text: referring to the drawings , there is shown in fig1 a a simple representative planetary gear set 1 consisting of a high - cycle gear element 2 and a plurality of lower - cycle gear elements 3 , in which the high - cycle gear teeth 4 are engaged or otherwise meshed with the gear teeth 5 of the lower - cycle gear elements 3 . such a planetary gear set is commonly used , for example , in automotive range or final drive gear sets . the cycle disparity between mating gear elements 2 , 3 as depicted in planetary gear set 1 of fig1 a results in variance in the damage profile observed at the respective mating surfaces of gear elements 2 and 3 . the actual damage profile of the mating gears 2 , 3 will depend upon various factors , for example gear ratio , loading , and gear speed , but damage variance would be observed in any gear set in which at least one gear member experiences a disproportionate number of cycles relative to the remaining gear elements of the gear set . fig1 b is a close - up view of an high - cycle gear tooth 4 and lower - cycle gear tooth 5 , both having a typical involute profile , in which the surface detail of high cycle gear tooth 4 and gear tooth 5 are shown both in unfinished condition 6 ( left - hand side ) and finished condition 7 ( right - hand side ). under unfinished condition 6 , micro - asperities 8 , i . e . micro - level surface irregularities producing surface roughness , are present along the mating surfaces 11 , 12 of high - cycle gear tooth 4 and gear tooth 5 , respectively . the micro - asperities 8 present on the surfaces of high - cycle gear tooth 4 and gear tooth 5 come into direct dynamic contact as gear teeth 4 , 5 engage , revolve , and disengage through one complete cycle , resulting in friction and plastic deformation . consequently , gear teeth 4 , 5 experience accumulative damage and potentially , premature failure of high - cycle gear element 2 , and as a result , planetary gear set 1 . furthermore , the system experiences loss in the form of friction and resulting heat . the right half of fig1 b depicts gear teeth 4 , 5 in finished condition 7 in accordance with this invention . in one aspect of the invention , finished condition 7 is accomplished solely by specifying and / or controlling the hardness differential between mating high cycle gear surface 9 and mating gear surface 10 . as used herein , the term “ hardness differential ” refers to the amount by which the surface hardness of mating hard gear surface 9 exceeds that of mating gear surface 10 . the term “ hard gear surface ” as used herein refers to the surface of the harder of two mating gears , with the term “ hard gear ” describing a general gear element having a surface hardness exceeding 70 hr - 30n . such hard gears are of the style typically used in high stress , high cycle automotive applications and similar applications . in the preferred embodiment , the contact surfaces of high - cycle gear tooth 4 are of a surface hardness range of approximately 2 . 5 to 7 hr - 30n above that of gear tooth 5 . a hardness differential range of 2 . 5 to 5 hr - 30n is preferred for gears in lubricated contact in systems in which the lubricant has properties similar to those of transmission fluid . gear element 3 , having a relatively lower cycle frequency , is retained at a standard or production - specified hardness . a typical production - specified gear hardness for automotive transmission gear elements is approximately 75 hr - 30n , and would therefore preferably engage with a higher - cycle gear 2 having a surface hardness range of approximately 77 . 5 to 80 hr - 30n . by employing a properly selected hardness differential between mating hard gears according to the terms of the invention , surface damage is balanced between the mating gear surfaces without the undesirable effect of high cycle gear 2 disproportionately wearing or cutting the surface of gear 3 . the wear - balancing effect therefore occurs at the micro - level , with resultant changes in respective surface layer plasticity leading to reduced pitting and crack initiation . by reducing crack initiation , the likelihood of crack propagation due to elastic deformation is greatly reduced . gear set life is thereby greatly extended , resulting in cost savings and improvements in overall system reliability . in another aspect of the invention , finished condition 7 is further enhanced by the use of surface finishing as applied to the mating surfaces 9 , 10 of gears 2 , 3 as represented by mating surfaces 9 , 10 in fig1 b . examples of surface finishing techniques include electro - polishing , chemical treating , honing or super - finishing , methods that operate at the micronic and sub - micronic levels to produce a more even surface profile . with reference to fig2 , the quantities ra , measured in micrometers or microns , and dx , measured in degrees , are known in the metal finishing art , with ra representing the arithmetic mean height of the asperities in a roughness profile , and dx representing the average absolute value of the slope of the asperities in a roughness profile . slope dx is a function both of the media type used within a polishing slurry and the resident time the part being finished is subjected to in the polishing process . when taken together with ra , dx defines the final parameters of a surface finish . in fig2 , a simplified representative surface roughness profile in sliding direction is shown as three discrete asperities 13 , 14 , and 15 , each with a unique height ra , measured in micrometers , and local slope dx , measured in degrees . in this example , asperity 13 is depicted with a height ra 13 and a local slope quantity dx 13 , asperity 14 is depicted with a height ra 14 and a local slope quantity dx 14 , and asperity 15 is depicted with a height ra 15 and a local slope quantity dx 16 . the overall slope dx is the average slope over the entire range of measurement , i . e . the full length of mating surfaces 11 , 12 . in the simplified example of fig3 , the average slope dx would be the absolute average of slopes dx 13 , 14 , 15 of asperities 13 , 14 , and 15 . an isotropic finish is preferred , i . e . a finish with no discernable pattern at the micro level , as such a finish facilitates unimpeded , even lubricant fluid flow across and around the surfaces of the mating hard gears . an isotropic finish therefore helps to minimize losses due to fluid friction imparted by the lubricant , and thereby enhance the beneficial effects of surface finishing . also in the preferred embodiment , the hardness differential between the mating gears is set at a suitable level , preferably a range of 2 . 5 to 5 hr - 30n for common transmission fluids having a viscosity of approximately 35 - 40 centistokes at 40 ° c ., wherein the softer of the two mating gears is of a hardness of approximately 75 hr - 30n . the mating surfaces are then isotropically finished by means of chemical polishing to an ra of approximately 0 . 05 microns , which is the preferred ra for gear sets in lubricated contact with transmission fluid . however , an ra range of 0 . 01 - 1 microns is suitable for most lubricated gear sets . the ra variable , representing the average asperity height on the gear surface , may be adjusted accordingly for other lubricant fluids depending on the operating conditions and fluid properties . for example , a relatively heavy weight fluid such as gear oil would permit a lesser ra value due to the thicker protective film and consequent reduction in friction produced by the higher viscosity fluid . the desired dx range after isotropic chemical polishing is 0 . 2 to 1 degrees . the desired range produces the best damage profile balancing and life extension results when coupled with a hardness differential range of approximately 2 . 5 to 5 hr - 30n as applied to gear sets in lubricated contact , with transmission fluid as the lubricant . as shown in fig3 , by coupling a properly selected hardness differential with isotropic surface finishing , the damage profile of mating hard gears can be optimized . fig3 a shows an unfinished condition 6 representative surface contact profile for mating gear surfaces 11 , 12 . fig3 b shows a finished condition 7 representative surface contact profile for mating gear surfaces 9 , 10 , according to the present invention . in fig3 a , plastically deformed layers 16 , 17 are relatively deep , approaching 15 to 20 nm ( nanometers ) for typical mating automotive transmission hard gears of over 70 hr - 30n . such a deep plastically deformed layers increases the likelihood of crack initiation , pitting , and other damage , damage which is then exacerbated by the effects of elastic deformation . the present invention further applies isotropic chemical polishing to the mating surfaces 11 , 12 to minimize , and preferably eliminate , the plastically deformed layer . in fig3 b , plastically deformed layers 18 and 19 are shown with a thickness that is substantially reduced in comparison to plastically deformed layers 16 and 17 of fig3 a . this reduction is accomplished by increasing the area of contact between mating surfaces 11 , 12 of fig3 a to produce the profile approximated by mating surfaces 9 , 10 of fig3 b . the preferred profile is brought about by the reduction in average slope dx and average height ra of the micro - asperities 8 , as previously disclosed . while absolute elimination of the plastically deformed layers 18 , 19 is the preferred situation , in practice such a result is difficult to achieve . the difficulty of measuring the thickness of plastically deformed layers between mating gear element surfaces greatly increases as the plastically deformed layer thickness approaches zero . a practical thickness of layers 18 , 19 would therefore be approximately 1 to 2 nm . therefore , this invention localizes the plastic deformation remaining after isotropic finishing primarily to the mating surfaces of the lower cycle gear elements 3 , thereby balancing accumulative damage due to run - in and subsequent use . while the best modes for carrying out the invention have been described in detail , those familiar with the art to which this invention relates will recognize various alternative designs and embodiments for practicing the invention within the scope of the appended claims .