Abstract:
An idler roller conveyor uses paired rollers set at an acute angle to each other with the rollers being coplanar and skewed toward opposite sides of a perpendicular to a longitudinal axis of the conveyor. Roller pairs are preferably mounted in sub-frames that pivot about on an axis transverse to the conveyor&#39;s longitudinal axis. This arrangement produces opposing transverse forces that are subtractive to result in negligible resultant transverse forces that are unlikely to make an object veer off course.

Description:
RELATED APPLICATIONS 
     This application relates to and replaces provisional patent application Ser. No. 61/731,539, filed on 30 Nov. 2012, entitled Improved Roller Conveyor System. 
     TECHNICAL FIELD 
     Idler roller conveyors 
     BACKGROUND 
     Idler roller conveyors are widely used to support the movement of objects to, through, or from workstations. In spite of extensive use for many different applications, idler roller conveyors can still cause serious problems. Many of these problems are caused by misalignment of conveyors with respect to workstations so that objects being moved over the rollers tend to move from their intended paths. These problems often occur from the way idler roller conveyors are manually set up relative to workstations. This is often done by eyeball positioning of a conveyor oriented in the intended direction of movement of an object. 
     Slight angular misalignments can easily occur as idler roller conveyors are manually set up. They can also be misaligned even when they are fixed in place by system design. The effects of minor misalignments of infeed or outfeed conveyors can cause surprisingly large and clearly undesirable forces (forces perpendicular to the intended conveyor path) which urge an object to veer away from its intended direction of travel. We aim to minimize such forces and the harm they cause. 
     An example of such a problematic system is an off-feed idler roller conveyor that supports boards as they are being fed through a table saw. Ideally, such boards should move parallel to and against a saw fence, but, it is difficult to precisely align existing roller conveyor systems accurately to a table saw fence, especially if the alignment is done manually. If not aligned accurately, the rollers will apply transverse forces to the board being moved through the saw. The transverse forces can greatly affect the system&#39;s functionality by urging the object away from its desired path. This can lead to poor quality cutting and operator safety problems. Many devices such as feather boards and spring loaded elastomer biasing wheels (Board Buddies) are available for table saws to help overcome such forces. These devices have to be very aggressive when used with existing roller conveyor systems due to the large forces they must counter. 
     We aim at greatly reducing forces that must be overcome by such devices, thus making their design simpler and less aggressive. Such reduction in these forces also makes it easier to move objects through a system with less chance for damage to materials or injury to people. 
     SUMMARY 
     Our proposed improvement in idler roller conveyors significantly reduces resultant transverse forces tending to make an object veer off course while being transported. This improvement is accomplished by arranging idler rollers in pairs mounted to have axes that are co-planar, non-parallel, acutely angled to each other, and skewed slightly toward opposite sides of a perpendicular to the longitudinal axis of the conveyor. The paired rollers use one roller to create a transverse force in one direction for an advancing object and produce an opposite direction force by the other paired roller. The opposing forces applied by the paired rollers are subtractive. This greatly reduces the resultant total transverse forces and significantly solves the problems created by parallel roller conveyors that are slightly misaligned with workstations. 
     To ensure optimum performance of our skewed roller conveyor system, the rollers of a roller pair are preferably mounted in a sub-frame that pivots slightly. The pivoting sub-frame extends across a path of movement of an object, and the axis of the pivoting sub-frame preferably is centered between the axes of the rollers in each idler roller pair. The pivoting action helps ensure that the weight of objects being transported is evenly distributed between each roller in a roller pair. This also helps ensure that the transverse forces produced by a roller pair are opposite and nearly equal. 
     The tilting sub-frame for paired rollers is arranged within a main conveyor frame. The axis of the pivoting frame is preferably perpendicular to a longitudinal axis of the conveyor. A single pair of rollers arranged in a pivoting frame can serve as an infeed or an outfeed support. In this case, the paired rollers are pivoted on an axis of a bisector of an angle between the rollers. Placing a pivot frame axis midway between the axes of an idler roller pair ensures that the object being transported experiences equal normal forces from the paired rollers. This arrangement leads to equal or nearly equal transverse forces that act subtractively in opposite directions. 
     A person setting up a conveyor having angled idler roller pairs tcnds to attcmpt attempts to align a longitudinal conveyor axis with the desired direction of feed. An eyeball adjustment can limit differences between the intended direction of travel and the longitudinal axis. To ensure that a person can get the desired reduction of resultant transverse forces, it only requires that the difference between the intended direction of travel and the longitudinal axis is limited to within plus/minus ½ the acute angle between the rollers in the roller pairs. In other words, if the rollers in the roller pairs are angled by 4° to each other, then the longitudinal axis can be misaligned from the intended direction of travel by up to, but not including 2° to the right and up to, but not including 2° to the left for a successful performance. The degree that the longitudinal axis can be misaligned with respect to the intended direction of travel is dependent on the acute angle between the idler rollers in the roller pairs. A larger acute angle between the idler rollers in the pairs of rollers allows for easier acceptable alignment for the user between the longitudinal axis and the intended direction of travel. 
    
    
     
       DRAWINGS 
         FIGS. 1-3  schematically illustrate a typical prior art idler roller conveyor construction as shown in  FIG. 1 . The transverse forces that can develop when an object is fed on such a conveyor, is shown in  FIGS. 2 and 3 . 
         FIGS. 4-6  show angled pairs of idler rollers schematically illustrating opposed transverse forces that are subtractive. 
         FIG. 7  is a plan view of an idler roller such as used in prior art conveyors. 
         FIGS. 8 and 9  show an angled assembly of paired idler rollers arranged to counteract transverse forces. 
         FIGS. 10A and 10B  schematically illustrate how a support sub-frame can pivot to accommodate an advancing object. 
         FIG. 11  illustrates a conveyor frame in which two roller pair assemblies are mounted to pivot to apply transverse forces subtractively and equally on an object being moved. 
         FIG. 12  shows that a conventional idler roller conveyor angle Θ is derived from an intended direction of feed and a line perpendicular to the rollers. 
         FIG. 13  graphically illustrates unbalanced and significant transverse force from a parallel idler roller conveyor. 
         FIG. 14  graphically illustrates the significantly balanced and minimized transverse forces and from paired and angled idler rollers. 
         FIG. 15  is a legend defining the symbols used in  FIGS. 13 and 14  and also applied to  FIGS. 8 and 12 . 
     
    
    
     DETAILED DESCRIPTION 
     Understanding the importance of our improvement in idler roller conveyors is significantly helped by understanding the forces involved, as follows:
         NORMAL FORCE is the engagement force between supported objects and conveyor idler rollers. The line of action of the normal force is perpendicular to the roller surface, and the normal force is usually due to the weight of the object.   TANGENTIAL FORCE is the total force tangent to an idler roller surface. When the idler roller is misaligned with the direction of travel of the object, slippage between their surfaces will occur, and the tangential force will be equal to the normal force of engagement multiplied by the coefficient of friction between their surfaces. If the idler roller contains quality bearings (i.e. bearings that offer no resistance to roller rotation) the line of action of the tangential force will be parallel to the roller axis.   TRANSVERSE FORCE is that component of the tangential force perpendicular to the direction of object travel. The magnitude of the transverse force is the product of the tangential force and the cosine of the angle between a perpendicular to the intended direction of travel and the idler roller axis. For small angles the magnitude of the transverse force is essentially the same as the magnitude of the tangential force.   RESULTANT FORCE is a force that represents a combination of two or more forces.       

     Another term that is important to understand is LONGITUDINAL AXIS. The direction of the longitudinal axis for conveyors containing parallel idler rollers is perpendicular to the roller axes. The direction of the longitudinal axis for conveyors containing skewed roller pairs is perpendicular to a bisector of the angle between the skewed rollers. As illustrated in  FIG. 12 , the longitudinal axis  15  of a conveyor is often slightly misaligned with a workstation or an intended direction of travel  40  of an object. This produces an angle θ that results in generation of tangential and transverse forces. 
     The drawings include some prior art conveyors and the problems they cause. This contrasts significantly with the conveyor improvements that solve these problems. For example,  FIGS. 1-3  show a conventional idler roller conveyor with parallel rollers  20  mounted within a frame  10 .  FIGS. 2 and 3  illustrate the substantial transverse forces applied to an object  60  being moved whenever the conveyor is misaligned (even if this misalignment is slight) with an intended direction of travel  40  for the object  60 . The transverse forces, as indicated by arrows on each roller, are nearly parallel with the roller axes and tend to move an object transversely of an intended direction of travel  40 , as indicated by the arrow on the long and narrow object  60 . Such transverse forces are often powerful enough to cause serious problems. 
     In contrast to the problems illustrated in  FIGS. 1-3 ,  FIGS. 4-6  illustrate an improved idle roller conveyor using a conventional frame  10  and conventional idle rollers  20  arranged not parallel with each other but at acute angles to each other. A significant difference from the prior art is illustrated in  FIGS. 5 and 6  where pairs of rollers are acutely angled to each other so that rollers of a pair produce opposite direction transverse forces between rollers  20  and an object  60 . These transverse forces are indicated by arrows on each roller, and the force arrows show that transverse forces are subtractive and thus the resultant transverse force is minimized. 
     A conventional roller  20  as shown in  FIG. 7  has an axis  21  and support bearings  22 . Such rollers and bearings need not change to satisfy our improvement. What is changed, however, is the mounting of the rollers to minimize the resultant transverse forces in a roller pair by making the two transverse forces subtractive. 
     Acute angled roller pairs  20  are preferably mounted in sub-frames  30  as shown in  FIGS. 8-11 . As many sub-frames  30  as desired can be arranged to cross a longitudinal axis  15  of an improved conveyor. Each of the sub-frames  30  is pivotal on an axis  31  transverse to the longitudinal axis  15 . This arrangement positions each roller in a roller pair in a common plane, in a non-parallel relationship, with the rollers  20  angled acutely from each other and ensures that the normal forces between the transported object and each roller of a roller pair are equal. The rollers are also skewed toward opposite sides of a perpendicular  31  to the longitudinal axis  15 , as shown in  FIG. 8 . Pivots  50  of sub-frames  30  are arranged on a pivot axis that is also perpendicular to longitudinal axis  15 . Pivot axis  31  also bisects the acute angle between axes  21  of a pair of rollers. This arrangement positions rollers  20  and their mounts  35  optimally to make transverse forces subtractive and therefore minimizes the resultant transverse force applied to a transported object by a roller pair. 
     A single pair of idler rollers  20  such as shown in  FIG. 8  can be used as an infeed or outfeed stand in place of a single roller that is often used this way. These single idler rollers are problematic, because the roller has to be accurately oriented to be perpendicular to the direction of feed over the roller. Otherwise transverse forces can make feeding of objects in the desired direction difficult, move the object off the roller or tip over the stand. When a single angled roller pair is used, it is preferable to mount the rollers in sub-frame  30 , as shown in  FIGS. 8-11 . Sub-frame  30  offers limited tilting range to a roller pair so that weight of an object  60  rests evenly on each roller. 
     It is also possible to arrange acutely angled rollers  20  within a conventional frame  10 , without using pivoting sub-frames  30 . This has the advantage of being simple and inexpensive, because it requires only relocating holes for roller support. Mounting the rollers within tilting sub-frames  30  better assures uniform normal forces between an object  60  and rollers  20  to most accurately have countering transverse forces that minimize their effect. 
     The improvement can be applied to idle roller conveyors of any length. In conveyor  10  in  FIG. 11 , two sub-frames  30  each holds a pair of rollers  20  to apply opposite direction transverse force to an object moving along the conveyor. Sub-frames  30  for each pair of rollers  20 , are pivotally mounted within conveyor frame  10 . This allows the roller assemblies within sub-frames  30  to pivot slightly, as shown by the arrows in  FIGS. 10A  and B. Rollers assembled within sub-frames  30  can have accurately predetermined skew angles δ to a perpendicular to the longitudinal axis. Such skew angles are usually well within 10° of a perpendicular to the longitudinal axis. The tilting of sub-frames  30  will be limited because they only need sufficient tilting capacity to evenly engage the load of an object  60 . Limited tilting of the sub-frame will also ensure that objects being transported can smoothly move onto and off of the roller pairs. 
     The prior art presents at least two problems in misalignment of idler roller conveyors. One is that the conveyor, while oriented in an intended direction of feed, is often angled slightly from that intended direction. This occurs when idler roller conveyors are set up by eyeball to function with a workstation such as a table saw. The other problem is that even rollers that are fixed in place with respect to a workstation may not be accurately aligned with the desired path of travel. This is especially true if there are separate alignment adjustments in the workstation. A case in point is a table saw that has blade and fence adjustments. 
     An acute angle between idler roller pairs can be selected when a conveyor is built. To ensure that the selected acute angle between the roller pairs will be workable under the conditions to be met requires only that the acute angle between the roller pairs be large enough. Eyeball set ups to align a conveyor with a workstation can easily hold any discrepancy between the longitudinal axis of the conveyor and the direction of feed of the conveyor to within plus or minus ½ the acute angle of the roller pairs. The plus or minus is to allow for error on either the right or left side of the longitudinal axis. Another way of looking at this is that a bisector of the acute angle between the roller pairs is perpendicular to the longitudinal axis. This assures that when a conveyor is set up and approximately aligned with a workstation, the direction of feed will stay within the ½ angular limitation bounded by the acute angle. Error can occur up to slightly less of ½ the acute roller pair angle on either side of the longitudinal axis with the transverse forces being subtractive so that the conveyor feeds without a tendency to veer off course. Fortunately, the acute angle between the roller pairs can be as small as a few degrees and still reduce transverse forces resulting from typical eyeball misalignments. 
     Misalignment problems are particularly likely to occur with systems that contain a single roller outfeed or infeed conveyor. Such systems have short roller path lengths which make them more difficult to set in an accurately perpendicular orientation to the feed direction through a workstation. Our improved conveyor solves both of these problems in a simple and inexpensive way. 
     The mathematics of the idler roller conveyor operation are graphically illustrated for a prior art conveyor with parallel rollers in  FIG. 13 , and for an improved conveyor with pairs of angled rollers in  FIG. 14 . The legend of  FIG. 15  defines the entities used in the mathematical description. 
     In  FIG. 13 , Θ is any angle that appears between the desired direction of movement and a longitudinal axis of a conveyor. Angle Θ is also illustrated in  FIG. 12 . The transverse force F ⊥  is affected by the normal force of engagement (F), the coefficient of friction between the object and the rollers (μ), and these quantities serve as multipliers of a cosine value for the angle Θ. 
     A prior art idler conveyor such as shown in  FIGS. 1-3  can generate substantial transverse force, even when Θ angles are minute. For example, a 10 lb. board moves across a plurality of parallel rollers with an intended line of travel misaligned 1° to the total conveyor assembly. There is a 0.5 coefficient of friction.
         Fn=10 lbs.   μ=0.5   Θ=1°       

     Plugging these values into a formula for parallel rollers Fμ(cos Θ), we get 10×(0.5)(cos 1°)=4.99 lbs. of transverse force. This could lead to serious problems due to a tendency to cause an object to veer off its desired path of travel. 
     In contrast to the transverse force of 4.99 lbs. for a parallel idle roller conveyor, consider the much reduced transverse force obtainable with angled roller pairs deployed under the same assumptions. The graphic design of  FIG. 14  applies to paired and angled rollers. The rollers as paired and angled on opposite sides of a perpendicular to the longitudinal axis by skew angles δ that result in opposite direction transverse forces. These skew angles are labeled plus (+) and minus (−) to show right and left generation of transverse force. 
     A 10 lb. board moves across an angled roller pair with an intended line of travel misaligned 1° to the longitudinal axis of the conveyor. There is a 0.5 coefficient of friction. The rollers skew angles δ are 2°. Plugging these values into a formula for angled pairs of roller: 
               F   ⁢           ⁢   μ   ⁢       [       Cos   ⁡     (     Θ   +   δ     )       -     Cos   ⁡     (     Θ   -   δ     )         ]     2       ,         
we get
 
     
       
         
           
             
               10 
               × 
               
                 ( 
                 .5 
                 ) 
               
               ⁢ 
               
                 
                   [ 
                   
                     
                       Cos 
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                         ( 
                         
                           
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                             ° 
                           
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                         ) 
                       
                     
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                         ( 
                         
                           
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                         ) 
                       
                     
                   
                   ] 
                 
                 2 
               
             
             = 
             
               
                 
                   5 
                   ⁢ 
                   
                     x 
                     ⁡ 
                     
                       [ 
                       
                         .9986 
                         - 
                         .9998 
                       
                       ] 
                     
                   
                 
                 2 
               
               = 
               
                 .003 
                 ⁢ 
                 
                     
                 
                 ⁢ 
                 
                   lbs 
                   . 
                   
                       
                   
                   ⁢ 
                   of 
                 
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                   force 
                   . 
                 
               
             
           
         
       
     
     The contrast between nearly 5 lbs. and 0.003 lbs. is quite surprising, but is mathematically verified. The paired and skewed rollers, with their production of oppositely canceling transverse forces results in a near perfect elimination of resultant transverse forces.