Abstract:
A method for designing a synchronizer in a transmission which has a plurality of components each defined by one or more parameters is provided. The method includes selecting a first parameter having a relationship to the transmission. A second parameter is selected based off of a relationship to the first parameter. Then, the synchronizer components are designed while simulating a synchronization episode using the first and second parameters. The synchronization episode is divided into stages wherein for any given stage at least one component parameter is calculated or selected.

Description:
FIELD OF THE INVENTION  
       [0001]     The present invention relates to synchronizers in powertrain systems and more particularly to the design of synchronizers in powertrain systems.  
       BACKGROUND OF THE INVENTION  
       [0002]     Modern day transmissions are expected to provide performance and comfort during a gear change. In order to accomplish this task, typical transmissions include an apparatus known as a synchronizer. A synchronizer is essentially a friction clutch which synchronizes the rotational speed of the transmission output shaft with the gear that is to be engaged. Accordingly, the synchronizer provides a smooth gear change. The location and design of synchronizers within the transmission is important in order to minimize the effects of the inertia and relative speeds of the various rotating components within the transmission. Moreover, with an increasing trend towards higher engine power and higher engine speeds due to various factors (such as multiple valves per engine cylinder, etc.), there is an increasing expectation of higher or improved shifting efforts (i.e. improved performance). Concurrently, the driver still demands smooth shiftability and comfort. Performance and comfort are typically conflicting expectations which in turn require greater efficiency from the synchronizer design.  
       SUMMARY OF THE INVENTION  
       [0003]     A method for designing a synchronizer in a transmission which has a plurality of components each defined by one or more parameters is provided. The method includes selecting a first parameter having a relationship to the transmission. A second parameter is selected based off of a relationship to the first parameter. Then, the synchronizer components are designed while simulating a synchronization episode using the first and second parameters. The synchronization episode is divided into stages wherein for any given stage at least one component parameter is calculated or selected.  
         [0004]     Further areas of applicability of the present invention will become apparent from the detailed description provided hereinafter. It should be understood that the detailed description and specific examples, while indicating the preferred embodiment of the invention, are intended for purposes of illustration only and are not intended to limit the scope of the invention.  
     
    
     BRIEF DESCRIPTION OF THE DRAWINGS  
       [0005]     The present invention will become more fully understood from the detailed description and the accompanying drawings, wherein:  
         [0006]      FIG. 1  is a cross-sectional view of an exemplary transmission having an exemplary synchronizer designed according to the principles of the present invention;  
         [0007]      FIG. 2A  is a perspective disassembled view of the exemplary synchronizer and gear designed according to the principles of the present invention;  
         [0008]      FIG. 2B  is a cross sectional view of the exemplary synchronizer designed according to the principles of the present invention  
         [0009]      FIG. 3  is a flow chart illustrating a design method according to the principles of the present invention for designing the exemplary synchronizer illustrated in  FIGS. 1, 2A , and  2 B;  
         [0010]      FIG. 4  is a free body diagram of a ball/strut and sleeve of the exemplary synchronizer of the present invention used in designing the exemplary synchronizer;  
         [0011]      FIG. 5  is a free body diagram of a ring of the exemplary synchronizer used in designing the exemplary synchronizer;  
         [0012]      FIG. 6  is a free body diagram of the ring tooth chamfer and the sleeve tooth chamfer of the exemplary synchronizer used in designing the exemplary synchronizer;  
         [0013]      FIG. 7  is an exemplary nomogram illustrating a relationship between significant parameters in the design of the exemplary synchronizer;  
         [0014]      FIG. 8A  is an alternate view of the nomogram of  FIG. 7  illustrating the relationship between significant parameters in the design of the exemplary synchronizer;  
         [0015]      FIG. 8B  is another alternate view of the nomogram of  FIG. 7  illustrating the relationship between significant parameters in the design of the exemplary synchronizer;  
         [0016]      FIG. 9  is a flow chart illustrating the steps in designing the exemplary synchronizer during an imaginary synchronization event;  
         [0017]      FIG. 10  is a free body diagram of the ball and sleeve of the exemplary synchronizer used in designing the exemplary synchronizer during a first synchronization event;  
         [0018]      FIG. 11  is a free body diagram of the ball/strut and sleeve of the exemplary synchronizer used in designing a ball/strut and sleeve detent during a second synchronization event;  
         [0019]      FIG. 12  is an exemplary chart illustrating various ball/strut and sleeve detent angles and ring loads used in designing the exemplary synchronizer during the second synchronization event;  
         [0020]      FIG. 13  is a free body diagram of the sleeve, strut, and ring used in designing the exemplary synchronizer during a third synchronization event;  
         [0021]      FIG. 14  is a free body diagram of the sleeve used in calculating a clocking angle used in the design of the exemplary synchronizer during the third synchronization event;  
         [0022]      FIG. 15  is a free body diagram of the ring blocker used in calculating a ring tooth width during a fourth synchronization event;  
         [0023]      FIG. 16  is a free body diagram of the sleeve and ring blocker used in calculating a gap distance during the fourth synchronization event; and  
         [0024]      FIG. 17  is a free body diagram of the sleeve, ring blocker, and gear tooth used in calculating a gap between the sleeve and the gear during a fifth and a sixth synchronization event. 
     
    
     DETAILED DESCRIPTION OF THE PREFERRED EMBODIMENTS  
       [0025]     The following description of the preferred embodiment(s) is merely exemplary in nature and is in no way intended to limit the invention, its application, or uses.  
         [0026]     With reference to  FIG. 1 , there is illustrated an exemplary synchronizer  10  shown in operative association with an exemplary transmission  12 . The synchronizer  10  has been designed according to a method  100  which will be described in greater detail below. The synchronizer  10  is disposed on an input shaft  14  between a first gear  16  and a second gear  18 . Likewise, a substantially identical synchronizer  10 ′ is disposed on an output shaft  20 , however, only one of the synchronizers  10  will be described. The input shaft  14  is coupled to an engine (not shown) and receives power therefrom. The output shaft  20  is in turn coupled to a drivetrain (not shown). The first and second gears  16 ,  18  are intermeshed with substantially similar gears on the output shaft  20  in order to transfer power from the input shaft  14  to the output shaft  20 . The synchronizer  10  acts to synchronize the rotational speed of the first and second gears  16 ,  18 .  
         [0027]     Turning now to  FIGS. 2A and 2B , the synchronizer assembly  10  generally includes a hub  22 , a sleeve  24 , a ball/strut  56 , a spring  60 , and a blocker ring  26 . The hub  22  includes splines  28  on an inner diameter thereof for engagement with the input shaft  14  ( FIG. 1 ). The hub  22  further includes external splines  30  located along an outer diameter thereof as best seen in  FIG. 2B . The sleeve  24  is disposed about the hub  22  and is moveable relative thereto into and out of engagement with the first and second gears  16 ,  18  ( FIG. 1 ) in order to synchronize the rotation of the first and second gears  16 ,  18  with the rotation of the input shaft  14 . Specifically, the sleeve  24  includes internal splines  32  adapted to engage the external splines  30  of the hub  22 . However, the sleeve  24  is movable relative to the hub  22  in a direction of the splines  30 ,  32  and parallel to the longitudinal axis of the input shaft  14 . To that end, the sleeve  24  includes an external annular groove  34  adapted to receive a shift fork  35  to move the sleeve  24  into and out of engagement with the first and second gears  16 ,  18 .  
         [0028]     The blocker ring  26  is disposed between the sleeve  24  and each of the first and second gears  16 ,  18 . Accordingly, only the blocker ring  26  between the sleeve  24  and the first gear  16  will be described, it being understood that the description applies equally to the second gear  18 . The blocker ring  26  includes external blocker teeth  36  and has a conical inner bore  38 . The blocker ring  26  is carried on a cone portion  40  extending axially from the first gear  16 . The external blocker teeth  36  are engaged by the internal splines  32  on the sleeve  24  as the sleeve  24  is moved into and out of engagement with the first gear  16 . At the same time, the blocker ring  26  is moved relative to the cone portion  40  on the first gear  16  such that the conical inner bore  38  of the blocker ring  26  engages the cone portion  40  to begin synchronization of the first gear  16  and such that clutch teeth  42  of the first gear  16  are aligned with the internal splines  32  on the sleeve  24  to fully synchronize the rotation of the first gear  16  with the input shaft  14 .  
         [0029]     With specific reference to  FIG. 2B , the synchronizer  10  further includes a retaining mechanism  44  for indexing the synchronizer sleeve  22  into and out of engagement with the adjacent gears  16 ,  18 . The detent mechanism  44  includes at least one, but preferably a plurality of, retaining mechanisms  46 . Similarly, the detent mechanism  44  includes at least one, but preferably a plurality of, detent pockets  48  disposed internally on the synchronizer sleeve  24  and corresponding to each retaining mechanism  46 . Preferably, the detent mechanism  44  includes three retaining mechanisms  46  and three detent pockets  48  corresponding to each of the retaining mechanisms  46 . Each pair of corresponding retaining mechanisms  46  and detent pockets  48  are equally spaced relative to an adjacent pair of corresponding retaining mechanisms  46  and detent pockets  48 .  
         [0030]     Each of the detent pockets  48  has an annular groove  52  disposed therebetween corresponding to a neutral position. The retaining mechanisms  46  include a ball  56  which is disposed between the hub  22  and the synchronizer sleeve  24  and disposed into engagement with the annular groove  52  on the detent pocket  48 . Alternatively, a strut may be used interchangeably with the ball  56 .  
         [0031]     The retaining mechanism  46  further includes a slot  58  extending radially inward from the outer radial surface of the hub  22  and a coiled spring  60  disposed within the slot  58  and between the hub  22  and the ball  56  to urge the ball  56  into engagement with the annular groove  52 .  
         [0032]     Preferably, each of the balls  56  of the retaining mechanism  46  is receivable in the annular groove  52  of the detent pockets  48  to positively hold the synchronizer sleeve  24  in the neutral position. As the synchronizer sleeve  24  is actuated by the shift fork  35 , the balls  56  are depressed against the force of the coiled spring  60  and ride against lands  62  on the sleeve  24 . The detent mechanism  44  allows the sleeve  24  to move into and out of engagement with adjacent gears  16 ,  18  to synchronize the rotation of the adjacent gears  16 ,  18  with the rotation of the input shaft  14 , while providing a detent force to urge the sleeve  24  into a neutral position when synchronization is complete.  
         [0033]     Turning now to  FIG. 3 , the method  100  of designing the synchronizer  10  will now be described. The method  100  begins by defining primary parameters at step  102 . This includes defining a break through load (BTL), a cone torque, and an index torque. The BTL is the amount of resultant axial force due to applied force at the sleeve  24  and the detent load needed to move the blocker ring  26  into a blocker position such that conical surface of blocker ring  26  engages the conical surface of gears  16  and  18 . The cone torque is the amount of torque generated when the conical inner bore  38  of the blocker ring  26  engages the cone portion  40  on a gear  16 ,  18 . The index torque is the amount of torque generated when the sleeve  24  first engages the blocker ring  26  and the chamfers of the internal splines  32  on the sleeve  24  engage the chamfers on the external blocker teeth  36  on the blocker ring  26 , thereby forcing the blocker ring  26  to slightly rotate or “index”. At step  104 , the components of the synchronizer  10  are designed based on the significant parameters calculated and selected in step  102 .  
         [0034]     The BTL should continue until the chamfers of the internal splines  32  of the sleeve  24  and the chamfers of the teeth  36  on the blocker ring  26  contact and pass through. The BTL calculated in step  102  of the method  100  will now be described in detail with general reference to  FIG. 4 . The BTL (also known as push through load) effectively sets the blocker ring  26  into block position. The BTL should start to build as soon as the applied force at the sleeve  24  (initiated by shifting) urges the sleeve  24  to begin its movement. The BTL should continue until the internal splines  32  of the sleeve  24  contact the gear teeth  36  on the blocker ring  26 . The axial distance from sleeve internal splines  32  to the blocker gear teeth  36  contact is called “proximity”. Proximity is dealt with at greater length below. The BTL must not be reduced prior to contact between the sleeve internal splines  32  and the blocker gear teeth  36  in order to avoid unloading the blocker ring  26  too soon, thereby interrupting oil wiping action and resulting in gear clash. On the other hand, if BTL continues for a time period beyond the time of contact, ring sticking will occur thereby creating a noticeable clash.  
         [0035]     BTL is a function of detent spring rate, ball height (or strut bump when the retaining mechanism  44  is a strut mechanism), coefficient of friction between the detent ball  56  and the sleeve  24 , and the ramp angle of the annulus groove  52  in the sleeve  24 . Mathematically analyzing the forces on one of the three ball detents, BTL can be calculated from the following derivations, wherein Fa is the axial load to overcome detent spring reaction, Ns is the normal force on the sleeve  24 , □ is the ramp angle of the annulus groove  52  on the sleeve  24 , fs is the friction force of the sleeve  24 , μ is the coefficient of friction between the detent ball  56  to the sleeve  24 , and Fr is the reaction force of the detent spring  60 :  
         [0036]     As shown in  FIG. 4 , taking the sum of forces on the sleeve  24  in x- and y-direction: 
 
 F   A   =N   s  Sin θ+ƒ s  Cos θ
 
ƒ s   =μN   s  
 
 F   A   =N   s (Sin θ+μ Cos θ)  (1) 
 
         [0037]     Taking the sum of forces on detent ball  56 :  
                 F   A     =           N   s     ⁢   Sin   ⁢           ⁢   θ     +       f   s     ⁢   Cos   ⁢           ⁢   θ       ⁢     
     ⁢           =         N   s     ⁢   Sin   ⁢           ⁢   θ     +     μ   ⁢           ⁢     N   s     ⁢   Cos   ⁢           ⁢   θ           ⁢     
     ⁢         F   R     +       f   s     ⁢   Sin   ⁢           ⁢   θ       =       N   s     ⁢   Cos   ⁢           ⁢   θ       ⁢     
     ⁢       F   R     =       N   s     ⁡     (       Cos   ⁢           ⁢   θ     -     μ   ⁢           ⁢   Sin   ⁢           ⁢   θ       )                 (   2   )             
 
         [0038]     Substituting for Ns from equations (1) in equation (2):  
                 F   R     =       F   A     ⁢         Cos   ⁢           ⁢   θ     -     μ   ⁢           ⁢   Sin   ⁢           ⁢   θ           Sin   ⁢           ⁢   θ     -     μ   ⁢           ⁢   Cos   ⁢           ⁢   θ             ⁢     
     ⁢       F   A     =         F   R     ⁢         Sin   ⁢           ⁢   θ     -     μ   ⁢           ⁢   Cos   ⁢           ⁢   θ           Cos   ⁢           ⁢   θ     -     μ   ⁢           ⁢   Sin   ⁢           ⁢   θ           ⁢     
     ⁢           =       F   R     ⁢       μ   +     Tan   ⁢           ⁢   θ         1   -     μ   ⁢           ⁢   Tan   ⁢           ⁢   θ               ⁢     
     ⁢     BTL   =       3   ×     F   A       =     3   ×     F   R     ⁢       μ   +     Tan   ⁢           ⁢   θ         1   -     μ   ⁢           ⁢   Tan   ⁢           ⁢   θ                       (   3   )             
 
         [0039]     The magnitude of the BTL should be smaller than the axial force applied at the sleeve groove  34  during shifting. However, too low a BTL could create a clash condition. Typically, approximately 9 to 11 lbs of BTL is sufficient to start activation of the blocker ring  26 .  
         [0040]     With reference to  FIG. 5 , the cone torque will now be described. As the blocker ring  26  pushes axially on to the cone portion  40  of the gear, the oil is wiped out and friction force is generated in the direction of the cone angle between the cone portion  40  and the conical inner bore  38  of the blocker ring  26 . The cone torque is primarily a function of the axial force applied to the sleeve  24 , the cone angle, the surface coefficient of friction, and active cone diameter. Cone torque can be calculated from the following equation, wherein Tc is the cone torque, F is the axial force of the sleeve  24  due to shifting, μ c  is the coefficient of friction of the cone surface, R is one half the cone gage diameter, and α is the cone angle of the conical inner bore  38 :  
               T   C     =       F   ×     μ   C     ×   R       Sin   ⁢           ⁢   α               (   4   )             
 
         [0041]     The cone torque is countered by the index torque, and cone torque must be greater in magnitude than the index torque in order to “index” the blocker ring  26  and complete synchronization successfully. Accordingly the following inequality must apply, wherein Ti is the index torque: 
 
T c &gt;T l   (5) 
 
         [0042]     With reference to  FIG. 6 , the index torque will now be described. When the sleeve  24  has traversed the “proximity” distance, the sleeve internal splines  32  point contact the blocker external blocker teeth  36 , and a friction force is generated between the two chamfers on each of the splines  32  and teeth  36 . This friction force is in the direction of the pointing angle, thereby resulting in torque, and is known as the index torque. The index torque is a function of axial force applied to the sleeve  24 , the tooth pointing angle, the pitch diameter of the blocking teeth  36 , and surface coefficient of friction between the point contact surfaces of the sleeve  24  and blocker ring  26 . The index torque can be calculated from the following derivations, wherein r is half the pitch diameter of the sleeve/ring teeth, β is the pointing angle of the sleeve/ring, and μ p  is the coefficient of friction between the sleeve and ring teeth: 
 
 T   l   =F   l   ×r  
 
         [0043]     Summation of forces in the x-direction on the sleeve  24 : 
 
 F   l   =N   s  Cos β−ƒ s  Sin β= N   s (Cos β−μ p  Sin β) 
 
         [0044]     Summation of forces in the y-direction on the sleeve  24 :  
                     ⁢       F   =       N   S     ⁡     (       Sin   ⁢           ⁢   β     +       μ   p     ⁢           ⁢   Cos   ⁢           ⁢   β       )         ⁢     
     ⁢       N   S     =     F       Sin   ⁢           ⁢   β     +       μ   p     ⁢           ⁢   Cos   ⁢           ⁢   β           ⁢     
     ⁢           ⁢       F   I     =     F   ⁢         Cos   ⁢           ⁢   β     -       μ   p     ⁢   Sin   ⁢           ⁢   β         Sin   ⁢           +       μ   p     ⁢   Cos   ⁢           ⁢   β             ⁢     
     ⁢           ⁢       T   I     =       F   ×   r   ⁢         Cos   ⁢           ⁢   β     -       μ   p     ⁢   Sin   ⁢           ⁢   β           Sin   ⁢           ⁢   β     ⁢           +       μ   p     ⁢   Cos   ⁢           ⁢   β           ⁢     
     ⁢           =     F   ×   r   ⁢       1   -       μ   p     ⁢   Tan   ⁢           ⁢   β           μ   p     +     Tan   ⁢           ⁢   β                         (   6   )             
 
         [0045]     In the inequality (5), substituting for T c  from (4) and for T l  from (6), produces:  
                 F   ×     μ   C     ×   R       Sin   ⁢           ⁢   α       ≥     F   ×   r   ×       1   -       μ   p     ⁢   Tan   ⁢           ⁢   β           μ   p     +     Tan   ⁢           ⁢   β                   (   7   )             
 
         [0046]     Inequality (7) can be simplified to  
               Tan   ⁢           ⁢   β     ≥         r   R     -       μ   p     ⁢       μ   C       Sin   ⁢           ⁢   α                 μ   C       Sin   ⁢           ⁢   α       +       μ   p     ⁢     r   R                   (   8   )             
 
         [0047]     It can be observed that the inequality (8) has four interdependent significant synchronizer parameters. Nomograms are then created using inequality (8) to size, select, and verify the parameters of a synchronizer for a given application. Exemplary nomograms are shown in  FIGS. 7, 8A , and  8 B.  
         [0048]     The nomogram in  FIG. 7  depicts the relationship of sleeve/ring pointing angle with the size of the synchronizer, cone coefficient of friction, and cone angle for a given μ p . This relationship resulted from the necessary condition in inequality (5) and the algorithms derived from it in inequality (8). It can be observed that the smaller the size to cone friction ratio, the smaller the pointing angle for a given μ p , thereby resulting in clash. On the other hand, the larger the ratio the larger the pointing angle, thereby resulting in hard shift. Again, from computations based on inequalities (5) and (8), plotted in the nomogram in  FIG. 7 , it is clear that for a given μ p , size to coefficient of friction ratios approximately above 2.5 could result in hard shift and approximately below 1.5 could result in clash. Accordingly, a comfortable shiftability zone lies between the two.  
         [0049]      FIGS. 8A and 8B  graphically represent the same relationship shown in  FIG. 7 , however, here all four significant parameters are separately charted. Accordingly,  FIGS. 8A and 8B  show that for a given μ p , the greater the r/R ratio, the greater the pointing angle, thereby resulting in a hard shift. Alternatively, the smaller the r/R ratio, the smaller the pointing angle, thereby resulting in clash. Any of the three nomograms shown in  FIGS. 7, 8A , and  8 B are used to select the significant parameters in step  102  of the method  100 .  
         [0050]     Returning to  FIG. 3 , after the significant parameters have been defined using the nomograms in  FIGS. 7, 8A , and  8 B and inequality (8), the method  100  goes on to step  104  wherein the components of the synchronizer are designed based on the significant parameters calculated and selected in step  102 .  
         [0051]     Turning now to  FIG. 9 , step  104  of the method  100  involves designing the synchronizer by stepping through an imaginary synchronizer event. After selecting the physical parameters of the synchronizer, namely sleeve and blocker ring pointing angle, cone angle, cone coefficient of friction, and the size in step  102 , step  104  begins the designing, dimensioning, and tolerancing of the synchronizer components. The intended objective of the design process in step  104  should be to dimension and tolerance the individual components in a manner such that, along with the selected parameters, the functional objectives are achieved satisfactorily (e.g. no clash or hard shift). The design process at step  104  includes charting the synchronization events, and iteratively dimensioning, stacking, and tolerancing for the best results. The synchronization episode has been broken up into six distinct events, including when the sleeve  24  contacts the ball  56  (Event  1 ) at step  106 , when ball  56  loading has ended and the ball  56  is out of the annulus groove  52  (Event  2 ) at step  108 , when the sleeve  24  engages the blocker ring  26  (Event  3 ) at step  110 , when the sleeve  24  meshes with the blocker ring  26  (Event  4 ) at step  112 , when the sleeve  24  first contacts the gear clutching teeth  42  (Event  5 ) at step  114 , and finally when the sleeve  24  meshes with the gear clutching teeth  42  (Event  6 ) at step  116 . Each of these events will be described in greater detail below.  
         [0052]     With reference to  FIG. 10 , Event  1  will now be described. Event  1  is the starting point of break through load (BTL) and strut/ball loading. The components involved in Event  1  are the sleeve  24 , detent strut/ball  56 , and the detent spring  60 . Note that a ball or strut may be used interchangeably in the design as each functions exactly the same way. Accordingly, for purposes of explanation, a strut has been illustrated in several views, it being understood that a ball may also be employed. Event  1  is pictorially illustrated in  FIG. 10  and the ball loading starts at the point of first contact, and the earlier the loading begins the better. What is also called zero (0) point will be the first contact of the strut/ball on the ring. The zero point implies maximum ball length, maximum ring lug thickness, and maximum gage point offset. At the other extreme, the last contact point implies minimum ball length, minimum ring lug thickness, and minimum gage point offset.  
         [0053]     Hence the total differences are: 
 
Max−Min ball length=( L   ST max   −L   ST min ) 
 
Max−Min ring thickness=( L   RMax   −L   RMin ) 
 
Max−Min gage point=( G   Max   −G   Min ) 
 
         [0054]     Taking the first contact point as the zero point, the last contact will occur at a distance: 
 
( L   ST Max   −L   ST Min )+( L   Rmax   −L   Rmin )+( G   Max   −G   Min )  (9) 
 
         [0055]     With reference to  FIG. 11 , Event  2  will now be described in detail. Event  2  is the end of strut/ball  56  loading and involves the sleeve  24 , strut/ball  56 , and the detent spring  60 . The strut/ball  56  snaps back and the sleeve  24  moves on towards the blocking ring  26 . It is to be noted here that the detent load is a function of the ramp angle of the sleeve annulus groove  52  and significantly influences the magnitude of BTL.  
         [0056]     Detent profile is critical in achieving desirable BTL. Since the desirable BTL has been calculated in step  102 , the task at hand is to dimension the detent profile accordingly, as shown in  FIG. 11 .  
         [0057]     Computing X &amp; Y:  
               ⁢     X   =     Y     tan   ⁢           ⁢   θ             
         Y   max     =         D   G     -     D   min       2         
               ⁢       Y   min     =         D   G     -     D   max       2           
 
         [0058]     For X to be minimum, ramp angle and minor diameter should be maximum, or Y minimum, hence  
               X   min     =         Y   min       tan   ⁢           ⁢     θ   max         =         D   G     -     D   max         2   ⁢   tan   ⁢           ⁢     θ   max                   (   10   )             
 
         [0059]     For X to be maximum, ramp angle and minor diameter should be minimum, or Y maximum, hence  
               X   max     =         Y   max       tan   ⁢           ⁢     θ   min         =         D   G     -     D   min         2   ⁢   tan   ⁢           ⁢     θ   min                   (   11   )             
 
         [0060]     Computing groove width Z: for Z to be minimum gage dimension a and X should be minimum, 
 
 Z   min =α min   +X   min   (12) 
 
         [0061]     For Z to be maximum gage, dimension a and X should be maximum, 
 
 Z   max =α max   +X   max   (13) 
 
         [0062]     The distance strut out of detent S can be found as follows: 
 
 S   max   =Z   max   −L   B min   (14) 
 
 S   min   =Z   min   −L   B max   (15) 
 
         [0063]     Equations (10) through (15) can be used to design the detent profile for a reasonable detent load to achieve the desired BTL. The sleeve groove  52  ramp angle contributes significantly to the detent load and to the BTL, and, as such, it is illustrated in  FIG. 12 . It can be observed that a ramp angle of 30 degrees for a given application will yield the desired BTL.  
         [0064]     With reference to  FIG. 13 , Event  3  will now be described in detail. Components involved in Event  3  include the sleeve  24 , blocker ring  26 , the cone portion  40 , and the conical inner bore  38 . In Event  3 , for the sleeve  24  point to hit the blocker ring  36  point as quickly as possible, the gap between them should be at a minimum. The minimum gap is obtained with maximum ring width, maximum ball, maximum gage point offset at ‘0’ point condition. Similarly, the maximum gap can be obtained with minimum ring width, minimum ball, and minimum gage point offset. The gap between the sleeve tooth pointing and ring tooth pointing is shown in  FIG. 13 , section A-A. The gap between sleeve tooth pointing and ring tooth pointing is called “proximity”, as noted above, and is equal to the following: 
 
( L   R   +L   ST   +L   B )− L   SL   (16) 
 
         [0065]     If sleeve and ring teeth have rake angle, then using trigonometry, L R  will increase by a fraction and L SL  will diminish by a fraction, thereby affecting the “proximity” by a fraction as well.  
         [0066]     During Event  3 , as soon as the sleeve pointing contacts the ring pointing, the blocker ring  26  starts to clock and “indexes” with the oncoming sleeve  24 . The clocking angle is a function of the widths of the lug integral to the ring and slot width in the hub. The lug and the slot widths should be dimensioned adequately while minimum and maximum clocking angles should be calculated to insure that there is enough time for BTL to develop. Moreover, if the time is too long, the ring  36  would take too much time to set for the oncoming sleeve  24 .  
         [0067]     The clocking angle is calculated by applying trigonometry using the lug and slot widths and the radius at the lug, as shown in  FIG. 14 . Maximum clocking is obtained from maximum slot width, minimum lug width, and minimum radius.  
                 Sin   ⁢           ⁢     α   SLOT       =       W   S       2   ×     r   S           ,     
     ⁢       α   SLOT     =       Sin     -   1       ⁢       W   S       2   ×     r   S                     (   17   )                   Sin   ⁢           ⁢     β   LUG       =       W   L       2   ×     r   S           ,     
     ⁢       β   LUG     =       Sin     -   1       ⁢       W   L       2   ×     r   S                     (   18   )             
 
         [0068]     Clocking angle 
 
ψ=α SLOT −β LUG   (19) 
 
         [0069]     From experience, the clocking angle should be approximately less than 4 but greater than 3 degrees (4         ψ         3), and the lug and slot width should be dimensioned accordingly.  
         [0070]     Turning back to  FIG. 13 , Section A-A, the dimension Z between the tooth points is an arc. The angle between the center of a sleeve tooth and the center of a space is as follows:  
                 360     N   +   N       =     180   N       ⁢     
     ⁢       AL   ⁡     (     180   /   N     )       =       180   N     ×     r   R                 (   20   )                 AL   ⁡     (   ψ   )       =     ψ   ×     r   R               (   21   )             
 
         [0071]     In equations (20) and (21) the angles (180/N) and ψ are in radians. For x to be small the pointing angle should be maximum,  
                 tan   ⁢           ⁢   β     =     z   x       ⁢     
     ⁢     z   =       AL   ⁡     (     180   N     )       -     AL   ⁡     (   ψ   )                   (   22   )             
 
         [0072]     Turning to  FIG. 15 , Event  4  will now be described in which the ring tooth width is calculated. During Event  4 , the sleeve  24  is engaging the ring blocker  26 . Given the pressure angle, the ring tooth thickness and the circular space width of the sleeve splines  32  can be calculated. Obtaining four values, maximum and minimum for each, they can be compared to determine the combination of tolerances at which the ring tooth thickness to sleeve space width would have positive or negative clearance. The combination of tolerances can be selected that provide desirable fit and that would be feasibly manufacturable.  
         [0073]     Using the ring outer diameter (D t ) and tooth width at the pitch diameter (t Dp ), two minimum and two maximum values of ring tooth width are calculated. The ring tooth width can be calculated by applying the following equation:  
                     t   t       D   t       =         t   DP       D   P       +     INV   ⁢           ⁢   ϕ     -     INV   ⁢           ⁢     ϕ   t           ,   or     ⁢     
     ⁢       t   t     =       D   t     ⁡     (         t   DP       D   P       +     INV   ⁢           ⁢   ϕ     -     INV   ⁢           ⁢     ϕ   t         )                 (   23   )             
 
         [0074]     Using the equation (23), sleeve spline space width can be calculated that would yield four values, two maximums and two minimums. By comparing the values of ring tooth width with the sleeve spline space width, the combination of tolerances can be assessed that yield positive running clearance.  
         [0075]     Having calculated sleeve tooth space width, the tooth width can be calculated as follows:  
               t     (     tooth   +   space     )       =         1   ⁢   tooth     +     1   ⁢   space       =       π   ⁢           ⁢     D   t         N   T                 (   24   )             
 
         [0076]     The sleeve space width has already been calculated, as noted above, accordingly the sleeve tooth width can be computed as follows: 
 
 t   S   =t   (tooth+space)   −t   space    (25) 
 
         [0077]     Finally, the distance traveled by the sleeve pointing chamfer from zero point to the ring pointing chamfer is then stacked, with reference to  FIG. 16 , as follows:  
                       tan   ⁢           ⁢   β     =       t   R       2   ×     a   R                     =       t   S       2   ×     a   S                     =         t   R     +     t   S         2   ⁢     (       a   R     +     a   S       )                 ⁢     
     ⁢     Or   ,         a   R     +     a   S       =         t   R     +     t   S         2   ×   tan   ⁢           ⁢   β                   (   26   )                     S   =     GAP   +     a   S     +     a   R                   =     GAP   +         t   R     +     t   S         2   ×   tan   ⁢           ⁢   β                       (   27   )             
 
         [0078]     Therefore, for minimum distance traveled by sleeve in Event IV, 
 
 S   min   =GAP   min +α R min +α S min   (28) 
 
         [0079]     For S min , the minimum GAP from Event  3  and the values of t R  and t S  are used for the conditions assigned for the minimum values in Event  4 . Similarly, for S max , the maximum GAP from Event  3  and the values t R  and t S  are used for the conditions assigned for maximum values in Event  4 .  
         [0080]     With reference to  FIG. 17 , Event  5  will be described. During Even  5 , the sleeve tooth point contacts the clutching tooth point. Here again, dimensions are stacked in order to calculate the distance traveled by the sleeve  24  from zero point to meet the clutching tooth point. The distance the sleeve  24  pointing has to travel from zero point to meet the clutch tooth pointing can be computed by stacking up the GAP in Event  3  along with the blocker ring  26  and clutching tooth dimensions as follows, wherein for P min  the dimension L SL  is maximum and all other dimensions are minimum, and for P max  the dimension L SL  is minimum and all other dimensions are maximum: 
 
 P=Δ+G+L   RW   +L   ST   +L   B   −L   SL  
 
 P=Δ+G+W   RT   +GAP   (29) 
 
         [0081]     With continued reference to  FIG. 17 , Event  6  will now be described. During Event  6  (the final event), when the sleeve  24  travels from the zero position, and its chamfer passes the gear clutching tooth chamfer to complete the gear engagement. During this event the blocker ring  26  is completely unloaded and freely gets back to zero position marking the end of cone torque. The total distance traveled by sleeve pointing from zero position to go past the gear clutching tooth chamfer can be computed as follows:  
             Q   =     P   +     a   S     +     a   G               (   30   )                   tan   ⁢           ⁢   β     =       t   S       2   ×     a   S           ,       or   ⁢           ⁢     a   S       =       t   S       2   ×   tan   ⁢           ⁢   β                 (   31   )                   tan   ⁢           ⁢   λ     =       t   G       2   ×     a   G           ,       or   ⁢           ⁢     a   G       =       t   G       2   ×   tan   ⁢           ⁢   λ                 (   32   )             
 
         [0082]     Substituting values from equations (31) and (32) in equation (30):  
             Q   =     P   +       t   S       2   ×   tan   ⁢           ⁢   β       +       t   G       2   ×   tan   ⁢           ⁢   λ                 (   33   )             
 
         [0083]     As described above, the method  100  can be used to establish accurate relationships among the synchronizer significant physical parameters (e.g., size, coefficient of friction, cone torque, cone angle, index torque, and sleeve/blocker ring pointing angle) to allow an intelligent synchronizer design. By using nomograms developed herein, significant physical parameters may have their relationships instantly and easily defined. Finally, the six distinct events of synchronization design help to dimension and tolerance the physical parameters as selected above to achieve the prime objective of smooth transition from one gear to the other.  
         [0084]     The description of the invention is merely exemplary in nature and, thus, variations that do not depart from the gist of the invention are intended to be within the scope of the invention. Such variations are not to be regarded as a departure from the spirit and scope of the invention.