Technical Brief

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

[+] Author and Article Information
M. Kolivand

American Axle & Manufacturing Inc.,
Detroit, MI 48307
e-mail: mohsen.kolivand@aam.com

V. Sun, D. Chemelli, J. Balenda, Z. Shi

American Axle & Manufacturing Inc.,
Detroit, MI 48307

1Corresponding author.

Contributed by the Power Transmission and Gearing Committee of ASME for publication in the JOURNAL OF MECHANICAL DESIGN. Manuscript received March 10, 2018; final manuscript received May 22, 2018; published online July 24, 2018. Assoc. Editor: Ettore Pennestri.

J. Mech. Des 140(10), 104501 (Jul 24, 2018) (5 pages) Paper No: MD-18-1206; doi: 10.1115/1.4040425 History: Received March 10, 2018; Revised May 22, 2018

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.

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Grahic Jump Location
Fig. 1

An example automotive differential gear system with two side gears and two differential pinions and a cross pin. Here upper differential pinion is misaligned by moving it out of mesh by δ.

Grahic Jump Location
Fig. 2

Total indexing run-out Fp based on AGMA quality of the gears (for 80 mm pitch diameter gear) [2]

Grahic Jump Location
Fig. 3

Differential system setup for calculating component and system compliances

Grahic Jump Location
Fig. 4

Overload factor Ko as a result of effective total indexing runout Fpe and equivalent misalignment δ (of one differential pinion as a result of all misalignments) at two different levelsofoverall system stiffness Ke. Here δ is in mm and Ke is in N·m/mm.



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