Gears having reduced roller element stresses and methods of manufacturing such gears

A gear assembly comprising:

• a sun gear;
• a ring gear;
• and
• a plurality of planet gears coupled to said ring gear and said sun gear, each planet gear of said plurality of planet gears having an axis of rotation, said gears comprising:
• a gear rim, wherein at least a portion of said gear rim is configured to:
• receive a load;
• and
• define a loaded gear rim arc corresponding to said at least a portion of said gear rim;
• and
• a bearing pin extending axially through said gear rim, said gear rim and said bearing pin defining a roller element gap therebetween;
• and
• a bearing disposed within said roller element gap, said bearing comprising a plurality of roller elements circumferentially disposed about said bearing pin, wherein said gear rim is configured to:
• define a loaded roller element gap arc substantially concentric with the loaded gear rim arc, the loaded roller element gap arc extending through a portion of the roller element gap and having a loaded roller element gap arc length;
• and
• retain a loaded bearing portion of said bearing within the portion of the roller element gap such that a loaded bearing portion length is in a first range from and including about 75% to and including about 125% of the loaded roller element gap arc length.

A method of manufacturing a gear having an axis of rotation, the gear including a bearing pin extending axially through the gear rim, the gear rim and the bearing pin defining a roller element gap therebetween, and a bearing disposed within the roller element gap, said method comprising:

• applying at least some load to the gear rim;
• identifying a loaded gear rim arc corresponding to a loaded portion of the gear rim when the load is applied to the gear rim;
• determining a loaded roller element gap arc extending through the roller element gap substantially concentric with the loaded gear rim arc, the loaded roller element gap arc having a roller element gap arc length;
• selecting the bearing such that, a loaded bearing portion of the bearing having a loaded bearing portion length is retained within the portion of the roller element gap, the loaded bearing portion length in a range from and including about 75% to and including about 125% of the loaded roller element gap arc length;
• and
• inserting the bearing into the roller element gap.