic flow of compressed gas to hydro bearings 105 which support the rotating impeller unit of the ventilator.

[0049] In branch A1, oxygen from the tank is fed via a valve V3 into a manifold 104 which combines the oxygen with ambient air, and channels the air-oxygen mixture through branch A2 into the centrifugal compressor or blower 103, which is driven by the turbine 102. From this point onwards, the air-oxygen mixture can be handled by a number of different flow control arrangements, a typical but non-limiting example being shown in route D. The blower directs the air-oxygen mixture via route D, through a flowmeter 107, past an oxygen sensor 108 and a pressure gauge (up to 2000 Pa) 106 to determine the flow and relative amount of oxygen going to the patient. After passing through one-way valve V4, the regulated air-oxygen mixture passes through a selector 112, which determines the cyclic intervals, typically from 1 to 4 seconds, at which the flow of gas will be directed to the patient. After passing through a filter 109, the gas mixture will be administered to the patient 111. During the times when the gas is not directed to the patient, i.e., during the expiratory phase of the respiratory cycle, the expired carbon dioxide from the patient is routed through one-way valve V5 to the environment.

[0050] FIGS. 1B and 10 are exemplary graphs illustrating the timing of the mechanical breaths provided to the patient 111 using the selector on/off switch 112 of FIG. 1A, and the resulting respiratory trace of the mechanical breath provided is shown in FIG. 10, in which inspiratory and expiratory phases of the respiratory cycle are shown.

[0051] Referring back now to FIG. 1A, in branch B, according to one exemplary arrangement, compressed oxygen is directed through valve V2 and is monitored by a pressure gauge 106, typically up to 4 bar, before being passed through a flow meter 107. The pressurized oxygen is then used to power a turbine 102, which is used to turn the compressor 103, the compressor and turbine being connected by an impeller structure or shaft 113. After providing the motive force for operating the blower or compressor 103, the oxygen gas can advantageously be directed through manifold 104 to be added to the air flow supplied to the patient, such that it is not wasted after performing its primary energy providing function. The impeller may, according to another advantageous implementation, be supported by a hydro bearing to enable it to rotate at high speeds, and this hydro bearing can use compressed oxygen supplied through branch C. The compressed oxygen passes through valve V1, is monitored by a pressure gauge, typically up to 4 bar, and is used to provide the fluid support for the hydrodynamic hydro bearing 105. The oxygen used to provide hydrodynamic support of the hydro bearings may subsequently be fed into the manifold 104 for routing to the patient, such that it too does not go to waste.

[0052] Such a ventilator system may have a compressor flow rate of 250 L/min (5 gr/s); oxygen enrichment of 50-80%; a turbine flow rate of 1.5-3 gr/s; a rotation speed of 36,000 RPM; and one way valves to prevent backflow. The pneumatic oscillatory valve may have a 1-4 second on/off cycle to simulate breathing. The described system of valves, flow meters, oxygen sensors, and tubing are shown for a typical, non-limiting implementation, and other configurations may equally well be used in other applications of the system.

[0053] Reference is now made to FIG. 2, showing a cross-sectional schematic view of a typical implementation of the disclosed ventilator system, highlighting important mechanical features and the flow of air and oxygen through the device. The finely dashed lines show the flow of high pressure gas, while the thicker dashed lines generally show the flow of low pressure gas. As in FIG. 1A, the compressed oxygen used to power the turbine-compressor unit may be provided from a high pressure cylinder 201 into inlet B, and is used to power the turbine 202. Rotation of the turbine turns the impeller 213, with the compressor or blower 203 at its opposite end, which draws in air via inlet A2. The oxygen exhaust from the turbine is channeled via the manifold 204 to the blower 203, also via inlet A2, and the regulated air-oxygen mixture is provided to the patient via outlet D. Compressed oxygen from the oxygen tank 201 is also routed through inlet C to the hydro bearings 205. As mentioned above, the components of the turbine engine may be additively manufactured using a standard three-dimensional printer. The process is easily scalable for the turbomachinery components, hydro-static bearings, and housing. The controls and one-way valves, filter, pressure and oxygen sensors may be supplied as commercial off-the-shelf parts. Variable characteristics of the device comprise a breathing rate controlled by an oscillating valve at 15-60 breaths/min. Air flow rate may vary between 200-350 L/min, which can be adjusted by a controllable valve. Breathing pressure is controllable between 10-30 cm H.sub.2O. Oxygen saturation may be controlled by an oxygen supply valve that enables the supplemental oxygen to be 0-100% of incoming air.

[0054] Advantages of such an implementation are that the device requires no electrical power supply, no lubrication, and no assembly, as it may be fully additively manufactured ready to use. The mechanical ventilator uses only the pressure from the oxygen supply tank to power the ventilator, the used oxygen then being rerouted back to the patient, thus conserving the oxygen for its usual use. Further, using an additive manufacturing approach allows the rapid production of simple and cheap automatic ventilation units. Such units can be used in case of emergency to provide critical lung ventilation for patients who might otherwise be unable to receive adequate treatment. Although missing non-essential features such as temperature and humidity control, implementations of the disclosed ventilator system provide the most critical functionality to save lives, i.e., automatic oxygen saturation for patients in respiratory failure.

[0055] Reference is now made to FIG. 3, illustrating an alternative schematic representation of the mechanical ventilator of FIGS. 1A and 2, showing how the compressed oxygen flow B, expended from the turbine 302 after providing the turbine with its rotational energy, is routed back into the blower 303 through passageway 304, shown schematically as the input manifold feature 104 in FIG. 1A, and feature 204 in FIG. 2, where it is mixed with the air intake A, for enriching the oxygen content of the ventilator air flow. This oxygen-enriched air flow is then provided to the patient though port D.

[0056] Reference is now made to FIGS. 4A and 4B, illustrating external views of the ventilator turbine-compressor unit from the turbine end 402 (FIG. 4A), showing the pressurized oxygen input port B, and from the blower/compressor end 403 (FIG. 4B) of the motor unit, showing the air intake A to the blower, and the regulated air/oxygen mixture output D to the patient. The endcap illustrated in FIGS. 5A to 5D, not shown in FIG. 4A or 4B, would be fitted over the end of the turbine 402.

[0057] Reference is now made to FIGS. 5A to 5D, illustrating the design and fitting of an endcap 59 for the ventilator rotor-stator turbine-blower assembly. The endcap is shown as a separate element, but it too may be additively manufactured as an integral part of the housing with the impeller inside. FIGS. 5A and 5C show cross-sectional views of the ventilator assembly, and FIGS. 5B and 5D show a side view of the assembly. In FIGS. 5A and 5B, the endcap is shown in position ready to be mounted onto the turbine 52 end of the ventilator engine, being secured in this exemplary construction by a pin 57 and groove 58 arrangements, which locks the cover on by means of a slight turning motion. Closing the end of the turbine prevents escape of the oxygen after it has performed its motive task, so that it can be added to the ventilation air flow. In FIGS. 5C and 5D, the endcap is shown in place after attachment.

[0058] Reference is now made to FIG. 6, illustrating another exemplary implementation of the present disclosure, showing a turbine-compressor rotor-stator assembly used in a gas turbine engine, such as may be employed to power an unmanned aerial vehicle or drone. This differs from the ventilator engine shown in FIGS. 1A to 5D, in that the motive force for the turbine comes from the combustion gases of a fuel-air mixture, instead of from the flow of compressed oxygen from an oxygen cylinder, or another compressed gas. The gas turbine can then be used to provide thrust, rather than just rotational energy to a ventilator blower. The targeted application may be to provide thrust to small-to-medium size UAVs, including disposable platforms. Currently small to medium UAVs are commonly powered by micro-gas turbine engines that cost from 30,000 to 150,000 USD, involving numerous parts and manufacturing methods in a lengthy process. This complicated process inflates the costs of both disposable and reusable platforms. In multi-mission platforms, significant efforts are invested towards prolonging service life as maintenance becomes increasingly important and costly. The present disclosure shows a low cost engine, which has the advantages of being produced through additive manufacturing in its final topology using a single simultaneous, uninterrupted printing process for both rotor and stator, thereby eliminating assembly costs. A typical sized engine for powering a small UAV could have a diameter of up to 30 cm, a thrust rating of 650 N and an air mass flow rate of ˜1.4 kg/s, though it is to be understood that these specifications are not intended to be limiting.

[0059] Production of the engine through additive manufacturing enables reduction of components to just two parts—a static casing 600 with an embedded impeller 607, in the form of a shell structure, completely enclosed within the outer casing 600. The rotating shell structure includes the compressor end 601 with its blades 602, and the turbine end 606, with its blades, 605. This construction enhances rotodynamic performance. The impeller of the engine is supported on hydro bearings 609, which support the high rotational speed impeller 607. Use of hydro bearings provides low friction and absence of wear, and the ability to support large loads. The hydrostatic bearing should also provide radial and axial support of the internal rotating impeller. Additionally, such a hydro bearing construction is compatible with the additive manufacturing method used to form the impeller and housing in one process, with the bearings per se, inbuilt during construction. However, the hydro bearings used in the present engine differ from those conventionally used, in that the support gas is not air, but the fuel used to power the engine. The fuel enters at port 603, and is first directed to the hydrostatic bearings 609. The use of the fuel flow in the “air” bearing has an additional benefit that would not arise from the conventional use of air. In addition to the cooling effect which the fuel flow has in the bearing, removing heat from the impeller, an additional advantage is that the heat removed from the bearing is used to preheat the fuel before combustion, thereby assisting in the fuel atomization, and enhancing the efficiency of its combustion by improving the thermal output available from the fuel.

[0060] After providing the support for the high speed rotating impeller, the fuel then mixes as an aerosol with incoming air 608, input by the compressor 601, 602. The combustion chamber 604, advantageously having a porous medium to ensure complete and efficient combustion, is used for combustion of the premixed fuel-air mixture. The hot combustion product gasses then pass through the turbine 605, 606, thereby generating the power for operating the compressor 601, 602 to provide a copious intake of air. The hot gasses then exit the turbine end 606 of the engine, generating the thrust desired from the engine in the case of a jet engine, or exhausted in the case of a power generating gas turbine engine. The inner rotating impeller component may be balanced after manufacture through external removal of mass from specific surfaces, to produce a rotating system that balances out centrifugal forces.

[0061] FIG. 7 is a cut-away isometric view of the engine of FIG. 6, showing more clearly the internal structure and the flow path of the fuel and hot gasses.

[0062] In the implementation of the gas turbine engine shown in FIGS. 6 and 7, the combustion chamber 604 is shown as being formed within the static casing or housing 600 of the engine. Besides such a structure, gas turbines and jet engines can alternatively have their combustion chambers embodied or attached externally to the engine housing, and such a structure can also be used for the presently described engines. When the combustion chamber is external to the housing, the pressurized air 608 from the compressor 601, 602, is ducted out of the housing 600 to an external unit (not shown in the drawings) where the combustion takes place inside that external combustion chamber. The hot and pressurized combustion product gasses are then ducted back into the housing 600 into the passageway(s) which direct the gas stream onto the turbine blades 605. In the same way as is shown in the gas turbine engine with an internal combustion chamber 604 of FIGS. 6 and 7, the turbine 605 drives the compressor 601, 602 and the remaining energy of the thermodynamic cycle can be converted to shaft power, or to kinetic energy at the exhaust 606. It should be noted that even with an external combustion chamber, the fuel may be first channeled through the hydro bearing 609 of the engine to provide the support medium therefor.

[0063] Reference is now made to FIGS. 8A and 8B, illustrating the principle of support-less additive manufacturing. In additive manufacturing, each layer is supported by the previously printed structure. Typically, three-dimensional printed objects are based on printing one layer at a time, each subsequent layer building on the previous one. When such a process is used to print an object 81 with upper layers having components that extend beyond the previously printed lower layers, as shown in FIG. 8A, current methods require the use of a temporary supporting structure 82 to provide a frame for the extension of the upper layer outwards beyond the lower layer. This temporary supporting structure will be removed, as described below, once the part has been completely produced. Additive manufacturing enables simultaneous printing of two interconnected components, e.g., in which a smaller piece fits inside a larger piece, by printing the component layer-by-layer from the print plate upwards. Thus, both the inner and the outer parts are generated together, one within the other. Current use of three-dimensional printing for concentric parts, however, is limited to items printed having non-enclosed spaces, having an opening for removal of the internal supporting structure 82, as otherwise the temporary structure 82 necessary to support the inner component remains enclosed inside the completed outer component.

[0064] Reference is now made to FIG. 8B, which illustrates a support-less method enabling the generation of completely enclosed integrated co-axial structures. The method is based on the design of the internal part having a gradient between successively printed layers sufficiently small that each layer may be supported only by the previously printed layer. By designing the parts in this manner, the need for internal support structures is eliminated. The parts designed may need to have some compromise properties over an ideal design, because of the limitations to the part profiles that may be used, but the savings thus generated by this method of additive manufacturing of integrated structures should provide an overall positive stimulus for the method for those applications where a satisfactorily functioning component may be produced using this method. Referring now to FIG. 8B, the prior art part 81 of FIG. 8A, has been redesigned as part 83, having a base section leading into the upper section by means of a sloped profile, instead of a right angled profile. The design of the sloped profile, which could be curved, as shown in FIG. 8B, or having straight line gradients, should be such that the overhang, d, of one layer 85 over the previously printed layer 84 should be no larger than the distance for which the strength of the printed layer 85 enables the layer 85 to remain self-supported. The allowed gradient should be calculated according to the mechanical properties of the material being deposited, and of the thickness of the layers being printed. Designs such as that shown in FIG. 8B minimize post-processing and enable the construction of mutually rotating surfaces of a stator and impeller to be printed together simultaneously, and without any internal supporting struts.

[0065] A method of designing an integrated composite structure having a movable inner part produced while entirely confined within an outer static housing, may thus be proposed by first defining the base plane of the composite structure, from which the printer will generate the entire structure. The spatial orientation of this base plane also defines the geometrical orientation of the subsequently printing layers superior to the base plane. The strength of a printed layer of the material being used to build the structure is then calculated, where the stiffness of the layer is determined using the Young's modulus of the material, and the thickness and width of each incremental printed layer. This will enable a calculation to be made, using the extent of bending that will be expected for the overhang of a single superior printed layer of the material, beyond the inferior layer previously printed. This maximum overhang will be dependent on the strength of the material being printed, the thickness of the layer being printed, and the sag of the overhang allowable for the part being produced. A permitted maximum level of bending should be defined, which will be determined according to the designed shape of the structure being produced. It is assumed that once a specific layer has been printed, the weight of successive layers printed vertically on top of it will not generate additional bending, since although the bending moment will be larger because of the additional gravitational forces, the layers thus produced will have a substantially increased strength because of the increased structural thickness.

[0066] A simplified method of determining the allowable overhang is to calculate the bending expected in a section of the printed layer, supported at one end by the layers below it, and experiencing a distributed force along the overhang length because of its weight. If the overhang were to be considered a cantilever beam, supported at one end, its bending d would be given by:

[00001]$d=\frac{{\mathrm{FL}}^3}{3\mathrm{EI}}$

where d is the deflection at the outer extremity of the overhang [0067] F is the force applied at the extremity of the overhang [0068] L is the length of the overhang [0069] E is the module of elasticity of the material [0070] I is the second moment of inertia of the overhang.

[0071] Though this is a very simplified model for the calculation of the overhand bending, mainly because the force is applied along the length of the overhang rather than at a point at its outer extremity, it enables an approximate calculation of the bending to be made. Thus, the deflection is seen to be proportional to the third power of the length of the overhang, such that the allowed extent of the overhang is highly dependent on the deviation that would be allowed of the shape of the layer from the intended shape

[0072] Once that criterion has been determined, it then becomes possible to determine the minimum angle from the horizontal that the profile of the structure being printed can accommodate, since at any angle less than that minimum allowed angle, the bending of the unsupported edges of a print layer may result in the shape of the structure departing from the intended shape by more than an allowed level.

[0073] It is appreciated by persons skilled in the art that the present invention is not limited by what has been particularly shown and described hereinabove. Rather the scope of the present invention includes both combinations and subcombinations of various features described hereinabove as well as variations and modifications thereto which would occur to a person of skill in the art upon reading the above description and which are not in the prior art.