The friction factor should always be a positive number.
It sounds like you were trying to calculate the friction factor for your KitchenAid unit. The way that this is ordinarily done is to make a test batch of dough and note the temperature of the water you use to make the test batch of dough (WT), the room temperature (RT), the flour temperature (FT), and the final dough temperature (FDT). Then, the friction factor (FF) can be calculated from the following expression:
FF = (3 x FDT) - (RT + FT +WT).
Using your numbers, FF = (3 x 80) - (82 + 77 + 89) = - 8, just as you indicated. The only way I can see how you could get a minus number is if you (1) erroneously recorded one or more of the temperatures, (2) you let the dough set somewhere along the way during kneading (for example, for an autolyse or similar rest period), so that the dough in fact did cool down by the time you took its temperature, (3) you didn't take the temperature of the dough as soon as it came off the hook, but sometime later, or (4) your thermometer has a long lag time to register temperatures and you read it too soon or in an inconsistent manner (some thermometers take several seconds to respond). Also, I am a bit puzzled that the room temperature and flour temperature readings weren't much closer. The flour might have a lower temperature reading if it was brought out from a refrigerator or freezer or from a pantry that is cooler than the kitchen, but usually the flour rises close to the room temperature by the time it is measured, set aside, and used. I rarely see more than about one degree difference between flour temperature and room temperature.
You will also note that the average of the room temperature RT, flour temperature FT and water temperature WT in your example is almost 83 degrees. Without even considering the temperature effects of your KitchenAid machine, that average is higher than the finished dough temperature FDT. Absent one of the possibilities (1)-(4) noted above, that would violate the laws of physics
. You may have to go back to the drawing board. I might also add that the Lehmann dough is quite sensitive to temperature. For that reason, I always temperature adjust the water so that the finished dough temperature doesn't exceed 80-85 degrees. Other doughs seem to tolerate higher water temperatures better than the Lehmann doughs.