Patent Publication Number: US-11047387-B2

Title: Rotor for a compressor

Description:
CROSS REFERENCE TO RELATED APPLICATIONS 
     This application claims priority from and the benefit of U.S. Provisional Application Ser. No. 62/563,793, entitled “ROTOR FOR A COMPRESSOR,” filed Sep. 27, 2017, which is hereby incorporated by reference in its entirety for all purposes. 
    
    
     BACKGROUND 
     The present disclosure relates generally to compressors, and more particularly, to screw compressors for heating, ventilating, air conditioning, and refrigeration (HVAC&amp;R) systems, fuel gas boosting systems, air compression, and process gas compressions systems. 
     Heating, ventilating, air conditioning, and refrigeration (HVAC&amp;R) systems typically maintain temperature control in a structure by circulating a refrigerant through a conduit to exchange thermal energy with another fluid. A compressor of the system receives a cool, low pressure vapor, or vapor and liquid mixture, and by virtue of compression, exhausts a hot, high pressure vapor, or vapor and liquid mixture. One type of compressor is a screw compressor, which generally includes one or more cylindrical rotors mounted on separate shafts inside a hollow casing. Twin screw compressor rotors typically have helically extending lobes (or flanks) and grooves (or flutes) on their outer surfaces forming a thread on the circumference of the rotor. During operation, the threads of the rotors mesh together, with the lobes on one rotor meshing with the corresponding grooves on the other rotor to form a series of gaps between the rotors. The gaps form a continuous compression chamber that communicates with the compressor inlet opening, or “port,” at one end of the casing and continuously reduces in volume as the rotors turn to compress the gas toward a discharge port at the opposite end of the casing. Existing screw compressor rotors are formed from a solid piece of material, and thus, are relatively costly and heavy, which may add cost and weight to the compressor. Additionally, the increased mass causes individual rotors to have a reduced natural frequency, which may lead to increased vibrations during compressor operation and reduce performance of the compressor. 
     SUMMARY 
     In one embodiment, a system includes a compressor configured to compress a vapor, or vapor and liquid mixture, and a first rotor of the compressor disposed on a first shaft, where the first rotor includes a first plurality of pockets in a first body portion to form a first semi-hollow internal volume. 
     In another embodiment, a system includes a compressor configured to compress a vapor, or vapor and liquid mixture, and a first rotor of the compressor disposed on a first shaft, where the first rotor includes a plurality of flanks and a plurality of flutes on a first external surface of the first rotor, where the plurality of flanks and the plurality of flutes have a first pitch to form first variable leads and where the first rotor includes a first plurality of pockets in a first body portion to form a first semi-hollow internal volume of the first rotor. 
     In an another embodiment, a method includes forming a first rotor using an additive manufacturing technique, where the first rotor includes a first plurality of pockets within a first body portion, or first variable leads, or both, and forming a second rotor using the additive manufacturing technique, where the second rotor includes a second plurality of pockets within a second body portion, or second variable leads, or both. 
    
    
     
       DRAWINGS 
         FIG. 1  is a cross-section of an embodiment of a first rotor of a compressor that may be included in a vapor compression system, in accordance with an aspect of the present disclosure; 
         FIG. 2  is a cross-section of an embodiment of a second rotor of the compressor that may be included in the vapor compression system, in accordance with an aspect the present disclosure; 
         FIG. 3  is a perspective view of an embodiment of the second rotor of  FIG. 2 , in accordance with an aspect of the present disclosure; and 
         FIG. 4  is a block diagram of an embodiment of a method for manufacturing the first and second rotors of  FIGS. 1-3 , in accordance with an aspect of the present disclosure. 
     
    
    
     DETAILED DESCRIPTION 
     Embodiments of the present disclosure are directed toward improved rotors for a screw compressor and methods for manufacturing such rotors. Existing screw compressors generally include one or more rotors formed from a solid material, thereby increasing a mass of the rotors. Rotors may incur vibration during operation of the compressor. In some cases, the vibration of solid rotors may reach a natural frequency, or a frequency that is substantially the same as a frequency of vibrations caused by pulsations of vapor (or another fluid) flowing through the compressor. Rotors that vibrate at the natural frequency may disrupt operation of the screw compressor, thereby leading to reduced performance, reliability, and/or durability of the compressor. 
     Embodiments of the present disclosure are directed to semi-hollow (or hollow) rotors that include a reduced mass when compared to existing rotors, but include substantially the same stiffness as solid rotors. As described in detail below, embodiments of the rotors include a honeycomb, webbed, or gyroid structure (e.g., internal volume) that may include pockets, gaps, or voids that do not include solid material. The semi-hollow (or hollow) rotors include less material than solid rotors, and thus may reduce capital costs of the compressor. Moreover, reducing the mass of the rotor increases a natural frequency of the rotor, and in some cases, increases the natural frequency above (or below) an excitation frequency of the compressor. In other words, a frequency of a lateral critical speed of semi-hollow (or hollow) rotors is greater than the frequency of the lateral critical speed of a solid rotor, which may facilitate adjustment of the natural frequency of rotor. For example, the natural frequency of the semi-hollow (or hollow) rotors may be adjusted or tuned based on a lobe passing frequency and/or a first harmonic of the lobe passing frequency of the semi-hollow (or hollow) rotors to reduce vibrations during operation of the compressor. Accordingly, the natural frequency of the semi-hollow (or hollow) rotors is adjusted to avoid excitation frequencies of the compressor. Therefore, disruptions to the operation of the compressor caused by vibrations may be eliminated or reduced by utilizing semi-hollow or hollow rotors. Additionally, reducing the mass of the rotors may enable the compressor to operate over a greater range of operating speeds when compared to existing solid rotors. 
     In some cases, rotors of the present disclosure are manufactured utilizing an additive manufacturing technique, such as three-dimensional (3-D) printing. The additive manufacturing techniques facilitate manufacturing of the rotors with the honeycomb, or webbed, structure (e.g., internal volume) because such techniques do not form the rotor from a solid piece of material. In other words, additive manufacturing techniques may create an object layer-by-layer until the final structure is achieved. Conversely, existing rotors are machined from a solid piece of material to create the final structure. Therefore, additive manufacturing techniques enable complex internal structures, such as honeycomb or webbed structures, to be formed quickly and efficiently. 
     In addition to having a semi-hollow or hollow structure (e.g., internal volume), some embodiments of the present disclosure are directed to variable lead rotors. As used herein, a variable lead rotor (e.g., a rotor having variable leads) is a rotor that includes varying helix lead and/or pitch of threads disposed along an axial length of the rotor. Variable lead rotors may increase a rate of compression of the screw compressor by increasing a helix lead and/or pitch of the rotor from an inlet of the screw compressor to the outlet of the screw compressor. Moreover, transitions between different helix leads and/or pitches of the variable lead rotor may be smooth as a result of utilizing additive manufacturing techniques for generating the variable lead rotors. As such, the use of additive manufacturing to form rotors of a screw compressor enable relatively simple manufacture of rotors having a semi-hollow or hollow structure (e.g., internal volume), as well as variable lead rotors. While the present discussion focuses on a twin screw compressor having two rotors, it should be recognized that embodiments of the rotors described herein may be utilized in any screw compressor having any suitable number of rotors (e.g., one, two, three, four, five, six, seven, eight, nine, ten, or more than ten rotors). 
     Existing compressors of HVAC&amp;R systems may include screw compressors that have solid rotors, which are relatively heavy. Embodiments of the present disclosure are directed to semi-hollow (or hollow) rotors for a screw compressor, which include a reduced mass compared to existing solid rotors. As such, semi-hollow rotors have an increased resonant frequency, which may reduce or eliminate disruption of compressor operation caused by vibrations of the rotor. In some embodiments, additive manufacturing techniques, such as three-dimensional (3-D) printing, are utilized to facilitate manufacturing of the semi-hollow (or hollow) rotors. Further, utilizing additive manufacturing techniques may enable the rotors to be variable lead rotors. As set forth above, variable lead rotors may enhance a compression rate of screw compressors, which may enhance the efficiency of the compressor and/or the overall HVAC&amp;R system. Additionally, variable lead rotors reduce contact forces between adjacent rotors and/or reduce stress experienced by the rotors, thereby reducing wear and prolonging an operating life of the rotors. While the present discussion focuses on a screw compressor that includes female and male rotors, it should also be noted that embodiments of the rotors disclosed herein may also apply to screw compressors that include one or more gate rotors. Further, the embodiments of the present disclosure may also apply to screw compressors having twin rotors, or rotors that are disposed side-by-side, in addition to or in lieu of, rotors that are disposed above-and-below one another. 
     For example,  FIG. 1  is a cross-section of an embodiment of a female rotor  100  (e.g., a first rotor) that includes a semi-hollow (or hollow) structure (e.g., internal volume). As shown in the illustrated embodiment, the female rotor  100  is formed on a shaft  102 . In some embodiments, the female rotor  100  and the shaft  102  are a single-piece, unitary component. In other embodiments, the female rotor  100  is coupled to the shaft  102  via welding, a coupling device (e.g., a flange), and/or another suitable technique. The shaft  102  is coupled to an actuator (e.g., motor, a turbine, or an expansion device) of a compressor, which drives rotation of the shaft  102 . Rotation of the shaft  102  causes the female rotor  100  to rotate in a first circumferential direction  104 . In some embodiments, the actuator is directly coupled to the shaft  102 . In other embodiments, the actuator is directly coupled to a shaft of a male rotor (see, e.g.,  FIG. 2 ), but not to the shaft  102  of the female rotor  100 . In such embodiments, rotation of the female rotor  100  is driven by rotation of the male rotor, and thus, indirectly by the actuator. As such, a transfer torque applied to the shaft  102  is reduced, thereby reducing contact stresses between the female rotor  100  and the male rotor. Further, rotation of the female rotor  102  (and/or the male rotor) may be driven by timing gears that are included on each rotor to rotate the female rotor  102  (and/or the male rotor) at a predetermined rate (e.g., rotations per minute). In some embodiments, the shaft  102  is semi-hollow (or hollow) or annular, such that an opening is formed within the shaft  102  along an axial direction  106 . In other embodiments, the shaft  102  is a solid cylinder. 
     As shown in the illustrated embodiment of  FIG. 1 , the female rotor  100  includes a plurality of pockets  108  (e.g., closed voids or gaps) within a body portion  110  of the female rotor  100 . The plurality of pockets  108  do not include solid material (e.g., a metallic material), and in some embodiments, include air, another suitable gas, and/or may be depressurized to form a vacuum. In any case, the pockets  108  reduce the mass of the female rotor  100  by decreasing an amount of material included in the female rotor  100 . In some embodiments, the pockets  108  extend circumferentially, or otherwise, through the female rotor  100  and/or around the shaft  102 . In other words, the pockets  108  may include annular passageways forming a honeycomb-like or gyroid pattern within the body portion  110  of the female rotor  100 . Further, the pockets  108  may include a cross-sectional shape in the form of a triangle, a square, a rectangle, a pentagon, a hexagon, a heptagon, an octagon, another suitable polygonal shape, or a combination thereof. In other embodiments, the pockets  108  may form another suitable pattern throughout the body portion  110  of the female rotor  100  that reduces a weight of the female rotor  100  and enables the female rotor  100  to have a predetermined stiffness. The stiffness of the female rotor is discussed in further detail below. In still further embodiments, the pockets  108  may be randomly spaced throughout the body portion  110  of the female rotor  100  and include various sizes, shapes, lengths, widths, and/or depths within the body portion  110 . Including the pockets  108  in the female rotor  100  reduces a weight of the female rotor  100 , but enables the female rotor  100  to include substantially the same (e.g., within 10% of, within 5% of, or within 1% of) stiffness as a rotor formed from a solid material (e.g., a rotor without the pockets  108 ). 
     As shown in the illustrated embodiment of  FIG. 1 , the pockets  108  include a reduced cross-sectional area when moving from a central axis  112  of the female rotor  100  towards flanks  114  positioned on an outer surface  116  of the female rotor  100 . However, in other embodiments, the pockets  108  include substantially the same (e.g., within 10% of, within 5% of, or within 1% of) cross-sectional area throughout the body portion  110  of the female rotor  100 . Further, in some embodiments, the female rotor  100  includes a central passage  118  that extends along the central axis  112  of the female rotor  100 . The central passage  118  may be an annular passage that extends from a first end  120  of the female rotor  100  to a second end  122  of the female rotor. In other embodiments, the female rotor  100  does not include the central passage  118 , but instead includes additional pockets  108  disposed along the central axis  112  of the female rotor  100 . 
     As discussed above, utilizing additive manufacturing techniques facilitates the formation of the female rotor  100  having the pockets  108  (e.g., a semi-hollow or hollow structure). For example, additive manufacturing techniques such as direct metal laser sintering (DMLS), laser-ultrasonic finishing, ultrasonic nanocrystal surface modification, selective laser sintering (SLS), selective laser melting (SLM), electronic beam melting (EBM), and/or another suitable technique may create the female rotor  100  in layers from the first end  120  to the second end  122  of the female rotor  100  or from a bottom portion  124  to a top portion  126  of the female rotor  100 . In other embodiments, the female rotor  100  is constructed using the additive manufacturing technique in layers from a first end of the rotor  102  to a second end of the rotor  102 . As such, the pockets  108  are formed within the body portion  110  of the female rotor  100  as the female rotor  100  is produced or created. In some embodiments, the female rotor  100  may incur further processing or machining (e.g., grinding or chemical etching) after formation via a suitable additive manufacturing technique. In existing systems, a rotor may be formed from a solid piece of material. Accordingly, forming the pockets  108  (e.g., closed gaps and/or voids) within the solid structure is time consuming, expensive, and complex. 
     Additionally, forming the female rotor  100  using additive manufacturing techniques enables the female rotor  100  to include variable leads. For example, as shown in the illustrated embodiment of  FIG. 1 , the female rotor  100  includes the flanks  114  and corresponding flutes  128  between adjacent flanks  114 . The flanks  114  and the corresponding flutes  128  form threads  130  along the central axis  112  of the female rotor  100 . The flanks  114  of the female rotor  100  become closer to one another when moving along the central axis  112  from the second end  122  to the first end  120  of the female rotor  100 . In other words, a width of the corresponding flutes  128  decreases moving along the central axis  112  from the second end  122  to the first end  120  of the female rotor  100 . As such, the female rotor  100  includes continuously variable leads where a helix lead and/or pitch of the flanks  114  continuously decreases along the central axis  112  from the second end  122  to the first end  120 . In other embodiments, the flanks  114  of the female rotor  100  may be spaced further apart from one another when moving along the central axis  112  from the second end  122  to the first end  120  of the female rotor  100 . In still further embodiments, the flanks  114  of the female rotor  100  may become closer to one another (or further apart from one another) for a predetermined distance along the central axis  112  from the second end  122  toward the first end  120  and then become spaced further apart from one another (or closer to one another) for a second predetermined distance along the central axis  112  from the second end  122  toward the first end  120 . In such embodiments, the flanks  114  are spaced closest to one another (or furthest from one another) in a central portion of the female rotor  100  (e.g., at approximately a halfway point along the central axis  112  between the first end  120  and the second end  122 ). 
     As discussed above, a distance  132  between the flanks  114  and/or the width of the corresponding flutes  128 , which may be referred to as a helix lead and/or pitch of the threads  130 , varies along the central axis  112  of the female rotor  100  to form the variable leads of the female rotor  100 . For example, the distance  132  at the second end  122  may be between two and three times larger than the distance  132  at the first end  120 . The variable leads adjust a compression rate of the compressor and, in some embodiments, increase the compression rate of the compressor, thereby increasing an efficiency of the compressor. 
     Forming variable leads in existing rotors is relatively time consuming because the variable leads are machined into a solid piece of material. Utilizing additive manufacturing techniques facilitates formation of the variable leads and improves (e.g., smooths) transitions between the changes in the helix lead and/or pitch. For example, existing variable lead rotors include distinct transition points at locations along the rotor where the helix lead and/or pitch changes. Utilizing additive manufacturing enables variable leads to be formed with improved accuracy and reduces and/or eliminates transitions along the rotor where the helix lead and/or pitch changes. 
       FIG. 2  is a cross-section of an embodiment of a male rotor  150  (e.g., a second rotor) that is configured to mesh with the female rotor  100  (e.g., see  FIG. 1 ) to compress vapor, or a vapor and liquid mixture, within the compressor. For example, the male rotor  150  includes lobes  152  that are configured to be disposed in the flutes  128  of the female rotor  100 . Further, the male rotor  150  includes grooves  154  that are configured to receive the flanks  114  of the female rotor  100 . As shown in the illustrated embodiment of  FIG. 2 , the male rotor  150  is formed on a shaft  156  (e.g., a second shaft). In some embodiments, the male rotor  150  and the shaft  156  are a single-piece, unitary component. In other embodiments, the male rotor  150  is coupled to the shaft  156  via welding, a coupling device (e.g., a flange), and/or another suitable technique. As discussed above, the shaft  156  may be coupled to an actuator (e.g., motor, a turbine, or an expansion device) of the compressor, which drives rotation of the shaft  156 . Rotation of the shaft  156  causes the male rotor  150  to rotate in a second circumferential direction  158 , opposite the first circumferential direction  104 , such that the female rotor  100  and the male rotor  150  mesh with one another and compress the vapor, or vapor and liquid mixture, flowing through the compressor. In some embodiments, the actuator is directly coupled to the shaft  156 , but not to the shaft  102 . In such embodiments, rotation of the female rotor  100  is driven by rotation of the male rotor  150 , and thus, indirectly by the actuator. As such, a transfer torque applied to the shaft  102  is reduced, thereby reducing contact stresses between the female rotor  100  and the male rotor  150 . Further, rotation of the male rotor  150  (and/or the female rotor  102 ) may be driven by timing gears that are included on each rotor to rotate the male rotor  150  (and/or the female rotor  102 ) at a predetermined rate (e.g., rotations per minute). In some embodiments, the shaft  156  is semi-hollow (or hollow) or annular, such that an opening is formed within the shaft  156  along an axial direction  160 . In other embodiments, the shaft  156  is a solid cylinder. 
     As shown in the illustrated embodiment of  FIG. 2 , the male rotor  150  includes a plurality of pockets  162 , which may be similar to the pockets  108  of the female rotor. For example, the plurality of pockets  162  do not include solid material (e.g., a metallic material), and in some embodiments, include air, another suitable gas, and/or may be depressurized to form a vacuum. In any case, the pockets  162  reduce the mass of the male rotor  150  by decreasing an amount of material included in the male rotor  150 . In some embodiments, the pockets  162  extend circumferentially, or otherwise, through the male rotor  150  and/or around the shaft  156 . In other words, the pockets  162  may include annular passageways forming a honeycomb-like or gyroid pattern within a body portion  164  of the male rotor  150 . Further, the pockets  162  may include a cross-sectional shape in the form of a triangle, a square, a rectangle, a pentagon, a hexagon, a heptagon, an octagon, another suitable polygonal shape, or a combination thereof. In other embodiments, the pockets  162  may form another suitable pattern throughout the body portion  164  of the male rotor  150  that reduces a mass of the male rotor  150  and enables the male rotor  150  to include a predetermined stiffness. In still further embodiments, the pockets  162  may be randomly spaced throughout the body portion  164  of the male rotor  150  and include various sizes, shapes, lengths, widths, and/or depths within the body portion  164 . As discussed above, including the pockets  162  in the male rotor  150  reduces a mass of the male rotor  150 , but enables the male rotor  150  to include substantially the same (e.g., within 10% of, within 5% of, or within 1% of) stiffness as a rotor formed from a solid material (e.g., a rotor without the pockets  162 ). 
     As shown in the illustrated embodiment of  FIG. 2 , the pockets  162  include a constant or varied cross-sectional area when moving from a central axis  166  of the male rotor  150  towards the lobes  152  positioned on an outer surface  168  of the male rotor  150 . However, in other embodiments, the pockets  162  include substantially the same (e.g., within 10% of, within 5% of, or within 1% of) cross-sectional area throughout the body portion  164  of the male rotor  150 . Further, in some embodiments, the male rotor  150  includes a central passage  170  that extends along the central axis  166  of the male rotor  150 . The central passage  170  may be an annular passage that extends from a first end  172  of the male rotor  150  to a second end  174  of the male rotor  150 . In other embodiments, the male rotor  150  does not include the central passage  170 , but instead includes additional pockets  162  disposed along the central axis  166 . 
     Additionally, the lobes  152  and the grooves  154  form threads  176  along the central axis  166  of the male rotor  150 . A distance  178  between the lobes  152  of the male rotor  150  become closer to one another when moving along the central axis  166  from the second end  174  to the first end  172  of the male rotor  150 . In other words, a width of the grooves  154  decreases moving along the central axis  166  from the second end  174  to the first end  172  of the male rotor  150 . As such, the male rotor  150  includes continuously variable leads where a helix lead and/or pitch of the lobes  152  continuously increases along the central axis  166  from the second end  174  to the first end  172 . In other embodiments, the lobes  152  of the male rotor  150  may be spaced further apart from one another when moving along the central axis  166  from the second end  174  to the first end  172  of the male rotor  150 . In still further embodiments, the lobes  152  of the male rotor  150  may become closer to one another (or further apart from one another) for a predetermined distance along the central axis  166  from the second end  174  toward the first end  172  and then become spaced further apart from one another (or closer to one another) for a second predetermined distance along the central axis  166  from the second end  174  toward the first end  172 . In such embodiments, the lobes  152  are spaced closest to one another (or furthest from one another) in a central portion of the male rotor  150  (e.g., at approximately a halfway point along the central axis  166  between the first end  172  and the second end  174 ). 
     As discussed above, the distance between the lobes  152  and/or the width of the grooves  154 , which may be referred to as a helix lead and/or pitch of the threads  176 , varies along the central axis  166  of the male rotor  150  to form the variable leads of the male rotor  150 . For example, the distance at the second end  174  may be between two and three times larger than the distance at the first end  172 . The variable leads adjust a compression rate of the compressor and, in some embodiments, increase the compression rate of the compressor, thereby increasing an efficiency of the compressor. 
       FIG. 3  is a perspective view of the male rotor  150  further illustrating the ends  172  and  174  of the male rotor  150 , as well as the threads  176 . As shown in the illustrated embodiment of  FIG. 3 , the threads  176  of the male rotor  150  form spirals along the central axis  166  of the male rotor  150  from the first end  172  to the second end  174 . As shown in the illustrated embodiment of  FIG. 3 , the male rotor  150  is a constant lead rotor, in that the helix lead and/or pitch of the threads  176  is substantially constant along the central axis  166  of the male rotor  150  from the first end  172  to the second end  174 . However, in other embodiments, as discussed above, the helix lead and/or pitch of the threads  176  may change along the central axis  166  of the male rotor  150 , such that the male rotor  150  is a variable lead rotor. 
       FIG. 4  is a block diagram of an embodiment of a process  190  that may be utilized to manufacture the female rotor  100  and/or the male rotor  150 . For example, at block  192 , the female rotor  100  is formed utilizing a additive manufacturing technique (e.g., 3-D printing and/or direct metal laser sintering (DMLS), laser-ultrasonic finishing, ultrasonic nanocrystal surface modification, selective laser sintering (SLS), selective laser melting (SLM), electronic beam melting (EBM), or a combination thereof). As discussed above, the female rotor  100  includes the plurality of pockets  108  and/or the variable lead threads  130 . The additive manufacturing technique facilitates formation of the pockets  108  and the variable lead threads  130  because additive manufacturing techniques generally form a structure in a layer-by-layer process, instead of machining or processing a solid piece of material. As such, a mass of the female rotor  100  is reduced and transitions between helix lead and/or pitch changes in the variable lead threads  130  are reduced or eliminated when compared to existing rotors. While the mass of the female rotor  100  is reduced, a stiffness remains relatively high as a result of a configuration of the plurality of pockets  108  (e.g., pockets  108  near the flanks  114  are smaller than pockets  108  near the central axis  112 ). Further, the natural frequency of the female rotor  100  is increased when compared to existing rotors, such that the female rotor  100  generally includes an operating frequency that is below the natural frequency. Increasing the natural frequency reduces vibrations (e.g., when harmonics generated by an operating speed of the rotor approach lateral natural frequencies of the rotor), and thus, disruptions to the compressor as a result of vibrations. As discussed above, in some embodiments, the female rotor  100  may incur further processing and/or machining (e.g., grinding) after being formed via the additive manufacturing technique. 
     Additionally, at block  194 , the male rotor  150  is formed utilizing the additive manufacturing technique (e.g., 3-D printing and/or direct metal laser sintering (DMLS), laser-ultrasonic finishing, ultrasonic nanocrystal surface modification, selective laser sintering (SLS), selective laser melting (SLM), electronic beam melting (EBM), or a combination thereof). As discussed above, the male rotor  150  includes the plurality of pockets  162  and/or the variable lead threads  176 . The additive manufacturing technique facilitates formation of the pockets  162  and the variable lead threads  176  because additive manufacturing techniques generally form a structure in a layer-by-layer process, instead of machining or processing a solid piece of material. As such, a mass of the male rotor  150  is reduced and transitions between helix lead and/or pitch changes in the variable lead threads  176  are reduced or eliminated when compared to existing rotors. While the mass of the male rotor  150  is reduced, a stiffness remains relatively high as a result of a configuration of the plurality of pockets  162  (e.g., pockets  162  near the lobes  152  are smaller than pockets  162  near the central axis  166 ). Further, the natural frequency of the male rotor  150  is increased when compared to existing rotors, such that the male rotor  150  generally includes an operating frequency that is below the natural frequency. Increasing the natural frequency reduces vibrations (e.g., when harmonics generated by an operating speed of the rotor approach lateral natural frequencies of the rotor), and thus, disruptions to the compressor as a result of vibrations. In some embodiments, the male rotor  150  may incur further processing and/or machining (e.g., grinding) after being formed via the additive manufacturing technique. 
     As set forth above, embodiments of the rotors of the present disclosure may provide one or more technical effects useful in the operation of HVAC&amp;R systems to improve a performance of a compressor. For example, embodiments of the present disclosure are directed to female and male rotors that are formed utilizing additive manufacturing techniques. The female and male rotors each include a plurality of pockets that reduce an overall mass of the rotors while maintaining a stiffness of the rotors. Reducing the mass of the rotors may increase a natural frequency of the rotors, which reduces and/or eliminates disruptions to compressor operation as a result of vibrations. Further still, the female and male rotors include variable lead threads that increase a compression rate of the compressor, and thus, further improve an efficiency of the compressor. Utilizing the additive manufacturing techniques may reduce and/or eliminate transitions between helix leads and/or pitches of the variable lead threads. The technical effects and technical problems in the specification are examples and are not limiting. It should be noted that the embodiments described in the specification may have other technical effects and can solve other technical problems. 
     While only certain features and embodiments have been illustrated and described, many modifications and changes may occur to those skilled in the art (e.g., variations in sizes, dimensions, structures, shapes and proportions of the various elements, values of parameters (e.g., temperatures, pressures, etc.), mounting arrangements, use of materials, colors, orientations, etc.) without materially departing from the novel teachings and advantages of the subject matter recited in the claims. The order or sequence of any process or method steps may be varied or re-sequenced according to alternative embodiments. It is, therefore, to be understood that the appended claims are intended to cover all such modifications and changes as fall within the true spirit of the disclosure. Furthermore, in an effort to provide a concise description of the exemplary embodiments, all features of an actual implementation may not have been described (i.e., those unrelated to the presently contemplated best mode, or those unrelated to enablement). It should be appreciated that in the development of any such actual implementation, as in any engineering or design project, numerous implementation specific decisions may be made. Such a development effort might be complex and time consuming, but would nevertheless be a routine undertaking of design, fabrication, and manufacture for those of ordinary skill having the benefit of this disclosure, without undue experimentation.