Patent Publication Number: US-2021179396-A1

Title: System and method for monitoring crane and crane having same

Description:
BACKGROUND 
     The following description relates generally to a crane and a system and method for monitoring the crane. 
     The rated capacity of a crane refers to a maximum total load the crane is designed to lift in a particular configuration. The particular configuration includes parameters which remain substantially constant during a lift operation, such as the weight of a counterweight and outrigger extension length, and parameters which may vary during the lift operation, such as an operating radius (i.e., the moment arm of the load suspended from the boom) and a swing angle (i.e., a rotational position of a boom relative to a reference point of a carrier unit of the crane in a horizontal plane). The operating radius varies with changes in boom length (for example, in response to extension or retraction of a telescoping boom) and lift angle (i.e., the angle between the boom and the horizontal plane). In general, as the operating radius increases, a load moment increases and the rated capacity decreases. Conversely, as the operating radius decreases, the load moment decreases and the rated capacity increases. To this end, load charts are provided which indicate the rated capacity at different operating radii and/or lift angles. 
     A conventional crane Rated Capacity Limiter (RCL) system is configured to monitor a current load lifted by the crane and the current operating radius, for example, based on information received from one or more crane sensors and/or operator input. For example, the conventional crane RCL system may determine the current load based at least in part on information received from a pressure sensor detecting hydraulic pressure in a lift cylinder supporting the boom. The current operating radius may be determined based at least in part on information received from a sensor detecting a length of the boom and a sensor detecting the lift angle of the boom. 
     The conventional crane RCL system is further configured to determine an operating condition of the crane and may control crane operations based on the operating condition. For example, the conventional crane RCL system may control the boom to prevent movement of the current load to an operating radius where the current load exceeds the rated capacity. 
     A mobile crane typically includes a plurality tires for rolling contact with a support surface such that the crane may be self-propelled for transport on a road or at a worksite. The mobile crane also includes outriggers which can be deployed to engage the ground, lift the tires from the ground and support the mobile crane during a lift operation. 
     It may be desirable to perform a lift operation for a relatively lightweight load without deploying the outriggers, such that the crane is supported on its tires during the lift operation. However, the crane may be susceptible to deflection in the direction of the load due to compression of the tires. Such deflection has the result of increasing the operating radius without changing a lift angle or boom length. Thus, the conventional RCL system does not detect the change in operating radius. Consequently, the conventional RCL system may compare the current load to a rated capacity in a load chart at a smaller operating radius than the current operating radius, which may affect accuracy of the comparison. 
     Accordingly, it is desirable to provide a crane and a system and method for the controlling crane in which deflection of a carrier unit is accounted for when monitoring the current load and the current operating radius. 
     SUMMARY 
     In one aspect, a crane includes a carrier unit having a chassis, tires connected to the chassis, a carrier deck and outriggers, the outriggers movable to a deployed condition in which the outriggers engage an underlying support surface and lift the tires from the support surface such that the outriggers support the carrier unit, and a retracted condition in which the outriggers are disengaged from the support surface and the tires are engaged with the support surface, such that the tires support the carrier unit. The crane further includes a superstructure mounted on the carrier unit, the superstructure having a telescoping boom, and a slope sensor operably connected to the carrier unit and configured to detect a pitch and/or a roll of the carrier unit during a lift operation. The crane also includes a system for monitoring a load lifted by the telescoping boom. The system is configured to determine the current load lifted by the telescoping boom, receive pitch and/or roll information of the carrier unit from the slope sensor, adjust coordinates of the crane in a coordinate system based on the pitch and/or roll information, determine a transformed operating radius using the adjusted coordinates, and compare the load lifted to a rated capacity at the transformed operating radius. 
     According to another aspect, a system is provided for monitoring a load lifted by a crane, the crane having a carrier unit and a superstructure mounted on the carrier unit, the superstructure having a telescoping boom. The system includes a processor and a non-transitory computer-readable storage medium configured to store program instructions and the processor is configured is interpret and execute the program instructions to determine a load lifted by the telescoping boom, receive pitch and/or roll information of the carrier unit from a slope sensor disposed on the carrier unit, adjust coordinates of the crane in a coordinate system based on the pitch and/or roll information, determine a transformed operating radius using the adjusted coordinates, and compare the load lifted to a rated capacity at the transformed operating radius. 
     In another aspect, a method is provided for monitoring a load lifted by a crane. The crane includes a carrier unit having a chassis, tires connected to the chassis, a carrier deck and outriggers, a superstructure mounted on the carrier unit, the superstructure having a telescoping boom. The crane also includes a slope sensor operably connected to the carrier unit and configured to detect a pitch and/or a roll of the carrier unit during a lift operation. The method includes determining a load lifted by the telescoping boom, receiving pitch and/or roll information of the carrier unit, adjusting coordinate of the crane in a coordinate system based on the pitch and/or roll information, determining a transformed operating radius using the adjusted coordinate, and comparing the load lifted to a rated capacity at the transformed operating radius. 
     Other objects, features, and advantages of the disclosure will be apparent from the following description, taken in conjunction with the accompanying sheets of drawings, wherein like numerals refer to like parts, elements, components, steps, and processes. 
    
    
     
       BRIEF DESCRIPTION OF THE DRAWINGS 
         FIG. 1  is a side view of a crane according to an embodiment; 
         FIG. 2  is a schematic partial system diagram of the crane of  FIG. 1  according to an embodiment; 
         FIG. 3  is a perspective view of a carrier unit of a crane according to an embodiment; 
         FIG. 4  is a diagram showing a geometric layout of a telescoping boom according to an embodiment; 
         FIG. 5  is another perspective view of a carrier unit of a crane according to an embodiment; 
         FIG. 6  is a diagram showing a geometric layout of a portion of a telescoping boom and a crane carrier unit according to an embodiment; 
         FIG. 7  is another diagram showing a geometric layout of a portion of a crane boom and a crane carrier according to an embodiment; and 
         FIG. 8  is a block diagram showing a method for monitoring a crane according to an embodiment. 
     
    
    
     DETAILED DESCRIPTION 
     While the present disclosure is susceptible of embodiment in various forms, there is shown in the drawings and will hereinafter be described one or more embodiments with the understanding that the present disclosure is to be considered illustrative only and is not intended to limit the disclosure to any specific embodiment described or illustrated. 
     Referring to  FIG. 1 , a crane  10  according to embodiments herein generally includes a carrier unit  20  and a superstructure  30  rotatably mounted on the carrier unit  20  and configured for rotation relative to the carrier unit  20 . The carrier unit  20  includes various crane components, such as a chassis  22 , one or more tires  24  connected to the chassis  22 , a carrier deck  26  and outriggers  28 . The chassis  22  supports the one or more tires  24 , the carrier deck  26  and the outriggers  28 , as well as other components such as a powertrain (not shown). The one or more tires  24  are configured for rolling engagement with the ground, a road, or similar support surface to facilitate rolling movement of the crane  10 . For example, the powertrain may provide torque to the one or more tires  24  to propel the crane  10  for movement along the support surface. The carrier deck  26  generally defines an upwardly facing top surface of the carrier unit  20 . 
     The outriggers  28  may be arranged in a deployed condition, in which the outriggers  28  are extended horizontally outward relative to the chassis  22  to one or more extension positions, and vertically to engage an underlying support surface. Continued vertical extension of the outriggers  28  may cause the outriggers  28  to lift the tires  24  from the support surface, such that the crane  10  is supported on the outriggers  28 . The outriggers  28  may also be arranged in a retracted condition, in which the outriggers  28  are retracted horizontally inward toward the chassis  22  and vertically to disengage the support surface. Accordingly, in the retracted condition, the tires  24  may engage the support surface and the crane  10  may be supported on the tires  24 . In an embodiment, horizontal extension and retraction of the outriggers may be accommodated by a telescoping box and arm assembly (not shown), and vertical extension and retraction may be accommodated by a jack (not shown) operably connected to the telescoping box and arm assembly, for example, at or near a distal end of the arm. 
     The superstructure  30  also includes various crane components, such as a rotating bed  32  rotatably mounted on the carrier unit  20 , an operator&#39;s cab  34 , a counterweight assembly  36  and a telescoping boom  38 . The rotating bed  32  is rotatably mounted to the carrier unit  20  via a bearing structure and is configured to be driven in a first rotational direction, or alternatively, a second rotational direction opposite to the first rotational direction, about a generally vertical axis. The rotating bed  32  directly or indirectly supports the operator&#39;s cab  34 , the counterweight assembly  36  and the telescoping boom  38 , as well as other crane components such as one or more hoists (not shown), such that these components are rotatable in the first and second rotational directions with the rotating bed  32 . The operator&#39;s cab  34  may include a user interface for allowing a crane operator to interact with a control system of the crane  10  as discussed further below, for example, to control operations of one or more crane components. The counterweight assembly  36  includes one or more weight units supported on a frame. The weight units may be installed and removed from the frame in a desired manner to provide a selected counterweight. 
     The telescoping boom  38  includes a base section  40  pivotably mounted on the rotating bed  32  for movement through a vertically oriented range of lift angles and one or more telescoping sections  42  configured for movement out of and into the base section  40  generally along a boom axis to change the boom length LG. One or more hoists (not shown) are configured to wind up and pay out a flexible member  44 , such as a rope or cable. A lifting appliance  46 , such as a hook block, is connected to a free end of the flexible member  44  and is suspended from a free end of the telescoping boom  38 . A lift cylinder  48  is pivotably connected directly or indirectly between the base section  40  and the rotating bed  32 . The lift cylinder  48  is operable to raise or lower the telescoping boom  38  through the range of lift angles. The rotating bed  32  is rotatable in the first and second rotational directions to cause rotation of the telescoping boom  38  through a range of horizontally oriented swing angles. 
     Referring now to  FIGS. 1 and 2 , the crane  10  further includes a control system  50 , sometimes referred to as a Crane Control System (CCS). The control system  50  may be implemented as one or more computing devices located at the crane  10 , remote from and communicably connected to the crane  10 , or a combination thereof. The control system  50  is operably connected to various crane components (including actuators of the crane components) of the carrier unit  20  and the superstructure  30  and may control operations of one or more of the crane components. For example, the control system  50  may control movements of one or more crane components, including starting, stopping, preventing and allowing movements of the crane component and/or controlling a speed, acceleration and/or deceleration of the crane component. 
     According to an embodiment, the control system  50  includes a crane controller  52 , a rated capacity limiter (RCL)  54  and a working range limiter (WRL)  56 . The crane controller  52  may be configured to send and/or receive control signals to various crane components to control movements of the crane components. 
     The RCL  54  is a system that generally operates to monitor a current load lifted (i.e., a hook load) by the telescoping boom  38  of the crane  10  relative to the rated capacity of the crane  10  at an operating radius (i.e., a hook radius). For example, the RCL  54  may determine the current load lifted and the operating radius based on information received from one or more crane sensors, user input, stored data and/or combinations thereof. The RCL  54  may identify a rated capacity at an operating radius, for example, from a stored load chart which includes rated capacities at different operating radii or lift angle and boom length combinations. The RCL  54  may compare the current load lifted by the crane to the rated capacity at the operating radius and control operations of one or more crane components based on the comparison. For example, the RCL  54  may control movements of the telescoping boom  38  (i.e., boom-up, boom-down, swing-left, swing-right, telescope-in and/or telescope-out movements) based on the comparison of the current load lifted to the rated capacity at the operating radius. In some embodiments, the RCL  54  may provide a control signal for controlling crane component movements directly to the crane component. In other embodiments, the RCL  54  may provide the control signal via the controller  52  to control movements of the crane component. 
     The WRL  56  is a system that generally operates to monitor a position of a crane component relative to a position of a restricted volume. For example, the WRL  56  may determine the position of the crane component based on information received from one or more crane sensors, user input, stored data and/or combinations thereof. The WRL  56  may identify the restricted volume, for example, based on stored position information, such as position information included in a worksite model, information received from one or more sensors (including crane sensors and/or external sensors communicably connected to the WRL  56 ), information received via user input and/or combinations thereof. The restricted volume may represent an obstacle, such as a building, at a worksite and define a volume in which operation of one or more crane components should be avoided. Accordingly, the WRL  56  may compare the crane component position information to the restricted volume position information and control operations of the crane component based on the comparison. For example, the WRL  56  may control movements of the telescoping boom  38  (i.e., boom-up, boom-down, swing-left, swing-right, telescope-in and/or telescope-out movements) based on the comparison of telescoping boom position information to the restricted volume position information. In some embodiments, the WRL  56  may provide a control signal for controlling crane component movements directly to the crane component. In other embodiments, the WRL  56  may provide the control signal via the controller  52  to control movements of the crane component. 
     The control system  50  further includes computer components  100 , such as a processor  58 , a memory device  60 , a storage device  62 , a communication device  64 , an input device  66  and/or an output device  68  which may be connected to one another, for example, on a bus (not shown). In an embodiment, the computer components  100  may be operably connected to the controller  52 , the RCL  54  and the WRL  56 . However, it will be appreciated that the computer components  100  may be implemented in each of the controller  52 , the RCL  54  and the WRL  56  or distributed among the controller  52 , the RCL  54  and the WRL  56 . It will be further appreciated that although shown independently, any of the controller  52 , the RCL  54  and the WRL  56  may be integrated with another one or more of the controller  52 , the RCL  54  and the WRL  56  and provided as a single unit configured to perform the operations of the individual components described above. 
     In an embodiment, the processor  58  may be a computer processor, such as a microprocessor, configured to interpret and execute program instructions. The processor  58  is further configured to effect various operations (including movements) of one or more crane components in response to executing the program instructions. For example, the processor  58  may cause the controller  52  to provide a control signal for controlling movements of the telescoping boom  38 . It will be appreciated that the operations of the controller  52 , the RCL  54  and the WRL  56  described herein may be carried out or otherwise effected by the processor  58  in response to executing program instructions. 
     The memory device  60  may be a non-transitory computer-readable storage medium configured to store information, such as the program instructions to be executed by the processor  58 . The memory device  60  may be, for example, Random-Access Memory (RAM), Read-Only Memory (ROM) or other type of suitable memory device for storing information and/or executable program instructions. The storage device  62  is configured to store, for example, information, software, executable program instructions and the like which may, for example, be accessed or referenced by the processor  58 . The storage device  62  may also store information collected during operation of the crane  10 , such as information received by the control system  50  from one or more sensors or user input. In one embodiment, one or more load charts may be stored in the storage device  62  and/or memory device  60  and can be accessed or referenced, for example, by the RCL  54 . The storage device  62  may be a non-transitory computer-readable storage medium and may include, for example, a hard disk and an associated drive and/or other similar, suitable storage devices and associated drives. 
     The communication device  64  is configured to transmit and/or receive information from/to the control system  50  and/or between components of the control system  50 . For example, the communication device  64  may be provided as a communication interface having a transceiver or transceiver-like component to transmitting information to, and/or receiving information from, one or more other devices, such as other communication-enabled devices, components, sensors and the like. 
     The input device  66  may include, or form part of, a user interface configured to receive information from a user, such as the crane operator. The input device  66  may include, or be operably connected to, one or more operator controls by operation of which the user may provide information to the input device  66 . The one or more operator controls may include, for example, a lever, joystick, knob, button, dial, switch, keyboard, keypad, pointer device, touch screen display, one or more sensors such as a biometric sensor, audio sensor, light sensor and the like, including various combinations thereof. The controller  52  may send a control signal to control movements of a crane component in response to information received by the input device  66 . 
     The output device  68  may also include, or form part of, a user interface configured to provide information to a user, such as the crane operator. The output information may be provided visually, for example, on a display screen or with one or more lights (e.g., LEDs), audibly, for example by one or more audio speakers, and/or by way of haptic or vibratory feedback or alerts, for example, at an operator control. In some embodiments, the input device  66  and the output device  68  may be provided as a single device or include components provided as a single device, for example, a display screen or touch screen display. The output information may serve as an alert or an alarm. 
     The crane components may be operated to conduct various movements by controlling operations of corresponding component actuators. To this end, the control system  50  may be operably connected to one or more component actuators to control operations of the component actuators. For example, the control system  50  may be operably connected to outrigger actuators  70  for controlling movements (e.g., horizontal extension and retraction and vertical extension and retraction) of the outriggers  28 ; a rotating bed actuator  72  for controlling movements (e.g., rotation in the first and second rotational directions) of the rotating bed  32  to cause swing-left and swing-right movements of the telescoping boom  38  through the range of swing angles; a boom actuator  74  for controlling movements (e.g., telescope-out and telescope-in) of the telescoping sections  42  of the telescoping boom  38  to increase or decrease the boom length; and a lift cylinder actuator  76  for controlling movements (e.g., extension and retraction) of the lift cylinder  48  to cause boom-up and boom-down movements of the telescoping boom  38  through a range of lift angles. 
     Further, the control system  50  may be operably connected to one or more crane sensors configured to provide information to the control system  50  about the crane, a crane component, crane surroundings, the environment, atmospheric conditions (e.g., temperature, wind speed, and the like), and/or other information which may affect crane operations. The information may be provided as a parameter value or information from which a parameter value may be derived. In an embodiment, the crane sensors may include one or more tire sensors  78  configured to provide tire pressure information of one or more tires  24 ; one or more slope sensors  80  configured to provide slope information (e.g., pitch information and/or roll information) of the crane  10 ; one or more outrigger sensors  82  configured to provide outrigger extension and/or pressure/load information of the outriggers  28 ; one or more swing angle sensors  84  configured to provide swing angle information of the rotating bed  32  and/or the telescoping boom  38 ; one or more boom length sensors  86  configured to provide boom length information of the telescoping boom  38 ; one more lift angle sensors  88  configured to provide lift angle information of the telescoping boom  38 ; and one or more lift cylinder pressure sensors  90  configured to provide lift cylinder pressure information of the lift cylinder  48 . Other sensors may be implemented as well, for example, a lift cylinder angle sensor for providing lift cylinder angle information to the control system  50 , and/or additional flow, pressure, load, proximity sensors and the like. It will be appreciated that although  FIG. 2  shows various crane sensors associated with particular crane components, the crane sensors may be mounted or positioned with different crane components suitable for providing the intended information described herein. 
     Referring now to  FIGS. 2 and 3 , the RCL  54  may determine a current load lifted by the crane  10 . In an embodiment, the RCL  54  may determine the load lifted by the crane  10  based, at least in part, on information received from one or more crane sensors. For example, the RCL may receive lift cylinder pressure information from the one or more lift cylinder pressure sensors  90  and determine the load lifted by the crane  10  based on the lift cylinder pressure information. In one embodiment, the RCL  54  may calculate the current load lifted based on a formulaic relationship between the lift cylinder pressure and the current load lifted. Alternatively, or in addition, the RCL  54  may retrieve the current load lifted from the memory device  60  or storage device  62  based on known load values corresponding to different lift cylinder pressures or based on user input information, for example, when the load is known. 
     The RCL  54  may also determine an operating radius of the current load lifted by the crane  10  based, at least in part, on information received from one or more crane sensors. For example, the RCL  54  may receive lift angle information from one or more lift angle sensors  88  and boom length information from one or more boom length sensors  86  and determine the operating radius based on the lift angle information and the boom length information. In one embodiment, the RCL  54  may calculate the operating radius based on formulaic relationship between the lift angle, boom length and operating radius. Alternatively, or in addition, the RCL  54  may retrieve the operating radius from the memory device  60  or storage device  62  based on known operating radii values corresponding to different lift angles and boom lengths. 
     The operating radius of the load lifted by the crane  10  may further be determined based on a pitch and/or roll of the crane  10 . The pitch of the crane  10  generally refers to rotation of the carrier unit  20  (e.g., chassis  22 , carrier deck  26 ) and/or rotating bed  32  about an axis extending laterally across the crane  10 . Thus, the pitch of the crane  10  results in an upward or downward deflection of a front end or a rear end of the carrier deck  26 . The roll of the crane  10  generally refers to rotation of the carrier unit  20  (e.g., chassis  22 , the carrier deck  26 ) and/or the rotating bed  32  about an axis extending longitudinally along the crane  10 . Thus, the roll of the crane  10  results in an upward or downward deflection of the left or right lateral sides of the carrier deck  26 . The RCL  54  may receive pitch information and roll information (referred to collectively as “slope information”) from one or more crane sensors. For example, the RCL  54  may receive information regarding deflection of the carrier unit  20  at different locations from one or more crane sensors and may then calculate slope information based on information regarding deflection of the carrier unit  20 . 
     The control system  50  (including the RCL  54 ) may receive slope information from one or more slope sensors  80 , mounted on the carrier unit  20 , for example, the chassis  22  or carrier deck  26 , or on the superstructure  30 , for example, on the rotating bed  32 . During movement of the outriggers  28  to the deployed condition, such that the tires  24  are lifted from the support surface and the crane  10  is supported on the outriggers  28 , the slope sensor  80  may provide pitch and roll information to the control system  50  to allow for leveling of carrier unit  20 , for example, the carrier deck  26 . For example, the control system  50  may control vertical extension of one or more outriggers  28  to effect a change in pitch and/or roll of the carrier deck  26  until the carrier deck  26  is substantially level. The crane  10  may perform a lift operation with the outriggers  28  deployed. During such a lift operation, pitch and/or roll of the carrier deck  26  is expected to be relatively small and may not substantially affect the operating radius. 
     However, in some scenarios, it may be beneficial or permissible to perform a lift operation with the outriggers  28  in the retracted condition, such that the crane  10  is supported on the tires  24 . Such a lift operation is commonly referred to as an “on-rubber” lift operation. Generally, during an on-rubber lift operation, the carrier deck  26  is expected to pitch and/or roll to a greater extent than during a lift operation performed with deployed outriggers  28 , due to deformation of the tires  24 . Pitch and/or roll of the crane  10  during the on-rubber lift operation may cause an increase in operating radius, and consequently, may cause a decrease in the rated capacity (i.e., maximum permissible load at an operating radius). 
     According to embodiments herein, the RCL  54  is configured to determine an operating radius further based, at least in part, on the slope information (i.e., pitch information and/or roll information). In one embodiment, the slope information may be received by the RCL  54  from the slope sensor  80 . The RCL  54  may monitor the current load lifted at the operating radius determined based at least in part on the slope information. For example, the RCL  54  may compare the current load lifted to a rated capacity of the of the crane  10  at the operating radius determined based at least in part on the slope information. Further still, the RCL  54  may control operations of one or more crane components, such as the telescoping boom  38 , based on the comparison of the current load lifted to the rated capacity at the operating radius determined based at least in part on the slope information. For example, the RCL  54  may reduce or limit a speed, and/or prevent or limit movement of the telescoping boom  38  in a direction which may cause the rated capacity to approach the current load lifted, within a predetermined threshold. 
     With reference to  FIGS. 4 and 5 , the RCL  54  is configured to provide a coordinate system XYZ for the carrier unit  20 . The RCL  54  may determine coordinates for a plurality of points in the coordinate system XYZ. For example, the RCL  54  may determine X and Z coordinates for three points u, v, w in the coordinate system XYZ which may correspond to predetermined points on the crane  10  as shown in  FIG. 4 . For example, point ‘u’ may correspond to a base pivot axis of the telescoping boom  38  and may serve as an origin for the coordinate system XYZ. Points ‘v’ and ‘w’ may also correspond to points in a geometric layout of the telescoping boom  38 . For example, point ‘v’ may correspond to a pivot axis formed by a connection of the lift cylinder  48  to the base section  40  of the boom  38 , and point ‘w’ may correspond to a base pivot axis of the lift cylinder  48 . 
     Referring to  FIGS. 4 and 6 , the RCL  54  may transform the coordinates based on the slope information. For example, the RCL  54  may determine a lean angle of the crane  10 , such as a lean angle of the carrier unit  20 , based on the slope information. In an embodiment, the lean angle may be determined based on a pitch angle and a roll angle, which may be determined based on the slope information. The coordinates may be adjusted using the lean angle. A lean angle for the actual position of the telescoping boom  28  may be determined as well. With a known lean angle, the coordinate transformations may account for the pitch and the roll of the crane  10  about a point on the carrier unit  20 . 
     General coordinates of points located on the telescoping boom  38 , or related components (e.g., the lift cylinder  48 ) may be translated to have the carrier unit  20  rotation point (i.e., the point on the carrier unit  20  about which the carrier unit  20  pitches and/or rolls) as the origin of the coordinate system. The coordinates may be rotated about the Y-axis using the lean angle. The coordinates may then be translated back to have the origin at the original location, i.e., at the base pivot axis (point ‘u’) of the telescoping boom  38 . Such operations may be performed by the RCL  54 . 
     Alternatively, with reference to  FIG. 7 , the RCL  54  may transform the coordinates of the of the points using a rotational coordinate system transformation for the base pivot axis (at point ‘u’) of the telescoping boom  38 . Thus, the base pivot axis of the telescoping boom  38  may remain at the origin of the coordinate system. However, the reference point ‘w’ does shift and the lift cylinder angle is altered. 
     Accordingly, in the embodiments above, the RCL  54  may determine an adjusted, or transformed operating radius based on the slope information, such that the transformed operating radius takes into account a pitch and/or roll of the crane  10 , for example, during an on-rubber lift operation. 
     The RCL  54  may additionally be configured to store, for example, crane geometry information, crane weight information, or both, and may use such information to determine the transformed operating radius. For example, the crane geometry information may be used by the RCL  54  to create a geometric model of the crane  10  or a crane component, such as the telescoping boom  38 . The crane geometry information may include, for example, various dimensions, distances between components, coordinate system information, coordinate information of reference points and/or crane components, and the like. The crane geometry information may be provided, for example, based on sensor information and/or user input. Weight information may include, for example, a weight profile of the crane  10 , a weight of the load lifted by the crane, weights of various crane components and the like. 
     Referring again to  FIG. 4 , a geometric layout of the telescoping boom  38  in XZ plane of an XYZ coordinate system includes the reference points ‘u’, ‘v’ and ‘w.’ In addition, the telescoping sections  42  are shown each having a first end A 1 , A 2  . . . A i  at a proximal end and a second end B 2 , B 3  . . . B i+1  at a distal end. A length L 1 , L 2  . . . L i  of each telescoping section  42  is the distance between the second end B 2 , B 3  . . . B i+1  and the first end A 1 , A 2  . . . A i  of the respective telescoping sections  42 . The base section  40  is shown having a second end B 1  at a distal end and having a length L 0 . In addition, a length of the base section  40  to the pivot connection axis at reference point ‘v’ is shown as L z . A length of the telescoping boom  38  is shown as L G . A lift angle of the telescoping boom  38  is shown as β 0 . A lift cylinder angle is shown as α z . 
     Accordingly, with further reference to  FIG. 4 , the following coordinates may be determined: 
         X   u =0, where:         X u : Horizontal (x-axis) position of the reference point ‘u’;       
         X   w   =h   B , where:         X w : Horizontal (x-axis) position of the reference point ‘w’; and   h B : Horizontal distance between the reference point ‘u’ and the reference point ‘w’; and       
         X   v   =L   z ·cos β 0 +( e   z   +e   f )·sin β 0 , where:
         X v : Horizontal (x-axis) position reference point ‘v’;   L z : Length of the base section  40  from the origin to the reference point ‘v’;   β 0 : Lift angle of the telescoping boom  38 ;   e z : Perpendicular distance between reference point ‘v’ and the base section  40  of the telescoping boom  38 ; and   e f : Perpendicular distance between the base section  40  the telescoping boom  38  and the reference point ‘u’.       

     Still referring to  FIG. 4 , the following ‘Z’ coordinates are determined: 
         Z   u =0, where:         Z u : Vertical (Z-axis) position of the reference point ‘u’;       
         Z   w   =−h   A , where:         Z w : Vertical (Z-axis) position of the reference point ‘w’; and   h A : Vertical distance between the reference point ‘u’ and the reference point ‘w’; and       
         Z   v   =L   z ·sin β 0 ·( e   z   +e   f )·cos β 0 , where:
         Z v : Vertical (Z-axis) position of the reference point ‘v’;       

     According to an embodiment, the lift cylinder angle α z  may be determined as: 
     
       
         
           
             
               
                 If 
                  
                 
                     
                 
                  
                 
                   X 
                   v 
                 
               
               &gt; 
               
                 
                   X 
                   w 
                 
                  
                 
                   : 
                 
                  
                 
                     
                 
                  
                 
                   α 
                   Z 
                 
               
             
             = 
             
               
                 tan 
                 
                   - 
                   1 
                 
               
                
               
                 ( 
                 
                   
                     
                       Z 
                       v 
                     
                     - 
                     
                       Z 
                       w 
                     
                   
                   
                     
                       X 
                       v 
                     
                     - 
                     
                       X 
                       w 
                     
                   
                 
                 ) 
               
             
           
         
       
       
         
           
             
               
                 If 
                  
                 
                     
                 
                  
                 
                   X 
                   w 
                 
               
               &gt; 
               
                 
                   X 
                   v 
                 
                  
                 
                   : 
                 
                  
                 
                     
                 
                  
                 
                   α 
                   Z 
                 
               
             
             = 
             
               π 
               - 
               
                 
                   tan 
                   
                     - 
                     1 
                   
                 
                  
                 
                     
                 
                  
                 
                   ( 
                   
                     
                       
                         Z 
                         v 
                       
                       - 
                       
                         Z 
                         w 
                       
                     
                     
                       
                         X 
                         w 
                       
                       - 
                       
                         X 
                         v 
                       
                     
                   
                   ) 
                 
               
             
           
         
       
     
       FIG. 5  is another perspective view of the carrier unit  20  according to an embodiment. In  FIG. 5 , the carrier unit  20  may be oriented in the first coordinate system XYZ. In an embodiment, the roll angle convention may be based on a right-handed positive direction of the carrier X-axis direction. A positive roll angle may lower the right-handed side of the crane and raise the left-handed side of the crane. A positive pitch angle may be based on the right-handed positive direction for the carrier Y-axis direction. A positive pitch angle may lower the front of the carrier unit  20  and may raise the rear of the carrier unit  20 . The X and Z coordinates may correspond to a midplane of the telescoping boom  38 . 
     A lean angle may be determined to adjust the coordinates in the first coordinate system XYZ, such as the X, Z coordinates in the midplane of the telescoping boom  38 . A unit vector near the X axis direction (“X unit vector”) based on the effect of the pitch angle may be determined. A unit vector near the Y axis direction (“Y unit vector”) based on the effect of the roll angle may be determined as well. A maximum lean angle may be determined from a Z unit vector based on the X unit vector and the Y unit vector. The maximum lean angle may then be determined based on the Z unit vector. 
     The lean angle may be identified as: 
     ω L    
     The X unit vector may be identified as: 
     
       
         
           
             
               
                 
                   X 
                   ^ 
                 
                 ′ 
               
               = 
               
                  
                 
                   
                     
                       
                         cos 
                          
                         
                             
                         
                          
                         
                           ω 
                           P 
                         
                       
                     
                   
                   
                     
                       0 
                     
                   
                   
                     
                       
                         
                           - 
                           s 
                         
                          
                         in 
                          
                         
                             
                         
                          
                         
                           ω 
                           P 
                         
                       
                     
                   
                 
                  
               
             
             , 
           
         
       
     
     where: 
     ω p : Pitch angle 
     The Y unit vector may be identified as: 
     
       
         
           
             
               
                 
                   Y 
                   ^ 
                 
                 ′ 
               
               = 
               
                  
                 
                   
                     
                       0 
                     
                   
                   
                     
                       
                         cos 
                          
                         
                             
                         
                          
                         
                           ω 
                           R 
                         
                       
                     
                   
                   
                     
                       
                         sin 
                          
                         
                             
                         
                          
                         
                           ω 
                           R 
                         
                       
                     
                   
                 
                  
               
             
             , 
           
         
       
     
     where: 
     ω R : Roll angle 
     The maximum lean angle may be determined from the following vector: 
         ′= {circumflex over (X)}′×Ŷ′ 
 
     The maximum lean angle may then become the following: 
       ω cos −1 ( {circumflex over (Z)}′·{circumflex over (k)} ) L,max  
 
     The Z unit vector may be projected to the XY plane as a projected Z unit vector  118  (see  FIG. 5 ). A projection  120  of the telescoping boom  38  to the XY plane may be determined based a swing (or slew) angle of the telescoping boom  38 . The lean angle for the actual position of the telescoping boom  38  may then be determined based on the maximum lean angle, the projected Z unit vector  118  and the projected boom  120  in the XY plane. 
     The projection  118  of the Z unit vector to the XY plane may be determined as follows: 
     
       
         
           
             
               
                 Z 
                 ⇀ 
               
               ″ 
             
             = 
             
                
               
                 
                   
                     
                       
                         
                           Z 
                           ⇀ 
                         
                         ′ 
                       
                        
                       x 
                     
                   
                 
                 
                   
                     
                       
                         
                           Z 
                           ⇀ 
                         
                         ′ 
                       
                        
                       y 
                     
                   
                 
                 
                   
                     0 
                   
                 
               
                
             
           
         
       
     
     The projection  120  of the telescoping boom  38  to the XY plane may be determined as follows: 
     
       
         
           
             
               
                 B 
                 ^ 
               
               = 
               
                  
                 
                   
                     
                       
                         cos 
                          
                         
                             
                         
                          
                         α 
                       
                     
                   
                   
                     
                       
                         
                           - 
                           sin 
                         
                          
                         
                             
                         
                          
                         α 
                       
                     
                   
                   
                     
                       0 
                     
                   
                 
                  
               
             
             , 
           
         
       
     
     where: 
     α: Swing angle 
     The lean angle for the actual position of the telescoping boom  38  may then become the following: 
       ω L =ω( {circumflex over (Z)}″·{circumflex over (B)} ) L,max  
 
     Referring now to  FIG. 6 , with the lean angle known, coordinate transformations may be used to account for the pitch and roll of the carrier unit  20  (and the crane  10 ). The crane  10  may rotate about a point on the carrier unit  20 , for example, at a horizontal distance h c  from the Z-axis. The point may be shown at a vertical distance (h p2d  in  FIG. 6 ). In one embodiment, the vertical distance may correspond to the distance from the base pivot axis ‘u’ of the telescoping boom  38  to the carrier deck  26 . The telescoping boom base section  40  elevation angle may be preserved when accounting for the lean effects because a separate sensor may be used to detect the elevation angle. Point ‘v’ may be a position of the boom, and not the turntable. The base pivot axis at point ‘u’ would shift. Thus, adjusted coordinates may then be determined. 
     The coordinates may be adjusted as follows: 
         X   v   =X   u   +L   z ·cos β 0 +( e   z   +e   f )·sin β 0  
 
         Z   v   =Z   u   +L   z ·sin β 0 −( e   z   +e   f )·cos β 0  
 
         X   A1   =X   u +( L   0   −e   1 )·cos β 0   +e   f ·sin β 0  
 
         X   B1   =X   u   +L   0 ·cos β 0   ·e   f ·sin β 0  
 
         Z   A1   =Z   u +( L   0   −e   1 )·sin β 0   ·e   f ·cos β 0  
 
         Z   B1   =Z   u   +L   0 ·sin β 0   −e   f ·cos β 0  
 
     In an embodiment, a general coordinate of a point on the boom system may have X and Z coordinates. The coordinates may be translated to have the carrier rotation point (see  FIG. 6 ) as the origin based on the general coordinate of a point on the telescoping boom system and the coordinate for the carrier rotation point. The coordinates may be rotated about the Y-axis based on the lean angle and the translated coordinates. The coordinates may then be translated back to have the origin at the original locations, i.e., where the boom base pivot axis ‘u’ originally was. 
     The following may indicate the general coordinate of a point on the boom system: 
     
       
     
     The coordinates may be translated to have the carrier rotation point as the origin, in the following manner: 
         ′= =   rot , where:
 
     
       
         
           
             
               
                 R 
                 ⇀ 
               
               rot 
             
             = 
             
                
               
                 
                   
                     
                       h 
                       c 
                     
                   
                 
                 
                   
                     0 
                   
                 
                 
                   
                     
                       - 
                       
                         h 
                         lean 
                       
                     
                   
                 
               
                
             
           
         
       
     
     The coordinates may be rotated about the Y-axis using the following (the lean angle calculated earlier may utilized): 
     
       
         
           
             
               
                 R 
                 ⇀ 
               
               ″ 
             
             = 
             
               
                 
                   R 
                   ⇀ 
                 
                 ′ 
               
               · 
               
                  
                 
                   
                     
                       
                         cos 
                          
                         
                             
                         
                          
                         
                           ω 
                           L 
                         
                       
                     
                     
                       0 
                     
                     
                       
                         sin 
                          
                         
                             
                         
                          
                         
                           ω 
                           L 
                         
                       
                     
                   
                   
                     
                       0 
                     
                     
                       1 
                     
                     
                       0 
                     
                   
                   
                     
                       
                         
                           - 
                           s 
                         
                          
                         in 
                          
                         
                             
                         
                          
                         
                           ω 
                           L 
                         
                       
                     
                     
                       0 
                     
                     
                       
                         cos 
                          
                         
                             
                         
                          
                         
                           ω 
                           L 
                         
                       
                     
                   
                 
                  
               
             
           
         
       
     
     The coordinates may be translated back to have the origin at the original locations (where the boom pivot originally was) as follows: 
         ′″= ″+   rot  
 
     With further reference to  FIG. 6 , coordinates of the telescoping boom  38  may be transformed in manner described above, and the transformed telescoping boom  38 ′ is shown in broken lines, taking into account the slope information. In addition, the transformed operating radius is shown at R′, while the original operating radius is shown at R. The transformed reference points u′, v′ and w′ are shown in  FIG. 6  taking into account the slope information. In an on-rubber lifting operation, the RCL  54  may measure an operating radius from a center line of rotation of the superstructure, which may have shifted in response to a pitch and/or roll of the carrier unit  20 . The RCL  54  may determine the operating radius during an on-rubber lifting operation in the manner described above. For example, the coordinates of different points on the crane may be adjusted to account for a pitch and/or roll of the carrier unit  20 . 
       FIG. 7  is a diagram showing a geometric layout of a portion of the telescoping boom  38  and the carrier unit  20  according to an embodiment. With reference to  FIG. 7 , another approach to account for the lean during an on-rubber lifting operation may be to use a rotational coordinate system transformation for the boom pivot. In such an approach, the boom pivot remains at the origin. However, point ‘w’ does shift and the angle α z  is altered. The change in angle may affect the FBD of the boom system that it may be seen to improve predicted values. 
     Referring to  FIG. 8 , according to an embodiment, a method  800  for monitoring a load lifted by a crane may include, at  810 , determining a load lifted by a telescoping boom  38  of the crane  10 , at  820 , receiving pitch and/or roll information of a carrier unit  20  of the crane  10 , for example, from a slope sensor  80 , and at  830 , adjusting coordinates of the crane  10  in a coordinate system based on the pitch and/or roll information. At  840 , the method may further include determining a transformed operating radius R′ using the adjusted coordinates, and at  850 , comparing the load lifted to a rated capacity at the transformed operating radius R′. 
     Accordingly, in the embodiments above, the RCL  54  may determine an operating radius (also referred to as a transformed operating radius R′) of a crane  10 , for example, during an on-rubber lift operation using pitch and/or roll information, i.e., slope information, received from the slope sensor  80 . In one embodiment, the transformed operating radius R′ may refer to an operating radius R that has been adjusted to account for pitch and/or roll of the crane  10 . The pitch and/or roll information may be indicative of a pitch and/or roll of the carrier unit  20 . The pitch and/or roll information may also be indicative of a pitch and/or roll of the superstructure  30 . 
     The RCL  54  may transform coordinates of the crane  10  based on the pitch and/or roll information from the slope sensor  80 , to account for the pitch and/or roll of the crane  10 . By accounting for the pitch and/or roll of the crane  10 , the RCL  54  may determine the transformed operating radius of the crane  10  during, for example, an on-rubber lift operation. 
     In the manner above, the RCL  54  may monitor the load lifted by the crane  10  and determine the operating condition (for example a load utilization) of the crane  10  during the on-rubber lifting operation based on a comparison of the load lifted by the crane  10  to the rated capacity at the transformed operating radius R′. That is, the RCL  54  may use an operating radius determined based on the pitch and/or roll information received from the slope sensor  80  to monitor the load lifted by the crane  10  and determine the operating condition of the crane. 
     It is understood that the relative directions described above, e.g, “upward,” “downward,” “upper,” “lower,” “above,” “below,” are used for illustrative purposes only and may change depending on an orientation of a particular component. Accordingly, this terminology is non-limiting in nature. In addition, it is understood that one or more various features of an embodiment above may be used in, combined with, or replace other features of a different embodiment described herein. 
     All patents referred to herein, are hereby incorporated herein in their entirety, by reference, whether or not specifically indicated as such within the text of this disclosure. 
     In the present disclosure, the words “a” or “an” are to be taken to include both the singular and the plural. Conversely, any reference to plural items shall, where appropriate, include the singular. 
     From the foregoing it will be observed that numerous modifications and variations can be effectuated without departing from the true spirit and scope of the novel concepts of the present invention. It is to be understood that no limitation with respect to the specific embodiments illustrated is intended or should be inferred. The disclosure is intended to cover by the appended claims all such modifications as fall within the scope of the claims.