MACROSCALE GEARS

STATEMENT OF FEDERAL FUNDING

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

FIELD OF THE INVENTION

[0002] The present invention generally relates to bulk metallic glass-based

macroscale gears.

BACKGROUND

[0003] Gears are pervasive engineering components that are commonly used in a variety of actuation mechanisms. For example, gears are typically used to drive automobiles, bicycles, extraterrestrial vehicles, and even watches. Because they experience constant stress during operation, it is desirable that gears be formed of strong and robust materials.

[0004] A relatively new class of materials that may be well suited for the fabrication of gears are metallic glasses, also known as amorphous alloys. Metallic glasses are characterized by their disordered atomic-scale structure in spite of their metallic constituent elements - i.e., whereas conventional metallic materials typically possess a highly ordered atomic structure, metallic glass materials are characterized by their disordered atomic structure. Notably, 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. They 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. In particular, the manufacture of a metallic glass can be compatible with an injection molding process. [0005] Nonetheless, the manufacture of metallic glasses presents challenges that limit their viability as engineering materials. In particular, metallic glasses are typically formed by raising a metallic alloy above its melting temperature, and rapidly cooling the melt to solidify it in a way such that its crystallization is avoided, thereby forming the metallic glass. The first metallic glasses required extraordinary cooling rates, e.g., on the order of 10 ⁶ K/s, and were thereby limited in the thickness with which they could be formed. Indeed, because of this limitation in thickness, metallic glasses were initially limited to applications that involved coatings. Since then, however, particular alloy compositions that are more resistant to crystallization have been developed, which can thereby form metallic glasses at much lower cooling rates, and can therefore be made to be much thicker (e.g., greater than 1 mm). These thicker metallic glasses are known as 'bulk metallic glasses' ("BMGs").

[0006] Although metallic glasses can now be formed in dimensions that can allow them to be more useful, the current state of the art has yet to understand BMG materials properties to an extent where 'macroscale' gears, for example those of the size that are typically used to drive robotics (e.g., those produced by Maxon Motor), can be efficiently designed. Accordingly, there exists a need to have a fuller understanding of the materials properties of BMGs such that a BMG-based macroscale gear can be efficiently designed, fabricated, and implemented.

SUMMARY OF THE INVENTION

[0007] Systems and methods in accordance with embodiments of the invention implement bulk metallic glass-based macroscale gears. In one embodiment, a method of fabricating a bulk metallic glass-based macroscale gear, where at least either the thickness of the gear is greater than 3 mm or the diameter of the gear is greater than 9 mm, includes: obtaining design parameters of the gear to be formed; selecting a bulk metallic glass from which the gear will be formed based on the obtained design parameters, where the selected bulk metallic glass is characterized by a resistance to standard modes of wear and a resistance to brittle fracture such that a gear can be formed from the selected bulk metallic glass that accords with the obtained design parameters; and fabricating the gear from the selected bulk metallic glass that accords with the obtained design parameters.

[0008] In another embodiment, the obtained design parameters are based on the gear's anticipated operational setting.

[0009] In yet another embodiment, the obtained design parameters include at least one of: the dimensions of the gear to be formed; the desired extent of the gear's resistance to brittle fracture; and the desired extent of the gear's resistance to standard modes of wear.

[0010] In still another embodiment, the obtained design parameters include the dimensions of the gear to be formed, the desired extent of the gear's resistance to brittle fracture, and the desired extent of the gear's resistance to standard modes of wear.

[0011] In still yet another embodiment, the extent of the gear's resistance to brittle fracture is determined based on its constituent material's fracture toughness.

[0012] In a further embodiment, the selected bulk metallic glass material is characterized by a fracture toughness of between approximately 20 MPa ^* m ^{1 2} and 80 MPa ^* m ^{1 2} .

[0013] In a yet further embodiment, the extent of a gear's resistance to standard modes of wear is determined based on its constituent material's hardness.

[0014] In a still further embodiment, the selected bulk metallic glass material has a Vickers hardness value of at least 400.

[0015] In a still yet further embodiment, the extent of the gear's resistance to standard modes of wear is determined based on its constituent material's performance in a pin-on-disk test.

[0016] In another embodiment, the selected bulk metallic glass is an alloy based on one of: Zr, Ti, Cu, Pd, and Pt.

[0017] In yet another embodiment, the selected bulk metallic glass is a TiZrBeX alloy, wherein X is a late transition metal.

[0018] In still another embodiment: the atomic percentage of Ti is between approximately 30% and 60%; the atomic percentage of Zr is between approximately 15% and 35%; the atomic percentage of Be is between approximately 7% and 35%; and the atomic percentage of the combination of all other constituent elements is less than approximately 20%.

[0019] In still yet another embodiment, the selected bulk metallic glass is one of: Ti ₄₅ Zri6Be2oCuioNi9,Ti3o r35Be ₂ 6.8Cu8.2, and Ti ₄ oZr ₂ 5Be3oCr ₅ .

[0020] In a further embodiment, the temperature of the environment at which the gear is anticipated to operate is below 0°C, and the selected bulk metallic glass is characterized by a resistance to brittle failure at the anticipated operating temperature and under the corresponding anticipated operating conditions.

[0021] In a yet further embodiment, the obtained design parameters include a desired threshold resistance to brittle failure at the anticipated temperature that is determined by constituent material's Charpy impact energy at the anticipated temperature.

[0022] In a still further embodiment, the desired threshold Charpy impact energy at the anticipated temperature is correlated with a threshold Charpy impact energy at room temperature using a known relationship of Charpy impact energy as a function of temperature; and selecting the bulk metallic glass based on its correlated threshold Charpy impact energy at room temperature.

[0023] In a still yet further embodiment, the known relationship of Charpy impact energy as a function of temperature is linear.

[0024] In another embodiment, the known relationship of Charpy impact energy as a function of temperature is .02 J/°C.

[0025] In still another embodiment, selecting a bulk metallic glass includes: identifying an alloy system that is known to have a resistance to brittle failure that accords with the obtained design parameters; and assessing micro-alloyed variants of the alloy system to select a particular composition that has a resistance to standard modes of wear as well as a resistance to brittle failure, from which a gear can be formed that accords with the obtained design parameters.

[0026] In a further embodiment, a method of fabricating a bulk metallic glass-based macroscale gear, where at least either the thickness of the gear is greater than 3 mm or the diameter of the gear is greater than 9 mm, includes: obtaining design parameters of the gear to be formed; selecting a bulk metallic glass from which the gear will be formed based on the obtained design parameters, where the selected bulk metallic glass is characterized by a resistance to brittle failure such that a gear can be formed from the selected bulk metallic glass that accords with the obtained design parameters; and fabricating the gear from the selected bulk metallic glass that accords with the obtained design parameters.

[0027] In another embodiment, a bulk metallic glass-based macroscale gear, where at least either the thickness of the gear is greater than 3 mm or the diameter of the gear is greater than 9 mm, includes a bulk metallic glass that is resistant to standard modes of wear and resistant to brittle failure.

[0028] In yet another embodiment, the fracture toughness of the bulk metal glass is between approximately 20 MPa*m ^{1 2} and 80 MPa*m ^{1 2} .

[0029] In still another embodiment, the bulk metallic glass has a Vickers hardness value of at least 450.

[0030] In still yet another embodiment, the bulk metallic glass is a TiZrBeX alloy, where X is a late transition metal.

[0031] In a further embodiment: the atomic percentage of Ti is between approximately 30% and 60%; the atomic percentage of Zr is between approximately 15% and 35%; the atomic percentage of Be is between approximately 7% and 35%; and the atomic percentage of the combination of all other constituent elements is less than approximately 20%.

[0032] In a yet further embodiment, the bulk metallic glass is one of: Ti ₄₅ Zri6Be2oCuioNi9,Ti3oZr ₃ 5Be26.8Cu8.2, and Ti ₄ oZr ₂ 5Be3oCr ₅ .

BRIEF DESCRIPTION OF THE DRAWINGS

[0033] FIG. 1 illustrates the pin-on-disk method that is virtually standardized in assessing a material's wear performance.

[0034] FIG. 2 illustrates a general understanding of how bulk metallic glass (BMG) wear performance is expected to vary with hardness. [0035] FIG. 3 illustrates a general understanding of the expected wear performance of BMGs relative to metals and ceramics.

[0036] FIG. 4 illustrates role of torque during the operation of gears.

[0037] FIGS. 5A and 5B illustrate how wear loss, as determined by the pin-on-disk method, and fracture toughness vary with Vickers hardness.

[0038] FIGS. 6A and 6B illustrate a 4-point flexure test that can be used to determine fracture toughness, in accordance with embodiments of the invention.

[0039] FIG. 7 illustrates a new paradigm for material selection for BMG-based macroscale gears in accordance with embodiments of the invention.

[0040] FIG. 8 illustrates a flowchart for the fabrication of a BMG-based macroscale gear in accordance with embodiments of the invention.

[0041] FIGS. 9A-9C illustrate the gear rig and gears that were used in testing the design principles described in the instant application.

[0042] FIGS. 10A-10D illustrate the types of gear failure seen during testing.

[0043] FIGS. 1 1A-1 1 B illustrate two plots that reflect the results of the testing.

[0044] FIG. 12 depicts the wear characteristics for various compositions of a TiZrBe BMG alloy system.

[0045] FIG. 13 illustrates gears that have been fabricated in accordance with embodiments of the invention.

[0046] FIGS. 14A and 14B illustrate two plots that depict Charpy impact energy as a function of temperature for a variety of alloy systems.

[0047] FIG. 15 illustrates design principles that can be used in fabricating BMG- based macroscale gears that are configured to operate at low temperature in accordance with embodiments of the invention.

DETAILED DESCRIPTION

[0048] Turning now to the drawings, systems and methods for implementing bulk metallic glass-based macroscale gears are illustrated. Bulk metallic glasses (BMGs) possess a number of useful materials properties (e.g., high tensile strength, corrosion resistance, electrical conductivity, processability), and have been well studied for their potential as advanced engineering materials. In particular, BMGs have been extensively studied for their potential implementation in applications that require wear resistance, (see e.g., Wu, Trans. Nonferrous Met. Soc. China 22 (2012), 585-589; Wu, Intermetallics 25 (2012) 1 15-125; Kong, Tribal Lett (2009) 35:151 -158; Zenebe, Tribol Lett (2012) 47:131 -138; Chen, J. Mater. Res., Vol. 26, No. 20, Oct 28, 201 1 ; Liu, Tribol Lett (2012) 46:131 -138; the disclosures of which are hereby incorporated by reference.) To be clear, "wear" conventionally refers to the displacement of the surface of a material as a direct result of its mechanical interaction with another material. It is generally understood that a material's resistance to wear generally increases with its hardness, i.e., the harder a material is, the less susceptible it is to wear. (See e.g., I.L. Singer, Wear, Volume 195, Issues 1 -2, July 1996, Pages 7-20.) Resistance to wear is typically determined by subjecting a sample to a process that causes wear, and measuring the mass of the sample before and after the 'wear-causing' process. For example, FIG. 1 depicts a pin-on-disk setup that is standard in determining a material's resistance to wear. In the illustration, a sphere with a diameter, d, is applied with a force, F, to a disk with a diameter, D. The force, F, is applied at a radial distance, R, from the disk's center. The disk is then rotated through w revolutions as the force, F, is being applied. The mass of the disk is determined before and after it has been subjected to the force F. Accordingly, the difference in mass reflects the amount of material that was 'worn away' by the process, i.e., the 'wear loss'. And of course, wear loss is inversely correlated with wear resistance; in other words, the more a material wears away, the less resistant it is to wear loss.

[0049] FIG. 2 illustrates the general understanding that the resistance to wear of BMGs is generally expected to increase with hardness - in other words, the harder a BMG is, the less susceptible it is expected to be to wear loss. FIG. 3 illustrates an Ashby plot that reflects a general understanding of the resistance to wear of BMGs relative to metals and ceramics. As can be seen from the plot, BMGs are generally harder materials than metals, but softer than ceramics. Accordingly, their resistance to wear is predicted to be in between that of ceramics and that of metals. Although they are typically not as hard as ceramics, they possess other materials properties that can make them advantageous over ceramics, and can thereby compensate for any potential shortcomings with respect to hardness. For example, generally speaking, BMGs are more processable than ceramics, and they are relatively less brittle.

[0050] Based on these understandings, it has been suggested that the predicted wear-resistance characteristics of BMGs may make them excellent candidates for materials from which to fabricate gears, given that gears are subject to extensive mechanical interaction and are thereby subject to wear. (See e.g., Chen, J. Mater. Res., Vol. 26, No. 20, Oct 28, 201 1 ; Huang, Intermetallics 19 (201 1 ) 1385-1389; Liu, Tribol Lett (2009) 33:205-210; Zhang, Materials Science and Engineering A, 475 (2008) 124- 127; Ishida, Materials Science and Engineering A, 449-451 (2007) 149-154; the disclosures of which are hereby incorporated by reference.) However, although using BMGs to make gears has been postulated on this basis, the current state of the art is lacking in a method for efficiently producing superior macroscale gears - e.g., gears where at least either the thickness is greater than approximately 3 mm or the diameter is greater than approximately 9 mm - using BMG materials. Gears of these dimensions are pervasive engineering components, and are frequently used, for example, to drive robotics. To be clear, m/ ^' croscale gears have been produced from BMG materials. (See e.g., Ishida, Materials Science and Engineering A, 449-451 (2007) 149-154, the disclosure of which is hereby incorporated by reference.) However, the inventors of the instant application have observed that modes of failure for macroscale gears and microscale gears differ in appreciable ways, such that simply forming a macroscale gear from a conventional BMG material without any further insight could result in a substandard gear. More specifically, the inventors have observed that the normal forces typically sustained during macroscale gear operation, aside from the surface-to-surface sliding interaction that are the typical focus of tribological studies, play a critical role in determining the viability of the macroscale gear insofar as these forces can cause brittle fracture. Conversely, as will be elaborated on more thoroughly below, brittle fracture is not as critical of a consideration on a microscale. Indeed, although Ishida et al. have reported the fabrication of a functional microgear, their gears were lubricated during during testing. (See e.g., Ishida, Materials Science and Engineering A, 449-451 (2007) 149-154.) Lubrication can help thwart tendencies for brittle fracture. In many instances, the superior BMG-based macroscale gears implemented in accordance with the instant application are sufficiently robust that they can achieve acceptable performance without the benefit of a lubricant. BMG-based macroscale gears that do not require lubrication during operation can be much more versatile engineering components.

[0051] Accordingly, the inventors have observed that it is not sufficient to form a macroscale gear from a BMG primarily considering the BMG's glass forming ability and/or its resistance to standard modes of wear. Instead, to produce a superior macroscale gear, the constituent BMG must be carefully selected/developed so that it has sufficient resistance to brittle fracture. Accordingly, in many embodiments of the invention, a method of fabricating a BMG-based macroscale gear, where at least either the thickness of the gear is greater than 3 mm or the diameter of the gear is greater than 9 mm, includes: obtaining design parameters of the gear to be formed; selecting a BMG from which the gear will be formed based on the obtained design parameters, where the selected BMG is characterized by a resistance to standard modes of wear and a resistance to brittle fracture such that a gear can be formed from the selected BMG that accords with the obtained design parameters; and fabricating the gear from the selected BMG that accords with the obtained design parameters. BMG-based macroscale gears produced in accordance with this design methodology can yield much more robust and practical gears than those that are typically produced from metals or ceramics using conventional processes. For example, these gears can have hardness values that approach those of ceramics, but at the same time have fracture toughness values that far exceed those of ceramics. These enhanced material properties can enable gears to be implemented in applications where they previously were not suitable. Moreover, it can be much easier to fabricate gears from BMGs than from ceramics. Furthermore, BMG material properties can be tunable by varying their composition. For example, they can be made to be more or less tough based on varying the ratios of the constituent elements. In particular, the inventors have observed that BMG can have fracture toughness values that range from 1 MPa ^* m ^{1 2} to 200 MPa ^* m ^{1 2} . Similarly, the hardness values also vary over a wide spectrum. [0052] Note that conventional methods of fabricating BMG-based macroscale gears tend to presume that BMGs will have sufficient fracture toughness, and typically focus largely on selecting harder materials. Conversely, in many embodiments, the fracture toughness is given preeminent consideration in the material selection process for a BMG-based macroscale gear; the selected material may then processed (e.g., by microalloying) to develop its hardness as necessary.

[0053] Furthermore, in connection with this design methodology, the inventors have observed that the wear performance for BMG-based macroscale gears is substantially impacted by the temperature at which the gears are expected to operate. In particular, the inventors have observed that relatively tougher BMGs that are typically prone to abrasive wear and galling at room temperatures, and are thereby generally worse candidate materials to make macroscale gears that operate at room temperature, can actually be more preferable candidate materials for gears that operate at extremely low temperatures.

[0054] The design principles and methodologies that the inventors of the instant application have determined will now be discussed.

BMG GEAR DESIGN

[0055] The material selection aspect of the design of BMG-based gears has conventionally been based on avoiding standard modes of wear, e.g.: abrasive wear, which refers to when a rough, hard surface or particle creates gouges or troughs in a softer surface; and adhesive wear (galling), which refers to when material is transferred from one substrate to the other through intimate contact at high pressure. Accordingly, the pin-on-disk method (discussed above and illustrated in FIG. 1 ) is typically extensively relied upon in the material selection process, as it is the standardized method for determining wear performance with respect to standard modes of wear. In many instances, a standardized ASTM pin-on-disk configuration is used to assess wear loss, that employs a steel wear ball 100 g weight, and 1 .2 km of wear track, run at 200 rpm. Conventionally, the BMG materials that demonstrate the best performance in the pin-on-disk test are presumed to be the preferred materials from which to form a gear. [0056] However, the inventors have observed that this design methodology premise is particularly deficient in designing gears that are larger than certain a critical dimension, and are thereby on a 'macroscale'. More specifically, above this critical dimension, the brittle nature of BMGs adopts an enhanced role in determining their viability as a gear material. Throughout this application, 'macroscale' is used to refer to dimensions, above which BMG-based gears begin to develop a strong tendency to demonstrate brittle failure during operation. This can happen when the gear dimensions are larger than the plastic zone size (where gear dimensions are smaller than the plastic zone size, brittle fracture can typically be avoided). For example, it has been observed that the ductility of a BMG material is inversely correlated with its thickness. (See e.g., Conner, Journal of Applied Physics, Volume 94, Number 2, July 15, 2003, pgs. 904- 91 1 , the disclosure of which is hereby incorporated by reference.) The inventors have particularly observed that gears that have a thickness that is slightly above approximately the plastic zone radius of the constituent BMG material begin to demonstrate susceptibility to brittle failure. Essentially, as gear dimensions become greater, they become more and more prone to brittle failure. Conversely, BMG-based gears that have relatively smaller dimensions, e.g., microscale gears, are not as prone to brittle failure because of their small size, and thereby the brittle nature that BMGs can demonstrate is not as significant of a consideration in the material selection process for such gears. The inventors have further observed that BMG-based gears that have dimensions such that at least either the thickness is greater than 3 mm or the diameter is greater than 9 mm, can be particularly prone to brittle fracture. In many embodiments, methods for designing BMG gears in this relatively larger size and above, where gears are commonly used in engineering applications, are implemented.

[0057] Importantly, note that, as illustrated in FIG. 4, gears experience torque during operation, which can serve to apply a force that precipitates brittle failure. Thus, relying largely on a BMG's performance in a pin-on-disk test as a measure of material suitability can be fallacious as a pin-on-disk test largely applies compressive forces and thereby does not provide any indication as to a sample's resistance to brittle failure. Hence, whereas a material selection process that relies on BMGs' respective performances in a pin-on-disk test may be suitable in the design of a microscale gear (i.e., where brittle failure is not as much of a consideration), relying exclusively on this methodology would be deficient in designing a macroscale gear.

[0058] For example, a plot of pin-on-disk wear loss as a function of Vickers hardness for Zirconium, Titanium, and Copper-based BMGs is illustrated in FIG. 5A. As is evident from the plot, and in accordance with the conventional understanding of materials properties, wear loss and hardness are negatively correlated for these alloys, i.e., materials with higher hardness tend to experience less wear loss generally speaking. This tends to be especially true in alloys with a hardness value greater than approximately 550 Vickers. Thus, in accordance with conventional design methodologies, the BMGs with the lowest wear loss, as measured by the pin-on-disk method, would be preferred as the constituent material from which to form a gear. In fact, this methodology drives much of the scientific literature on improving wear resistance in BMGs. However, a corresponding plot of fracture toughness vs. hardness for the exact same alloys in FIG. 5A is depicted in FIG. 5B. As is evident from the plot, and also in conformance with conventional understanding of materials properties, fracture toughness is also inversely correlated with hardness, i.e., materials with higher hardness values tend to have lower fracture toughness values (and correspondingly, they tend to be more brittle). Thus, where a BMG-based macroscale gear is to be formed, the material selection aspect of the design process should not simply focus on selecting the material that has a minimal wear loss in accordance with a pin-on-disk method (typically the materials that have higher hardness values), because as demonstrated by FIG. 5B, such materials may not have the requisite fracture toughness. Therefore, in accordance with many embodiments of the invention, in selecting a material to form a macroscale BMG-based gear, both a BMG material's resistance to standard modes of wear (e.g., indicated by pin-on-disk tests) and its resistance to brittle fracture (e.g., as indicated by its fracture toughness) are accounted for.

[0059] In a number of embodiments, a particular alloy composition is selected based on its resistance to brittle fracture, and the particular alloy composition is then processed (e.g., by microalloying) to develop its resistance to standard modes of wear as necessary. For example, in some embodiments, selecting the BMG includes identifying an alloy system that is known to have a resistance to brittle failure that is desired, and assessing variants of the alloy system to select a particular composition that achieves the desired resistance to wear and the desired resistance to brittle fracture. The variants can be achieved by for example micro-alloying the system, or even by processing. Of course, any way of selecting a BMG that results in a BMG that meets a desired criterion for resistance to wear and resistance to brittle fracture can be implemented. Note that conventional material selection processes for forming BMG- based gears seemingly presume that a BMG has the requisite resistance to brittle failure.

[0060] Of course, a material's fracture toughness can be determined by any of a variety of methods. For example, a 4-point flexure test, as depicted in FIG. 6, may be used. In essence, in accordance with the test, a specimen (or 'sample') is placed on supporting pins, and loading pins are applied with a force at a horizontal distance away from the supporting pins. The plot in FIG. 5B was obtained using 3.5 mm x 3.5 mm beams of BMG material that were notched and then bent. FIG. 6B illustrates the particular setup that was used to obtain the data depicted in FIG. 5B. ASTM standards can be used to calculate the fracture toughness from these tests (and were used in computing the data depicted in the plot in FIG. 5B).

[0061] Accordingly, the inventors present a novel paradigm, illustrated in FIG. 7, for the material selection process in the fabrication of BMG-based macroscale gears; the paradigm is well-suited for the cases when BMG hardness can be correlated with wear loss and fracture toughness (i.e., when an increase in hardness results in a corresponding reduction in fracture toughness and a corresponding reduction in wear loss). Specifically, FIG. 7 depicts a plot of gear failure as a function of hardness. Note that the straight solid line that continues into the dashed line reflects the considerations of the material selection process in accordance with conventional design methodology. Conventionally, the materials selection process was largely concerned with avoiding abrasion and galling wear; thus the conventional materials selection process was largely focused on selecting the material that demonstrated the best performance in pin- on-disk testing, which typically were the harder materials. However, as discussed above, the brittle nature of BMGs must be accounted for when designing BMG-based macroscale gears. Accordingly, FIG. 7 shows an upward trend in gear failure beyond a particular hardness, which is reflective of brittle fracture, e.g., gear teeth shearing off. Generally, as discussed above, in selecting a material from which to form a BMG, a BMG must be selected that adequately balances the need to avoid standard modes of wear such as abrasion and galling, and brittle failure. This balance is reflected in the lower points on the curve, and designated Optimal BMG Gears." Thus, in a sense, it is desirable to implement a BMG that is relatively toward the 'minimum' of this curve. BMG-based macroscale gears fabricated from BMG materials with these relative properties will exhibit reduced occurrences of brittle fracture, while still retaining wear resistance that is superior to tougher metal alternatives.

[0062] Hence, in a number of embodiments of the invention, a method of fabricating a BMG-based macroscale gear includes selecting a BMG from which to form the gear wherein the selection criterion includes considering the BMG's resistance to conventional modes of wear (e.g., abrasive wear and galling); and its resistance to brittle failure. The selection criterion may further include the BMG's glass forming ability, which is a commonly desired trait in BMG-component manufacturing applications. A method of fabricating a BMG-based macroscale gear that includes: obtaining the desired design parameters of the BMG-based macroscale gear to be formed; selecting a BMG from which the gear will be formed based on its suitability for the desired design parameters, its resistance to standard modes of wear, and its resistance to brittle fracture; and fabricating the gear from the selected BMG is illustrated in FIG. 8. Of course, any criterion may be used to judge a BMG's resistance to standard modes of wear and its resistance to brittle failure in accordance with embodiments of the invention. For example, as alluded to above, a BMG's resistance to standard modes of wear can be determined by its performance in a pin-on-disk test, and it's resistance to brittle failure can be determined by its fracture toughness. Alternatively, a BMG's resistance to standard modes of wear can be determined by measuring its hardness. Additionally, in many embodiments, the BMG is further selected based on its glass forming ability.

[0063] The fabrication process initially begins with obtaining (810) the design parameters for the BMG-based macroscale gear to be formed. For example, the following parameters may be obtained: the dimensions of the gear, the desired extent of the gear's resistance to brittle fracture, the desired extent of the gear's resistance to standard modes of wear loss, the anticipated operating temperature, the anticipated operating environment; desired robustness in view of the anticipated operating contact stress and/or torque; the desired density; the desired corrosion resistance; and any desired corresponding factor of safety. Of course, this list is not meant to be exhaustive, and merely meant to be illustrative of the sorts of parameters that may be obtained in accordance with embodiments of the invention. Note that in many embodiments, the design parameters include a requisite resistance to brittle fracture and a requisite resistance to standard modes of wear. And of course, the design parameters may be based on the anticipated operational setting for the gear to be formed.

[0064] Accordingly, a BMG is selected (820) based on its suitability in view of the desired design parameters, its resistance to standard modes of wear, and its resistance to brittle fracture. As alluded to above, in some embodiments the BMG is selected in further view of its glass forming ability. Typically, the glass forming ability of a BMG is a universally desired trait, but based upon the particular fabrication process, a BMG with relatively lesser glass forming ability may suffice. As discussed above, the dimensions of the gear to be formed impacts the requisite material properties, and thereby impacts material selection. Specifically, as discussed above, gears that are manufactured on a macroscale are more prone to brittle fracture, and thereby BMGs that are sufficiently resistant to brittle fracture are required to form macroscale gears. Accordingly, in many embodiments, the material selection is made in view of the desired gear dimensions. Of course, the stress and/or torque that are expected to be applied to the gear (along with any desired factor of safety) also impact the required resistance to standard modes of wear and to brittle fracture, and thereby influence the material selection process. In many embodiments, a BMG is selected that has a wear volume loss of less than 2 mm ³ in an ASTM pin-on-disk testing setup that uses a steel wear ball 100 g weight, 1 .2 km of total wear track, run at 200 rpm. In a number of embodiments, a BMG is selected that has a hardness value of greater than approximately 400 on the Vickers scale.

[0065] The anticipated operating environment also impacts BMG material selection. For example, it has been determined that BMGs may be less prone to abrasive wear and galling when they are in an oxygen-free environment. (See e.g., Hong, Trans. Nonferrous Met. Soc. China 22(2012) 585-589.) Accordingly, where it is known that the gear to be formed will operate in an oxygen-free environment, then more emphasis can be placed on finding a suitable BMG with sufficient resistance to brittle fracture (e.g., as indicated by fracture toughness). Moreover, as will be more fully elaborated on below, the anticipated operating temperature will also impact the material selection process; if the gear is expected to be operating at low temperatures, then it is generally more preferable to select materials that are more resistant to brittle fracture at room temperature, even though they may have poorer resistance to standard modes of wear at room temperature.

[0066] The inventors have also observed that in many instances it is preferable to select a BMG material as opposed to a BMG composite material (e.g., a material that is characterized by crystalline phases within an amorphous matrix). In particular, the inventors have observed that BMG composites do not perform well as gear materials as they tend undergo brittle fracture during operation if the reinforcing phase is hard, and they undergo severe abrasive wear loss if the reinforcing phase is soft. Thus, in many embodiments, a BMG that is substantially free of any crystalline phases is selected.

[0067] Of course these are merely examples of how the material selection process is impacted by obtained design parameters in accordance with embodiments of the invention. But it should be clear that the obtained design parameters can be assessed in any of a variety of ways in order to facilitate the material selection process in accordance with embodiments of the invention. With these parameters and assessments in mind, a material can be selected that satisfies the design parameters.

[0068] Based on the material selection, a macroscale gear may be fabricated (830). Of course, any suitable fabrication process may be implemented in accordance with embodiments of the invention. For example, the gear may be fabricated using casting plates, and then using EDM to form the gear teeth. Alternatively, the gear may be cast to a net gear shape outright.

[0069] In a number of embodiments, the BMG is coated with a hard, wear-resistant coating (e.g., Mo-based alloys) to further improve its wear characteristics. Of course, the BMG can be augmented in any way in accordance with embodiments of the invention.

[0070] Laboratory results that validate the above-described approach are now described below.

DEMONSTRATION OF VIABILITY OF APPROACH

[0071] The above-described approach has been validated through lab experimentation. Zr, Ti, and Cu BMG gears were fabricated by casting plates and EDM - EDM was used to shape the gear teeth. The gears had 30 teeth, 48 diametral pitch gears, with a pressure angle of 20°. Wear loss was determined by weighing the gears before and after the tests. FIG. 9A depicts a diagram of the gear testing rig; FIG. 9B depicts a photograph of the gear testing rig; and FIG. 9C depicts a photograph of the gears tested. Essentially, the gears were subject to a simulated operational environment. In particular, they were run at 10in.-lbs. of torque for 61 ,500 revolutions in open air at room temperature.

[0072] FIGS. 10A-10D illustrate the types of wear/failure that were seen during the testing. In particular, FIG. 10A illustrates a gear that fractured through its body. FIGS. 10B and 10C illustrate tooth fractures. And FIG. 10D illustrates abrasive wear (which can be seen as a notch in the gear tooth).

[0073] FIGS. 1 1A and 1 1 B depict the plots that reflect the results that were obtained. In particular, FIG. 1 1A is a plot of the wear loss as a function of fracture toughness for the fabricated Zr, Ti, and Cu BMG gears. Similarly, FIG. 1 1 B is a plot of wear loss as a function of hardness. Note that open circles reflect the gears that failed under a brittle mode - their teeth sheared off or the gear outright fractured (the data point that reflects a 300 mg 'wear loss' was actually an outright fracture of the gear). Essentially, wear loss improved with decreasing fracture toughness until the alloys became too brittle and their respective teeth sheared off. Accordingly, in many embodiments, BMG materials are iteratively tested in a gear rig setup (similar to that seen in FIGS. 9A and 9B) to ensure their viability as a prospective macroscale gear material. Note generally, that the-above described results reflect the above-described novel understanding of BMG-based macroscale gear design, i.e., to construct a superior BMG-based macroscale gear, the constituent BMG must possess sufficient resistance to brittle fracture as well as sufficient resistance to standard modes of wear.

[0074] The inventors have generally observed that resistance to brittle fracture (e.g., which can be measured by fracture toughness) is generally more important than resistance to standard modes of wear (e.g., which can be measured by pin-on-disk tests) in designing BMG-based macroscale gears. In other words, in selecting a BMG material from which to form a macroscale gear, it is generally best to begin with the understanding that BMGs are substantially glass-like or ceramic-like (e.g., hard and brittle), and then selecting/developing BMG that have sufficient fracture toughness without overly compromising their beneficial glass-like qualities (i.e., their hardness). By contrast, conventional material selection methodology (where harder materials are typically selected for their presumed ability to withstand standard modes of wear) seemingly adopts a contrary approach; i.e., the conventional approach seemingly assumes that BMGs are sufficiently metallic (have sufficient fracture toughness, but may be lacking in hardness) and therefore seems primarily focused on developing/implementing BMGs that have the highest hardness under the presumption that they will still have sufficient fracture toughness.

[0075] Indeed, in many embodiments, a BMG material, from which to fabricate a gear, is selected primarily based on its resistance to brittle fracture. Primarily focusing on resistance to brittle fracture as a selection criterion is partly based on the notion that many BMGs have a sufficient resistance to standard modes of wear loss for many gear applications, and thus resistance to brittle fracture is the primary variable. Further, in some senses, resistance to brittle failure can be related to resistance to wear loss. For example as demonstrated above, materials that are resistant to brittle fracture tend to be softer, and thereby more prone to standard modes of wear. Accordingly, in many instances it is preferable to select a material from which to form a macroscale gear that is sufficiently resistant to brittle fracture, but not too resistant to brittle fracture.

[0076] With these understandings, the inventors have observed that BMG materials with fracture toughness values of between 20 and 80 MPa ^* m ^{1 2} generally make for superior BMG-based macroscale gears. However, for low torque gears, a fracture toughness of between 10 and 20 MPa ^* m ^{1 2} may be sufficient. Moreover, the inventors note that almost all Ni, Fe, Nb, Mg, Al, La-based BMGs have lower fracture toughness values than is required for the described superior macroscale gears.

[0077] However, Ti-based BMGs offer excelling combinations of glass-forming ability, toughness, low wear loss, and low density. The development of Ti-based BMG macroscale gears in accordance with the above-described design principles is now discussed below.

TI-BASED BMG MACROSCALE GEARS

[0078] Through their works, the inventors have determined that Ti-based BMG has shown particular promise as a material from which to form BMG-based macroscale gears. More specifically, TiZrBeX BMGs (where X can be one or more element, and is typically a late transition metal, e.g., Cu, Ni, Cr, Fe, Co, Al, etc.), which are low-density and have a fracture toughness and wear loss which can be controlled through alloying, were developed to produce superior candidates for the fabrication of a macroscale gear. Typically, the alloys can have the following composition (in atomic percentages): 30- 60% Ti; 15-35% Zr; 7-35 % Be; and less than 20% any other elements. The densities can be between 4.5-6.0 g/cm ³ . The Young's Modulus can be between 90-1 15GPa. The hardness can be between 400-550 on the Vickers scale (2.0k). And the alloys can have a glass forming ability of at least 4mm. Gear diameters with diameters of at least 5 mm and a thickness of at least 1 mm were formed.

[0079] Table 1 below enumerates the results of the testing of gears formed with the various listed compositions: Table 1 : Wear Characteristics of TiZrBeX BMGs

[0080] Additionally, FIG. 12 depicts of a plot of these results. Specifically, FIG. 12 plots the wear loss as a function of hardness.

[0081] Importantly, these wear characteristics, e.g., wear loss, hardness, and fracture toughness, can be controlled through composition changes. The following general guidelines are provided:

• the alloys become more brittle as the Ti% increases;

• Increasing the Zr relative to the Ti increases the toughness and the galling wear loss;

o Thus, with respect to toughness:

O (Τΐ3θΖΓ35Β ^β 35)ΐΟΟ-γ γ > (Ti ₄ oZr2sBe35)l OO-y y > (Tl ₄ 5Zr2oBe35)lOO-y y

• Adding Cu increases the toughness compared to TiZrBe, but adding Ni, Fe, Al, Co, and Cr tend to decrease toughness;

o Thus, with respect to toughness:

o (TiZrBe)Cus > (TiZrBe) < (TiZrBe)Ni ₅ ~ (TiZrBe)Cr ₅ ~ (TiZrBe)Fe ₅ < (TiZrBe)AI ₅ < (TiZrBe)Co ₅

• Increasing the Zr increases the density and the glass forming ability;

o Thus, with respect to glass forming ability:

o (Ti ₄₅ Zr ₂ oBe35) < (Ti ₄ oZr ₂₅ Be35) < (TissZrsoBess)

• Adding a late transition metal to any ratio of Zr:Ti increases the glass forming ability. Adding more than -10% Fe, Cr, Co, or Al actually decreases the glass forming. However, adding approximately 1 :1 Cu to Ni increases glass forming up to about 20% of both. Adding Cu and Ni in quantities greater than 10% by themselves, improves glass forming. o Thus, with respect to glass forming ability:

o (TiZrBe) < (TiZrBe)Ni ₅ ~(TiZrBe)Cr ₅ ~(TiZrBe)Fe ₅ ~(TiZrBe)Cu ₅ < (TiZrBe)Co ₅ < (TiZrBe)Cuio < (TiZrBe)Cu ₉ Ni ₈

[0082] Generally, to make suitable gears, you can add a late transition metal to a TiZrBe alloy, and then modify the ratio of Ti:Zr and the quantity and type of the added late transition metal(s) to increase or lower the toughness, which either improves or decreases wear performance.

[0083] Of course, there exist many alloy systems that can be implemented in accordance with embodiments of the invention. And they may be tweaked to obtain the desired wear performance. The above description of the TiZrBe was not meant to be limiting in any way, and was provided merely to give an example as to how an alloy system may be modified to obtain desired wear characteristics.

[0084] FIG. 13 illustrates TiZrBeCu BMG-based macroscale gears that were fabricated in accordance with embodiments of the invention. For purposes of scale, the housing 1310 is approximately two inches in length. This image is an exploded view of the gears when removed from the housing and the ceramic shafts that the gears spin on while in the gearbox.

[0085] Below, it is discussed how low temperature applications for BMG-based macroscale gears present unique material selection considerations.

LOW TEMPERATURE APPLICATIONS FOR BMG-BASED MACROSCALE GEARS

[0086] BMG-based macroscale gears may sometimes be required to function at low temperatures (e.g., below 0°C), and the dependence of BMG material properties on temperature must be accounted for in selecting a material from which such gears will be based. For example, the resistance to brittle failure of BMG materials tends to linearly decrease with temperature. FIG. 14A illustrates how a BMG, DH3 BMG Matrix, along with a corresponding composite, DH3 composite, have Charpy impact energies (which are indicative of resistance to brittle failure, or alternatively how brittle a material is) that decrease approximately linearly as a function of temperature. Notably, FIG. 14B illustrates that whereas BMGs (e.g., Vitreloy, a ZrTiCuNiBe BMG) tend to linearly become more brittle at lower temperatures, many crystalline metals (e.g., Tin and especially bcc and bet metals) tend to demonstrate a well-defined ductile-to-brittle transition temperature.

[0087] FIG. 15 illustrates a plot that conveys design considerations when selecting a material for BMG-based macroscale gear low temperature operation. Specifically, the plot illustrates the expected wear loss for three BMG materials as a function of temperature: a BMG material that is tough at room temperature, a BMG material that is brittle at room temperature, and a BMG material that is somewhere in between at room temperature. Each of the three materials becomes excessively brittle at a certain temperature, such that brittle fracture is expected if they were to be implemented in macroscale gears below that critical temperature. The inventors have observed that many BMGs tend to have a similar linear relationship characterizing their brittle nature as a function of temperature. In other words, many BMGs become more brittle by the same extent for any given reduction in temperature. Thus, in the illustration the slopes of the respective lines characterizing wear loss as a function of temperature seen in FIG. 15 are parallel prior to brittle fracture. The inventors have particularly observed that many BMGs decrease in Charpy impact energy in accordance with .02 J/°C. Hence, a material that is not tough enough at room temperature, such that it experiences excessive abrasive wear and galling at room temperature and therefore is not a good material selection for a macroscale gear that will operate at room temperature, may actually be a preferable material for a gear that operates at a low temperature. Conversely, BMG materials that may be optimal for room temperature operation may not be suitable for low temperature operation, because at low temperature operation, they become excessively brittle.

[0088] Accordingly, in many embodiments of the invention, these design principles are utilized in the material selection process for a BMG-based macroscale gear. In some embodiments, in selecting a material for low temperature gear operation, the required resistance to brittle fracture at the low temperature is obtained (e.g., based on anticipated torque, life time, contact stress, etc.), and a BMG material is selected based on the required resistance to brittle fracture at the low temperature. For example, if the required resistance to brittle fracture at low temperature is known as a function of Charpy impact energy, then the general relationship of .02 J/°C may be used to compute what the room temperature resistance to brittle fracture of the BMG should be, and based on this information, a BMG material can be selected. Of course, it is to be understood that the general relationship .02 J/°C does not have to be used. For example, a more precise relationship of Charpy impact energy as a function of temperature can be determined through experimentation and used to compute the desired BMG's room temperature Charpy impact energy in accordance with embodiments of the invention; accordingly, a BMG material can be selected based on this information.

[0089] As can be inferred from the above discussion, the above-mentioned concepts can be implemented in a variety of arrangements in accordance with embodiments of the invention. Accordingly, although the present invention has been described in certain specific aspects, many additional modifications and variations would be apparent to those skilled in the art. It is therefore to be understood that the present invention may be practiced otherwise than specifically described. Thus, embodiments of the present invention should be considered in all respects as illustrative and not restrictive.