TECHNICAL FIELD 
     This disclosure relates to bearing systems. 
     BACKGROUND 
     Equipment and machinery often contain moving (e.g., rotating, translating) members, which require support during operation. A bearing, or similar device, may be used to support the moving member. Although some bearings may require direct contact with the member to provide the necessary support, some applications benefit from non-contact, or nearly non-contact, support for the member. Application of non-contact bearings may also include direct contact bearings for backup security. 
     SUMMARY 
     The present disclosure describes a mechanical backup bearing system arrangement to work in conjunction with non-contact magnetic bearings and capable of coping with thermal expansions of the bearing components during operation. Expansions or contractions of an inner or outer race of a bearing can be compensated using particular springs providing a low profile and a proper stiffness. In a general aspect, an electric machine system includes a rotational portion and a stationary portion. The electric machine further includes a magnetic bearing configured to support the rotational portion to rotate within the stationary portion. A mechanical back-up bearing resides in a cavity between the rotational portion and the stationary portion. A flat spring is carried by the stationary portion and abuts the back-up bearing. 
     One or more of the following features can be included with the general aspect. The back-up bearing can further include an inner backup bearing race that comes in contact with the rotational portion when the rotational portion is not supported by the magnetic bearing. An outer backup bearing race is also carried by the stationary portion. The outer race and the inner race can encase backup bearing balls. The flat spring can contact the lateral side of the outer race. The flat spring may be configured to deflect upon an axial movement of the lateral side of the outer race. The flat spring can apply a preloaded force to the outer race. 
     Additional features can be included with the general aspect. The electric machine system can further include a retainer that clamps the flat spring against the stationary portion. The retainer is separated from at least a portion of the flat spring by an air gap. The flat spring can be configured to deflect towards the air gap upon thermal expansion of the inner race of the back-up bearing. The retainer may be a hard stop for deflection of the flat spring upon thermal expansion of the inner race. The stationary portion of the electric machine system can further include an end housing. The flat spring can be carried by the end housing and supported against the end housing by a shim. In some implementations, the flat spring includes a flat circular disk with a central hole. The flat spring may also include a number of radial slots. In some implementations, the back-up bearing can be a duplex bearing. 
    
    
     
       DESCRIPTION OF DRAWINGS 
         FIG. 1  is a half cross-sectional view of an electric machine system using magnetic bearings in accordance with the present disclosure. 
         FIG. 2  is a detailed cross-sectional view of a backup bearing system of the electric machine system of  FIG. 1 . 
         FIG. 3A  is a detailed half cross-sectional view of a flat spring in loaded condition as implemented in  FIG. 2 . 
         FIG. 3B  is a detailed half cross-sectional view of the flat spring of  FIG. 3A  in pre-assembled condition. 
         FIG. 3C  is a detailed half-cross-sectional view of the flat spring of  FIG. 3A  in a full-stop condition. 
         FIG. 4A  is a perspective view of an example spring in accordance with the present disclosure. 
         FIG. 4B  is a perspective view of another example spring in accordance with the present disclosure. 
     
    
    
     Like reference symbols in the various drawings indicate like elements. 
     DETAILED DESCRIPTION 
     This disclosure relates to a mechanical backup bearing arrangement to work in conjunction with a magnetic bearing system, which features a mechanism for accommodating thermal expansions or contractions of the mechanical bearing components, particularly occurring when the inner races of a backup bearing suddenly come into contact with a moving member. Thermal expansions or contractions of an inner or outer race of a bearing can be compensated by using a flat spring configuration. In an electric machine system, a magnetic bearing system can be backed up by mechanical bearings. The mechanical backup bearings are used in case the magnetic bearings are not used or cannot provide sufficient support, such as due to overloading, component malfunction, or other reasons. The mechanical backup bearing can include two angular contact ball bearings mounted face to face (e.g., two bearings in juxtaposition and opposite in the axial loading direction of each bearing). The ball bearings can include an inner race mounted concentrically with the rotor of the electric machine with a clearance sufficient that there will be no mechanical contact between the rotor and the backup bearing when the rotor is supported by a magnetic bearing. The inner races and the outer races of two ball bearings can be aligned facing each other and each bearing can be dimensioned so that there will be a small gap between the outer races when a clamping pressure is applied to their outer faces bringing the inner races together. In this configuration, clearances between the bearing balls and the inner and outer races can be effectively removed, making the assembly axially and radially very stiff. The clamping force needed to just bring the outer races into contact is referred to as the preload. If the preload is not excessively high, the balls will still maintain an ability to roll around the races. The clamping pressure in this configuration, however, can increase uncontrollably due to thermal expansion of the bearing inner races if the outer races are rigidly clamped against each other. For example, in an electric machine system (e.g., a motor or a generator) having a rotating rotor, the shaft of the rotor can have a much higher temperature than the housing, e.g., as a result of cooling condition differences and the heat generated by rotation and friction at or near the shaft, particularly when a rotating shaft comes into a mechanical contact with the inner races of a backup bearing. Heat of the shaft can be transferred to the bearing inner races, which thermal expansion can result in an increased outward pressure on the bearing balls, which, in turn, will apply more pressure on the bearing outer races. The present disclosure describes a system, method, and apparatus for maintaining adequate/appropriate/correct clamping pressure in a preloaded duplex backup bearing arrangement when the inner race temperature changes. 
     As described previously, an electric machine system can use magnetic bearings to support a rotor. An Active Magnetic Bearing (AMB) uses an electromagnetic actuator to apply a controlled electromagnetic force to support the moving member in a non-contact, or nearly non-contact, manner. The non-contact or nearly non-contact support provided by the magnetic bearing can allow for frictionless or nearly frictionless rotation of the rotor. 
       FIG. 1  is a cross-sectional view of an electric rotational machine  100  in accordance with the present disclosure.  FIG. 1  shows an example of using an AMB system in an electric rotational machine  100 . The electric rotational machine  100  can be, for example, an electric motor  104  driving an impeller  106  (e.g., liquid and/or gas impeller) mounted directly on the motor shaft  108 . The electric motor  104  shown in  FIG. 1  has a rotor  110  and a stator  112 . Alternatively, the impeller  106  can be driven by a flow of gas or liquid and spin the rotor  110  attached to it through the motor shaft  108 . In this case, the electric motor  104  can be used as a generator which would convert the mechanical energy of the rotor  110  into electricity. In embodiments, the rotor  110  of the electric rotational machine  100  can be supported radially and axially without mechanical contact by means of front and rear radial AMBs  114  and  116 . The front combination AMB  114  provides an axial suspension of the rotor  110  and a radial suspension of the front end of the rotor, whereas the rear radial AMB  116  provides only radial suspension of the rear end of the rotor  110 . 
     When the radial AMBs  114  and  116  are deactivated, the rotor rests on the mechanical backup bearings  120  and  122 . The front mechanical backup bearing  122  may provide the axial support of the rotor  110  and a radial support of the rotor front end, whereas the rear mechanical backup bearing  120  may provide radial support of the rear end of the rotor  110 . There are radial clearances between the inner diameters of the mechanical backup bearings  120 ,  122  and the outer diameters of the rotor portions interfacing with those bearings to allow the rotor  110  to be positioned radially without touching the mechanical backup bearings  120 ,  122  when radial AMBs  114  and  116  are activated. Similarly, there are axial clearances between the mechanical backup bearings  120 ,  122  and the portions of the rotor  110  interfacing with those bearings to allow the rotor  110  to be positioned axially without touching the mechanical backup bearings  120  and  122  when radial AMBs  114  and  116  are activated. 
     The front mechanical backup bearing  122  is further discussed in  FIG. 2 , which depicts details of the view  190 . As described above,  FIG. 2  is a detailed cross-sectional view  190  of the front mechanical backup bearing  122  of the electric rotational machine system  100  of  FIG. 1 . Details of the axial spring  230  are further discussed in  FIGS. 3A to 3C . Briefly, and in conjunction with  FIG. 2 , view  190  illustrates a front mechanical backup bearing  122  formed by two angular-contact ball bearings  242  and  244  aligned concentrically to each other and to the rotor  210  while maintaining a radial clearance  250  and axial clearances  252  and  254  between the backup bearing inner races  211  and  213  and the rotor  210  when the rotor  210  is supported by front and rear radial Active Magnetic Bearings  114  and  116  as shown in  FIG. 1 . When the rotor  210  is not supported by front and rear radial Active Magnetic Bearings  114  and  116 , their displacement on this end of the machine is limited in extent since either the cylindrical landing surface  260  or axial landing surfaces  262  or  264  of the rotor  210  will come into contact with the backup bearing inner races  211  and  213 . 
     As it is commonly done in backup bearings for Active Magnetic Bearing systems, the angular-contact ball bearings  242  and  244  are mounted in a resilient mount cartridge  237  which is located inside of a stationary cavity formed by the machine housing  270  and a resilient mount cover  235 . The resilient mount cartridge  237  is dimensioned so that by itself it is free to move radially within the cavity, but has minimal ability to move axially. The radial movements of the resilient mount cartridge  237  are constrained by flexible elements  280  (e.g. O-rings), which also may dampen possible radial oscillations of the resilient mount cartridge  237  and angular-contact ball bearings  242  and  244  that it supports. Such arrangement may be needed to improve radial system dynamics when the rotor  210  comes in contact with the backup bearings after being supported by AMBs. 
     The angular-contact ball bearings  242  and  244  are dimensioned so that when a clamping pressure is applied to the outer faces  221  and  223  of their outer races  212  and  214 , their backup bearing inner races  211  and  213  come in contact, whereas a small axial gap  275  is maintained between the inner faces of the outer races  212  and  214 . Such a scheme eliminates a free play between the bearing balls  217 ,  218  and the inner and outer backup bearing races  211  through  214 . It is also possible to completely close the gap  275  if a sufficient preload is applied. 
     As disclosed, the clamping pressure is generated by an axial spring  230 , which can be dimensioned to have a right amount of axial stiffness: large enough to maintain the outer race  214  in contact with the right hard stop  282 , but not so excessive that thermal growth of the backup bearing inner races  211  and  213  would result in excessive clamping pressure to cause the bearing balls  217  and  218  to cease rotating around the bearing races. 
     In case an excessive axial loading is exerted by the rotor  210  on angular-contact ball bearings  242  and  244  in the direction to deflect the axial spring  230  outboard (to the left in  FIG. 2 ), a hard mechanical stop  284  can be added to limit the spring deflection and the amount of the axial travel allowable for the rotor  210 . 
     Front AMB  114  consists of a combination radial and axial electromagnetic actuator  101 , radial position sensors  124 , axial position sensor  126  and control electronics  150 . The combination radial and axial electromagnetic actuator  101  may be capable of exerting axial forces on the axial actuator target  109  and radial forces on the radial actuator target  111 , both rigidly mounted on the rotor  110 . The axial force is the force in the direction of Z-axis  117  and the radial forces are forces in the direction of X-axis  118  (directed out-of-the-page) and the direction of Y-axis  119 . The actuator may have at least three sets of coils corresponding to each of the axes and the forces that may be produced when the corresponding coils are energized with control currents produced by control electronics  150 . The position of the front end of the rotor is constantly monitored by non-contact position sensors, such as radial position sensors  124  and axial position sensors  126 . The non-contact radial position sensors  124  can monitor the radial position of the front end of the rotor  110 , whereas the non-contact axial position sensors  126  can monitor the axial position of the rotor  110 . 
     Signals from the non-contact radial position sensors  124  and axial position sensors  126  may be input into the control electronics  150 , which may generate currents in the control coils of the combination radial and axial electromagnetic actuator  101  when it finds that the rotor  110  is deflected from the desired position such that these currents may produce forces pushing the rotor  110  back to the desired position. 
     At the rear radial AMB  116  is an electromagnetic actuator  128 , radial non-contact position sensors  130 , and control electronics  152 . The rear radial AMB  116  may function similarly to the front radial AMB  114  except that it might not be configured to control the axial position of the rotor  110  because this function is already performed by the front radial AMB  114 . Correspondingly, the electromagnetic actuator  128  may not be able to produce controllable axial force and there may be no axial position sensor. 
     As described above,  FIG. 2  is a detailed cross-sectional view  190  of the front mechanical backup bearing  122  of the electric rotational machine system  100  of  FIG. 1 . Details of the axial spring  230  are further discussed in  FIGS. 3A to 3C . 
       FIG. 3A  is a detailed half cross-sectional view of a flat spring in loaded condition as implemented in  FIG. 2 . There is a gap  305  between the axial spring  230  and the resilient mount cover  235 . The gap  305  is created by a thickness difference in the resilient mount cover  235 . The insertion of a shim  234  between the axial spring  230  and the resilient mount cartridge  237  can be used to adjust a clearance  307 . The clearance  307  allows the axial spring  230  to be in direct contact with the outer race  212  without any interference with the resilient mount cartridge  237 . The axial spring  230  supports the outer race  212  by applying a pre-load compression onto the outer faces  221  of the outer race  212 . The pre-load compression associates to the clamping force discussed above. When the outer race  212  translates due to thermal expansion of the backup bearing inner races  211 , the axial spring  230  deflects outwards into the gap  305  to allow for the thermal expansion while maintaining a similar level of pre-load compression. In some instances when the thermal expansion causes excessive expansion (e.g., machine being overheated), the axial spring  230  can be stopped by the resilient mount cover  235  when the deflection has travelled across the gap  305 . The resilient mount cover  235  therefore acts as a hard stop for deflection of the axial spring  230  upon thermal expansion of the backup bearing inner race  211 . 
     In some implementations, the axial spring  230  is an annular plate having a suitable thickness, outer diameter, and inner diameter to provide sufficient stiffness for supporting the pre-load compression to the outer race  212 . In some implementations, the axial spring  230  is a wave spring that includes one or more layers of circular, wavy, flat wires. In some implementations, the axial spring  230  is a Belleville washer or spring, having a frusto-conical shape. Other types of axial springs are also contemplated and described in  FIGS. 4A-B . 
       FIG. 3B  illustrates the axial spring  230  prior to assembly (i.e., the resilient mount cover  235  has not yet been tightened to the end resilient mount cartridge  237 ). The original shape of the axial spring  230  may be tilted towards the front mechanical backup bearings  122  as illustrated. As the fastener  238  assembles the resilient mount cover  235  to the resilient mount cartridge  237 , the axial spring  230  elastically deforms into the position shown in  FIG. 3A . The elastic deformation allows the axial spring  230  to generate the pre-load compression to clamp the front mechanical backup bearings  122  in place.  FIG. 3C  illustrates the axial spring  230  being deflected as the thermal expansion of the front mechanical backup bearings  122  translates the outer race  212  outwards. 
       FIG. 4A  is a perspective view of an example spring  400  in accordance with the present disclosure.  FIG. 4A  is a perspective view of an example spring  400  having a circular profile resembling a washer. Spring  400  may have a certain conical curvature for providing pre-load compression. The stiffness of the spring  400  may be varied by using different materials, changing the outer diameter, the inner diameter, and the thickness of the spring  400 .  FIG. 4B  is a perspective view of another example spring  405  in accordance with the present disclosure. Spring  405  has fingers  407  that may be used to cover a larger outer diameter at a lower stiffness to allow for thermal expansion. Other implementations are possible and are within the scope of this disclosure. 
     The present disclosure describes embodiments of an axial spring for allowing thermal expansion in a bearing system. Other embodiments and advantages are recognizable by those of skill in the art by the forgoing description and the claims.
The present disclosure describes a mechanical backup bearing system arrangement to work in conjunction with non-contact magnetic bearings and capable of coping with thermal expansions of the bearing components during operations. Expansions or contractions of an inner or outer race of a bearing can be compensated using particular springs providing a low profile and a proper stiffness. An electric machine system includes a rotational portion and a stationary portion. The electric machine further includes a magnetic bearing configured to support the rotational portion to rotate within the stationary portion. A mechanical back-up bearing resides in a cavity between the rotational portion and the stationary portion. A flat spring is carried by the stationary portion and abutting the back-up bearing.