Patent Publication Number: US-11643973-B2

Title: Electrically geared turbofan

Description:
CROSS-REFERENCE TO RELATED APPLICATIONS 
     This application is a continuation of U.S. patent application Ser. No. 16/850,671 filed Apr. 16, 2020, which is herein incorporated in its entirety. 
    
    
     FIELD 
     The present disclosure generally relates to turbofan engines. More particularly, the present disclosure relates to turbofan engines configured to convert the mechanical rotational energy from a turbine-driven spool shafts into mechanical rotational energy in the fan via electromotive forces. 
     BACKGROUND 
     In a turbofan engine, high pressure exhaust from burning fuel in a combustion chamber rotates various turbines. These turbines, when rotated, in turn impart rotation on spool shafts. The spool shafts, in turn, are connected to various compressors that feed air into the combustion chamber and are further connected to a fan that propels air through a bypass chamber around the turbine. The air propelled by the fan provides a portion (often a significant portion) of the motive force for the turbofan engine, while air ejected from the combustion chamber provides the remainder of the motive force. 
     During operation of a conventional turbofan engine, the fan rotates at a different rotational speed than the spool shaft that provides rotational forces to the fan via a mechanical gearing arrangement (e.g., planetary gears). Mechanical gearing arrangements are often heavy and bulky, and are prone to mechanical issues (e.g., wear, material fatigue, material stress, lubricant leaks), and thus require frequent inspection and maintenance to keep in working order. Additionally, the physical engagement of mechanical gearing arrangements creates mechanical stresses on the gearing arrangements and causes noise and vibration in the turbofan engine, which impacts aircraft passenger comfort. 
     SUMMARY 
     The present disclosure provides a system in one aspect, the system including: a fan of a turbofan engine; a first spool shaft of the turbofan engine; and an electrical gearbox including: an armature winding connected to the first spool shaft and coupled to a power source; and a magnetic receiver connected to the fan, and wherein an air gap is defined between the armature winding and the magnetic receiver. 
     In one aspect, in combination with any example system above or below, the electrical gearbox is an induction motor, wherein the magnetic receiver is a receiver armature winding. 
     In one aspect, in combination with any example system above or below, the electrical gearbox is a permanent magnet motor, wherein the magnetic receiver is a permanent magnet array. 
     In one aspect, in combination with any example system above or below, the magnetic receiver is positioned coaxially within a cavity defined by the armature winding. 
     In one aspect, in combination with any example system above or below, the armature winding is positioned coaxially within a cavity defined by the magnetic receiver. 
     In one aspect, in combination with any example system above or below, the armature winding and the magnetic receiver are linked via a radial magnetic field. 
     In one aspect, in combination with any example system above or below, the system further includes: a second spool shaft, coaxial with the first spool shaft; wherein the power source includes: a permanent magnet connected to the second spool shaft at an interface between a the first spool shaft and the second spool shaft; and a generator armature winding connected to the first spool shaft at the interface and located in a generator magnetic field produced by the permanent magnet; and a frequency converter, coupled to the generator armature winding and to the armature winding. 
     In one aspect, in combination with any example system above or below, the generator magnetic field propagates radially outward from an axis of rotation for the first spool shaft over a second air gap defined between the permanent magnet and the generator armature winding. 
     In one aspect, in combination with any example system above or below, the generator magnetic field propagates coaxially to an axis of rotation for the first spool shaft over a second air gap defined between the permanent magnet and the generator armature winding. 
     The present disclosure provides a turbofan engine in one aspect, the turbofan engine including: a fan; a turbine enclosure, comprising: an air intake at an upstream end; a compression section downstream of the air intake; a combustion section downstream of the compression section; a turbine section downstream of the combustion section; and an exhaust at a downstream end; a first spool shaft coupled with a first compressor of the compression section, with a first turbine of the turbine section; and an electrical gearbox located upstream of the turbine enclosure and coupled with the first spool shaft and the fan, configured to transfer rotational energy from the first spool shaft rotating at a first rotational speed to the fan to rotate the fan at a second rotational speed. 
     In one aspect, in combination with any example turbofan engine above or below, the first rotational speed is greater than the second rotational speed, wherein the electrical gearbox generates an armature magnetic field that rotates in a first direction opposite to a second direction in which the fan and the first spool shaft rotate. 
     In one aspect, in combination with any example turbofan engine above or below, the first rotational speed is less than the second rotational speed, wherein the electrical gearbox generates an armature magnetic field that rotates in a shared direction in which the fan and the first spool shaft rotate. 
     In one aspect, in combination with any example turbofan engine above or below, the turbofan engine of claim  10  further includes a nacelle in which the fan and the turbine enclosure are defined, and wherein the turbine enclosure and the nacelle define a bypass flow chamber therebetween. 
     In one aspect, in combination with any example turbofan engine above or below, the electrical gearbox comprises: an armature winding, coupled to a power source, and coupled to the first spool shaft; and a magnetic receiver, separated from the armature winding by an air gap, and coupled to the fan. 
     In one aspect, in combination with any example turbofan engine above or below, the turbofan engine further includes: a second spool shaft coupled with a second compressor of the compression section and with a second turbine of the turbine section and running coaxially with the first spool shaft, wherein the second spool shaft is configured to rotate at a third rotational speed; and wherein the power source comprises: a generator armature winding connected to the first spool shaft; a permanent magnet connected to the second spool shaft and separated from the generator armature winding via a second air gap, wherein the permanent magnet is configured to: emit a generator magnetic field; rotate relative to the generator armature winding at a differential rotational speed corresponding to a difference between the first rotational speed and the third rotational speed; and induce a generated current in the generator armature winding; and a frequency converter connected to the generator armature winding and the electrical gearbox, configured to receive the generated current and transmit an input current of a different frequency than the generated current to power the armature winding in the electrical gearbox. 
     In one aspect, in combination with any example turbofan engine above or below, the magnetic receiver is a receiver armature winding. 
     In one aspect, in combination with any example turbofan engine above or below, the magnetic receiver is a permanent magnet array. 
     The present disclosure provides a method in one aspect, the method including: rotating a spool shaft in a turbofan engine at a first rotational speed; powering an armature winding on a first end of the spool shaft to generate an armature magnetic field, wherein the armature magnetic field rotates at a second rotational speed; transferring rotational energy from the spool shaft to a magnetic receiver coupled to a fan via the armature magnetic field; and rotating the fan at a third rotational speed. 
     In one aspect, in combination with the method above, the third rotational speed is controlled via a direction and a magnitude of the second rotational speed relative to the first rotational speed. 
     The present disclosure provides a method in one aspect, the method including: affixing an armature winding to a low pressure compressor spool shaft of a turbofan engine; affixing a magnetic receiver to a hub of a fan of the turbofan engine, wherein the armature winding and the magnetic receiver define an air gap therebetween; and coupling the armature winding to a power source having a controllable frequency current output. 
    
    
     
       BRIEF DESCRIPTION OF THE DRAWINGS 
       So that the manner in which the above recited features can be understood in detail, a more particular description, briefly summarized above, may be had by reference to example aspects, some of which are illustrated in the appended drawings. 
         FIGS.  1 A and  1 B  illustrate cross-sectional views of turbofan engines that include an electrical gearbox, according to aspects of the present disclosure. 
         FIGS.  2 A- 2 C  illustrate various configurations of electrical gearboxes for turbofan engines, according to aspects of the present disclosure. 
         FIG.  3    illustrates a functional block diagram of an electrical gearbox, according to aspects of the present disclosure. 
         FIGS.  4 A and  4 B  illustrate component arrangements for electrical generators, according to aspects of the present disclosure. 
         FIG.  5    illustrates a circuit diagram of an electrical generator in use as a power supply for an armature winding of an electrical gearbox, according to aspects of the present disclosure. 
         FIG.  6    is a flowchart of a method for operating a turbofan engine having an electrical gearbox, according to aspects of the present disclosure. 
         FIG.  7    is a flowchart of a method for fabricating a turbofan engine with an electrical gearbox, according to aspects of the present disclosure. 
     
    
    
     DETAILED DESCRIPTION 
     The present disclosure provides for electrically geared turbofan engines, which substitute the mechanical gearing arrangement between the spool shafts and the fans of conventional implementations for electromagnetic couplings. An electromagnetic coupling beneficially allows for the transfer of rotational energy without physical contact between the gear components, which can reduce the weight and size as well as the maintenance needs of the gearing arrangement compared to mechanical gearing arrangements. Additionally, in some aspects, the (effective) gear ratio between the spool shaft and the fan can be dynamically adjusted to increase or decrease a difference in rotational speeds between the fan and the spool shaft. Stated differently, the rotational speed of the fan can be controlled independently of the rotational speed of the spool shaft, which can provide greater fuel efficiency, greater thrust, and/or greater control over the turbofan engine than is provided by statically geared turbofan engines. 
     Although the examples provided in the present disclosure primarily illustrate a turbofan of an aircraft, the electrical gearing arrangements described in the present disclosure may be used in conjunction with turbofan engines in various other vehicles. 
       FIGS.  1 A and  1 B  illustrate cross-sectional views of turbofan engines  100 , (individually, turbofan engine  100 A and turbofan engine  100 B) which include an electrical gearbox  110 , according to aspects of the present disclosure. The turbofan engines  100  include a turbine enclosure  120  defining an air intake  121  at an upstream end, a compression section  122  downstream of the air intake  121 , a combustion section  123  downstream of the compression section  122 , a turbine section  124  downstream of the combustion section  123 , and an exhaust  125  at a downstream end. In various aspects, the turbine enclosure  120  is included inside of a nacelle  130  (also referred to as a housing), and a bypass flow chamber  131  is defined between an outer surface of the turbine enclosure  120  and an inner surface of the nacelle  130 . A fan  150  is positioned in the nacelle  130  upstream of the air intake  121  of the turbine enclosure  120 , and during operation rotates to propel air inward to the air intake  121  of turbine enclosure  120  as well as through the bypass flow chamber  131 . 
     The turbofan engines  100  include a first spool shaft  160 A (generally, spool shaft or shaft  160  or collectively, shaft assembly) and a second spool shaft  160 B. Although the illustrated turbofan engines  100  are shown as have two spool shafts  160  in  FIGS.  1 A and  1 B , in various aspects a turbofan engine  100  can include one, two, three, or more spool shafts  160 . In the depicted embodiments, each shaft  160  extends coaxially with the other shafts  160 , and rotates during operation at different rates relative to one another due to the ejection of high pressure exhaust rotating the turbines  180 A-B (generally, turbine  180 ), which in turn drive the associated compressors  170 A-B (generally, compressor  170 ) at different rates via the associated spool shafts  160 . For example, a first spool shaft  160 A rotates (due to forces imparted by the first turbine  180 A) to drive the rotation of a first compressor  170 A at a first rotational speed, while a second spool shaft  160 B rotates (due to forces imparted by the second turbine  180 B) to drive the rotation of a second compressor  170 B at a second rotational speed. 
     The compressors  170  are disposed in the compression section  122  of the turbine enclosure  120 , and may each include several fan blades arranged in one or more rows. The turbines  180  are disposed in the turbine section  124  of the turbine enclosure  120 , and may each include several fan blades arranged in one or more rows. Although not illustrated, various bearings or low friction surfaces may be located between the shafts  160  to improve rotational characteristics of the shafts  160  (e.g., to reduce friction). 
     As illustrated, the first spool shaft  160 A is a low-pressure shaft relative to the high-pressure shaft of the second spool shaft  160 B. Accordingly, the first compressor  170 A is located upstream of the second compressor  170 B, and rotates at a lower rotational speed than the second compressor  170 B during operation of the turbofan engine  100 . Similarly, the first turbine  180 A is located downstream of the second turbine  180 B, and rotates at a lower rotational speed than the second turbine  180 B during operation of the turbofan engine  100 . 
     The rotation of the low-pressure first spool shaft  160 A is transferred to a fan  150  via the electrical gearbox  110 . The fan  150 , when rotated, forces air through the bypass flow chamber  131  of the turbofan engine  100  to provide motive force to a vehicle using the turbofan engine  100 . The fan  150  includes of a plurality of fan blades  151  extending from a central hub  152 , and is generally larger in radius than the corresponding blades of the compressors  170  (and turbines  180 ) in the turbofan engine  100 . As such, if rotated at the same angular velocity or rotational speed (e.g., in revolutions per minute) as the compressors  170 , the fan  150  would be subject to higher velocities (and mechanical stresses) at the distal ends of the fan blades  151  than the blades of the compressors  170  and turbines  180 . For example, the tips of the blades of the compressors  170  (and turbines  180 ) may travel at subsonic speeds, but the tips of the fan  150  rotating with the subsonic compressors  170  (and turbines  180 ) may travel at supersonic speeds due to the greater radius of the fan  150 , which can cause noise and vibration issues (in addition to mechanical stresses) as the tips of the fan blades  151  break the sound barrier. In a further example, a slower fan speed can allow for a better Specific Fuel Consumption (SFC) efficiency such as when the fan speed, and speeds of the low and high pressure compressors are all controlled and coordinated relative to one another. By using an electrically geared turbofan engine  100 , an operator can control the relative fan speed to compressor speeds and thus provide greater SFC efficiently than if selecting from one of a set of fixed gear ratios (as in a mechanically geared system). 
     The electrical gearbox  110 , described in greater detail in regard to  FIGS.  2 A- 2 C and  3   , couples the first spool shaft  160 A with the hub  152  of the fan  150 , and allows the first spool shaft  160 A (and the associated first compressors  170 A) to rotate at one rotational speed, and the fan  150  to rotate at an independent rotational speed. The independent rotational speeds can include cases in which the fan  150  rotates faster than, slower than, or the same speed as the first spool shaft  160 A. In some aspects, an operator can also cause the speeds of the fan  150  and the first spool shaft  160 A to change relative to one another (e.g., speeding up or slowing down the fan  150 ). 
     The electrical gearbox  110  electromagnetically couples the first spool shaft  160 A with the fan  150 , using magnetically coupled components as a gearing system, rather than physically interlocking gears, so that the portions of the electrical gearbox  110  physically connected to the first spool shaft  160 A and the fan  150  are not in physical contact with one another. Instead, controllable electromagnetic fields selectively link the first spool shaft  160 A and the fan  150  over an air gap. The electrical gearbox  110  can be powered and/or controlled to vary the strength, speed of rotation, and direction of rotation of the electromagnetic fields linking the shaft-side and fan-side components in the electrical gearbox  110 . The power to create these electromagnetic fields can be supplied by a power distribution bus  145  or other power transfer mechanism for a vehicle in which the turbofan engine  100  is disposed (e.g., via a transfer cable  140  or wireless resonant power transmitter), such as in  FIG.  1 A , or via an electrical generator  190  connected between two spool shafts  160 , such as in  FIG.  1 B , which are discussed in greater detail in regard to  FIGS.  4 A- 4 B and  5   . In some aspects using an electrical generator  190 , the power distribution bus  145  and/or transfer cable  140  can be omitted. 
     In various aspects, control signals can be transmitted to the electrical gearbox  110  and/or a power supply of the electrical gearbox  110  (or included frequency converter) to alter the (effective) gearing ratio of the electrical gearbox  110  by changing, the strength, speed of rotation, and direction of rotation of the electromagnetic fields to thereby alter a ratio between the fan speed and the shaft speed to control the fan speed. In some aspects, the electrical gearbox  110  is configured to maintain a static gearing ratio, or is controlled via the shaft-speed without further control signal inputs. 
     An operator can dynamically control the electromagnetic forces applied from the shaft-side of the electrical gearbox  110  to vary how the fan-side of the electrical gearbox  110  is rotated relative to the shafts  160 . In some aspects, an operator dynamically controls the gearing ratio of the electrical gearbox  110  to vary the relative speeds of the fan  150  and the first spool shaft  160 A, for example, to achieve a steady fan speed while varying the compressor/turbine speeds, to achieve a higher bypass ratio and/or to keep the tip speed of the fan blades  151  below the speed of sound (e.g., improving fuel efficiency, reducing noise and vibration), to alter the amount of thrust provided by the fan  150  relative to the core engine, to rotate the fan  150  faster than the spool shafts  160 , etc. 
       FIGS.  2 A- 2 C  illustrate cross-sections for various configurations of the electrical gearbox  110 , according to aspects of the present disclosure. As will be appreciated, the electrical gearbox  110  can include a housing or other cover that protects internal components from debris, reduces air resistance, etc., mounting hardware to secure the electrical gearbox  110  to the fan  150  and/or spool shaft  160 , etc. Such mechanical features have been omitted from the Figures for clarity in discussing the electromagnetic components and the operation thereof. 
     In each of the configurations illustrated in  FIGS.  2 A- 2 C , an armature winding  111  is connected to the first spool shaft  160 A, and when the first spool shaft  160 A rotates, so too does the armature winding  111 . The armature winding  111 , when powered, generates a rotating armature magnetic field, that magnetically couples the armature winding  111  to magnetic receiver  112  connected to the fan  150 ; transferring rotational energy from the armature winding  111  to the magnetic receiver  112 . The magnetic receiver  112  can include permanent magnets or a second armature winding that are configured to receive the armature magnetic field and to cause the fan  150  to rotate based on the combined rotation of the armature magnetic field and the first spool shaft  160 A. When the armature windings  111  receives AC currents (i.e., electrical energy), a rotational magnetic field is produced, which interacts with the magnetic field of the magnetic receiver  112  (if permanent magnetics or activated electromagnets are included therein), which produces an electromagnetic torque between the armature winding  111  and the magnetic receiver  112 , which causes the magnetic receiver  112  (and the fan  150  attached thereto) to rotate and therefore convert the electrical energy supplied via the AC currents into mechanical energy. An operator can thereby change the frequency of the AC currents provided to the armature windings  111  to change the frequency of the rotational magnetic field, and thus control the rotational speed of the magnetic receiver  112 . 
     In  FIG.  2 A , the armature winding  111  defines a cavity in which the magnetic receiver  112  is positioned with an air gap between the physical components thereof. The armature winding  111  and the magnetic receiver  112  are coaxially aligned with one another, the hub  152 , and the first spool shaft  160 A, and are arranged planetary to one another so that the armature magnetic field is projected radially from the armature winding  111  to link the armature winding  111  and the magnetic receiver  112 . As used herein, when two objects are described as being “planetary” with one another, it will be understood that the objects rotate about a shared axis of rotation (at the same or different radial distances from the axis of rotation), but at different points along the length of the axis of rotation so as to be clear of the orbit (i.e., not physically contact) of the other object. The selective and dynamic control of the armature magnetic field frequency and rotational direction thereby enables the controllable transfer of rotational energy from the first spool shaft  160 A to the fan  150 , thus the speed. 
     In  FIG.  2 B , the magnetic receiver  112  defines a cavity in which the armature winding  111  is positioned with an air gap between the physical components thereof. The armature winding  111  and the magnetic receiver  112  are coaxially aligned with one another, the hub  152 , and the first spool shaft  160 A, and are arranged planetary to one another so that the armature magnetic field is projected radially from the armature winding  111  to link the armature winding  111  and the magnetic receiver  112 . The selective and dynamic control of the armature magnetic field thereby enables the controllable transfer of rotational energy from the first spool shaft  160 A to the fan  150 . 
     In  FIG.  2 C , the armature winding  111  and the magnetic receiver  112  are positioned in a facing relationship to one another with an air gap between the physical components thereof. The armature winding  111  and the magnetic receiver  112  are coaxially aligned with one another, the hub  152 , and the first spool shaft  160 A, and are arranged facially to one another so that the armature magnetic field is projected coaxially from the armature winding  111  to link the armature winding  111  and the magnetic receiver  112 . The selective and dynamic control of the armature magnetic field thereby enables the controllable transfer of rotational energy from the first spool shaft  160 A to the fan  150 . 
     The relative sizes and positions of the electromagnetically coupled components in  FIGS.  2 A- 2 C  have been illustrated for easy identification and differentiation. However, in various aspects, the relative sizes, shapes, and orientations of these components may be altered based on the physical properties of the turbofan engine  100  in which the components are installed (e.g., length, thickness, circumference, gap distance, rotational torque, and speed, operating temperature), the desired power transfer characteristics for the extracted rotational energy (e.g., gearing ratios, field strengths, relative speeds), and the like. The lengths of the components along the axis of the shafts  160  are determined by the torque and/or power rating requirements of the vehicle from the turbofan engine  100 , and the relative sizes and distances of individual components are sized to optimize torque production and speed from the turbofan engine  100  and power transfer efficiency in the electrical gearbox  110  within the physical confines of the turbofan engine  100 . Thus,  FIGS.  2 A- 2 C  are intended to demonstrate the concepts of operation, and not necessarily a specific implementation, which may be modified based on the power requirements, thrust requirements, turbofan engine  100  specific fuel consumption, and material properties of various components. 
       FIG.  3    illustrates a functional block diagram  300  of the electrical gearbox  110 , according to aspects of the present disclosure. The armature winding  111  is coupled to a power source  310  (e.g., a power distribution bus  145  or an electrical generator  190 ), which supplies an input current (I i ). Although the input current I i  is denoted as being supplied in in three phases (as I iϕ1 , I iϕ2 , and I iϕ3 ), in various aspects, the input current I i  may be provided in more or fewer phases. The power source  310  supplies the input current I i  as an Alternating Current (AC) to the armature winding  111  to produce the armature magnetic field  320 , and the frequency at which the power source  310  supplies the input current I i  can be changed by a frequency converter (e.g.,  520  as is discussed in relation to  FIG.  5   ) that is either part of the power source  310  or provided as a separate device between the power source  310  and the armature winding  111 . In some aspects, the frequency converter is secured to the first spool shaft  160 A and is configured to receive control signals to alter the frequency of the input current I i  provided to the armature winding  111 . 
     The armature magnetic field  320  links the armature winding  111  to the magnetic receiver  112  so that rotation imparted on the armature winding  111  by the first spool shaft  160 A is selectively transferred to the magnetic receiver  112  and thereby to the fan  150 . In some aspects, the electrical gearbox  110  is a permanent magnet motor, in which the magnetic receiver  112  includes an array of permanent magnets  330  arranged to receive the armature magnetic field  320 . In other aspects, the electrical gearbox  110  is an induction motor, in which the magnetic receiver  112  includes a receiver armature winding  340  arranged to receive the armature magnetic field  320 . In yet other aspects, the electrical gearbox  110  is a hybrid motor, in which the magnetic receiver  112  include a combination of an array of permanent magnets  330  and a receiver armature winding  340  that are arranged to receive the armature magnetic field  320 . 
     The rotation of the first spool shaft  160 A affects the rotation of the armature magnetic field, regardless of the relative orientations of the physical components of the electrical gearbox  110 , and an operator can control the rotation of the armature magnetic field  320  with reference to the shaft-rotation to rotate faster or slower than the rotation of the first spool shaft  160 A. As a convention used herein, the rotating speed of the low-pressure compressor shaft (i.e., the first spool shaft  160 A) is denoted as n LPC , the rotating speed of the armature magnetic field  320  is denoted as n m  (in which positive values indicate co-rotation with the first spool shaft  160 A and negative values indicate counter-rotation), and the machine synchronous speed is denoted as n s . The machine synchronous speed n s  can therefore be derived according to Formula 1 as:
 
 n   s   =n   m   +n   LPC   (Formula 1)
 
     The rotor slip rate, denoted as s, in the electrical gearbox  110  can therefore be derived according to Formula 2, in which the rotor speed is denoted as n r : 
     
       
         
           
             
               
                 
                   s 
                   = 
                   
                     
                       
                         
                           n 
                           s 
                         
                         - 
                         
                           n 
                           r 
                         
                       
                       
                         n 
                         s 
                       
                     
                     = 
                     
                       
                         
                           n 
                           m 
                         
                         + 
                         
                           n 
                           
                             L 
                             ⁢ 
                             P 
                             ⁢ 
                             C 
                           
                         
                         - 
                         
                           n 
                           r 
                         
                       
                       
                         
                           n 
                           m 
                         
                         + 
                         
                           n 
                           
                             L 
                             ⁢ 
                             P 
                             ⁢ 
                             C 
                           
                         
                       
                     
                   
                 
               
               
                 
                   ( 
                   
                     Formula 
                     ⁢ 
                     
                         
                     
                     ⁢ 
                     2 
                   
                   ) 
                 
               
             
           
         
       
     
     The rotor speed, n r , can therefore be derived according to Formula 3 as:
 
 n   r =(1− s )( n   m   +n   LPC )  (Formula 3)
 
     Accordingly, the rotor speed n r  can be controlled dynamically to be different from the shaft-speed n LPC  by varying the rotation speed n m  of the armature magnetic field  320 . By controlling the frequency of the input current I i  used to excite the armature winding  111 , an operator can control the rotation speed n m  of the armature magnetic field  320 , and thus the speed of the fan  150  (i.e., the rotor speed n r ). When the armature magnetic field  320  is produced by a three-phase input current (e.g., I iϕ1 , I iϕ2 , and I iϕ3 ), the field rotation direction can be controlled by changing the sequence and frequency of supplying the input current I i , according to Formula 4, in which the frequency is denoted as f, and the number of pair of poles is denoted as p, in which a positive value indicates rotation in the same direction as the first spool shaft  160 A (i.e., co-rotation; both rotating clockwise or counterclockwise) and a negative value indicates counter-rotation (i.e., one rotating clockwise and the other rotating counterclockwise). 
     
       
         
           
             
               
                 
                   
                     n 
                     m 
                   
                   = 
                   
                     
                       120 
                       ⁢ 
                       f 
                     
                     p 
                   
                 
               
               
                 
                   ( 
                   
                     Formula 
                     ⁢ 
                     
                         
                     
                     ⁢ 
                     4 
                   
                   ) 
                 
               
             
           
         
       
     
     Therefore, an operator can control the rotational speed n r  of the fan  150  according to Formula 5 by adjusting one or more of the number of pairs of poles p or the frequency f of the input current I i .
 
 n   r =(1− s )(120 f/p+n   LPC )  (Formula 5)
 
     Accordingly, control of the frequency f at which the input current I i  is provided to the armature winding  111  can control the relative speed n r  of the fan  150  to the speed n LPC  of the first spool shaft  160 A used to impart rotational energy to the fan  150 . For example, by counter-rotating the armature magnetic field  320  relative to the first spool shaft  160 A, an operator can slow the fan  150  compared to the first spool shaft  160 A, which can optimize a fuel burn rate for a desired amount of thrust produced by the fan  150  through the bypass flow chamber  131 . In a further example, by co-rotating the armature magnetic field  320  relative to the first spool shaft  160 A, an operator can generate additional thrust from the fan  150 , such as may be desirable during takeoff procedures for an aircraft. 
     Although the number of paired poles p is typically fixed based on the construction of the electrical gearbox  110 , in some aspects an operator can selectively activate or deactivate poles to alter the value of p for further control of the rotor speed n r . 
     In a permanent magnet motor, in contrast to an induction motor (as is generally described in relation to Formulas 1-5) the rotor runs at a synchronous speed based on the armature field frequency with no slip (i.e., s=0). Accordingly, an operator can use Formulas 6 and 4 to control a permanent magnet motor in an electrical gearbox  110  in a turbofan engine  100  to rotate at a desired rotor speed n r .
 
 n   r   =n   s   =n   m   +n   LCP   (Formula 6)
 
       FIGS.  4 A and  4 B  illustrate component arrangements for electrical generators  190 , as may be used as power sources  310  to produce a generated current I g  to provide as the input current I i  used by the armature winding  111  to generate the armature magnetic field  320 , according to aspects of the present disclosure. 
     In a multi-shaft turbofan engine  100 , each spool shaft  160  can rotate at a different speed from the other spool shafts  160 . Accordingly, a differential rotational speed exists between the first spool shaft  160 A and the second spool shaft  160 B (and any components attached thereto) during operation. By attaching components of the electrical generators  190  to two different spool shafts (e.g.,  160 A and  160 B) or to two different compressors (e.g.,  170 A and  170 B) at the respective interfaces therebetween, the electrical generator  190  can, based on the differential rotational speed, convert rotational energy into electrical energy via a series of induced magnetic fields that can then be transferred to the armature winding  111  without requiring physical contact between the generator components rotating at different rates. The electrical generators  190  capitalize on the different rotational speeds of the compressors  170  attached to different shafts  160  to rotate the components relative to one another using the operational rotation of the components of the turbofan engine  100 . 
       FIG.  4 A  illustrates a first component arrangement  400 A for an electrical generator  190 , according to aspects of the present disclosure. A first rotor assembly  410 A is connected to a second (higher-pressure) compressor  170 B and a second rotor assembly  410 B is connected to a first (lower-pressure) compressor  170 A at an interface between the two compressors  170 . In various aspects, the rotor assemblies  410  are connected to one or more blades of the associated compressor  170 , to a ring/connection point of the blades to an associated spool shaft  160 , or to the associated spool shaft  160 . The rotor assemblies  410  position various electromagnetic components of the electrical generator  190  at known distances and orientations relative to one another, the shafts  160 , and the compressors  170 . 
     In  FIG.  4 A , the first rotor assembly  410 A includes a permanent magnet  420 , which produces a generator magnetic field  415 . The permanent magnet  420  emits the generator magnetic field  415  radially through an air gap defined coaxially to the shafts  160  to magnetically link the permanent magnet  420  with a generator armature winding  430  included in the second rotor assembly  410 B. In various aspects, the permanent magnet  420  may include a plurality of magnets arranged circumferentially around the shaft  160  to emit a plurality of generator magnetic fields  415 . 
     The second rotor assembly  410 B includes the generator armature winding  430  arranged concentrically and radially, but not in physical contact with, the permanent magnet  420  or the shafts  160 , and positions the generator armature winding  430  within a predefined field strength of the generator magnetic field  415 . Accordingly, the generator magnetic field  415  radially links the permanent magnet  420  and the generator armature winding  430 . In various aspects, when rotated relative to the permanent magnet  420 , the generator armature winding  430  produces the generated currents I g  as a multiphase alternating current, which powers the armature winding  111  to generate the armature magnetic field  320  either directly (e.g., I g =I i ) or via a frequency converter to change the frequency of the generated current f g  to desired frequency f of the input current I i    
       FIG.  4 B  illustrates a second component arrangement  400 B for an electrical generator  190 , according to aspects of the present disclosure. A first rotor assembly  410 A is connected to a higher-pressure first compressor  170 A and a second rotor assembly  410 B is connected to a lower-pressure second compressor  170 B at an interface between the two compressors  170 . In various aspects, the rotor assemblies  410  are connected to one or more blades of the associated compressor  170 , to a ring/connection point of the blades to an associated spool shaft  160 , or to the associated spool shaft  160 . The rotor assemblies  410  position various electromagnetic components of the electrical generator  190  at known distances and orientations relative to one another, the shafts  160 , and the compressors  170 . 
     In  FIG.  4 B , the first rotor assembly  410 A includes a permanent magnet  420 , which produces a generator magnetic field  415 . The permanent magnet  420  emits the generator magnetic field  415  through an air gap defined in a plane intersecting the axis of rotation for the shafts  160  to magnetically link the permanent magnet  420  with a generator armature winding  430  included in the second rotor assembly  410 B. Although illustrated as defining an air gap in a plane orthogonal to the axis of rotation (e.g., for a coaxial magnetic linkage between the permanent magnet  420  and the generator armature winding  430 ), in other aspects, the air gap may be defined at other angles relative to the shafts  160 . In various aspects, the permanent magnet  420  may include a plurality of magnets arranged radially around the shaft  160  to emit a plurality of generator magnetic fields  415 . 
     The second rotor assembly  410 B includes the generator armature winding  430  arranged radially around, but not in physical contact with, the shafts  160  and arranged planetary to the permanent magnet  420 . The relative positions and lengths of the rotor assemblies  410  position the generator armature winding  430  within a predefined field strength of the generator magnetic field  415 . Accordingly, the generator magnetic field  415  axially links the permanent magnet  420  and the generator armature winding  430 . In various aspects, when rotated relative to the permanent magnet  420 , the generator armature winding  430  produces the generated current I g  as a multiphase alternating current, which powers the armature winding  111  to generate the armature magnetic field  320  either directly (e.g., I g =I i ) or via a frequency converter to change the frequency of the generated current f g  to desired frequency f of the input current I i . 
     During operation of the turbofan engine  100  in which the components are disposed, the rotational forces imparted by turbines  180  cause the compressors  170  and attached EM components to rotate relative to one another and the stationary turbine enclosure  120 . Due to the differential in the rotational speeds of the higher-pressure compressor  170 B and the lower-pressure compressor  170 A, the generator magnetic field  415  rotates relative to the generator armature winding  430 . Accordingly, electrical energy is extracted from the rotational forces of the shafts  160  and is transferred to power the armature winding  111  of the electrical gearbox  110 . 
     The relative sizes and positions of the electromagnetically coupled components in  FIGS.  4 A and  4 B  have been illustrated for easy identification and differentiation. However, in various aspects, the relative sizes, shapes, and orientations of these components may be altered based on the physical properties of the turbofan engine  100  in which the components are installed (e.g., length, thickness, circumference, gap distance, rotational torque, and speed, operating temperature), the desired power characteristics for the extracted power (e.g., number of power phases, voltage/current levels), and the like. The lengths of the components along the axis of the shafts  160  are determined by the torque and/or power rating requirements of the vehicle from the turbofan engine  100 , and the relative sizes and distances of individual components are sized to optimize torque production and speed from the turbofan engine  100  and power transfer efficiency in the electrical generator  190  within the physical confines of the turbofan engine  100 . Thus,  FIGS.  4 A and  4 B  are intended to demonstrate the concepts of operation, and not necessarily a specific implementation, which may be modified based on the power requirements, thrust requirements, turbofan engine  100  specific fuel consumption, and material properties of various components. For example, a fabricator can design the permanent magnet  420  and the generator armature winding  430  according to  FIG.  4 A  when radial space along the length of blades of the compressors  170  is more readily available or according to  FIG.  4 B  when axial space between the compressors  170  is more readily available. 
       FIG.  5    illustrates a circuit diagram of the electrical generator  190  in use as the power source  310  for the armature winding  111  of the electrical gearbox  110 , according to aspects of the present disclosure. The first rotor assembly  410 A (which includes the permanent magnet  420 ) is arranged in magnetic contact, but not physical contact, with the second rotor assembly  410 B (which includes the generator armature winding  430 ) via the generator magnetic field  415 . As used herein, magnetic contact describes the state in which a magnetic field produced by a permanent or electromagnet is of at least a predefined strength between two components. The generator armature winding  430  includes a plurality of receiving windings  510 A-C (generally, receiving winding  510 ) that each produce one phase of power from the received generator magnetic field  415 . Although illustrated as providing three-phase current to three corresponding receiving windings  510 A-C, in other aspects, more or fewer than three phases may be used by, for example, using more or fewer receiving windings  510 . 
     The first rotor assembly  410 A is connected to one compressor  170  of the turbofan engine  100 , such as shown in  FIGS.  4 A and  4 B  and the second rotor assembly  410 B is connected to a second compressor  170  of the turbofan engine  100 , such as shown in  FIGS.  4 A and  4 B . Due to the difference in rotational speeds of each compressor  170  when the turbofan engine  100  is in operation, the first rotor assembly  410 A rotates at a different speed from the second rotor assembly  410 B. 
     The second rotor assembly  410 B is supplies the generated current I g  to the frequency converter  520 , which selectively controls the frequency f of the input current I i  based on control signals (e.g., from a vehicle operator) indicating the desired rotational speed n m  for the armature magnetic field  320 . In some aspects, the frequency converter  520  increases or decreases the frequency f i  of the input current I 1  relative to the frequency f g  of the generated current I g , but may also leave the frequency f unchanged (e.g., f g =f i ). 
       FIG.  6    is a flowchart of a method  600  for operating a turbofan engine  100  having an electrical gearbox  110 , according to aspects of the present disclosure. Method  600  begins with block  610 , where the spool shafts  160  of the turbofan engine  100  rotate. In a turbofan engine  100 , an operator may cause spool shafts  160  to rotate by engaging the turbofan engine  100  to produce thrust for a vehicle; inducing rotational energy upon spool shafts  160  by the combustion of fuel in a combustion chamber and expelling the exhaust through a turbine section  124 , thus causing the turbines  180  to rotate the corresponding spool shafts  160 . Depending on the number of spool shafts  160  in the turbofan engine  100 , the thrust requirements of the vehicle using the turbofan engine  100 , the altitude of the vehicle using the turbofan engine  100 , etc., the spool shafts  160  may rotate at various different speeds. 
     At block  620 , an operator powers an armature winding  111  to generate an armature magnetic field  320  that rotates at a desired speed n m  relative to the rotational speed n LPC  of the first (low-pressure) spool shaft  160 A. In various aspects, a multiphase input current I i  is provided to produce the armature magnetic field by various different sources according to a desired magnitude to magnetically couple the armature winding  111  with the magnetic receiver  112  and at a desired input frequency f to rotate at the desired speed n m . 
     In some aspects, the vehicle in which the turbofan engine  100  is included supplies the input current I i  to the armature winding  111  from a power distribution bus  145  (e.g., via a transfer cable  140 ). In some aspects, the input current I i  received from the power distribution bus  145  is transmitted by the power distribution bus  145  at the input frequency f i  used by the armature winding  111  to produce the armature magnetic field  320  at the desired speed n m . In other aspects, the input current I i  is converted by a frequency converter  520  to the input frequency f used by the armature winding  111  to produce the armature magnetic field  320  at the desired speed n m  from an original frequency provided by the power distribution bus  145 . 
     In aspects including an electrical generator  190  in the interface region between two spool shafts  160  or compressors  170 , the different rotational speeds of adjacent rotating spool shafts  160  can be used to also rotate a first rotor assembly  410 A relative to a second rotor assembly  410 B to generate a generated current I g  at a generated frequency f g , which may be converted (according to control signals) by a frequency converter  520  to an input current I i  at an input frequency I i  for use by an armature winding  111  to produce an armature magnetic field  320  that rotates at a desired speed n m  relative to the first (low-pressure) spool shaft  160 A. 
     At block  630 , the electrical gearbox  110  transfers rotational energy from the first spool shaft  160 A to the fan  150  via the magnetic coupling between the armature winding  111  and the magnetic receiver  112 . Because the armature winding  111  and the magnetic receiver  112  are magnetically coupled, when the armature winding  111  moves, the armature magnetic field  320  causes the magnetic receiver  112  to follow the rotation of the armature winding  111 . Accordingly, as the first spool shaft  160 A imparts rotation on the armature winding  111 , when the armature winding  111  generates the armature magnetic field  320 , the rotation of the armature winding  111  is imparted on the magnetic receiver  112 . The magnetic receiver  112 , in turn, imparts rotational energy on the fan  150  to which the magnetic receiver  112  is physically connected. 
     At block  640 , the fan  150  rotates according to the rotor speed n r  imparted by the armature magnetic field  320  on the magnetic receiver  112 . The speed n r  of the fan  150  may be equal to the speed n LPC  of the first spool shaft  160 A (e.g., when n m =0), greater than the speed n LPC  of the first spool shaft  160 A (e.g., when n m &gt;0; co-rotating with the first spool shaft  160 A), or less than the speed n LPC  of the first spool shaft  160 A (e.g., when n m &lt;0; counter-rotating to the first spool shaft  160 A). 
       FIG.  7    is a flowchart of a method  700  for fabricating a turbofan engine  100  with an electrical gearbox  110 , according to aspects of the present disclosure. 
     At block  710 , a fabricator affixes the armature winding  111  of an electrical gearbox  110  with a distal end of the low-pressure spool shaft  160  of a turbofan engine  100  projecting upstream from the compressors  170  (or where the compressors  170  will be later installed). 
     At block  720 , the fabricator affixes the magnetic receiver  112  of the electrical gearbox  110  with a fan  150  for the turbofan engine  100 . In various aspects, the magnetic receiver  112  is affixed to the hub  152  of the fan  150  or to a shaft projecting from the hub  152 . 
     When blocks  710  and  720  have been performed, the electrical gearbox  110 , the fan  150 , and the low-pressure spool shaft  160  share a common axis of rotation. An air gap is defined within the electrical gearbox  110  between the armature winding  111  and the magnetic receiver  112 , and when the armature winding  111  is unpowered, each of the fan  150  and the low-pressure spool shaft  160  can rotate independently of one another. For example, a technician can rotate the fan  150  without rotating the low-pressure spool shaft  160  or vice versa when the armature winding  111  does not generate the armature magnetic field  320 . 
     Therefore, at block  730 , the fabricator couples the armature winding  111  to a power source  310  to enable the armature winding  111  to selectively generate an armature magnetic field  320  to magnetically couple the armature winding  111  and the magnetic receiver  112  to transfer rotational energy between the spool shaft  160  and the fan  150 . In various aspects, the fabricator includes a frequency converter  520  either in the power source  310  or in communication between the power source  310  and the armature winding  111  to selectively control the frequency f of the input current I i  supplied to the armature winding  111  to thereby increase or decrease the rotational speed of the fan  150  relative to the low-pressure spool shaft  160 . The fabricator can couple the armature winding  111  to various power sources  310 , including, but not limited to, the power distribution bus  145  of the vehicle in which the turbofan engine  100  is included and an electrical generator  190  disposed at the interface between two spool shafts  160  configured to generate power based on the differential rotational speed between the two spool shafts  160 . The fabricator can couple the frequency converter  520  to various control systems (e.g., a flight control system for an aircraft including the turbofan engine  100 ) to vary the frequency f of the input current I i  to change or maintain the speed of the fan  150  relative to the rotational speed of the low-pressure spool shaft  160 A. 
     In the current disclosure, reference is made to various aspects. However, it should be understood that the present disclosure is not limited to specific described aspects. Instead, any combination of the following features and elements, whether related to different aspects or not, is contemplated to implement and practice the teachings provided herein. Additionally, when elements of the aspects are described in the form of “at least one of A and B,” it will be understood that aspects including element A exclusively, including element B exclusively, and including element A and B are each contemplated. Furthermore, although some aspects may achieve advantages over other possible solutions and/or over the prior art, whether or not a particular advantage is achieved by a given aspect is not limiting of the present disclosure. Thus, the aspects, features, aspects and advantages disclosed herein are merely illustrative and are not considered elements or limitations of the appended claims except where explicitly recited in a claim(s). Likewise, reference to “the invention” shall not be construed as a generalization of any inventive subject matter disclosed herein and shall not be considered to be an element or limitation of the appended claims except where explicitly recited in a claim(s). 
     As will be appreciated by one skilled in the art, aspects described herein may be embodied as a system, method or computer program product. Accordingly, aspects may take the form of an entirely hardware aspect, an entirely software aspect (including firmware, resident software, micro-code, etc.) or an aspect combining software and hardware aspects that may all generally be referred to herein as a “circuit,” “module” or “system.” Furthermore, aspects described herein may take the form of a computer program product embodied in one or more computer readable storage medium(s) having computer readable program code embodied thereon. 
     Program code embodied on a computer readable storage medium may be transmitted and received using any appropriate medium, including but not limited to wireless, wireline, optical fiber cable, RF, etc., or any suitable combination of the foregoing. 
     Computer program code for carrying out operations for aspects of the present disclosure may be written in any combination of one or more programming languages, including an object oriented programming language such as Java, Smalltalk, C++ or the like and conventional procedural programming languages, such as the “C” programming language or similar programming languages. The program code may execute entirely on the user&#39;s computer, partly on the user&#39;s computer, as a stand-alone software package, partly on the user&#39;s computer and partly on a remote computer or entirely on the remote computer or server. In the latter scenario, the remote computer may be connected to the user&#39;s computer through any type of network, including a local area network (LAN) or a wide area network (WAN), or the connection may be made to an external computer (for example, through the Internet using an Internet Service Provider). 
     Aspects of the present disclosure are described herein with reference to flowchart illustrations and/or block diagrams of methods, apparatuses (systems), and computer program products according to aspects of the present disclosure. It will be understood that each block of the flowchart illustrations and/or block diagrams, and combinations of blocks in the flowchart illustrations and/or block diagrams, can be implemented by computer program instructions. These computer program instructions may be provided to a processor of a general purpose computer, special purpose computer, or other programmable data processing apparatus to produce a machine, such that the instructions, which execute via the processor of the computer or other programmable data processing apparatus, create means for implementing the functions/acts specified in the block(s) of the flowchart illustrations and/or block diagrams. 
     These computer program instructions may also be stored in a computer readable medium that can direct a computer, other programmable data processing apparatus, or other device to function in a particular manner, such that the instructions stored in the computer readable medium produce an article of manufacture including instructions which implement the function/act specified in the block(s) of the flowchart illustrations and/or block diagrams. 
     The computer program instructions may also be loaded onto a computer, other programmable data processing apparatus, or other device to cause a series of operational steps to be performed on the computer, other programmable apparatus or other device to produce a computer implemented process such that the instructions which execute on the computer, other programmable data processing apparatus, or other device provide processes for implementing the functions/acts specified in the block(s) of the flowchart illustrations and/or block diagrams. 
     The flowchart illustrations and block diagrams in the Figures illustrate the architecture, functionality, fabrication, and operation of possible implementations of systems, methods, and computer program products according to various aspects of the present disclosure. In this regard, each block in the flowchart illustrations or block diagrams may represent a module, segment, or portion of code, which comprises one or more executable instructions for implementing the specified logical function(s). It should also be noted that, in some alternative implementations, the functions noted in the block may occur out of the order noted in the Figures. For example, two blocks shown in succession may, in fact, be executed substantially concurrently, or the blocks may sometimes be executed in the reverse order or out of order, depending upon the functionality involved. It will also be noted that each block of the block diagrams and/or flowchart illustrations, and combinations of blocks in the block diagrams and/or flowchart illustrations, can be implemented by special purpose hardware-based systems that perform the specified functions or acts, or combinations of special purpose hardware and computer instructions. 
     While the foregoing is directed to aspects of the present disclosure, other and further aspects of the disclosure may be devised without departing from the basic scope thereof, and the scope thereof is determined by the claims that follow.