Patent Publication Number: US-9845580-B2

Title: Compaction system including articulated joint force measurement

Description:
TECHNICAL FIELD 
     The present disclosure relates generally to compaction systems and, more particularly, to a surface material compaction system including force measurement through an articulated joint and a controller configured to determine compaction performance of the compaction system based at least in part on the measured articulated joint force. 
     BACKGROUND 
     Compaction systems and machines incorporating compaction systems are known for compacting surface materials to increase a density or a stiffness of the surface material. Examples of applications where surface compaction is desired include construction sites to avoid further natural settling of the ground, landfill sites where compaction of the landfill waste into a minimum volume is desired, and asphalt roads and parking lots to avoid further settling of the asphalt, and therefore avoid future cracking of the road or parking lot. 
     The amount of compaction of these materials may be monitored to determine when the material is compressed to a desired density or stiffness. And in the past, various methods for determining an amount of compaction have been employed. For example, direct measurements of material density may be performed at either random or predetermined locations. The measurements may be made by removing core samples of the material for density measurements, or by sand or water displacement devices. Alternatively, the measurements may be made by some means which does not disturb the material, such as by nuclear gauges, electromagnetic measurement devices, and the like. 
     The above-noted methods for determining the density or stiffness of the material being compacted only provide indications of density at the sample locations chosen for testing. In addition, the above-noted methods require additional time and work by the persons performing the tests, which may increase costs and reduce efficiency of the compaction process. Furthermore, the methods discussed above which disturb portions of the compacted area are not desirable in some situations, for example, when compacting blacktop in a parking lot, as the disturbance of the surface material may adversely affect the finished product. 
     U.S. Pat. No. 6,973,821 (“the &#39;821 patent”), entitled “Compaction Quality Assurance Based Upon Quantifying Compactor Interaction with Base Material,” describes effective apparatus and methods for on-board determination of compaction quality based upon a sinkage deformation interaction between the compactor and the base material. One strategy described by the &#39;821 patent includes monitoring an energy interaction between the compactor and the base material. The &#39;821 patent further states that propelling power corresponds to the compactive energy delivered by the compactor to the base material, and may be used as a basis for monitoring the above-noted energy interaction. 
     However, the apparatus and methods described in the &#39;821 patent may benefit from new apparatus and methods to further reduce uncertainty and to promote accuracy of the on-board determination of compaction quality. Accordingly, aspects of the present disclosure address the above-noted opportunities for improvement in the determination of compaction quality and/or other challenges in the art. 
     It will be appreciated that this background description has been created to aid the reader, and is not a concession that any of the indicated problems were themselves known previously in the art. 
     SUMMARY 
     According to an aspect of the disclosure, a compaction system comprises a first frame; a second frame coupled to the first frame via an articulated joint; a first propulsion device operatively coupled to the first frame via a first propulsion motor, the first propulsion device being configured to propel the compaction system over a work surface in response to a power applied by the first propulsion motor; a compaction drum operatively coupled to the second frame, the compaction drum being configured to compact the work surface via rolling engagement with the work surface; a force sensor configured and arranged to generate a signal that is indicative of a propulsion force transferred through the articulated joint; and a controller operatively coupled to the force sensor. The controller is configured to determine compaction performance of the compaction system against the work surface based at least in part on the signal from the force sensor. 
     Another aspect of the disclosure provides a method for compacting a work surface with a compaction system. The compaction system includes a first propulsion device operatively coupled to a compaction drum via an articulated joint, a force sensor configured and arranged to generate a signal indicative of a propulsion force transferred from the first propulsion device to the compaction drum via the articulated joint, and a controller operatively coupled to the force sensor. The method comprises propelling the compaction system over the work surface by applying a propulsion power to a first propulsion device in contact with the work surface; compacting the work surface in response to the propelling the compaction system over the work surface; and determining via the controller a first compaction performance of the compaction system against the work surface based at least in part on the signal from the force sensor. 
     According to another aspect of the disclosure, a machine for compacting a work surface comprises a first frame; a second frame coupled to the first frame via an articulated joint; a first propulsion device operatively coupled to the first frame via a first propulsion motor, the first propulsion device being configured to propel the machine over a work surface in response to a power applied by the first propulsion motor; a compaction drum operatively coupled to the second frame, the compaction drum being configured to compact the work surface via rolling engagement with the work surface; a force sensor configured and arranged to generate a signal that is indicative of a propulsion force transferred through the articulated joint; and a controller operatively coupled to the force sensor. The controller is configured to determine compaction performance of the machine the work surface based at least in part on the signal from the force sensor. 
    
    
     
       BRIEF DESCRIPTION OF THE DRAWINGS 
         FIG. 1  is a side view of a compactor machine including a compaction system, according to an aspect of the disclosure. 
         FIG. 2  is a schematic view of a power train for a compaction system, according to an aspect of the disclosure. 
         FIG. 3  is a side view of a compactor machine while performing a compaction process on a work surface, according to an aspect of the disclosure. 
         FIG. 4  is a top view of a compactor machine, according to an aspect of the disclosure. 
         FIG. 5  is a top view of an articulated joint for a compactor machine, according to an aspect of the disclosure. 
         FIG. 6  is a partial cross-sectional view of an articulated joint along the section line  6 - 6  shown in  FIG. 5 , according to an aspect of the disclosure. 
         FIG. 7  is an exemplary plot of relative rolling slump versus a number of passes over a work surface, according to an aspect of the disclosure. 
         FIG. 8  is an exemplary plot of a distance ratio h 6 /h 3  versus a number of passes over a work surface, according to an aspect of the disclosure. 
     
    
    
     DETAILED DESCRIPTION 
     Aspects of the disclosure will now be described in detail with reference to the drawings, wherein like reference numbers refer to like elements throughout, unless specified otherwise. 
       FIG. 1  is a side view of a compactor machine  100  including a compaction system  102 , according to an aspect of the disclosure. The compactor machine  100  may be configured in a variety of ways to perform a variety of compaction operations. For example, aspects of the present disclosure find application to landfill compactors that may be configured with tipped rollers for compacting landfill waste, paving compactors that may be designed with smooth rollers to compact asphalt for roads or parking lots, and other compactors that may be configured for compacting soil or to otherwise prepare earthworks. 
     The compaction system  102  includes one or more rolling elements  104  that are configured to compact a work surface  106  through rolling engagement with the work surface  106 . The work surface  106  may include soil, gravel, landfill waste, asphalt, combinations thereof, or any other surface material known in the art to benefit from a compaction process. 
     The one or more rolling elements  104  may include a propulsion device  108 , a compaction drum  110 , or combinations thereof. The propulsion device  108  is operatively coupled to a mechanical power source  112  for transfer of mechanical power from the mechanical power source  112  to the propulsion device  108  to propel the compactor machine  100  over the work surface  106 . The propulsion device  108  may include one or more pneumatic tires, a compaction drum, a track drive, a belt drive, or any other land-based propulsion device known in the art. 
     The compaction drum  110  may be optionally or selectively coupled to the mechanical power source  112  to transfer mechanical power from the mechanical power source  112  to the compaction drum  110  to propel the compaction drum  110  over the work surface  106 , drive a compaction mechanism  130  (see  FIGS. 2 and 4 ) within the compaction drum  110 , or combinations thereof. A compaction mechanism  130  of the compaction drum  110  may include a vibratory compaction mechanism. A circumferential surface of the compaction drum  110  may be a smooth surface, a textured surface, such as that on a tipped drum, or any other compaction drum surface structure known in the art. 
     The mechanical power source  112  may include a reciprocating piston internal combustion engine, a gas turbine, an electric motor, or any other prime mover known in the art. The operative coupling between the mechanical power source  112  and the propulsion device  108  or the compaction drum  110  may include a geared transmission, a belt and pulley drive, an electric generator-motor drive, a hydraulic pump-motor fluid coupling, combinations thereof, or any other mechanical power transmission known in the art. 
     The compactor machine  100  may include a first frame  114  coupled to a second frame  116  via an articulated joint  118 . The articulated joint  118  is configured to enable a rotational degree of freedom between the first frame  114  and the second frame  116  about an axis that extends at least partly along a vertical direction  122 , and to transmit propulsion force between the first frame  114  and the second frame  116  along a longitudinal direction  120 . The longitudinal direction  120  of the compactor machine  100  may extend at least partly from the first frame  114  toward the second frame  116 , and a height or vertical direction  122  of the compactor machine  100  may extend transverse to the longitudinal direction  120  from the work surface  106  toward the compactor machine  100 . 
     In some applications, the portion of the compactor machine  100  disposed aft or rearward of the articulated joint  118 , along the longitudinal direction  120 , may be referred to as the trolley. The trolley may include, the first frame  114 , the cab  124 , the mechanical power source  112 , and the one or more propulsion devices  108 , for example. 
     As shown in the non-limiting aspect illustrated in  FIG. 1 , the propulsion device  108  is coupled to the first frame  114  via a rotational bearing  134 , and the compaction drum  110  is coupled to the second frame via a rotational bearing  132 . However, it will be appreciated that other configurations for the compactor machine are contemplated to fall within the scope of the present disclosure, including, but not limited to, towed compaction drums. The propulsion device  108  may rotate on a first axle that is centered on a first axis of rotation, and the compaction drum  110  may rotate around a second axle that is centered on a second axis of rotation. 
     The compactor machine  100  may include a cab  124  configured to accommodate an operator of the compactor machine  100 . The cab may include a seat and one or more control devices  126 . The one or more control devices  126  may include a steering mechanism, a speed/throttle input, a console, a data display, a network telemetry link, combinations thereof, or any other input or output device known in the art to benefit operation of the compactor machine  100 . The one or more control devices  126  may be operatively coupled to a controller  128  for transmission of control inputs, machine state feedback, environmental state feedback, or any other control signals therebetween. 
       FIG. 2  is a schematic view of a power train  150  for a compaction system  102 , according to an aspect of the disclosure. The power train  150  includes the mechanical power source  112  and mechanical couplings between the mechanical power source  112  and the at least one propulsion device  108 , the compaction drum  110 , the compaction mechanism  130 , or combinations thereof, for transmission of mechanical power therebetween. Although  FIG. 2  shows a power train  150  with predominately hydraulic-based transmission of mechanical power, it will be appreciated that the power train  150  may include any other means for transmitting mechanical power known in the art, including, but not limited to, geared transmissions, belt and pulley transmissions, electric motor-generator transmissions, and combinations thereof. 
     The at least one propulsion device  108  may be operatively coupled to a differential gear assembly  152  via an axle shaft  154  for transmission of mechanical power therebetween. According to an aspect of the disclosure, the at least one propulsion device  108  includes two wheels, where each wheel is operatively coupled to the differential gear assembly  152  by a respective axle shaft  154  for transmission of mechanical power therebetween. Pneumatic tires may be mounted to each of the two wheels. 
     The differential gear assembly  152  may be operatively coupled to a first propulsion motor  156  via a shaft  158  for transmission of mechanical power therebetween. The first propulsion motor  156  may be configured as a bi-directional hydraulic motor with a fixed displacement; however, it will be appreciated that the first propulsion motor  156  may embody other configurations to meet application requirements. 
     A first port  160  of the first propulsion motor  156  may be fluidly coupled to a first port  162  of a first propulsion pump  164  via the conduit  166 , for transmission of hydraulic power therebetween; and a second port  168  of the first propulsion motor  156  may be fluidly coupled to a second port  170  of the first propulsion pump  164  via the conduit  172 , for transmission of hydraulic power therebetween. The first propulsion pump  164  may be configured as a bi-directional flow pump with a variable displacement, however, it will be appreciated that the first propulsion pump  164  may embody other configurations to meet application requirements. Further, the first propulsion pump  164  may be operatively coupled to the mechanical power source  112  via a shaft  174 , for transmission of mechanical power therebetween. 
     Accordingly, the first propulsion motor  156 , the first propulsion pump  164 , and the conduits  166 ,  172  may compose a closed-loop, hydrostatic drive circuit for transmitting mechanical power from the mechanical power source  112  to the propulsion devices  108 . When configured in a first flow direction, the first port  162  is an outlet port of the first propulsion pump  164 , and the first port  160  is an inlet port of the first propulsion motor  156 . And in the first configuration, flow from the first port  162  of the first propulsion pump  164  to the first port  160  of the first propulsion motor  156  causes the shaft  158  and the propulsion devices  108  to rotate in a first direction, respectively. 
     When configured in a second flow direction, which is opposite the first flow direction, the second port  170  is an outlet port of the first propulsion pump  164 , and the second port  168  is an inlet port of the first propulsion motor  156 . And in the second configuration, flow from the second port  170  of the first propulsion pump  164  to the second port  168  of the first propulsion motor  156  causes the shaft  158  and the propulsion devices  108  to rotate in a second direction, respectively, that is opposite the first direction. Accordingly, the first configuration of the first propulsion pump  164  may propel the compactor machine  100  forward along the longitudinal direction  120 , and the second configuration of the first propulsion pump  164  may propel the compactor machine  100  backward along the longitudinal direction  120 . 
     The first propulsion pump  164  may be operatively coupled to an actuator  176  that is configured to adjust a flow direction through the first propulsion pump  164 , displacement of the first propulsion pump  164 , or combinations thereof. The actuator  176  may be a swash plate actuator or any other hydraulic pump actuator known in the art. Further, the actuator  176  may be operatively coupled to the controller  128 , such that the controller  128  may adjust a flow direction through the first propulsion pump  164 , displacement of the first propulsion pump  164 , or combinations thereof via the actuator  176 . It will be appreciated that adjusting the displacement of the first propulsion pump  164  via the actuator  176  may be used to vary a travel speed of a compactor machine  100  incorporating the power train  150  by varying a hydraulic flow rate through the first propulsion motor  156 . 
     A pressure sensor  178  may be fluidly coupled to the conduit  166 , the conduit  172 , or both, and be configured for generating a signal that is indicative of a pressure potential driving the first propulsion motor  156 . According to an aspect of the disclosure, the pressure sensor  178  is a differential pressure sensor that is configured and arranged to measure a pressure drop across the first propulsion motor  156 . Further, the pressure sensor  178  may be operatively coupled to the controller  128  for transmitting the pressure signal from the pressure sensor  178  to the controller  128 . 
     The power train  150  may optionally include a first bypass valve  180  that is configured to bypass hydraulic fluid around the first propulsion motor  156 , the first propulsion pump  164 , or both. Accordingly, when the first bypass valve  180  is configured in an open position, the first propulsion motor  156  and the propulsion devices  108  may be placed in a neutral configuration, such that the first propulsion motor  156  and the propulsion devices  108  may rotate freely and independent of the operation of the first propulsion pump  164 . 
     The first bypass valve  180  may be operatively coupled to an actuator  182 , and the actuator  182  may be operatively coupled to the controller  128 . Accordingly, the controller  128  may actuate the first bypass valve  180  via the actuator  182 . 
     The power train  150  may optionally include a first clutch  184  that is configured and arranged to effect selective mechanical coupling or uncoupling between the first propulsion motor  156  and the propulsion devices  108 . The first clutch  184  may be operatively coupled to the controller  128 , such that the controller  128  may selectively cause the first clutch  184  to mechanically couple or uncouple the first propulsion motor  156  and the propulsion devices  108 . Although the first clutch  184  is shown disposed in series between the shaft  158  and the differential gear assembly  152  in  FIG. 2 , it will be appreciated that the first clutch  184  may be disposed anywhere along a power transmission path between the first propulsion motor  156  and the propulsion devices  108 . 
     Referring still to  FIG. 2 , the compaction drum  110  may include two mechanical power inputs, namely a mechanical power input for transmitting propulsion power to the compaction drum  110 , which causes the compaction drum  110  to rotate relative to the second frame  116 , for example, and a mechanical power input for transmitting power to a compaction mechanism  130 . The compaction mechanism  130  of the compaction drum  110  may include a vibratory compaction mechanism, that is capable of varying an amplitude, a frequency, or both, of a periodic compaction force applied to the work surface  106  via the compaction drum  110 . According to an aspect of the disclosure, a second propulsion motor  186  provides mechanical power to propel the compaction drum  110  in rolling engagement with the work surface  106 , and a compaction motor  188  provides mechanical power to the compaction mechanism  130 . 
     The compaction drum  110  may be operatively coupled to the second propulsion motor  186  via a shaft  190  for transmission of mechanical power therebetween. The second propulsion motor  186  may be configured as a bi-directional hydraulic motor with a fixed displacement; however, it will be appreciated that the second propulsion motor  186  may embody other configurations to meet application requirements. 
     A first port  192  of the second propulsion motor  186  may be fluidly coupled to a first port  194  of a second propulsion pump  196  via the conduit  198 , for transmission of hydraulic power therebetween; and a second port  200  of the second propulsion motor  186  maybe fluidly coupled to a second port  202  of the second propulsion pump  196  via the conduit  204 , for transmission of hydraulic power therebetween. The second propulsion pump  196  may be configured as a bi-directional flow pump with a variable displacement; however, it will be appreciated that the second propulsion pump  196  may embody other configurations to meet application requirements. Further, the second propulsion pump  196  may be operatively coupled to the mechanical power source  112  via a shaft  206 , for transmission of mechanical power therebetween. 
     Accordingly, the second propulsion motor  186 , the second propulsion pump  196 , and the conduits  198 ,  204  may compose a closed-loop, hydrostatic drive circuit for transmitting propulsion power from the mechanical power source  112  to the compaction drum  110 . When configured in a first flow direction, the first port  194  is an outlet port of the second propulsion pump  196 , and the first port  192  is an inlet port of the second propulsion motor  186 . And in the first configuration, flow from the first port  194  of the second propulsion pump  196  to the first port  192  of the second propulsion motor  186  causes the shaft  190  and the compaction drum  110  to rotate in a first direction, respectively. 
     When configured in a second flow direction, which is opposite the first flow direction, the second port  202  is an outlet port of the second propulsion pump  196 , and the second port  200  is an inlet port of the second propulsion motor  186 . And in the second configuration, flow from the second port  202  of the second propulsion pump  196  to the second port  200  of the second propulsion motor  186  causes the shaft  190  and the propulsion devices  108  to rotate in a second direction, respectively, that is opposite the first direction. Accordingly, the first configuration of the second propulsion pump  196  may propel the compaction drum  110  forward along the longitudinal direction  120 , and the second configuration of the second propulsion pump  196  may propel the compaction drum backward along the longitudinal direction. 
     The second propulsion pump  196  may be operatively coupled to an actuator  208  that is configured to adjust a flow direction through the second propulsion pump  196 , displacement of the second propulsion pump  196 , or combinations thereof. The actuator  208  may be a swash plate actuator or any other hydraulic pump actuator known in the art. Further, the actuator  208  may be operatively coupled to the controller  128 , such that the controller  128  may adjust a flow direction through the second propulsion pump  196 , a displacement of the second propulsion pump  196 , or combinations thereof, via the actuator  208 . It will be appreciated that adjusting the displacement of the second propulsion pump  196  via the actuator  208  may be used to vary a travel speed of a compactor machine  100  incorporating the power train  150  by varying a hydraulic flow rate through the second propulsion motor  186 . 
     A pressure sensor  210  may be fluidly coupled to the conduit  198 , the conduit  204 , or both, and be configured for generating a signal that is indicative of a pressure potential driving the second propulsion motor  186 . According to an aspect of the disclosure, the pressure sensor  210  is a differential pressure sensor that is configured and arranged to measure a pressure drop across the second propulsion motor  186 . Further, the pressure sensor  210  may be operatively coupled to the controller  128  for transmitting the pressure signal from the pressure sensor  210  to the controller  128 . 
     The power train  150  may optionally include a second bypass valve  212  that is configured to bypass hydraulic fluid around the second propulsion motor  186 , the second propulsion pump  196 , or both. Accordingly, when the second bypass valve  212  is configured in an open position, the second propulsion motor  186  and the compaction drum  110  may be placed in a neutral configuration, such that the second propulsion motor  186  and the compaction drum  110  may rotate freely and independent of the operation of the second propulsion pump  196 . 
     The second bypass valve  212  may be operatively coupled to an actuator  214 , and the actuator  214  may be operatively coupled to the controller  128 . Accordingly, the controller  128  may actuate the second bypass valve  212  via the actuator  214 . 
     The power train  150  may optionally include a second clutch  216  that is configured and arranged to effect selective mechanical coupling or uncoupling between the second propulsion motor  186  and the compaction drum  110 . The second clutch  216  may be operatively coupled to the controller  128 , such that the controller  128  may selectively cause the second clutch  216  to mechanically couple or uncouple the second propulsion motor  186  and the compaction drum  110 . 
     Referring still to  FIG. 2 , the compaction mechanism  130  may be operatively coupled to the compaction motor  188  via a shaft  218  for transmission of mechanical power therebetween. An inlet port  220  of the compaction motor  188  may be fluidly coupled to an outlet port  222  of a compaction pump  224  via a conduit  226 , for transmission of hydraulic power therebetween. The compaction motor  188  may be configured as a single-direction, fixed displacement hydraulic motor, and the compaction pump  224  may be configured as a single flow-direction, variable displacement hydraulic pump. However, it will be appreciated that the compaction motor  188 , the compaction pump  224 , or both, may embody different configurations to meet application requirements. 
     The compaction pump  224  may include an actuator  240  that is configured to vary a displacement of the compaction pump  224 . The actuator  240  may be operatively coupled to the controller  128  to enable the controller  128  to vary a displacement of the compaction pump  224  via the actuator  240 . Accordingly, the controller  128  may vary a hydraulic flow rate to the compaction motor  188 , and thereby vary a speed of the compaction motor  188 . 
     An inlet port  228  of the compaction pump  224  may take suction from a reservoir  230  via an intake conduit  232 , and an outlet port  234  of the compaction motor  188  may be fluidly coupled to the reservoir  230  via a return conduit  236 . Further, the compaction pump  224  may be operatively coupled to the mechanical power source  112  via a shaft  238  for transmission of mechanical power therebetween. Accordingly, the compaction pump  224 , the compaction motor  188 , and the conduits  232 ,  226 ,  236  may form an open loop hydraulic circuit for transmitting mechanical power from the mechanical power source  112  to the compaction mechanism  130 . 
     Although the hydraulic circuit to drive the compaction motor  188  is illustrated as an open-loop hydraulic circuit in  FIG. 2 , it will be appreciated that the hydraulic circuit to drive the compaction motor  188  may alternatively be configured as a closed-loop hydrostatic circuit, like those illustrated in  FIG. 2  for driving the first propulsion motor  156  and the second propulsion motor  186 , or any other hydraulic drive circuit known in the art. Similarly, although the hydraulic circuits to drive the first propulsion motor  156  and the second propulsion motor  186  are illustrated as closed-loop hydrostatic circuits in  FIG. 2 , it will be appreciated that hydraulic circuits for either of the first propulsion motor  156  and the second propulsion motor  186  may alternatively be configured as open-loop hydraulic circuits, including diverter valves to effect both forward and reverse operation, or any other hydraulic drive circuit known in the art. 
     Each of the shafts  238 ,  206 ,  174 , and therefore each of the compaction pump  224 , the second propulsion pump  196 , and the first propulsion pump  164 , may operate at the same rotational speed, as shown in  FIG. 2 . However, it will be appreciated that any of the shafts  238 ,  206 ,  174 , and therefore any of the compaction pump  224 , the second propulsion pump  196 , and the first propulsion pump  164 , may have separate and distinct connections to the mechanical power source  112 , and therefore operate at a speed that is different from the other shafts or pumps. 
     Although  FIG. 2  shows separate and distinct hydraulic circuits for the first propulsion pump  164  and the first propulsion motor  156 , and the second propulsion pump  196  and the second propulsion motor  186 , respectively, it will be appreciated that the first propulsion motor  156  and the second propulsion motor  186  may be incorporated into a single hydraulic circuit including any number of hydraulic pumps greater than or equal to one. 
       FIG. 3  is a side view of a compactor machine  100  while performing a compaction process on a work surface  106 , according to an aspect of the disclosure. The compactor machine  100  may include at least one forward distance sensor  250 , at least one middle distance sensor  252 , and at least one rear distance sensor  254 . 
     The at least one forward distance sensor  250  may be fixed to the second frame  116  forward of the compaction drum  110 , where the forward direction extends along the longitudinal direction  120  from the propulsion device  108  toward the compaction drum  110 . The at least one rear distance sensor  254  may be fixed to the first frame  114  aft of the propulsion device  108 , where the aft direction is opposite the forward direction. The at least one middle distance sensor  252  may be fixed to the compactor machine between the propulsion device  108  and the compaction drum  110  along the longitudinal direction  120 , and may be fixed to either the first frame  114  or the second frame  116 . As shown in  FIG. 3 , the at least one middle distance sensor  252  is mounted to the second frame  116 . 
     Furthermore, each or any of the distance sensors  250 ,  252 ,  254  may be mounted below the first frame  114  or the second frame  116  of the compactor machine  100  along the vertical direction  122 , where the downward direction extends along the vertical direction  122  from the compactor machine  100  toward the work surface  106 . Alternatively or additionally, each or any of the distance sensors  250 ,  252 ,  254  may be mounted on the compactor machine  100  such that the sensor has unobstructed line-of-sight or optical communication with the work surface  106 . 
     Each of the distance sensors  250 ,  252 ,  254  may be configured to measure a distance between the compactor machine  100  and the work surface  106 . According to an aspect of the disclosure, each of the distance sensors  250 ,  252 ,  254  is configured to measure a distance from a reference plane  256  of the compactor machine  100  to the work surface  106 , normal or perpendicular to the reference plane  256 . The reference plane  256  may be fixed in relation to the first frame  114 , the second frame  116 , or both, as the compactor machine  100  travels along the work surface  106 . Alternatively or additionally, a first reference plane  262  may be defined in fixed relation to the first frame  114 , and a second reference plane  264  may be defined in fixed relation to the second frame  116 , where the second reference plane  264  is distinct from the first reference plane  262 . 
     The reference plane  256  may be defined as a plane located above the work surface  106  and fixed in relation to the first frame  114  or the second frame  116  of the compactor machine  100 , where the reference plane  256  is parallel to the work surface  106  when the work surface  106  is rigid and level. Thus, when the compactor machine  100  is disposed stationary on a rigid and level surface, a height h 1  from the reference plane  256  to the lowest point  258  on the compaction drum  110  may be equal to a height h 2  from the reference plane  256  to a lowest point  260  on the propulsion device  108 . The first reference plane  262 , the second reference plane  264 , or both, may be defined similarly to the reference plane  256 . 
     It will be appreciated that any of the reference planes  256 ,  262 ,  264  defined parallel to a rigid and level work surface  106  may only be a theoretical construct to aid the measurement of distances between the compactor machine  100  and the work surface  106  using the distance sensors  250 ,  252 ,  254 , and may not correspond to any material surface of the compactor machine  100 . 
       FIG. 3  shows the compactor machine  100  progressing in a forward longitudinal direction while compacting the work surface  106 . A first portion  280  of the work surface  106  lies forward of the compaction drum  110  and is yet to be compacted by the compactor machine  100  during the current compaction pass. The at least one forward distance sensor  250  may be configured and arranged to measure the height h 3  to the first portion  280  of the work surface  106 . A difference in height between h 1  and h 3  may define a sinking distance e B  of the compaction drum  110 . The sinking distance e B  of the compaction drum  110  may include both elastic and plastic deformation of the work surface  106  in response to compaction by the compaction drum  110 . 
     A second portion  282  of the work surface  106  is disposed between the compaction drum  110  and the propulsion device  108  along the longitudinal direction  120 , and has been compacted by the compaction drum  110  but not by the propulsion device  108  during the current compaction pass. The at least one middle distance sensor  252  may be configured and arranged to measure the height h 6  to the second portion  282  of the work surface  106 . A difference in height between h 3  and h 6  may be indicative of the plastic deformation of the work surface  106  in response to compaction by the compaction drum  110 . 
     A third portion  284  of the work surface  106  is disposed aft of the propulsion device  108  along the longitudinal direction, within the track of the compaction drum  110 , but outside the track of the propulsion device  108  along a transverse direction  286 . The at least one rear distance sensor  254  may be configured and arranged to measure the height h 4  to the third portion  284  of the work surface. Accordingly, the height h 4  may be substantially equal to the height h 6 , within variation of the work surface in the second portion  282  and the third portion  284 , and within measurement uncertainty of the distance sensors  252  and  254 . However, it will be appreciated that the height h 4  does not necessarily equal h 6  because a sinking depth of the compaction drum  110  into the work surface  106  may differ from a sinking distance of the one or more propulsion devices  108  in to the work surface  106 . 
     A fourth portion  288  of the work surface  106  is disposed aft of the propulsion device  108  along the longitudinal direction, and in line with both the compaction drum  110  and the propulsion device  108  along the transverse direction  286 . Therefore, the fourth portion  288  has been compacted by both the compaction drum  110  and the propulsion device  108 . The at least one rear distance sensor  254  may be configured and arranged to measure the height  115  to the fourth portion  288  of the work surface. 
     A difference in height between h 5  and h 4  may define a sinking distance e R  of the propulsion device  108  into the work surface  106 . Accordingly, the sinking distance e R  of the propulsion device  108  may include just the plastic deformation of the work surface  106  in response to compaction by the propulsion device  108 . Alternatively, another sinking distance of the propulsion device  108  may be defined as the difference in height between h 2  and h 4 , which may be indicative of both the plastic deformation and the elastic deformation of the work surface  106  in response to compaction by the propulsion device  108 . 
     The at least one forward distance sensor  250  is located a distance l 1  from the point  258  along the longitudinal direction  120 , and the at least one middle distance sensor  252  is located a distance l 2  from the point  258  along the longitudinal direction. The at least one rear distance sensor  254  is located a distance l 3  from the point  260  along the longitudinal direction  120 . The point  258  is located a distance l 4  from the point  260  along the longitudinal direction, which may coincide with a distance from a rotational axis of the compaction drum  110  to a rotational axis of the propulsion device  108  along the longitudinal direction  120 . 
     The compactor machine  100  may further include a longitudinal inclinometer  290 , a cross slope sensor  292 , a global positioning system (GPS) unit  294 , or combinations thereof, fixed to either the first frame  114  or the second frame  116 . According to an aspect of the disclosure, both the longitudinal inclinometer  290  and the cross slope sensor  292  are fixed to the second frame  116 . Further, each of the longitudinal inclinometer  290 , the cross slope sensor  292 , and the GPS unit  294  may be operatively coupled to the controller  128  for transmission of measurement signals thereto. 
     The longitudinal inclinometer  290  may be configured and arranged to generate a signal that is indicative of a slope of the compactor machine  100  in a plane defined by the longitudinal direction  120  and the vertical direction  122 . According to an aspect of the disclosure, the longitudinal inclinometer  290  measures the longitudinal inclination of the compactor machine  100  with respect to a gravity direction (g). Thus, it will be appreciated that the vertical direction  122  in machine coordinates need not align with the gravity direction (g). 
     The cross slope sensor  292  may be configured and arranged to generate a signal that is indicative of a slope of the compactor machine  100  in a plane defined by the vertical direction  122  and the transverse direction  286 . According to an aspect of the disclosure, the cross slope sensor  292  measures the cross slope inclination of the compactor machine  100  with respect to the gravity direction (g). Each of the longitudinal inclinometer  290  and the cross slope sensor  292  may be operatively coupled to the controller  128  for communication of measurement signals therewith. 
       FIG. 4  is a top view of a compactor machine  100 , according to an aspect of the disclosure. The at least one forward distance sensor  250  may include a first forward distance sensor  300 , a second forward distance sensor  302 , a third forward distance sensor  304 , or combinations thereof. Each of the first forward distance sensor  300 , the second forward distance sensor  302 , and the third forward distance sensor  304  may be located at the same longitudinal location along the longitudinal direction  120 , and lie within a track of the compaction drum  110  along the transverse direction  286 . Alternatively or additionally, the first forward distance sensor  300  and the second forward distance sensor  302  may be aligned with a track of a right propulsion device  306  and a track of a left propulsion device  308 , respectively, along the transverse direction  286 , and the third forward distance sensor  304  may be disposed between and outside of the tracks of the right propulsion device  306  and the left propulsion device  308  along the transverse direction  286 . 
     Each of the first forward distance sensor  300 , the second forward distance sensor  302 , and the third forward distance sensor  304  may be operatively coupled to the controller  128  for transmission of height signals thereto. The controller  128  may be configured to perform arithmetic manipulations, statistical analysis, or both, on the signals from the first forward distance sensor  300 , the second forward distance sensor  302 , and the third forward distance sensor  304  to synthesize a value or a range of values indicative of distance to the first portion  280  of the work surface  106 . According to an aspect of the disclosure, the controller  128  is configured to calculate an average value based on any two or more signals from the first forward distance sensor  300 , the second forward distance sensor  302 , and the third forward distance sensor  304 . 
     The at least one middle distance sensor  252  may include a first middle distance sensor  310 , a second middle distance sensor  312 , a third middle distance sensor  314 , or combinations thereof. Each of the first middle distance sensor  310 , the second middle distance sensor  312 , and the third middle distance sensor  314  may be located at the same longitudinal location along the longitudinal direction  120 , and lie within a track of the compaction drum  110  along the transverse direction  286 . Alternatively or additionally, the first middle distance sensor  310  and the second middle distance sensor  312  may be aligned with a track of a right propulsion device  306  and a track of a left propulsion device  308 , respectively, along the transverse direction  286 , and the third middle distance sensor  314  may be disposed between and outside of the tracks of the right propulsion device  306  and the left propulsion device  308  along the transverse direction  286 . 
     Each of the first middle distance sensor  310 , the second middle distance sensor  312 , and the third middle distance sensor  314  may be operatively coupled to the controller  128  for transmission of height signals thereto. The controller  128  may be configured to perform arithmetic manipulations, statistical analysis, or both, on the signals from the first middle distance sensor  310 , the second middle distance sensor  312 , and the third middle distance sensor  314  to synthesize a value or a range of values indicative of distance between the first portion  280  of the work surface  106 . According to an aspect of the disclosure, the controller  128  is configured to calculate an average value based on any two or more signals from the first middle distance sensor  310 , the second middle distance sensor  312 , and the third middle distance sensor  314 . 
     The at least one rear distance sensor  254  may include a first rear distance sensor  316 , a second rear distance sensor  318 , a third rear distance sensor  320 , or combinations thereof. Each of the first rear distance sensor  316 , the second rear distance sensor  318 , and the third rear distance sensor  320  may be located at the same longitudinal location along the longitudinal direction  120 , and lie within a track of the compaction drum  110  along the transverse direction  286 . Alternatively or additionally, the first rear distance sensor  316  and the second rear distance sensor  318  may be aligned with a track of a right propulsion device  306  and a track of a left propulsion device  308 , respectively, along the transverse direction  286 , and the third rear distance sensor  320  may be disposed between and outside of the tracks of the right propulsion device  306  and the left propulsion device  308  along the transverse direction  286 . 
     Each of the first rear distance sensor  316 , the second rear distance sensor  318 , and the third rear distance sensor  320  may be operatively coupled to the controller  128  for transmission of height signals thereto. The controller  128  may be configured to perform arithmetic manipulations, statistical analysis, or both, on the signals from the first rear distance sensor  316 , the second rear distance sensor  318 , and the third rear distance sensor  320  to synthesize a value or a range of values indicative of distance between the first portion  280  of the work surface  106  and the reference plane  256 , and distance between the third portion  284  of the work surface  106  and the reference plane  256 . According to an aspect of the disclosure, the controller  128  is configured to calculate an average value based on signals from the first rear distance sensor  316  and the second rear distance sensor  318 . 
     Referring now to  FIGS. 5 and 6 , it will be appreciated that  FIG. 5  is a top view of an articulated joint  118  for a compactor machine  100 , according to an aspect of the disclosure; and  FIG. 6  is a partial cross-sectional view of an articulated joint  118  along the section line  6 - 6  shown in  FIG. 5 , according to an aspect of the disclosure. As shown in  FIGS. 5 and 6 , the compactor machine  100  includes at least one force sensor disposed along a force load path between the at least one propulsion device  108  and the compaction drum  110 , such that the at least one force sensor is configured to generate a signal that is indicative of force transferred through the articulated joint  118 . 
     According to an aspect of the disclosure, a force sensor  350  is incorporated into a pivot shaft  352  of the articulated joint  118 . The articulated joint  118  may include a first yoke  354  pivotally coupled to a second yoke  356  via the pivot shaft  352 , where the pivot shaft  352  passes through an aperture  358  of the first yoke  354  and an aperture  360  of the second yoke  356 . The first yoke  354  may be fixed to the first frame  114 , and the second yoke  356  may be fixed to the second frame  116 , by fasteners, welding, combinations thereof, or any other fastening method known in the art. 
     The force sensor  350  may be operatively coupled to the controller  128  for transmission of force measurement signals thereto. According to an aspect of the disclosure, the force sensor  350  is subjected to the entirety of force transferred through the articulated joint  118 , and the signal from the force sensor  350  is indicative of the entirety of the force being transferred through the articulated joint  118 . Alternatively, the force sensor  350  may be subjected to only a portion of the force transferred through the articulated joint  118 , and the controller  128  may be configured to determine the total force transfer through the articulated joint  118  based on the signal from the force sensor  350 , calibration data, a physics-based model of force transfer through the articulated joint  118 , or combinations thereof. 
     Alternatively or additionally, a force sensor  362  may be incorporated into a force load path between the articulated joint  118  and the at least one propulsion device  108 . According to an aspect of the disclosure, the force sensor  362  may be disposed between the first yoke  354  and the first frame  114 . Further, at least one spacer  364  may also be disposed between the first yoke  354  and the first frame  114 . 
     Alternatively or additionally, a force sensor  366  may be incorporated into a force load path between the articulated joint  118  and the compaction drum  110 . According to an aspect of the disclosure, the force sensor  366  may be disposed between the second yoke  356  and the second frame  116 . Further, at least one spacer  368  may also be disposed between the second yoke  356  and the second frame  116 . 
     The force sensor  362  and the force sensor  366  may be operatively coupled to the controller  128  for transmission of force measurement signals thereto. According to an aspect of the disclosure, the force sensor  362 , the force sensor  366 , or both, are subjected to the entirety of force transferred through the articulated joint  118 , and the signal from respective force sensors are indicative of the entirety of the force being transferred through the articulated joint  118 . Alternatively, the force sensor  362 , the force sensor  366 , or both, are subjected to only a portion of the force transferred through the articulated joint  118 , and the controller  128  is configured to determine the total force transfer through the articulated joint  118  based on the signal from the force sensor  362 , the signal from the force sensor  366 , calibration data, a physical model of force transfer through the articulated joint  118 , or combinations thereof. For example, a known fraction of the force transferred through the articulated joint  118  may be carried by the at least one spacer  364  or the at least one spacer  368 , and the controller  128  may be configured to determine the total force transfer through the articulated joint  118  based at least in part on the force transferred by the at least one spacer  364  or the at least one spacer  368  relative to the force transferred through the force sensor  362  and the force sensor  366 , respectively. 
     According to an aspect of the disclosure, the compactor machine  100  includes the force sensor  350  incorporated into the pivot shaft  352 , and does not include either of the force sensors  362 ,  366 . According to another aspect of the disclosure, the compactor machine  100  includes the force sensor  362 , the force sensor  366 , or both, but does not include the force sensor  350  incorporated into the pivot shaft  352 . 
     Any of the force sensor  350 , the force sensor  362 , or the force sensor  366  may include a strain-gage type load cell, or any other force measurement device known in the art. Further, it will be appreciated that the representations of the articulated joint  118  in  FIGS. 5 and 6  are simplified conceptual figures, which omit some practical features, such as bearings, to promote clarity of other features intended to be highlighted. 
     INDUSTRIAL APPLICABILITY 
     The present disclosure is applicable to compaction machines in general, and more particularly to compaction machines incorporating an articulated joint. The present disclosure is also applicable to methods for determination of compaction performance during a compaction process, and methods for calibrating a compaction system for determination of compaction performance during a compaction process. 
     Improved Determination of Longitudinal Slope 
     Determination of compaction performance during a compaction process may depend upon, or be at least partly based upon, a determination of the longitudinal slope (a) of the work surface  106  relative to the gravity direction (g) in a plane defined by the longitudinal direction  120  and the vertical direction  122  of the compactor machine  100 . The compactor machine  100  may include the longitudinal inclinometer  290 , which is configured to generate a signal (as) indicative of a longitudinal slope of the compactor machine  100  relative to the gravity direction (g) in a plane defined by the longitudinal direction  120  and the vertical direction  122 . 
     However, the Applicant recognized that the longitudinal slope of the compactor machine  100  may differ from the longitudinal slope of the work surface  106  because of a zero-offset error (α 0 ) in the slope indication of the longitudinal inclinometer  290  when the compactor machine  100  is at rest on a rigid and level surface, because of a difference between the sinking distance (e B ) of the compaction drum  110  into the work surface  106  and the sinking distance (e R ) of the propulsion devices  108  into the work surface  106 , or combinations thereof. Accordingly, the Applicant discloses herein apparatus and methods for adjusting a longitudinal slope measurement signal (α S ) to be more indicative of the true longitudinal slope (α) of the work surface  106  by correcting for deviations therebetween. 
     The zero-offset error (α 0 ) of the longitudinal inclinometer  290  may result, for example, from change in overall diameter of the propulsion devices  108  due to tread wear or changes in pneumatic tire inflation pressure, from change in the outer diameter of the compaction drum  110  due to wear, drift in the calibration of the longitudinal inclinometer  290 , or combinations thereof. The magnitude of the zero-offset error (α 0 ) of the longitudinal inclinometer  290  may be determined by measuring a slope output signal from the longitudinal inclinometer  290  while the compactor machine  100  is resting on a firm reference surface of known longitudinal slope, thereby performing a zero calibration of the longitudinal inclinometer  290 . According to an aspect of the disclosure the known longitudinal slope is a level longitudinal slope. 
     The result from the zero calibration of the longitudinal inclinometer  290  may be applied in at least two ways. First, the difference (α 0 ) between the measured slope based on the slope signal of the longitudinal inclinometer  290  and the known longitudinal slope of the reference surface may be recorded, for example, in a memory of the controller  128  and applied as a correction to longitudinal slope measurements using the longitudinal inclinometer  290 . Alternatively, relationships for determining the longitudinal slope based on the slope signal from the longitudinal inclinometer  290  may be adjusted such that following the calibration procedure, the slope indicated by the longitudinal inclinometer  290  matches the longitudinal slope of the reference surface, such that α 0  equals zero following calibration. 
     As discussed previously with reference to  FIG. 3 , the sinking distance (e B ) of the compaction drum  110  into the work surface  106  may be calculated based on one or more height measurements (h 3 ) from the at least one forward distance sensor  250  and design information (h 1 ) of the compactor machine  100  as shown in Equation 1.
 
 e   B   =h   1   −h   3   Equation 1
 
     Also as previously discussed with reference to  FIG. 3 , the sinking distance (e R ) of the at least one propulsion device  108  into the work surface  106  may be calculated based on one or more height measurements (h 4 ) from the at least one rear distance sensor  254  and design information (h 2 ) of the compactor machine  100  as shown in Equation 2.
 
 e   R   =h   5   −h   4   Equation 2
 
     Accordingly, the longitudinal slope (α) of the work surface  106  may be calculated based at least in part on the longitudinal slope signal (α S ) measured from the longitudinal inclinometer  290  and select correction factors as shown in Equation 3.
 
α=α S −α 0 −arctan(( e   B   −e   R )/( l   4   +l   1   +l   3 ))  Equation 3
 
     Machine Drive Power (MDP) Indication of Compactor Performance 
     The Applicant recognized that rolling resistance of a load in rolling engagement with a work surface  106  depends upon the density of the material, the stiffness of the material, or combinations thereof. In turn, the Applicant developed the MDP material compaction measurement technology based on rolling resistance of the compactor machine  100  over the work surface  106  to help the operator of the compactor machine  100  determine when the load bearing strength of the material being compacted meets specification. For example, as the material of a work surface  106  is progressively compacted by multiple passes of a compactor machine  100 , the power required to propel the compactor machine  100  over the work surface  106  decreases with each successive pass that further compacts the work surface  106 . 
     The minimum rolling resistance of a compactor machine  100  corresponds to an ideally flat, bearing (i.e., optimally stiff, dense, or both), and level (i.e., normal to gravity direction) surface. The force necessary to propel the compactor machine  100  over such an idealized surface is designated herein as F MDP . The value of F MDP  may be evaluated using physics-based models, or by measuring a rolling resistance of a compactor machine  100  over the real surface of a test strip that approaches the idealized surface, or that corresponds to a target density and flatness. A stiffness or density of a test strip of material on a work surface  106  may be characterized by conventional means such as analysis of extracted core samples, nuclear gages, electromagnetic measurement devices, or any other work surface density or stiffness measurement technique known in the art. 
     Accordingly, an MDP value may be defined by normalizing a current rolling resistance (F) of a compactor machine  100  over a work surface  106  by the idealized MDP rolling resistance (F MDP ) as shown in Equation 4.
 
 MDP=F/F   MDP ≧1  Equation 4
 
     As the value of F MDP  corresponds to an absolute or virtual minimum of rolling resistance, it will be appreciated that any current rolling resistance (F) will be larger than F MDP , and therefore MDP will be greater than or equal to one. It will be further appreciated that as the density or stiffness of the work surface  106  approaches the target or ideal density or stiffness, the measured MDP value will approach a value of one. 
     To help make the increase in material density or stiffness more intuitive to an operator of the compactor machine  100 , a scaled reciprocal of the MDP value (MDP*) may be presented on a display of the one or more control devices  126 , as defined in Equation 5.
 
 MDP*=k/MDP   Equation 5
 
     Therefore, MDP* will always be less than or equal to the scaling constant, k, and higher values of MDP* correspond to higher values of density or stiffness of the material of the work surface  106 . According to a non-limiting aspect of the disclosure, k=150, and therefore MDP*≦150. 
     According to conventional approaches of the MDP compactor performance measurement technique, rolling resistance force was not directly measured, but instead was estimated using other measurements and physical models for the interaction of the compactor machine  100  with the work surface  106 . For example, a sum of propulsion power delivered to the work surface via the one or more rolling elements  104  could be estimated by determining a total amount of mechanical power generated by the mechanical power source  112 , and then determining or estimating the fraction of the total power from the mechanical power source  112  that is delivered to the one or more rolling elements  104 . Then, the rolling resistance for the rolling elements  104  could be determined as the mechanical power to the rolling elements  104  divided by the land speed of the compactor machine  100  that corresponds to the mechanical power of the rolling elements  104  so determined. 
     Alternatively, when the one or more rolling elements  104  are powered by hydraulic circuits, for example, power for all of the rolling element  104  could be determined or estimated as the product of pressure drop across and hydraulic flow rate through corresponding hydraulic motors. Next, the rolling resistance force could be determined or estimated by dividing the sum of hydraulic power to the rolling elements  104  by the land speed of the compactor machine  100  that corresponds to the sum of hydraulic power to the rolling elements  104 . 
     It may be desirable to consider power consumed or contributed to the compactor machine  100  when the compactor machine  100  travels up a longitudinal slope (α) or down a longitudinal slope (α), respectively, when performing an MDP analysis. Indeed, when the compactor machine  100  is traveling up a longitudinal slope, against the acceleration of gravity (g), additional force must be applied to perform work against gravity, but this additional force is not necessarily indicative of increased rolling resistance at any of the rolling elements  104 . Therefore, the total force (F total ) acting to propel the compactor machine  100  should be reduced by the component of the compactor machine&#39;s mass (m machine ) acting down the longitudinal slope (α) to determine or estimate the rolling resistance force (F) as shown in Equation 6.
 
 F=F   total   −m   machine   *g *sin(α)  Equation 6
 
     Similarly, when the compactor machine  100  is traveling down a longitudinal slope, aided by the acceleration of gravity (g), less force must be derived from the mechanical power source  112  because of the aid of gravity. Therefore, the total force (F total ) acting to propel the compactor machine  100  should be increased by the component of the compactor machine&#39;s mass (m machine ) acting down the longitudinal slope (α) to determine or estimate the rolling resistance force (F). Thus, as presented in Equation 6, the longitudinal slope angle (α) is positive when the compactor machine  100  is traveling uphill, and the longitudinal slope angle (α) is negative when the compactor machine  100  is traveling downhill. The coordinate system could alternately be arranged such that the longitudinal slope (α) is negative when the compactor machine  110  is traveling uphill, and positive when traveling downhill, and in turn the sign of sin(a) will change with the sign of α. It will be appreciated, as discussed above, that the longitudinal slope (α) of the work surface  106  may be determined by correcting a measured longitudinal slope (α S ) of the compactor machine  100 , using a signal from the longitudinal inclinometer  290 . 
     Although conventional MDP approaches to continuous measurement of work surface  106  density or stiffness greatly benefit operators of a compactor machine  100 , the Applicant discovered that variations in the geometry of the rolling elements  104  themselves could contribute variability and uncertainty in the resulting rolling force determinations. Especially with respect to pneumatic tires, changes in inflation pressure and changes in the tire tread through normal wear could bias determinations or estimates of rolling resistance based on propulsive power delivered to the pneumatic tires as propulsion devices  108 . 
     Drum-Scale MDP Based on Drum Rolling Resistance with Direct Force Measurement and Drum Propulsion Deactivated 
     The Applicant discovered that direct measurement of rolling resistance force through the articulated joint  118  could reduce or eliminate some of the aforementioned variances and uncertainties associated with propulsion devices  108 , such as pneumatic tires. By deactivating propulsion power delivered to the compaction drum  110 , and thereby providing all propulsion power to the compactor machine  100  via the one or more propulsion devices  108  on the first frame  114 , measurement of force transferred through the articulated joint  118  from the first frame  114  to the second frame  116  may be a direct measurement of the rolling resistance force of the compaction drum  110 , after adjustment for the longitudinal slope. This mode of operation may be referred to as a “measurement mode” of the compactor machine  100 . 
     Accordingly, an MDP method may be applied where the idealized MDP force (F MDP ) is an idealized MDP rolling resistance force of the compaction drum  110  alone (F MDP, B ) over an idealized work surface  106 , and the current rolling resistance of the compaction drum  110  (F S ) is directly measured using one or more of the force sensors  350 ,  362 ,  366 , as previously described with respect to  FIGS. 5 and 6 , for example. Furthermore, adjustments for the longitudinal slope (α) may be applied by determining a component of the axle load acting on the compaction drum  110  (F A, B ) along the gravity direction (g). Accordingly an MDP* indication for the compaction drum  110  using measured force transferred through the articulated joint  118  may be calculated as shown in Equation 7.
 
 MDP*   drum   =k*F   MDP,B /( F   S   −F   A,B )  Equation 7
 
     The axle force (F A, B ) acting on the axle of the compaction drum  110  may depend upon a mass (m B ) of the compactor machine  100  disposed forward of the articulated joint  118 , and a force (F T ) corresponding to a portion of the mass of the trolley acting on the axle of the compaction drum via the articulated joint  118 . The forward mass (m B ) may include the mass of the compaction drum  110 , and its corresponding driving mechanisms, and the second frame  116 . The trolley force (F T ) acting on the axle of the compaction drum  110  along the gravity direction (g) may be determined as a function of the longitudinal slope (α) from a physics-based model of the compactor machine  100 , lab or field measurements of the load carried by the axle of the compaction drum  110 , combinations thereof, or any other method known in the art for determining an axle load. According to an aspect of the disclosure, the axle load (F A,B ) in Equation 7 may be determined or estimated by the relation in Equation 8.
 
 F   A,B   =F   T   +m   B   *g *sin(α)  Equation 8
 
     Referring to  FIG. 2 , it will be appreciated that propulsion power to the second propulsion motor  186  may be deactivated by setting the second propulsion pump  196  displacement to zero using the actuator  208 , and the compaction drum  110  is configured to rotate freely by opening the second bypass valve  212  via the actuator  214 , opening the second clutch  216 , combinations thereof, or any other method known in the art for causing the compaction drum  110  to rotate freely independent of the second propulsion pump  196 . 
     It will be appreciated that a value for F MDP, drum  may be determined from measurement of the force transferred through the articulated joint  118  when the above-noted method is performed with the compactor machine  100  disposed on a compacted work surface  106  that closely approximates the idealized flat, bearing, and level surface associated with minimum rolling resistance, or a work surface  106  that approximates a target compaction for the work surface  106 . Further, it will be appreciated that the above-noted procedure may be performed with or without power transfer to the compaction mechanism  130 . 
     Although the MDP* value calculated in Equation 7 does not include rolling resistance for the one or more propulsion devices  108 , it will be appreciated that considering rolling resistance of the compaction drum  110  alone may provide a repeatable and reproducible way for determining or estimating progress toward a target density or stiffness for the work surface  106 , when force transferred through the articulated joint  118  is directly measured. 
     According to another aspect of the disclosure, the controller  128  may configure the compactor machine  100  to operate in an alternate measurement mode, where propulsion power to the one or more propulsion devices  108  is deactivated, the compactor machine  100  is propelled over the work surface  106  by applying propulsion power to the compaction drum  110 , and a rolling resistance of the one or more propulsion devices  108  is determined based on a measurement of force transmitted from the second frame  116  to the first frame  114  via the articulated joint  118 . 
     In this alternate mode, propulsion power to the propulsion devices  108  may be deactivated by setting a displacement of the first propulsion pump  164  to zero. Further, the propulsion devices  108  may be configured to operate in a neutral or free-wheeling mode by opening the first bypass valve  180 , disengaging or opening the first clutch  184 , or combinations thereof. It will be appreciated that this alternate measurement mode may be used to characterize or calibrate a rolling resistance of the propulsion devices  108 . 
     Drum-Scale MDP Based on Drum Rolling Resistance with Direct Force Measurement and Drum Propulsion Activated 
     While the drum-scale MDP method described above, with propulsion power to the compaction drum  110  deactivated, may be a useful for determining density or stiffness of the work surface  106 , it may still be desirable to incorporate the articulated joint  118  force measurement into a drum-scale MDP method when propulsion power is delivered to both the compaction drum  110  and the one or more propulsion devices  108 . This mode of operation may be referred to as a “working mode” of the compactor machine  100 . 
     It will be appreciated that the direct force measurement through the articulated joint  118  will tend to underestimate the force required to overcome rolling resistance of the compaction drum  110  when additional propulsion power is delivered to the compaction drum  110  in addition to the one or more propulsion devices  108 . However, the force necessary to propel the compaction drum  110  against rolling resistance of the work surface  106  and the longitudinal slope may include the force measured through the articulated joint  118  in addition to a propulsion force derived from propulsion power consumed by the compaction drum  110 . 
     Propulsion power delivered to the compaction drum  110 , for example via the second propulsion motor  186  (see  FIG. 2 ) will impart a propulsion force to the second frame  116  that is not included in the articulated joint  118  force measurement. However, an effective force acting on the compaction drum  110  in response to propulsion power applied to the compaction drum  110  may be derived as follows, and incorporated into the drum MDP method. 
     Referring now to  FIG. 2 , a propulsion power delivered to the compaction drum  110  may be determined or estimated as the product of the pressure drop across the second propulsion motor  186  and the flow rate of hydraulic fluid through the second propulsion motor  186 . The pressure drop across the second propulsion motor  186  may be measured directly by the pressure sensor  210 , and the flow rate of hydraulic fluid through the second propulsion motor  186  may be determined or estimated based on a speed of the second propulsion pump  196  and a displacement of the second propulsion pump  196 . If present in the system, it will be appreciated that the second bypass valve  212  will be closed and the second clutch  216  will be engaged to transfer hydraulic power from the second propulsion pump  196  to the second propulsion motor  186 . 
     Simultaneously with determining pressure drop and flow rate through the second propulsion motor  186 , a land speed of the compactor machine  100  over the work surface  106  and a longitudinal slope of the work surface  106  are determined. Next, an effective force based on drum propulsion (F drum, propulsion ) may be calculated as the propulsion power delivered to the compaction drum  110  divided by the land speed of the compactor machine  100 . Then, the effective force based on drum propulsion (F drum, propulsion ) may be integrated into the MDP* drum  calculation as shown in Equation 9.
 
 MDP*   drum   =k*F   MDP,B /( F   S   +F   drum,propulsion   −F   A,B )  Equation 9
 
     According to an aspect of the disclosure, the axle load (F A,B ) in Equation 9 may be determined or estimated by the relation in Equation 8 above. 
     Thus, although the MDP* calculation shown in Equation 9 introduces some additional complexity and perhaps some uncertainty regarding propulsion power delivered to the compaction drum  110 , it enables an MDP approach where both the compaction drum  110  and the propulsion devices  108  are simultaneously driven by propulsion power, without adding uncertainties that may result from introduction of propulsion power applied to pneumatic tires, for example, into the MDP calculations. 
     Determination of Relative Rolling Slump without Elastic Deformation of the Work Surface 
     Using measurements from the at least one middle distance sensor  252  in conjunction with aforementioned measurements from the at least one forward distance sensor  250  and the at least on rear distance sensor  254 , a relative rolling slump (Δe B ) may be determined, and may be used to estimate the development of the stiffness of the material being compacted in the work surface  106  over multiple passes. 
     Referring to  FIG. 3 , a measurement of the distance h 6  may be performed by the one or more middle distance sensors  252 . According to an aspect of the disclosure, the distance h 6  may result from an average of two or more distance sensors included in the at least one middle distance sensor  252 . It will be appreciated, however, that the measurement of the distance h 6  and the measurement h 3  may be confounded by the distance (e B ) that the compaction drum  110  sinks into the work surface  106 , and the distance (e R ) that the at least one propulsion device  108  sinks into the work surface  106 . As next described, the measured values of the distances h 3  and h 6  may be corrected using a correction angle (β) to yield corrected values, h 3 * and h 6 *, which may in turn be used to calculate the relative rolling slump (Δe B ). 
     The correction angle (β) may be defined by the following relationship in Equation 10.
 
arctan(β)= e   R /( l   4   +l   3 )  Equation 10
 
     The correction magnitudes, h 3 ′ and h 6 ′, corresponding to the measurement values of h 3  and h 6 , respectively, can be calculated as shown in Equations 11 and 12.
 
 h   6   ′=l   2 *tan(β)  Equation 11
 
 h   3   ′=l   1 *tan(β)  Equation 12
 
     The corrected values, h 3 * and h 6 *, may be calculated as shown in Equations 13 and 14.
 
 h   6   *=h   6   −h   6 ′  Equation 13
 
 h   3   *=h   3   −h   3 ′  Equation 14
 
     And finally, including the elastic recovery of the soil, the relative rolling slump (Δe B ) may be calculated as shown in Equation 15.
 
Δ e   B   =|h   3   *−h   6 *|  Equation 15
 
     In practice, the absolute value of Δe B  may be convenient for use as the relative rolling slump for the purpose of tracking incremental increases in stiffness or density of the working surface  106 , as next discussed. 
       FIG. 7  is an exemplary plot  380  of relative rolling slump versus a number of passes over a work surface, according to an aspect of the disclosure. As shown in  FIG. 7 , successive passes of the compactor machine  100  over the work surface  106  may result in a monotonically decreasing trend in the magnitude of the relative rolling slump Δe B  that asymptotically approaches zero. It will be appreciated that GPS technology, or any other technology known in the art for tracking a machine on a work surface  106 , may be used to pair relative rolling slump values with a specific location on the work surface  106 . Accordingly, a trend of relative rolling slump may be provided to an operator of the compactor machine  100  as the compactor machine traverses successive passes over the work surface  106 , to aid the operator in knowing when optimum or target compaction is achieved. 
       FIG. 8  is an exemplary plot  382  of a distance ratio h 6 /h 3  versus a number of passes over a work surface, according to an aspect of the disclosure. As shown in  FIG. 8 , the distance ratio of h 6 /h 3 , measured from the at least one middle distance sensor  252  and the at least one forward distance sensor  250 , may initially decreases monotonically with successive passes of the compactor machine  100  over the work surface  106 . However, the distance ratio h 6 /h 3  may eventually exhibit a local minimum  384 , near a value of one, beyond which indicating that additional passes may tend to decrease the density or stiffness of the work surface  106 . It will be appreciated that GPS technology, or any other technology known in the art for tracking a machine on a work surface  106 , may be used to pair values of the distance ratio h 6 /h 3  with a specific location on the work surface  106 . Accordingly, a trend of the distance ratio h 6 /h 3  may be provided to an operator of the compactor machine  100  as the compactor machine traverses successive passes over the work surface  106 , to aid the operator in knowing when optimum or target compaction is achieved. 
     It will be appreciated that the foregoing description provides examples of the disclosed system and technique. However, it is contemplated that other implementations of the disclosure may differ in detail from the foregoing examples. All references to the disclosure or examples thereof are intended to reference the particular example being discussed at that point and are not intended to imply any limitation as to the scope of the disclosure more generally. All language of distinction and disparagement with respect to certain features is intended to indicate a lack of preference for those features, but not to exclude such from the scope of the disclosure entirely unless otherwise indicated. 
     Recitation of ranges of values herein are merely intended to serve as a shorthand method of referring individually to each separate value falling within the range, unless otherwise indicated herein, and each separate value is incorporated into the specification as if it were individually recited herein. All methods described herein can be performed in any suitable order unless otherwise indicated herein or otherwise clearly contradicted by context. 
     The controller  128  may be any purpose-built processor for effecting control of the compactor machine  100  or the compaction system  102 . It will be appreciated that the controller  128  may be embodied in a single housing, or a plurality of housings distributed throughout the compactor machine  100  or the compaction system  102 . Further, the controller  128  may include power electronics, preprogrammed logic circuits, data processing circuits, volatile memory, non-volatile memory, software, firmware, input/output processing circuits, combinations thereof, or any other controller structures known in the art. 
     Any of the methods or functions described herein may be performed by or controlled by the controller  128 . Further, any of the methods or functions described herein may be embodied in a computer-readable non-transitory medium for causing the controller  128  to perform the methods or functions described herein. Such computer-readable non-transitory media may include magnetic disks, optical discs, solid state disk drives, combinations thereof, or any other computer-readable non-transitory medium known in the art. Moreover, it will be appreciated that the methods and functions described herein may be incorporated into larger control schemes for an engine, a machine, or combinations thereof, including other methods and functions not described herein.