Differential Gear Bending Stresses in Presence of Misalignments and Runout

Automotive differential gears are usually operating at very low speed and high load conditions and hence are usually designed to be protected against the root bending fatigue failure. Depending on application requirements and lubrication regime surface failures may occasionally be encountered as well. Mainstream existing design procedures published by AGMA is based on analyzing one single gear pair engagement while up to four potential engagements, between two side gears and two differential pinions, exist. There are also differential designs with three or four differential pinions that increase potential number of engagements to respectively six and eight. Usually the hypoid gear loading is divided by number of side gears, two, differential pinion loads are also usually assumed to be equal; this is a good estimate when no misalignments are present. When misalignments are present however, load sharing between the differential pinions become greatly imbalanced. This study tries to come up with a simplified analytical approach to evaluate overload factor between the differential pinions as a result of misalignments realized by differential gears inside a differential case. The total indexing runout quality of gears is also studied through treating it as a source of misalignment. This study will help designers to evaluate the effects of tolerancing limits and differential case machining errors on differential gear bending lives.