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I bought a 2006 OB a few weeks ago with different brand tires. Mastercraft on the rear and Yokohama on the front. All are 225/55/17 and I measured around each tire to check that they are within 1/4" of each other and they are. . Do I have a problem?
The idea of measuring the circumference applies to tires that are the same make/model/size. It's less applicable to different models, and certainly different makes. This is due to different ways the tire will react in actual use, e.g. because of different sidewall or tread stiffness based on how the tires are made.
. . . . for a little more confidence, I guess you could find a long, straight shot in a big parking lot or little-used service road, mark the bottom of each tire, then drive straight forward as far as possible. Stop and see if the marks are all 'clocked' at the same position. The AWD system is just happiest when the tires all roll the same distance. If there is a 'slight' difference, it's hard to predict if that takes off 500 miles or 50,000 miles of service life. You might be OK.
Very good advice. This will help provide additional confidence by establishing if the slow speed rolling circumference of the four tires might be significantly different.
I'd suggest rolling the car so that one marked wheel makes exactly ten revolutions. This way, if the marks on the other tires are not at the bottom again, the distance of the mark from the bottom (in inches), divided by 10, indicates the difference in apparent rolling circumference. (A 2.5 inch difference = 1/4 inch difference in circumference.)
The rolling circumference will be different at different pressure, load (weight) and speed. But by measuring the circumference, and doing the rolling test, will provide a first approximation.