Abstract:
A random engagement roller chain sprocket for use primarily in automotive engine chain drive applications which incorporates different asymmetrical tooth profiles for improved noise reduction. In particular, the sprocket includes a first plurality of sprocket teeth each having a first tooth profile including a first engaging flank, a first engaging root, and a first flat positioned between the first engaging flank and first engaging root wherein a first roller initially contacts the first flat at the onset of the first roller meshing with the sprocket. The sprocket also includes a second plurality of sprocket teeth each having a second tooth profile different from the first tooth profile and including a second engaging flank, a second engaging root, and a second flat tangent to the second engaging root remote from the second engaging flank wherein a second roller initially contacts the second flat at the onset of meshing between the second roller and the sprocket.

Description:
CROSS-REFERENCE TO RELATED APPLICATIONS 
     This application is a continuation of application Ser. No. 08/992,306, filed Dec. 17, 1997, now U.S. Pat. No. 5,921,879, which claims priority from U.S. Provisional Patent Application Serial No. 60/032,379, filed Dec. 19, 1996. 
    
    
     BACKGROUND OF THE INVENTION 
     The present invention relates to the automotive timing chain art. It finds particular application in conjunction with a unidirectional roller chain sprocket for use in automotive camshaft drive applications and will be described with particular reference thereto. However, the present invention may also find application in conjunction with other types of chain drive systems and applications where reducing the noise levels associated with chain drives is desired. 
     Roller chain sprockets for use in camshaft drives of automotive engines are typically manufactured according to ISO (International Organization for Standardization) standard 606:1994(E). The ISO-606 standard specifies requirements for short-pitch precision roller chains and associated chain wheels or sprockets. 
     FIG. 1 illustrates a symmetrical tooth space form for an ISO-606 compliant sprocket. The tooth space has a continuous fillet or root radius R i  extending from one tooth flank (i.e., side) to the adjacent tooth flank as defined by the roller seating angle α. The flank radius R f  is tangent to the roller seating radius R i  at the tangency point TP. A chain with a link pitch P has rollers of diameter D 1  in contact with the tooth spaces. The ISO sprocket has a chordal pitch also of length P, a root diameter D 2 , and Z number of teeth. The pitch circle diameter PD, tip or outside diameter OD, and tooth angle A (equal to 360°/Z) further define the ISO-606 compliant sprocket. The maximum and minimum roller seating angle a is defined as: 
     
       
         α max =(140°−90°)/Z and α min =(120°−90)/Z 
       
     
     With reference to FIG. 2, an exemplary ISO-606 compliant roller chain drive system  10  rotates in a clockwise direction as shown by arrow  11 . The chain drive system  10  includes a drive sprocket  12 , a driven sprocket  14  and a roller chain  16  having a number of rollers  18 . The sprockets  12 ,  14 , and chain  16  each generally comply with the ISO-606 standard. 
     The roller chain  16  engages and wraps about sprockets  12  and  14  and has two spans extending between the sprockets, slack strand  20  and taut strand  22 . The roller chain  16  is under tension as shown by arrows  24 . The taut strand  22  may be guided from the driven sprocket  14  to the drive sprocket  12  with a chain guide  26 . A first roller  28  is shown at the onset of meshing at a 12 o&#39;clock position on the drive sprocket  12 . A second roller  30  is adjacent to the first roller  28  and is the next roller to mesh with the drive sprocket  12 . 
     Chain drive systems have several components of undesirable noise. A major source of roller chain drive noise is the sound generated as a roller leaves the span and collides with the sprocket during meshing. The resultant impact noise is repeated with a frequency generally equal to that of the frequency of the chain meshing with the sprocket. The loudness of the impact noise is a function of the impact energy (E A ) that must be absorbed during the meshing process. The impact energy absorbed is related to engine speed, chain mass, and the impact velocity between the chain and the sprocket at the onset of meshing. The impact velocity is affected by the chain-sprocket engagement geometry, of which an engaging flank pressure angle (FIG. 3) is a factor, where:                  E   A     =       wP   2000          V   A   2         ;                   V   A     =         π                 nP     30000          sin        (       360   Z     +   γ     )           ;                 γ   =       180   -   A   -   α     2       ;   and                     E   A         =         Impact                   Energy              [     N   ·   m     ]                 V   A         =         Roller                 Impact                   Velocity              [     m        /        s     ]               γ       =         Engaging                 Flank                 Pressure                 Angle             n       =         Engine                   Speed              [   RPM   ]               w       =         Chain                   Mass              [     Kg        /        m     ]               Z       =         Number                 of                 Sprocket                 Teeth             A       =         Tooth                 Angle                   (     360      °        /        Z     )               α       =         Roller                 Seating                 Angle             P       =         Chain                 Pitch                   (     Chordal                 Pitch     )                                        
     The impact energy (E A ) equation presumes the chain drive kinematics will conform generally to a quasi-static analytical model and that the roller-sprocket driving contact will occur at a tangent point TP (FIG. 3) of the flank and root radii as the sprocket collects a roller from the span. 
     As shown in FIG. 3, the pressure angle y is defined as the angle between a line A extending from the center of the engaging roller  28 , when it is contacting the engaging tooth flank at the tangency point TP, through the center of the flank radius R f , and a line B connecting the centers of the fully seated roller  28 , when it is seated on root diameter D 2 , and the center of the next meshing roller  30 , as if it were also seated on root diameter D 2  in its engaging tooth space. The roller seating angles a and pressure angles listed in FIG. 27 are calculated from the equations defined above. It should be appreciated that y is a minimum when a is a maximum. The exemplary 18-tooth, ISO-606 compliant, sprocket  12  of FIG. 3 will have a pressure angle in the range of 12.5° to 22.5° as listed in the table of FIG.  27 . 
     FIG. 3 also shows the engagement path (phantom rollers) and the driving contact position of roller  28  (solid) as the drive sprocket  12  rotates in the direction of arrow  11 . FIG. 3 depicts the theoretical case with chain roller  27  seated on root diameter D 2  of a maximum material sprocket with both chain pitch and sprocket chordal pitch equal to theoretical pitch P. For this theoretical case, the noise occurring at the onset of roller engagement has a radial component F IR  as a result of roller  30  colliding with the root surface R i  and a tangential component F IT  generated as the same roller  28  collides with the engaging tooth flank at point TP as the roller moves into driving contact. It is believed that the radial impact occurs first, with the tangential impact following nearly simultaneously. Roller impact velocity V A  is shown to act through, and is substantially normal to, engaging flank tangent point TP with roller  28  in driving contact at point TP. 
     The impact energy (E A ) equation accounts only for a tangential roller impact during meshing. The actual roller engagement, presumed to have a tangential and radial impact (occurring in any order), would therefore seem to be at variance with the impact energy (E A ) equation. The application of this quasi-static model, which is beneficially used as a directional tool, permits an analysis of those features that may be modified to reduce the impact energy that must be absorbed during the tangential roller-sprocket collision at the onset of meshing. The radial collision during meshing, and its effect on noise levels, can be evaluated apart from the impact energy (E A ) equation. 
     Under actual conditions as a result of feature dimensional tolerances, there will normally be a pitch mismatch between the chain and sprocket, with increased mismatch as the components wear in use. This pitch mismatch serves to move the point of meshing impact, with the radial collision still occurring at the root surface R i  but not necessarily at D 2 . The tangential collision will normally be in the proximity of point TP, but this contact could take place high up on the engaging side of root radius R i  or even radially outward from point TP on the engaging flank radius R f  as a function of the actual chain-sprocket pitch mismatch. 
     Reducing the engaging flank pressure angle γ reduces the meshing noise levels associated with roller chain drives, as predicted by the impact energy (E A ) equation set forth above. It is feasible but not recommended to reduce the pressure angle γ while maintaining a symmetrical tooth profile, which could be accomplished by simply increasing the roller seating angle α, effectively decreasing the pressure angle for both flanks. This profile as described requires that a worn chain would, as the roller travels around a sprocket wrap (discussed below), interface with a much steeper incline and the rollers would necessarily ride higher up on the coast flank prior to leaving the wrap. 
     Another source of chain drive noise is the broadband mechanical noise generated in part by shaft torsional vibrations and slight dimensional inaccuracies between the chain and the sprockets. Contributing to a greater extent to the broadband mechanical noise level is the intermittent or vibrating contact that occurs between the unloaded rollers and the sprocket teeth as the rollers travel around the sprocket wrap. In particular, ordinary chain drive system wear comprises sprocket tooth face wear and chain wear. The chain wear is caused by bearing wear in the chain joints and can be characterized as pitch elongation. It is believed that a worn chain meshing with an ISO standard sprocket will have only one roller in driving contact and loaded at a maximum loading condition. 
     With reference again to FIG. 2, driving contact at maximum loading occurs as a roller enters a drive sprocket wrap  32  at engagement. Engaging roller  28  is shown in driving contact and loaded at a maximum loading condition. The loading on roller  28  is primarily meshing impact loading and the chain tension loading. The next several rollers in the wrap  32  forward of roller  28  share in the chain tension loading, but at a progressively decreasing rate. The loading of roller  28  (and to a lesser extent for the next several rollers in the wrap) serves to maintain the roller in solid or hard contact with the sprocket root surface  34 . 
     A roller  36  is the last roller in the drive sprocket wrap  32  prior to entering the slack strand  20 . Roller  36  is also in hard contact with drive sprocket  12 , but at some point higher up (e.g., radially outwardly) on the root surface  34 . With the exception of rollers  28  and  36 , and the several rollers forward of roller  28  that share the chain tension loading, the remaining rollers in the drive sprocket wrap  32  are not in hard contact with the sprocket root surface  34 , and are therefore free to vibrate against the sprocket root surfaces as they travel around the wrap, thereby contributing to the generation of unwanted broadband mechanical noise. 
     A roller  38  is the last roller in a sprocket wrap  40  of the driven sprocket  14  before entering the taut strand  22 . The roller  38  is in driving contact with the sprocket  14 . As with the roller  36  in the drive sprocket wrap  32 , a roller  42  in the sprocket wrap  40  is in hard contact with a root radius  44  of driven sprocket  14 , but generally not at the root diameter. 
     It is known that providing pitch line clearance (PLC) between sprocket teeth promotes hard contact between the chain rollers and sprocket in the sprocket wrap, even as the roller chain wears. The amount of pitch line clearance added to the tooth space defines a length of a short arc that is centered in the tooth space and forms a segment of the root diameter D 2 . The root fillet radius R is tangent to the flank radius R F  and the root diameter arc segment. The tooth profile is still symmetrical, but R i  is no longer a continuous fillet radius from one flank radius to the adjacent flank radius. This has the effect of reducing the broadband mechanical noise component of a chain drive system. However, adding pitch line clearance between sprocket teeth does not reduce chain drive noise caused by the roller-sprocket collision at impact. 
     Chordal action, or chordal rise and fall, is another important factor affecting the operating smoothness and noise levels of a chain drive, particularly at high speeds. Chordal action occurs as the chain enters the sprocket from the free span during meshing and it can cause a movement of the free chain in a direction perpendicular to the chain travel but in the same plane as the chain and sprockets. This chain motion resulting from chordal action will contribute an objectionable noise level component to the meshing noise levels, so it is therefore beneficial to reduce chordal action inherent in a roller chain drive. 
     FIGS. 4 a  and  4   b  illustrate the chordal action for an 18-tooth, ISO-606 compliant, sprocket having a chordal pitch of 9.525 mm. Chordal rise  45  may conventionally be defined as the displacement of the chain centerline as the sprocket rotates through an angle A/2, where: 
     
       
         Chordal rise=r p −r c =r p [1-cos(180°/Z)] 
       
     
     where r c  is the chordal radius, or the distance from the sprocket center to a pitch chord of length P; r p  is the actual theoretical pitch radius; and Z is the number of sprocket teeth. 
     It is known that a short pitch chain provides reduced chordal action compared to a longer pitch chain having a similar pitch radius. FIGS. 4 a  and  4   b  show only the drive sprocket and assume a driven sprocket (not shown) also having 18-teeth and in phase with the drive sprocket shown. In other words, at T=0 (FIG. 4 a ), both sprockets will have a tooth center at the 12 o&#39;clock position. Accordingly, this chain drive arrangement under quasi-static conditions will have a top or taut strand that will move up and down in a uniform manner a distance equal to that of the chordal rise. At T=0, a roller  46  is at the onset of meshing, with chordal pitch P horizontal and in line with taut strand  22 . At T=0+(A/2), (FIG. 4 b ), roller  46  has moved to the 12 o&#39;clock position. 
     For many chain drives, the drive and driven sprockets will be of different sizes and will not necessarily be in phase. The chain guide  26  (FIG. 2) has the primary purpose to control chain strand vibration in the taut span. The geometry of the guide-chain interface also defines the length of free span chain over which chordal rise and fall is allowed to operate. FIG. 5 is an enlarged view of FIG. 2 showing the first roller  28  at the onset of engagement and the second roller  30  as the next roller about to mesh with sprocket  12 . In this example, the chain guide  26  controls and guides the engaging portion of the taut strand  22  except for five (5) unsupported or “free” link pitches extending between the chain guide  26  and the engaging roller  28 . This length of unsupported link pitches for the engaging portion of taut strand  22  in this example is horizontal when roller  28  is at the  12  o&#39;clock position. 
     With reference to FIGS. 6 and 7, the drive sprocket  12  is rotated in a clockwise direction to advance roller  28  to a new angular position (A/2)+ω, where ω is the added rotation angle as determined by a quasi-static engagement geometry with roller  28  being fully seated and roller  30  is at the instant of sprocket engagement. As shown in FIG. 6, roller  28  is considered to be seated and in hard contact with the root surface at D 2  at the onset of meshing of roller  30 , and a straight line is assumed for the chain span from roller  28  to a chain pin center  48 , about which the unsupported or “free” span from pin  48  to engaging roller  30  is considered to rotate. 
     As a result of the chordal action, the engaging free span is no longer horizontal to satisfy the roller engaging geometry. This is in contrast to the chain drive as described in FIG. 4 a  in which chordal action causes the taut strand to move uniformly, but in a horizontal path because the drive and driven sprockets have the same number of teeth and the sprocket teeth are in phase. It should be appreciated that the straight line assumption is valid only in a quasi-static model. The amount of movement or deviation from the straight line assumption will be a function of the drive dynamics, the chain control devices, and the chain drive and sprocket geometry. The location and chain-interfacing contour of the chain guide  26  will determine the number of free span pitches for which chain motion will take place as a result of the chordal rise and fall during the roller meshing process. 
     As best seen in FIG. 7, assuming that rollers  28  and  30  are in hard contact with the sprocket root surfaces at D 2 , the chordal rise is the perpendicular displacement of the center of roller  30  (located on the pitch diameter PD) from the taut span  22  path as it moves from its initial meshing position shown to the 12 o&#39;clock position. 
     Accordingly, it is desirable to develop a new and improved roller chain drive system which meets the above-stated needs and overcomes the foregoing disadvantages and others while providing better and more advantageous results. 
     SUMMARY OF THE INVENTION 
     In accordance with one aspect of the present invention, a sprocket is disclosed. The sprocket includes a first plurality of sprocket teeth each having a first tooth profile including a first engaging flank, a first engaging root, and a first flat positioned between the first engaging flank and first engaging root, a first roller initially contacting the first flat at the onset of the first roller meshing with the sprocket. The sprocket further includes a second plurality of sprocket teeth each having a second tooth profile different from the first tooth profile and including a second engaging flank, a second engaging root, and a second flat tangent to the second engaging root remote from the second engaging flank, a second roller initially contacting the second flat at the onset of meshing between the second roller and the sprocket. 
     In accordance with another aspect of the present invention, a sprocket is disclosed. The sprocket includes a first plurality of sprocket teeth each having a first asymmetrical tooth profile which is constructed for providing a tangential contact with a first roller at an onset of the first roller meshing with the sprocket, and a second plurality of sprocket teeth each having a second asymmetrical tooth profile which is constructed for providing a radial contact with a second roller at an onset of the second roller meshing with the sprocket. 
     In accordance with a further aspect of the present invention, a unidirectional roller chain drive system is disclosed. The unidirectional roller chain drive system includes a first sprocket, a second sprocket, and a roller chain having rollers in engaging contact with the first and second sprockets. At least one of the first and second sprockets includes a first plurality of sprocket teeth each having a first tooth profile including a first engaging flank, a first engaging root, and a first flat positioned between the first engaging flank and first engaging root wherein a first roller initially contacts the first flat at the onset of the first roller meshing with the sprocket. At least one of the first and second sprockets also includes a second plurality of sprocket teeth each having a second tooth profile different from the first tooth profile and including a second engaging flank, a second engaging root, and a second flat tangent to the second engaging root remote from the second engaging flank, a second roller initially contacting the second flat at the onset of meshing between the second roller and the sprocket. 
     In accordance with yet another aspect of the present invention, a method of modifying a meshing impact frequency of a roller chain meshing with a sprocket is disclosed. The method includes (a) rotating the sprocket to cause a first roller of the roller chain to tangentially contact an engaging flank of a first sprocket tooth at an onset of the first roller meshing with the first sprocket tooth, and (b) rotating the sprocket to cause a second roller of the roller chain to radially contact a root surface of a second sprocket tooth at an onset of the second roller meshing with the second sprocket tooth. 
     One advantage of the present invention is the provision of a roller chain sprocket which incorporates a flank flat on an engaging tooth surface which facilitates altering a meshing contact from a first tooth profile to a second tooth profile. 
     Another advantage of the present invention is the provision of a roller chain sprocket which incorporates a flank flat on an engaging tooth surface which effects a time delay between an initial roller-to first sprocket tooth profile contact and an initial roller-to-second sprocket tooth profile contact. 
     Another advantage of the present invention is the provision of a roller chain sprocket which incorporates a flank flat on an engaging tooth surface of a first tooth profile which facilitates phasing a frequency of initial roller-to-engaging flank contacts of the first tooth profile relative to initial roller-to-engaging flank contacts of a second tooth profile to alter the rhythm of the initial roller-to-first engaging flank and the roller-to-second engaging flank contacts. 
     Another advantage of the present invention is the provision of a roller chain sprocket which incorporates added pitch mismatch between the sprocket and roller chain to facilitate a “staged” roller-to-sprocket impact. 
     Still another advantage of the present invention is the provision of a roller chain sprocket which incorporates an inclined root surface on an engaging flank, a coast flank, or both an engaging flank and a coast flank to provide tooth space clearance. 
     Yet another advantage of the present invention is the provision of a roller chain sprocket which minimizes impact noise generated by a roller-sprocket collision during meshing. 
     A further advantage of the present invention is the provision of a roller chain sprocket which minimizes broadband mechanical noise generated by unloaded rollers in a sprocket wrap. 
     A still further advantage of the present invention is the provision of a roller chain sprocket which provides a “staged” roller impact wherein a tangential impact occurs first followed by a radial impact at full mesh. 
     Yet a further advantage of the present invention is the provision of a roller chain sprocket which spreads roller engagement over a significant time interval to provide for a more gradual load transfer, thereby minimizing roller-sprocket impact and the inherent noise generated therefrom. 
     Yet a further advantage of the present invention is the provision of a roller chain sprocket having two sets of sprocket teeth incorporating different tooth profiles which cooperate to reduce chain drive system noise levels below a noise level which either tooth profile used alone would produce. 
     Further advantages of the present invention will become apparent to those of ordinary skill in the art upon reading and understanding the following detailed description of the preferred embodiments. 
    
    
     BRIEF DESCRIPTION OF THE DRAWINGS 
     The invention may take form in various components and arrangements of components, and in various steps and arrangements of steps. The drawings are only for purposes of illustrating a preferred embodiment and are not to be construed as limiting the invention. 
     FIG. 1 illustrates a symmetrical tooth space form for a ISO-606 compliant roller chain sprocket; 
     FIG. 2 is an exemplary roller chain drive system having a ISO-606 compliant drive sprocket, driven sprocket, and roller chain; 
     FIG. 3 shows an engagement path (phantom) and a roller (solid) in a driving position as an ISO-606 compliant drive sprocket rotates in a clockwise direction; 
     FIG. 4 a  shows a roller at the onset of meshing with an exemplary 18-tooth sprocket; 
     FIG. 4 b  shows the drive sprocket of FIG. 4 a  rotated in a clockwise direction until the roller is at a 12 o&#39;clock position; 
     FIG. 5 is an enlarged view of the drive sprocket of FIG. 2 with a roller fully seated in a tooth space and a second roller about to mesh with the drive sprocket; 
     FIG. 6 shows the drive sprocket of FIG. 5 rotated in a clockwise direction until the second roller initially contacts the drive sprocket; 
     FIG. 7 is an enlarged view of FIG. 6 showing that the second roller initially contacts a root surface (i.e., radial impact) of the drive sprocket, under theoretical conditions; 
     FIG. 8 illustrates a roller chain drive system having a roller chain drive sprocket and driven sprocket which incorporate the features of the present invention therein; 
     FIG. 9 illustrates the roller chain drive sprocket of FIG. 8 with an asymmetrical tooth space form in accordance with one embodiment of the present invention; 
     FIG. 10 is an enlarged view of the asymmetrical tooth space form of FIG. 9 showing a roller in two-point contact with the sprocket; 
     FIG. 11 shows an engagement path (phantom) and the instant of full mesh (solid) of a roller as the drive sprocket of FIG. 8 rotates in a clockwise direction; 
     FIG. 12 is an enlarged view of the drive sprocket of FIG. 8 with a first roller fully seated in a tooth space and a second roller as the next roller to be collected from the taut span of the roller chain; 
     FIG. 13 shows the drive sprocket of FIG. 12 rotated in a clockwise direction until the second roller initially contacts the drive sprocket; 
     FIG. 14 is an enlarged view of FIG. 13 showing the first roller in two-point contact and second roller at initial tangential contact with the drive sprocket; 
     FIG. 14 a  illustrates the progression of the first and second rollers as the drive sprocket of FIG. 14 is rotated in a clockwise direction; 
     FIG. 14 b  is an enlarged view of the drive sprocket of FIG. 14 rotated in a clockwise direction to advance the second roller to the instant of full mesh at a 12 o&#39;clock position; 
     FIG. 15 illustrates a roller chain drive sprocket with an asymmetrical tooth space form in accordance with another embodiment of the present invention; 
     FIG. 16 is an enlarged partial view of FIG. 8, showing the contact progression as the rollers travel around the drive sprocket wrap; 
     FIG. 17 is an enlarged view of a roller exiting a sprocket wrap of the sprocket of FIG. 16; 
     FIG. 18 illustrates a roller chain sprocket with an asymmetrical tooth space form in accordance with another embodiment of the present invention; 
     FIG. 19 illustrates a roller chain sprocket with an asymmetrical tooth space form in accordance with a further embodiment of the present invention; 
     FIG. 20 is a front view of an exemplary random-engagement roller chain sprocket which incorporates the features of the present invention therein; 
     FIG. 21 is an enlarged view of the sprocket of FIG. 20 showing an asymmetrical tooth space form which incorporates engaging flank relief and tooth space clearance in accordance with the present invention; 
     FIG. 21 a  is an enlarged view of the sprocket of FIG. 21 showing an inclined root surface thereof which provides flank relief and tooth space clearance; 
     FIG. 22 is another embodiment of the inclined root surface of FIG. 21 which only provides flank relief; 
     FIG. 23 illustrates the asymmetrical tooth space form of FIG. 9 overlaid with the asymmetrical tooth space form of FIG. 21; 
     FIG. 24 illustrates the meshing progression of a first roller and the meshing of a second adjacent roller with the sprocket of FIG. 20 as the sprocket is rotated in a clockwise direction; 
     FIG. 25 illustrates the sprocket of FIG. 20 with a first roller in two-point contact, a second roller at initial tangential contact, and a third roller about to mesh with the drive sprocket; 
     FIG. 26 illustrates the sprocket of FIG. 25 rotated in a clockwise direction until the instant of initial engagement of the third roller at a root surface of the sprocket; 
     FIG. 27 is a table listing roller seating angles α and pressure angles for a number of different ISO-606 compliant sprocket sizes; and 
     FIG. 28 is a table listing the maximum Beta (β) angles and the corresponding minimum pressure angles (γ) for three different asymmetrical tooth space profiles ( 1 - 3 ) of varying sprocket sizes. 
    
    
     DETAILED DESCRIPTION OF THE PREFERRED EMBODIMENTS 
     With reference now to FIG. 8, a roller chain drive system  110  includes a drive sprocket  112  and a driven sprocket  114  which incorporate the features of the present invention therein. The roller chain drive system  110  further includes a roller chain  116  having a number of rollers  118  which engage and wrap about sprockets  112 ,  114 . The roller chain rotates in a clockwise direction as shown by arrow  11 . 
     The roller chain  116  has two spans extending between the sprockets, slack strand  120  and taut strand  122 . The roller chain  116  is under tension as shown by arrows  124 . A central portion of the taut strand  122  may be guided from the driven sprocket  114  to the drive sprocket  112  with a chain guide  126 . A first roller  128  is shown fully seated at a 12 o&#39;clock position on the drive sprocket  112 . A second roller  130  is adjacent to the first roller  128  and is about to mesh with the drive sprocket  112 . 
     To facilitate a description of the asymmetrical tooth profiles of the present invention, reference will be made only to the drive sprocket  112 . However, the asymmetrical tooth profiles of the present invention can be equally applied to the driven sprocket  114 , as well as to other types of sprockets such as idler sprockets and sprockets associated with counter rotating balance shafts. 
     Referring now to FIGS. 9 and 10, the sprocket  112  includes a first tooth  132  having an engaging flank  134 , and a second tooth  136  having a coast or disengaging flank  138 . The engaging flank  134  and coast flank  138  cooperate to define a tooth space  140  having a root surface  141 . The tooth space  140  receives the engaging roller  128  (shown in phantom). The engaging roller  128  has a diameter D 1 , and is shown fully seated in two-point contact within the tooth space  140  as described further below. More particularly, the engaging roller  128 , when fully seated in the tooth space, contacts two lines B and C that extend axially along each sprocket tooth surface or face (i.e., in a direction orthogonal to the plane of the drawings). However, to facilitate a description thereof, the lines A, B, and C are hereafter shown and referred to as contact points within the tooth space. 
     The engaging flank  134  has a radius R f  which is tangent to a radially outer end of a flank flat  144 . The asymmetrical engaging flank radius Rf is smaller than the R fISO  radius specified by the ISO-606 standard. However, the magnitude of the asymmetrical engaging flank radius R f  should be as large as possible while still satisfying the roller meshing (engaging) and disengaging geometry. The location of the flank flat  144  is defined by an angle β, with the flat orientation being normal or perpendicular to a line that passes through Point B and the center of roller  128  when the roller is contacting the sprocket at Points B and C. The length of the flank flat, which extends radially outward from Point B, affects a time delay between an initial tangential impact between sprocket  112  and roller  128  at a first contact Point A along the flank flat  144 , and a subsequent radial impact at Point C. It is believed that the roller stays in contact with the flank flat from its initial tangential contact at Point A until the roller moves to a fully engaged two-point contact position at Points B and C. The pressure angle γ, the amount of pitch mismatch between the chain and the sprocket, and the length of the flank flat can be varied to achieve a desired initial roller contact Point A at the onset of roller-sprocket meshing. 
     It should be appreciated that flank (tangential) contact always occurs first, with radial contact then occurring always at Point C regardless of chain pitch length. In contrast, with known tooth space forms (e.g., ISO-606 compliant and asymmetrical) incorporating single-point contact (e.g. single line contact), an engaging roller must move to a driving position after making radial contact. The pressure angles γ therefore assume that the engaging roller will contact at the flank radius/root radius tangent point. Thus, the meshing contact location of the known single point/line tooth space forms is pitch “sensitive” to determine where the radial impact as well as tangential impact will occur. 
     The engaging flank roller seating angle β (FIG. 9) and a disengaging flank roller seating angle β′ replace the ISO-606 roller seating angle α (ISO profile shown in phantom). As illustrated in FIG. 9, β is the angle defined by the line  152  passing through the center of roller  128  and the sprocket center to a second line which also passes through the center of roller  128  and Point B. Also shown in FIG. 9, β′ is the angle defined by a line passing through the arc center of R i ′ and the sprocket center to a second line which also passes through the arc center of R i ′ and the arc center of R f ′. The pressure angle γ is a function of the engaging flank roller seating angle β. That is, as β increases, γ decreases. A minimum asymmetrical pressure angle can be determined from the following equation, where: 
     
       
         γ min =β max −(α max /2+γ ISO min ) 
       
     
     Therefore, an asymmetrical pressure angle γ min =0 when β max =(α max /2+γ ISO min ) as illustrated in the table of FIG.  28 . FIG. 28 lists the maximum Beta (β) angles and the corresponding minimum pressure angles (γ) for several sprocket sizes of three different asymmetrical tooth space profiles ( 1 - 3 ). It should be appreciated that reducing the engaging flank pressure angle γ reduces the tangential impact force component F IA  (FIG. 14) and thus the tangential impact noise contribution to the overall noise level at the onset of engagement. 
     That is, the impact force F IA  is a function of the impact velocity which in turn is related to pressure angle γ. As pressure angle γ is reduced, it provides a corresponding reduction in the impact velocity between the chain and the sprocket at the onset of meshing. A minimum pressure angle γ also facilitates a greater separation or distance between tangential contact points A and B to further increase or maximize engagement “staging”. In the preferred embodiment, the engaging flank pressure angle γ is in the range of about −2.0° to about +5° to optimize the staged impact between the roller and the sprocket. 
     In the embodiment being described, roller seating angle β is greater than ISO α max /2 at a maximum material condition and β can be adjusted until a desired engaging flank pressure angle γ is achieved. For instance, the roller seating angle β of FIG. 9 provides a pressure angle γ that is less than zero, or a negative value. The negative pressure angle γ is best seen in FIG. 11, as contrasted with the ISO-606 compliant tooth profile of FIG. 3 with a positive pressure angle γ. As shown in FIG. 11, the asymmetrical profile pressure angle γ is defined as the angle between a line A extending from the center of the fully engaged roller  128 , when it is contacting the engaging tooth flank at points B and C, through point B, and a line B connecting the centers of the fully seated roller  128 , and the center of the next meshing roller  130  as if it were also two-point seated at full mesh in its engaging tooth space. It is believed that a small negative pressure angle for the theoretical chain/sprocket interface beneficially provides a pressure angle γ closer to zero (0) for a “nominal” system or for a system with wear. However, the engaging flank roller seating angle β may be beneficially adjusted so as to provide any engaging flank pressure angle γ having a value less than the minimum ISO-606 pressure angle. 
     Referring again to FIGS. 9 and 10, a first root radius R i  is tangent to a radially inner end of the flank flat  144 , and tangent to a radially outer end of an inclined root surface  146 . As best seen in FIG. 10, a maximum root radius R i  must be equal to, or less than, a minimum roller radius 0.5D 1  to facilitate the fully engaged two-point/line contact at Points B and C. Accordingly, this will define a small clearance  148  (FIG. 10) between the engaging flank  134  at root radius and the roller  128  at full mesh (i.e. two-point/line contact). The flank flat  144  and the inclined root surface  146  necessarily extend inside Points B and C respectively to facilitate the two-point/line roller contact at full engagement for all dimensional tolerance conditions of the roller  128  diameter D 1  and the root radius R i . A second root radius R i ′ is tangent to a radially inner end of the inclined root surface  146  at line  150 . The disengaging flank radius R f ′ is tangent to R i ′ at a point defined by disengaging flank roller seating angle β′. The radius R f ′ can have a value in the ISO-606 range. 
     The inclined root surface  146  is a flat surface having a finite length which defines a tooth space clearance (TSC). The tooth space clearance compensates for chain pitch elongation or chain wear by accommodating a specified degree of chain pitch elongation ΔP. In other words, the tooth space clearance TSC enables rollers of a worn chain to be maintained in hard contact with the inclined root surface of the sprocket teeth. In addition, the inclined root surface  146  facilitates reducing the radial reaction force thereby reducing the roller radial impact noise contribution to the overall noise level. 
     The inclined root surface  146  may be inclined at any angle φ necessary to satisfy a specific chain drive geometry and chain pitch elongation. As shown in FIG. 9, the inclined root surface angle φ is measured from a line  152  passing through the center of roller  128  and the sprocket center to a second line  154  which also passes through the center of roller  128  and Point C. The inclined root surface  146  is normal to the line  154 , and the inclined root surface extends radially inward to line  150  where it is tangent to R i ′. In the embodiment being described, the inclined root surface angle φ is preferably in the range of about 20° to about 35°. 
     FIG. 12 is an enlarged view of FIG. 8 showing the first roller  128  at full engagement in two-point/line contact across the thickness or width of the sprocket tooth profile, and the second roller  130  as the next roller about to mesh with sprocket  112 . As with the ISO-606 compliant drive system  10 , the chain guide  126  controls and guides a central portion of the taut strand  122  except for five unsupported link pitches extending between the chain guide  126  and the engaging roller  128  (and except for the unsupported link pitches extending between the driven sprocket and the chain guide). The taut strand  122  is horizontal when roller  128  is at the 12 o&#39;clock position. 
     FIG. 13 shows the drive sprocket  112  rotated in a clockwise direction (A/2)+ω, as determined by the instant of sprocket engagement by roller  130 . A straight line is assumed for the chain span from roller  128  to a chain pin center  156 , about which the unsupported span from pin center  156  to engaging roller  130  is considered to rotate. It should be appreciated that the straight line assumption is valid only in a quasi-static model. The amount of movement (or deviation from the straight line assumption) previously mentioned will be a function of the drive dynamics as well as the drive and sprocket geometry. 
     The sprocket contact at the onset of mesh for roller  130  occurs earlier than for the ISO-606 counterpart, thereby reducing the amount of chordal rise and, just as importantly, allows the initial contact to beneficially occur at a desired pressure angle γ on the engaging flank at Point A. Furthermore, the radial sprocket contact for roller  130 , with its contribution to the overall noise level, does not occur until the sprocket rotation places roller  130  at the 12 o&#39;clock position. This is referred to as staged engagement. 
     FIG. 14, an enlarged view of FIG. 13, more clearly shows the onset of meshing for roller  130 . Just prior to the onset of mesh, roller  128  is assumed to carry the entire taut strand load F TB +F φ , which load is shown as force vector arrows. Actually, the arrows represent reaction forces to the taut strand chain force. At the instant of mesh for roller  130 , a tangential impact occurs as shown by impact force vector F IA . The tangential impact is not the same as the taut strand chain loading. In particular, impact loading or impact force is related to the impact velocity V A . It is known that impact occurs during a collision between two bodies, resulting in relatively large forces over a comparatively short interval of time. A radial impact force vector F IC  is shown only as an outline in that the radial impact does not occur until the sprocket has rotated sufficiently to place roller  130  at a 12 o&#39;clock position. 
     FIG. 14 a  shows the same roller positions (solid) for rollers  128  and  130  as shown in FIG. 14, but in addition, shows the roller positions (in phantom) relative to the sprocket profile once roller  130  reaches its two-point/line mesh at the 12 o&#39;clock position. As a result of the pitch mismatch between the chain and sprocket, roller  128  must move to a new position. In particular, as roller  130  moves from initial contact to full mesh, roller  128  progresses forward in its tooth space. Small clearances in the chain joints, however, reduce the amount of forward progression required for roller  128 . Also occurring at the onset of meshing is the beginning of the taut strand load transfer from roller  128  to roller  130 . 
     The asymmetrical profile provides for the previously described “staged” meshing. In particular, referring again to FIG. 14, the Point A tangential contact occurs at the onset of mesh, with its related impact force F IA . The roller  130  is believed to stay in hard contact with the engaging flank  134  as the sprocket rotation moves the roller into full mesh with its resulting radial contact at Point C. 
     FIG. 14 b  is an enlarged view of FIG. 14, except that sprocket  112  has been rotated to advance roller  130  to the instant of full mesh at the 12 o&#39;clock position. At this instant of full mesh, the radial impact force F IC  occurs and the taut strand load transfer is considered to be complete. At the instant of the radial collision by roller  130  at Point C, with its resultant radial impact force F IC , the tangential impact force of F IA  has already occurred and is no longer a factor. The time delay (“staged” engagement) between the tangential and radial roller-sprocket collisions effectively spreads the roller-sproket meshing impact energy over a greater time interval, thereby reducing its contribution to the generated noise level at mesh frequency. Additionally, it is believed that the present asymmetrical sprocket tooth profile beneficially permits a more gradual taut strand load transfer from a fully engaged roller  128  to a meshing roller  130  as the meshing roller  130  moves from its Point A initial mesh to its full two-point mesh position. 
     Referring again to FIG. 14, the chordal rise (and fall) with the present asymmetrical profile is the perpendicular displacement of the center of roller  130  from the taut strand  122  path as it moves from its initial meshing contact Point A to the mesh position presently occupied by roller  128 . It is believed that roller  130  will stay in hard contact with the engaging flank  134  as the roller moves from initial tangential contact to full mesh, and accordingly, the chordal rise is reduced as the distance between Points A and B is increased. As shown in FIG. 14, chain pitch P C  is beneficially greater than sprocket  112  chordal pitch P S . 
     Referring now to FIG. 15, the length of the inclined root surface  146  (FIG. 10) may be reduced to zero (0), thereby eliminating the inclined root surface  146  and permitting root radius R i ′ to be tangent to the root surface and the roller  128  at Point C. That is, R i ′ is tangent to a short flat at Point C, and the flat is tangent to R i . If the inclined root surface  146  is eliminated, the engaging flank pressure angle γ would generally be in the range of some positive value to zero, but normally not less than zero. The reason is that a negative γ requires chordal pitch reduction so that the roller can exit the sprocket wrap  60  (FIG. 16) without interfering with R f . 
     FIG. 16 shows the roller contact to the sprocket  112  profile for all the rollers in the wrap  60 . Roller  128  is in full two-point mesh as shown. Line  160  shows the contact point for each of the rollers, as well as the contact progression as the rollers travel around the wrap. The inherent pitch mismatch between the sprocket and roller chain causes the rollers to climb up the coast side flank as the rollers progress around the sprocket wrap. With the addition of appreciable chordal pitch reduction, the extent to which the rollers climb up the coast side flank in increased. 
     It is important to note that chordal pitch reduction is required when the pressure angle γ has a negative value. Otherwise, as shown in FIGS. 16 and 17, roller  162  would interfere with the engaging flank (with a maximum material sprocket and a theoretical pitch [shortest] chain) as it exits the wrap  60  back into the span. That is, chordal pitch reduction permits the roller  162  to exit the wrap  60  with a clearance  163  at the engaging flank. Also, the reduced chordal pitch assists the staged mesh as previously mentioned. FIG. 16, showing the roller contact progression in the wrap  60 , serves also to show why the shallow β angle and tooth space clearance TSC helps maintain “hard” roller-sprocket contact for the rollers in the wrap. 
     In addition, the disengaging flank roller seating angle β (FIG. 9) may be adjusted to have a maximum value which is equal to α min /2 or even less. This reduced roller seating angle β′ promotes faster separation when the roller leaves the sprocket and enters the span. This reduced angle β′ also allows for the roller in a worn chain to ride up the coast flank surface to a less severe angle as the roller moves around the sprocket in the wrap. Accordingly, chordal pitch reduction, if used in this embodiment, should be a small value. 
     It is contemplated that the above-described asymmetrical tooth profile features can be altered without substantially deviating from the chain and sprocket meshing kinematics that produce the noise reduction advantages of the present invention. For example, the engaging asymmetrical flank profile could be approximated by an involute form, and the disengaging asymmetrical flank profile could be approximated by a different involute form. Slight changes to the asymmetrical tooth profiles may be made for manufacturing and/or quality control reasons, or simply to improve part dimensioning. These changes are within the scope of the invention as disclosed herein. 
     In a further embodiment, the engaging flank inclined root surface  146  (FIG. 9) may be replaced with a coast flank inclined root surface  164  as shown in FIG.  18 . The coast flank inclined root surface  164  provides tooth space clearance (TSC) in the same manner as described above with regard to the inclined root surface  146 . In addition, the disengaging flank inclined root surface  164  beneficially moves the roller to a preferred radially outward position as the chain wears. 
     Alternatively, the coast flank inclined root surface  164  may be included with the engaging flank inclined root surface  146  as shown in FIG.  19 . The engaging flank and coast flank inclined root surfaces  146 ,  164  cooperate to provide tooth space clearance (TSC) in the same manner as previously described. 
     Referring now to FIG. 20, any one of the above-described asymmetrical tooth profile embodiments of FIGS. 9,  15 ,  18 , and  19  may be incorporated into a random-engagement roller chain sprocket  300 . The sprocket  300  is shown as an 18-tooth sprocket. However, the sprocket  300  may have more or less teeth, as desired. The sprocket  300  includes a first group of arbitrarily positioned sprocket teeth  302  each having a profile which incorporates the flank flat  144  shown in FIGS. 9,  15 ,  18  and  19 . Further, the sprocket teeth  302  can incorporate none, one or both inclined root surfaces  146 ,  164  as shown in FIGS. 9,  15 ,  18  and  19 . The remaining sprocket teeth  304  (sprocket teeth  1 ,  3 ,  4 ,  9 ,  13 ,  14 , and  16 ) are randomly positioned around the sprocket and incorporate a tooth profile different from that of the first group of sprocket teeth  302 . As described further bdlow, the first and second groups of sprocket teeth  302 ,  304  cooperate to reduce chain drive system noise levels below a noise level which either tooth profile used alone would produce. 
     FIG. 21 illustrates an exemplary tooth profile for one of the sprocket teeth  304 . An engaging flank  306  and a coast or disengaging flank  308  of an adjacent tooth cooperate to define a tooth space  310  having a root surface  311 . The tooth space  310  receives an engaging roller  314  (shown in phantom). The engaging roller  314  has a roller diameter D 1  and is shown fully seated with single point (line) contact within the tooth space  310 . As best seen in FIG. 21 a , the engaging roller  314  does not contact the engaging flank  306  at the onset of meshing, moving instead directly from the span to full-mesh root contact on a inclined root surface  316  at a contact point C′ located radially outward of contact point C in a direction toward the engaging flank  306 . Contact point C′ is a roller/tooth contact line that extends axially along each sprocket tooth surface (i.e., in a direction orthogonal to the plane of the drawings). Thus, a clearance  318  is defined between the roller  314  and the engaging flank  306 . 
     As shown in FIGS. 21 and 21 a , the first or engaging root radius R i  is tangent to inclined root surface  316  at line  319 , and also tangent to R f  as defined by angle β. Angle β has no functional requirements specific to the onset of roller meshing since roller/flank contact will not take place with tooth profile  304 . It should be noted that Ri can be equal to the ISO-606 root radius for tooth profile  304 . 
     The length of the inclined root surface from point C to its radially outer end at line  319  is determined by the amount of flank offset required to ensure that the roller will not have engaging flank contact for any expected chain pitch elongation (wear) throughout its design life. In the preferred embodiment, the flank offset  323  is in the range of about 0.025 to about 0.13 mm. The flank offset  323  is an extension of inclined root surface  316  which provides tooth space clearance (TSC) in the same manner described above with regard to inclined root surface  146 . 
     As previously mentioned, tooth space clearance compensates for chain pitch elongation or chain wear by accommodating a specified degree of chain pitch elongation. In other words, the tooth space clearance TSC enables rollers of a worn chain to be maintained in hard contact with the inclined root surface of the sprocket teeth. In addition, the inclined root surface  316  facilitates reducing the radial reaction force thereby reducing the roller radial impact noise contribution to the overall noise level. 
     The inclined root surface  316  may be inclined at any angle φ necessary to satisfy a specific chain drive geometry and chain pitch elongation. The inclined root surface angle φ is measured from a line  320  passing through the center of roller  314  and the sprocket center to a second line  322  which also passes through the center of roller  314  and through contact point C. The inclined root surface  316  is normal to the line  322 , and the inclined root surface extends radially inward to line  318  where it is tangent to R i ′. In the embodiment being described, the inclined root surface angle φ is preferably in the range of about 20° to about 35°. 
     FIG. 22 shows another embodiment of the tooth profile  304  where no tooth space clearance TSC is provided. That is, the flat surface portion of the inclined root surface from line  318  to line  322  is not present. Thus, the profile of the tooth  304  from point C to the outside or tip diameter at the disengaging side of the tooth space is substantially identical to the tooth profile shown in FIG.  15 . The remaining flat surface portion  323  of the inclined root surface  316  from line  322  to line  319  functions only to provide the engaging flank offset as described above. 
     It should be appreciated that the portion of the engaging flank inclined root surface from line  318  to line  322  may be replaced with a coast flank inclined root surface  164  as in FIG.  18 . That is, the tooth profile  304  may be substantially identical to the tooth profile for sprocket  112  shown in FIG. 18 from contact point C to the outer diameter of the coast flank  138 . The coast flank inclined root surface  164  provides tooth space clearance (TSC) in the same manner as the inclined root surface  316 . In addition, the coast flank inclined root surface beneficially moves the roller to a preferred radially outward position as the chain wears. Alternatively, the coast flank inclined root surface  164  may be included with the engaging flank inclined root surface  316  in the same manner as shown in FIG. 19 (where the inclined surface  164  is included with the inclined surface  146 ). Thus, the tooth profile  304  may also be substantially identical to the tooth profile for sprocket  112  shown in FIG. 19 from contact point C to the outer diameter of the coast flank  138 . 
     Pitch mismatch is inherent in a chain/sprocket interface except at one condition—the theoretical condition which is defined as a chain at its shortest pitch (shortest being theoretical pitch) and a maximum material sprocket. This theoretical condition therefore defines one limit (zero, or no pitch mismatch) of the tolerance range of the pitch mismatch relationship of chain and sprocket. The other limit is defined when a longest “as built” chain is used with a sprocket at minimum material conditions—or in other words, a sprocket having a minimum profile. This limit produces the greatest amount of pitch mismatch. The pitch mismatch range is therefore determined by the part feature tolerances. 
     Additional pitch mismatch may be introduced to facilitate a greater time delay, or “staged” meshing, between the initial tangential contact at point A and the full seated contact at points B and C for tooth profile  302 . It should be appreciated that staged contact for profile  302  is enhanced due to the flank flat  144  which causes initial contact to occur higher up on the engaging flank. This will result in reduced mesh frequency noise levels because the point and rhythm of the initial roller-to-sprocket contacts are altered for each tooth profile  302 ,  304  since profile  304  does not have a tangential contact. 
     The sprocket chordal pitch is necessarily shorter than the chain pitch to facilitate the “staged” roller-tooth contact. In addition, chordal pitch reduction also provides roller-to-flank clearance as the roller exits the sprocket wrap back into the strand. Added chordal pitch reduction, when used, is preferably in the range of about 0.005 to about 0.030 mm. 
     The staged roller contact for tooth profile  302  may be further assisted by providing a sprocket tooth pressure angle γ that is substantially less than the ISO-606 standard. Pressure angles γ equal to or very close to zero (0), or even negative pressure angles, are contemplated. 
     FIG. 23 illustrates the tooth profile  304  overlaid with the tooth profile  302  (phantom). An engaging roller is shown at the onset of initial tangential contact at point A along the engaging flank of the tooth profile  302 . The engaging roller will maintain contact with the engaging flank until it is at full mesh and seated at points B and C as previously described with reference to FIG.  9 . The tooth profile  304  is overlaid on the tooth profile  302  to show that an engaging roller only has radial contact on the inclined root surface of the tooth profile  304  (see FIGS. 21 a  and  22 ) and does not have tangential contact with the tooth profile  304 . 
     The pressure angle γ for tooth profile  304  has no functional purpose during the onset of roller meshing since the roller does not contact the engaging flank. The pressure angle γ 302  for the tooth profile  302  is shown as a negative value. Thus γ min  may be a small negative value, and γ max  may be a positive value equal to some value less than the ISO-606 minimum pressure angle γ. As a result, initial roller-to-sprocket contact for tooth profile  302  of sprocket  300  (FIG. 20) occurs at point A followed by full engagement contact at points B and C. The sprocket  300  may, or may not incorporate additional chordal pitch reduction, and may, or may not incorporate tooth space clearance (TSC), as described above. 
     FIG. 24 shows the engagement path of an additional roller  342  from initial contact at point A (phantom) to fully-seated, two-point contact (solid) in a sprocket tooth  302 , and an engagement path of the roller  314  engaging an adjacent sprocket tooth  304  of the random engagement sprocket  300 . At the onset of meshing for roller  314 , a small portion of the chain load transfer takes place with tooth  304  picking up a share of the loading. However, tooth  302  continues to carry a larger portion of the chain loading until an engaging roller meshes with another tooth  302  with its attendant flank contact. The reference  1  in FIG. 24 indicates the amount of “staging” for the tooth  302  from the initial contact at point A to the full mesh contact at points B and C. 
     FIGS. 25 and 26 illustrate the meshing delay between the tooth profiles  302 ,  304 . In particular, as shown in FIG. 25, the sprocket  300  has a further roller  344  fully-seated in two-point contact with a sprocket tooth incorporating the tooth profile  302 . The roller  342  is shown at the instant of initial tangential contact at point A of a second sprocket tooth also incorporating the tooth profile  302 . The roller  314  is the next roller in the span and will mesh with a sprocket tooth incorporating the tooth profile  304 . The sprocket  300  must rotate through an angle τ for roller  342  to move from its initial contact position at point A to full mesh, seated in two-point contact with the tooth profile  302  at a 12 o&#39;clock position. 
     With reference to FIG. 26, the sprocket  300  of FIG. 25 is shown rotated in a clockwise direction until roller  314  is at the onset of meshing with the tooth profile  304 . The sprocket  300  must now rotate through a smaller angle  K  to have roller  314  seated at the 12 o&#39;clock position. Thus, the sprocket  300  must rotate through an additional angle  T-K  for an engaging roller to be fully seated in the tooth profile  302 . 
     Referring again to FIG. 20, the two sets of tooth profiles  302 ,  304  are arranged in a random pattern in order to modify the meshing impact frequency by altering the point and rhythm of initial roller-to-sprocket contact. However, the two sets of tooth profiles  302 ,  304  could be arranged in many different random patterns. Further, it is also contemplated that the two sets of tooth profiles  302 ,  304  could be arranged in many regular patterns that would work equally as well. In all cases, the arrangement of two sets of different tooth profiles on a sprocket provides a means for breaking up the mesh frequency impact noise normally associated with and induced by a full complement of substantially identically shaped sprocket teeth. The mesh frequency noise reduction is achieved by altering the point and rhythm of initial roller-to-sprocket contact. 
     The crankshaft sprocket, generally the smallest sprocket in the chain drive, is usually the major noise contributor. The typically larger driven camshaft sprocket, however, will also contribute to the generated noise levels, but generally to a lesser extent than the crankshaft sprocket. However, the driven sprocket, particularly if it is nearly the same size or smaller than the driving sprocket, may be the prime noise generator, as in the case with balance shaft sprockets and pump sprockets. Thus, the features of the present invention may also be used advantageously with camshaft or other driven sprockets as well. 
     It should be appreciated that the tooth profile features of FIGS. 20-26 can be altered slightly without substantially deviating from the chain and sprocket meshing kinematics that produce the noise reduction advantages of the present invention. For example, the engaging asymmetrical flank profile could be approximated by an involute form, and the disengaging asymmetrical flank profile could be approximated by a different involute form. Slight changes to the profile may be done for manufacturing and/or quality control reasons—or simply to improve part dimensioning. 
     The invention has been described with reference to the preferred embodiments. Obviously, modifications will occur to others upon a reading and understanding of this specification and this invention is intended to include same insofar as they come within the scope of the appended claims or the equivalents thereof.