Abstract:
An objective method is provided for selecting gear ratios for use in a motor vehicle transmission having multiple selectable gears. The method includes selecting gear ratios for a specific application includes calculating a low gear ratio, and a high gear ratio based upon vehicle parameters and performance requirements. The total ratio spread is determined by dividing the low gear ratio by the high gear ratio. Using the total ratio spread, a geometric sequence is created with a plurality of terms, such that each of the terms respectively represent the ratio steps between the gears. Lastly, each gear ratio is divided by its respective ratio step plus one to find the gear ratio for the next gear. This method provides an objective method for selecting gear ratios, such that the steps between each of the ratios are uniformly progressive.

Description:
FIELD OF THE INVENTION  
       [0001]     The present invention relates to a method of selecting gear ratios for an automobile transmission during a design phase thereof, more particularly, to a method of selecting gear ratios having uniformly progressive ratio steps for an automobile transmission having a plurality of gears.  
       BACKGROUND OF THE INVENTION  
       [0002]     For any given vehicle, transmission gear ratios are selected to satisfy performance requirements of gradability, fuel economy, acceleration, and ease of operation. Fuel economy considerations are essential to the selection of gear ratios. Numerically too high a gear ratio causes the engine to run too fast and thus, failing to operate at optimum fuel efficiency. Alternatively, an extremely low numerical gear ratio adversely effects vehicle performance, such as acceleration. Hence, acceleration is also an important concern in gear ratio selection. To maximize acceleration, gear ratios should be selected such that upshifts occur only when the next higher gear will provide more torque to the drive wheels.  
         [0003]     Providing maximum torque to the drive wheels in each gear requires consideration of the ratio steps. Wide ratio steps in the lower gears provide for favorable fuel efficiency due to less frequent shifting. However, shifting through wide ratio steps requires skillful execution, otherwise a loss in fuel efficiency occurs. Alternatively, narrow ratio steps keep the engine running at or near full speed, thus supplying near maximum torque to the drive wheels. By skipping gears in narrow ratio step configurations, what is commonly referred to as skip shifting, a driver can simulate driving a wider step configuration, thus increasing fuel efficiency. Hence, selection of transmission gear ratios requires a balancing of various performance factors with the skill required of the end user.  
         [0004]     Implementing ratio steps that decrease from low gear to high gear typically help to balance these performance factors. This decreasing trend between ratio steps illustrates what is called progressively smaller ratio steps. Progressively smaller ratio steps lend to maximum vehicle performance and maximum fuel efficiency, while providing a linear feel to the shifting process.  
         [0005]     Historically, transmission designers have subjectively implemented progressive ratio steps. This subjective approach however, fails to produce truly uniform progressive ratio steps, meaning ratio steps which uniformly decrease from low gear to high gear. Thus, there stands a desire to eliminate the guesswork and subjectivity involved with selecting ratio steps. More specifically, there stands a desire to objectively select uniformly progressive ratio steps in order to maximize vehicle output efficiency.  
       SUMMARY OF THE INVENTION  
       [0006]     The above objectives are satisfied with a logical method of selecting gear ratios. Typical transmissions contain multiple forward drive gears, thus, for each drive gear, there exists a fixed input to output gear ratio. Hence, a first step in selecting gear ratios includes calculating a low gear ratio, and a high gear ratio based upon the specific vehicle parameters and performance requirements. Next, the total ratio spread is determined by dividing the low gear ratio by the high gear ratio. Using the total ratio spread, a geometric sequence is created having a plurality of terms, such that each of the terms respectively represent the ratio steps between the two consecutive gears. Once the geometric sequence is created, its terms enable one to determine the gear ratio for each gear by dividing the immediately previous gear ratio by its respective ratio step plus one. This method ensures the selection of gear ratios having truly uniform progressive ratio steps.  
         [0007]     Further areas of applicability of the present invention will become apparent from the detailed description provided hereinafter. It should be appreciated that the Applicant intends for the detailed description and specific examples discussed herein to only illustrate the preferred embodiment of the present invention and not to limit the scope of the invention. 
     
    
     BRIEF DESCRIPTION OF THE DRAWINGS  
       [0008]     The present invention will become more fully understood from the detailed description and the accompanying drawings, wherein:  
         [0009]      FIG. 1  is a block diagram representing the steps for the method of selecting gear ratios in accordance with the preferred embodiment of the present invention.  
         [0010]      FIG. 2  is a schematic of an exemplary five-speed manual transmission with reverse and having forward drive gear ratios in accordance with the present invention.  
         [0011]      FIG. 3  is a schematic view of an exemplary four-speed automatic transmission with reverse and having forward drive gear ratios selected in accordance with the present invention. 
     
    
     DETAILED DESCRIPTION OF THE PREFERRED EMBODIMENT  
       [0012]     The following description of the preferred embodiment merely exemplifies the nature of the invention and is in no way intended to limit its scope, its application, or its uses.  
         [0013]     The preferred embodiment of the present invention includes a method for selecting lay to output gear ratios for a transmission capable of producing multiple input to output gear ratios. The diagram shown in  FIG. 1  represents the steps of the preferred embodiment. First, a low gear ratio is calculated at block  10 , and a high gear ratio is calculated at block  12 , each based on the specific parameters and performance requirements of the application. It should be appreciated that a number of well-known methods may be used for determining low and high gear ratios for specific vehicles and that this invention is not limited by any one method.  
         [0014]     An exemplary method for determining the low gear ratio is based upon engine piston displacement. It can be shown that piston displacement is related to acceleration, fuel economy, and launchability as follows: N/V=(R t *R a *TR)/60, 
 
 where N is engine revolutions per minute, V is the vehicle velocity, R t  is the transmission gear ratio, R a  is the output or axle gear ratio, and TR is the tire revolutions per mile. For one revolution of the engine, E/2 in 3  fuel is displaced, where E is the total engine displacement; and W (the gross vehicle weight) is moved 1/(R t *R a *TR) miles. Hence, the piston displacement can be calculated as:  
             D   =       ⁢       (     60   *   E   *   N     )     /     (     2   *   W   *   V     )                   =       ⁢       E   2     ⁢       (     ft   12     )     3     ×     1     W   ⁢           ⁢   lbs       ×     (       2000   ⁢           ⁢   lbs     ton     )     ×     N   V     ×   60                   =       ⁢     34.7   *       (     E   *   N     )     /     (     V   *   W     )       ⁢           ⁢     ft   3     ⁢     /     ⁢   ton   ⁢     -     ⁢   mile       ,             
 
 or in metric units, 
        D=(30*I*N)/(V*W), where I is the engine displacement in liters. Finally, from the piston displacement, the overall low gear ratio is defined as, 
 
 R   oal   =R   l   *R   a =(1.73 *D*W )/( E*TR ). 
       
 
         [0018]     Once the overall low gear ratio R oal  is determined, the low gear ratio (R l ) can be determined by dividing the overall low gear ratio by the axle or final drive gear ratio (R a ), which is pre-selected and thus, known.  
         [0019]     An exemplary embodiment includes determining the high gear ratio based upon the desired terminal velocity of the vehicle using the same relationship deduced above, N/V=(R t *R a *TR)/60. Knowing the desired terminal velocity, V, the axle or output gear ratio, R a , the number of tire revolutions per mile, TR, and the engine revolutions per minute, N, R t  is solved for, which in this instance is equal to R h , the high gear ratio. This high gear ratio can be verified from determining the power required and power available versus the road speed. If the power required and the power available in each gear are plotted against the corresponding speed, then the top speed in that gear will occur at the point where the power available curve crosses the power required curve. The tractive force at the wheels supplied by the power available from the vehicle power plant is opposed by various external forces called resistances. The sum of the respective powers required to overcome these resistances should be less than the power available to move the vehicle.  
         [0020]     Referring again to  FIG. 1 , after determining the low and high gear ratios, a total ratio spread (S) is determined at block  14 , by dividing the low gear ratio by the high gear ratio (R l /R h ). Next, the number of gear ratios (n) is determined at block  16 , typically this is predetermined to be 4, 5, or 6 for a specific automobile application. Thus, the number of ratio steps (rs) is then determined at block  18 , which includes subtracting one from the number of gear ratios (rs=n−1). Hence, a five-speed forward drive transmission would have four ratio steps.  
         [0021]     The number of ratio steps and the total ratio spread is then utilized to define a new variable called the ratio variable (K) at block  20 , by raising the total ratio spread to one over the number of ratio steps (K=S 1/n ). In the preferred embodiment, the next step of creating a geometric sequence at block  22  is done such that the percent step of the ratio of any two consecutive terms of the geometric sequence equals a constant, called the step ratio constant, thus establishing uniformly progressive ratio steps. More specifically, at block  24  the sequence is solved wherein the general expression (K−1) x  denotes the ratio step between any two gear ratios for different values of x. Letting (K−1)=a, each ratio step can be expressed as n 1 =(K−1) x     1   =a x     1   , n 2 =(K−1) x     2   =a x     2   , n 3 =(K−1) x     3   =a x     3    . . . n n =(K−1) x     n   =a x     n   , whereby each of the values of n represent the terms of a geometric sequence. Therefore, there exists a constant relationship, represented as a x     2   /a x     1   =a x     3   /a x     2   =a x     n   /a x     n     −1 =r, wherein r is the step ratio constant. The resulting step ratio constant is what defines the ratio steps as uniformly progressive. This step ratio constant, r, is substituted into the above equations such that, n 1 =a x     1   , n 2 =ra x     1   , n 3 =r 2 a x     1    . . . n n =r n−1 a x     1    for all subscripts of n from 1 to n−1. Therefore, gear ratios for each gear between the low gear and the high gear are calculated using the following equations, where R 1 , R 2 , R 3 , and so on are the first, second, third, and so on, gear ratios; 
 
 R   2   =R   1 /(1+ n   1 )= R   1 /(1+ a   x     1   ); 
 
 R   3   =R   2 /(1+ n   2 )= R   1 /((1+ n   1 )(1+ n   2 ))= R   1 /((1+ a   x     1   )(1+ ra   x     1   )) . . . and so on; such that, 
 
 R   n   =R   n−1 /(1+ n   n−1 )= R   n−1 /(1+ r   n−2   a   x     1   )= R   1 /((1+ a   x     1   )(1+ ra   x     1   )(1+ r   2   a   x     1   )(1+ r   3   a   x     1   ) . . . (1+ r   n−2   a   x     1   )), 
 
 for all subscripts of n from 2 to n. In the final equation stated above, R 1  and R n  were previously determined to be the low and high gear ratios. Hence, r and a x     1    remain unsolved. Simplifying the equation by assuming that r=a x     1    reveals the following equation: R 1 /R n =(1+r)(1+r 2 )(1+r 3 ) . . . (1+r n− 1). This equation is solved for r using any mathematical computer program such as MICROSOFT XL SOLVER or MATLAB, and then its value is plugged back into the above equations to solve for R 1 , R 2 , R 3  and so on. 
 
         [0023]     The magnitude of r, the step ratio constant, varies with the size and application of the vehicle. An application having a first ratio step of approximately seventy percent (0.70) or higher between the first and second gears, meaning the second gear ratio equals 170% that of the first gear ratio, will reveal a step ratio constant of approximately thirty percent (0.30) or higher. Alternatively, a different application having a first step ratio of less than seventy percent (0.70) will reveal a step ratio constant between twenty and thirty percent (0.20-0.30). Hence, closer ratio steps will reveal a smaller step ratio constant, enabling one to tailor the ratio steps in accordance with the vehicle application, such as gradability, acceleration, or terminal velocity. Furthermore, narrower steps enable the engine to operate at or near maximum speed most of the time, and the user can increase fuel efficiency further by skip shifting. It has been observed that a ratio of the skip shifted gears, i.e., every other gear, less than or equal to 2.5 promotes smoother shifting. Hence, assessing the skip shift index lends to the tailoring of the specific application and end user. A highly skilled driver may prefer a wider skip shift index for increased torque, while an average driver may prefer a narrower skip shift index for smoother shifting.  
         [0024]     In another embodiment, particularly an off-road embodiment, the terms of the sequence are determined such that the ratios of the terms to their immediately previous terms, or in other words, the ratios of the ratio steps to their immediately previous ratio steps, create a geometric sequence themselves. This provides taller steps for creeping in low gears and shorter steps for faster speeds in high gears. This type of sequence is accomplished in a manner similar to that above, just that it produces a different result. In an exemplary embodiment, this relationship can be expressed as r=a x     2   /a x     1   , r 2 =a x     3   /a x     2   , r 4 =a x     4   /a x     3   , r 8 =a x     5   /a x     4   , and so on. Thus, the ratio steps between gears become n 1 =a x     1   , n 2 =ra x     1   , n3=r 3 a x     1   , n 4 =r 7 a x     1   , n 5 =r 15 a x     1   , and so on. Again, beginning with an equation such as R n =R 1 /(1+a x     1   )(1+ra x     1   )(1+r 3 a x     1   )(1+r 7 a x     1   ) . . . and so on, and assuming that r=a x     1   , this equation simplifies to R 1 /R n =(1+r)(1+r 2 )(1+r 4 )(1+r 8 ) . . . and so on. Solving for r, at block  24 , enables the specific gear ratios for an off road application to be determined using the aforementioned equations for R 1 , R 2 , R 3  and so on, at block  26 .  
       Manual Transmission  
       [0025]     For a manual transmission application, it is behooving to determine the number of teeth for each gear. Thus, after determining the gear ratios for each of the gears in accordance with the preferred method, the number of teeth is calculated for each gear using techniques well known in the art. Then, the appropriate gears are selected for the design and assembly of the manual transmission.  
         [0026]     With reference to  FIG. 2 , an exemplary manual transmission is shown having gear ratios selected in accordance with the preferred embodiment of the present invention. The manual transmission shown in  FIG. 2  comprises an input shaft  110 , an output shaft  112 , and a lay shaft  114 . The input shaft  110  includes a master input gear  116  in constant mesh engagement with a driven lay gear  118  fixed to the lay shaft  114 . The lay shaft  114  further includes a set of lay gears rotatably attached to the lay shaft  114  including a first lay gear  120 , a second lay gear  122 , a third lay gear  124 , a fourth lay gear  126 , a fifth lay gear  128 , and a reverse lay gear  130 . The output shaft  112  includes a set of output gears rotatably attached to the output shaft  112  including a first output gear  132 , a second output gear  134 , a third output gear  136 , a fourth output gear  138 , a fifth output gear  140 , and a reverse output gear  142  meshingly engaged with the reverse lay gear  130  via an idler gear  144 . Output gears  132 - 140  are in constant mesh engagement with respective lay gears  120 - 128  in accordance with gear ratios selected in accordance with the preferred embodiment of the present invention.  
         [0027]     The manual transmission of  FIG. 2  further includes a gear selector rod and shift fork assembly  146  adapted to actuate a plurality of collars  148  rotatably attached to the output shaft  112  and adapted for manual selection between the output gears. It should be appreciated that alternatively, the plurality of collars  148  could be rotatably attached to the lay shaft  114  and in mechanical communication with the gear selector rod and shift fork assembly  146  to selectively engage a lay gear. Furthermore, the gear selector rod and shift fork assembly  146  could mechanically communicate with one or more gear synchronizers for selectively engaging a specific gear.  
         [0028]     When a user manually engages a gear, whether it be an output gear or a lay gear, the user effectively selects a gear ratio. Regarding the transmission of  FIG. 2 , a user may manually select one of five forward drive gear ratios. A user may manually manipulate the gear selector rod and shift fork assembly  146  to engage the first output gear  132  with the first lay gear  120 , thus selecting a low gear ratio. Likewise, it should be appreciated that a user may manipulate the gear selector rod and shift fork assembly  146  to engage any of the corresponding output gears and lay gears, thus selecting a different input to output gear ratio specific to each gear.  
       Automatic Transmission  
       [0029]     Referring now to  FIG. 3 , an exemplary automatic transmission is shown, which is capable of producing a plurality of input to output gear ratios having gears ratios selected in accordance with the preferred embodiment of the present invention.  FIG. 3  shows a simple embodiment of an automatic transmission having an input shaft  200 , an output shaft  210 , a torque converter  202 , and a planetary gear system having a first planetary gear set  206 , a second planetary gear set  208 , and a third planetary gear set  220 . Each planetary gear set includes a sun gear, a ring gear and planet gears as is known in the art. Further, the automatic transmission of  FIG. 3  includes an actuating system including a first clutch mechanism  212 , a second clutch mechanism  214 , a first brake mechanism  216 , a second brake mechanism  218 , and a reverse brake mechanism  204  for selectively engaging components of the planetary gear system to produce different input shaft  200  to output shaft  210  rotational ratios, or gear ratios.  
         [0030]     It should be appreciated that the automatic transmission of  FIG. 3  has four forward drive gears and one reverse gear. In low gear, the first brake mechanism  216  and the second brake mechanism  218  are actuated to prevent rotation of the sun gear of the first planetary gear set  206  and the ring gear of the second planetary gear set  208 . In second gear, the first clutch mechanism  212  is actuated to rotate the sun gear of the first planetary gear set  206  with its planet gears, and the second brake mechanism  218  is actuated to prevent rotation of the ring gear of the second planetary gear set  280 . In third gear, the first brake mechanism  216  is actuated to prevent rotation of the sun gear of the first planetary gear set  206 , and the second clutch mechanism  214  is actuated to rotate the ring gear of the second planetary gear set  208 . Finally, in fourth gear, the first clutch mechanism  212  is actuated to rotate the sun gear of the first planetary gear set  206  with its planet gears, and the second clutch mechanism  214  is actuate to rotate the ring gear of the second planetary gear set  208 . The third planetary gear set  220  and the reverse brake mechanism  204  are only utilized in the event of reversing the rotation of the output shaft  210  relative to the rotation of the input shaft  200 , thus establishing a reverse mode.  
         [0031]     The variety of gear ratios for the automatic transmission of  FIG. 3  depend upon the gears in the planetary gear system, more specifically the sun gear, the ring gear, and the planet gears in the first planetary gear set  206  and the second planetary gear set  208 . Thus, these gears are selected in accordance with the preferred embodiment of the present invention.  
         [0032]     This description of the invention is merely exemplary in nature and, thus, variations that do not depart from the heart of the invention are intended to be within its scope. Such variations are not to be regarded as a departure from the spirit and scope of the invention.