Patent Publication Number: US-10775272-B2

Title: Rubber footprint and rolling resistance measurement

Description:
CROSS-REFERENCE TO RELATED APPLICATION 
     This application claims the benefit of priority from U.S. Provisional Patent Application Ser. No. 62/594,558, filed on Dec. 5, 2017, and entitled “SIMULTANEOUS MEASUREMENT OF RUBBER FOOTPRINT AND ROLLING RESISTANCE,” which is incorporated herein by reference in its entirety. 
    
    
     TECHNICAL FIELD 
     The present disclosure relates to systems and methods for testing and measuring properties of materials, particularly relates to systems and methods for measurement of rubber footprint and rolling resistance of rubber substrates. 
     BACKGROUND 
     Rolling resistance of a tire may be defined as the amount of energy dissipated in rolling of the tire per unit normal load and unit distance travelled by the tire. For a tire made of rubber, the main contributor to rolling resistance is hysteresis due to the viscoelastic behavior of rubber. Repeated cycles of deformation and recovery experienced by a rubber tire as it rotates under the weight of a vehicle leads to hysteresis energy loss being dissipated from the rubber tire as heat. The rolling resistance may cause an increase in fuel consumption and vehicle greenhouse gas emissions. Therefore, there is a need for designing rubber tires with lower rolling resistance. To this end, systems and methods are required for measuring and comparing rolling resistances and energy dissipations in rubber tires under rolling conditions. 
     Developing systems and methods for measuring the rolling resistance of a rubber tire may have numerous challenges such as finding optimal ways of applying the rolling driving force, measuring the rolling resistance, and providing a continuous flat surface for rolling. Systems and methods have been developed in which rubber tires are rolled against a rotating drum using complex mechanical and electronic devices to apply the rolling driving force and measuring the rolling resistance. However, in such systems and methods due to the complexity of the system, losses in gears and motors may not be properly accounted for, which may considerably affect the accuracy of the measurements. 
     In order to replace the complex mechanical and electronic devices in the aforementioned measuring systems, an independent pendulum driving force may be utilized to create a reciprocating rolling movement that may simulate a continuous rolling motion of the rubber tire. Damping of the oscillatory motion of the rubber tire that is connected to the pendulum may be utilized for measuring the rolling resistance of the rubber tire. However, systems and methods that are developed based on damping of oscillatory motion of a pendulum need to be further improved to ensure a repeatable release of the pendulum at a specific angle, a straight rolling path for the rubber tire, and a balanced pendulum motion against centrifugal forces acting on the pendulum. There is further a need for developing systems and methods that allow for an accurate non-contact measurement of rolling resistance without imposing unwanted limitations in the oscillatory rolling motion of the rubber tire. 
     SUMMARY 
     This summary is intended to provide an overview of the subject matter of the present disclosure, and is not intended to identify essential elements or key elements of the subject matter, nor is it intended to be used to determine the scope of the claimed implementations. The proper scope of the present disclosure may be ascertained from the claims set forth below in view of the detailed description below and the drawings. 
     According to one or more exemplary embodiments, the present disclosure is directed to a system for measuring rolling resistance of a substrate. The exemplary system may include a transparent support member including a transparent contact surface, a rolling member including a cylindrical convex surface with the substrate attached on the cylindrical convex surface, the cylindrical convex surface configured to be in constant contact with the contact surface, an oscillation mechanism coupled with the rolling member configured to drive an oscillatory rotational movement of the rolling member about a longitudinal axis of the rolling member. The oscillation mechanism may include two parallel arms attached at their respective midpoints to either base end of the rolling member on a pivot axis overlapping the longitudinal axis of the rolling member, the two parallel arms attached to one another at respective ends of the two parallel arms by two links, and two adjustable weights, each of the two adjustable weights mounted on a respective link of the two links. The exemplary system may further include a light source arranged at one side of the transparent body such that light from the light source may be emitted within the transparent support member, and an image capturing device placed below the contact surface that may be configured to capture images of contact patch of the substrate through the transparent support member. 
     In an exemplary embodiment, the exemplary system may further include a control unit that may be coupled with the image capturing device. The control unit may include a processor, and a memory that may be configured to store executable instructions to cause the processor to identify a pressure center for the rubber footprint of the substrate based on the images captured by the image capturing device, where the pressure center may correspond to a region within the images of the rubber footprint with the highest black pixel density, and to obtain a rate of change in a motion range of the rubber footprint by tracking back and forth motion of the pressure center of the images. 
     In an exemplary embodiment, the memory may be configured to store further executable instructions to cause the processor to calculate a pressure distribution within the rubber footprint by dividing an average black pixel density of the captured images by the highest black pixel density in the captured images. 
     In an exemplary embodiment, the memory may be configured to store further executable instructions to cause the processor to calculate rolling resistance of the substrate by equation below: 
             RR   =         ∑     n   =   0       n   =   ∞       ⁢       2   ⁢     mgL   ⁡     [     cos   ⁢           ⁢     θ   0       ]           R   ⁢           ⁢     θ   n           =       2   ⁢     mgL   ⁡     [     cos   ⁢           ⁢     θ   0       ]             ∑     n   =   0       n   =   ∞       ⁢     R   ⁢           ⁢     θ   n                   
where, RR is the amount of rolling resistance, m is the mass of each of the two adjustable weights, g is the standard gravity, L is the distance between either one of the two adjustable weights from a center of rolling member, θ 0  is the initial angle of oscillation mechanism with a normal axis of the transparent support member, θ n  is the angle of oscillation mechanism with the normal axis of the transparent support member in an n th  oscillation of the rocking motion of the rolling member, and R is a radius of the rolling member.
 
     In an exemplary embodiment, the longitudinal axis of the rolling member may be an axis passing through a center of the mass of the rolling member on a similar plane with a rolling direction of the rolling member perpendicular to the rolling direction. 
     In an exemplary embodiment, the rolling member may further include two adjustable side-weights that may be removably attached to either base ends of the rolling member. 
     In an exemplary embodiment, the exemplary system may further include a main chassis. The main chassis may include a base support, and a mounting rig that may be attached on the base support. The mounting rig may include two parallel vertical poles mounted on the base support, and a horizontal pole mounted between the two parallel vertical poles with an adjustable height relative to the transparent support member. 
     In an exemplary embodiment, the exemplary system may further a weight release mechanism that may be mounted on the horizontal pole. The weight release mechanism may include a shaft that may be pivotally mounted on the horizontal pole at a first end of the shaft, and a receptacle that may be attached to a second end of the shaft. In an exemplary embodiment, the receptacle may include an electromagnet selectively engaging one of the two adjustable weights. 
     In an exemplary embodiment, the receptacle may be a longitudinal section of a cylinder including a semi-cylindrical recess longitudinally formed on the receptacle, where one of the two adjustable weights may be received within the semi-cylindrical recess. 
     In an exemplary embodiment, the image capturing device may be mounted on the base support below the transparent support member. The image capturing device may be enclosed by a cover. The cover may extend downward from immediately below a lower surface of the transparent support member to immediately above an upper surface of the base support. 
     In an exemplary embodiment, the rolling member may be a cylinder-shaped roller with two adjustable side weights removably attached to either base ends of the cylinder-shaped roller. 
     In an exemplary embodiment, the rolling member may be a longitudinal section of a cylinder including a lower cylindrical convex surface and an upper flat surface, the substrate attached under the lower cylindrical convex surface. 
     In an exemplary embodiment, the rolling member may further comprises adjustable weights removably mounted on the upper flat surface. In an exemplary embodiment, the rolling member may be a wheel with the substrate attached to a rim of the wheel. 
     In an exemplary embodiment, the transparent support member may be a box-shaped member with parallel and flat upper surface and lower surface. The upper surface may provide the transparent contact surface. 
     According to one or more exemplary embodiments, the present disclosure is directed to a method for testing properties of a rubber substrate. The method may include attaching the rubber substrate on a convex cylindrical surface of a rolling member, rocking the rolling member with an initial amplitude over a transparent surface, capturing consecutive images of a rubber footprint of the rubber substrate from under the transparent surface, obtaining, using one or more processors, a rate of change in the initial amplitude of the rocking motion of the rolling member on the transparent surface based at least in part on a rate of change in a range of back and forth motion of the rubber footprint by optically processing the captured consecutive images, and calculating, using one or more processors, an amount of rolling resistance for the rubber substrate based at least in part on the rate of change in the amplitude of the rocking motion of the rolling member on the transparent surface. 
     In an exemplary embodiment, rocking the rolling member with the initial amplitude over the transparent surface may include coupling the rolling member with an oscillation mechanism. The oscillation mechanism may include two parallel arms attached at their respective midpoints to either base ends of the rolling member on a pivot axis overlapping a longitudinal axis of the rolling member, the two parallel arms attached to one another at respective ends of the two parallel arms by two links, and two adjustable weights, each of the two adjustable weights mounted on a respective link of the two links. In an exemplary embodiment, rocking the rolling member with the initial amplitude over the transparent surface may further include adjusting the initial amplitude by adjusting an initial orientation of the two parallel arms with respect to the transparent surface, and releasing the oscillation mechanism from the initial orientation to freely oscillate in a rocking motion back and forth about the longitudinal axis of the rolling member. 
     In an exemplary embodiment, obtaining the rate of change in the initial amplitude of the rocking motion of the rolling member on the transparent surface may include optically processing the captured images to track the position of the rubber footprint on transparent surface at every instant of the test. 
     In an exemplary embodiment, obtaining the rate of change in the initial amplitude of the rocking motion of the rolling member on the transparent surface may include processing the captured images to find a pressure center for the rubber footprint by finding a region with the highest black pixel density, and calculating, at any given moment a distance between the pressure center and a reference line. 
    
    
     
       BRIEF DESCRIPTION OF THE DRAWINGS 
       The drawing figures depict one or more implementations in accord with the present teachings, by way of example only, not by way of limitation. In the figures, like reference numerals refer to the same or similar elements. 
         FIG. 1A  illustrates a block diagram of a system for measuring rolling resistance of a substrate, consistent with one or more exemplary embodiments of the present disclosure; 
         FIG. 1B  illustrates a perspective view of measurement apparatus, consistent with one or more exemplary embodiments of the present disclosure; 
         FIG. 2A  illustrates a perspective view of an oscillation mechanism coupled with a rolling member, consistent with one or more exemplary embodiments of the present disclosure; 
         FIG. 2B  illustrates a perspective view of an oscillation mechanism coupled with a rolling member, consistent with one or more exemplary embodiments of the present disclosure; 
         FIG. 2C  illustrates a perspective view of an oscillation mechanism coupled with a wheel, consistent with one or more exemplary embodiments of the present disclosure; 
         FIG. 3  illustrates a perspective view of a weight release mechanism, consistent with one or more exemplary embodiments of the present disclosure; 
         FIG. 4  illustrates a method for testing properties of a rubber substrate, consistent with one or more exemplary embodiments of the present disclosure; 
         FIG. 5A  illustrates a schematic of a rolling member and an oscillation mechanism in three stages during rocking motion of the rolling member and corresponding images captured by an image capturing device, consistent with one or more exemplary embodiments of the present disclosure; 
         FIG. 5B  illustrates a schematic of an exemplary image of a rubber footprint of a rubber substrate captured by an image capturing device, consistent with one or more exemplary embodiments of the present disclosure; and 
         FIG. 6  illustrates a graph of rubber footprint position versus time during an exemplary test, consistent with one or more exemplary embodiments of the present disclosure. 
     
    
    
     DETAILED DESCRIPTION 
     In the following detailed description, numerous specific details are set forth by way of examples to provide a thorough understanding of the relevant teachings related to the exemplary embodiments. However, it should be apparent that the present teachings may be practiced without such details. In other instances, well known methods, procedures, components, and/or circuitry have been described at a relatively high level, without detail, in order to avoid unnecessarily obscuring aspects of the present teachings. 
     The following detailed description is presented to enable a person skilled in the art to make and use the methods and devices disclosed in exemplary embodiments of the present disclosure. For purposes of explanation, specific nomenclature is set forth to provide a thorough understanding of the present disclosure. However, it will be apparent to one skilled in the art that these specific details are not required to practice the disclosed exemplary embodiments. Descriptions of specific exemplary embodiments are provided only as representative examples. Various modifications to the exemplary implementations will be plain to one skilled in the art, and the general principles defined herein may be applied to other implementations and applications without departing from the scope of the present disclosure. The present disclosure is not intended to be limited to the implementations shown but is to be accorded the widest possible scope consistent with the principles and features disclosed herein. 
     Contact patch or rubber footprint is the portion of a rubber tire that is in contact with a road surface. In the assessment of a tire, especially a pressurized rubber tire, factors like the pressure distribution within the contact patch of the tire, as well as the size and shape of the contact patch are factors that may affect the wear characteristics of the rubber tire. Furthermore, the amount of energy dissipation during the rolling motion of the rubber tire due to the rolling resistance is another important design factor in manufacturing rubber tires. Designing an efficient rubber tire may depend on accurate measurement and evaluation of the rubber footprint and rolling resistance of a rubber substrate that is used for manufacturing that rubber tire. 
     The present disclosure is directed to exemplary systems and exemplary methods for testing properties of a rubber substrate. An exemplary system for testing properties of a rubber substrate may be utilized to simulate rolling motion of the rubber substrate on a surface and then to measure and calculate the shape and size of the rubber footprint of the rubber substrate on the surface, the pressure distribution within the rubber footprint of the substrate, and the amount of the rolling resistance of the substrate. An exemplary system for testing properties of a rubber substrate may include a rolling member with a convex cylindrical surface, on which a rubber substrate may be attached. The rolling member of different exemplary embodiments of the present disclosure may be placed over a transparent surface and may further be coupled with an oscillation mechanism. The exemplary oscillation mechanism may cause a rocking motion of the exemplary rolling member back and forth on the transparent surface. The mechanism may also cause pressing of the substrate onto the transparent surface while an image-capturing device may capture images of the rubber footprint of the substrate from under the transparent surface. The exemplary system may further include a control unit that may receive the captured images and may process the images to measure and calculate the shape and size of the rubber footprint of the rubber substrate on the surface, the pressure distribution within the rubber footprint of the substrate, and the amount of the rolling resistance of the substrate. 
       FIG. 1A  illustrates a block diagram of a system  100  for testing properties of a substrate  102 , consistent with one or more exemplary embodiments of the present disclosure. In an exemplary embodiment, system  100  may include a testing apparatus  104  that may be utilized for simulating a rolling movement of substrate  102  on a surface and capturing consecutive images of the rolling movement of substrate  102  on the surface, a control unit  106  coupled with testing apparatus  104  and configured to receive and process the captured consecutive images, and optionally a user interface unit  108 . 
       FIG. 1B  illustrates a perspective view of testing apparatus  104 , consistent with one or more exemplary embodiments of the present disclosure. Referring to  FIGS. 1A and 1B , in an exemplary embodiment, testing apparatus  104  may include a transparent support member  140 , a rolling member  142  that may include a cylindrical convex surface  1420  on which substrate  102  may be attached, an oscillation mechanism  144  that may be coupled with rolling member  142  and may be configured to drive an oscillatory rocking motion of rolling member  142  about a longitudinal axis  1422  of rolling member  142  along a rolling direction as shown by arrow  1425 , light sources  146   a - b,  and an image capturing device  148  that may be placed below transparent support member  140  and may be configured to capture consecutive images of rubber footprint of substrate  102  through transparent support member  140 . 
     In an exemplary embodiment, transparent support member  140  may be a box-shaped member that may be made of a transparent material such as glass with a predetermined thickness  1402 . An upper surface  1404  and a lower surface  1406  of transparent support member  140  may be smooth and flat and may be parallel to each other. Upper surface  1404  of transparent support member  140  may provide a transparent surface on which substrate  102  may rock back and forth. 
     In an exemplary embodiment, light sources  146   a - b  may be attached on either side of transparent support member  140  and may be arranged such that the light from light sources  146   a - b  is emitted within the thickness of transparent support member  140 . In an exemplary embodiment, such configuration of light sources  146   a - b  may provide enough light for image capturing device  148  to efficiently capture the reflected light from the rubber footprint of substrate  102  through transparent support member  140 . In an exemplary embodiment, light sources  146   a - b  may include long light emitting devices such as fluorescent lamps with a predetermined length or a number of light sources that may be place at regular intervals along the sides of transparent support member  140  in order to supply a stable light within transparent support member  140 . 
       FIG. 2A  illustrates a perspective view of oscillation mechanism  144  coupled with rolling member  142 , consistent with one or more exemplary embodiments of the present disclosure. In an exemplary embodiment, oscillation mechanism  144  may include two parallel arms  1440   a - b  that may be attached at their respective midpoints  1441   a - b  to either base ends  1424   a - b  of rolling member  142  on a pivot axis overlapping longitudinal axis  1422  of rolling member  142 . In an exemplary embodiment, two parallel arms  1440   a - b  may further be attached together at respective ends of two parallel arms  1440   a - b  by two links  1442   a - b.  For example, first ends  1444   a - b  of two parallel arms  1440   a - b  may be connected by link  1442   a  and second ends  1446   a - b  of two parallel arms  1440   a - b  may be connected by link  1442   b.    
     In an exemplary embodiment, oscillation mechanism  144  may further include two adjustable weights  1448   a - b.  Each of two adjustable weights  1448   a - b  may be mounted on a respective link of the two links  1442   a - b.  For example, adjustable weight  1448   a  may be mounted on link  1442   a  and adjustable weight  1448   b  may be mounted on link  1442   b.  In an exemplary embodiment, links  1442   a - b  may either be attached or integrally formed with parallel arms  1440   a - b.    
     In an exemplary embodiment, rolling member  142  may be a cylinder-shaped roller capable of assuming an oscillatory rocking motion back and forth about longitudinal axis  1422 , when urged by oscillation mechanism  144 , which will be described later in this disclosure. In exemplary embodiments, such configuration of the rolling member  142  and oscillation mechanism  144  may allow for simulating a rolling movement of substrate on a surface under a predetermined load without a need for a long and impractical test surface on which rolling member  142  may assume a full rolling motion about longitudinal axis  1422 . In an exemplary embodiment, in order to adjust the predetermined load on substrate  102 , rolling member  142  may further include two adjustable side-weights  1426   a - b  that may be removably attached to either base ends  1424   a - b  of rolling member  142 . In exemplary embodiments, in order to increase the load exerted on substrate  102 , adjustable weights  1426   a - b  may be replaced by heavier weights and in order to reduce the load exerted on substrate  102 , adjustable weights  1426   a - b  may be replaced by lighter weights or be removed all together. 
       FIG. 2B  illustrates a perspective view of oscillation mechanism  144  coupled with rolling member  142 , consistent with one or more exemplary embodiments of the present disclosure. In an exemplary embodiment, rolling member  142  may be a longitudinal section of a cylinder with substrate  102  attached under cylindrical convex surface  1420  of rolling member  142 . In an exemplary embodiment, in order to adjust the predetermined load on substrate  102 , rolling member  142  may further include a weight support structure  1428  mounted or attached on a flat upper surface  14210  of rolling member  142 . Weight support structure  1428  may be sized and shaped to be capable of receiving weights  14212 . In an exemplary embodiment, in order to increase the load exerted on substrate  102 , weights  14212  may be added onto weight support structure  1428  and in order to reduce the load exerted on substrate  102 , weights  14212  may be removed from weight support structure  1428 . 
       FIG. 2C  illustrates a perspective view of oscillation mechanism  144  coupled with a wheel  202 , consistent with one or more exemplary embodiments of the present disclosure. In an exemplary embodiment, instead of rolling member  142  of  FIGS. 2A and 2C , wheel  202  may be coupled with oscillation mechanism  144  and substrate  102  may be a tire mounted on a rim of wheel  202 . In an exemplary embodiment, two parallel arms  1440   a - b  of oscillation mechanism  144  may be attached at their respective midpoints  1441   a - b  to either sides of wheel  202  on a pivot axis overlapping longitudinal axis  204  of wheel  202 . Rolling member  142  may have any other shapes that allow for providing a consistent rolling or rocking motion in system  100 . 
     Referring back to  FIGS. 1A and 1B , in an exemplary embodiment, testing apparatus  104  may further include a weight release mechanism  1410  that may be placed at either one of the sides of oscillation mechanism  144  and may be configured to hold and then selectively release one of adjustable weights  1448   a  or  1448   b.  In an exemplary embodiment, weight release mechanism  1410  may be mounted on a main chassis  1412  of testing apparatus  104 . Main chassis  1412  may include a base support  1414  and a mounting rig  1416  attached on base support  1414 . 
     In an exemplary embodiment, mounting rig  1416  may allow for vertical and horizontal adjustment of the position of weight release mechanism  1410  relative to transparent support member  140 . In an exemplary embodiment, mounting rig  1416  may include two parallel vertical poles  1418   a - b  and a horizontal pole  1421  which may be mounted on two parallel vertical poles  1418   a - b  by two lock-screw joints  1423   a - b  at either ends of horizontal pole  1421 . In exemplary embodiments, mounting horizontal pole  1421  on two parallel vertical poles  1418   a - b  by two lock-screw joints  1423   a - b  may allow for vertically adjusting the height at which horizontal pole  1421  may be mounted relative to transparent support member  140 . 
       FIG. 3  illustrates a perspective view of weight release mechanism  1410 , consistent with one or more exemplary embodiments of the present disclosure. Referring to  FIGS. 1B and 3 , in an exemplary embodiment, weight release mechanism  1410  may include a receptacle  302  mounted at a distal end of a shaft  304 . In an exemplary embodiment, receptacle  302  may be a holder that may be sized and shaped to hold either one of adjustable weights  1448   a  or  1448   b.  In an exemplary embodiment, receptacle  302  may be an electromagnet that may selectively engage the adjustable weight which is received inside receptacle  302 . In detail, holding either one of adjustable weights  1448   a  or  1448   b  may entail placing either one of adjustable weights  1448   a  or  1448   b  within receptacle  302  and then keeping either one of adjustable weights  1448   a  or  1448   b  in place by techniques such as magnetically engaging either one of adjustable weights  1448   a  or  1448   b.    
     Referring to  FIGS. 1A and 3 , in an exemplary embodiment, weight release mechanism  1410  may be coupled with control unit  106  and may receive control signals in the form of an electric current from control unit  106 . Upon receiving the electric current, a magnetic field may be created in receptacle  302  and either one of adjustable weights  1448   a  or  1448   b,  for example, adjustable weight  1448   b  as shown in  FIG. 1A  may be held within receptacle  302  under the created magnetic force. When the electric current is cut off by control unit  106 , the magnetic field may disappear and receptacle  302  may disengage adjustable weight  1448   b  and oscillation mechanism  144  may be free to start its rocking motion. 
     In an exemplary embodiment, weight release mechanism  1410  may be mounted on horizontal pole  1421  by a pivot joint  308  that may allow for pivoting shaft  304  about axis  306  which is parallel to longitudinal axis  1422  and extending/retracting shaft  302  along linear axis  310 . In an exemplary embodiment, pivot joint  308  may be coupled with shaft  304  via a ring connection  312  with a lock screw  314  that may be utilized to selectively grip/release shaft  304  from ring connection  312 . In an exemplary embodiment, pivot joint  308  may be slidably mounted on horizontal pole  1421  and may allow for horizontally moving weight release mechanism  1410  along horizontal pole  1421 . In exemplary embodiments, such a configuration of pivot joint  308  on horizontal pole  1421  may allow for horizontally adjusting the position of weight release mechanism  1410  relative to transparent support member  140 . 
     In an exemplary embodiment, receptacle  302  may be a longitudinal section of a cylinder with a semi-cylindrical recess  316  longitudinally formed on receptacle  302 . Semi-cylindrical recess  316  may be sized and shaped to match the shape of and hold either one of adjustable weights  1448   a  or  1448   b.  For example, semi-cylindrical recess  316  may be sized and shaped to hold adjustable weight  1448   b.  In detail, when adjustable weight  1448   b  is held by receptacle  302  it means that adjustable weight  1448   b  may sit within semi-cylindrical recess  316 . Receptacle  302  may further include two openings  318  at either ends of receptacle  302  to accommodate link  1442   b.    
     In an exemplary embodiment, image capturing device  148  may be a camera mounted below transparent support member  140 . Image capturing device  148  may be enclosed by a cover  150  that may extend downward from immediately below lower surface  1406  of transparent support member  140  to immediately above the upper surface of base support  1414 . In exemplary embodiments, such configuration of cover  150  may allow for isolating image capturing device  148  from ambient light or any light sources other than light sources  146   a - b.  In exemplary embodiments, such a configurations may allow for image capturing device  148  to capture high quality consecutive images of rubber footprint of substrate  102  on transparent support member  140  as rolling member rocks substrate  102  back and forth over transparent support member  140 , an oscillatory motion urged by oscillation mechanism  144 . 
     Referring to  FIG. 1A , in an exemplary embodiment, control unit  106  may be coupled to testing apparatus  104  and user interface unit  108  through wired links, wireless links, or a combination of wired and wireless links. In an exemplary embodiment, control unit  106  may be configured to process the captured images from substrate  102  by image capturing device  148  to observe contact patch and measure rolling resistance of substrate  102 . In an exemplary embodiment, control unit  106  may further be configured to control testing apparatus  104  for purposes that may include adjusting the intervals between consecutive images captured by image capturing device  148 , adjusting the initial position of weight release mechanism  1410 , and adjusting the intensity of light that may be emitted by light sources  146   a - b  on substrate  102 . 
     In an exemplary embodiment, control unit  106  may include a memory  1062  and a processor  1064 . Memory  1062  may include executable instructions that, when executed, cause processor  1064  to perform operations that in an exemplary embodiment may include processing the received images from image capturing device  148  to evaluate contact patch of substrate  102  and to measure rolling resistance of substrate  102 . In an exemplary embodiment, such operations may include measuring rolling resistance of substrate  102  based at least in part on damping characteristics of the oscillatory rocking motion of rolling member  142 . In exemplary embodiments, such measurements may be performed by operations that may compare consecutively captured images of substrate  102  during oscillatory rocking motion of rolling member  142  on transparent support member  140 . 
     In an exemplary embodiment, user interface unit  108  may be configured to display measurement results of contact patch and rolling resistance of substrate  102 . In an exemplary embodiment, user interface unit  108  may include a graphical user interface unit (GUI) that may be optionally configured to receive data input from a user. In an exemplary embodiment, data input by the user may include a desirable interval for capturing the consecutive images by the image capturing device  148 , a desirable intensity for light emitted by light sources  146   a - b  on substrate  102 , a desirable value for the initial position of weight release mechanism  1410  or commands regarding the release of adjustable weight  1448   b  by weight release mechanism  1410 . 
       FIG. 4  illustrates a method  400  for testing properties of a rubber substrate, consistent with one or more exemplary embodiments of the present disclosure. In an exemplary embodiment, system  100  of  FIG. 1A  may be utilized for implementing method  400 . Referring to  FIG. 4 , method  400  may include a step  402  of attaching the rubber substrate on a convex cylindrical surface of a rolling member, a step  404  of rocking the rolling member with an initial amplitude over a transparent surface, a step  406  of capturing consecutive images of a rubber footprint of the rubber substrate from under the transparent surface, a step  408  of obtaining a rate of change in the initial amplitude of the rocking motion of the rolling member on the transparent surface by optically processing the captured consecutive images, and a step  410  of calculating an amount of rolling resistance for the rubber substrate based at least in part on the rate of change in the amplitude of the rocking motion of the rolling member on the transparent surface. 
     Referring to  FIGS. 1A and 4 , in an exemplary embodiment, step  402  may involve attaching the rubber substrate on a convex cylindrical surface of a rolling member, for example, rubber substrate may be a rubber sheet such as substrate  102  that may be attached on convex cylindrical surface  1420  of rolling member  142 . 
     In an exemplary embodiment, step  404  of rocking the rolling member with an initial amplitude over a transparent surface may include rocking the rolling member with an initial amplitude over the transparent surface utilizing an oscillation mechanism. For example, rolling member  142  may be rocked over transparent support member  140  utilizing oscillation mechanism  144 . In an exemplary embodiment, rocking the rolling member with the initial amplitude over the transparent surface may include adjusting the initial amplitude of the rocking motion of the rolling member, for example, placing adjustable weight  1448   b  of oscillation mechanism  144  within weight release mechanism  1410  may put oscillation mechanism  144  in an initial orientation which in turn may determine an initial position and orientation of rolling member  142  over transparent support member  140 . With further reference to  FIGS. 1B and 3 , the position of weight release mechanism  1410  may be changed relative to transparent support member  140  by changing the height of weight release mechanism  1410  by vertically moving horizontal pole  1421  on vertical poles  1418   a - b,  changing the horizontal position of weight release mechanism  1410  by sliding weight release mechanism  1410  on horizontal pole  1421  along an axis parallel to longitudinal axis  1422 , changing the lateral distance of weight release mechanism  1410  with transparent support member  140  by extending/retracting shaft  302  along linear axis  310 . In an exemplary embodiment, initial position of weight release mechanism  1410  may be manipulated in order to adjust the initial position and orientation of oscillation mechanism  144  which in turn may determine the initial position and orientation of rolling member  142  before rolling member  142  may start its rocking motion. This initial position and orientation of rolling member  142  may set the initial amplitude at which oscillation mechanism  144  may urge rolling member  142  to rock back and forth on transparent support member  140 . As used herein, a rocking motion may refer to a motion similar to the motion of a seesaw in oscillation mechanism  144  about longitudinal axis  1422  that may urge rolling member  142  to rock back and forth about longitudinal axis  1422 . 
     Referring to  FIGS. 1A and 4 , in an exemplary embodiment, step  406  may involve capturing consecutive images of a rubber footprint of the rubber substrate from under the transparent surface. For example, image capturing device  148  may be utilized for capturing consecutive images of the rubber footprint of substrate  102  from below transparent support member  140  and light sources  146   a - b  may be utilized to shine light on the rubber footprint of substrate  102  to allow for high quality images to be captured of the rubber footprint of substrate  102 . As used herein, capturing consecutive images may also refer to continuously filming the back and forth motion of the rubber footprint on transparent support member  140 . 
       FIG. 5A  illustrates a schematic of rolling member  142  and oscillation mechanism  144  in three stages  502 ,  504 , and  506  during rocking motion of rolling member  142  and corresponding images  508 ,  510 , and  512  captured by image capturing device  148 , consistent with one or more exemplary embodiments of the present disclosure. In an exemplary embodiment, as rolling member  142  rolls forward on transparent support member  140 , a corresponding rubber foot print  520  of substrate  102  captured in corresponding images  508 ,  510 , and  512  also moves forward. Therefore, the back and forth rocking motion of rolling member  142  on transparent support member  140  may be tracked in corresponding images  508 ,  510 , and  512  as the back and forth motion of rubber foot print  520 . 
     Referring to  FIGS. 1A and 4 , in an exemplary embodiment, step  408  of obtaining the rate of change in the initial amplitude of the rocking motion of the rolling member on the transparent surface by optically processing the captured consecutive images may include tracking a back and forth movement of the rubber footprint of the rubber substrate on the transparent surface by processing the captured consecutive images by an image processor. For example, the consecutive images that may be captured by image capturing device  148  may be transferred to control unit  106  where the captured images may be stored on memory  1062 . The stored captured images may then be read from memory  1062  by processor  1064  during the test or at some time after the test has been run. Processor  1064  may optically process the captured images to track the back and forth movement of the rubber footprint of substrate  102  based at least in part on the position of the rubber footprint on transparent support member  140  at every instance of the test. In an exemplary embodiment, the test may begin by releasing oscillation mechanism  144  from its initial orientation by weight release mechanism  1410  and the test may end with an amplitude of the rocking motion of oscillation mechanism  144  reaching zero. In other words, the test ends when the back and forth rocking motion of oscillation mechanism  144  comes to an end. 
       FIG. 5B  illustrates a schematic of an exemplary image  530  of rubber footprint of a rubber substrate captured by image capturing device  148 , consistent with one or more exemplary embodiments of the present disclosure. Pixel density within the captured rubber footprint is higher near its central region  532  where the pressure exerted on the rubber substrate is higher and pixel density is lower toward the edges  534  of rubber footprint, where the pressure exerted on the rubber substrate is lower. With further reference to  FIGS. 1A and 4 , in an exemplary embodiment, step  408  of obtaining the rate of change in the initial amplitude of the rocking motion of the rolling member on the transparent surface may include processing the captured images to find a pressure center  536  for the rubber footprint by finding a region with the highest pixel density and then calculating, at any given moment during the test, a distance  538  between pressure center  536  and a reference line which may be one of the lateral edges of the captured image, for example edge  540 . This way, in exemplary embodiments, a range of motion may be obtained for the rubber footprint which may be considered as a measure of how far rolling member  142  is rocking back and forth. In an exemplary embodiment, the position of rubber footprint at any given moment during the test may be calculated as a distance between pressure center  536  and a center line  542 . In an exemplary embodiment, center line  542  may be the midpoint of the motion path of rolling member  142 . 
       FIG. 6  illustrates a graph of rubber footprint position versus time during an exemplary test, consistent with one or more exemplary embodiments of the present disclosure. With further reference to  FIG. 5B , in this exemplary graph, rubber footprint position is calculated as a distance between pressure center  536  of the rubber footprint and center line  542 . Referring to  FIGS. 5A and 6 , it is evident that the range of motion or the amplitude for rolling member  142  decreases with time. The amount of rolling resistance of substrate  102  is proportional to the rate at which the amplitude decreases. For example, for a substrate with a high rolling resistance the amplitude decreases rapidly while for a substrate with a lower rolling resistance the amplitude decreases more slowly. The rate of decrease of amplitude of rocking motion of rolling member  142  may be a measure of the rolling resistance of substrate  102 . In the exemplary test shown in  FIG. 6 , the amplitude has decreased down to zero after 30 seconds, meaning that rolling member  142  starts its rocking motion at a high initial amplitude and then as time goes by, due to the rolling resistance of substrate  102 , the initial amplitude starts to decrease an after 30 seconds the amplitude becomes zero and rolling member  142  stops. 
     Referring to  FIGS. 1A and 4 , in an exemplary embodiment, step  410  involves calculating an amount of rolling resistance for the rubber substrate based at least in part on the rate of change in the amplitude of the rocking motion of the rolling member on the transparent surface. For example, memory  1062  may further include executable instructions that when executed by processor  1064 , may urge control unit  106  to optically process the captured images to find pressure center of the rubber footprint of substrate  102  at any given moment during the test as was discussed in connection with  FIG. 5B . Then control unit  106  may utilize the movement of pressure center of substrate  102  to calculate change in the amplitude of the rocking motion of the rolling member  142  on transparent support member  140 . 
     Referring to  FIGS. 1A and 5B , in an exemplary embodiment, memory  1062  may further include executable instructions that when executed by processor  1064 , may urge control unit  106  to calculate a pressure distribution for the rubber footprint by dividing an average pixel density of captured images by a maximum pixel density of the captured images. For example, in exemplary image  530 , a pressure distribution may be calculated by dividing an average pixel density of image  530  by the pixel density of pressure center  536 . 
     Referring to  FIG. 5A , in an exemplary embodiment, in stage  502  which may be an exemplary initial stage of a forward movement of rolling member  142 , oscillation mechanism  144  may be arranged such that it makes an initial angle  514  of θ 0  with a vertical axis  516 . Stage  504  is a stage during a forward movement of rolling member  142 , where oscillation mechanism  144  makes a 90° angle with vertical axis  516 , and stage  506  is an exemplary final stage of a forward movement of rolling member  142 , where oscillation mechanism  144  may make a final angle  518  of θ 1  with vertical axis  516 . In an exemplary embodiment, corresponding images  508 ,  510 , and  512  captured by image capturing device  148  show rubber footprint  520  of substrate  102 . As rolling member  142  rolls from initial stage  502  to final stage  506 , a distance between a pressure center of rubber footprint  520  and a reference line  522  may increase from an initial distance  524  of a 0  to a final distance  528  of a 1 . In stage  504 , pressure center of ground rubber footprint  520  is at a distance  526  of a ∞  from reference point  522 . With further reference to  FIG. 1A , in an exemplary embodiment, control unit  106  may be calibrated to calculate the angle that oscillation mechanism  144  makes with vertical axis  516  at any given moment during the test and the angle may be labeled as θ n , which is the angle of oscillation mechanism  144  with vertical axis  516  in the n th  oscillation of rolling member  142 . 
     In an exemplary embodiment, memory  1062  may further include executable instructions that when executed by processor  1064 , may urge control unit  106  to calculate rolling resistance of substrate  102  by Equation (1) below: 
     
       
         
           
             
               
                 
                   RR 
                   = 
                   
                     
                       
                         ∑ 
                         
                           n 
                           = 
                           0 
                         
                         
                           n 
                           = 
                           ∞ 
                         
                       
                       ⁢ 
                       
                         
                           2 
                           ⁢ 
                           
                             mgL 
                             ⁡ 
                             
                               [ 
                               
                                 cos 
                                 ⁢ 
                                 
                                     
                                 
                                 ⁢ 
                                 
                                   θ 
                                   0 
                                 
                               
                               ] 
                             
                           
                         
                         
                           R 
                           ⁢ 
                           
                               
                           
                           ⁢ 
                           
                             θ 
                             n 
                           
                         
                       
                     
                     = 
                     
                       
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                           mgL 
                           ⁡ 
                           
                             [ 
                             
                               cos 
                               ⁢ 
                               
                                   
                               
                               ⁢ 
                               
                                 θ 
                                 0 
                               
                             
                             ] 
                           
                         
                       
                       
                         
                           ∑ 
                           
                             n 
                             = 
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                             n 
                             = 
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                         ⁢ 
                         
                           R 
                           ⁢ 
                           
                               
                           
                           ⁢ 
                           
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                   Equation 
                   ⁢ 
                   
                       
                   
                   ⁢ 
                   
                     ( 
                     1 
                     ) 
                   
                 
               
             
           
         
       
     
     In Equation (1) above, RR is the amount of rolling resistance, m is the mass of each of adjustable weights  1448   a - b,  g is the standard gravity, L is the distance between either one of adjustable weights  1448   a  or  1448   b  from the center of rolling member  142 , θ 0  is the initial angle of oscillation mechanism  144  with vertical axis  516 , θ n  is the angle of oscillation mechanism  144  with vertical axis  516  in the n th  oscillation, and R is the radius of rolling member  142 . 
     Referring back to  FIG. 1B , as mentioned in preceding sections, testing apparatus  104  of exemplary embodiments of the present disclosure may utilize oscillation mechanism  144  to rock rolling member  142  back and forth on transparent support member  140 . Two adjustable weights  1448   a - b  of oscillation mechanism  144  may be coupled with rolling member  142  such that adjustable weights  1448   a - b  may be symmetrically arranged at either sides of oscillation mechanism  144 . In exemplary embodiments, symmetrical arrangement of adjustable weights  1448   a - b  may allow for ensuring a stable rocking motion of rolling member  142  in a straight motion path without any deviation from the motion path as would be the case if a single pendulum were utilized for inducing the rocking motion. Moreover, in exemplary embodiments, utilizing symmetrical arrangement of adjustable weights  1448   a - b  may allow for ensuring an even load distribution of rolling member  142  on substrate  102 . Furthermore, weight release mechanism  1410  may allow for releasing oscillation mechanism  144  in the same manner for each sample substrate tested. This may standardize the motion of rolling member  142  so that consistent initial conditions such as consistent initial amplitudes may be provided to testing apparatus  104  for each test run and for each individual sample. In other words, utilizing weight release mechanism  1410  may allow for providing a same amplitude for rocking motion of rolling member  142  in different test runs. Therefore, exemplary systems consistent with one or more exemplary embodiments of the present disclosure allows for an accurate measurement and calculation of the shape and size of the rubber footprint of substrate  102  on transparent support member  140 , the pressure distribution within the rubber footprint of substrate  102 , and the amount of the rolling resistance of substrate  102 . 
     While the foregoing has described what are considered to be the best mode and/or other examples, it is understood that various modifications may be made therein and that the subject matter disclosed herein may be implemented in various forms and examples, and that the teachings may be applied in numerous applications, only some of which have been described herein. It is intended by the following claims to claim any and all applications, modifications and variations that fall within the true scope of the present teachings. 
     Unless otherwise stated, all measurements, values, ratings, positions, magnitudes, sizes, and other specifications that are set forth in this specification, including in the claims that follow, are approximate, not exact. They are intended to have a reasonable range that is consistent with the functions to which they relate and with what is customary in the art to which they pertain. 
     The scope of protection is limited solely by the claims that now follow. That scope is intended and should be interpreted to be as broad as is consistent with the ordinary meaning of the language that is used in the claims when interpreted in light of this specification and the prosecution history that follows and to encompass all structural and functional equivalents. Notwithstanding, none of the claims are intended to embrace subject matter that fails to satisfy the requirement of Sections 101, 102, or 103 of the Patent Act, nor should they be interpreted in such a way. Any unintended embracement of such subject matter is hereby disclaimed. 
     Except as stated immediately above, nothing that has been stated or illustrated is intended or should be interpreted to cause a dedication of any component, step, feature, object, benefit, advantage, or equivalent to the public, regardless of whether it is or is not recited in the claims. 
     It will be understood that the terms and expressions used herein have the ordinary meaning as is accorded to such terms and expressions with respect to their corresponding respective areas of inquiry and study except where specific meanings have otherwise been set forth herein. Relational terms such as first and second and the like may be used solely to distinguish one entity or action from another without necessarily requiring or implying any actual such relationship or order between such entities or actions. The terms “comprises,” “comprising,” or any other variation thereof, are intended to cover a non-exclusive inclusion, such that a process, method, article, or apparatus that comprises a list of elements does not include only those elements but may include other elements not expressly listed or inherent to such process, method, article, or apparatus. An element proceeded by “a” or “an” does not, without further constraints, preclude the existence of additional identical elements in the process, method, article, or apparatus that comprises the element. 
     The Abstract of the Disclosure is provided to allow the reader to quickly ascertain the nature of the technical disclosure. It is submitted with the understanding that it will not be used to interpret or limit the scope or meaning of the claims. In addition, in the foregoing Detailed Description, it can be seen that various features are grouped together in various implementations. This is for purposes of streamlining the disclosure, and is not to be interpreted as reflecting an intention that the claimed implementations require more features than are expressly recited in each claim. Rather, as the following claims reflect, inventive subject matter lies in less than all features of a single disclosed implementation. Thus, the following claims are hereby incorporated into the Detailed Description, with each claim standing on its own as a separately claimed subject matter. 
     While various implementations have been described, the description is intended to be exemplary, rather than limiting and it will be apparent to those of ordinary skill in the art that many more implementations and implementations are possible that are within the scope of the implementations. Although many possible combinations of features are shown in the accompanying figures and discussed in this detailed description, many other combinations of the disclosed features are possible. Any feature of any implementation may be used in combination with or substituted for any other feature or element in any other implementation unless specifically restricted. Therefore, it will be understood that any of the features shown and/or discussed in the present disclosure may be implemented together in any suitable combination. Accordingly, the implementations are not to be restricted except in light of the attached claims and their equivalents. Also, various modifications and changes may be made within the scope of the attached claims.