I have an Audi Quattro with 29000 miles on the tires. One has developed a bubble and tire shop said I need to replace all 4 because of 4 wheel drive could damage differential. Is this true?
I'm not an Audi mechanic, so I can't say for sure that you could harm your car over the next 20K miles with the imbalanced tires, but this is the foundation for the warning.
The differential is designed to allow the wheels to spin at different speeds when cornering, and also designed to (along with other systems) detect when one wheel is losing grip (spinning at a different rate) so power can be transferred to other wheels.
Normal operation assumes that all wheels are the exact same size and spinning at the same rate. When you put one new tire on a car with three worn tires, it will put extra work on the differential. The new tire will be rotating slower than the others because it will have a larger circumference.
Tires with 29,000 miles are probably more than half gone in terms of wear. If it was 10,000 miles, the size difference might be negligible, but with well worn tires, it's probably a valid warning.
Please comment if you know how severe the situation is.
If the car has limited slip diffs, the constant slight difference in wheel speed can cause wear of the friction plates, fairly quickly wearing them out. If the diffs are normal open diffs, this is not quite so important, but if you look at how the planetary gears work in a differential, you will see that the difference in wheel size will cause some of the gears that normally only turn when going around corners to be turning slowly all the time, which will add a little wear. As I said before, this is much more important for limited slip diffs.