Since this is the same LSD as on the CTS, look what I found on the Cadillac website:
http://www.cadillacfaq.com/faq/tsb/data/pip3152g.pdf
Quote:
Service Information Document ID# 1824733
2004 Cadillac CTS
Subject: Shudder or Bind On Low Speed Turns - keywords axle differential
groan growl moan noise rear slow vibration #PIP3152G - (05/03/2006)
Models: 2004-2006 Cadillac SRX, CTS, CTSV
2005-2006 Cadillac STS
2006 Pontiac Solstice
2007 Saturn Sky
Equipped with Limited Slip Differential (RPO - G80)
This PI is being updated to include 2007 Saturn Sky and also update the Part number for the axle fluid and include part number disclaimer. Please discard PIP3152F
The following diagnosis might be helpful if the vehicle exhibits the symptom(s) described in this PI.
Condition/Concern:
Service Information: Customer may comment of a shudder or bind from the rear of vehicle on low speed turns such as parking lot maneuvers on vehicles equipped with G80 limited slip rear axle. This condition may be more noticeable with the vehicle at operating temperatures.
Recommendation/Instructions:
Drive the vehicle to warm the rear axle and then drain the axle fluid. Refill with just the 89021677 (in Canada, use 89021678) axle lube and drive the vehicle about 10 minutes performing mostly parking lot turning maneuvers. Drain the rear axle again and mix 1200 ml of 89021677 (in Canada, use 89021678) and 74-89 ml of 1052358 (Canadian P/N 992694) additive outside of the axle and then fill the rear axle with this mixture and re-evaluate.
Part numbers are subject to change. Use any superseded part numbers if the part numbers in this document become discontinued.
Please follow this diagnostic or repair process thoroughly and complete each step. If the condition exhibited is resolved without completing every step, the remaining steps do not need to be performed.
GM bulletins are intended for use by professional technicians, NOT a "do-it-yourselfer". They are written to inform these technicians of conditions that may occur on some vehicles, or to provide information that could assist in the proper service of a vehicle. Properly trained technicians have the equipment, tools, safety instructions, and know-how to do a job properly and safely. If a condition is described, DO NOT assume that the bulletin applies to your vehicle, or that your vehicle will have that condition. See your GM dealer for information on whether your vehicle may benefit from the information.
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Document ID# 1824733
2004 Cadillac CTS