USING METAL ADDITIVE MANUFACTURING

STATEMENT OF FEDERAL FUNDING

[0001] The invention described herein was made in the performance of work under a NASA contract N NN12AA01C, and is subject to the provisions of Public Law 96-517 (35 USC 202) in which the Contractor has elected to retain title.

FIELD OF THE INVENTION

[0002] The present invention generally relates to methods for the fabrication of strain wave gears using additive manufacturing technology.

BACKGROUND OF THE INVENTION

[0003] Strain wave gears, also known as a harmonic drives (HDs), are gear systems that rely on the elastic flexing of one of its members. Typically, a strain wave gear has two sets of slightly off-set gear teeth, which meet and transmit torque through the flexing of one of the gear com ponents. Accordingly, these gearing systems can provide high reduction ratios, high torque- to-weight and torque-to-volume ratios, near-zero backlash (which mitigates the potential wearing of the components), and a host of other benefits. For example, many of HDs' beneficial characteristics make their use critical in robotics applications and, indeed, HDs are widely used in robotics as a method for achieving high gear reductions and for driving force transmissions. More specifically, the beneficial properties and features of HDs include, among others: highspeed reduction ratios of 1/30 to 1/320 (relative to gearing systems), which provide high efficiency gearing without using complex mechanisms; nearly zero backlash in operation; extremely high precision; high torque capacity due to the use of fatigue resistance steel in the flexspline component; high efficiency; and small number of components that assemble easily. Moreover, HDs can achieve all these benchmarks in a very small form factor and can be very light weight. [0004] Due to various functionality-specific constraints, heritage strain wave gears have largely been fabricated from steel via machining. In some instances, when materials strength can be sacrificed in favor of lower manufacturing costs, harmonic drives are fabricated from thermoplastic materials, such as polymers, which can be cast into the shapes of the constituent components, including via inexpensive injection molding processes.

[0005] Metal additive manufacturing, also commonly known as 3D printing, is an emerging manufacturing technology which is being rapidly integrated into commercial applications, such as fabrication of nozzles in aircraft and rocket engines. The most common forms of metal additive manufacturing are based on either powder bed systems or powder feed systems. In 3D printing based on powder bed systems, a laser or electron beam melts a thin layer of metal powder and continuously applies it to construct the part, which becomes buried in the powder. The most common forms of powder bed systems are direct metal laser sintering (DMLS) or selective laser melting (SLM). In contrast, in printing systems based on powder feed systems, metal powder is blown into a laser or electron beam and deposited as a metal pool. In addition, there exist 3D printing systems in which a metal is deposited directly from a building head in the absence of a powder bed. Such bed-less technologies are termed directed energy deposition (DED), of which the most common form is laser engineered net shaping (LENS).

SUMMARY OF THE INVENTION

[0006] Embodiments of the invention are directed to methods for fabricating a strain wave gear flexspline.

[0007] Many embodiments of methods for the manufacture of flexsplines use a metal additive manufacturing system to form an entirety of the strain wave gear flexspline as a single piece, wherein the strain wave gear flexspline is a cylindrical cup including:

a bottom defining a circumference, a cup wall disposed atop the bottom and defining a cylindrical volume, and gear teeth disposed on an upper outer surface of the cup wall's edge, wherein

the cup wall has a thickness of between 0.05 and 2 mm, and the cup wall having a height that is at least 50 times larger than the smallest thickness of the cup wall; and

wherein the strain wave gear flexspline is fabricated in a vertical orientation, such that the bottom is disposed on a build platform and the cup wall is oriented perpendicularly to the build platform of the metal additive manufacturing system at all times during fabrication, and the properties of the strain wave gear flexspline in any single deposition layer are the same and are axially symmetric.

[0008] In other embodiments the strain wave gear flexspline is attached to the building platform for support during fabrication only at the bottom and no supporting material is added to the cup wall during fabrication.

[0009] I n still other embodiments the feature sizes of the strain wave gear flexspline are less than 1 mm in dimension.

[0010] In yet other embodiments the metal additive manufacturing system is selected from the group consisting of: powder bed fusion printing, powder bed selective laser melting, direct energy deposition printing, metal extrusion, fused filament modeling, metal binder jetting, wire arc additive manufacturing, ultrasonic additive manufacturing, thermal spray additive manufacturing, liquid jetting, laser sintering, electron beam freeform, laser melting, or any combination thereof.

[0011] In still yet other embodiments the thickness of the cup wall is within 15% of the spot size of the laser of the metal additive manufacturing system.

[0012] In still yet other embodiments the cup wall is fabricated using a single width of the laser scanning of the metal additive manufacturing system or a single wire deposition extrusion process.

[0013] I n still yet other embodiments at least one of the properties, composition, or microstructure of the strain wave gear flexspline are uniform in the direction parallel to the building platform but vary in the directing perpendicular to the building platform. [0014] In still yet other embodiments the strain wave gear flexspline has a horizontally laminated structure such that the strain wave gear flexspline has a 10% higher fracture toughness than a strain wave gear flexspline made of monolithic metal.

[0015] In still yet other embodiments the strain wave gear flexspline is fabricated from a material with a fracture toughness between 30 and 150 MPa m ^1/2 . In some such embodiments the fracture toughness of the material is variable along the direction perpendicular to the building platform.

[0016] In still yet other embodiments the elastic limit of the strain wave gear flexspline ranges from 0.1-2%.

[0017] In still yet other embodiments the strain wave gear flexspline comprises at least two regions with the same chemical composition but distinct physical properties disposed along the direction perpendicular to the building platform.

[0018] In still yet other embodiments the strain wave gear flexspline comprises at least two regions of distinct chemical compositions disposed along the direction perpendicular to the building platform.

[0019] In still yet other embodiments a gear teeth region of the strain wave gear flexspline comprising the gear teeth comprises a material that is chemically, physically, or both, distinct from the rest of the strain wave gear flexspline, and wherein the gear teeth region is more resistant to wear than the rest of the strain wave gear flexspline.

[0020] In still yet other embodiments a gear teeth-less region of the strain wave gear flexspline that excludes gear teeth comprises a material that is chemically, physically, or both, distinct from the gear teeth region of the strain wave gear flexspline, and wherein the gear teeth- less region is more resistant to fracture than the rest of the strain wave gear flexspline.

[0021] In still yet other embodiments a material used in the fabrication of the strain wave flexspline is introduced from the building head rather than from a bed of metal.

[0022] In still yet other embodiments the metal additive manufacturing system utilizes a material in one of the forms chosen from the group consisting of: powder, wire, molten metal, liquid metal, metal in a binder, metal in dissolvable inks, metal bound in polymer, sheet metal, any other printing form allowing vertical printing, or any combination thereof.

[0023] In still yet other embodiments the gear teeth have a vertically oriented curvature.

[0024] In still yet other embodiments the strain wave gear flexspline undergoes a post- fabrication process selected from the group consisting of:

chemical treatment to smooth the surface of the gear teeth and the inner surface of the cup wall;

mechanically grinding, sanding or polishing to reduce surface roughness;

coating with another metal;

heat treating to alter one or more properties chosen from the group consisting of physical properties, porosity, temper, precipitate growth, other properties as compared to the as-fabricated state; and

any combination thereof.

[0025] In still yet other embodiments the strain wave gear flexspline is fabricated from an alloy, a bulk metallic glass or metallic glass composite based on one or more elements chosen from the group consisting of: Fe, Ni, Zr, Ti, Cu, Al, Nb, Ta, W, Mo, V, Hf, Au, Pd, Pt, Ag, Zn, Ga, Mg, or any combination thereof.

[0026] In still yet other embodiments the strain wave gear flexspline is fabricated from a metal matrix composite, and wherein the volume fraction or the chemical composition of the metal matrix composite, or both, is uniform in the direction parallel to the building platform but variable in the directing perpendicular to the building platform.

[0027] In still yet other embodiments the strain wave gear flexspline is fabricated from both a crystalline metal alloy and a metallic glass alloy, and wherein the two materials are interchanged in the directing perpendicular to the building platform.

[0028] In still yet other embodiments the strain wave gear flexspline is fabricated from a high melting temperature alloy with a melting temperature greater than 1,500 Celsius. In some such embodiments the high melting temperature alloy is Inconel or an alloy based on one of the elements chosen from the list: Nb, Ta, W, Mo, V, any combination thereof. [0029] In still yet other embodiments the gear teeth can have a curved or arbitrary shape so that the performance of the stain wave gear can be enhanced or modified for a particular application.

[0030] Additional embodiments and features are set forth in part in the description that follows, and in part will become apparent to those skilled in the art upon examination of the specification or may be learned by the practice of the disclosed subject matter. A further understanding of the nature and advantages of the present disclosure may be realized by reference to the remaining portions of the specification and the drawings, which forms a part of this disclosure.

BRIEF DESCRIPTION OF THE DRAWINGS

[0031] These and other features and advantages of the present invention will be better understood by reference to the following detailed description when considered in conjunction with the accompanying data and figures, wherein:

[0032] FIGs. 1 illustrates the design and components of a typical harmonic drive in accordance with the prior art.

[0033] FIGs. 2a-d provide detailed illustration of a harmonic drive's operation in accordance with the prior art.

[0034] FIG. 3 shows a hybrid steel/BMG strain wave gear, wherein the circular spline and the wave generator components are fabricated from conventional steel and the flexspline is fabricated by casting of BMG in accordance with prior art.

[0035] FIG. 4 shows flow lines that can lead to cracks in a flexspline cast from BMG in accordance with prior art.

[0036] FIG. 5 illustrates flexspline gear teeth having non-flat curvatures in accordance with prior art and embodiments of the invention.

[0037] FIGs. 6a and 6b illustrate various print orientations of typical additive manufacturing processes in accordance with prior art, wherein FIG 6a shows a standard build platform of a powder bed fusion (PBF) metal additive manufacturing system, wherein parts are shown in vertical (z-direction) and horizontal directions of printing; and FIG. 6b shows a schematic for a powder bed fusion printer, wherein parts are tilted at an angle and support material is added to the parts during printing.

[0038] FIG. 7 provides an image of a bottom view of a metal printed, steel flexspline and demonstrates the rough finish resulting from the removal of the supporting material in accordance with embodiments of the invention.

[0039] FIG. 8 provides an image of a flexspline fabricated in accordance with embodiments of the invention, wherein an arrow indicates the building direction relative to the build platform.

[0040] FIG. 9 provides images showing crack propagation forming in a flexspline in accordance with the prior art.

[0041] FIG. 10 provides a schematic of the crack inhibition of a laminate flexspline structure in accordance with embodiments of the invention.

[0042] FIG. 11 provides a table showing properties of metal alloys that could be used for fabrication of the flexsplines in accordance with embodiments, as well as the variety of properties that can be achieved in such flexsplines.

[0043] FIG. 12 shows an actual operation of an as-printed flexspline incorporated into a fully assembled standard strain wave gear in accordance with embodiments of the invention.

[0044] FIGs. 13a-13d compare examples of heritage flexsplines fabricated in accordance with prior art and examples of flexsplines fabricated in accordance with embodiments of the invention, where FIG. 13a compares the top and bottom views of printed (left), cast (center) and machined (right) flexsplines; FIG. 13b compares micrometer readings (wall thinness) flexsplines that are machined (left) and printed (right); FIG. 13c shows the difference in roughness between the teeth on a printed flexspline (left) and a heritage machined flexspline (right); and FIG. 13d shows the difference between flexsplines printed using embodiments of the invention (left & center), and a flexspline using conventional heating and recoating techniques (right). DETAILED DISCLOSURE

[0045] Turning to the drawings and data, methods for the facile and efficient fabrication of metal flexsplines for use in harmonic drives are provided. It will be understood that the embodiments of the invention described herein are not intended to be exhaustive or to limit the invention to precise forms disclosed. Rather, the embodiments selected for description have been chosen to enable one skilled in the art to practice the invention.

[0046] Harmonic drives were developed to take advantage of the elastic dynamics of metals, particularly the expansion of a metal ring to engage gear teeth without exceeding the elastic limit of the ring, which would cause permanent (i.e. plastic) deformation. To this end, a typical HD is made of three components (as shown in FIG. 1): a wave generator, a flexspline (also known as "inner race"), and a circular spline (also known as "outer race"). The wave generator is an elliptical can with small ball-bearings built into the outer ci rcumference and is usually attached to the input shaft. As shown in the figure, the flexspline itself is a thin-walled metal cup with external gear teeth at its rim and a diaphragm at the bottom of the cup for connecting to an output shaft. The circular spline is a ring with internal teeth and is usually fixed to a casing. The circular spline has more (e.g. two more) teeth than the flexspline and its diameter is slightly larger than the flexspline's, such that if they were put together without the wave generator, they would be concentric and their teeth wouldn't touch.

[0047] FIGs. 2a-d illustrate operations of a typical harmonic drive. As shown, first, the flexspline is deflected by the motion of the elliptical wave generator into an elliptical shape causing the flexspline teeth to engage with the cooperative teeth of the circular spline at the major axis of the wave generator ellipse, with the teeth completely disengaged across the minor axis of the ellipse (FIG 2a). Next, as the wave generator is rotated clockwise with the circular spline fixed, the flexspline is subjected to elastic deformation and its tooth engagement position moves by turns relative to the circular spline (FIG. 2b). When the wave generator rotates 180 degrees clockwise, the flexspline moves counterclockwise by one tooth relative to the circular spline (FIG 2c). Finally, when the wave generator rotates one revolution clockwise (360 degrees), the flexspline moves counterclockwise by two teeth relative to the circular spline because the flexspline has two fewer teeth than the circular spline (FIG. 2d). I n general terms, this movement is treated as output power. It should also be noted that, in some alternative arrangements, the flexspline is held fixed, and the circular spline is used to provide an output torque.

[0048] Accordingly, as can be inferred, the operation of a strain wave gear is particularly nuanced and relies on a very precisely engineered gearing system. Therefore, the geometries of the constituent parts of strain wave gears must be fabricated with extreme accuracy in order to provide the desired operation. Moreover, the strain wave gear components must be fabricated from materials that can provide for the desired functionality. I n particular, the flexspline must be flexible enough to withstand high-frequency periodic deformation, while at the same time being strong enough to accommodate the loads that the strain wave gear is anticipated to be subjected to.

[0049] One material that has been demonstrated to possess the requisite properties for use in strain wave gears is wrought steel, which can also be precisely machined into the desired geometries. However, machining of strain wave gear components from steel is difficult and very expensive, especially for manufacturing of elliptical wave generators and thin-walled flexsplines. In particular, the wall of a flexspline must be thin enough to be able to flex elastically millions of times, while still being mechanically robust enough to transmit torque. Typically, the wall of the flexspline is at least <2mm thick, in most cases <1.5mm thick, in many cases <lmm thick, and can be as low as 0.05mm thick. For example, the wall of the steel flexspline in a common CSG-20 strain wave gear with a roughly 50 mm diameter (produced by Harmonic Drive) has to be machined to below 0.4 mm thick. I n other instances of even sma ller flexsplines, the wall has to be machined to as low as 0.15 mm thick. Moreover, wrought steel machining is expensive, wherein components must be machined from a billet, leaving more than 90% of the initial material as scrap waste.

[0050] In some instances, harmonic drives are fabricated from thermoplastic materials. Thermoplastic materials (e.g. polymers) can be cast (e.g. via i njection molding processes) into the shapes of the constituent components, and thereby circumvent the expensive machining processes that are typically implemented in manufacturing of steel-based strain wave gears. However, strain wave gears fabricated from thermoplastics are not as strong and wear resistant as strain wave gears fabricated from steel.

[0051] Hofmann et al. have recently disclosed that metal flexsplines can be cast into a near- net shape from bulk metallic glass (BMG). (See, e.g., U.S. Patent Application. No. 14/177,608, the disclosure of which is incorporated herein by reference.) Here, BMG refers to a complex, precisely composed alloy which can be quenched into a vitreous state at a relatively large casting thickness (generally over 1 mm). More specifically, in stark contrast to conventional metallic materials that have highly ordered atomic structure, metallic glasses, also known as amorphous alloys (or alternatively amorphous metals), are characterized by disordered atomic-scale structure in spite of their metallic constituent elements. Furthermore, an in-situ composite or bulk metallic glass matrix composite (BMGMC) is defined as an alloy which, upon rapid cooling (1-1000 K/s), chemically partitions into two or more phases, one being an amorphous matrix and the other(s) being crystalline inclusions. As such, it will be understood that, in the embodiments of the invention described herein, the term "metallic glass based materials" is understood to mean both BMGs and BMGMCs. In principle, metallic glasses typically possess a number of useful material properties that can allow them to be implemented as highly effective engineering materials. For example, metallic glasses are generally much harder than conventional metals, and are generally tougher than ceramic materials. BMGs are also relatively corrosion resistant, and, unlike conventional glass, they can have good electrical conductivity. Importantly, the manufacture of metallic glass materials lends itself to relatively easy processing and, in particular, the manufacture of a metallic glass can be compatible with an injection molding process or any similar casting process, as demonstrated by Hofmann et al. for a flexspline. For example, FIG. 3 shows a hybrid steel/BMG strain wave gear, wherein the circular spline and wave generator components are fabricated from conventional steel, while the flexspline is cast from BMG. Here, the BMG cast part fits directly into the otherwise steel-made strain wave gear to complete the hybrid gearbox.

[0052] However, manufacturing of flexsplines via casting of BMGs according to the method disclosed by Hofmann et al., also presents a number of drawbacks. First, the casting process often affects the overall physical properties of the materials being cast, including BMGs. Specifically, the turbulence in the molten material during the casting injection leaves flow marks (FIG. 4) and other defects on the part being cast, which, in turn, result in a weaker, crack-prone part. I n fact, the flexsplines cast from BMGs readily crack from casting process caused defects. Second, the thin wall of a flexspline is very difficult to cast. I n general, if the thickness of the wall is less than 1 mm it is difficult to get the fluid to flow into such small mold voids, and since the fragility of the walls at such dimension can lead to failure during mold removal. Third, in many instances, gear teeth of flexsplines may have a profile that is not flat, but rather has a curve or another arbitrary shape, as shown schematically in FIG. 5. I n such instances, the gear teeth of the flexsplines are slightly curved in the vertical direction, which can result in the whole part getting trapped in the mold during casting. This makes the casting of flexsplines with such curved teeth difficult if not impossible. Fourth, the holes at the bottom of the flexspline, which are required for mounting the flexspline to the rotary elements of the HD, cannot be cast into the flexspline and must be machined or drilled in at a later step, which introduces an extra step in fabrication of flexsplines via casting.

[0053] One manufacturing technique that hasn't been explored for manufacturing flexsplines is metal additive manufacturing. Although this manufacturing technology is well-known for printing conventional gears and gear teeth, metal additive manufacturing was believed to be unsuitable for fabrication of thin-walled structures, where the height of the structure is much larger than the wall thickness, such as in an HD flexspline, wherein the cup wall may have a height that is 50 times (or more) larger than the smallest thickness of the cup wall. Specifically, existing DMLS and SLM powder bed machines can only achieve feature tolerances of approximately 0.04 to 0.2 mm, depending on the orientation of the build. Moreover, the orientation in which a part is printed affects not only its build quality, but its mechanical properties as well. To this end, FIG. 6a shows a standard build platform of a powder bed fusion (PBF) metal additive manufacturing system and various orientations of the parts, including standing-on-end (vertical) build orientation, also called the z-direction of printing. I n addition, since surfaces parallel to the build platform cannot be supported, they end up with very rough finishes, as, for example, shown in FIG. 7.

[0054] Accordingly, in order to achieve a smooth surface of the conventional techniques, flat surfaces in powder bed metal additive manufacturing machines are positioned at an angle to the build plate, as shown in FIG. 6b. Consequently, the build/print orientation has significant consequences in the manufacture of flexsplines. Specifically, since the mating surfaces of a strain wave gear (i.e., the engaging surfaces of the circular spline and wave generator's teeth and the bottom surface of the flexspline, which mates with the bottom of the wave generator) must be flat and precisely finished, the conventional approach to additively manufacturing these gear components would be to tilt them at an angle relative to the build platform during printing (as shown in FIG. 6b) to improve the bottom surface finish. However, printing the wall and/or the teeth of the flexspline at an angle to the build platform requires the use of support structures and materials (as shown in FIG. 6b). The support material, which is typically also metal and strongly adheres to the printed object and needs to be removed post-fabrication. In turn, the post-fabrication removal of support structures and materials can damage the delicate structures of the flexspline's teeth and wall and is, therefore, highly undesirable. Moreover, any support material remaining stuck to the wall of the cup will change the flexing behavior of the flexspline. Consequently, the teeth and the wall of the cup must be absolutely free from all support material in the fabrication of flexsplines. In addition, 3D printing of flexsplines at an angle hinders the ability to achieve the perfect radial symmetry and gear teeth curvature essential to flexspline's functionality.

[0055] As a result of the deficiencies of these conventional additive manufacturing techniques, metal additive manufacturing techniques are currently considered unsuitable for the fabrication of flexsplines and other sensitive to manufacturing components of HDs. In particular, flexspline manufacturing includes at least the following geometrical constraints and considerations: (1) an extreme thinness of the flexspline's wall (e.g., < 2mm or even < 1.0mm, and as low as 0.05mm), (2) the requisite flatness and smoothness of the mating surface (e.g., the surfaces that must engage with the circular spline and wave generator), (3) the extreme geometrical precision of the gear teeth (e.g., the teeth must be manufactured with a typical tolerance of <100 micrometers and the overall radial (z-axis) symmetry of the flexspline cup, (4) the overall need for geometrical precision of all component surface (e.g., inner surface teeth of the circular spline and the outer teeth of the wave generator). In addition, certain metal additive manufacturing technologies, such as DED, are often unable to achieve a feature size small enough to print a flexspline wall or other flexspline features of the required dimensions, or produce the gear teeth with the correct shape (such as less than 1mm). Accordingly, no currently available metal additive manufacturing technology appears to be suitable for printing metal flexsplines.

[0056] The current application is directed to embodiments of a method for fabrication of metal strain wave gear flexsplines using a specialized metal additive manufacturing technique. In many embodiments, the method allows the entire flexspline to be metal printed, including all the components: the output surface with mating features, the thin wall of the cup, and the teeth integral to the flexspline. In many embodiments, the flexspline can be used directly upon removal from the build tray. In some such embodiments, during the printing process, the wall of the flexspline is oriented vertically on the build platform (i.e. perpendicularly to the metal material being applied), as shown in FIG. 8. In addition, in many embodiments, the standard building parameters are modified so as to achieve the desired flexspline wall thinness and the precisely defined gear teeth. In many embodiments, the method is well-suited for use with DMLS, SLM, or other systems currently available on the market. In some embodiments, the method may be used with DED systems, wherein the deposition spot size of such system is within 15% of the wall thickness of the desired flexspline. In some embodiments, the metal printed flexspline is further finished via a mechanical or chemical finishing operation. In many embodiments, the entirety of the flexspline is metal printed to a net or near-net shape. In many embodiments, the wall thickness of the flexspline printed according to the method of the application is as low as 0.3 mm. In many embodiments, the method of the application allows for fast, facile, low cost, low waste fabrication of flexsplines of the desired geometry. In some embodiments, the method allows to print multiple flexsplines in a single print. In many embodiments, the method of the application yields significant cost and time savings, as compared to conventional metal machining techniques.

[0057] The advantages of metal printing the flexsplines, as opposed to machining them, are significant, even if the part quality is somewhat sacrificed. For example, approximately eighteen 50 mm diameter flexsplines can be printed at one time in less than a 6 hour build time on EOS M290 3D printer with a standard build tray size. In contrast, an automated CNC machining platform of similar size and cost can only produce one flexspline at a time, wherein machining time can be up to an hour and the scrap rate is over 90% of the billet material.

Embodiments of Forming Flexsplines by Additive Manufacturing

[0058] Many embodiments are directed to printing systems based on a material deposition method chosen from the list: powder bed fusion (PBF) printing, direct energy deposition (DED) printing, metal extrusion, fused filament modeling, metal binder jetting, wire arc additive manufacturing, ultrasonic additive manufacturing, thermal spray additive manufacturing, liquid jetting, laser sintering, electron beam freeform, laser melting, or another technique that can be used to print the flexspline in the vertical orientation with the build layers perpendicular to the teeth and the cup facing up, any combination thereof. In many such embodiments, the metal additive manufacturing system utilizes a material in one of the forms chosen from the list: powder, wire, molten metal, fluid liquid metal, metal in a binder, metal in dissolvable inks, metal bound in polymer, sheet metal, any other printing form allowing vertical printing, any combination thereof. In many embodiments, the method of the application is especially advantageous for fabrication of flexsplines.

[0059] Specifically, in many embodiments, the method of the application allows for the fabrication flexspline walls with thicknesses less than 2 mm down to thicknesses as small as 0.35 mm to be produced without the requirement for the use of support pillars or support materials beyond a bottom supporting build plate. Indeed, using additive manufacturing techniques in accordance with embodiments to fabricate flexsplines with wall thickness less than 2 mm is particularly advantageous. In such embodiments, the wall thickness is on the order of the build beam (e.g., laser spot) such that the melt pool associated with one laser pass is approximately the same width as the wall and the heat affected zone (or process zone) spans the entire wall thickness in all cases. This means that the whole flexspline wall is being processed at the same time instead of in several passes where cold material is being joined to hot material, and the whole thickness of the flexspline wall is heated at once. Accordingly, the method of the application is especially advantageous for fabrication of flexsplines from metallic glass materials. Specifically, the method allows for the formation of a fully amorphous flexspline part without any of concerns about reheating or crystallization of the metallic glass material that can arise with other thermal manufacturing techniques, yielding a flexspline with superior properties.

[0060] In order to ensure proper manufacture of flexsplines in accordance with appropriate tolerances, many embodiments of the flexspline manufacturing methods according to the disclosure may include one or more of the following specific manufacturing parameters, which will be discussed in greater detail below:

• The specific orientation of the walls of the flexspline in a vertical direction perpendicular to the build plate (z-direction).

• Positioning the bottom of the cup of the flexspline at the bottom of the build such that no overhangs are formed during fabrication.

• Ensuring that each layer of the flexspline wall is formed in a continuous seamless circle and such that an overall laminate structure of stacked layers is formed.

• Keeping the walls of the flexspline to a thickness small enough such that the melt pool associated with one build beam pass is at least the same size as the wall thickness.

• In cases where optics are immobile, positioning the flexspline close enough to the center of the build plate such that the build beam does not need to be deflected and the circularity of the flexspline can be maintained.

• Altering the material, material state, or build parameter along the vertical direction of the flexspline wall to allow for the fabrication of flexsplines with customized properties. • Forming the recoater blade of the additive manufacturing apparatus of a soft material (e.g., softer than conventional steel recoater blades) to avoid placing undue stress on the flexspline walls. This modification to conventional additive manufacturing apparatus is particularly important when thin-walled flexsplines are being formed, as will be discussed in greater detail below.

Embodiments Incorporating Vertical Build Orientations

[0061] As an initial matter, many embodiments of flexspline additive manufacturing methods are configured such that the flexspline is printed facing upwards, with the thin vertical wall parallel to the z-axis of the build. Although orienting the flexspline vertically to the build platform forces the bottom cup mating surface of the flexspline to face downwards to avoid overhangs, resulting in the mating surface having the roughest surface, such a vertical build orientation allows for the additive manufacture of flexsplines and creates other unexpected advantages.

[0062] For example, the vertical orientation of the flexspline during the fabrication process allows the precise printing of the gear teeth without the need for support material anywhere on the part, except on the bottom. Moreover, in some instances, when the gear teeth of a flexspline have a profile that is not flat but rather has a curve or another arbitrary shape (as shown in FIG. 5), strictly vertical orientation during fabrication is critical for achieving the exactly same curvature and curve shape, with the exactly same feature size, for each tooth and, thus, properly functional flexsplines. Moreover, as previously discussed, such non-flat teeth can be difficult to form using other manufacturing techniques. In addition, since a flexspline needs to be absolutely circular, printing vertically, according to the method of the application, assures that the wall is concentric to the gear teeth and the output shaft, which is a critical consideration to the proper function of a flexspline. This requirement for absolute circularity is so great that in many embodiments, when the printing system's optics cannot be moved (such as in powder bed fusion printers), embodiments call for the flexspline to be printed near the center of the build platform, so as to avoid the need to deflect the build beam and thus maintain the circularity of the flexspline. In contrast, printing near the edges of the build platform of such systems requires that the laser beam is bent to reach the print area, which, in turn, results in the laser spot size that is not precisely circular.

[0063] Furthermore, in many embodiments, the vertical orientation of the flexspline during printing has advantages in terms of enhanced mechanical properties for the resulting flexspline. As is well-known in the art of additive manufacturing, in a 3D printed metal part, the material formed along the z-axis of the print has lower ductility than the material deposited along the x or y planes of the print. However, since the operation of the flexspline mainly relies on the flexing of its wall in the horizontal directions (sideways), the material ductility along flexspline's z-axis (i.e. the direction of the flexspline's print according to the embodiments of the invention) carries less importance to the flexspline's overall functionality. -

[0064] In addition, in many embodiments, the vertical orientation of the flexspline during printing according to the method of the application produces fracture resistant flexsplines. Specifically, flexing of the flexspline cup during the strain wave gear operation promotes fracture formation in the cup, wherein the cracks tend to form from the gear teeth down, towards the bottom of the cup, and parallel to the gear teeth alignment (as is clearly seen in FIG. 9). However, the fabrication method of the application produces the flexspline that is, effectively, a crack resistant "laminate" structure comprised of a plurality of vertically stacked 3D printed layers (FIG. 10). More specifically, orienting the flexspline vertically during the fabrication process of the application, turns the flexspline cup into a laminate structure made up of many thin layers (e.g., on the order of 20 microns thick). Here, it should be noted, that it is well-known in the art of additive manufacturing that melting metal materials during the deposition process does not completely erase the distinctions between the deposition layers, and that evidence layering remains detectable in the vertical direction of building. For example, this effect can be seen upon careful inspection of FIG. 8 and FIG. 13c. Accordingly, such "laminate" structures as described herein are unexpectedly advantageous for forming flexsplines as they are resistant to a crack growing through the layers, making it difficult to grow a crack through the laminate (see, for example, work on Ti-AI ₃ Ti laminates from Vecchio et a I, the disclosure of which is incorporated herein by reference). Specifically, the "laminated" printed flexspline of the application has at least a 10% higher fracture toughness than a flexsplines made entirely of a monolithic metal alloy.

[0065] Furthermore, in many embodiments, the vertical fabrication method of the application produces a stronger flexspline with fewer potential points of failure along its body. Specifically, in many embodiments, as the flexspline is printed vertically, each deposited layer of material may be deposited in a continuous strand of metal (ring) with no attachment/fusion points along each individual circumference, e.g. one continuous laser pass of melted metal when powder bed system is used. Consequently, there exist no circumference "breaks" in the material layers laminated into the circular flexspline wall, and, therefore, no potential points of failure. It should be noted here that 3D printing processes are known in the art to often produce porous and similarly defective structures, and, that, therefore, they would be expected to produce faulty and weak flexsplines as well. However, since the flexspline is operationally loaded by flexing of the flexspline's cup in XY-plane, and since this load is being applied to the laminate of the continuous "rings" of deposited material (as described herein), which have no fabrication faults in their individual circumferences, the flexsplines fabricated according to the methods of the application unexpectedly demonstrate very strong performance.

[0066] Finally, orienting the flexspline vertically during building dictates that the strongest part of the flexspline (the cup's bottom) is attached to the build platform. Most printed flexsplines will have to undergo heat treatment in post-processing to smooth surface roughness or to affect other surface treatments, which tends to warp them. However, printing vertically and attaching the most robust part of the flexspline to the base allows for such flexsplines to be heat treated safely, without causing any deformation of the wall, because the greater part of the flexspline's mass is concentrated in the secured to the platform bottom preventing overheating of the more delicate portions of the flexspline.

Embodiments Incorporating Gear Teeth with Improved Curvature

[0067] As previously discussed, prior art manufacturing techniques are disadvantaged in being able to form flexsplines with teeth that do not have a flat profile. Printing in accordance with embodiments allows the teeth on the flexspline to have a profile that is not flat, but rather has a curve or another arbitrary shape (as shown schematically in FIG. 5). In many embodiments, flexsplines incorporating such gear teeth are printed vertically to avoid manufacturing difficulties. For example, in an additive manufacturing technique where an object is printed at an angle, it would be impossible for each tooth to have the same curvature with the same feature size. Accordingly, in many embodiments the gear teeth are not flat but have a curvature. Specifically, as shown in FIG. 5 this means the teeth are actually slightly curved in the vertical direction. As discussed, it has been found that printing is the only way to add this curvature onto the gear teeth without conventional machining. The vertical print orientation, according to embodiments, also avoids some of the problems associated with horizontal build configurations. For example, printing horizontally with powder bed systems limits the printable feature size by the possible thickness of the layer of deposition powder, which is typically about 20 micron. By printing vertically, it is possible to achieve a much finer resolution without creating a "step." This allows for the formation of smaller curves and other shapes on the flexspline teeth that would not be possible if the flexsplines were orientated differently.

Embodiments Incorporating Engineered Heat Effected Zones

[0068] In various embodiments, the metal additive manufacturing of flexsplines according to the method of the application, may incorporate flexsplines fabricated in a vertical orientation where the flexspline wall is built with a single pass of the laser per layer, affording flexsplines of better quality. Specifically, since the melt pool associated with one laser pass is approximately the same width as the wall, and since the heat affected zone (or process zone) spans the entire wall thickness, the entirety of the flexspline wall thickness is being processed at the same time, instead of in several passes. Therefore, the method of the application allows to avoid situations, wherein a cold material is being joined to a hot material, and, thus, the whole thickness of the flexspline wall is heated at once. In addition, where metallic glass materials are used this is particularly advantageous as it avoids issues associated with crystallization that may occur during reheating of such metallic glasses. [0069] In many embodiments, the metal additive manufacturing of flexsplines according to the method of the application is rapid. Specifically, the parallel orientation of the flexspline's mating surface against the build plate dictated by the method of the application ensures that most of the metal deposition occurs in the beginning of the printing process. Therefore, since the construction of the thin wall of the flexspline may be configured to require only one pass from the laser (which is as small as 0.38 mm in, for example, an EOS M290) per layer, the vertical building of the flexspline requires very little rastering time and, thus, is extremely rapid. In addition, in many embodiments, modification of the machine parameters results in a flexspline wall thickness that is equal to or less than then spot size of the laser (and in many cases wherein the thickness of the cup wall is within 15% of the spot size of the laser of the metal additive manufacturing system), which, in turn, allows the flexspline to be used in harmonic drives directly after printing. However, in some embodiments, larger diameter flexsplines with proportionally thicker walls are manufactured with more than a single pass of the laser.

Embodiments of Additive Manufacturing Techniques Incorporating Custom Build Parameters [0070] In many embodiments, the vertical orientation of the flexspline during 3D printing fabrication results in each print-deposited layer having radial symmetry relative to the cylindrical geometry of the flexspline. Therefore, in such embodiments, each individual deposition layer in the vertically printed flexspline features consistently continuous material properties throughout the layer, wherein the material properties are governed by the user-defined building parameters, such as, for example, laser power and material feed rate. At the same time, the 3D printing systems allow for facile control over the physical properties of the materials in the direction of their deposition (z-direction) during printing, including via material microstructuring.

[0071] Specifically, material physical properties such as, for example, the material's grain size, toughness, hardness, fracture toughness, fatigue limit, ductility, and elastic modulus can be controlled and varied in z-direction of the print via adjustments of the building/deposition parameters. Accordingly, printing the flexspline in the z-direction, according to the embodiments of the invention, allows the different sections of the flexspline along the z-axis to exhibit different mechanical properties. For example, in many embodiments, since larger grain size improves the fracture toughness and fatigue limit of a material, this property may be easily introduced/increased (via adjustment of printing parameters) around the region the flexsplines most likely to fail by these modes. For example, in some embodiments the flexspline fabricated according to the method of the application may feature higher wear resistance near the flexspline's teeth and higher resistance to fracturing in the thin wall. Consequently, in contrast to methods based on metal machining, the method of the invention allows for fabrication of flexsplines with "functionally graded" properties.

[0072] In other embodiments, by printing the flexspline, it is possible to form microstructures that cannot be made with casting or machining forged billets. Specifically, because the cooling rate is very high, embodiments of the method allow for the formation of flexsplines that are at least partially formed out of metallic glass or out of nanocrystalline metal. Accordingly, the flexspline can have properties that cannot be obtained from other methods.

Embodiments of Additive Manufacturing Techniques Incorporating Variable Materials

[0073] In many embodiments, the printing method of the application is extendable to directed energy (DED) systems. DED systems offer additional benefits to the method of the application, wherein DED systems allow to vary material composition in the z-direction of printing. Specifically, in contrast to powder bed printers, in directed energy printers the metal is introduced in the build head, and, therefore, the composition of the metal can be changed in the vertical z-direction. Accordingly, DED systems would allow different regions of the flexspline to be printed in different materials. For example, table of FIG 11 shows the properties of six examples of metal alloys that could be fabricated using the method of the application. These examples include: stainless steel 15-5, Ti-6AI-4V, Nitronic 60 steel, Vascomax C300 maraging steel, Zr-based bulk metallic glass, and Ti-based bulk metallic glass composite. The table also illustrates the combination of properties that can be achieved by printing different parts of the flexspline with different alloys according to many embodiments. As another example, when a DED or similarly functioning system with appropriate laser spot size is used according to the embodiments of the application, a flexspline with teeth made of wear resistant maraging steel and a wall made of a low density titanium alloy can be fabricated. As yet another example, a DED-type system can be used according to some embodiments to fabricate a flexspline, wherein TiC is blended with Ti during the printing of and near the gear teeth portion of the flexspline, so as to create a wear resistant composite selectively in that area of the flexspline. As another example, in some embodiments, the flexspline is vertically printed from two different materials according to the method of the application, so as to have the wall made out of a tough steel, such as 304L alloy, and the gear teeth made out of a wear resistant steel, such as 15-5PH. A table providing a summary of properties for exemplary materials is provided in FIG. 11, however, materials having a fracture toughness between 30 and 150 MPa m ^{1 2} and/or an elastic limit between 0.1 and 2% have been shown to be particularly advantageous in forming flexsplines according to embodiments.

Embodiments Incorporating Exotic Materials

[0074] In many embodiments, the method of the application allows for fabrication of flexsplines from all the heritage materials currently used in the production of steel flexsplines, including, but not limited to: maraging steel, tool steel, precipitation hardened steel, low carbon steel and high carbon steel. Accordingly, the flexsplines fabricated according to the method of the application can be used with the same HD systems and within the same design parameters as the traditional wrought steel flexsplines. In addition, in some embodiments, the method of the application allows for facile fabrication of flexsplines from alloys that are incompatible with the conventional methods of flexspline fabrication, such as difficult or impossible to machine metal alloys, or alloys that cannot be made in any form larger than powder (such as, for example, marginal glass forming materials and nanocrystalline metals).

[0075] In addition, the method of the application can be used to further improve the specific properties of flexsplines prepared from less than optimal materials, wherein adjustments of the printing parameters can, for example, harden materials which would normally be too soft to function well in a flexspline. For example, high strength metals, such as titanium and Inconel, which are typically hard to machine, can be printed into flexsplines in accordance with the method of the application. Furthermore, in some embodiments, the 3D printing method of the application can be used to fabricate flexsplines from metal matrix composites and bulk metallic glasses (also known as amorphous metals), which typically cannot be machined and must be cast in a net shape. Furthermore, in some embodiments, the flexsplines are printed from refractory or other high melting temperature materials, such as Nb, Ta, Mo, W, or V alloys, which are notoriously hard to machine. Ability to print the components from such alloys, could lead to development of strain wave gears capable of operating at extremely high temperatures and enable high-temperature applications for strain wave gears. Accordingly, in many embodiments, the method of 3D printing allows for use of customized metals in fabrication of flexsplines and allows for improved specific properties and manufacturing costs, especially as compared to traditional machining methods.

Embodiments Incorporating Finishing Techniques

[0076] In many embodiments, the flexsplines made using metal additive manufacturing of the application can undergo a simple finishing operation to improve the surface roughness or match a dimensional tolerance inexpensively and easily. Accordingly, flexsplines printed according to the method of the application can be mechanically finished through grinding or milling to achieve a smooth surface, including minimal grinding to only remove the roughness from the gear teeth. Furthermore, in many embodiments, the flexspline surfaces can be smoothed using one of processes including (but not limited to): a chemical process, such as etching; a mechanical finish process, such as water blasting; sand or bead blasting; any combination thereof. In many embodiments, the radial symmetry of the flexspline vertically printed according to the method of the application also simplifies and makes post-fabrication processing more effective. For example, in many embodiments, the mating surface of the flexspline has axial symmetry and is easily lathed. In many embodiments, the flexspline's rough surfaces are easily smoothed using a chemical etching process, such as, for example, electrolysis, wherein the flexspline's radial symmetry and uniform thickness ensure even and effective etching. In addition, in many embodiments, the flexspline's radial symmetry also simplifies post- fabrication machining with a computer numerical control milling machine (CNC) by ensuring that a uniform amount of material is removed. More specific examples of post-fabrication treatments that might improve operability of flexsplines of the application include (but are not limited to): chemical treatment to smooth the surface of the gear teeth and the inner surface of the cup wall (for example to reduce the surface roughness to feature size of less than 50 micrometers); treatment with sanding (for example with 240 grit sand paper); mechanically grinding to reduce surface roughness; polishing operation (for example to reduce the surface roughness by at least 25%); coating with another metal; and heat treating to alter one or more properties chosen from the group consisting of physical properties, porosity, temper, precipitate growth, other properties as compared to the as-fabricated state; any combination thereof.

[0077] However, in some embodiments, the flexspline surfaces are left as-printed to save cost and the flexspline is used as is. In such embodiments, while the performance of the as- printed flexspline will be lower compared to a machined flexspline due to the rough surface finish, it can still be used directly out of the printer to significantly reduce cost of production. To this ends, FIG 12 shows the operation of a flexspline that was 3D printed according to embodiments and assembled into a standard strain wave gear directly out of the printer with no machining. Although the printed flexspline had a very rough surface, it still proved to be functional in actual tests.

[0078] As new metal deposition technologies become available, the method of the application can be extended to other 3D printing methods. For example, when available, high resolution ink jet metal printing or liquid metal printing used with the method of the application will allow for fabrication of smooth precisely executed flexspline ready to be utilized directly after printing with no post processing. As another example, metal printers that combine both 3D printing with CNC machining in the same process have recently became available and, in many embodiments, can be used to manufacture and finish flexsplines according to the method of the application. Specifically, the flexspline may be oriented vertically (according to the method of the application) during the fabrication with such systems in order to take advantage of the CNC tool bit, which can only move up, down, or in a circle.

Exemplary Embodiments of Manufactured Flexsplines

[0079] Accordingly, in many embodiments, the method disclosed herein allows for facile, rapid, and inexpensive fabrication of strain wave gear flexsplines using metal additive manufacturing. Due to various functionality-specific constraints imposed on strain wave gears and specifically on flexspline components (e.g. must have high material tolerance and smooth surface finishes), and in view of limitations of metal printing capabilities, the method of the application is unexpected and nonobvious. Furthermore, in many embodiments, the method of the application allows for fabrication of flexsplines from previously inaccessible for this purpose alloys and material compositions. In addition, in some embodiments, the method of the application allows for material properties gradient or material composition gradient within a flexspline structure, which is not possible to achieve via heritage steel machining methods. In many embodiments, the method is used to efficiently fabricate functional flexsplines featuring: exquisitely thin walls, precisely net-shaped gear teeth, and enhanced mechanical properties, such as enhanced ductility. In addition, in many embodiments, the flexsplines fabricated according to the method of the application require little to none post-production machining or post-production finishing. Examples of flexsplines manufactured according to the methods disclosed herein are shown and compared to heritage flexsplines in FIGs. 13a to 13d

[0080] Specifically, FIGs. 13a compares the top and bottom views of a printed (left), cast (center) and machined (right) flexsplines, wherein the flexspline printed according to embodiments has the roughest appearance, but may be made with metals that are difficult to machine or cast, and/or may have a gradient of properties in the bottom to the teeth direction. FIG 13b compares micrometer readings (i.e. wall thickness) of a machined steel flexspline (0.02 inches, left) and a flexspline printed from steel according to embodiments (0.015 inches, right), and demonstrates that the method of the application can achieve a thickness that is the same or even thinner than machining methods. It should be noted that such low wall thickness can never be fully realized via casting methods. Finally, FIG 13c shows the difference in roughness between the teeth on a printed flexspline (left) and a heritage machined flexspline (right). Although the finish of the printed flexspline is much rougher, it also clearly shows a "laminate" structure formed of the build layers, which is perpendicular to the direction of the expected normal failure mode, and therefore, implies a higher resistance to crack growth than a monolithic material. In addition, the method of the application allows to achieve complex curvatures in the teeth that are hard to achieve via machining and cannot be achieved through casting.

[0081] Finally, FIG. 13d shows two flexsplines (left and center) printed according to current embodiments, and one (right) printed where the laser properties have not been modified in such a way to assure that the entire flexspline wall is heated throughout during each building layer such that the wall of the flexspline is resistant to fracturing, and using a conventional hard steel recoater blade. As shown, this combination can result in the catastrophic failure of flexspline wall.

DOCTRINE OF EQUIVALENTS

[0082] This description of the invention has been presented for the purposes of illustration and description. It is not intended to be exhaustive or to limit the invention to the precise form described, and many modifications and variations are possible in light of the teaching above. The embodiments were chosen and described in order to best explain the principles of the invention and its practical applications. This description will enable others skilled in the art to best utilize and practice the invention in various embodiments and with various modifications as are suited to a particular use. The scope of the invention is defined by the following claims.