Differential Gear Bending Stresses in the Presence of Misalignments and Run-out

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 are 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, also differential pinion loads are usually assumed to be equal; this is a good estimate when no misalignments are present. When misalignments are present, load sharing between the differential pinions becomes 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 run-out quality of gears is also studied through treating it as a source of misalignment. This study will help designers to evaluate the effects of tolerance limits and differential case machining errors on differential gear bending lives.